Finite Group Databasebeta

← #14926644

Subgroups — #14926644

Order 2816.

4298 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623120C214yesmaximal, complemented
2C22×#66991C211yesmaximal, characteristic, complemented
3C2×D11×#121C211yesmaximal, characteristic, complemented
4#13076960C212yesmaximal, complemented
5#13076958C212yesmaximal, complemented
6#13074717C214yesmaximal, complemented
7#13073544C214yesmaximal, complemented
8#13073541C214yesmaximal, complemented
9#13073088C211yesmaximal, characteristic, complemented
10#13073087C211yesmaximal, characteristic, complemented
11#13073086C212yesmaximal, complemented
12#13072250C212yesmaximal, complemented
13#13072249C211yesmaximal, characteristic, complemented
14C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
15C11×#2433C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic, complemented
17C23×C22⋊D11C2212yes—
18C22×D4×D11C2212yes—
19C22×D4×D11C2211yescharacteristic, complemented
20C23×C4×D11C2211yescharacteristic
21C2×C11×#127C2212yescomplemented
22C2×C11×#121C2211yescharacteristic
23C2×C11×#120C2214yescomplemented
24C2×#67006C2214yescomplemented
25C22×C22⋊Dic11C2212yescomplemented
26C2×#66993C2212yescomplemented
27C2×#66992C2212yes—
28C2×#66991—28no—
29C2×#66991C2212yes—
30C2×#66991C2212yes—
31C2×#66991C2212yescomplemented
32C2×#66991C2218yescomplemented
33C2×#66991C2211yescharacteristic, complemented
34C2×#66991C2212yescomplemented
35C2×#66990C2218yescomplemented
36C2×#66988C2214yescomplemented
37C2×#66983C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic, complemented
39D11×#121—28no—
40#10623120—232no—
41C2×#66948C2211yescharacteristic, complemented
42C2×C4⋊C4×D11C2211yescharacteristic, complemented
43C2×#66939C2214yescomplemented
44C2×#66937C2212yescomplemented
45C2×#66937C2218yescomplemented
46C2×#66936C2218yescomplemented
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yescomplemented
49C2×C42×D11C2212yescomplemented
50C11×#392C2214yescomplemented
51C11×#390C2212yescomplemented
52C4×C11×C22⋊C4C2211yescharacteristic, complemented
53#10622836C2214yescomplemented
54#10622836C2218yescomplemented
55#10622834C2212yescomplemented
56#10622834C2212yescomplemented
57#10622834C2218yescomplemented
58C4×C22⋊Dic11C2211yescharacteristic, complemented
59#10622589C2212yescomplemented
60#10622570C2218yescomplemented
61#10622562C2214yescomplemented
62#10622562C2218yescomplemented
63C22⋊C4×Dic11C2212yescomplemented
64#10622552C2212yescomplemented
65C4×(C2×D11)⋊C4C2212yescomplemented
66#10622548C2212yescomplemented
67#10622290C2214yescomplemented
68#10622279C2212yescomplemented
69D11×#95C2212yescomplemented
70C25×C11C2312yes—
71C24×D11C2312yes—
72C24×D11C2311yescharacteristic
73C22×D4×C11—24no—
74C22×D4×C11—44no—
75C22×D4×C11C2312yes—
76C22×D4×C11C2312yes—
77C22×D4×C11C2311yescharacteristic
78C22×D4×C11C2318yes—
79C22×D4×C11C2312yes—
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—28no—
82C22×C22⋊D11—216no—
83C22×C22⋊D11C2314yes—
84C22×C22⋊D11C2314yes—
85C22×C22⋊D11C2312yes—
86C22×C22⋊D11C2312yes—
87C22×C22⋊D11C2318yes—
88C22×C22⋊D11C2312yes—
89C23×Dic11C2312yes—
90C23×Dic11C2311yescharacteristic
91C2×D4×D11—216no—
92C2×D4×D11—28no—
93C2×D4×D11—24no—
94C2×D4×D11—44no—
95C22×D44C2312yes—
96C22×D44C2311yescharacteristic
97C22×C4×D11—44no—
98C22×C4×D11D418yescomplemented
99C22×C4×D11C2312yes—
100C22×C4×D11C2311yescharacteristic
101C22×C4×D11C2311yescharacteristic
102C22×C4×D11C2311yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2314yes—
105C11×#127—44no—
106C11×#121—24no—
107C11×#120—216no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2318yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C42×C11C2312yes—
113#67006—216no—
114C2×C22⋊Dic11—28no—
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2318yes—
117C2×C22⋊Dic11C2318yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2312yes—
121#66993—44no—
122#66992—28no—
123#66991—28no—
124#66991—28no—
125#66991—28no—
126#66991—28no—
127#66991—24no—
128#66991—232no—
129#66990—232no—
130#66988—216no—
131#66983—24no—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2318yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×C4⋊Dic11—24no—
137C2×C4⋊Dic11C2318yes—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2312yes—
140C2×C4⋊Dic11C2312yes—
141C2×Dic11⋊C4C2318yes—
142C2×Dic11⋊C4C2312yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2314yes—
145#66948—24no—
146C4⋊C4×D11—24no—
147#66939—216no—
148#66937—28no—
149#66937—232no—
150#66936—232no—
151C22⋊C4×D11—28no—
152C22⋊C4×D11D4116yescomplemented
153C42×D11—44no—
154C11×#95C2312yes—
155C11⋊#95C2312yes—
156C11⋊#95C2314yes—
157#35001—111nomaximal, Sylow
158C24×C11—24no—
159C24×C11—28no—
160C24×C11—44no—
161C24×C11—44no—
162C24×C11C2412yes—
163C24×C11C2414yes—
164C24×C11C2411yescharacteristic
165C23×D11—24no—
166C23×D11—28no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—44no—
170C23×D11—44no—
171C23×D11C2×D418yes—
172C23×D11C2×D414yes—
173C23×D11C2412yes—
174C23×D11C2411yescharacteristic
175C23×D11C2411yescharacteristic
176C2×D4×C11—28no—
177C2×D4×C11—24no—
178C2×D4×C11—24no—
179C2×D4×C11—24no—
180C2×D4×C11—22no—
181C2×D4×C11—216no—
182C2×D4×C11—24no—
183C2×D4×C11—24no—
184C2×D4×C11—24no—
185C2×D4×C11—44no—
186C2×D4×C11—416no—
187C2×D4×C11—48no—
188C2×D4×C11—48no—
189C22×C4×C11—24no—
190C22×C4×C11C2×D414yes—
191C22×C4×C11C2412yes—
192C22×C4×C11C2411yescharacteristic
193C22×C4×C11C2414yes—
194C22×C4×C11C2411yescharacteristic
195C2×C22⋊D11—24no—
196C2×C22⋊D11—216no—
197C2×C22⋊D11—28no—
198C2×C22⋊D11—24no—
199C2×C22⋊D11—216no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—216no—
202C2×C22⋊D11—28no—
203C2×C22⋊D11—28no—
204C2×C22⋊D11—28no—
205C2×C22⋊D11—44no—
206C2×C22⋊D11—48no—
207C2×C22⋊D11—48no—
208C2×C22⋊D11—432no—
209C22×Dic11—28no—
210C22×Dic11—24no—
211C22×Dic11—42no—
212C22×Dic11C2×D414yes—
213C22×Dic11C2414yes—
214C22×Dic11C2412yes—
215C22×Dic11C2411yescharacteristic
216C22×Dic11C2414yes—
217C22×Dic11C2411yescharacteristic
218D4×D11—416no—
219D4×D11—432no—
220C2×D44—28no—
221C2×D44—24no—
222C2×D44—22no—
223C2×D44—24no—
224C2×C4×D11—24no—
225C2×C4×D11—28no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—44no—
229C2×C4×D11—42no—
230C2×C4×D11—42no—
231C2×C4×D11—44no—
232C2×C4×D11—416no—
233C2×C4×D11C2×D414yes—
234C2×C4×D11C2×D414yes—
235C2×C4×D11C2×D414yes—
236C2×C4×D11C2×D414yes—
237C2×C4×D11C2×D4116yescomplemented
238C11×C4⋊C4—22no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—216no—
241C11×C22⋊C4C2×D418yescomplemented
242C42×C11—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—216no—
245C22⋊Dic11—216no—
246C22⋊Dic11—28no—
247C22⋊Dic11—28no—
248C22⋊Dic11C2×D418yescomplemented
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—216no—
252(C2×D11)⋊C4C2×D4116yescomplemented
253C4⋊Dic11—216no—
254C4⋊Dic11—22no—
255C4⋊Dic11—24no—
256C4⋊Dic11—24no—
257Dic11⋊C4—216no—
258Dic11⋊C4—24no—
259C4×Dic11—24no—
260C4×Dic11—44no—
261C2×#534—114no—
262C22×#121—111no—
263C22×#121—111no—
264#2856—112no—
265#2856—112no—
266#2656—114no—
267#2539—114no—
268#2539—114no—
269#2501—112no—
270#2501—111no—
271#2501—111no—
272#2433—111no—
273#2433—112no—
274#2433D1111yescharacteristic, complemented
275C2×C4×C22⋊C4—111no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—28no—
281C23×C11—22no—
282C23×C11—24no—
283C23×C11—24no—
284C23×C11—24no—
285C23×C11—28no—
286C23×C11—24no—
287C23×C11—48no—
288C23×C11—48no—
289C23×C11—48no—
290C23×C11—816no—
291C23×C11C22×D414yes—
292C23×C11C22×D412yes—
293C23×C11C2511yescharacteristic
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—24no—
300C22×D11—24no—
301C22×D11—24no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—416no—
305C22×D11—48no—
306C22×D11—48no—
307C22×D11—48no—
308C22×D11—816no—
309C22×D11#127116yescomplemented
310C22×D11C22×D414yes—
311C22×D11C22×D412yes—
312C22×D11C22×D412yes—
313C22×D11C22×D414yes—
314D4×C11—48no—
315D4×C11—48no—
316D4×C11—44no—
317D4×C11—48no—
318D4×C11—816no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—24no—
322C2×C4×C11—28no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11C22×D418yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11H(5,𝔽2)14yes—
329C22⋊D11—48no—
330C22⋊D11—48no—
331C22⋊D11—48no—
332C22⋊D11—416no—
333C22⋊D11—416no—
334C22⋊D11—816no—
335C2×Dic11—24no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—24no—
339C2×Dic11—22no—
340C2×Dic11—28no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—44no—
344C2×Dic11—48no—
345C2×Dic11C22×D418yes—
346C2×Dic11C22×D412yes—
347C2×Dic11C22×D412yes—
348D44—48no—
349D44—44no—
350C4×D11—28no—
351C4×D11—28no—
352C4×D11—44no—
353C4×D11—44no—
354C4×D11—416no—
355C4×D11—48no—
356C23×D4—112no—
357C23×D4—112no—
358C23×D4—111no—
359C23×D4C2×D1111yescharacteristic, complemented
360C24×C4—111no—
361#534—2232no—
362C2×#127—112no—
363C2×#127C2×D1112yescomplemented
364C2×#123—114no—
365C2×#123—118no—
366C2×#123—114no—
367C2×#121—112no—
368C2×#121—111no—
369C2×#121—118no—
370C2×#121—112no—
371C2×#121—112no—
372C2×#121—112no—
373C2×#121—112no—
374C2×#121—111no—
375C2×#121—111no—
376C2×#121—118no—
377C2×#121—112no—
378C2×#121—228no—
379C2×#121—228no—
380C2×#121C2×D1111yescharacteristic
381C2×#120—114no—
382C2×#120—118no—
383C2×#120C2×D1114yescomplemented
384C22×C4⋊C4—111no—
385C22×C4⋊C4—111no—
386C22×C22⋊C4—112no—
387C22×C22⋊C4—112no—
388C22×C22⋊C4—112no—
389C22×C42—112no—
390#399—118no—
391#399—114no—
392#399—114no—
393#392—118no—
394#392—114no—
395#392C2×D1114yescomplemented
396#390—112no—
397#390—112no—
398#390—118no—
399#390—118no—
400#390—112no—
401#390C2×D1112yescomplemented
402#384—112no—
403#384—112no—
404C4×C22⋊C4—111no—
405C4×C22⋊C4—112no—
406C4×C22⋊C4—112no—
407C4×C22⋊C4—112no—
408C4×C22⋊C4C2×D1111yescharacteristic, complemented
409C2×#95—112no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—28no—
413C22×C11—42no—
414C22×C11—44no—
415C22×C11—44no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—44no—
419C22×C11—48no—
420C22×C11—48no—
421C22×C11—48no—
422C22×C11—816no—
423C22×C11C2×#12714yes—
424C22×C11C23×D411yescharacteristic
425C22×C11C23×D412yes—
426C22×C11C2×H(5,𝔽2)12yes—
427C22×C11#58512yes—
428C2×D11—22no—
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—28no—
433C2×D11—28no—
434C2×D11—416no—
435C2×D11—42no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—48no—
439C2×D11—816no—
440C2×D11C2×#12714yes—
441C2×D11C2×#12714yes—
442C4×C11—22no—
443C4×C11—28no—
444C4×C11—42no—
445C4×C11#53414yescomplemented
446Dic11—22no—
447Dic11—22no—
448Dic11—28no—
449Dic11—42no—
450Dic11—44no—
451C25—111no—
452C25—112no—
453C25C22×D1112yes—
454C22×D4—24no—
455C22×D4—44no—
456C22×D4—114no—
457C22×D4—112no—
458C22×D4—112no—
459C22×D4—114no—
460C22×D4—118no—
461C22×D4—112no—
462C22×D4—112no—
463C22×D4—111no—
464C22×D4—224no—
465C22×D4—228no—
466C22×D4—2216no—
467C22×D4—228no—
468C22×D4—2216no—
469C22×D4—444no—
470C22×D4C22×D1112yes—
471C22×D4C22×D1112yes—
472C22×D4C22×D1111yescharacteristic
473C22×D4C22×D1118yes—
474C22×D4C22×D1112yes—
475C23×C4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—118no—
479C23×C4—111no—
480C23×C4—114no—
481C23×C4—111no—
482C23×C4—112no—
483C23×C4—112no—
484C23×C4—444no—
485C23×C4C22×D1111yescharacteristic
486#127—44no—
487#127—444no—
488#123—2232no—
489#123—2216no—
490#123—2216no—
491#121—24no—
492#121—228no—
493#121—2232no—
494#121—224no—
495#121—228no—
496#121—224no—
497#121—228no—
498#121—228no—
499#121—228no—
500#121—228no—
501#121—2232no—
502#121—224no—
503#120—216no—
504#120—2232no—
505#120—2216no—
506C2×C4⋊C4—112no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—112no—
509C2×C4⋊C4—112no—
510C2×C4⋊C4—118no—
511C2×C4⋊C4—118no—
512C2×C4⋊C4—224no—
513C2×C4⋊C4—224no—
514C2×C4⋊C4C22×D1111yescharacteristic
515C2×C22⋊C4—112no—
516C2×C22⋊C4—114no—
517C2×C22⋊C4—1116no—
518C2×C22⋊C4—112no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—114no—
521C2×C22⋊C4—118no—
522C2×C22⋊C4—118no—
523C2×C22⋊C4—112no—
524C2×C22⋊C4—112no—
525C2×C22⋊C4—118no—
526C2×C22⋊C4—228no—
527C2×C22⋊C4—228no—
528C2×C22⋊C4C22×D1112yes—
529C2×C22⋊C4C22×D1118yes—
530C2×C22⋊C4C22×D1112yes—
531C2×C42—112no—
532C2×C42—114no—
533C2×C42—444no—
534C2×C42C22×D1112yes—
535#95—114no—
536#95—112no—
537#95C22×D1112yes—
538C2×C11—24no—
539C2×C11—82no—
540C2×C11—84no—
541C2×C11C22×#12711yescharacteristic
542C2×C11C2×#53411yescharacteristic
543C2×C11#344911yescharacteristic
544C2×C11#349614yes—
545D11—24no—
546D11—24no—
547D11—82no—
548C24—24no—
549C24—28no—
550C24—44no—
551C24—44no—
552C24—111no—
553C24—111no—
554C24—118no—
555C24—114no—
556C24—112no—
557C24—224no—
558C24—228no—
559C24—442no—
560C24—442no—
561C24—444no—
562C24—444no—
563C24C23×D1112yes—
564C24C23×D1114yes—
565C24C23×D1111yescharacteristic
566C2×D4—28no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—216no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—44no—
576C2×D4—416no—
577C2×D4—48no—
578C2×D4—48no—
579C2×D4—228no—
580C2×D4—224no—
581C2×D4—224no—
582C2×D4—2216no—
583C2×D4—2216no—
584C2×D4—224no—
585C2×D4—2216no—
586C2×D4—228no—
587C2×D4—228no—
588C2×D4—228no—
589C2×D4—228no—
590C2×D4—224no—
591C2×D4—222no—
592C2×D4—224no—
593C2×D4—4416no—
594C2×D4—444no—
595C2×D4—448no—
596C2×D4—448no—
597C2×D4—4432no—
598C2×D4—4432no—
599C22×C4—24no—
600C22×C4—111no—
601C22×C4—114no—
602C22×C4—111no—
603C22×C4—114no—
604C22×C4—114no—
605C22×C4—114no—
606C22×C4—1116no—
607C22×C4—114no—
608C22×C4—114no—
609C22×C4—114no—
610C22×C4—112no—
611C22×C4—224no—
612C22×C4—228no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4—228no—
617C22×C4—4416no—
618C22×C4—444no—
619C22×C4—442no—
620C22×C4—442no—
621C22×C4—444no—
622C22×C4—442no—
623C22×C4D4×D1114yes—
624C22×C4C23×D1112yes—
625C22×C4C23×D1111yescharacteristic
626C22×C4C23×D1114yes—
627C22×C4C23×D1111yescharacteristic
628C4⋊C4—22no—
629C4⋊C4—224no—
630C4⋊C4—2216no—
631C4⋊C4—224no—
632C4⋊C4—222no—
633C4⋊C4—224no—
634C4⋊C4—2216no—
635C22⋊C4—24no—
636C22⋊C4—216no—
637C22⋊C4—118no—
638C22⋊C4—1116no—
639C22⋊C4—224no—
640C22⋊C4—224no—
641C22⋊C4—228no—
642C22⋊C4—228no—
643C22⋊C4—2216no—
644C22⋊C4—2216no—
645C22⋊C4—224no—
646C22⋊C4—2216no—
647C22⋊C4D4×D1118yescomplemented
648C42—24no—
649C42—224no—
650C42—444no—
651C11#3500111yescharacteristic, complemented, Sylow
652C23—22no—
653C23—22no—
654C23—22no—
655C23—28no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—28no—
663C23—48no—
664C23—48no—
665C23—48no—
666C23—816no—
667C23—114no—
668C23—112no—
669C23—114no—
670C23—112no—
671C23—1116no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23—224no—
677C23—222no—
678C23—224no—
679C23—224no—
680C23—444no—
681C23—4416no—
682C23—444no—
683C23—448no—
684C23—448no—
685C23—448no—
686C23—8816no—
687C23C2×D4×D1114yes—
688C23C2×D4×D1112yes—
689C23C24×D1111yescharacteristic
690D4—48no—
691D4—48no—
692D4—48no—
693D4—44no—
694D4—816no—
695D4—448no—
696D4—448no—
697D4—448no—
698D4—4416no—
699D4—4416no—
700D4—448no—
701D4—444no—
702D4—8816no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—28no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—118no—
710C2×C4—112no—
711C2×C4—112no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—224no—
716C2×C4—228no—
717C2×C4—228no—
718C2×C4—224no—
719C2×C4—228no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—444no—
723C2×C4—444no—
724C2×C4—4416no—
725C2×C4—448no—
726C2×C4—444no—
727C2×C4—448no—
728C2×C4C2×D4×D1118yes—
729C2×C4C2×D4×D1112yes—
730C2×C4C2×D4×D1112yes—
731C2×C4#6703714yes—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—48no—
736C22—48no—
737C22—48no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—42no—
742C22—44no—
743C22—42no—
744C22—816no—
745C22—114no—
746C22—114no—
747C22—228no—
748C22—228no—
749C22—222no—
750C22—222no—
751C22—222no—
752C22—222no—
753C22—4416no—
754C22—448no—
755C22—442no—
756C22—442no—
757C22—442no—
758C22—8816no—
759C22D11×#12714yes—
760C22C22×D4×D1112yes—
761C22C22×D4×D1111yescharacteristic
762C22C2×#6703712yes—
763C22#1062345512yes—
764C4—28no—
765C4—22no—
766C4—42no—
767C4—228no—
768C4—222no—
769C4—222no—
770C4—442no—
771C4—444no—
772C4#1062312014yescomplemented
773C2—24no—
774C2—84no—
775C2—82no—
776C2—224no—
777C2—224no—
778C2—882no—
779C2C2×D11×#12711yescharacteristic
780C2C2×#1062312011yescharacteristic
781C2#1308194711yescharacteristic
782C2#1308237214yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2433C2
hypercenter#2433D11
hypocenterC11#35001
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2433

Complements

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

NH ≅ G/Ntype
1. C2×#10623120C2semidirect
2. C22×#66991C2semidirect
3. C2×D11×#121C2semidirect
4. #13076960C2semidirect
5. #13076958C2semidirect
6. #13074717C2semidirect
7. #13073544C2semidirect
8. #13073541C2semidirect
9. #13073088C2semidirect
10. #13073087C2semidirect
11. #13073086C2semidirect
12. #13072250C2semidirect
13. #13072249C2semidirect
14. C4×C22⋊C4×D11C2semidirect
15. C11×#2433C2semidirect
16. C23×D4×C11C22semidirect
19. C22×D4×D11C22semidirect
21. C2×C11×#127C22semidirect
23. C2×C11×#120C22semidirect
24. C2×#67006C22semidirect
25. C22×C22⋊Dic11C22semidirect
26. C2×#66993C22semidirect
31. C2×#66991C22semidirect
32. C2×#66991C22semidirect
33. C2×#66991C22semidirect
34. C2×#66991C22semidirect
35. C2×#66990C22semidirect
36. C2×#66988C22semidirect
38. C22×C4⋊Dic11C22semidirect
41. C2×#66948C22semidirect
42. C2×C4⋊C4×D11C22semidirect
43. C2×#66939C22semidirect
44. C2×#66937C22semidirect
45. C2×#66937C22semidirect
46. C2×#66936C22semidirect
48. C2×C22⋊C4×D11C22semidirect
49. C2×C42×D11C22semidirect
50. C11×#392C22semidirect
51. C11×#390C22semidirect
52. C4×C11×C22⋊C4C22semidirect
53. #10622836C22semidirect
54. #10622836C22semidirect
55. #10622834C22semidirect
56. #10622834C22semidirect
57. #10622834C22semidirect
58. C4×C22⋊Dic11C22semidirect
59. #10622589C22semidirect
60. #10622570C22semidirect
61. #10622562C22semidirect
62. #10622562C22semidirect
63. C22⋊C4×Dic11C22semidirect
64. #10622552C22semidirect
65. C4×(C2×D11)⋊C4C22semidirect
66. #10622548C22semidirect
67. #10622290C22semidirect
68. #10622279C22semidirect
69. D11×#95C22semidirect
98. C22×C4×D11D4semidirect
152. C22⋊C4×D11D4semidirect
237. C2×C4×D11C2×D4semidirect
241. C11×C22⋊C4C2×D4semidirect
248. C22⋊Dic11C2×D4semidirect
252. (C2×D11)⋊C4C2×D4semidirect
274. #2433D11semidirect
309. C22×D11#127semidirect
359. C23×D4C2×D11semidirect
363. C2×#127C2×D11semidirect
383. C2×#120C2×D11semidirect
395. #392C2×D11semidirect
401. #390C2×D11semidirect
408. C4×C22⋊C4C2×D11semidirect
445. C4×C11#534semidirect
647. C22⋊C4D4×D11semidirect
651. C11#35001semidirect
772. C4#10623120semidirect

Maximal subgroups

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

subgroupindex
C2×#106231202
C22×#669912
C2×D11×#1212
#130769602
#130769582
#130747172
#130735442
#130735412
#130730882
#130730872
#130730862
#130722502
#130722492
C4×C22⋊C4×D112
C11×#24332
#3500111