Finite Group Databasebeta

← #14920623

Subgroups — #14920623

Order 2816.

2934 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic, complemented
2C2×C4×D4×D11C211yesmaximal, characteristic, complemented
3#13074516C212yesmaximal, complemented
4#13074512C212yesmaximal, complemented
5#13074489C212yesmaximal, complemented
6#13074474C212yesmaximal, complemented
7#13074420C212yesmaximal, complemented
8#13074403C212yesmaximal, complemented
9#13074351C212yesmaximal, complemented
10#13074329C212yesmaximal, complemented
11#13071899C211yesmaximal, characteristic, complemented
12#13071897C211yesmaximal, characteristic, complemented
13#13071895C211yesmaximal, characteristic, complemented
14#13071860C214yesmaximal, complemented
15C4×#66935C214yesmaximal, complemented
16#13071008C211yesmaximal, characteristic, complemented
17C11×#2398C211yesmaximal, characteristic, complemented
18C22×D4×D11C2211yescharacteristic
19C23×C4×D11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic, complemented
21C2×C4×D4×C11C2211yescharacteristic
22C2×#67000C2211yescharacteristic, complemented
23C2×#66999C2211yescharacteristic
24C2×D4×Dic11C2211yescharacteristic
25C2×C4×C22⋊D11C2212yes—
26C2×C4×C22⋊D11C2214yescomplemented
27#10623111—28no—
28C4×D4×D11—28no—
29C2×#66951C2212yescomplemented
30C2×#66948C2211yescharacteristic
31C2×#66947C2212yes—
32C2×#66946C2211yescharacteristic
33C2×C4⋊C4×D11C2211yescharacteristic
34C2×#66943C2211yescharacteristic, complemented
35C2×#66935C2214yes—
36C2×(C22⋊D11)⋊C4C2212yes—
37C2×C22⋊C4×D11C2212yes—
38C2×C4×D44C2212yes—
39C2×C4×D44C2211yescharacteristic
40C2×C4×D44C2211yescharacteristic, complemented
41C2×C4×D44C2214yescomplemented
42C2×#66925C2212yescomplemented
43C2×C42×D11C2211yescharacteristic
44C11×#400C2212yescomplemented
45C11×#397C2212yescomplemented
46C11×#394C2212yes—
47C11×#393C2212yescomplemented
48C4×C11×C22⋊C4C2214yescomplemented
49C11×#376C2211yescharacteristic, complemented
50#10622844C2212yescomplemented
51#10622836C2212yes—
52#10622606C2212yescomplemented
53#10622605C2212yescomplemented
54#10622604C2212yes—
55#10622599C2212yescomplemented
56#10622573C2214yes—
57#10622573C2212yescomplemented
58#10622572C2214yes—
59#10622572C2214yescomplemented
60#10622571C2214yescomplemented
61#10622568C2214yes—
62#10622563C2214yescomplemented
63#10622562C2212yescomplemented
64#10622561C2214yescomplemented
65C4×(C2×D11)⋊C4C2212yes—
66C4×(C2×D11)⋊C4C2214yescomplemented
67#10622545C2211yescharacteristic, complemented
68C4×Dic11⋊C4C2212yescomplemented
69#10622290C2212yescomplemented
70#10622290C2212yescomplemented
71#10622289C2214yescomplemented
72#10622288C2214yescomplemented
73#10622285C2214yescomplemented
74#10622284C2212yes—
75#10622284C2212yescomplemented
76#10622281C2214yes—
77#10622281C2214yescomplemented
78#10622280C2212yes—
79#10622278C2214yes—
80#10622278C2214yescomplemented
81#10622277C2212yes—
82#10622270C2214yescomplemented
83#10622264C2212yescomplemented
84#10622263C2212yescomplemented
85C24×D11C2312yes—
86C22×Q8×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C23×C4×C11C2312yes—
89C22×C22⋊D11C2312yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2312yes—
92C2×D4×D11—28no—
93C2×D4×D11—24no—
94C22×D44C2312yes—
95C22×D44C2311yescharacteristic
96C22×D44C2314yes—
97C22×D44C2311yescharacteristic
98C22×C4×D11—28no—
99C22×C4×D11—48no—
100C22×C4×D11C2312yes—
101C22×C4×D11C2312yes—
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2312yes—
105C22×C4×D11C2312yes—
106C22×C4×D11C2311yescharacteristic
107C4×Q8×C11—24no—
108C4×D4×C11—24no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C42×C11C2312yes—
116C2×C42×C11C2312yes—
117C2×C42×C11C2311yescharacteristic
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2314yes—
120#67000—24no—
121#66999—24no—
122D4×Dic11—24no—
123C4×C22⋊D11—28no—
124C4×C22⋊D11—48no—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2312yes—
127C2×(C2×D11)⋊C4C2312yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11C2312yes—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2314yes—
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2311yescharacteristic
149C2×C4×Dic11C2311yescharacteristic
150C2×C4×Dic11C2311yescharacteristic
151#66951—28no—
152#66948—24no—
153#66947—28no—
154#66946—24no—
155C4⋊C4×D11—24no—
156#66943—24no—
157#66935—216no—
158(C22⋊D11)⋊C4—28no—
159C22⋊C4×D11—28no—
160C4×D44—28no—
161C4×D44—24no—
162C4×D44—24no—
163C4×D44—48no—
164#66925—28no—
165C42×D11D418yescomplemented
166C11×#95C2312yes—
167C11×#95C2312yes—
168C11×#95C2314yes—
169C11×#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2312yes—
172C11⋊#95C2314yes—
173C11⋊#95C2312yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176#34593—111nomaximal, Sylow
177C24×C11C2412yes—
178C23×D11—24no—
179C23×D11—24no—
180C23×D11—44no—
181C23×D11—44no—
182C23×D11#4118yes—
183C23×D11C2412yes—
184C23×D11C2412yes—
185C23×D11C2411yescharacteristic
186C2×Q8×C11—22no—
187C2×Q8×C11—42no—
188C2×D4×C11—24no—
189C2×D4×C11—22no—
190C22×C4×C11—24no—
191C22×C4×C11—28no—
192C22×C4×C11C2414yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—28no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—44no—
205C22×Dic11—24no—
206C22×Dic11—44no—
207C22×Dic11C2414yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2411yescharacteristic
211C22×Dic11C2411yescharacteristic
212C22×Dic11C2411yescharacteristic
213D4×D11—232no—
214C2×D44—24no—
215C2×D44—24no—
216C2×D44—28no—
217C2×D44—28no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44—44no—
221C2×D44—42no—
222C2×D44—44no—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—28no—
230C2×C4×D11—28no—
231C2×C4×D11—44no—
232C2×C4×D11—44no—
233C2×C4×D11—42no—
234C2×C4×D11—432no—
235C2×C4×D11C2×D414yes—
236C2×C4×D11C2×D414yes—
237C2×C4×D11C2×D414yes—
238C11×C4⋊C4—22no—
239C11×C4⋊C4—22no—
240C11×C4⋊C4—24no—
241C11×C22⋊C4—28no—
242C11×C22⋊C4—24no—
243C11×C22⋊C4—44no—
244C42×C11—24no—
245C42×C11—24no—
246C42×C11C2×D414yes—
247C22⋊Dic11—24no—
248C22⋊Dic11—44no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—28no—
255(C2×D11)⋊C4—28no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—44no—
259(C2×D11)⋊C4—44no—
260(C2×D11)⋊C4—44no—
261(C2×D11)⋊C4—44no—
262C4⋊Dic11—24no—
263C4⋊Dic11—22no—
264C4⋊Dic11—22no—
265C4⋊Dic11—44no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—44no—
270Dic11⋊C4—44no—
271C4×Dic11—24no—
272C4×Dic11C2×D414yes—
273C4×Dic11C2×D414yes—
274C4×Dic11C2×D414yes—
275C2×#529—111no—
276C22×C4×D4—111no—
277#2636—112no—
278#2636—112no—
279#2633—112no—
280#2631—112no—
281#2626—112no—
282#2623—112no—
283#2617—112no—
284#2613—112no—
285#2398—111no—
286#2398D1111yescharacteristic, complemented
287#2397—111no—
288#2397—111no—
289#2392—114no—
290C4×#120—114no—
291#2283—111no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—24no—
295C23×C11—24no—
296C23×C11C2×#4114yes—
297C23×C11C2511yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—24no—
303C22×D11—24no—
304C22×D11—216no—
305C22×D11—22no—
306C22×D11—24no—
307C22×D11—24no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—416no—
311C22×D11—48no—
312C22×D11—48no—
313C22×D11—416no—
314C22×D11C22×D412yes—
315C22×D11C2×#4114yes—
316C22×D11C2×#4114yes—
317Q8×C11—44no—
318D4×C11—28no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—48no—
332C2×C4×C11C22×D412yes—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D412yes—
335C2×C4×C11H(5,𝔽2)14yes—
336C22⋊D11—216no—
337C22⋊D11—416no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—48no—
349C2×Dic11C22×D412yes—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352D44—28no—
353D44—44no—
354D44—416no—
355D44—48no—
356C4×D11—28no—
357C4×D11—28no—
358C4×D11—44no—
359C4×D11—48no—
360C4×D11—48no—
361C4×D11—48no—
362C4×D11—48no—
363C23×D4—111no—
364C24×C4—112no—
365#529—228no—
366C2×#126—112no—
367C2×#125—111no—
368C2×#124—111no—
369C2×#123—112no—
370C2×C22⋊Q8—111no—
371C2×#121—111no—
372C2×#120—114no—
373C2×C4×Q8C2×D1111yescharacteristic, complemented
374C2×C4×D4—111no—
375C2×C4×D4—112no—
376C2×C4×D4—114no—
377C2×C4×D4—111no—
378C2×C4×D4—112no—
379C2×C4×D4—111no—
380C2×C4×D4—112no—
381C2×C4×D4—111no—
382C2×C4×D4—114no—
383C2×C4×D4—228no—
384C2×C4×D4C2×D1111yescharacteristic
385C2×#117—112no—
386C22×C4⋊C4—111no—
387C22×C22⋊C4—112no—
388C22×C42—111no—
389#400—112no—
390#400C2×D1112yescomplemented
391#399—112no—
392#399—112no—
393#399—112no—
394#399—112no—
395#398—114no—
396#397—112no—
397#397—114no—
398#397C2×D1112yescomplemented
399#396—114no—
400#396—114no—
401#394—112no—
402#394—114no—
403#394—114no—
404#394—114no—
405#394C2×D1112yes—
406#393—112no—
407#393C2×D1112yescomplemented
408#392—112no—
409#392—114no—
410#392—112no—
411#392—112no—
412#392—112no—
413#386—114no—
414#386—114no—
415#386—114no—
416#385—114no—
417#385—114no—
418#385—114no—
419#383—112no—
420#382—112no—
421#381—112no—
422#380—112no—
423#379—114no—
424C4×C4⋊C4—112no—
425C4×C22⋊C4—112no—
426C4×C22⋊C4—114no—
427C4×C22⋊C4C2×D1114yescomplemented
428#376—111no—
429#376C2×D1111yescharacteristic, complemented
430C22×C11—24no—
431C22×C11—28no—
432C22×C11—42no—
433C22×C11—42no—
434C22×C11—44no—
435C22×C11C23×D411yescharacteristic
436C22×C11C22×#4112yes—
437C22×C11C2×H(5,𝔽2)12yes—
438C22×C11#58512yes—
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—28no—
442C2×D11—24no—
443C2×D11—28no—
444C2×D11—432no—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—44no—
448C2×D11—42no—
449C2×D11—42no—
450C2×D11—42no—
451C2×D11—44no—
452C2×D11—44no—
453C2×D11#52514yes—
454C4×C11—22no—
455C4×C11—22no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11—42no—
459C4×C11—44no—
460C4×C11#53514yes—
461Dic11—22no—
462Dic11—22no—
463Dic11—22no—
464Dic11—42no—
465Dic11—42no—
466Dic11—44no—
467C25—112no—
468C22×Q8C22×D1111yescharacteristic
469C22×D4—112no—
470C22×D4—114no—
471C22×D4—111no—
472C22×D4—112no—
473C22×D4—114no—
474C22×D4—111no—
475C22×D4—224no—
476C22×D4—228no—
477C22×D4C22×D1111yescharacteristic
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—111no—
481C23×C4—112no—
482C23×C4—112no—
483C23×C4—112no—
484C23×C4—112no—
485C23×C4—112no—
486C23×C4—228no—
487C23×C4—448no—
488C23×C4C22×D1112yes—
489#126—228no—
490#125—224no—
491#124—224no—
492#123—228no—
493C22⋊Q8—224no—
494#121—224no—
495#120—2216no—
496C4×Q8—24no—
497C4×D4—24no—
498C4×D4—228no—
499C4×D4—228no—
500C4×D4—224no—
501C4×D4—228no—
502C4×D4—224no—
503C4×D4—224no—
504C4×D4—224no—
505C4×D4—448no—
506C4×D4—448no—
507#117—228no—
508C2×C4⋊C4—112no—
509C2×C4⋊C4—111no—
510C2×C4⋊C4—112no—
511C2×C4⋊C4—112no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—112no—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—224no—
518C2×C4⋊C4C22×D1111yescharacteristic
519C2×C4⋊C4C22×D1111yescharacteristic
520C2×C4⋊C4C22×D1112yes—
521C2×C22⋊C4—112no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—112no—
524C2×C22⋊C4—112no—
525C2×C22⋊C4—112no—
526C2×C22⋊C4—112no—
527C2×C22⋊C4—112no—
528C2×C22⋊C4—112no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—114no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—114no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—228no—
537C2×C22⋊C4C22×D1112yes—
538C2×C22⋊C4C22×D1114yes—
539C2×C22⋊C4C22×D1114yes—
540C2×C42—111no—
541C2×C42—111no—
542C2×C42—111no—
543C2×C42—118no—
544C2×C42—112no—
545C2×C42C22×D1112yes—
546C2×C42C22×D1112yes—
547C2×C42C22×D1111yescharacteristic
548#95—112no—
549#95—112no—
550#95—114no—
551#95—114no—
552#95—114no—
553#95—114no—
554#95C22×D1112yes—
555#95C22×D1112yes—
556#95C22×D1114yes—
557#95C22×D1114yes—
558C2×C11—44no—
559C2×C11C2×#52511yescharacteristic
560C2×C11C2×#53511yescharacteristic
561C2×C11#344911yescharacteristic
562C2×C11#345914yes—
563D11—24no—
564D11—44no—
565D11—82no—
566C24—111no—
567C24—112no—
568C24—118no—
569C24—112no—
570C24—224no—
571C24—224no—
572C24—444no—
573C24—444no—
574C24C23×D1112yes—
575C2×Q8—22no—
576C2×Q8—42no—
577C2×D4—24no—
578C2×D4—22no—
579C2×D4—224no—
580C2×D4—224no—
581C2×D4—228no—
582C2×D4—228no—
583C2×D4—224no—
584C2×D4—2232no—
585C2×D4—224no—
586C2×D4—224no—
587C2×D4—228no—
588C2×D4—222no—
589C2×D4—222no—
590C2×D4—444no—
591C2×D4—442no—
592C2×D4—444no—
593C2×D4—444no—
594C2×D4—444no—
595C22×C4—24no—
596C22×C4—28no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—114no—
601C22×C4—114no—
602C22×C4—114no—
603C22×C4—114no—
604C22×C4—112no—
605C22×C4—112no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—224no—
609C22×C4—224no—
610C22×C4—224no—
611C22×C4—224no—
612C22×C4—224no—
613C22×C4—228no—
614C22×C4—228no—
615C22×C4—444no—
616C22×C4—444no—
617C22×C4—442no—
618C22×C4—4432no—
619C22×C4—444no—
620C22×C4C23×D1114yes—
621C22×C4C23×D1112yes—
622C22×C4C23×D1112yes—
623C22×C4C23×D1112yes—
624C22×C4C23×D1111yescharacteristic
625C22×C4C23×D1111yescharacteristic
626C22×C4C23×D1111yescharacteristic
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—24no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4—224no—
634C4⋊C4—222no—
635C4⋊C4—222no—
636C4⋊C4—444no—
637C4⋊C4—444no—
638C4⋊C4—444no—
639C22⋊C4—28no—
640C22⋊C4—24no—
641C22⋊C4—44no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—224no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—228no—
648C22⋊C4—228no—
649C22⋊C4—224no—
650C22⋊C4—224no—
651C22⋊C4—224no—
652C22⋊C4—444no—
653C22⋊C4—444no—
654C22⋊C4—444no—
655C22⋊C4—444no—
656C22⋊C4—444no—
657C42—24no—
658C42—24no—
659C42—114no—
660C42—114no—
661C42—114no—
662C42—224no—
663C42D4×D1114yes—
664C11#3459311yescharacteristic, complemented, Sylow
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—112no—
670C23—114no—
671C23—114no—
672C23—2216no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23—222no—
677C23—224no—
678C23—224no—
679C23—222no—
680C23—224no—
681C23—224no—
682C23—222no—
683C23—222no—
684C23—4416no—
685C23—448no—
686C23—448no—
687C23—4416no—
688C23#41×D1114yes—
689C23C24×D1111yescharacteristic
690Q8—44no—
691D4—28no—
692D4—228no—
693D4—2216no—
694D4—444no—
695D4—448no—
696D4—4416no—
697D4—4416no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—48no—
711C2×C4—112no—
712C2×C4—112no—
713C2×C4—112no—
714C2×C4—228no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—228no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—444no—
727C2×C4—448no—
728C2×C4—448no—
729C2×C4—448no—
730C2×C4—448no—
731C2×C4—448no—
732C2×C4C2×D4×D1112yes—
733C2×C4C2×D4×D1112yes—
734C2×C4C2×D4×D1112yes—
735C2×C4#6704214yes—
736C22—28no—
737C22—24no—
738C22—42no—
739C22—42no—
740C22—44no—
741C22—114no—
742C22—222no—
743C22—222no—
744C22—228no—
745C22—228no—
746C22—224no—
747C22—4432no—
748C22—442no—
749C22—442no—
750C22—444no—
751C22—442no—
752C22—442no—
753C22—444no—
754C22—444no—
755C22—442no—
756C22C22×D4×D1111yescharacteristic
757C22C2×#41×D1112yes—
758C22C2×#6704212yes—
759C22#1062345312yes—
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—44no—
765C4—42no—
766C4—222no—
767C4—222no—
768C4—222no—
769C4—442no—
770C4—442no—
771C4—444no—
772C4#1062320514yes—
773C2—44no—
774C2—224no—
775C2—444no—
776C2—882no—
777C2D11×#52511yescharacteristic
778C2C2×#1062320511yescharacteristic
779C2#1308194611yescharacteristic
780C2#1308202614yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2398C2
hypercenter#2398D11
hypocenterC11#34593
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2398

Complements

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

NH ≅ G/Ntype
1. C2×#10623111C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13074516C2semidirect
4. #13074512C2semidirect
5. #13074489C2semidirect
6. #13074474C2semidirect
7. #13074420C2semidirect
8. #13074403C2semidirect
9. #13074351C2semidirect
10. #13074329C2semidirect
11. #13071899C2semidirect
12. #13071897C2semidirect
13. #13071895C2semidirect
14. #13071860C2semidirect
15. C4×#66935C2semidirect
16. #13071008C2semidirect
17. C11×#2398C2semidirect
20. C2×C4×Q8×C11C22semidirect
22. C2×#67000C22semidirect
26. C2×C4×C22⋊D11C22semidirect
29. C2×#66951C22semidirect
34. C2×#66943C22semidirect
40. C2×C4×D44C22semidirect
41. C2×C4×D44C22semidirect
42. C2×#66925C22semidirect
44. C11×#400C22semidirect
45. C11×#397C22semidirect
47. C11×#393C22semidirect
48. C4×C11×C22⋊C4C22semidirect
49. C11×#376C22semidirect
50. #10622844C22semidirect
52. #10622606C22semidirect
53. #10622605C22semidirect
55. #10622599C22semidirect
57. #10622573C22semidirect
59. #10622572C22semidirect
60. #10622571C22semidirect
62. #10622563C22semidirect
63. #10622562C22semidirect
64. #10622561C22semidirect
66. C4×(C2×D11)⋊C4C22semidirect
67. #10622545C22semidirect
68. C4×Dic11⋊C4C22semidirect
69. #10622290C22semidirect
70. #10622290C22semidirect
71. #10622289C22semidirect
72. #10622288C22semidirect
73. #10622285C22semidirect
75. #10622284C22semidirect
77. #10622281C22semidirect
80. #10622278C22semidirect
82. #10622270C22semidirect
83. #10622264C22semidirect
84. #10622263C22semidirect
165. C42×D11D4semidirect
286. #2398D11semidirect
373. C2×C4×Q8C2×D11semidirect
390. #400C2×D11semidirect
398. #397C2×D11semidirect
407. #393C2×D11semidirect
427. C4×C22⋊C4C2×D11semidirect
429. #376C2×D11semidirect
664. C11#34593semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
C2×C4×D4×D112
#130745162
#130745122
#130744892
#130744742
#130744202
#130744032
#130743512
#130743292
#130718992
#130718972
#130718952
#130718602
C4×#669352
#130710082
C11×#23982
#3459311