Finite Group Databasebeta

← #15630796

Subgroups — #15630796

Order 2816.

2088 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082174C211yesmaximal, characteristic
2#13080910C212yesmaximal, complemented
3#13080899C212yesmaximal, complemented
4#13080787C214yesmaximal, complemented
5#13080667C214yesmaximal, complemented
6#13080492C212yesmaximal, complemented
7#13080481C212yesmaximal, complemented
8#13078996C211yesmaximal, characteristic, complemented
9#13078560C212yesmaximal, complemented
10#13078421C211yesmaximal, characteristic, complemented
11#13078242C212yesmaximal, complemented
12#13078099C211yesmaximal, characteristic, complemented
13#13077850C212yesmaximal, complemented
14C4×#66995C211yesmaximal, characteristic, complemented
15D4×#4318C211yesmaximal, characteristic, complemented
16C2×#10622838C212yesmaximal, complemented
17C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
18C23×Q8×C11C2212yes—
19D4×Q8×C11—21no—
20D4×Q8×C11—22no—
21D4×Q8×C11—21no—
22D4×Q8×C11C2212yes—
23D4×Q8×C11C2214yes—
24D4×Q8×C11C2212yes—
25C2×C11×C4⋊Q8—21no—
26C2×C11×C4⋊Q8C2211yescharacteristic
27C2×C11×C22⋊Q8—22no—
28C2×C11×C22⋊Q8C2212yes—
29C2×C4×Q8×C11C2211yescharacteristic
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×#66995C2211yescharacteristic
33C2×#66995C2212yes—
34#10623337—21no—
35#10623322C2212yes—
36C2×#66979C2212yes—
37C22×#4318C2212yes—
38#10623096C2212yes—
39#10623094C2211yescharacteristic
40#10623088—21no—
41#10623086C2211yescharacteristic
42#10623074C2211yescharacteristic
43#10623073C2211yescharacteristic
44#10623072C2212yes—
45#10623069—22no—
46C4×#4341—21no—
47#10623044—21no—
48#10623026—22no—
49C4×#4339C2211yescharacteristic
50#10623001C2211yescharacteristic
51#10622841C2214yescomplemented
52#10622841C2214yescomplemented
53#10622840C2214yescomplemented
54#10622840C2214yescomplemented
55#10622838C2212yes—
56#10622838C2212yes—
57#10622838C2212yes—
58#10622838C2211yescharacteristic
59#10622838C2212yes—
60#10622838C2214yescomplemented
61#10622838C2214yescomplemented
62C2×#66899C2214yescomplemented
63C2×#66899C2214yescomplemented
64#10622820C2212yes—
65#10622703C2212yescomplemented
66#10622703C2212yescomplemented
67#10622696C2212yescomplemented
68#10622696C2212yescomplemented
69#10622695C2214yescomplemented
70#10622694C2212yescomplemented
71#10622694C2212yescomplemented
72#10622665C2214yescomplemented
73#10622664C2214yescomplemented
74#10622662C2214yescomplemented
75#10622661C2214yescomplemented
76#10622658C2214yescomplemented
77#10622658C2214yescomplemented
78#10622657C2214yescomplemented
79#10622656C2214yescomplemented
80#10622643C2212yescomplemented
81C4×#4326C2212yescomplemented
82#10622639C2212yescomplemented
83C4×#4325C2212yescomplemented
84#10622635C2214yescomplemented
85#10622634C2212yescomplemented
86#10622633C2212yescomplemented
87#10622625C2212yes—
88#10622624C2214yes—
89D4×C11⋊C8C2212yes—
90#10622579C2211yescharacteristic
91#10622577C2211yescharacteristic
92#10622577C2212yes—
93#10622537C2211yescharacteristic
94C4×#4318C2211yescharacteristic
95C22×Q8×C11—22no—
96C22×Q8×C11—22no—
97C22×Q8×C11—22no—
98C22×Q8×C11—28no—
99C22×Q8×C11—44no—
100C22×Q8×C11C2312yes—
101C22×Q8×C11C2314yes—
102C22×Q8×C11C2314yes—
103C22×Q8×C11C2311yescharacteristic
104C22×D4×C11D411yescharacteristic
105C23×C4×C11—22no—
106C23×C4×C11C2312yes—
107C2×#4341—21no—
108C2×#4339C2311yescharacteristic
109C11×C4⋊Q8—22no—
110C11×C4⋊Q8—24no—
111C11×C4⋊Q8—22no—
112C11×C4⋊Q8—21no—
113C11×C4⋊Q8—21no—
114C11×C4⋊Q8C2312yes—
115C11×C4⋊Q8C2312yes—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8—24no—
119C11×C22⋊Q8—24no—
120C11×C22⋊Q8—24no—
121C11×C22⋊Q8—24no—
122C11×C22⋊Q8C2314yes—
123C11×C22⋊Q8C2314yes—
124C4×Q8×C11—21no—
125C4×Q8×C11—21no—
126C4×Q8×C11C2312yes—
127C4×Q8×C11C2312yes—
128C4×D4×C11—24no—
129C4×D4×C11—22no—
130C4×D4×C11—22no—
131C4×D4×C11D411yescharacteristic
132C4×D4×C11D412yes—
133C4×D4×C11D411yescharacteristic
134C4×D4×C11C2312yes—
135C4×D4×C11C2311yescharacteristic
136C4×D4×C11C2311yescharacteristic
137C2×C11×C4⋊C4—21no—
138C2×C11×C4⋊C4—21no—
139C2×C11×C4⋊C4—21no—
140C2×C11×C4⋊C4—22no—
141C2×C11×C4⋊C4D411yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C22⋊C4—22no—
144C2×C11×C22⋊C4D412yes—
145C2×C42×C11—21no—
146C2×C42×C11C2311yescharacteristic
147#67006—22no—
148C2×C22⋊Dic11—22no—
149C2×#4326C2312yes—
150C2×#4326C2314yes—
151#66995—24no—
152#66995—44no—
153C2×#4325C2312yes—
154C2×#4325C2314yes—
155#66992—22no—
156#66991—21no—
157#66989—21no—
158#66988—22no—
159D4×Dic11—21no—
160#66983C2312yes—
161#66983C2312yes—
162#66982—22no—
163C4×C22⋊D11—21no—
164C4×C22⋊D11—21no—
165C4×C22⋊D11—22no—
166C4×C22⋊D11—22no—
167#66979—22no—
168#66979—22no—
169#66979C2312yes—
170#66979C2311yescharacteristic
171#66979C2312yes—
172#66979C2312yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2312yes—
175#66977—21no—
176#66977—21no—
177#66977C2312yes—
178#66977C2312yes—
179C2×C4×Dic11—22no—
180C2×#4318—44no—
181C2×#4318C2311yescharacteristic
182C2×#4318C2311yescharacteristic
183C2×#4318C2312yes—
184C2×#4318C2314yes—
185C22×C11⋊C8C2314yes—
186#66951—22no—
187#66950—21no—
188#66945—21no—
189#66943—21no—
190#66942—22no—
191#66940—21no—
192#66939—22no—
193#66938—22no—
194#66936—22no—
195(C22⋊D11)⋊C4—22no—
196#66932—22no—
197#66932—22no—
198#66931—22no—
199#66930—22no—
200C4×D44C2311yescharacteristic
201C4×D44C2311yescharacteristic
202#66925—21no—
203C42×D11—21no—
204#66923C2312yes—
205#66922C2311yescharacteristic
206#66922C2311yescharacteristic
207C4×Dic22—21no—
208C4×Dic22—21no—
209C4×Dic22C2311yescharacteristic
210C4×Dic22C2311yescharacteristic
211#66899C2312yes—
212#66899C2312yes—
213#66899C2314yes—
214#66899C2314yes—
215#66899C2314yes—
216#66899C2314yes—
217#66899C2314yes—
218#66899C2314yes—
219#66899C2314yes—
220#66899C2314yes—
221C22⋊(C11⋊C8)C2314yes—
222C22⋊(C11⋊C8)C2314yes—
223#66874C2312yes—
224#66873C2312yes—
225#66872C2314yes—
226#66872C2312yes—
227#66871C2314yes—
228#66871C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231#66867C2312yes—
232C4×C11⋊C8C2312yes—
233#61157—111nomaximal, Sylow
234C24×C11C2×D412yes—
235C2×Q8×C11—21no—
236C2×Q8×C11—24no—
237C2×Q8×C11—24no—
238C2×Q8×C11—22no—
239C2×Q8×C11—22no—
240C2×Q8×C11—28no—
241C2×Q8×C11—28no—
242C2×Q8×C11—24no—
243C2×Q8×C11—24no—
244C2×Q8×C11—48no—
245C2×Q8×C11—44no—
246C2×Q8×C11—44no—
247C2×Q8×C11—48no—
248C2×Q8×C11—48no—
249C2×Q8×C11#4114yescomplemented
250C2×Q8×C11C2414yes—
251C2×Q8×C11C2412yes—
252C2×D4×C11—24no—
253C2×D4×C11C2×D412yes—
254C2×D4×C11C2×D411yescharacteristic
255C2×D4×C11C2×D411yescharacteristic
256C22×C4×C11—21no—
257C22×C4×C11—24no—
258C22×C4×C11—24no—
259C22×C4×C11—21no—
260C22×C4×C11—22no—
261C22×C4×C11—24no—
262C22×C4×C11—24no—
263C22×C4×C11—48no—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D412yes—
267C22×C4×C11C2×D412yes—
268C22×C4×C11C2×D411yescharacteristic
269C22×C4×C11C2412yes—
270C22×C4×C11C2412yes—
271C22×C4×C11C2411yescharacteristic
272C2×C22⋊D11—22no—
273C2×C22⋊D11—21no—
274C2×C22⋊D11—22no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277#4341—44no—
278#4339—22no—
279#4339—22no—
280C2×D44C2411yescharacteristic
281C2×C4×D11—21no—
282C2×C4×D11—21no—
283C2×C4×D11—21no—
284C2×Dic22—21no—
285C2×Dic22—21no—
286C2×Dic22C2411yescharacteristic
287C11×C4⋊C4—22no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—22no—
291C11×C4⋊C4—22no—
292C11×C4⋊C4—22no—
293C11×C4⋊C4—24no—
294C11×C4⋊C4—24no—
295C11×C4⋊C4—21no—
296C11×C4⋊C4C2×D411yescharacteristic
297C11×C4⋊C4C2×D412yes—
298C11×C4⋊C4C2×D411yescharacteristic
299C11×C4⋊C4C2412yes—
300C11×C22⋊C4—24no—
301C11×C22⋊C4—24no—
302C11×C22⋊C4C2×D412yes—
303C11×C22⋊C4C2×D412yes—
304C11×C22⋊C4C2×D412yes—
305C11×C22⋊C4C2×D412yes—
306C42×C11—22no—
307C42×C11—22no—
308C42×C11C2×D411yescharacteristic
309C42×C11C2×D411yescharacteristic
310C42×C11C2411yescharacteristic
311C42×C11C2411yescharacteristic
312C22⋊Dic11—22no—
313C22⋊Dic11—22no—
314C22⋊Dic11—22no—
315C22⋊Dic11—22no—
316C22⋊Dic11—22no—
317C22⋊Dic11—21no—
318#4326—24no—
319#4326—44no—
320#4325—24no—
321#4325—44no—
322(C2×D11)⋊C4—21no—
323(C2×D11)⋊C4—21no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326C4⋊Dic11—21no—
327C4⋊Dic11—21no—
328C4⋊Dic11—22no—
329C4⋊Dic11—22no—
330C4⋊Dic11C2411yescharacteristic
331C4⋊Dic11C2412yes—
332C4⋊Dic11C2411yescharacteristic
333C4⋊Dic11C2412yes—
334Dic11⋊C4—22no—
335Dic11⋊C4—22no—
336Dic11⋊C4—21no—
337Dic11⋊C4—21no—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340C4×Dic11—22no—
341C4×Dic11—21no—
342C4×Dic11—21no—
343C4×Dic11—21no—
344C4×Dic11—22no—
345C4×Dic11—22no—
346#4318—22no—
347#4318—22no—
348#4318—24no—
349#4318—44no—
350C2×C11⋊C8—44no—
351C2×C11⋊C8C2412yes—
352C2×C11⋊C8C2412yes—
353C2×C11⋊C8C2414yes—
354#3475—111no—
355C2×D4×Q8D1111yescharacteristic, complemented
356#3329—112no—
357#3328—112no—
358#3320—114no—
359#3312—114no—
360#3299—112no—
361#3298—112no—
362#3139—111no—
363#3095—112no—
364#3078—111no—
365#3056—112no—
366#3039—111no—
367#3004—112no—
368C4×#137—111no—
369D4×M16—111no—
370C2×#419—112no—
371C23×C11—24no—
372C23×C11—24no—
373C23×C11—42no—
374C23×C11C22×D412yes—
375C23×C11C22×D411yescharacteristic
376C23×C11C22×D412yes—
377C22×D11—21no—
378Q8×C11—24no—
379Q8×C11—22no—
380Q8×C11—24no—
381Q8×C11—24no—
382Q8×C11—48no—
383Q8×C11—48no—
384Q8×C11—44no—
385Q8×C11C2×#4114yes—
386D4×C11—24no—
387D4×C11—22no—
388D4×C11#13714yescomplemented
389C2×C4×C11—24no—
390C2×C4×C11—24no—
391C2×C4×C11—22no—
392C2×C4×C11—24no—
393C2×C4×C11—24no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—22no—
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—24no—
401C2×C4×C11—41no—
402C2×C4×C11—48no—
403C2×C4×C11—48no—
404C2×C4×C11—42no—
405C2×C4×C11—44no—
406C2×C4×C11C22×D412yes—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D412yes—
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D411yescharacteristic
413C2×C4×C11C2×#4112yes—
414C2×C4×C11H(5,𝔽2)12yes—
415C2×C4×C11C2511yescharacteristic
416C22⋊D11—42no—
417C22⋊D11—44no—
418C22⋊D11—82no—
419C2×Dic11—21no—
420C2×Dic11—21no—
421C2×Dic11—21no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—44no—
425C2×Dic11—82no—
426D44—21no—
427D44—21no—
428C4×D11—42no—
429C4×D11—42no—
430C4×D11—81no—
431Dic22—21no—
432Dic22—21no—
433Dic22—42no—
434Dic22—81no—
435C11⋊C8—22no—
436C11⋊C8—22no—
437C11⋊C8—24no—
438C23×Q8C2×D1112yes—
439C2×#137—111no—
440C2×#137—112no—
441C22×M16—112no—
442#556—111no—
443#555—111no—
444#554—111no—
445#553—112no—
446#552—112no—
447#552—221no—
448#551—222no—
449D4×Q8—21no—
450D4×Q8—22no—
451D4×Q8—21no—
452D4×Q8C2×D1112yes—
453D4×Q8C2×D1112yes—
454D4×Q8C2×D1114yes—
455#547—111no—
456#546—221no—
457#533—111no—
458C2×C4⋊Q8—21no—
459C2×C4⋊Q8C2×D1111yescharacteristic
460#529—222no—
461#529—221no—
462#525—112no—
463C2×C22⋊Q8—22no—
464C2×C22⋊Q8C2×D1112yes—
465C4×#41—111no—
466C4×#41—221no—
467C2×C4×Q8C2×D1111yescharacteristic
468C2×C4×D4—21no—
469C2×C4×D4C2×D1111yescharacteristic
470C2×#117—112no—
471#491—114no—
472#487—112no—
473#487—112no—
474#485—114no—
475#485—114no—
476#484—114no—
477#483—114no—
478#479—114no—
479#477—112no—
480#475—112no—
481#470—114no—
482#468—114no—
483#467—114no—
484#465—114no—
485#462—112no—
486#462—112no—
487#461—112no—
488#461—112no—
489#451—114no—
490#451—114no—
491#448—114no—
492#448—114no—
493#441—112no—
494#440—112no—
495C4×Q16—112no—
496C4×SD16—112no—
497#436—112no—
498#435—114no—
499C8×D4—112no—
500#428—112no—
501#428—111no—
502#423—111no—
503#419—114no—
504#419—114no—
505#419—112no—
506#419—112no—
507#419—112no—
508#419—112no—
509#419—111no—
510#417—111no—
511C2×#103—114no—
512C2×#103—114no—
513#407—112no—
514C4×M16—111no—
515C22×C11—21no—
516C22×C11—22no—
517C22×C11—22no—
518C22×C11—21no—
519C22×C11—22no—
520C22×C11—22no—
521C22×C11—22no—
522C22×C11—48no—
523C22×C11#54612yes—
524C22×C11C2×#13714yes—
525C22×C11C23×D411yescharacteristic
526C2×D11—41no—
527C2×D11—41no—
528C2×D11—41no—
529C4×C11—21no—
530C4×C11—21no—
531C4×C11—22no—
532C4×C11—22no—
533C4×C11—24no—
534C4×C11—21no—
535C4×C11—42no—
536C4×C11—44no—
537C4×C11#54612yes—
538C4×C11C2×#13712yes—
539C4×C11C22×#4111yescharacteristic
540C4×C11C2×H(5,𝔽2)11yescharacteristic
541Dic11—42no—
542Dic11—41no—
543Dic11—41no—
544Dic11—42no—
545Dic11—41no—
546C2×#41—111no—
547C2×#41—221no—
548C22×Q8—22no—
549C22×Q8—22no—
550C22×Q8—22no—
551C22×Q8—28no—
552C22×Q8—44no—
553C22×Q8C22×D1112yes—
554C22×Q8C22×D1114yes—
555C22×Q8C22×D1114yes—
556C22×Q8C22×D1111yescharacteristic
557C22×D4C22⋊D1111yescharacteristic
558C23×C4—22no—
559C23×C4C22×D1112yes—
560#137—224no—
561#137—444no—
562C2×Q16—112no—
563C2×Q16—114no—
564C2×SD16—112no—
565C2×SD16—114no—
566C2×M16—111no—
567C2×M16—112no—
568C2×M16—111no—
569C2×M16—114no—
570C2×M16—444no—
571C22×C8—114no—
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—24no—
575C4⋊Q8—21no—
576C4⋊Q8—21no—
577C4⋊Q8—111no—
578C4⋊Q8—111no—
579C4⋊Q8C22×D1112yes—
580C4⋊Q8C22×D1112yes—
581#126—222no—
582#126—222no—
583#126—222no—
584#125—112no—
585#125—222no—
586#125—221no—
587#124—221no—
588#124—222no—
589#123—222no—
590#123—222no—
591#123—222no—
592#123—222no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—24no—
596C22⋊Q8—24no—
597C22⋊Q8—24no—
598C22⋊Q8—24no—
599C22⋊Q8—112no—
600C22⋊Q8—112no—
601C22⋊Q8—221no—
602C22⋊Q8—221no—
603C22⋊Q8—221no—
604C22⋊Q8—222no—
605C22⋊Q8C22×D1114yes—
606C22⋊Q8C22×D1114yes—
607#121—112no—
608#121—112no—
609#121—222no—
610#121—221no—
611#120—222no—
612C4×Q8—21no—
613C4×Q8—21no—
614C4×Q8—111no—
615C4×Q8—111no—
616C4×Q8—221no—
617C4×Q8—221no—
618C4×Q8—221no—
619C4×Q8C22×D1112yes—
620C4×Q8C22×D1112yes—
621C4×D4—24no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4—111no—
625C4×D4—111no—
626C4×D4—221no—
627C4×D4—221no—
628C4×D4—221no—
629C4×D4—222no—
630C4×D4—222no—
631C4×D4—222no—
632C4×D4C22⋊D1111yescharacteristic
633C4×D4C22⋊D1111yescharacteristic
634C4×D4C22⋊D1112yes—
635C4×D4C22×D1111yescharacteristic
636C4×D4C22×D1112yes—
637C4×D4C22×D1111yescharacteristic
638#117—111no—
639#117—112no—
640#117—112no—
641#117—112no—
642#117—222no—
643#117—222no—
644#117—221no—
645#117—222no—
646#117—221no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—112no—
652C2×C4⋊C4—112no—
653C2×C4⋊C4C22⋊D1111yescharacteristic
654C2×C4⋊C4C22×D1111yescharacteristic
655C2×C22⋊C4—22no—
656C2×C22⋊C4—222no—
657C2×C22⋊C4C22⋊D1112yes—
658C2×C42—21no—
659C2×C42—222no—
660C2×C42—221no—
661C2×C42C22×D1111yescharacteristic
662#107—112no—
663#107—114no—
664#106—112no—
665#106—114no—
666C4⋊C8—112no—
667C4⋊C8—112no—
668#103—112no—
669#103—112no—
670#103—114no—
671#103—114no—
672#103—114no—
673#103—114no—
674#103—114no—
675#103—114no—
676#103—114no—
677#103—114no—
678#103—112no—
679#102—112no—
680C22⋊C8—114no—
681C22⋊C8—114no—
682#97—112no—
683C4×C8—112no—
684C2×C11—22no—
685C2×C11—24no—
686C2×C11—42no—
687C2×C11C2×#54611yescharacteristic
688C2×C11C22×#13711yescharacteristic
689C2×C11#358611yescharacteristic
690D11—81no—
691C24C2×C22⋊D1112yes—
692#41—222no—
693#41—222no—
694#41—444no—
695C2×Q8—22no—
696C2×Q8—21no—
697C2×Q8—24no—
698C2×Q8—24no—
699C2×Q8—22no—
700C2×Q8—28no—
701C2×Q8—28no—
702C2×Q8—24no—
703C2×Q8—24no—
704C2×Q8—48no—
705C2×Q8—44no—
706C2×Q8—44no—
707C2×Q8—48no—
708C2×Q8—48no—
709C2×Q8—111no—
710C2×Q8—221no—
711C2×Q8—221no—
712C2×Q8#434114yescomplemented
713C2×Q8C23×D1114yes—
714C2×Q8C23×D1112yes—
715C2×D4—24no—
716C2×D4—111no—
717C2×D4—221no—
718C2×D4—222no—
719C2×D4—222no—
720C2×D4C2×C22⋊D1112yes—
721C2×D4C2×C22⋊D1111yescharacteristic
722C2×D4C2×C22⋊D1111yescharacteristic
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—48no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4C2×C22⋊D1111yescharacteristic
737C22×C4C2×C22⋊D1112yes—
738C22×C4C2×C22⋊D1112yes—
739C22×C4C2×C22⋊D1112yes—
740C22×C4C2×C22⋊D1111yescharacteristic
741C22×C4C23×D1112yes—
742C22×C4C23×D1112yes—
743C22×C4C23×D1111yescharacteristic
744Q16—224no—
745Q16—444no—
746SD16—224no—
747SD16—444no—
748M16—222no—
749M16—222no—
750M16—224no—
751M16—444no—
752C2×C8—112no—
753C2×C8—112no—
754C2×C8—114no—
755C2×C8—444no—
756C4⋊C4—22no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—22no—
760C4⋊C4—22no—
761C4⋊C4—22no—
762C4⋊C4—24no—
763C4⋊C4—24no—
764C4⋊C4—21no—
765C4⋊C4—111no—
766C4⋊C4—112no—
767C4⋊C4—111no—
768C4⋊C4—112no—
769C4⋊C4—222no—
770C4⋊C4—222no—
771C4⋊C4—221no—
772C4⋊C4—221no—
773C4⋊C4—221no—
774C4⋊C4—222no—
775C4⋊C4—222no—
776C4⋊C4—222no—
777C4⋊C4—222no—
778C4⋊C4—221no—
779C4⋊C4C2×C22⋊D1111yescharacteristic
780C4⋊C4C2×C22⋊D1111yescharacteristic
781C4⋊C4C2×C22⋊D1112yes—
782C4⋊C4C23×D1112yes—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—221no—
786C22⋊C4—222no—
787C22⋊C4—222no—
788C22⋊C4—222no—
789C22⋊C4—222no—
790C22⋊C4—222no—
791C22⋊C4—221no—
792C22⋊C4—221no—
793C22⋊C4—222no—
794C22⋊C4—222no—
795C22⋊C4C2×C22⋊D1112yes—
796C22⋊C4C2×C22⋊D1112yes—
797C22⋊C4C2×C22⋊D1112yes—
798C22⋊C4C2×C22⋊D1112yes—
799C42—22no—
800C42—22no—
801C42—221no—
802C42—222no—
803C42—222no—
804C42—222no—
805C42—221no—
806C42—221no—
807C42C2×C22⋊D1111yescharacteristic
808C42C2×C22⋊D1111yescharacteristic
809C42C23×D1111yescharacteristic
810C42C23×D1111yescharacteristic
811C11#6115711yescharacteristic, complemented, Sylow
812C23—24no—
813C23—24no—
814C23—42no—
815C23—221no—
816C23C22×C22⋊D1112yes—
817C23C22×C22⋊D1111yescharacteristic
818C23C22×C22⋊D1112yes—
819Q8—24no—
820Q8—22no—
821Q8—24no—
822Q8—24no—
823Q8—48no—
824Q8—48no—
825Q8—44no—
826Q8—221no—
827Q8—221no—
828Q8—442no—
829Q8—881no—
830Q8C2×#434114yes—
831D4—24no—
832D4—22no—
833D4—221no—
834D4—221no—
835D4—442no—
836D4—444no—
837D4—882no—
838D4#6699514yescomplemented
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—22no—
842C2×C4—24no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—24no—
851C2×C4—41no—
852C2×C4—48no—
853C2×C4—48no—
854C2×C4—42no—
855C2×C4—44no—
856C2×C4—221no—
857C2×C4—221no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—221no—
861C2×C4—444no—
862C2×C4—442no—
863C2×C4—442no—
864C2×C4—881no—
865C2×C4—882no—
866C2×C4C2×#434112yes—
867C2×C4#6703712yes—
868C2×C4C22×C22⋊D1111yescharacteristic
869C2×C4C22×C22⋊D1112yes—
870C2×C4C22×C22⋊D1111yescharacteristic
871C2×C4C22×C22⋊D1111yescharacteristic
872C2×C4C22×C22⋊D1112yes—
873C2×C4C22×C22⋊D1111yescharacteristic
874C2×C4C22×C22⋊D1111yescharacteristic
875C2×C4C24×D1111yescharacteristic
876C8—222no—
877C8—222no—
878C8—224no—
879C22—21no—
880C22—22no—
881C22—22no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—48no—
887C22—441no—
888C22—441no—
889C22—441no—
890C22#1062333712yes—
891C22C2×#6699514yes—
892C22C23×C22⋊D1111yescharacteristic
893C4—21no—
894C4—21no—
895C4—22no—
896C4—22no—
897C4—24no—
898C4—21no—
899C4—42no—
900C4—44no—
901C4—441no—
902C4—442no—
903C4—441no—
904C4—441no—
905C4—442no—
906C4#1062333712yes—
907C4C2×#6699512yes—
908C4C22×#434111yescharacteristic
909C4C2×#6703711yescharacteristic
910C2—22no—
911C2—24no—
912C2—42no—
913C2—881no—
914C2C2×#1062333711yescharacteristic
915C2C22×#6699511yescharacteristic
916C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D4×Q8×C11C2
socleC22×C11C23×D4
prime radical#13082174C2
hypercenterC2×D4×Q8D11
hypocenterC11#61157
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #13080910C2semidirect
3. #13080899C2semidirect
4. #13080787C2semidirect
5. #13080667C2semidirect
6. #13080492C2semidirect
7. #13080481C2semidirect
8. #13078996C2semidirect
9. #13078560C2semidirect
10. #13078421C2semidirect
11. #13078242C2semidirect
12. #13078099C2semidirect
13. #13077850C2semidirect
14. C4×#66995C2semidirect
15. D4×#4318C2semidirect
16. C2×#10622838C2semidirect
17. C2×D4×Q8×C11C2semidirect
51. #10622841C22semidirect
52. #10622841C22semidirect
53. #10622840C22semidirect
54. #10622840C22semidirect
60. #10622838C22semidirect
61. #10622838C22semidirect
62. C2×#66899C22semidirect
63. C2×#66899C22semidirect
65. #10622703C22semidirect
66. #10622703C22semidirect
67. #10622696C22semidirect
68. #10622696C22semidirect
69. #10622695C22semidirect
70. #10622694C22semidirect
71. #10622694C22semidirect
72. #10622665C22semidirect
73. #10622664C22semidirect
74. #10622662C22semidirect
75. #10622661C22semidirect
76. #10622658C22semidirect
77. #10622658C22semidirect
78. #10622657C22semidirect
79. #10622656C22semidirect
80. #10622643C22semidirect
81. C4×#4326C22semidirect
82. #10622639C22semidirect
83. C4×#4325C22semidirect
84. #10622635C22semidirect
85. #10622634C22semidirect
86. #10622633C22semidirect
249. C2×Q8×C11#41semidirect
355. C2×D4×Q8D11semidirect
388. D4×C11#137semidirect
712. C2×Q8#4341semidirect
811. C11#61157semidirect
838. D4#66995semidirect

Maximal subgroups

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

subgroupindex
#130821742
#130809102
#130808992
#130807872
#130806672
#130804922
#130804812
#130789962
#130785602
#130784212
#130782422
#130780992
#130778502
C4×#669952
D4×#43182
C2×#106228382
C2×D4×Q8×C112
#6115711