Finite Group Databasebeta

← C2×#22563021 #31014749

Subgroups — C2×#22563021 #31014749

Order 17152.

3046 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524032C211yesmaximal, characteristic
2#22563021C2116yesmaximal, direct product factor
3C2×#16863303C211yesmaximal, characteristic, complemented
4C2×#16863288C211yesmaximal, characteristic, complemented
5C2×#16863287C211yesmaximal, characteristic, complemented
6C2×#16863286C211yesmaximal, characteristic, complemented
7C2×#16863285C211yesmaximal, characteristic, complemented
8C2×#16863274C211yesmaximal, characteristic
9C2×#16863274C211yesmaximal, characteristic
10C2×#16863270C211yesmaximal, characteristic, complemented
11C2×#16863267C211yesmaximal, characteristic, complemented
12C2×#16863263C211yesmaximal, characteristic, complemented
13C2×#16863247C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
15C2×#16863243C211yesmaximal, characteristic, complemented
16C2×#391×C67C211yesmaximal, characteristic, complemented
17C23×D268C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C2×#14524032C4116yescomplemented
21C2×#14524032C2218yes—
22C22×C4⋊Dic67C2211yescharacteristic
23C22×Dic67⋊C4C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×(C2×D67)⋊C4C2211yescharacteristic
26C22×(C2×D67)⋊C4C2211yescharacteristic
27C22×(C2×D67)⋊C4C2211yescharacteristic
28C22×(C2×D67)⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2211yescharacteristic
32C22×(C2×D67)⋊C4C2211yescharacteristic
33C22×(C2×D67)⋊C4C2211yescharacteristic
34C22×(C2×D67)⋊C4C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37C22×C4×Dic67C2211yescharacteristic
38C22×C4×Dic67C2211yescharacteristic
39#16863303C2218yescomplemented
40#16863288C2218yescomplemented
41#16863287C2218yescomplemented
42#16863286C2218yescomplemented
43#16863285C2218yescomplemented
44#16863274C2218yes—
45#16863274C2218yes—
46#16863270C2218yescomplemented
47#16863267C2218yescomplemented
48#16863263C2218yescomplemented
49#16863247C2218yescomplemented
50C4×(C2×D67)⋊C4C2218yescomplemented
51#16863243C2218yescomplemented
52C2×C67⋊#95C2211yescharacteristic
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C23×Q8×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C42×C67C2211yescharacteristic
63#391×C67C2218yescomplemented
64C2×#95×C67C2211yescharacteristic
65C2×#95×C67C2211yescharacteristic
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C24×D67C2311yescharacteristic
69C24×D67C2311yescharacteristic
70C22×D268—42no—
71C22×D268—42no—
72C22×D268C2×C418yes—
73C22×D268C2314yes—
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C22×C4×D67—24no—
81C22×C4×D67—24no—
82C22×C4×D67—42no—
83C22×C4×D67—42no—
84C22×C4×D67—42no—
85C22×C4×D67—42no—
86C22×C4×D67C2314yes—
87C22×C4×D67C2314yes—
88#14524032C2×C4164yescomplemented
89C2×C4⋊Dic67—42no—
90C2×C4⋊Dic67C2314yes—
91C2×Dic67⋊C4—24no—
92C2×Dic67⋊C4—24no—
93C2×Dic67⋊C4C2314yes—
94C2×Dic67⋊C4C2314yes—
95C2×(C2×D67)⋊C4—24no—
96C2×(C2×D67)⋊C4—24no—
97C2×(C2×D67)⋊C4—42no—
98C2×(C2×D67)⋊C4—42no—
99C2×(C2×D67)⋊C4—42no—
100C2×(C2×D67)⋊C4—42no—
101C2×(C2×D67)⋊C4C2×C418yescomplemented
102C2×(C2×D67)⋊C4C2×C418yescomplemented
103C2×(C2×D67)⋊C4C2×C418yescomplemented
104C2×(C2×D67)⋊C4C2×C418yescomplemented
105C2×(C2×D67)⋊C4C2314yes—
106C2×(C2×D67)⋊C4C2314yes—
107C2×(C2×D67)⋊C4C2314yes—
108C2×(C2×D67)⋊C4C2314yes—
109C2×(C2×D67)⋊C4C2314yes—
110C2×(C2×D67)⋊C4C2314yes—
111C2×(C2×D67)⋊C4C2314yes—
112C2×(C2×D67)⋊C4C2314yes—
113C2×(C2×D67)⋊C4C2314yes—
114C2×(C2×D67)⋊C4C2314yes—
115C2×C4×Dic67—42no—
116C2×C4×Dic67—42no—
117C2×C4×Dic67—42no—
118C2×C4×Dic67C2×C418yescomplemented
119C2×C4×Dic67C2314yes—
120C2×C4×Dic67C2314yes—
121C2×C4×Dic67C2314yes—
122C2×C4×Dic67C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C22×Q8×C67—42no—
132C22×Q8×C67—42no—
133C22×Q8×C67C2×C418yescomplemented
134C22×Q8×C67C2314yes—
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C23×C4×C67C2311yescharacteristic
138C23×C4×C67C2311yescharacteristic
139C23×C4×C67C2311yescharacteristic
140C23×C4×C67C2311yescharacteristic
141C23×C4×C67C2311yescharacteristic
142C2×C4⋊C4×C67—42no—
143C2×C4⋊C4×C67C2314yes—
144C2×C42×C67—42no—
145C2×C42×C67C2314yes—
146#95×C67C2314yes—
147#95×C67C2314yes—
148#95×C67C2314yes—
149#95×C67C2314yes—
150C23×D67—22no—
151C23×D67—22no—
152C23×D67—22no—
153C23×D67—22no—
154C23×D67—22no—
155C23×D67—22no—
156C23×D67—22no—
157C23×D67—22no—
158C23×D67—22no—
159C23×D67—22no—
160C23×D67—22no—
161C23×D67—22no—
162C23×D67C22×C414yes—
163C23×D67C22×C414yes—
164C23×D67C2412yes—
165C23×D67C2412yes—
166C2×D268—416no—
167C2×D268—44no—
168C2×D268—44no—
169C2×D268C22×C4116yes—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67—22no—
173C22×Dic67—22no—
174C22×Dic67—22no—
175C22×Dic67—22no—
176C22×Dic67—22no—
177C22×Dic67—22no—
178C22×Dic67—22no—
179C22×Dic67—22no—
180C22×Dic67—22no—
181C22×Dic67—22no—
182C22×Dic67—22no—
183C22×Dic67—22no—
184C22×Dic67—22no—
185C22×Dic67C22×C414yes—
186C22×Dic67C22×C414yes—
187C22×Dic67#4114yes—
188C22×Dic67C2412yes—
189C22×Dic67C2412yes—
190C22×Dic67C2412yes—
191C22×Dic67C2412yes—
192C22×Dic67C2412yes—
193C22×Dic67C2412yes—
194C2×C4×D67—28no—
195C2×C4×D67—28no—
196C2×C4×D67—44no—
197C2×C4×D67—44no—
198C2×C4×D67—44no—
199C2×C4×D67—44no—
200C2×C4×D67—416no—
201C2×C4×D67—416no—
202C4⋊Dic67—44no—
203Dic67⋊C4—28no—
204Dic67⋊C4—28no—
205(C2×D67)⋊C4—28no—
206(C2×D67)⋊C4—28no—
207(C2×D67)⋊C4—44no—
208(C2×D67)⋊C4—44no—
209(C2×D67)⋊C4—44no—
210(C2×D67)⋊C4—44no—
211(C2×D67)⋊C4C22×C4116yescomplemented
212(C2×D67)⋊C4C22×C4116yescomplemented
213(C2×D67)⋊C4C22×C4116yescomplemented
214(C2×D67)⋊C4C22×C4116yescomplemented
215C4×Dic67—44no—
216C4×Dic67—44no—
217C4×Dic67—44no—
218C4×Dic67C22×C4116yescomplemented
219C24×C67C2411yescharacteristic
220C2×Q8×C67—416no—
221C2×Q8×C67—44no—
222C2×Q8×C67—44no—
223C2×Q8×C67C22×C4116yescomplemented
224C22×C4×C67—22no—
225C22×C4×C67—22no—
226C22×C4×C67—22no—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—22no—
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67—22no—
237C22×C4×C67—22no—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67C22×C414yes—
242C22×C4×C67C22×C414yes—
243C22×C4×C67C22×C414yes—
244C22×C4×C67#4114yes—
245C22×C4×C67C2412yes—
246C22×C4×C67C2412yes—
247C22×C4×C67C2412yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2412yes—
250C22×C4×C67C2412yes—
251C22×C4×C67C2412yes—
252C4⋊C4×C67—44no—
253C42×C67—44no—
254C23×C67C23×C412yes—
255C23×C67C2×#4112yes—
256C23×C67C2×#4112yes—
257C23×C67H(5,𝔽2)12yes—
258C23×C67H(5,𝔽2)12yes—
259C23×C67H(5,𝔽2)12yes—
260C23×C672−1+412yes—
261C23×C67C2511yescharacteristic
262C22×D67—28no—
263C22×D67—28no—
264C22×D67—28no—
265C22×D67—28no—
266C22×D67—28no—
267C22×D67—28no—
268C22×D67—22no—
269C22×D67—22no—
270C22×D67—22no—
271C22×D67—22no—
272C22×D67—22no—
273C22×D67—22no—
274C22×D67—22no—
275C22×D67—22no—
276C22×D67—22no—
277C22×D67—22no—
278C22×D67—22no—
279C22×D67—22no—
280C22×D67—44no—
281C22×D67—44no—
282C22×D67—44no—
283C22×D67—44no—
284C22×D67—44no—
285C22×D67—44no—
286C22×D67—44no—
287C22×D67—44no—
288C22×D67C23×C414yes—
289C22×D67C23×C414yes—
290Q8×C67—416no—
291C2×C4×C67—28no—
292C2×C4×C67—28no—
293C2×C4×C67—28no—
294C2×C4×C67—28no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—44no—
313C2×C4×C67—44no—
314C2×C4×C67—44no—
315C2×C4×C67C23×C414yes—
316C2×C4×C67C23×C414yes—
317C2×C4×C67C23×C414yes—
318C2×C4×C67C2×#4114yes—
319C2×Dic67—28no—
320C2×Dic67—28no—
321C2×Dic67—28no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—22no—
328C2×Dic67—22no—
329C2×Dic67—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—22no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—44no—
338C2×Dic67—44no—
339C2×Dic67—44no—
340C2×Dic67C23×C414yes—
341C2×Dic67C23×C414yes—
342C2×Dic67C2×#4114yes—
343D268—416no—
344C4×D67—416no—
345C4×D67—416no—
346C22×C67C4×#4114yes—
347C22×C67#51814yes—
348C22×C67#52014yes—
349C22×C67#53814yes—
350C22×C67#53814yes—
351C22×C67#54214yes—
352C22×C67#54214yes—
353C22×C67C24×C411yescharacteristic
354C22×C67C22×#4111yescharacteristic
355C22×C67C22×#4111yescharacteristic
356C22×C67C2×H(5,𝔽2)11yescharacteristic
357C22×C67C2×H(5,𝔽2)11yescharacteristic
358C22×C67C2×H(5,𝔽2)11yescharacteristic
359C22×C67C2×2−1+411yescharacteristic
360C2×D67—24no—
361C2×D67—24no—
362C2×D67—24no—
363C2×D67—24no—
364C2×D67—24no—
365C2×D67—24no—
366C2×D67—416no—
367C2×D67—416no—
368C2×D67—42no—
369C2×D67—42no—
370C2×D67—42no—
371C2×D67—42no—
372C2×D67—42no—
373C2×D67—42no—
374C2×D67—42no—
375C2×D67—42no—
376C4×C67—24no—
377C4×C67—24no—
378C4×C67—24no—
379C4×C67—24no—
380C4×C67—42no—
381C4×C67—42no—
382C4×C67—42no—
383Dic67—24no—
384Dic67—24no—
385Dic67—24no—
386Dic67—42no—
387Dic67—42no—
388Dic67—42no—
389C2×#2337—671nomaximal, Sylow
390C2×C67#233718yescomplemented
391C2×C67C2×C4×#4111yescharacteristic
392C2×C67C2×#51811yescharacteristic
393C2×C67C2×#52011yescharacteristic
394C2×C67C2×#53811yescharacteristic
395C2×C67C2×#53811yescharacteristic
396C2×C67C2×#54211yescharacteristic
397C2×C67C2×#54211yescharacteristic
398D67—44no—
399D67—44no—
400C22×#124—671no—
401#2337—6716no—
402C2×#391—671no—
403C2×#391D6711yescharacteristic, complemented
404C2×#388—671no—
405C2×#388—671no—
406C2×#388—671no—
407C2×#388—671no—
408C2×#386—671no—
409C2×#386—671no—
410C2×#385—671no—
411C2×#385—671no—
412C2×#383—671no—
413C2×C4×C4⋊C4—671no—
414C2×C4×C22⋊C4—671no—
415C2×C4×C22⋊C4—671no—
416C67C2×#233711yescharacteristic, complemented, Sylow
417C23×Q8C2×D6711yescharacteristic
418C23×D4—671no—
419C24×C4—671no—
420C24×C4—671no—
421C2×#124—6716no—
422C2×#124—678no—
423C22×C4⋊C4—671no—
424C22×C4⋊C4—671no—
425C22×C4⋊C4—671no—
426C22×C4⋊C4C2×D6711yescharacteristic
427C22×C22⋊C4—671no—
428C22×C22⋊C4—671no—
429C22×C22⋊C4—671no—
430C22×C22⋊C4—671no—
431C22×C22⋊C4—671no—
432C22×C22⋊C4—671no—
433C22×C22⋊C4—671no—
434C22×C22⋊C4—671no—
435C22×C22⋊C4—671no—
436C22×C22⋊C4—671no—
437C22×C42—671no—
438C22×C42—671no—
439C22×C42—671no—
440C22×C42—671no—
441C22×C42C2×D6711yescharacteristic
442#391—678no—
443#391C2×D6718yescomplemented
444#388—678no—
445#388—678no—
446#388—678no—
447#388—678no—
448#386—678no—
449#386—678no—
450#385—678no—
451#385—678no—
452#383—678no—
453C4×C4⋊C4—678no—
454C4×C22⋊C4—678no—
455C4×C22⋊C4—678no—
456C2×#95—671no—
457C2×#95—671no—
458C2×#95—671no—
459C2×#95—671no—
460C2×#95—671no—
461C2×#95—671no—
462C2×#95—671no—
463C2×#95—671no—
464C2×#95C2×D6711yescharacteristic
465C2×#95C2×D6711yescharacteristic
466C2×#95C2×D6711yescharacteristic
467C2×#95C2×D6711yescharacteristic
468C25—671no—
469C25—671no—
470C22×Q8—42no—
471C22×Q8—42no—
472C22×Q8C4×D6718yescomplemented
473C22×Q8C22×D6714yes—
474C22×D4—2682no—
475C22×D4—2682no—
476C22×D4—678no—
477C22×D4—674no—
478C23×C4—2682no—
479C23×C4—2682no—
480C23×C4—2682no—
481C23×C4—2682no—
482C23×C4—674no—
483C23×C4—674no—
484C23×C4—671no—
485C23×C4—671no—
486C23×C4—671no—
487C23×C4—671no—
488C23×C4—671no—
489C23×C4—671no—
490C23×C4—1344no—
491C23×C4—1344no—
492C23×C4C22×D6711yescharacteristic
493C23×C4C22×D6711yescharacteristic
494C23×C4C22×D6711yescharacteristic
495C23×C4C22×D6711yescharacteristic
496C23×C4C22×D6711yescharacteristic
497C23×C4C22×D6711yescharacteristic
498C23×C4C22×D6711yescharacteristic
499#124—6764no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—2682no—
502C2×C4⋊C4—674no—
503C2×C4⋊C4—674no—
504C2×C4⋊C4—674no—
505C2×C4⋊C4—1344no—
506C2×C4⋊C4—1344no—
507C2×C4⋊C4C22×D6714yes—
508C2×C22⋊C4—2682no—
509C2×C22⋊C4—2682no—
510C2×C22⋊C4—2682no—
511C2×C22⋊C4—2682no—
512C2×C22⋊C4—674no—
513C2×C22⋊C4—674no—
514C2×C22⋊C4—674no—
515C2×C22⋊C4—674no—
516C2×C22⋊C4—678no—
517C2×C22⋊C4—678no—
518C2×C22⋊C4—678no—
519C2×C22⋊C4—678no—
520C2×C22⋊C4—674no—
521C2×C22⋊C4—674no—
522C2×C22⋊C4—674no—
523C2×C22⋊C4—674no—
524C2×C22⋊C4—674no—
525C2×C22⋊C4—674no—
526C2×C22⋊C4—1344no—
527C2×C22⋊C4—1344no—
528C2×C42—42no—
529C2×C42—2682no—
530C2×C42—2682no—
531C2×C42—2682no—
532C2×C42—674no—
533C2×C42—674no—
534C2×C42—674no—
535C2×C42—678no—
536C2×C42—674no—
537C2×C42C22×D6714yes—
538#95—674no—
539#95—674no—
540#95—674no—
541#95—674no—
542#95—674no—
543#95—674no—
544#95—674no—
545#95—674no—
546#95C22×D6714yes—
547#95C22×D6714yes—
548#95C22×D6714yes—
549#95C22×D6714yes—
550C24—674no—
551C24—674no—
552C24—672no—
553C24—672no—
554C24—1342no—
555C24—1342no—
556C24—1342no—
557C24—1342no—
558C24—1342no—
559C24—1342no—
560C24—1342no—
561C24—1342no—
562C24—1342no—
563C24—1342no—
564C24—1342no—
565C24—1342no—
566C24C23×D6711yescharacteristic
567C2×Q8—416no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8C2×C4×D67116yescomplemented
571C2×D4—26816no—
572C2×D4—2684no—
573C2×D4—2684no—
574C2×D4—6716no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—26816no—
593C22×C4—2684no—
594C22×C4—2684no—
595C22×C4—2684no—
596C22×C4—2684no—
597C22×C4—26816no—
598C22×C4—674no—
599C22×C4—674no—
600C22×C4—674no—
601C22×C4—672no—
602C22×C4—672no—
603C22×C4—672no—
604C22×C4—672no—
605C22×C4—672no—
606C22×C4—672no—
607C22×C4—1348no—
608C22×C4—1342no—
609C22×C4—1342no—
610C22×C4—1342no—
611C22×C4—1342no—
612C22×C4—1342no—
613C22×C4—1342no—
614C22×C4—1342no—
615C22×C4—1342no—
616C22×C4—1342no—
617C22×C4—1348no—
618C22×C4—1342no—
619C22×C4—1342no—
620C22×C4—1342no—
621C22×C4—1342no—
622C22×C4—1342no—
623C22×C4—1342no—
624C22×C4C2×C4×D6714yes—
625C22×C4C2×C4×D6714yes—
626C22×C4C2×C4×D6714yes—
627C22×C4#1176162914yes—
628C22×C4C23×D6712yes—
629C22×C4C23×D6712yes—
630C22×C4C23×D6712yes—
631C22×C4C23×D6712yes—
632C22×C4C23×D6712yes—
633C22×C4C23×D6712yes—
634C22×C4C23×D6712yes—
635C4⋊C4—44no—
636C4⋊C4—2684no—
637C4⋊C4—1348no—
638C4⋊C4—1348no—
639C22⋊C4—2684no—
640C22⋊C4—2684no—
641C22⋊C4—2684no—
642C22⋊C4—2684no—
643C22⋊C4—6716no—
644C22⋊C4—6716no—
645C22⋊C4—6716no—
646C22⋊C4—6716no—
647C22⋊C4—1348no—
648C22⋊C4—1348no—
649C42—44no—
650C42—2684no—
651C42—2684no—
652C42—2684no—
653C42—6716no—
654C23—2684no—
655C23—2684no—
656C23—2684no—
657C23—2684no—
658C23—2684no—
659C23—2684no—
660C23—2684no—
661C23—2684no—
662C23—674no—
663C23—674no—
664C23—1348no—
665C23—1348no—
666C23—1348no—
667C23—1348no—
668C23—1348no—
669C23—1348no—
670C23—1342no—
671C23—1342no—
672C23—1342no—
673C23—1342no—
674C23—1342no—
675C23—1342no—
676C23—1342no—
677C23—1342no—
678C23—1342no—
679C23—1342no—
680C23—1342no—
681C23—1342no—
682C23C22×C4×D6712yes—
683C23#41×D6712yes—
684C23C2×#1176162912yes—
685C23#1452408812yes—
686C23#1452408812yes—
687C23#1452408912yes—
688C23#1452409112yes—
689C23C24×D6711yescharacteristic
690Q8—416no—
691D4—26816no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—26816no—
717C2×C4—26816no—
718C2×C4—2684no—
719C2×C4—2684no—
720C2×C4—2684no—
721C2×C4—674no—
722C2×C4—674no—
723C2×C4—674no—
724C2×C4—1342no—
725C2×C4—1342no—
726C2×C4—1342no—
727C2×C4—1342no—
728C2×C4—1342no—
729C2×C4—1342no—
730C2×C4—1342no—
731C2×C4—1342no—
732C2×C4—1342no—
733C2×C4—1348no—
734C2×C4—1348no—
735C2×C4—1342no—
736C2×C4—1342no—
737C2×C4—1342no—
738C2×C4—1342no—
739C2×C4—1342no—
740C2×C4—1342no—
741C2×C4—1348no—
742C2×C4C22×C4×D6714yes—
743C2×C4C22×C4×D6714yes—
744C2×C4C22×C4×D6714yes—
745C2×C4C2×#1176162914yes—
746C22—2682no—
747C22—2682no—
748C22—2682no—
749C22—2682no—
750C22—26816no—
751C22—26816no—
752C22—2682no—
753C22—2682no—
754C22—2682no—
755C22—2682no—
756C22—1344no—
757C22—1344no—
758C22—1344no—
759C22—1344no—
760C22—1344no—
761C22—1344no—
762C22C4×#1176162914yes—
763C22#1686386914yes—
764C22#1686387814yes—
765C22#1686398014yes—
766C22#1686398614yes—
767C22#1686401614yes—
768C22#1686402014yes—
769C22C23×C4×D6711yescharacteristic
770C22C2×#41×D6711yescharacteristic
771C22C22×#1176162911yescharacteristic
772C22C2×#1452408811yescharacteristic
773C22C2×#1452408811yescharacteristic
774C22C2×#1452408911yescharacteristic
775C22C2×#1452409111yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—2682no—
784C4—2682no—
785C4—2682no—
786C4—1344no—
787C4—1344no—
788C4—1344no—
789C2—2684no—
790C2—2684no—
791C2#2256302118yesdirect product factor
792C2C2×C4×#1176162911yescharacteristic
793C2C2×#1686386911yescharacteristic
794C2C2×#1686387811yescharacteristic
795C2C2×#1686398011yescharacteristic
796C2C2×#1686398611yescharacteristic
797C2C2×#1686401611yescharacteristic
798C2C2×#1686402011yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#391×C67C2
socleC24×C67C24
prime radicalC23×D268C22
cosocleC23×C67C25
hypercenterC2×#391D67
hypocenterC67C2×#2337
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. #22563021C2direct (N × H)
3. C2×#16863303C2semidirect
4. C2×#16863288C2semidirect
5. C2×#16863287C2semidirect
6. C2×#16863286C2semidirect
7. C2×#16863285C2semidirect
10. C2×#16863270C2semidirect
11. C2×#16863267C2semidirect
12. C2×#16863263C2semidirect
13. C2×#16863247C2semidirect
14. C2×C4×(C2×D67)⋊C4C2semidirect
15. C2×#16863243C2semidirect
16. C2×#391×C67C2semidirect
20. C2×#14524032C4semidirect
39. #16863303C22semidirect
40. #16863288C22semidirect
41. #16863287C22semidirect
42. #16863286C22semidirect
43. #16863285C22semidirect
46. #16863270C22semidirect
47. #16863267C22semidirect
48. #16863263C22semidirect
49. #16863247C22semidirect
50. C4×(C2×D67)⋊C4C22semidirect
51. #16863243C22semidirect
63. #391×C67C22semidirect
88. #14524032C2×C4semidirect
101. C2×(C2×D67)⋊C4C2×C4semidirect
102. C2×(C2×D67)⋊C4C2×C4semidirect
103. C2×(C2×D67)⋊C4C2×C4semidirect
104. C2×(C2×D67)⋊C4C2×C4semidirect
118. C2×C4×Dic67C2×C4semidirect
133. C22×Q8×C67C2×C4semidirect
211. (C2×D67)⋊C4C22×C4semidirect
212. (C2×D67)⋊C4C22×C4semidirect
213. (C2×D67)⋊C4C22×C4semidirect
214. (C2×D67)⋊C4C22×C4semidirect
218. C4×Dic67C22×C4semidirect
223. C2×Q8×C67C22×C4semidirect
390. C2×C67#2337semidirect
403. C2×#391D67semidirect
416. C67C2×#2337semidirect
443. #391C2×D67semidirect
472. C22×Q8C4×D67semidirect
570. C2×Q8C2×C4×D67semidirect
791. C2#22563021direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240322
#225630212
C2×#168633032
C2×#168632882
C2×#168632872
C2×#168632862
C2×#168632852
C2×#168632742
C2×#168632702
C2×#168632672
C2×#168632632
C2×#168632472
C2×C4×(C2×D67)⋊C42
C2×#168632432
C2×#391×C672
C2×#233767