Finite Group Databasebeta

← C2×#22574179 #31763940

Subgroups — C2×#22574179 #31763940

Order 17152.

7142 conjugacy classes of subgroups.

The subgroup lattice has 1864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574179C2132yesmaximal, direct product factor
2C2×#16864123C211yesmaximal, characteristic, complemented
3C2×#16864100C211yesmaximal, characteristic, complemented
4C2×#16864100C211yesmaximal, characteristic, complemented
5C2×#16864091C211yesmaximal, characteristic, complemented
6C2×#16864089C211yesmaximal, characteristic, complemented
7C2×#16864088C211yesmaximal, characteristic, complemented
8C2×#16864083C211yesmaximal, characteristic, complemented
9C2×#16864083C211yesmaximal, characteristic, complemented
10C2×#16864083C211yesmaximal, characteristic, complemented
11C2×#16864082C211yesmaximal, characteristic, complemented
12C2×#16864082C211yesmaximal, characteristic, complemented
13C2×#16864080C211yesmaximal, characteristic, complemented
14C2×#16864078C211yesmaximal, characteristic, complemented
15C2×#16864046C211yesmaximal, characteristic, complemented
16C2×#16864044C211yesmaximal, characteristic, complemented
17C2×#16864044C211yesmaximal, characteristic, complemented
18C2×#16864005C211yesmaximal, characteristic, complemented
19C2×#16864003C211yesmaximal, characteristic, complemented
20C2×#16863992C211yesmaximal, characteristic, complemented
21C2×#16863989C211yesmaximal, characteristic, complemented
22C2×#16863988C211yesmaximal, characteristic, complemented
23C2×#16863948C211yesmaximal, characteristic, complemented
24C2×#16863929C211yesmaximal, characteristic, complemented
25C2×#16863926C211yesmaximal, characteristic, complemented
26C2×#16863923C211yesmaximal, characteristic, complemented
27C22×#14524033C211yesmaximal, characteristic, complemented
28C2×#125×D67C211yesmaximal, characteristic, complemented
29C2×#16863877C211yesmaximal, characteristic, complemented
30C2×#16863875C211yesmaximal, characteristic, complemented
31C2×C4×#11761627C211yesmaximal, characteristic, complemented
32C2×#539×C67C211yesmaximal, characteristic, complemented
33C22×#11761628C2211yescharacteristic
34C22×#11761627C2211yescharacteristic
35C22×#11761627C2211yescharacteristic
36#16864123C22116yescomplemented
37#16864100C22116yescomplemented
38#16864100C22116yescomplemented
39#16864091C22116yescomplemented
40#16864089C22116yescomplemented
41#16864088C22116yescomplemented
42#16864083C22116yescomplemented
43#16864083C22116yescomplemented
44#16864083C22116yescomplemented
45#16864082C22116yescomplemented
46#16864082C22116yescomplemented
47#16864080C22116yescomplemented
48#16864078C22116yescomplemented
49#16864046C22116yescomplemented
50#16864044C22116yescomplemented
51#16864044C22116yescomplemented
52#16864005C22116yescomplemented
53#16864003C22116yescomplemented
54#16863992C22116yescomplemented
55#16863989C22116yescomplemented
56#16863988C22116yescomplemented
57#16863948C22116yescomplemented
58C2×#14524042C2211yescharacteristic
59C2×#14524042C2211yescharacteristic
60C2×#14524042C2211yescharacteristic
61C2×#14524041C2211yescharacteristic
62#16863929C22116yescomplemented
63#16863926C22116yescomplemented
64#16863923C22116yescomplemented
65C2×#14524038C2211yescharacteristic
66C2×#14524038C2211yescharacteristic
67C2×#14524038C2211yescharacteristic
68C2×#14524038C2211yescharacteristic
69C2×#14524037C2211yescharacteristic
70C2×#14524036C2211yescharacteristic
71C2×#14524036C2211yescharacteristic
72C2×#14524036C2211yescharacteristic
73C2×#14524036C2211yescharacteristic
74C2×#14524036C2211yescharacteristic
75C2×#14524036C2211yescharacteristic
76C2×#14524036C2211yescharacteristic
77C2×#14524035C2211yescharacteristic
78C2×#14524034C2211yescharacteristic
79C2×#14524034C2211yescharacteristic
80C2×#14524034C2211yescharacteristic
81C2×#14524034C2211yescharacteristic
82C2×#14524034C2211yescharacteristic
83C2×#14524033C2211yescharacteristic
84C2×#14524033C2211yescharacteristic
85C2×#14524033C2211yescharacteristic
86C2×#14524033C2211yescharacteristic
87C2×#14524033C2211yescharacteristic
88C2×#14524033C2211yescharacteristic
89C2×#14524033C2211yescharacteristic
90C2×#14524033C2211yescharacteristic
91C2×#14524033C2211yescharacteristic
92C2×#14524033C2211yescharacteristic
93C2×#14524033C2211yescharacteristic
94C2×#14524033C2211yescharacteristic
95C2×#14524033C2211yescharacteristic
96C2×#14524033C2211yescharacteristic
97C2×#14524033C2211yescharacteristic
98C2×#14524033C2211yescharacteristic
99C2×#14524033C2211yescharacteristic
100C2×#14524033C22116yescomplemented
101#125×D67C22116yescomplemented
102C2×#14524029C2211yescharacteristic
103C2×#14524028C2211yescharacteristic
104C2×#14524028C2211yescharacteristic
105C2×#14524027C2211yescharacteristic
106C2×#14524027C2211yescharacteristic
107C2×#14524026C2211yescharacteristic
108C2×#14524025C2211yescharacteristic
109C2×#14524025C2211yescharacteristic
110C2×#14524025C2211yescharacteristic
111C2×#14524025C2211yescharacteristic
112C2×#14524025C2211yescharacteristic
113C2×#14524025C2211yescharacteristic
114C2×#14524024C2211yescharacteristic
115C2×#14524024C2211yescharacteristic
116C2×#14524024C2211yescharacteristic
117C2×#14524022C2211yescharacteristic
118C2×#14524021C2211yescharacteristic
119C2×#14524021C2211yescharacteristic
120C2×#14524021C2211yescharacteristic
121C2×#14524021C2211yescharacteristic
122C2×#14524021C2211yescharacteristic
123C2×#14524020C2211yescharacteristic
124C2×#14524020C2211yescharacteristic
125C2×#14524020C2211yescharacteristic
126C2×#14524020C2211yescharacteristic
127C2×#14524020C2211yescharacteristic
128C2×#14524020C2211yescharacteristic
129C2×#14524020C2211yescharacteristic
130C2×#14524020C2211yescharacteristic
131C2×#14524019C2211yescharacteristic
132C2×#14524019C2211yescharacteristic
133C2×#14524016C2211yescharacteristic
134C2×#14524016C2211yescharacteristic
135C2×#14524015C2211yescharacteristic
136C2×#14524015C2211yescharacteristic
137C2×#14524015C2211yescharacteristic
138C2×#14524014C2211yescharacteristic
139#16863877C22116yescomplemented
140#16863875C22116yescomplemented
141C4×#11761627C22116yescomplemented
142C2×Q8×Dic67C2211yescharacteristic
143C2×C4×Dic134C2211yescharacteristic
144C2×C4×Dic134C2211yescharacteristic
145C2×C4×Dic134C2211yescharacteristic
146C2×#14524008C2211yescharacteristic
147C2×#14524008C2211yescharacteristic
148C2×#14524008C2211yescharacteristic
149C2×#14524008C2211yescharacteristic
150C2×#14524008C2211yescharacteristic
151C2×#14524008C2211yescharacteristic
152C2×#14524008C2211yescharacteristic
153C2×D4×Dic67C2211yescharacteristic
154C2×D4×Dic67C2211yescharacteristic
155C2×D4×Dic67C2211yescharacteristic
156C2×#14524005C2211yescharacteristic
157C2×#14524005C2211yescharacteristic
158C2×C4×C22⋊D67C2211yescharacteristic
159C2×C4×C22⋊D67C2211yescharacteristic
160C2×C4×C22⋊D67C2211yescharacteristic
161C2×C4×C22⋊D67C2211yescharacteristic
162C2×C4×C22⋊D67C2211yescharacteristic
163C2×C4×C22⋊D67C2211yescharacteristic
164C2×C4×C22⋊D67C2211yescharacteristic
165C2×(C22⋊D67)⋊C4C2211yescharacteristic
166C2×(C22⋊D67)⋊C4C2211yescharacteristic
167C2×(C22⋊D67)⋊C4C2211yescharacteristic
168C2×(C22⋊D67)⋊C4C2211yescharacteristic
169C2×(C22⋊D67)⋊C4C2211yescharacteristic
170C2×(C22⋊D67)⋊C4C2211yescharacteristic
171C2×(C22⋊D67)⋊C4C2211yescharacteristic
172C2×#14524002C2211yescharacteristic
173C2×#14524002C2211yescharacteristic
174C2×#14524001C2211yescharacteristic
175C2×#14524001C2211yescharacteristic
176C2×#14524001C2211yescharacteristic
177C2×#14524001C2211yescharacteristic
178C2×#14524000C2211yescharacteristic
179C2×#14524000C2211yescharacteristic
180C2×#14523999C2211yescharacteristic
181C2×#14523999C2211yescharacteristic
182C2×#14523999C2211yescharacteristic
183C2×#14523999C2211yescharacteristic
184C2×#14523999C2211yescharacteristic
185C2×#14523999C2211yescharacteristic
186C2×#14523999C2211yescharacteristic
187C22×C4⋊Dic67C2211yescharacteristic
188C22×Dic67⋊C4C2211yescharacteristic
189C22×Dic67⋊C4C2211yescharacteristic
190C22×Dic67⋊C4C2211yescharacteristic
191C22×Dic67⋊C4C2211yescharacteristic
192C22×Dic67⋊C4C2211yescharacteristic
193C2×C4⋊C4×D67C2211yescharacteristic
194C2×C4⋊C4×D67C2211yescharacteristic
195C2×C4⋊C4×D67C2211yescharacteristic
196C2×C4⋊C4×D67C2211yescharacteristic
197C2×C4⋊C4×D67C2211yescharacteristic
198C2×C4⋊C4×D67C2211yescharacteristic
199C2×C4⋊C4×D67C2211yescharacteristic
200C22×C4×Dic67C2211yescharacteristic
201C22×C4×Dic67C2211yescharacteristic
202C2×C42×D67C2211yescharacteristic
203#539×C67C22116yescomplemented
204C2×#126×C67C2211yescharacteristic
205C2×#126×C67C2211yescharacteristic
206C2×#125×C67C2211yescharacteristic
207C2×#125×C67C2211yescharacteristic
208C2×#123×C67C2211yescharacteristic
209C2×#123×C67C2211yescharacteristic
210C2×#123×C67C2211yescharacteristic
211C2×#123×C67C2211yescharacteristic
212C2×C22⋊Q8×C67C2211yescharacteristic
213C2×C22⋊Q8×C67C2211yescharacteristic
214C2×C22⋊Q8×C67C2211yescharacteristic
215C2×#121×C67C2211yescharacteristic
216C2×C4×D4×C67C2211yescharacteristic
217C2×C4×D4×C67C2211yescharacteristic
218C22×C4⋊C4×C67C2211yescharacteristic
219C2×#11761628—28no—
220C2×#11761628C2318yes—
221C2×#11761627—28no—
222C2×#11761627—28no—
223C2×#11761627C2318yes—
224C2×#11761627C2318yes—
225C22×Dic134C2311yescharacteristic
226C22×Dic134C2311yescharacteristic
227C22×Dic134C2311yescharacteristic
228C22×Dic134C2311yescharacteristic
229C22×Dic134C2311yescharacteristic
230C22×D268C2311yescharacteristic
231C22×C22⋊D67C2311yescharacteristic
232C22×C22⋊D67C2311yescharacteristic
233C22×C22⋊D67C2311yescharacteristic
234C22×C22⋊D67C2311yescharacteristic
235C22×C22⋊D67C2311yescharacteristic
236C22×C22⋊D67C2311yescharacteristic
237C23×Dic67C2311yescharacteristic
238C23×Dic67C2311yescharacteristic
239C23×Dic67C2311yescharacteristic
240C23×Dic67C2311yescharacteristic
241C23×Dic67C2311yescharacteristic
242C23×Dic67C2311yescharacteristic
243C23×Dic67C2311yescharacteristic
244C23×Dic67C2311yescharacteristic
245C22×C4×D67C2311yescharacteristic
246C22×C4×D67C2311yescharacteristic
247C22×C4×D67C2311yescharacteristic
248C22×C4×D67C2311yescharacteristic
249C22×C4×D67C2311yescharacteristic
250C22×C4×D67C2311yescharacteristic
251C22×C4×D67C2311yescharacteristic
252C22×C4×D67C2311yescharacteristic
253C22×C4×D67C2311yescharacteristic
254C22×C4×D67C2311yescharacteristic
255#14524042C2318yes—
256#14524042C2318yes—
257#14524042C2318yes—
258#14524041C2318yes—
259#14524038C2318yes—
260#14524038C2318yes—
261#14524038C2318yes—
262#14524038C2318yes—
263#14524037C2318yes—
264#14524036C2318yes—
265#14524036C2318yes—
266#14524036C2318yes—
267#14524036C2318yes—
268#14524036C2318yes—
269#14524036C2318yes—
270#14524036C2318yes—
271#14524035C2318yes—
272#14524034C2318yes—
273#14524034C2318yes—
274#14524034C2318yes—
275#14524034C2318yes—
276#14524034C2318yes—
277#14524033C2318yes—
278#14524033C2318yes—
279#14524033C2318yes—
280#14524033C2318yes—
281#14524033C2318yes—
282#14524033C2318yes—
283#14524033C2318yes—
284#14524033C2318yes—
285#14524033C2318yes—
286#14524033C2318yes—
287#14524033C2318yes—
288#14524033C2318yes—
289#14524033C2318yes—
290#14524033C2318yes—
291#14524033C2318yes—
292#14524033C2318yes—
293#14524033C2318yes—
294#14524029C2318yes—
295#14524028C2318yes—
296#14524028C2318yes—
297#14524027C2318yes—
298#14524027C2318yes—
299#14524026C2318yes—
300#14524025C2318yes—
301#14524025C2318yes—
302#14524025C2318yes—
303#14524025C2318yes—
304#14524025C2318yes—
305#14524025C2318yes—
306#14524024C2318yes—
307#14524024C2318yes—
308#14524024C2318yes—
309#14524022C2318yes—
310#14524021C2318yes—
311#14524021C2318yes—
312#14524021C2318yes—
313#14524021C2318yes—
314#14524021C2318yes—
315#14524020C2318yes—
316#14524020C2318yes—
317#14524020C2318yes—
318#14524020C2318yes—
319#14524020C2318yes—
320#14524020C2318yes—
321#14524020C2318yes—
322#14524020C2318yes—
323#14524019C2318yes—
324#14524019C2318yes—
325#14524016C2318yes—
326#14524016C2318yes—
327#14524015C2318yes—
328#14524015C2318yes—
329#14524015C2318yes—
330#14524014C2318yes—
331Q8×Dic67C2318yes—
332C4×Dic134C2318yes—
333C4×Dic134C2318yes—
334C4×Dic134C2318yes—
335#14524008C2318yes—
336#14524008C2318yes—
337#14524008C2318yes—
338#14524008C2318yes—
339#14524008C2318yes—
340#14524008C2318yes—
341#14524008C2318yes—
342D4×Dic67C2318yes—
343D4×Dic67C2318yes—
344D4×Dic67C2318yes—
345#14524005C2318yes—
346#14524005C2318yes—
347C4×C22⋊D67C2318yes—
348C4×C22⋊D67C2318yes—
349C4×C22⋊D67C2318yes—
350C4×C22⋊D67C2318yes—
351C4×C22⋊D67C2318yes—
352C4×C22⋊D67C2318yes—
353C4×C22⋊D67C2318yes—
354(C22⋊D67)⋊C4C2318yes—
355(C22⋊D67)⋊C4C2318yes—
356(C22⋊D67)⋊C4C2318yes—
357(C22⋊D67)⋊C4C2318yes—
358(C22⋊D67)⋊C4C2318yes—
359(C22⋊D67)⋊C4C2318yes—
360(C22⋊D67)⋊C4C2318yes—
361#14524002C2318yes—
362#14524002C2318yes—
363#14524001C2318yes—
364#14524001C2318yes—
365#14524001C2318yes—
366#14524001C2318yes—
367#14524000C2318yes—
368#14524000C2318yes—
369#14523999C2318yes—
370#14523999C2318yes—
371#14523999C2318yes—
372#14523999C2318yes—
373#14523999C2318yes—
374#14523999C2318yes—
375#14523999C2318yes—
376C2×C4⋊Dic67C2318yes—
377C2×C4⋊Dic67C2311yescharacteristic
378C2×C4⋊Dic67C2311yescharacteristic
379C2×C4⋊Dic67C2311yescharacteristic
380C2×C4⋊Dic67C2311yescharacteristic
381C2×C4⋊Dic67C2311yescharacteristic
382C2×C4⋊Dic67C2311yescharacteristic
383C2×C4⋊Dic67C2311yescharacteristic
384C2×C4⋊Dic67C2311yescharacteristic
385C2×C4⋊Dic67C2311yescharacteristic
386C2×C4⋊Dic67C2311yescharacteristic
387C2×C4⋊Dic67C2311yescharacteristic
388C2×C4⋊Dic67C2311yescharacteristic
389C2×C4⋊Dic67C2311yescharacteristic
390C2×C4⋊Dic67C2311yescharacteristic
391C2×Dic67⋊C4C2318yes—
392C2×Dic67⋊C4C2318yes—
393C2×Dic67⋊C4C2318yes—
394C2×Dic67⋊C4C2318yes—
395C2×Dic67⋊C4C2311yescharacteristic
396C2×Dic67⋊C4C2311yescharacteristic
397C2×Dic67⋊C4C2311yescharacteristic
398C2×Dic67⋊C4C2311yescharacteristic
399C2×Dic67⋊C4C2311yescharacteristic
400C2×Dic67⋊C4C2311yescharacteristic
401C2×Dic67⋊C4C2311yescharacteristic
402C2×Dic67⋊C4C2311yescharacteristic
403C2×Dic67⋊C4C2311yescharacteristic
404C2×Dic67⋊C4C2311yescharacteristic
405C2×Dic67⋊C4C2311yescharacteristic
406C2×Dic67⋊C4C2311yescharacteristic
407C2×Dic67⋊C4C2311yescharacteristic
408C2×Dic67⋊C4C2311yescharacteristic
409C2×Dic67⋊C4C2311yescharacteristic
410C2×Dic67⋊C4C2311yescharacteristic
411C2×Dic67⋊C4C2311yescharacteristic
412C2×Dic67⋊C4C2311yescharacteristic
413C2×Dic67⋊C4C2311yescharacteristic
414C2×Dic67⋊C4C2311yescharacteristic
415C2×Dic67⋊C4C2311yescharacteristic
416C2×Dic67⋊C4C2318yes—
417C2×Dic67⋊C4C2311yescharacteristic
418C2×Dic67⋊C4C2311yescharacteristic
419C2×Dic67⋊C4C2311yescharacteristic
420C2×Dic67⋊C4C2311yescharacteristic
421C2×Dic67⋊C4C2311yescharacteristic
422C2×Dic67⋊C4C2311yescharacteristic
423C2×Dic67⋊C4C2311yescharacteristic
424C2×Dic67⋊C4C2311yescharacteristic
425C2×Dic67⋊C4C2311yescharacteristic
426C2×Dic67⋊C4C2311yescharacteristic
427C2×Dic67⋊C4C2311yescharacteristic
428C2×Dic67⋊C4C2311yescharacteristic
429C2×Dic67⋊C4C2311yescharacteristic
430C2×Dic67⋊C4C2311yescharacteristic
431C2×Dic67⋊C4C2311yescharacteristic
432C4⋊C4×D67C2318yes—
433C4⋊C4×D67C2318yes—
434C4⋊C4×D67C2318yes—
435C4⋊C4×D67C2318yes—
436C4⋊C4×D67C2318yes—
437C4⋊C4×D67C2318yes—
438C4⋊C4×D67C2318yes—
439C2×C22⋊Dic67C2311yescharacteristic
440C2×C22⋊Dic67C2311yescharacteristic
441C2×C22⋊Dic67C2311yescharacteristic
442C2×C22⋊Dic67C2311yescharacteristic
443C2×C22⋊Dic67C2311yescharacteristic
444C2×C22⋊Dic67C2311yescharacteristic
445C2×C22⋊Dic67C2311yescharacteristic
446C2×C22⋊Dic67C2311yescharacteristic
447C2×C22⋊Dic67C2311yescharacteristic
448C2×C22⋊Dic67C2311yescharacteristic
449C2×(C2×D67)⋊C4C2311yescharacteristic
450C2×(C2×D67)⋊C4C2311yescharacteristic
451C2×(C2×D67)⋊C4C2311yescharacteristic
452C2×(C2×D67)⋊C4C2311yescharacteristic
453C2×(C2×D67)⋊C4C2311yescharacteristic
454C2×(C2×D67)⋊C4C2311yescharacteristic
455C2×(C2×D67)⋊C4C2311yescharacteristic
456C2×(C2×D67)⋊C4C2311yescharacteristic
457C2×(C2×D67)⋊C4C2311yescharacteristic
458C2×(C2×D67)⋊C4C2311yescharacteristic
459C2×(C2×D67)⋊C4C2311yescharacteristic
460C2×(C2×D67)⋊C4C2311yescharacteristic
461C2×C4×Dic67C2311yescharacteristic
462C2×C4×Dic67C2311yescharacteristic
463C2×C4×Dic67C2311yescharacteristic
464C2×C4×Dic67C2311yescharacteristic
465C2×C4×Dic67C2311yescharacteristic
466C2×C4×Dic67C2311yescharacteristic
467C2×C4×Dic67C2311yescharacteristic
468C2×C4×Dic67C2311yescharacteristic
469C2×C4×Dic67C2311yescharacteristic
470C2×C4×Dic67C2318yes—
471C2×C4×Dic67C2318yes—
472C2×C4×Dic67C2311yescharacteristic
473C2×C4×Dic67C2311yescharacteristic
474C2×C4×Dic67C2311yescharacteristic
475C2×C4×Dic67C2311yescharacteristic
476C2×C4×Dic67C2311yescharacteristic
477C2×C4×Dic67C2311yescharacteristic
478C2×C4×Dic67C2311yescharacteristic
479C2×C4×Dic67C2311yescharacteristic
480C2×C4×Dic67C2311yescharacteristic
481C42×D67C2318yes—
482C22×Q8×C67C2311yescharacteristic
483C22×D4×C67C2311yescharacteristic
484C22×D4×C67C2311yescharacteristic
485C22×D4×C67C2311yescharacteristic
486C23×C4×C67C2311yescharacteristic
487C23×C4×C67C2311yescharacteristic
488C23×C4×C67C2311yescharacteristic
489C23×C4×C67C2311yescharacteristic
490C23×C4×C67C2311yescharacteristic
491#126×C67C2318yes—
492#126×C67C2318yes—
493#125×C67C2318yes—
494#125×C67C2318yes—
495#123×C67C2318yes—
496#123×C67C2318yes—
497#123×C67C2318yes—
498#123×C67C2318yes—
499C22⋊Q8×C67C2318yes—
500C22⋊Q8×C67C2318yes—
501C22⋊Q8×C67C2318yes—
502#121×C67C2318yes—
503C4×D4×C67C2318yes—
504C4×D4×C67C2318yes—
505C2×C4⋊C4×C67C2311yescharacteristic
506C2×C4⋊C4×C67C2311yescharacteristic
507C2×C4⋊C4×C67C2311yescharacteristic
508C2×C4⋊C4×C67C2311yescharacteristic
509C2×C4⋊C4×C67C2318yes—
510C2×C4⋊C4×C67C2311yescharacteristic
511C2×C4⋊C4×C67C2311yescharacteristic
512C2×C4⋊C4×C67C2311yescharacteristic
513C2×C4⋊C4×C67C2311yescharacteristic
514C2×C4⋊C4×C67C2311yescharacteristic
515C2×C4⋊C4×C67C2311yescharacteristic
516C2×C4⋊C4×C67C2311yescharacteristic
517C2×C4⋊C4×C67C2311yescharacteristic
518C2×C4⋊C4×C67C2311yescharacteristic
519C2×C4⋊C4×C67C2311yescharacteristic
520C2×C22⋊C4×C67C2311yescharacteristic
521C2×C22⋊C4×C67C2311yescharacteristic
522C2×C22⋊C4×C67C2311yescharacteristic
523C2×C22⋊C4×C67C2311yescharacteristic
524C2×C22⋊C4×C67C2311yescharacteristic
525C2×C22⋊C4×C67C2311yescharacteristic
526C2×C22⋊C4×C67C2311yescharacteristic
527C2×C22⋊C4×C67C2311yescharacteristic
528C2×C22⋊C4×C67C2311yescharacteristic
529C2×C22⋊C4×C67C2311yescharacteristic
530C2×C42×C67C2311yescharacteristic
531C2×C42×C67C2311yescharacteristic
532C23×D67C2411yescharacteristic
533C23×D67C2411yescharacteristic
534#11761628—232no—
535#11761627—232no—
536#11761627—232no—
537C2×Dic134—24no—
538C2×Dic134—24no—
539C2×Dic134—24no—
540C2×Dic134—24no—
541C2×Dic134—42no—
542C2×Dic134C2414yes—
543C2×Dic134C2414yes—
544C2×Dic134C2414yes—
545C2×Dic134C2414yes—
546C2×Dic134C2414yes—
547C2×D268—24no—
548C2×D268C2414yes—
549C2×C22⋊D67—24no—
550C2×C22⋊D67—24no—
551C2×C22⋊D67—24no—
552C2×C22⋊D67—24no—
553C2×C22⋊D67—42no—
554C2×C22⋊D67#4118yes—
555C2×C22⋊D67C2414yes—
556C2×C22⋊D67C2414yes—
557C2×C22⋊D67C2414yes—
558C2×C22⋊D67C2414yes—
559C2×C22⋊D67C2414yes—
560C2×C22⋊D67C2414yes—
561C22×Dic67—24no—
562C22×Dic67—24no—
563C22×Dic67—24no—
564C22×Dic67—24no—
565C22×Dic67—24no—
566C22×Dic67—24no—
567C22×Dic67—42no—
568C22×Dic67—42no—
569C22×Dic67C2411yescharacteristic
570C22×Dic67C2411yescharacteristic
571C22×Dic67C2411yescharacteristic
572C22×Dic67C2411yescharacteristic
573C22×Dic67C2411yescharacteristic
574C22×Dic67C2411yescharacteristic
575C22×Dic67C2411yescharacteristic
576C22×Dic67C2411yescharacteristic
577C22×Dic67C2414yes—
578C22×Dic67C2414yes—
579C22×Dic67C2414yes—
580C22×Dic67C2414yes—
581C22×Dic67C2411yescharacteristic
582C22×Dic67C2411yescharacteristic
583C22×Dic67C2411yescharacteristic
584C22×Dic67C2411yescharacteristic
585C22×Dic67C2414yes—
586C22×Dic67C2414yes—
587C22×Dic67C2414yes—
588C22×Dic67C2414yes—
589C22×Dic67C2411yescharacteristic
590C22×Dic67C2411yescharacteristic
591C2×C4×D67—24no—
592C2×C4×D67—24no—
593C2×C4×D67—24no—
594C2×C4×D67—24no—
595C2×C4×D67—24no—
596C2×C4×D67—42no—
597C2×C4×D67—42no—
598C2×C4×D67—42no—
599C2×C4×D67—42no—
600C2×C4×D67—42no—
601C2×C4×D67C2414yes—
602C2×C4×D67C2414yes—
603C2×C4×D67C2414yes—
604C2×C4×D67C2414yes—
605C2×C4×D67C2414yes—
606C2×C4×D67C2414yes—
607C2×C4×D67C2414yes—
608C2×C4×D67C2414yes—
609C2×C4×D67C2414yes—
610C2×C4×D67C2414yes—
611C4⋊Dic67C2414yes—
612C4⋊Dic67C2414yes—
613C4⋊Dic67C2414yes—
614C4⋊Dic67C2414yes—
615C4⋊Dic67C2414yes—
616C4⋊Dic67C2414yes—
617C4⋊Dic67C2414yes—
618C4⋊Dic67C2414yes—
619C4⋊Dic67C2414yes—
620C4⋊Dic67C2414yes—
621C4⋊Dic67C2414yes—
622C4⋊Dic67C2414yes—
623C4⋊Dic67C2414yes—
624C4⋊Dic67C2414yes—
625Dic67⋊C4C2414yes—
626Dic67⋊C4C2414yes—
627Dic67⋊C4C2414yes—
628Dic67⋊C4C2414yes—
629Dic67⋊C4C2414yes—
630Dic67⋊C4C2414yes—
631Dic67⋊C4C2414yes—
632Dic67⋊C4C2414yes—
633Dic67⋊C4C2414yes—
634Dic67⋊C4C2414yes—
635Dic67⋊C4C2414yes—
636Dic67⋊C4C2414yes—
637Dic67⋊C4C2414yes—
638Dic67⋊C4C2414yes—
639Dic67⋊C4C2414yes—
640Dic67⋊C4C2414yes—
641Dic67⋊C4C2414yes—
642Dic67⋊C4C2414yes—
643Dic67⋊C4C2414yes—
644Dic67⋊C4C2414yes—
645Dic67⋊C4C2414yes—
646Dic67⋊C4C2414yes—
647Dic67⋊C4C2414yes—
648Dic67⋊C4C2414yes—
649Dic67⋊C4C2414yes—
650Dic67⋊C4C2414yes—
651Dic67⋊C4C2414yes—
652Dic67⋊C4C2414yes—
653Dic67⋊C4C2414yes—
654Dic67⋊C4C2414yes—
655Dic67⋊C4C2414yes—
656Dic67⋊C4C2414yes—
657Dic67⋊C4C2414yes—
658Dic67⋊C4C2414yes—
659Dic67⋊C4C2414yes—
660Dic67⋊C4C2414yes—
661C22⋊Dic67C2414yes—
662C22⋊Dic67C2414yes—
663C22⋊Dic67C2414yes—
664C22⋊Dic67C2414yes—
665C22⋊Dic67C2414yes—
666C22⋊Dic67C2414yes—
667C22⋊Dic67C2414yes—
668C22⋊Dic67C2414yes—
669C22⋊Dic67C2414yes—
670C22⋊Dic67C2414yes—
671(C2×D67)⋊C4C2414yes—
672(C2×D67)⋊C4C2414yes—
673(C2×D67)⋊C4C2414yes—
674(C2×D67)⋊C4C2414yes—
675(C2×D67)⋊C4C2414yes—
676(C2×D67)⋊C4C2414yes—
677(C2×D67)⋊C4C2414yes—
678(C2×D67)⋊C4C2414yes—
679(C2×D67)⋊C4C2414yes—
680(C2×D67)⋊C4C2414yes—
681(C2×D67)⋊C4C2414yes—
682(C2×D67)⋊C4C2414yes—
683C4×Dic67C2414yes—
684C4×Dic67C2414yes—
685C4×Dic67C2414yes—
686C4×Dic67C2414yes—
687C4×Dic67C2414yes—
688C4×Dic67C2414yes—
689C4×Dic67C2414yes—
690C4×Dic67C2414yes—
691C4×Dic67C2414yes—
692C4×Dic67C2414yes—
693C4×Dic67C2414yes—
694C4×Dic67C2414yes—
695C4×Dic67C2414yes—
696C4×Dic67C2414yes—
697C4×Dic67C2414yes—
698C4×Dic67C2414yes—
699C4×Dic67C2414yes—
700C4×Dic67C2414yes—
701C24×C67C2411yescharacteristic
702C24×C67C2411yescharacteristic
703C24×C67C2411yescharacteristic
704C2×Q8×C67—42no—
705C2×Q8×C67C2414yes—
706C2×D4×C67—24no—
707C2×D4×C67—24no—
708C2×D4×C67—42no—
709C2×D4×C67C2414yes—
710C2×D4×C67C2414yes—
711C2×D4×C67C2414yes—
712C22×C4×C67—24no—
713C22×C4×C67—42no—
714C22×C4×C67—42no—
715C22×C4×C67—42no—
716C22×C4×C67—42no—
717C22×C4×C67C2411yescharacteristic
718C22×C4×C67C2411yescharacteristic
719C22×C4×C67C2411yescharacteristic
720C22×C4×C67C2411yescharacteristic
721C22×C4×C67C2411yescharacteristic
722C22×C4×C67C2411yescharacteristic
723C22×C4×C67C2411yescharacteristic
724C22×C4×C67C2411yescharacteristic
725C22×C4×C67C2411yescharacteristic
726C22×C4×C67C2411yescharacteristic
727C22×C4×C67C2411yescharacteristic
728C22×C4×C67C2411yescharacteristic
729C22×C4×C67C2414yes—
730C22×C4×C67C2414yes—
731C22×C4×C67C2414yes—
732C22×C4×C67C2414yes—
733C22×C4×C67C2414yes—
734C4⋊C4×C67C2414yes—
735C4⋊C4×C67C2414yes—
736C4⋊C4×C67C2414yes—
737C4⋊C4×C67C2414yes—
738C4⋊C4×C67C2414yes—
739C4⋊C4×C67C2414yes—
740C4⋊C4×C67C2414yes—
741C4⋊C4×C67C2414yes—
742C4⋊C4×C67C2414yes—
743C4⋊C4×C67C2414yes—
744C4⋊C4×C67C2414yes—
745C4⋊C4×C67C2414yes—
746C4⋊C4×C67C2414yes—
747C4⋊C4×C67C2414yes—
748C22⋊C4×C67C2414yes—
749C22⋊C4×C67C2414yes—
750C22⋊C4×C67C2414yes—
751C22⋊C4×C67C2414yes—
752C22⋊C4×C67C2414yes—
753C22⋊C4×C67C2414yes—
754C22⋊C4×C67C2414yes—
755C22⋊C4×C67C2414yes—
756C22⋊C4×C67C2414yes—
757C22⋊C4×C67C2414yes—
758C42×C67C2414yes—
759C42×C67C2414yes—
760C23×C67—22no—
761C23×C67—22no—
762C23×C67—22no—
763C23×C67—22no—
764C23×C67—22no—
765C23×C67—22no—
766C23×C67—22no—
767C23×C67—22no—
768C23×C67C2×#4114yes—
769C23×C67C2512yes—
770C23×C67C2512yes—
771C23×C67C2512yes—
772C23×C67C2511yescharacteristic
773C22×D67—22no—
774C22×D67—22no—
775C22×D67—22no—
776C22×D67—22no—
777C22×D67—22no—
778C22×D67C2×#4114yes—
779C22×D67C2512yes—
780C22×D67C2512yes—
781Q8×C67—44no—
782D4×C67—28no—
783D4×C67—28no—
784D4×C67—44no—
785C2×C4×C67—22no—
786C2×C4×C67—22no—
787C2×C4×C67—28no—
788C2×C4×C67—22no—
789C2×C4×C67—22no—
790C2×C4×C67—22no—
791C2×C4×C67—22no—
792C2×C4×C67—22no—
793C2×C4×C67—22no—
794C2×C4×C67—22no—
795C2×C4×C67—22no—
796C2×C4×C67—22no—
797C2×C4×C67—22no—
798C2×C4×C67—44no—
799C2×C4×C67—44no—
800C2×C4×C67—44no—
801C2×C4×C67—44no—
802C2×C4×C67C2512yes—
803C2×C4×C67C2512yes—
804C2×C4×C67C2512yes—
805C2×C4×C67C2512yes—
806C2×C4×C67C2512yes—
807C2×C4×C67C2512yes—
808C2×C4×C67C2512yes—
809C2×C4×C67C2512yes—
810C2×C4×C67C2512yes—
811C2×C4×C67C2512yes—
812C2×C4×C67C2512yes—
813C2×C4×C67C2512yes—
814C22⋊D67—28no—
815C22⋊D67—28no—
816C22⋊D67—28no—
817C22⋊D67—28no—
818C22⋊D67—44no—
819C22⋊D67C2×#41116yes—
820C2×Dic67—22no—
821C2×Dic67—22no—
822C2×Dic67—22no—
823C2×Dic67—22no—
824C2×Dic67—22no—
825C2×Dic67—28no—
826C2×Dic67—28no—
827C2×Dic67—22no—
828C2×Dic67—22no—
829C2×Dic67—22no—
830C2×Dic67—22no—
831C2×Dic67—22no—
832C2×Dic67—22no—
833C2×Dic67—22no—
834C2×Dic67—28no—
835C2×Dic67—28no—
836C2×Dic67—28no—
837C2×Dic67—28no—
838C2×Dic67—44no—
839C2×Dic67—44no—
840C2×Dic67C2×#4114yes—
841C2×Dic672−1+414yes—
842C2×Dic67C2512yes—
843C2×Dic67C2512yes—
844C2×Dic67C2512yes—
845C2×Dic67C2512yes—
846C2×Dic67C2512yes—
847C2×Dic67C2512yes—
848C2×Dic67C2512yes—
849C2×Dic67C2512yes—
850C2×Dic67C2512yes—
851C2×Dic67C2512yes—
852C2×Dic67C2512yes—
853C2×Dic67C2512yes—
854C2×Dic67C2512yes—
855C2×Dic67C2512yes—
856D268—28no—
857C4×D67—28no—
858C4×D67—28no—
859C4×D67—28no—
860C4×D67—28no—
861C4×D67—28no—
862C4×D67—44no—
863C4×D67—44no—
864C4×D67—44no—
865C4×D67—44no—
866C4×D67—44no—
867Dic134—28no—
868Dic134—28no—
869Dic134—28no—
870Dic134—28no—
871Dic134—44no—
872C22×C67—22no—
873C22×C67—22no—
874C22×C67—28no—
875C22×C67—22no—
876C22×C67—22no—
877C22×C67—22no—
878C22×C67—22no—
879C22×C67—22no—
880C22×C67—22no—
881C22×C67—44no—
882C22×C67—44no—
883C22×C67C22×#4114yes—
884C22×C67C22×#4112yes—
885C22×C67C2×2−1+412yes—
886C22×C67#58512yes—
887C22×C67C2611yescharacteristic
888C2×D67—22no—
889C2×D67—22no—
890C2×D67—28no—
891C2×D67—22no—
892C2×D67—22no—
893C2×D67—22no—
894C2×D67—44no—
895C2×D67C22×#4114yes—
896C4×C67—22no—
897C4×C67—22no—
898C4×C67—22no—
899C4×C67—22no—
900C4×C67—22no—
901C4×C67—22no—
902C4×C67—22no—
903C4×C67—22no—
904C4×C67—22no—
905C4×C67—22no—
906C4×C67—22no—
907C4×C67—22no—
908Dic67—22no—
909Dic67—22no—
910Dic67—22no—
911Dic67—22no—
912Dic67—22no—
913Dic67—22no—
914Dic67—22no—
915Dic67—22no—
916Dic67—22no—
917Dic67—22no—
918Dic67—22no—
919Dic67—22no—
920Dic67C22×#4114yes—
921Dic67C2×2−1+414yes—
922C2×#3515—671nomaximal, Sylow
923C2×C67—24no—
924C2×C67—42no—
925C2×C67—42no—
926C2×C67#351514yescomplemented
927C2×C67C23×#4111yescharacteristic
928C2×C67C22×2−1+411yescharacteristic
929C2×C67C2×#58511yescharacteristic
930D67—24no—
931D67—42no—
932#3515—6732no—
933C2×#557—671no—
934C2×#554—671no—
935C2×#554—671no—
936C2×#553—671no—
937C2×#553—671no—
938C2×#552—671no—
939C2×#552—671no—
940C2×#552—671no—
941C2×#552—671no—
942C2×#552—671no—
943C2×#552—671no—
944C2×#552—671no—
945C2×#552—671no—
946C2×#547—671no—
947C2×#547—671no—
948C2×#547—671no—
949C2×#541—671no—
950C2×#541—671no—
951C2×#539—671no—
952C2×#539—671no—
953C2×#539—671no—
954C2×#539D6711yescharacteristic, complemented
955C2×#533—671no—
956C2×#529—671no—
957C2×#529—671no—
958C2×#529—671no—
959C22×#125—671no—
960C22×#125—671no—
961C2×#520—671no—
962C2×#520—671no—
963C2×C4×#41—671no—
964C67C2×#351511yescharacteristic, complemented, Sylow
965C22×#41—671no—
966C22×#41—671no—
967C22×#41—671no—
968#557—6716no—
969#554—6716no—
970#554—6716no—
971#553—6716no—
972#553—6716no—
973#552—6716no—
974#552—6716no—
975#552—6716no—
976#552—6716no—
977#552—6716no—
978#552—6716no—
979#552—6716no—
980#552—6716no—
981#547—6716no—
982#547—6716no—
983#547—6716no—
984#541—6716no—
985#541—6716no—
986#539—6716no—
987#539—6716no—
988#539—6716no—
989#539C2×D67116yescomplemented
990#533—6716no—
991C2×C4⋊Q8—671no—
992C2×C4⋊Q8—671no—
993C2×C4⋊Q8—671no—
994C2×C4⋊Q8—671no—
995#529—6716no—
996#529—6716no—
997#529—6716no—
998C2×#126—671no—
999C2×#126—671no—
1000C2×#126—671no—
1001C2×#126—671no—
1002C2×#126—671no—
1003C2×#126—671no—
1004C2×#126—671no—
1005C2×#126—671no—
1006C2×#126—671no—
1007C2×#126—671no—
1008C2×#126—671no—
1009C2×#126—671no—
1010C2×#126C2×D6711yescharacteristic
1011C2×#126C2×D6711yescharacteristic
1012C2×#125—6716no—
1013C2×#125—671no—
1014C2×#125—671no—
1015C2×#125—671no—
1016C2×#125—671no—
1017C2×#125—671no—
1018C2×#125—671no—
1019C2×#125—671no—
1020C2×#125—671no—
1021C2×#125—671no—
1022C2×#125—671no—
1023C2×#125—671no—
1024C2×#125—671no—
1025C2×#125—671no—
1026C2×#125—6716no—
1027C2×#125—671no—
1028C2×#125—671no—
1029C2×#125—671no—
1030C2×#125—671no—
1031C2×#125—671no—
1032C2×#125—671no—
1033C2×#125—671no—
1034C2×#125—671no—
1035C2×#125—671no—
1036C2×#125—671no—
1037C2×#125C2×D6711yescharacteristic
1038C2×#125C2×D6711yescharacteristic
1039C2×#124—671no—
1040C2×#123—671no—
1041C2×#123—671no—
1042C2×#123—671no—
1043C2×#123—671no—
1044C2×#123—671no—
1045C2×#123—671no—
1046C2×#123—671no—
1047C2×#123—671no—
1048C2×#123—671no—
1049C2×#123—671no—
1050C2×#123—671no—
1051C2×#123—671no—
1052C2×#123—671no—
1053C2×#123—671no—
1054C2×#123C2×D6711yescharacteristic
1055C2×#123C2×D6711yescharacteristic
1056C2×#123C2×D6711yescharacteristic
1057C2×#123C2×D6711yescharacteristic
1058C2×C22⋊Q8—671no—
1059C2×C22⋊Q8—671no—
1060C2×C22⋊Q8—671no—
1061C2×C22⋊Q8—671no—
1062C2×C22⋊Q8—671no—
1063C2×C22⋊Q8—671no—
1064C2×C22⋊Q8—671no—
1065C2×C22⋊Q8—671no—
1066C2×C22⋊Q8—671no—
1067C2×C22⋊Q8—671no—
1068C2×C22⋊Q8—671no—
1069C2×C22⋊Q8—671no—
1070C2×C22⋊Q8—671no—
1071C2×C22⋊Q8—671no—
1072C2×C22⋊Q8—671no—
1073C2×C22⋊Q8—671no—
1074C2×C22⋊Q8C2×D6711yescharacteristic
1075C2×C22⋊Q8C2×D6711yescharacteristic
1076C2×C22⋊Q8C2×D6711yescharacteristic
1077C2×#121—671no—
1078C2×#121—671no—
1079C2×#121—671no—
1080C2×#121—671no—
1081C2×#121—671no—
1082C2×#121—671no—
1083C2×#121C2×D6711yescharacteristic
1084#520—6716no—
1085#520—6716no—
1086C4×#41—6716no—
1087C2×C4×Q8—671no—
1088C2×C4×Q8—671no—
1089C2×C4×Q8—671no—
1090C2×C4×Q8—671no—
1091C2×C4×Q8—671no—
1092C2×C4×Q8—671no—
1093C2×C4×Q8—671no—
1094C2×C4×Q8—671no—
1095C2×C4×Q8—671no—
1096C2×C4×Q8—671no—
1097C2×C4×Q8—671no—
1098C2×C4×D4—671no—
1099C2×C4×D4—671no—
1100C2×C4×D4—671no—
1101C2×C4×D4—671no—
1102C2×C4×D4—671no—
1103C2×C4×D4—671no—
1104C2×C4×D4—671no—
1105C2×C4×D4—671no—
1106C2×C4×D4—671no—
1107C2×C4×D4—671no—
1108C2×C4×D4—671no—
1109C2×C4×D4—671no—
1110C2×C4×D4—671no—
1111C2×C4×D4—671no—
1112C2×C4×D4—671no—
1113C2×C4×D4—671no—
1114C2×C4×D4—671no—
1115C2×C4×D4—671no—
1116C2×C4×D4—671no—
1117C2×C4×D4C2×D6711yescharacteristic
1118C2×C4×D4C2×D6711yescharacteristic
1119C2×#117—671no—
1120C2×#117—671no—
1121C2×#117—671no—
1122C2×#117—671no—
1123C2×#117—671no—
1124C2×#117—671no—
1125C2×#117—671no—
1126C2×#117—671no—
1127C2×#117—671no—
1128C2×#117—671no—
1129C2×#117—671no—
1130C2×#117—671no—
1131C2×#117—671no—
1132C2×#117—671no—
1133C2×#117—671no—
1134C22×C4⋊C4—671no—
1135C22×C4⋊C4—671no—
1136C22×C4⋊C4—671no—
1137C22×C4⋊C4—671no—
1138C22×C4⋊C4—671no—
1139C22×C4⋊C4—671no—
1140C22×C4⋊C4—671no—
1141C22×C4⋊C4—671no—
1142C22×C4⋊C4—671no—
1143C22×C4⋊C4—671no—
1144C22×C4⋊C4—671no—
1145C22×C4⋊C4—671no—
1146C22×C4⋊C4—671no—
1147C22×C4⋊C4C2×D6711yescharacteristic
1148C22×C42—671no—
1149C22×C42—671no—
1150C22×C42—671no—
1151C2×#41—678no—
1152C2×#41—678no—
1153C2×#41—678no—
1154C2×#41—1348no—
1155C2×#41—1348no—
1156C2×#41—1348no—
1157C22×Q8—671no—
1158C22×Q8—671no—
1159C22×Q8—671no—
1160C22×Q8—671no—
1161C22×Q8—671no—
1162C22×Q8C22×D6711yescharacteristic
1163C22×D4—671no—
1164C22×D4—671no—
1165C22×D4—671no—
1166C22×D4—671no—
1167C22×D4—671no—
1168C22×D4—671no—
1169C22×D4—671no—
1170C22×D4C22×D6711yescharacteristic
1171C22×D4C22×D6711yescharacteristic
1172C22×D4C22×D6711yescharacteristic
1173C23×C4—671no—
1174C23×C4—671no—
1175C23×C4—671no—
1176C23×C4—671no—
1177C23×C4—671no—
1178C23×C4—671no—
1179C23×C4—671no—
1180C23×C4—671no—
1181C23×C4—671no—
1182C23×C4—671no—
1183C23×C4—671no—
1184C23×C4—671no—
1185C23×C4—671no—
1186C23×C4—671no—
1187C23×C4—671no—
1188C23×C4—671no—
1189C23×C4—671no—
1190C23×C4—671no—
1191C23×C4C22×D6711yescharacteristic
1192C23×C4C22×D6711yescharacteristic
1193C23×C4C22×D6711yescharacteristic
1194C23×C4C22×D6711yescharacteristic
1195C23×C4C22×D6711yescharacteristic
1196C4⋊Q8—678no—
1197C4⋊Q8—678no—
1198C4⋊Q8—678no—
1199C4⋊Q8—678no—
1200#126—678no—
1201#126—678no—
1202#126—678no—
1203#126—678no—
1204#126—678no—
1205#126—678no—
1206#126—678no—
1207#126—678no—
1208#126—678no—
1209#126—678no—
1210#126—678no—
1211#126—678no—
1212#126C22×D6718yes—
1213#126C22×D6718yes—
1214#125—678no—
1215#125—678no—
1216#125—678no—
1217#125—678no—
1218#125—678no—
1219#125—678no—
1220#125—678no—
1221#125—678no—
1222#125—678no—
1223#125—678no—
1224#125—678no—
1225#125—678no—
1226#125—678no—
1227#125—678no—
1228#125—678no—
1229#125—678no—
1230#125—678no—
1231#125—678no—
1232#125—678no—
1233#125—678no—
1234#125—678no—
1235#125—678no—
1236#125—678no—
1237#125C22×D6718yes—
1238#125C22×D6718yes—
1239#124—678no—
1240#123—678no—
1241#123—678no—
1242#123—678no—
1243#123—678no—
1244#123—678no—
1245#123—678no—
1246#123—678no—
1247#123—678no—
1248#123—678no—
1249#123—678no—
1250#123—678no—
1251#123—678no—
1252#123—678no—
1253#123—678no—
1254#123C22×D6718yes—
1255#123C22×D6718yes—
1256#123C22×D6718yes—
1257#123C22×D6718yes—
1258C22⋊Q8—678no—
1259C22⋊Q8—678no—
1260C22⋊Q8—678no—
1261C22⋊Q8—678no—
1262C22⋊Q8—678no—
1263C22⋊Q8—678no—
1264C22⋊Q8—678no—
1265C22⋊Q8—678no—
1266C22⋊Q8—678no—
1267C22⋊Q8—678no—
1268C22⋊Q8—678no—
1269C22⋊Q8—678no—
1270C22⋊Q8—678no—
1271C22⋊Q8—678no—
1272C22⋊Q8—678no—
1273C22⋊Q8—678no—
1274C22⋊Q8C22×D6718yes—
1275C22⋊Q8C22×D6718yes—
1276C22⋊Q8C22×D6718yes—
1277#121—678no—
1278#121—678no—
1279#121—678no—
1280#121—678no—
1281#121—678no—
1282#121—678no—
1283#121C22×D6718yes—
1284C4×Q8—678no—
1285C4×Q8—678no—
1286C4×Q8—678no—
1287C4×Q8—678no—
1288C4×Q8—678no—
1289C4×Q8—678no—
1290C4×Q8—678no—
1291C4×Q8—678no—
1292C4×Q8—678no—
1293C4×Q8—678no—
1294C4×Q8—678no—
1295C4×D4—678no—
1296C4×D4—678no—
1297C4×D4—678no—
1298C4×D4—678no—
1299C4×D4—678no—
1300C4×D4—678no—
1301C4×D4—678no—
1302C4×D4—678no—
1303C4×D4—678no—
1304C4×D4—678no—
1305C4×D4—678no—
1306C4×D4—678no—
1307C4×D4—678no—
1308C4×D4—678no—
1309C4×D4—678no—
1310C4×D4—678no—
1311C4×D4—678no—
1312C4×D4—678no—
1313C4×D4—678no—
1314C4×D4C22×D6718yes—
1315C4×D4C22×D6718yes—
1316#117—678no—
1317#117—678no—
1318#117—678no—
1319#117—678no—
1320#117—678no—
1321#117—678no—
1322#117—678no—
1323#117—678no—
1324#117—678no—
1325#117—678no—
1326#117—678no—
1327#117—678no—
1328#117—678no—
1329#117—678no—
1330#117—678no—
1331C2×C4⋊C4—671no—
1332C2×C4⋊C4—671no—
1333C2×C4⋊C4—671no—
1334C2×C4⋊C4—671no—
1335C2×C4⋊C4—671no—
1336C2×C4⋊C4—671no—
1337C2×C4⋊C4—671no—
1338C2×C4⋊C4—671no—
1339C2×C4⋊C4—671no—
1340C2×C4⋊C4—671no—
1341C2×C4⋊C4—671no—
1342C2×C4⋊C4—671no—
1343C2×C4⋊C4—671no—
1344C2×C4⋊C4—671no—
1345C2×C4⋊C4—671no—
1346C2×C4⋊C4—671no—
1347C2×C4⋊C4—671no—
1348C2×C4⋊C4—671no—
1349C2×C4⋊C4—671no—
1350C2×C4⋊C4—671no—
1351C2×C4⋊C4—671no—
1352C2×C4⋊C4—671no—
1353C2×C4⋊C4—671no—
1354C2×C4⋊C4—671no—
1355C2×C4⋊C4—678no—
1356C2×C4⋊C4—678no—
1357C2×C4⋊C4—671no—
1358C2×C4⋊C4—671no—
1359C2×C4⋊C4—671no—
1360C2×C4⋊C4—671no—
1361C2×C4⋊C4—671no—
1362C2×C4⋊C4—671no—
1363C2×C4⋊C4—671no—
1364C2×C4⋊C4—671no—
1365C2×C4⋊C4—671no—
1366C2×C4⋊C4—671no—
1367C2×C4⋊C4—671no—
1368C2×C4⋊C4—671no—
1369C2×C4⋊C4—678no—
1370C2×C4⋊C4—678no—
1371C2×C4⋊C4—678no—
1372C2×C4⋊C4—678no—
1373C2×C4⋊C4—671no—
1374C2×C4⋊C4—671no—
1375C2×C4⋊C4—671no—
1376C2×C4⋊C4—671no—
1377C2×C4⋊C4—671no—
1378C2×C4⋊C4—671no—
1379C2×C4⋊C4—671no—
1380C2×C4⋊C4—671no—
1381C2×C4⋊C4—671no—
1382C2×C4⋊C4—671no—
1383C2×C4⋊C4—671no—
1384C2×C4⋊C4—671no—
1385C2×C4⋊C4—671no—
1386C2×C4⋊C4—671no—
1387C2×C4⋊C4—678no—
1388C2×C4⋊C4—678no—
1389C2×C4⋊C4—678no—
1390C2×C4⋊C4—678no—
1391C2×C4⋊C4—678no—
1392C2×C4⋊C4—678no—
1393C2×C4⋊C4—678no—
1394C2×C4⋊C4C22×D6711yescharacteristic
1395C2×C4⋊C4C22×D6711yescharacteristic
1396C2×C4⋊C4C22×D6711yescharacteristic
1397C2×C4⋊C4C22×D6711yescharacteristic
1398C2×C4⋊C4C22×D6711yescharacteristic
1399C2×C4⋊C4C22×D6711yescharacteristic
1400C2×C4⋊C4C22×D6711yescharacteristic
1401C2×C4⋊C4C22×D6711yescharacteristic
1402C2×C4⋊C4C22×D6711yescharacteristic
1403C2×C4⋊C4C22×D6718yes—
1404C2×C4⋊C4C22×D6711yescharacteristic
1405C2×C4⋊C4C22×D6711yescharacteristic
1406C2×C4⋊C4C22×D6711yescharacteristic
1407C2×C4⋊C4C22×D6711yescharacteristic
1408C2×C4⋊C4C22×D6711yescharacteristic
1409C2×C22⋊C4—671no—
1410C2×C22⋊C4—671no—
1411C2×C22⋊C4—671no—
1412C2×C22⋊C4—671no—
1413C2×C22⋊C4—671no—
1414C2×C22⋊C4—671no—
1415C2×C22⋊C4—671no—
1416C2×C22⋊C4—671no—
1417C2×C22⋊C4—671no—
1418C2×C22⋊C4—671no—
1419C2×C22⋊C4—671no—
1420C2×C22⋊C4—671no—
1421C2×C22⋊C4—671no—
1422C2×C22⋊C4—671no—
1423C2×C22⋊C4—671no—
1424C2×C22⋊C4—671no—
1425C2×C22⋊C4—671no—
1426C2×C22⋊C4—671no—
1427C2×C22⋊C4—671no—
1428C2×C22⋊C4—671no—
1429C2×C22⋊C4—671no—
1430C2×C22⋊C4—671no—
1431C2×C22⋊C4C22×D6711yescharacteristic
1432C2×C22⋊C4C22×D6711yescharacteristic
1433C2×C22⋊C4C22×D6711yescharacteristic
1434C2×C22⋊C4C22×D6711yescharacteristic
1435C2×C22⋊C4C22×D6711yescharacteristic
1436C2×C22⋊C4C22×D6711yescharacteristic
1437C2×C22⋊C4C22×D6711yescharacteristic
1438C2×C22⋊C4C22×D6711yescharacteristic
1439C2×C22⋊C4C22×D6711yescharacteristic
1440C2×C22⋊C4C22×D6711yescharacteristic
1441C2×C42—671no—
1442C2×C42—671no—
1443C2×C42—671no—
1444C2×C42—671no—
1445C2×C42—671no—
1446C2×C42—671no—
1447C2×C42—671no—
1448C2×C42—671no—
1449C2×C42—671no—
1450C2×C42—671no—
1451C2×C42—671no—
1452C2×C42—671no—
1453C2×C42—671no—
1454C2×C42—671no—
1455C2×C42—671no—
1456C2×C42—671no—
1457C2×C42—671no—
1458C2×C42—678no—
1459C2×C42—678no—
1460C2×C42—671no—
1461C2×C42—678no—
1462C2×C42C22×D6711yescharacteristic
1463C2×C42C22×D6711yescharacteristic
1464C24—671no—
1465C24—671no—
1466C24C23×D6711yescharacteristic
1467C24C23×D6711yescharacteristic
1468C24C23×D6711yescharacteristic
1469#41—13432no—
1470#41—13432no—
1471#41—13432no—
1472C2×Q8—42no—
1473C2×Q8—2682no—
1474C2×Q8—674no—
1475C2×Q8—674no—
1476C2×Q8—674no—
1477C2×Q8—674no—
1478C2×Q8—674no—
1479C2×Q8—1344no—
1480C2×Q8—1344no—
1481C2×Q8—1344no—
1482C2×Q8—1344no—
1483C2×Q8C23×D6714yes—
1484C2×D4—24no—
1485C2×D4—24no—
1486C2×D4—42no—
1487C2×D4—2682no—
1488C2×D4—674no—
1489C2×D4—678no—
1490C2×D4—674no—
1491C2×D4—674no—
1492C2×D4—674no—
1493C2×D4—674no—
1494C2×D4—674no—
1495C2×D4—674no—
1496C2×D4—1344no—
1497C2×D4—1344no—
1498C2×D4—1344no—
1499C2×D4—1344no—
1500C2×D4—1344no—
1501C2×D4C23×D6714yes—
1502C2×D4C23×D6714yes—
1503C2×D4C23×D6714yes—
1504C22×C4—24no—
1505C22×C4—42no—
1506C22×C4—42no—
1507C22×C4—42no—
1508C22×C4—42no—
1509C22×C4—2682no—
1510C22×C4—2682no—
1511C22×C4—2682no—
1512C22×C4—2682no—
1513C22×C4—2682no—
1514C22×C4—2682no—
1515C22×C4—2682no—
1516C22×C4—674no—
1517C22×C4—674no—
1518C22×C4—674no—
1519C22×C4—674no—
1520C22×C4—674no—
1521C22×C4—674no—
1522C22×C4—674no—
1523C22×C4—671no—
1524C22×C4—671no—
1525C22×C4—674no—
1526C22×C4—674no—
1527C22×C4—674no—
1528C22×C4—674no—
1529C22×C4—674no—
1530C22×C4—674no—
1531C22×C4—671no—
1532C22×C4—671no—
1533C22×C4—671no—
1534C22×C4—671no—
1535C22×C4—671no—
1536C22×C4—671no—
1537C22×C4—671no—
1538C22×C4—671no—
1539C22×C4—671no—
1540C22×C4—671no—
1541C22×C4—671no—
1542C22×C4—671no—
1543C22×C4—674no—
1544C22×C4—674no—
1545C22×C4—674no—
1546C22×C4—674no—
1547C22×C4—674no—
1548C22×C4—1344no—
1549C22×C4—1344no—
1550C22×C4—1344no—
1551C22×C4—1344no—
1552C22×C4—1344no—
1553C22×C4—1344no—
1554C22×C4—1344no—
1555C22×C4—1344no—
1556C22×C4—1344no—
1557C22×C4—1344no—
1558C22×C4—1344no—
1559C22×C4C23×D6714yes—
1560C22×C4C23×D6711yescharacteristic
1561C22×C4C23×D6711yescharacteristic
1562C22×C4C23×D6711yescharacteristic
1563C22×C4C23×D6711yescharacteristic
1564C22×C4C23×D6711yescharacteristic
1565C22×C4C23×D6711yescharacteristic
1566C22×C4C23×D6711yescharacteristic
1567C22×C4C23×D6711yescharacteristic
1568C22×C4C23×D6711yescharacteristic
1569C22×C4C23×D6711yescharacteristic
1570C22×C4C23×D6711yescharacteristic
1571C22×C4C23×D6711yescharacteristic
1572C22×C4C23×D6714yes—
1573C22×C4C23×D6714yes—
1574C22×C4C23×D6714yes—
1575C22×C4C23×D6714yes—
1576C4⋊C4—674no—
1577C4⋊C4—674no—
1578C4⋊C4—674no—
1579C4⋊C4—674no—
1580C4⋊C4—674no—
1581C4⋊C4—674no—
1582C4⋊C4—674no—
1583C4⋊C4—674no—
1584C4⋊C4—674no—
1585C4⋊C4—674no—
1586C4⋊C4—674no—
1587C4⋊C4—674no—
1588C4⋊C4—674no—
1589C4⋊C4—674no—
1590C4⋊C4—674no—
1591C4⋊C4—674no—
1592C4⋊C4—674no—
1593C4⋊C4—674no—
1594C4⋊C4—674no—
1595C4⋊C4—674no—
1596C4⋊C4—674no—
1597C4⋊C4—674no—
1598C4⋊C4—674no—
1599C4⋊C4—674no—
1600C4⋊C4—674no—
1601C4⋊C4—674no—
1602C4⋊C4—674no—
1603C4⋊C4—674no—
1604C4⋊C4—674no—
1605C4⋊C4—674no—
1606C4⋊C4—674no—
1607C4⋊C4—674no—
1608C4⋊C4—674no—
1609C4⋊C4—674no—
1610C4⋊C4—674no—
1611C4⋊C4—674no—
1612C4⋊C4—674no—
1613C4⋊C4—674no—
1614C4⋊C4—674no—
1615C4⋊C4—674no—
1616C4⋊C4—674no—
1617C4⋊C4—674no—
1618C4⋊C4—674no—
1619C4⋊C4—674no—
1620C4⋊C4—674no—
1621C4⋊C4—674no—
1622C4⋊C4—674no—
1623C4⋊C4—674no—
1624C4⋊C4—674no—
1625C4⋊C4—674no—
1626C4⋊C4C23×D6714yes—
1627C4⋊C4C23×D6714yes—
1628C4⋊C4C23×D6714yes—
1629C4⋊C4C23×D6714yes—
1630C4⋊C4C23×D6714yes—
1631C4⋊C4C23×D6714yes—
1632C4⋊C4C23×D6714yes—
1633C4⋊C4C23×D6714yes—
1634C4⋊C4C23×D6714yes—
1635C4⋊C4C23×D6714yes—
1636C4⋊C4C23×D6714yes—
1637C4⋊C4C23×D6714yes—
1638C4⋊C4C23×D6714yes—
1639C4⋊C4C23×D6714yes—
1640C22⋊C4—674no—
1641C22⋊C4—674no—
1642C22⋊C4—674no—
1643C22⋊C4—674no—
1644C22⋊C4—674no—
1645C22⋊C4—674no—
1646C22⋊C4—674no—
1647C22⋊C4—674no—
1648C22⋊C4—674no—
1649C22⋊C4—674no—
1650C22⋊C4—674no—
1651C22⋊C4—674no—
1652C22⋊C4—674no—
1653C22⋊C4—674no—
1654C22⋊C4—674no—
1655C22⋊C4—674no—
1656C22⋊C4—674no—
1657C22⋊C4—674no—
1658C22⋊C4—674no—
1659C22⋊C4—674no—
1660C22⋊C4—674no—
1661C22⋊C4—674no—
1662C22⋊C4C23×D6714yes—
1663C22⋊C4C23×D6714yes—
1664C22⋊C4C23×D6714yes—
1665C22⋊C4C23×D6714yes—
1666C22⋊C4C23×D6714yes—
1667C22⋊C4C23×D6714yes—
1668C22⋊C4C23×D6714yes—
1669C22⋊C4C23×D6714yes—
1670C22⋊C4C23×D6714yes—
1671C22⋊C4C23×D6714yes—
1672C42—674no—
1673C42—674no—
1674C42—674no—
1675C42—674no—
1676C42—674no—
1677C42—674no—
1678C42—674no—
1679C42—674no—
1680C42—674no—
1681C42—674no—
1682C42—674no—
1683C42—674no—
1684C42—674no—
1685C42—674no—
1686C42—674no—
1687C42—674no—
1688C42—674no—
1689C42—674no—
1690C42C23×D6714yes—
1691C42C23×D6714yes—
1692C23—22no—
1693C23—22no—
1694C23—22no—
1695C23—22no—
1696C23—22no—
1697C23—22no—
1698C23—22no—
1699C23—22no—
1700C23—674no—
1701C23—672no—
1702C23—672no—
1703C23—1342no—
1704C23—1342no—
1705C23—1342no—
1706C23—1342no—
1707C23—1342no—
1708C23#41×D6714yes—
1709C23C24×D6712yes—
1710C23C24×D6712yes—
1711C23C24×D6712yes—
1712C23C24×D6711yescharacteristic
1713Q8—44no—
1714Q8—2684no—
1715Q8—1348no—
1716Q8—1348no—
1717Q8—1348no—
1718Q8—1348no—
1719D4—28no—
1720D4—28no—
1721D4—44no—
1722D4—2684no—
1723D4—6716no—
1724D4—1348no—
1725D4—1348no—
1726D4—1348no—
1727D4—1348no—
1728D4—1348no—
1729C2×C4—22no—
1730C2×C4—22no—
1731C2×C4—28no—
1732C2×C4—22no—
1733C2×C4—22no—
1734C2×C4—22no—
1735C2×C4—22no—
1736C2×C4—22no—
1737C2×C4—22no—
1738C2×C4—22no—
1739C2×C4—22no—
1740C2×C4—22no—
1741C2×C4—22no—
1742C2×C4—44no—
1743C2×C4—44no—
1744C2×C4—44no—
1745C2×C4—44no—
1746C2×C4—2684no—
1747C2×C4—2684no—
1748C2×C4—2684no—
1749C2×C4—2684no—
1750C2×C4—2684no—
1751C2×C4—2684no—
1752C2×C4—2684no—
1753C2×C4—674no—
1754C2×C4—674no—
1755C2×C4—672no—
1756C2×C4—672no—
1757C2×C4—672no—
1758C2×C4—672no—
1759C2×C4—672no—
1760C2×C4—672no—
1761C2×C4—672no—
1762C2×C4—672no—
1763C2×C4—672no—
1764C2×C4—672no—
1765C2×C4—672no—
1766C2×C4—672no—
1767C2×C4—672no—
1768C2×C4—672no—
1769C2×C4—1348no—
1770C2×C4—1348no—
1771C2×C4—1348no—
1772C2×C4—1348no—
1773C2×C4—1348no—
1774C2×C4—1348no—
1775C2×C4—1348no—
1776C2×C4—1348no—
1777C2×C4—1348no—
1778C2×C4—1342no—
1779C2×C4—1342no—
1780C2×C4—1342no—
1781C2×C4—1342no—
1782C2×C4—1342no—
1783C2×C4—1348no—
1784C2×C4—1348no—
1785C2×C4—1342no—
1786C2×C4—1342no—
1787C2×C4—1342no—
1788C2×C4—1342no—
1789C2×C4—1342no—
1790C2×C4—1342no—
1791C2×C4—1342no—
1792C2×C4C24×D6712yes—
1793C2×C4C24×D6712yes—
1794C2×C4C24×D6712yes—
1795C2×C4C24×D6712yes—
1796C2×C4C24×D6712yes—
1797C2×C4C24×D6712yes—
1798C2×C4C24×D6712yes—
1799C2×C4C24×D6712yes—
1800C2×C4C24×D6712yes—
1801C2×C4C24×D6712yes—
1802C2×C4C24×D6712yes—
1803C2×C4C24×D6712yes—
1804C22—28no—
1805C22—22no—
1806C22—22no—
1807C22—22no—
1808C22—22no—
1809C22—22no—
1810C22—22no—
1811C22—22no—
1812C22—22no—
1813C22—44no—
1814C22—44no—
1815C22—2684no—
1816C22—674no—
1817C22—1342no—
1818C22—1342no—
1819C22—1342no—
1820C22—1348no—
1821C22—1342no—
1822C22—1342no—
1823C22C2×#41×D6714yes—
1824C22C2×#41×D6712yes—
1825C222−1+4×D6712yes—
1826C22#1686423112yes—
1827C22C25×D6711yescharacteristic
1828C4—22no—
1829C4—22no—
1830C4—22no—
1831C4—22no—
1832C4—22no—
1833C4—22no—
1834C4—22no—
1835C4—22no—
1836C4—22no—
1837C4—22no—
1838C4—22no—
1839C4—22no—
1840C4—674no—
1841C4—674no—
1842C4—1342no—
1843C4—1342no—
1844C4—1342no—
1845C4—1342no—
1846C4—1342no—
1847C4—1342no—
1848C4—1342no—
1849C4—1342no—
1850C4—1342no—
1851C4—1342no—
1852C4—1342no—
1853C4—1342no—
1854C2—24no—
1855C2—42no—
1856C2—42no—
1857C2—2682no—
1858C2—1344no—
1859C2#2257417914yesdirect product factor
1860C2C22×#41×D6711yescharacteristic
1861C2C2×2−1+4×D6711yescharacteristic
1862C2C2×#1686423111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#539×C67C2
socleC23×C67C25
hypercenterC2×#539D67
hypocenterC67C2×#3515
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#539

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #22574179C2direct (N × H)
2. C2×#16864123C2semidirect
3. C2×#16864100C2semidirect
4. C2×#16864100C2semidirect
5. C2×#16864091C2semidirect
6. C2×#16864089C2semidirect
7. C2×#16864088C2semidirect
8. C2×#16864083C2semidirect
9. C2×#16864083C2semidirect
10. C2×#16864083C2semidirect
11. C2×#16864082C2semidirect
12. C2×#16864082C2semidirect
13. C2×#16864080C2semidirect
14. C2×#16864078C2semidirect
15. C2×#16864046C2semidirect
16. C2×#16864044C2semidirect
17. C2×#16864044C2semidirect
18. C2×#16864005C2semidirect
19. C2×#16864003C2semidirect
20. C2×#16863992C2semidirect
21. C2×#16863989C2semidirect
22. C2×#16863988C2semidirect
23. C2×#16863948C2semidirect
24. C2×#16863929C2semidirect
25. C2×#16863926C2semidirect
26. C2×#16863923C2semidirect
27. C22×#14524033C2semidirect
28. C2×#125×D67C2semidirect
29. C2×#16863877C2semidirect
30. C2×#16863875C2semidirect
31. C2×C4×#11761627C2semidirect
32. C2×#539×C67C2semidirect
36. #16864123C22semidirect
37. #16864100C22semidirect
38. #16864100C22semidirect
39. #16864091C22semidirect
40. #16864089C22semidirect
41. #16864088C22semidirect
42. #16864083C22semidirect
43. #16864083C22semidirect
44. #16864083C22semidirect
45. #16864082C22semidirect
46. #16864082C22semidirect
47. #16864080C22semidirect
48. #16864078C22semidirect
49. #16864046C22semidirect
50. #16864044C22semidirect
51. #16864044C22semidirect
52. #16864005C22semidirect
53. #16864003C22semidirect
54. #16863992C22semidirect
55. #16863989C22semidirect
56. #16863988C22semidirect
57. #16863948C22semidirect
62. #16863929C22semidirect
63. #16863926C22semidirect
64. #16863923C22semidirect
100. C2×#14524033C22semidirect
101. #125×D67C22semidirect
139. #16863877C22semidirect
140. #16863875C22semidirect
141. C4×#11761627C22semidirect
203. #539×C67C22semidirect
926. C2×C67#3515semidirect
954. C2×#539D67semidirect
964. C67C2×#3515semidirect
989. #539C2×D67semidirect
1859. C2#22574179direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#225741792
C2×#168641232
C2×#168641002
C2×#168640912
C2×#168640892
C2×#168640882
C2×#168640832
C2×#168640822
C2×#168640802
C2×#168640782
C2×#168640462
C2×#168640442
C2×#168640052
C2×#168640032
C2×#168639922
C2×#168639892
C2×#168639882
C2×#168639482
C2×#168639292
C2×#168639262
C2×#168639232
C22×#145240332
C2×#125×D672
C2×#168638772
C2×#168638752
C2×C4×#117616272
C2×#539×C672
C2×#351567