Finite Group Databasebeta

← C2×#22626468 #34030675

Subgroups — C2×#22626468 #34030675

Order 18688.

2726 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626468C2116yesmaximal, direct product factor
2C2×#17989538C211yesmaximal, characteristic, complemented
3C2×#17989537C211yesmaximal, characteristic
4C2×#17989537C211yesmaximal, characteristic
5C2×#17989537C211yesmaximal, characteristic
6C2×#17989536C211yesmaximal, characteristic, complemented
7C2×#17989536C211yesmaximal, characteristic, complemented
8C2×#17989536C211yesmaximal, characteristic, complemented
9C2×#17989534C211yesmaximal, characteristic
10C2×C4⋊C4×#64408C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×#64408C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊#64408C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×#64408C211yesmaximal, characteristic
14C2×C22⋊C4×#64408C211yesmaximal, characteristic
15C2×#17989523C211yesmaximal, characteristic, complemented
16C2×#126×D73C211yesmaximal, characteristic
17C24×#64408C2211yescharacteristic
18C22×C4⋊#64408C2211yescharacteristic
19C22×C4⋊#64408C2211yescharacteristic
20C22×C4⋊#64408C2211yescharacteristic
21C22×C4⋊#64408C2211yescharacteristic
22C22×C4⋊#64408C2211yescharacteristic
23C22×C22⋊#64408C2211yescharacteristic
24C22×C22⋊#64408C2211yescharacteristic
25C22×C22⋊#64408C2211yescharacteristic
26C22×C4×#64408C2211yescharacteristic
27C22×C4×#64408C2211yescharacteristic
28C22×C4×#64408C2211yescharacteristic
29C22×C4×#64408C2211yescharacteristic
30C22×C4×#64408C2211yescharacteristic
31C22×C4×#64408C2211yescharacteristic
32C22×C4×#64408C2211yescharacteristic
33#17989538C2218yescomplemented
34#17989537C2218yes—
35#17989537C2218yes—
36#17989537C2218yes—
37#17989536C2218yescomplemented
38#17989536C2218yescomplemented
39#17989536C2218yescomplemented
40#17989534C2218yes—
41C4⋊C4×#64408C2218yescomplemented
42C4⋊C4×#64408C2218yescomplemented
43C4×C4⋊#64408C2218yescomplemented
44C22⋊C4×#64408C2218yes—
45C22⋊C4×#64408C2218yes—
46#17989523C2218yescomplemented
47C2×(C2×#64408)⋊C4C2211yescharacteristic
48C2×(C2×#64408)⋊C4C2211yescharacteristic
49C2×(C2×#64408)⋊C4C2211yescharacteristic
50C2×(C2×#64408)⋊C4C2211yescharacteristic
51C2×(C2×#64408)⋊C4C2211yescharacteristic
52C2×(C2×#64408)⋊C4C2211yescharacteristic
53C2×(C2×#64408)⋊C4C2211yescharacteristic
54C2×(C2×#64408)⋊C4C2211yescharacteristic
55C2×(C2×#64408)⋊C4C2211yescharacteristic
56C2×(C2×#64408)⋊C4C2211yescharacteristic
57C2×(C2×#64408)⋊C4C2211yescharacteristic
58C2×(C2×#64408)⋊C4C2211yescharacteristic
59C2×#14556586C411yescharacteristic, complemented
60C2×#14556586C411yescharacteristic, complemented
61C2×#14556586C411yescharacteristic, complemented
62C2×#14556585C411yescharacteristic, complemented
63C2×#14556584C411yescharacteristic, complemented
64C2×#14556584C411yescharacteristic, complemented
65C2×#14556584C411yescharacteristic, complemented
66#126×D73C418yescomplemented
67#126×D73C2218yes—
68C2×C4⋊C4×D73C2211yescharacteristic
69C2×C4⋊C4×D73C2211yescharacteristic
70C2×C4⋊C4×D73C2211yescharacteristic
71C2×C22⋊C4×D73C2211yescharacteristic
72C2×C22⋊C4×D73C2211yescharacteristic
73C2×C22⋊C4×D73C2211yescharacteristic
74C2×C42×D73C2211yescharacteristic
75C2×#126×C73C411yescharacteristic, complemented
76C23×#64408—24no—
77C23×#64408—24no—
78C23×#64408—42no—
79C23×#64408C2311yescharacteristic
80C23×#64408C2311yescharacteristic
81C23×#64408C2311yescharacteristic
82C23×#64408C2311yescharacteristic
83C23×#64408C2314yes—
84C23×#64408C2311yescharacteristic
85C23×#64408C2311yescharacteristic
86C23×#64408C2311yescharacteristic
87C23×#64408C2311yescharacteristic
88C2×C4⋊#64408—24no—
89C2×C4⋊#64408—24no—
90C2×C4⋊#64408—24no—
91C2×C4⋊#64408—24no—
92C2×C4⋊#64408—42no—
93C2×C4⋊#64408C2314yes—
94C2×C4⋊#64408C2314yes—
95C2×C4⋊#64408C2314yes—
96C2×C4⋊#64408C2314yes—
97C2×C4⋊#64408C2314yes—
98C2×C22⋊#64408—24no—
99C2×C22⋊#64408—24no—
100C2×C22⋊#64408—42no—
101C2×C22⋊#64408C2314yes—
102C2×C22⋊#64408C2314yes—
103C2×C22⋊#64408C2314yes—
104C2×C4×#64408—24no—
105C2×C4×#64408—24no—
106C2×C4×#64408—24no—
107C2×C4×#64408—24no—
108C2×C4×#64408—42no—
109C2×C4×#64408—42no—
110C2×C4×#64408—42no—
111C2×C4×#64408C2314yes—
112C2×C4×#64408C2314yes—
113C2×C4×#64408C2314yes—
114C2×C4×#64408C2314yes—
115C2×C4×#64408C2314yes—
116C2×C4×#64408C2314yes—
117C2×C4×#64408C2314yes—
118(C2×#64408)⋊C4C2314yes—
119(C2×#64408)⋊C4C2314yes—
120(C2×#64408)⋊C4C2314yes—
121(C2×#64408)⋊C4C2314yes—
122(C2×#64408)⋊C4C2314yes—
123(C2×#64408)⋊C4C2314yes—
124(C2×#64408)⋊C4C2314yes—
125(C2×#64408)⋊C4C2314yes—
126(C2×#64408)⋊C4C2314yes—
127(C2×#64408)⋊C4C2314yes—
128(C2×#64408)⋊C4C2314yes—
129(C2×#64408)⋊C4C2314yes—
130C24×D73C2311yescharacteristic
131C22×C4×D73C2311yescharacteristic
132C22×C4×D73C2311yescharacteristic
133C22×C4×D73C2311yescharacteristic
134C22×C4×D73C2311yescharacteristic
135C22×C4×D73C2311yescharacteristic
136C22×C4×D73C2311yescharacteristic
137#14556586C2×C418yescomplemented
138#14556586C2×C418yescomplemented
139#14556586C2×C418yescomplemented
140#14556585C2×C418yescomplemented
141#14556584C2×C418yescomplemented
142#14556584C2×C418yescomplemented
143#14556584C2×C418yescomplemented
144C2×C4⋊Dic73C2×C411yescharacteristic, complemented
145C2×C4⋊Dic73C2×C411yescharacteristic, complemented
146C2×C4⋊Dic73C2×C411yescharacteristic, complemented
147C2×#11924007C2×C411yescharacteristic, complemented
148C2×#11924007C2×C411yescharacteristic, complemented
149C2×#11924007C2×C411yescharacteristic, complemented
150C2×#11924007C2×C411yescharacteristic, complemented
151C2×#11924007C2×C411yescharacteristic, complemented
152C2×#11924007C2×C411yescharacteristic, complemented
153C4⋊C4×D73C2×C414yescomplemented
154C4⋊C4×D73C2×C414yescomplemented
155C4⋊C4×D73C2×C414yescomplemented
156C4⋊C4×D73C2314yes—
157C4⋊C4×D73C2314yes—
158C4⋊C4×D73C2314yes—
159C2×C22⋊Dic73C2×C411yescharacteristic
160C2×C22⋊Dic73C2×C411yescharacteristic
161C2×C22⋊Dic73C2×C411yescharacteristic
162C2×#11924005C2×C411yescharacteristic
163C2×#11924005C2×C411yescharacteristic
164C2×#11924005C2×C411yescharacteristic
165C2×#11924005C2×C411yescharacteristic
166C2×#11924005C2×C411yescharacteristic
167C2×#11924005C2×C411yescharacteristic
168C22⋊C4×D73C2×C414yes—
169C22⋊C4×D73C2×C414yes—
170C22⋊C4×D73C2×C414yes—
171C22⋊C4×D73C2314yes—
172C22⋊C4×D73C2314yes—
173C22⋊C4×D73C2314yes—
174C2×C4×Dic73C2×C411yescharacteristic, complemented
175C2×C4×Dic73C2×C411yescharacteristic, complemented
176C2×C4×Dic73C2×C411yescharacteristic, complemented
177C42×D73C2×C414yescomplemented
178C42×D73C2314yes—
179#126×C73C2×C418yescomplemented
180C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
181C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
182C2×C4⋊C4×C73C2×C411yescharacteristic, complemented
183C2×C22⋊C4×C73C2×C411yescharacteristic
184C2×C22⋊C4×C73C2×C411yescharacteristic
185C2×C22⋊C4×C73C2×C411yescharacteristic
186C2×C42×C73C2×C411yescharacteristic, complemented
187C22×#64408—22no—
188C22×#64408—22no—
189C22×#64408—22no—
190C22×#64408—22no—
191C22×#64408—22no—
192C22×#64408—22no—
193C22×#64408—22no—
194C22×#64408—22no—
195C22×#64408—22no—
196C22×#64408—22no—
197C22×#64408—22no—
198C22×#64408—22no—
199C22×#64408—22no—
200C22×#64408—22no—
201C22×#64408—22no—
202C22×#64408—22no—
203C22×#64408—22no—
204C22×#64408—22no—
205C22×#64408—22no—
206C22×#64408—22no—
207C22×#64408—28no—
208C22×#64408—28no—
209C22×#64408—44no—
210C22×#64408—416no—
211C22×#64408#4114yes—
212C22×#64408#4114yes—
213C22×#64408#4114yes—
214C22×#64408#4114yes—
215C22×#64408C2412yes—
216C22×#64408C2412yes—
217C22×#64408C2412yes—
218C22×#64408C2412yes—
219C22×#64408C2412yes—
220C22×#64408C2412yes—
221C22×#64408C2412yes—
222C22×#64408C2412yes—
223C4⋊#64408—28no—
224C4⋊#64408—28no—
225C4⋊#64408—28no—
226C4⋊#64408—28no—
227C4⋊#64408—44no—
228C22⋊#64408—28no—
229C22⋊#64408—28no—
230C22⋊#64408—44no—
231C4×#64408—28no—
232C4×#64408—28no—
233C4×#64408—28no—
234C4×#64408—28no—
235C4×#64408—44no—
236C4×#64408—44no—
237C4×#64408—44no—
238C23×D73—22no—
239C23×D73—22no—
240C23×D73—22no—
241C23×D73—22no—
242C23×D73—22no—
243C23×D73—22no—
244C23×D73C22×C412yes—
245C23×D73C22×C411yescharacteristic
246C23×D73C2412yes—
247C23×D73C2411yescharacteristic
248C22×Dic73C22×C411yescharacteristic
249C22×Dic73C22×C411yescharacteristic
250C22×Dic73C22×C411yescharacteristic
251C22×Dic73C22×C411yescharacteristic
252C22×Dic73C22×C411yescharacteristic
253C22×Dic73C22×C411yescharacteristic
254C2×C4×D73—22no—
255C2×C4×D73—22no—
256C2×C4×D73—22no—
257C2×C4×D73—22no—
258C2×C4×D73—22no—
259C2×C4×D73—22no—
260C2×C4×D73—22no—
261C2×C4×D73—22no—
262C2×C4×D73—22no—
263C2×C4×D73—22no—
264C2×C4×D73—22no—
265C2×C4×D73—22no—
266C2×C4×D73C22×C412yes—
267C2×C4×D73C22×C412yes—
268C2×C4×D73C22×C412yes—
269C2×C4×D73C22×C412yes—
270C2×C4×D73C22×C412yes—
271C2×C4×D73C22×C412yes—
272C2×C4×D73C2412yes—
273C2×C4×D73C2412yes—
274C2×C4×D73C2412yes—
275C2×C4×D73C2412yes—
276C2×C4×D73C2412yes—
277C2×C4×D73C2412yes—
278C4⋊Dic73C22×C414yescomplemented
279C4⋊Dic73C22×C414yescomplemented
280C4⋊Dic73C22×C414yescomplemented
281#11924007C22×C414yescomplemented
282#11924007C22×C414yescomplemented
283#11924007C22×C414yescomplemented
284#11924007C22×C414yescomplemented
285#11924007C22×C414yescomplemented
286#11924007C22×C414yescomplemented
287C22⋊Dic73C22×C414yes—
288C22⋊Dic73C22×C414yes—
289C22⋊Dic73C22×C414yes—
290#11924005C22×C414yes—
291#11924005C22×C414yes—
292#11924005C22×C414yes—
293#11924005C22×C414yes—
294#11924005C22×C414yes—
295#11924005C22×C414yes—
296C4×Dic73C22×C414yescomplemented
297C4×Dic73C22×C414yescomplemented
298C4×Dic73C22×C414yescomplemented
299C24×C73C22×C411yescharacteristic
300C22×C4×C73C22×C411yescharacteristic
301C22×C4×C73C22×C411yescharacteristic
302C22×C4×C73C22×C411yescharacteristic
303C22×C4×C73C22×C411yescharacteristic
304C22×C4×C73C22×C411yescharacteristic
305C22×C4×C73C22×C411yescharacteristic
306C4⋊C4×C73C22×C414yescomplemented
307C4⋊C4×C73C22×C414yescomplemented
308C4⋊C4×C73C22×C414yescomplemented
309C22⋊C4×C73C22×C414yes—
310C22⋊C4×C73C22×C414yes—
311C22⋊C4×C73C22×C414yes—
312C42×C73C22×C414yescomplemented
313C23×C73—22no—
314C23×C73—22no—
315C23×C73—22no—
316C23×C73C23×C412yes—
317C23×C73C23×C411yescharacteristic
318C22×D73—22no—
319C22×D73—22no—
320C22×D73—22no—
321C22×D73—24no—
322C22×D73—24no—
323C22×D73—24no—
324C22×D73—22no—
325C22×D73—22no—
326C22×D73—22no—
327C22×D73—22no—
328C22×D73—22no—
329C22×D73—22no—
330C22×D73—44no—
331C22×D73—44no—
332C22×D73—44no—
333C22×D73—44no—
334C22×D73C23×C412yes—
335C22×D73C23×C411yescharacteristic
336C22×D73C2×#4112yes—
337C22×D73C2×#4112yes—
338C22×D73C2×#4112yes—
339C22×D73C2×#4112yes—
340C22×D73H(5,𝔽2)12yes—
341C22×D732−1+412yes—
342C22×D73C2511yescharacteristic
343C2×#64408—28no—
344C2×#64408—28no—
345C2×#64408—28no—
346C2×#64408—28no—
347C2×#64408—22no—
348C2×#64408—22no—
349C2×#64408—22no—
350C2×#64408—22no—
351C2×#64408—22no—
352C2×#64408—22no—
353C2×#64408—22no—
354C2×#64408—22no—
355C2×#64408—22no—
356C2×#64408—22no—
357C2×#64408—22no—
358C2×#64408—22no—
359C2×#64408—22no—
360C2×#64408—22no—
361C2×#64408—22no—
362C2×#64408—22no—
363C2×#64408—22no—
364C2×#64408—22no—
365C2×#64408—22no—
366C2×#64408—22no—
367C2×#64408—416no—
368C2×#64408—44no—
369C2×#64408—44no—
370C2×#64408—44no—
371C2×#64408—44no—
372C2×#64408C2×#4114yes—
373C2×#64408C2×#4114yes—
374C2×#64408C2×#4114yes—
375C2×#64408C2×#4114yes—
376C2×C4×C73—22no—
377C2×C4×C73—22no—
378C2×C4×C73—22no—
379C2×C4×C73—22no—
380C2×C4×C73—22no—
381C2×C4×C73—22no—
382C2×C4×C73C23×C412yes—
383C2×C4×C73C23×C412yes—
384C2×C4×C73C23×C412yes—
385C2×C4×C73C23×C412yes—
386C2×C4×C73C23×C412yes—
387C2×C4×C73C23×C412yes—
388C2×Dic73—22no—
389C2×Dic73—22no—
390C2×Dic73—22no—
391C2×Dic73—22no—
392C2×Dic73—22no—
393C2×Dic73—22no—
394C2×Dic73C23×C412yes—
395C2×Dic73C23×C412yes—
396C2×Dic73C23×C412yes—
397C2×Dic73C23×C412yes—
398C2×Dic73C23×C412yes—
399C2×Dic73C23×C412yes—
400C4×D73—24no—
401C4×D73—24no—
402C4×D73—24no—
403C4×D73—24no—
404C4×D73—24no—
405C4×D73—24no—
406C4×D73—22no—
407C4×D73—22no—
408C4×D73—22no—
409C4×D73—22no—
410C4×D73—22no—
411C4×D73—22no—
412C4×D73—22no—
413C4×D73—22no—
414C4×D73—22no—
415C4×D73—22no—
416C4×D73—22no—
417C4×D73—22no—
418C22×C73—22no—
419C22×C73—22no—
420C22×C73—22no—
421C22×C73—44no—
422C22×C73C4×#4112yes—
423C22×C73C4×#4112yes—
424C22×C73#52012yes—
425C22×C73C24×C411yescharacteristic
426C2×D73—22no—
427C2×D73—22no—
428C2×D73—22no—
429C2×D73—44no—
430C2×D73—48no—
431C2×D73—42no—
432C2×D73—42no—
433C2×D73—42no—
434C2×D73—42no—
435C2×D73C4×#4112yes—
436C2×D73C4×#4112yes—
437C2×D73#52012yes—
438C2×D73#55114yes—
439C2×D73#55214yes—
440C2×D73#55314yes—
441C2×D73#55614yes—
442C2×D73C22×#4111yescharacteristic
443C2×D73C22×#4111yescharacteristic
444C2×D73C22×#4111yescharacteristic
445C2×D73C22×#4111yescharacteristic
446C2×D73C2×H(5,𝔽2)11yescharacteristic
447C2×D73C2×2−1+411yescharacteristic
448#64408—24no—
449#64408—24no—
450#64408—24no—
451#64408—24no—
452#64408—42no—
453#64408—42no—
454#64408—42no—
455#64408—42no—
456C4×C73—22no—
457C4×C73—22no—
458C4×C73—22no—
459C4×C73—22no—
460C4×C73—22no—
461C4×C73—22no—
462Dic73—22no—
463Dic73—22no—
464Dic73—22no—
465Dic73—22no—
466Dic73—22no—
467Dic73—22no—
468C2×#2373—731nomaximal, Sylow
469C2×C73—42no—
470C2×C73#237314yescomplemented
471C2×C73C2×C4×#4111yescharacteristic
472C2×C73C2×C4×#4111yescharacteristic
473C2×C73C2×#52011yescharacteristic
474D73—42no—
475D73#237314yescomplemented
476D73C2×#55111yescharacteristic
477D73C2×#55211yescharacteristic
478D73C2×#55311yescharacteristic
479D73C2×#55611yescharacteristic
480C22×#126—731no—
481#2373—7316no—
482C2×#389—731no—
483C2×#388—731no—
484C2×#388—731no—
485C2×#388—731no—
486C2×#387—731no—
487C2×#387—731no—
488C2×#387—731no—
489C2×#385—731no—
490C2×C4×C4⋊C4—731no—
491C2×C4×C4⋊C4—731no—
492C2×C4×C4⋊C4—731no—
493C2×C4×C22⋊C4—731no—
494C2×C4×C22⋊C4—731no—
495C2×#376—731no—
496C73C2×#237311yescharacteristic, complemented, Sylow
497C24×C4—731no—
498C2×#126—738no—
499C2×#126—738no—
500C2×#126—731no—
501C2×#126—731no—
502C2×#126—731no—
503C2×#126—731no—
504C2×#126—731no—
505C2×#126—731no—
506C2×#126—731no—
507C2×#126#6440811yescharacteristic, complemented
508C22×C4⋊C4—731no—
509C22×C4⋊C4—731no—
510C22×C4⋊C4—731no—
511C22×C4⋊C4—731no—
512C22×C4⋊C4—731no—
513C22×C4⋊C4—731no—
514C22×C4⋊C4—731no—
515C22×C4⋊C4—731no—
516C22×C22⋊C4—731no—
517C22×C22⋊C4—731no—
518C22×C22⋊C4—731no—
519C22×C22⋊C4—731no—
520C22×C22⋊C4—731no—
521C22×C22⋊C4—731no—
522C22×C42—731no—
523C22×C42—731no—
524C22×C42—731no—
525C22×C42—731no—
526C22×C42—731no—
527C22×C42—731no—
528C22×C42—731no—
529C22×C42—731no—
530#389—738no—
531#388—738no—
532#388—738no—
533#388—738no—
534#387—738no—
535#387—738no—
536#387—738no—
537#385—738no—
538C4×C4⋊C4—738no—
539C4×C4⋊C4—738no—
540C4×C4⋊C4—738no—
541C4×C22⋊C4—738no—
542C4×C22⋊C4—738no—
543#376—738no—
544C2×#95—731no—
545C2×#95—731no—
546C2×#95—731no—
547C2×#95—731no—
548C2×#95—731no—
549C2×#95—731no—
550C2×#95—731no—
551C2×#95—731no—
552C2×#95—731no—
553C2×#95—731no—
554C2×#95—731no—
555C2×#95—731no—
556C25—731no—
557C23×C4—2922no—
558C23×C4—734no—
559C23×C4—731no—
560C23×C4—731no—
561C23×C4—731no—
562C23×C4—731no—
563C23×C4—731no—
564C23×C4—731no—
565C23×C4—731no—
566C23×C4—731no—
567C23×C4—731no—
568C23×C4—731no—
569C23×C4—731no—
570C23×C4—731no—
571C23×C4—731no—
572C23×C4—731no—
573C23×C4—1464no—
574C23×C4—1464no—
575#126—738no—
576#126—738no—
577#126—738no—
578#126—738no—
579#126—738no—
580#126—738no—
581#126—738no—
582#126C2×#6440818yescomplemented
583C2×C4⋊C4—2922no—
584C2×C4⋊C4—734no—
585C2×C4⋊C4—731no—
586C2×C4⋊C4—731no—
587C2×C4⋊C4—731no—
588C2×C4⋊C4—731no—
589C2×C4⋊C4—731no—
590C2×C4⋊C4—731no—
591C2×C4⋊C4—731no—
592C2×C4⋊C4—731no—
593C2×C4⋊C4—731no—
594C2×C4⋊C4—734no—
595C2×C4⋊C4—734no—
596C2×C4⋊C4—734no—
597C2×C4⋊C4—734no—
598C2×C4⋊C4—734no—
599C2×C4⋊C4—734no—
600C2×C4⋊C4—734no—
601C2×C4⋊C4—734no—
602C2×C4⋊C4—734no—
603C2×C4⋊C4—734no—
604C2×C4⋊C4—1464no—
605C2×C4⋊C4—1464no—
606C2×C4⋊C4—1464no—
607C2×C4⋊C4—1464no—
608C2×C4⋊C4C2×#6440811yescharacteristic, complemented
609C2×C4⋊C4C2×#6440811yescharacteristic, complemented
610C2×C4⋊C4C2×#6440811yescharacteristic, complemented
611C2×C22⋊C4—2922no—
612C2×C22⋊C4—734no—
613C2×C22⋊C4—731no—
614C2×C22⋊C4—731no—
615C2×C22⋊C4—731no—
616C2×C22⋊C4—731no—
617C2×C22⋊C4—731no—
618C2×C22⋊C4—731no—
619C2×C22⋊C4—731no—
620C2×C22⋊C4—731no—
621C2×C22⋊C4—731no—
622C2×C22⋊C4—734no—
623C2×C22⋊C4—734no—
624C2×C22⋊C4—734no—
625C2×C22⋊C4—734no—
626C2×C22⋊C4—734no—
627C2×C22⋊C4—734no—
628C2×C22⋊C4—734no—
629C2×C22⋊C4—734no—
630C2×C22⋊C4—1464no—
631C2×C22⋊C4—1464no—
632C2×C22⋊C4C2×#6440811yescharacteristic
633C2×C22⋊C4C2×#6440811yescharacteristic
634C2×C22⋊C4C2×#6440811yescharacteristic
635C2×C42—2922no—
636C2×C42—2922no—
637C2×C42—2922no—
638C2×C42—734no—
639C2×C42—734no—
640C2×C42—734no—
641C2×C42—731no—
642C2×C42—731no—
643C2×C42—731no—
644C2×C42—734no—
645C2×C42—734no—
646C2×C42—734no—
647C2×C42—734no—
648C2×C42—734no—
649C2×C42—734no—
650C2×C42—1464no—
651C2×C42—1464no—
652C2×C42—1464no—
653C2×C42—1464no—
654C2×C42C2×#6440811yescharacteristic, complemented
655#95—734no—
656#95—734no—
657#95—734no—
658#95—734no—
659#95—734no—
660#95—734no—
661#95—734no—
662#95—734no—
663#95—734no—
664#95—734no—
665#95—734no—
666#95—734no—
667C24—731no—
668C24—732no—
669C24—732no—
670C24—731no—
671C24—1462no—
672C24—1462no—
673C24—1462no—
674C24—1462no—
675C24—1462no—
676C24—1462no—
677C24C22×#6440811yescharacteristic
678C22×C4—29216no—
679C22×C4—2924no—
680C22×C4—734no—
681C22×C4—734no—
682C22×C4—734no—
683C22×C4—734no—
684C22×C4—732no—
685C22×C4—732no—
686C22×C4—732no—
687C22×C4—732no—
688C22×C4—731no—
689C22×C4—731no—
690C22×C4—731no—
691C22×C4—731no—
692C22×C4—731no—
693C22×C4—731no—
694C22×C4—732no—
695C22×C4—732no—
696C22×C4—732no—
697C22×C4—732no—
698C22×C4—732no—
699C22×C4—732no—
700C22×C4—732no—
701C22×C4—732no—
702C22×C4—732no—
703C22×C4—732no—
704C22×C4—732no—
705C22×C4—732no—
706C22×C4—732no—
707C22×C4—732no—
708C22×C4—732no—
709C22×C4—732no—
710C22×C4—1462no—
711C22×C4—1462no—
712C22×C4—1462no—
713C22×C4—1462no—
714C22×C4—1462no—
715C22×C4—1462no—
716C22×C4—1462no—
717C22×C4—1462no—
718C22×C4—1462no—
719C22×C4—1462no—
720C22×C4—1462no—
721C22×C4—1462no—
722C22×C4—1468no—
723C22×C4—1468no—
724C22×C4—1462no—
725C22×C4—1462no—
726C22×C4—1462no—
727C22×C4—1462no—
728C22×C4—1462no—
729C22×C4—1462no—
730C22×C4—1462no—
731C22×C4—1462no—
732C22×C4—1462no—
733C22×C4—1462no—
734C22×C4—1462no—
735C22×C4—1462no—
736C22×C4—1462no—
737C22×C4—1462no—
738C22×C4—1462no—
739C22×C4—1462no—
740C22×C4—1462no—
741C22×C4—1462no—
742C22×C4—1462no—
743C22×C4—1462no—
744C22×C4C22×#6440811yescharacteristic
745C22×C4C22×#6440811yescharacteristic
746C22×C4C22×#6440811yescharacteristic
747C22×C4C22×#6440811yescharacteristic
748C22×C4C22×#6440811yescharacteristic
749C22×C4C22×#6440811yescharacteristic
750C4⋊C4—2924no—
751C4⋊C4—734no—
752C4⋊C4—734no—
753C4⋊C4—734no—
754C4⋊C4—734no—
755C4⋊C4—734no—
756C4⋊C4—734no—
757C4⋊C4—734no—
758C4⋊C4—734no—
759C4⋊C4—734no—
760C4⋊C4—1468no—
761C4⋊C4—1468no—
762C4⋊C4—1468no—
763C4⋊C4—1468no—
764C4⋊C4C22×#6440814yescomplemented
765C4⋊C4C22×#6440814yescomplemented
766C4⋊C4C22×#6440814yescomplemented
767C22⋊C4—2924no—
768C22⋊C4—734no—
769C22⋊C4—734no—
770C22⋊C4—734no—
771C22⋊C4—734no—
772C22⋊C4—734no—
773C22⋊C4—734no—
774C22⋊C4—734no—
775C22⋊C4—734no—
776C22⋊C4—734no—
777C22⋊C4—1468no—
778C22⋊C4—1468no—
779C22⋊C4C22×#6440814yes—
780C22⋊C4C22×#6440814yes—
781C22⋊C4C22×#6440814yes—
782C42—2924no—
783C42—2924no—
784C42—2924no—
785C42—734no—
786C42—734no—
787C42—734no—
788C42—1468no—
789C42—1468no—
790C42—1468no—
791C42—1468no—
792C42C22×#6440814yescomplemented
793C23—22no—
794C23—22no—
795C23—22no—
796C23—2924no—
797C23—2924no—
798C23—2924no—
799C23—2924no—
800C23—732no—
801C23—732no—
802C23—732no—
803C23—732no—
804C23—732no—
805C23—732no—
806C23—731no—
807C23—731no—
808C23—732no—
809C23—1462no—
810C23—1462no—
811C23—1462no—
812C23—1462no—
813C23—1462no—
814C23—1464no—
815C23—1464no—
816C23—1462no—
817C23—1464no—
818C23—1462no—
819C23—1462no—
820C23—1462no—
821C23C23×#6440812yes—
822C23C23×#6440811yescharacteristic
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—2924no—
830C2×C4—2924no—
831C2×C4—2924no—
832C2×C4—2924no—
833C2×C4—29216no—
834C2×C4—734no—
835C2×C4—734no—
836C2×C4—734no—
837C2×C4—734no—
838C2×C4—732no—
839C2×C4—732no—
840C2×C4—732no—
841C2×C4—732no—
842C2×C4—732no—
843C2×C4—732no—
844C2×C4—1462no—
845C2×C4—1462no—
846C2×C4—1462no—
847C2×C4—1462no—
848C2×C4—1462no—
849C2×C4—1462no—
850C2×C4—1462no—
851C2×C4—1462no—
852C2×C4—1462no—
853C2×C4—1462no—
854C2×C4—1464no—
855C2×C4—1464no—
856C2×C4—1464no—
857C2×C4—1464no—
858C2×C4—1462no—
859C2×C4—1462no—
860C2×C4—1464no—
861C2×C4—1464no—
862C2×C4—1462no—
863C2×C4—1462no—
864C2×C4—1462no—
865C2×C4—1462no—
866C2×C4—1462no—
867C2×C4—1462no—
868C2×C4—1462no—
869C2×C4—1462no—
870C2×C4—1462no—
871C2×C4—1462no—
872C2×C4—1462no—
873C2×C4—1462no—
874C2×C4—1462no—
875C2×C4—1462no—
876C2×C4—1462no—
877C2×C4—1462no—
878C2×C4—1462no—
879C2×C4—1468no—
880C2×C4—1468no—
881C2×C4—1462no—
882C2×C4—1462no—
883C2×C4—1462no—
884C2×C4—1468no—
885C2×C4—1468no—
886C2×C4—1462no—
887C2×C4—1462no—
888C2×C4—1462no—
889C2×C4—1462no—
890C2×C4—1462no—
891C2×C4—1462no—
892C2×C4C23×#6440812yes—
893C2×C4C23×#6440812yes—
894C2×C4C23×#6440812yes—
895C2×C4C23×#6440812yes—
896C2×C4C23×#6440812yes—
897C2×C4C23×#6440812yes—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—44no—
902C22—2922no—
903C22—2922no—
904C22—2922no—
905C22—2922no—
906C22—2928no—
907C22—2924no—
908C22—731no—
909C22—731no—
910C22—731no—
911C22—731no—
912C22—732no—
913C22—732no—
914C22—731no—
915C22—731no—
916C22—732no—
917C22—734no—
918C22—734no—
919C22—734no—
920C22—734no—
921C22—1462no—
922C22—1462no—
923C22—1462no—
924C22#41×#6440812yes—
925C22#41×#6440812yes—
926C22#1798965612yes—
927C22C24×#6440811yescharacteristic
928C4—22no—
929C4—22no—
930C4—22no—
931C4—22no—
932C4—22no—
933C4—22no—
934C4—2922no—
935C4—2922no—
936C4—2922no—
937C4—2922no—
938C4—1464no—
939C4—1464no—
940C4—1464no—
941C4—1464no—
942C4—1462no—
943C4—1462no—
944C4—1462no—
945C4—1462no—
946C4—1462no—
947C4—1462no—
948C2—42no—
949C2—2922no—
950C2—731no—
951C2—731no—
952C2—731no—
953C2—731no—
954C2—734no—
955C2#2262646814yesdirect product factor
956C2C2×#41×#6440811yescharacteristic
957C2C2×#41×#6440811yescharacteristic
958C2C2×#1798965611yescharacteristic
subgroupG/H
centerC23C23×#64408
commutatorC22×C73C24×C4
FrattiniC22C24×#64408
FittingC2×#126×C73C4
socleC23×C73C23×C4
prime radicalC24×D73C23
cosocleC22×D73C25
hypercenterC2×#126#64408
hypocenterC73C2×#2373
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #22626468C2direct (N × H)
2. C2×#17989538C2semidirect
6. C2×#17989536C2semidirect
7. C2×#17989536C2semidirect
8. C2×#17989536C2semidirect
10. C2×C4⋊C4×#64408C2semidirect
11. C2×C4⋊C4×#64408C2semidirect
12. C2×C4×C4⋊#64408C2semidirect
15. C2×#17989523C2semidirect
33. #17989538C22semidirect
37. #17989536C22semidirect
38. #17989536C22semidirect
39. #17989536C22semidirect
41. C4⋊C4×#64408C22semidirect
42. C4⋊C4×#64408C22semidirect
43. C4×C4⋊#64408C22semidirect
46. #17989523C22semidirect
59. C2×#14556586C4semidirect
60. C2×#14556586C4semidirect
61. C2×#14556586C4semidirect
62. C2×#14556585C4semidirect
63. C2×#14556584C4semidirect
64. C2×#14556584C4semidirect
65. C2×#14556584C4semidirect
66. #126×D73C4semidirect
75. C2×#126×C73C4semidirect
137. #14556586C2×C4semidirect
138. #14556586C2×C4semidirect
139. #14556586C2×C4semidirect
140. #14556585C2×C4semidirect
141. #14556584C2×C4semidirect
142. #14556584C2×C4semidirect
143. #14556584C2×C4semidirect
144. C2×C4⋊Dic73C2×C4semidirect
145. C2×C4⋊Dic73C2×C4semidirect
146. C2×C4⋊Dic73C2×C4semidirect
147. C2×#11924007C2×C4semidirect
148. C2×#11924007C2×C4semidirect
149. C2×#11924007C2×C4semidirect
150. C2×#11924007C2×C4semidirect
151. C2×#11924007C2×C4semidirect
152. C2×#11924007C2×C4semidirect
153. C4⋊C4×D73C2×C4semidirect
154. C4⋊C4×D73C2×C4semidirect
155. C4⋊C4×D73C2×C4semidirect
174. C2×C4×Dic73C2×C4semidirect
175. C2×C4×Dic73C2×C4semidirect
176. C2×C4×Dic73C2×C4semidirect
177. C42×D73C2×C4semidirect
179. #126×C73C2×C4semidirect
180. C2×C4⋊C4×C73C2×C4semidirect
181. C2×C4⋊C4×C73C2×C4semidirect
182. C2×C4⋊C4×C73C2×C4semidirect
186. C2×C42×C73C2×C4semidirect
278. C4⋊Dic73C22×C4semidirect
279. C4⋊Dic73C22×C4semidirect
280. C4⋊Dic73C22×C4semidirect
281. #11924007C22×C4semidirect
282. #11924007C22×C4semidirect
283. #11924007C22×C4semidirect
284. #11924007C22×C4semidirect
285. #11924007C22×C4semidirect
286. #11924007C22×C4semidirect
296. C4×Dic73C22×C4semidirect
297. C4×Dic73C22×C4semidirect
298. C4×Dic73C22×C4semidirect
306. C4⋊C4×C73C22×C4semidirect
307. C4⋊C4×C73C22×C4semidirect
308. C4⋊C4×C73C22×C4semidirect
312. C42×C73C22×C4semidirect
470. C2×C73#2373semidirect
475. D73#2373semidirect
496. C73C2×#2373semidirect
507. C2×#126#64408semidirect
582. #126C2×#64408semidirect
608. C2×C4⋊C4C2×#64408semidirect
609. C2×C4⋊C4C2×#64408semidirect
610. C2×C4⋊C4C2×#64408semidirect
654. C2×C42C2×#64408semidirect
764. C4⋊C4C22×#64408semidirect
765. C4⋊C4C22×#64408semidirect
766. C4⋊C4C22×#64408semidirect
792. C42C22×#64408semidirect
955. C2#22626468direct (N × H)

Maximal subgroups

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

subgroupindex
#226264682
C2×#179895382
C2×#179895372
C2×#179895362
C2×#179895342
C2×C4⋊C4×#644082
C2×C4×C4⋊#644082
C2×C22⋊C4×#644082
C2×#179895232
C2×#126×D732
C2×#237373