Finite Group Databasebeta

← #15639701

Subgroups — #15639701

Order 2816.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082843C211yesmaximal, characteristic, complemented
2#13080954C212yesmaximal, complemented
3#13080697C212yesmaximal, complemented
4#13080607C212yesmaximal, complemented
5#13080429C212yesmaximal, complemented
6#13080353C212yesmaximal, complemented
7#13080223C212yesmaximal, complemented
8#13080157C212yesmaximal, complemented
9#13080107C212yesmaximal, complemented
10#13079710C212yesmaximal, complemented
11#13079513C212yesmaximal, complemented
12#13079422C211yesmaximal, characteristic, complemented
13#13079364C211yesmaximal, characteristic, complemented
14#13078878C212yesmaximal, complemented
15#13077920C212yesmaximal, complemented
16#13077868C211yesmaximal, characteristic, complemented
17C2×#10622852C211yesmaximal, characteristic, complemented
18#13077664C211yesmaximal, characteristic, complemented
19C11×#3488C211yesmaximal, characteristic, complemented
20C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
21C22×C11×#41C2211yescharacteristic
22C11×#550C2212yes—
23C11×#548C2212yescomplemented
24C11×#546—22no—
25C11×#546C2212yes—
26D42×C11—22no—
27D42×C11C2212yescomplemented
28C11×#537—21no—
29C11×#537C2211yescharacteristic, complemented
30C11×#535—21no—
31C11×#535C2211yescharacteristic, complemented
32C11×#525—21no—
33C11×#525C2211yescharacteristic
34C2×C11×#121—21no—
35C2×C11×#121C2211yescharacteristic
36C11×#520C2211yescharacteristic, complemented
37#10623364C2212yescomplemented
38C2×#67003C2212yescomplemented
39C2×#67002C2211yescharacteristic, complemented
40C2×#67002C2211yescharacteristic, complemented
41C22×#4326C2211yescharacteristic, complemented
42C22×#4324C2211yescharacteristic, complemented
43C2×#66985C2212yescomplemented
44C2×#66983C2211yescharacteristic, complemented
45C2×#66977C2211yescharacteristic, complemented
46#10623198—22no—
47#10623176—21no—
48#10623165—21no—
49#10623148—21no—
50#10623128—21no—
51#10623122—22no—
52#10623086C2212yescomplemented
53#10623083C2212yescomplemented
54#10623081C2212yescomplemented
55#10623074C2212yescomplemented
56#10623065C2212yescomplemented
57#10622852C2212yescomplemented
58#10622852C2212yescomplemented
59#10622852C2212yescomplemented
60#10622852C2212yescomplemented
61#10622852C2212yescomplemented
62#10622851C2212yes—
63#10622851C2212yescomplemented
64#10622851C2212yescomplemented
65#10622847C2212yescomplemented
66#10622845C2212yescomplemented
67#10622845C2211yescharacteristic, complemented
68#10622845C2211yescharacteristic, complemented
69#10622840C2212yescomplemented
70C2×#66899C2211yescharacteristic, complemented
71#10622831C2212yescomplemented
72#10622831C2212yescomplemented
73#10622830C2212yescomplemented
74#10622830C2212yescomplemented
75#10622830C2212yescomplemented
76C2×#66896C2211yescharacteristic, complemented
77C2×#66896C2212yescomplemented
78#10622820C2211yescharacteristic, complemented
79C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
80#10622688C2212yescomplemented
81#10622687C2212yescomplemented
82#10622685C2212yescomplemented
83#10622683C2212yescomplemented
84#10622672C2212yescomplemented
85#10622670C2212yescomplemented
86#10622668C2212yescomplemented
87#10622667C2212yescomplemented
88#10622664C2212yescomplemented
89#10622662C2212yescomplemented
90#10622660C2212yescomplemented
91#10622657C2212yescomplemented
92#10622655C2212yescomplemented
93#10622655C2212yescomplemented
94#10622655C2212yescomplemented
95#10622653C2212yescomplemented
96#10622651C2212yescomplemented
97#10622651C2212yescomplemented
98#10622651C2212yescomplemented
99#10622650C2212yescomplemented
100#10622649C2212yescomplemented
101#10622646C2212yescomplemented
102#10622646C2212yescomplemented
103#10622646C2212yescomplemented
104C4×#4326C2212yescomplemented
105#10622641C2212yescomplemented
106#10622639C2212yescomplemented
107#10622634C2212yescomplemented
108#10622631C2212yescomplemented
109#10622629C2212yescomplemented
110C4×#4323C2212yescomplemented
111#10622625C2212yescomplemented
112#10622624C2212yescomplemented
113#10622624C2212yescomplemented
114D4×C11⋊C8C2212yescomplemented
115#10622620C2212yescomplemented
116#10622613C2212yescomplemented
117#10622583C2212yescomplemented
118#10622580C2212yescomplemented
119C11×H(5,𝔽2)—42no—
120C11×H(5,𝔽2)—42no—
121C2×C11×#41—21no—
122C2×C11×#41—21no—
123C2×C11×#41—21no—
124C2×C11×#41—42no—
125C2×C11×#41—42no—
126C2×C11×#41C2311yescharacteristic
127C2×C11×#41C2311yescharacteristic
128C2×C11×#41C2311yescharacteristic
129C2×C11×#41C2312yes—
130C2×C11×#41C2311yescharacteristic
131C2×C11×#41C2311yescharacteristic
132C22×Q8×C11C2311yescharacteristic
133C22×D4×C11—21no—
134C22×D4×C11—21no—
135C22×D4×C11—21no—
136C22×D4×C11—22no—
137C22×D4×C11—22no—
138C22×D4×C11C2312yes—
139C22×D4×C11C2311yescharacteristic
140C22×D4×C11C2311yescharacteristic
141C23×C4×C11—21no—
142C23×C4×C11C2311yescharacteristic
143C22×C22⋊D11—21no—
144C2×#4341—22no—
145C2×#4339C2312yes—
146C22×D44C2311yescharacteristic
147C22×Dic22C2311yescharacteristic
148C11×#127—22no—
149C11×#127C2312yes—
150C11×#124—22no—
151C11×#124C2312yes—
152C11×#123—22no—
153C11×#123D412yes—
154C11×C22⋊Q8—21no—
155C11×C22⋊Q8—22no—
156C11×C22⋊Q8D411yescharacteristic
157C11×C22⋊Q8D411yescharacteristic
158C11×C22⋊Q8C2312yes—
159C11×#121—21no—
160C11×#121—22no—
161C11×#121—22no—
162C11×#121—21no—
163C11×#121—21no—
164C11×#121—21no—
165C11×#121—21no—
166C11×#121—22no—
167C11×#121—22no—
168C11×#121—22no—
169C11×#121—22no—
170C11×#121D411yescharacteristic
171C11×#121D411yescharacteristic
172C11×#121C2312yes—
173C11×#121C2312yes—
174C11×#121C2312yes—
175C11×#120—22no—
176C11×#120—22no—
177C11×#120—22no—
178C11×#120—22no—
179C11×#120D412yes—
180C4×Q8×C11C2312yes—
181C4×D4×C11—22no—
182C4×D4×C11—22no—
183C4×D4×C11—22no—
184C4×D4×C11C2312yes—
185C4×D4×C11C2312yes—
186C4×D4×C11C2312yes—
187C11×#117—21no—
188C11×#117C2311yescharacteristic
189C2×C11×C4⋊C4—21no—
190C2×C11×C4⋊C4C2311yescharacteristic
191C2×C11×C22⋊C4—21no—
192C2×C11×C22⋊C4—22no—
193C2×C22⋊Dic11—21no—
194#67003—44no—
195#67002—42no—
196#67002—42no—
197#66999—22no—
198C2×#4326—42no—
199C2×#4326C2312yes—
200C2×#4326C2312yes—
201C2×#4325C2312yes—
202C2×#4325C2312yes—
203#66992—22no—
204#66992—22no—
205#66992—22no—
206#66991—22no—
207#66990—22no—
208D4×Dic11—22no—
209C2×#4324—42no—
210C2×#4324C2312yes—
211C2×#4324C2312yes—
212C2×#4324C2312yes—
213C2×#4324C2312yes—
214#66985—44no—
215C2×#4323C2312yes—
216C2×#4323C2312yes—
217C2×#4323C2312yes—
218C2×#4323C2312yes—
219#66983—21no—
220#66983—21no—
221#66983C2312yes—
222#66983C2312yes—
223#66983C2312yes—
224C2×(C2×D11)⋊C4—21no—
225C2×C4⋊Dic11C2311yescharacteristic
226C2×C4⋊Dic11C2311yescharacteristic
227C2×C4⋊Dic11C2312yes—
228#66977—21no—
229#66977—21no—
230#66977C2312yes—
231#66977C2312yes—
232#66977C2312yes—
233C2×Dic11⋊C4—21no—
234C2×#4318C2312yes—
235C2×#4318C2311yescharacteristic
236C2×#4318C2311yescharacteristic
237C22×C11⋊C8C2311yescharacteristic
238C22×C11⋊C8C2311yescharacteristic
239C22×C11⋊C8C2312yes—
240#66951—22no—
241#66950—22no—
242#66949—22no—
243#66949—22no—
244#66947—22no—
245#66943—22no—
246#66939—22no—
247#66939—22no—
248#66938—22no—
249#66938—22no—
250#66937—22no—
251#66936—22no—
252(C22⋊D11)⋊C4—22no—
253C22⋊C4×D11—22no—
254#66931—22no—
255#66931—22no—
256#66928C2312yes—
257C4×D44C2312yes—
258#66922C2312yes—
259C4×Dic22C2312yes—
260#66899C2312yes—
261#66899C2312yes—
262#66899C2312yes—
263#66899C2312yes—
264#66896C2312yes—
265#66896C2312yes—
266#66896C2312yes—
267#66896C2312yes—
268#66896C2312yes—
269#66896C2312yes—
270#66896C2312yes—
271#66896C2312yes—
272C22⋊(C11⋊C8)C2312yes—
273C22⋊(C11⋊C8)C2312yes—
274C22⋊(C11⋊C8)C2312yes—
275C22⋊(C11⋊C8)C2312yes—
276C22⋊(C11⋊C8)C2312yes—
277C22⋊(C11⋊C8)C2312yes—
278#66874C2312yes—
279#66874C2312yes—
280#66873C2312yes—
281#66873C2312yes—
282#66871C2312yes—
283#66871C2312yes—
284#66871C2312yes—
285#66871C2312yes—
286C4⋊(C11⋊C8)C2312yes—
287C4⋊(C11⋊C8)C2312yes—
288#66867C2312yes—
289C4×C11⋊C8C2312yes—
290#61624—111nomaximal, Sylow
291C24×C11—21no—
292C24×C11—22no—
293C24×C11—21no—
294C24×C11C2×D411yescharacteristic
295C23×D11—21no—
296C11×#41—22no—
297C11×#41—22no—
298C11×#41—22no—
299C11×#41—24no—
300C11×#41—22no—
301C11×#41—41no—
302C11×#41—41no—
303C11×#41—41no—
304C11×#41—41no—
305C11×#41—41no—
306C11×#41—41no—
307C11×#41—42no—
308C11×#41—44no—
309C11×#41—44no—
310C11×#41—44no—
311C2×Q8×C11—21no—
312C2×Q8×C11—22no—
313C2×Q8×C11—41no—
314C2×Q8×C11C2×D411yescharacteristic
315C2×Q8×C11C2411yescharacteristic
316C2×Q8×C11C2411yescharacteristic
317C2×D4×C11—21no—
318C2×D4×C11—24no—
319C2×D4×C11—22no—
320C2×D4×C11—22no—
321C2×D4×C11—21no—
322C2×D4×C11—21no—
323C2×D4×C11—22no—
324C2×D4×C11—21no—
325C2×D4×C11—22no—
326C2×D4×C11—22no—
327C2×D4×C11—21no—
328C2×D4×C11—22no—
329C2×D4×C11—21no—
330C2×D4×C11—22no—
331C2×D4×C11—22no—
332C2×D4×C11—41no—
333C2×D4×C11—42no—
334C2×D4×C11—41no—
335C2×D4×C11—41no—
336C2×D4×C11—44no—
337C2×D4×C11—44no—
338C2×D4×C11—48no—
339C2×D4×C11—84no—
340C2×D4×C11—82no—
341C2×D4×C11C2×D412yes—
342C2×D4×C11C2×D412yes—
343C2×D4×C11C2×D412yes—
344C2×D4×C11C2×D411yescharacteristic
345C2×D4×C11C2412yes—
346C2×D4×C11C2411yescharacteristic
347C2×D4×C11C2411yescharacteristic
348C22×C4×C11—21no—
349C22×C4×C11—21no—
350C22×C4×C11—21no—
351C22×C4×C11—21no—
352C22×C4×C11—21no—
353C22×C4×C11—22no—
354C22×C4×C11—21no—
355C22×C4×C11—22no—
356C22×C4×C11—41no—
357C22×C4×C11—41no—
358C22×C4×C11—44no—
359C22×C4×C11C2×D411yescharacteristic
360C22×C4×C11C2×D411yescharacteristic
361C22×C4×C11C2×D411yescharacteristic
362C22×C4×C11C2411yescharacteristic
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2412yes—
365C22×C4×C11C2411yescharacteristic
366C2×C22⋊D11—22no—
367C2×C22⋊D11—22no—
368C2×C22⋊D11—22no—
369C2×C22⋊D11—22no—
370C2×C22⋊D11—82no—
371C22×Dic11—21no—
372C22×Dic11—21no—
373C22×Dic11—22no—
374C22×Dic11—21no—
375#4341—84no—
376#4339—42no—
377#4339—42no—
378C2×D44—21no—
379C2×D44—41no—
380C2×D44—41no—
381C2×D44C2412yes—
382C2×C4×D11—22no—
383C2×C4×D11—22no—
384C2×Dic22—22no—
385C2×Dic22—21no—
386C2×Dic22—41no—
387C2×Dic22—41no—
388C2×Dic22C2412yes—
389C11×C4⋊C4—21no—
390C11×C4⋊C4—22no—
391C11×C4⋊C4—22no—
392C11×C4⋊C4C2×D412yes—
393C11×C4⋊C4C2×D411yescharacteristic
394C11×C4⋊C4C2×D412yes—
395C11×C4⋊C4C2×D411yescharacteristic
396C11×C4⋊C4C2412yes—
397C11×C22⋊C4—22no—
398C11×C22⋊C4—22no—
399C11×C22⋊C4—22no—
400C11×C22⋊C4—22no—
401C11×C22⋊C4—22no—
402C11×C22⋊C4—22no—
403C11×C22⋊C4—22no—
404C11×C22⋊C4C2×D412yes—
405C11×C22⋊C4C2×D412yes—
406C11×C22⋊C4C2×D412yes—
407C11×C22⋊C4C2×D412yes—
408C11×C22⋊C4C2×D412yes—
409C42×C11—22no—
410C42×C11C2412yes—
411C22⋊Dic11—22no—
412C22⋊Dic11—22no—
413C22⋊Dic11—22no—
414#4326—24no—
415#4326—42no—
416#4325—24no—
417#4325—42no—
418#4324—24no—
419#4324—42no—
420#4324—42no—
421#4324—42no—
422#4323—24no—
423#4323—42no—
424#4323—42no—
425#4323—42no—
426(C2×D11)⋊C4—22no—
427(C2×D11)⋊C4—22no—
428(C2×D11)⋊C4—22no—
429(C2×D11)⋊C4—22no—
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432C4⋊Dic11—22no—
433C4⋊Dic11—21no—
434C4⋊Dic11—22no—
435C4⋊Dic11—21no—
436C4⋊Dic11C2412yes—
437C4⋊Dic11C2412yes—
438Dic11⋊C4—22no—
439Dic11⋊C4—22no—
440Dic11⋊C4—22no—
441Dic11⋊C4—22no—
442C4×Dic11—22no—
443#4318—42no—
444#4318—41no—
445#4318—41no—
446C2×C11⋊C8—41no—
447C2×C11⋊C8—41no—
448C2×C11⋊C8—42no—
449C2×C11⋊C8C2412yes—
450C2×C11⋊C8C2412yes—
451C2×C11⋊C8C2412yes—
452C2×C11⋊C8C2412yes—
453#3536—111no—
454#3488D1111yescharacteristic, complemented
455#3333—112no—
456#3314—112no—
457#3308—112no—
458#3294—112no—
459#3285—112no—
460#3273—112no—
461#3268—112no—
462#3265—112no—
463#3224—112no—
464#3203—112no—
465#3193—111no—
466#3186—111no—
467#3124—112no—
468#3012—112no—
469#3006—111no—
470C2×#452—111no—
471#2976—111no—
472C23×C11—21no—
473C23×C11—22no—
474C23×C11—22no—
475C23×C11—21no—
476C23×C11—41no—
477C23×C11—41no—
478C23×C11—42no—
479C23×C11—44no—
480C23×C11—42no—
481C23×C11—42no—
482C23×C11—81no—
483C23×C11—81no—
484C23×C11—82no—
485C23×C11—82no—
486C23×C11—81no—
487C23×C11C22×D411yescharacteristic
488C23×C11C22×D411yescharacteristic
489C23×C11C22×D412yes—
490C23×C11C22×D411yescharacteristic
491C22×D11—22no—
492C22×D11—42no—
493C22×D11—81no—
494C22×D11—81no—
495Q8×C11—21no—
496Q8×C11—21no—
497Q8×C11—21no—
498Q8×C11—41no—
499Q8×C11—42no—
500Q8×C11H(5,𝔽2)12yes—
501D4×C11—24no—
502D4×C11—24no—
503D4×C11—21no—
504D4×C11—21no—
505D4×C11—22no—
506D4×C11—22no—
507D4×C11—21no—
508D4×C11—41no—
509D4×C11—42no—
510D4×C11—42no—
511D4×C11—44no—
512D4×C11—42no—
513D4×C11—44no—
514D4×C11—42no—
515D4×C11—42no—
516D4×C11—42no—
517D4×C11—42no—
518D4×C11—44no—
519D4×C11—82no—
520D4×C11—82no—
521D4×C11—82no—
522D4×C11—82no—
523D4×C11H(5,𝔽2)12yes—
524C2×C4×C11—24no—
525C2×C4×C11—21no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—22no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—22no—
532C2×C4×C11—21no—
533C2×C4×C11—21no—
534C2×C4×C11—22no—
535C2×C4×C11—21no—
536C2×C4×C11—41no—
537C2×C4×C11—41no—
538C2×C4×C11—41no—
539C2×C4×C11—42no—
540C2×C4×C11—44no—
541C2×C4×C11—42no—
542C2×C4×C11—42no—
543C2×C4×C11—42no—
544C2×C4×C11—82no—
545C2×C4×C11—81no—
546C2×C4×C11C22×D412yes—
547C2×C4×C11C22×D411yescharacteristic
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D412yes—
550C2×C4×C11C22×D412yes—
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C2511yescharacteristic
553C22⋊D11—44no—
554C22⋊D11—82no—
555C22⋊D11—82no—
556C22⋊D11—82no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—42no—
561C2×Dic11—81no—
562C2×Dic11—82no—
563C2×Dic11—81no—
564D44—22no—
565D44—22no—
566D44—81no—
567C4×D11—82no—
568C4×D11—82no—
569Dic22—22no—
570Dic22—22no—
571Dic22—81no—
572Dic22—82no—
573C11⋊C8—22no—
574C11⋊C8—22no—
575C11⋊C8—22no—
576C11⋊C8—22no—
577C2×H(5,𝔽2)C2×D1111yescharacteristic, complemented
578C22×#41C2×D1111yescharacteristic
579C2×AGL(1,ℤ/8)—111no—
580C2×AGL(1,ℤ/8)—111no—
581C2×AGL(1,ℤ/8)—112no—
582C2×#135—112no—
583C22×Q16—111no—
584C22×SD16—111no—
585#562—222no—
586#554—112no—
587#550C2×D1112yes—
588#548—112no—
589#548C2×D1112yescomplemented
590#547—112no—
591#546—22no—
592#546—112no—
593#546—222no—
594#546C2×D1112yes—
595D42—22no—
596D42C2×D1112yescomplemented
597#543—221no—
598#542—112no—
599#539—221no—
600#538—221no—
601#537—21no—
602#537—112no—
603#537—221no—
604#537C2×D1111yescharacteristic, complemented
605#535—21no—
606#535C2×D1111yescharacteristic, complemented
607#525—21no—
608#525C2×D1111yescharacteristic
609C2×C22⋊Q8—111no—
610C2×#121—21no—
611C2×#121—111no—
612C2×#121C2×D1111yescharacteristic
613#520C2×D1111yescharacteristic, complemented
614#496—112no—
615#495—112no—
616#489—112no—
617#486—112no—
618#484—112no—
619#484—112no—
620#480—112no—
621#480—112no—
622#480—112no—
623#480—112no—
624#477—112no—
625#474—112no—
626#468—112no—
627#468—112no—
628#468—112no—
629#468—112no—
630#467—112no—
631#466—112no—
632#466—112no—
633#466—112no—
634#464—112no—
635#464—112no—
636#463—112no—
637#463—112no—
638#460—112no—
639#459—112no—
640#452—112no—
641#452—112no—
642#452—112no—
643#452—112no—
644#452—112no—
645#452—112no—
646#450—112no—
647#450—112no—
648#449—112no—
649#449—112no—
650#449—112no—
651#449—112no—
652#448—112no—
653#448—112no—
654#447—112no—
655#447—112no—
656#447—112no—
657#447—112no—
658#440—112no—
659#440—112no—
660C4×Q16—112no—
661C4×D8—112no—
662#436—112no—
663#435—112no—
664#435—112no—
665C8×D4—112no—
666#433—112no—
667#417—111no—
668#417—112no—
669#417—111no—
670C2×#103—111no—
671C2×#102—111no—
672C2×#102—112no—
673#408—112no—
674#407—111no—
675C2×C22⋊C8—111no—
676C22×C11—21no—
677C22×C11—21no—
678C22×C11—21no—
679C22×C11—22no—
680C22×C11—21no—
681C22×C11—21no—
682C22×C11—22no—
683C22×C11—21no—
684C22×C11—22no—
685C22×C11—21no—
686C22×C11—22no—
687C22×C11—21no—
688C22×C11—41no—
689C22×C11—41no—
690C22×C11—41no—
691C22×C11—42no—
692C22×C11—41no—
693C22×C11—42no—
694C22×C11—42no—
695C22×C11—41no—
696C22×C11—82no—
697C22×C11—84no—
698C22×C11—164no—
699C22×C11—162no—
700C22×C11#57612yes—
701C22×C11C23×D411yescharacteristic
702C2×D11—42no—
703C2×D11—42no—
704C2×D11—42no—
705C2×D11—162no—
706C4×C11—22no—
707C4×C11—21no—
708C4×C11—22no—
709C4×C11—21no—
710C4×C11—22no—
711C4×C11—21no—
712C4×C11—22no—
713C4×C11—41no—
714C4×C11—42no—
715C4×C11C2×H(5,𝔽2)11yescharacteristic
716C4×C11C2×H(5,𝔽2)11yescharacteristic
717Dic11—42no—
718Dic11—42no—
719Dic11—42no—
720H(5,𝔽2)—42no—
721H(5,𝔽2)—42no—
722C2×#41—21no—
723C2×#41—21no—
724C2×#41—21no—
725C2×#41—42no—
726C2×#41—42no—
727C2×#41—112no—
728C2×#41—222no—
729C2×#41C22×D1111yescharacteristic
730C2×#41C22×D1111yescharacteristic
731C2×#41C22×D1112yes—
732C2×#41C22×D1111yescharacteristic
733C2×#41C22×D1111yescharacteristic
734C2×#41C22×D1111yescharacteristic
735C22×Q8—111no—
736C22×Q8C22×D1111yescharacteristic
737C22×D4—21no—
738C22×D4—21no—
739C22×D4—21no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—111no—
743C22×D4—221no—
744C22×D4C22×D1111yescharacteristic
745C22×D4C22×D1112yes—
746C22×D4C22×D1111yescharacteristic
747C23×C4—21no—
748C23×C4C22×D1111yescharacteristic
749AGL(1,ℤ/8)—442no—
750AGL(1,ℤ/8)—444no—
751AGL(1,ℤ/8)—442no—
752#135—444no—
753C2×Q16—112no—
754C2×Q16—112no—
755C2×Q16—442no—
756C2×SD16—112no—
757C2×SD16—112no—
758C2×SD16—112no—
759C2×SD16—112no—
760C2×SD16—112no—
761C2×SD16—112no—
762C2×SD16—442no—
763C2×D8—112no—
764C2×D8—112no—
765C2×D8—112no—
766C2×D8—112no—
767C2×M16—111no—
768C2×M16—111no—
769C2×M16—112no—
770C22×C8—111no—
771C22×C8—111no—
772C22×C8—112no—
773C4⋊Q8—112no—
774#127—22no—
775#127C22×D1112yes—
776#126—222no—
777#125—222no—
778#124—22no—
779#124—112no—
780#124—222no—
781#124—222no—
782#124C22×D1112yes—
783#123—22no—
784#123—222no—
785#123—222no—
786#123—222no—
787#123—222no—
788#123C22⋊D1112yes—
789C22⋊Q8—21no—
790C22⋊Q8—22no—
791C22⋊Q8—112no—
792C22⋊Q8—112no—
793C22⋊Q8—112no—
794C22⋊Q8—222no—
795C22⋊Q8—221no—
796C22⋊Q8—221no—
797C22⋊Q8—222no—
798C22⋊Q8—222no—
799C22⋊Q8—222no—
800C22⋊Q8—222no—
801C22⋊Q8—222no—
802C22⋊Q8C22⋊D1111yescharacteristic
803C22⋊Q8C22⋊D1111yescharacteristic
804C22⋊Q8C22×D1112yes—
805#121—21no—
806#121—22no—
807#121—22no—
808#121—21no—
809#121—21no—
810#121—21no—
811#121—21no—
812#121—22no—
813#121—22no—
814#121—22no—
815#121—22no—
816#121—112no—
817#121—112no—
818#121—112no—
819#121—222no—
820#121—222no—
821#121—222no—
822#121—222no—
823#121—221no—
824#121—221no—
825#121—222no—
826#121C22⋊D1111yescharacteristic
827#121C22⋊D1111yescharacteristic
828#121C22×D1112yes—
829#121C22×D1112yes—
830#121C22×D1112yes—
831#120—22no—
832#120—22no—
833#120—22no—
834#120—22no—
835#120—222no—
836#120C22⋊D1112yes—
837C4×Q8—112no—
838C4×Q8C22×D1112yes—
839C4×D4—22no—
840C4×D4—22no—
841C4×D4—22no—
842C4×D4—112no—
843C4×D4—222no—
844C4×D4—222no—
845C4×D4C22×D1112yes—
846C4×D4C22×D1112yes—
847C4×D4C22×D1112yes—
848#117—21no—
849#117C22×D1111yescharacteristic
850C2×C4⋊C4—21no—
851C2×C4⋊C4—111no—
852C2×C4⋊C4—111no—
853C2×C4⋊C4—112no—
854C2×C4⋊C4—221no—
855C2×C4⋊C4C22×D1111yescharacteristic
856C2×C22⋊C4—21no—
857C2×C22⋊C4—22no—
858C2×C22⋊C4—221no—
859C2×C22⋊C4—221no—
860C2×C22⋊C4—222no—
861#107—112no—
862#107—112no—
863#107—112no—
864#107—112no—
865C4⋊C8—112no—
866C4⋊C8—112no—
867#103—112no—
868#103—112no—
869#103—112no—
870#103—112no—
871#103—112no—
872#103—112no—
873#102—112no—
874#102—112no—
875#102—112no—
876#102—112no—
877#102—112no—
878#102—112no—
879#102—112no—
880#102—112no—
881#102—112no—
882#102—112no—
883C22⋊C8—112no—
884C22⋊C8—112no—
885C22⋊C8—112no—
886C22⋊C8—112no—
887C22⋊C8—112no—
888C22⋊C8—112no—
889#97—112no—
890C4×C8—112no—
891C2×C11—22no—
892C2×C11—41no—
893C2×C11—41no—
894C2×C11—42no—
895C2×C11—42no—
896C2×C11—81no—
897C2×C11—82no—
898C2×C11#348411yescharacteristic
899C2×C11C2×#57611yescharacteristic
900C2×C11#358611yescharacteristic
901D11—82no—
902C24—21no—
903C24—22no—
904C24—21no—
905C24—221no—
906C24C2×C22⋊D1111yescharacteristic
907#41—22no—
908#41—22no—
909#41—24no—
910#41—22no—
911#41—22no—
912#41—41no—
913#41—41no—
914#41—41no—
915#41—41no—
916#41—41no—
917#41—41no—
918#41—42no—
919#41—44no—
920#41—44no—
921#41—44no—
922#41—442no—
923#41—442no—
924#41—884no—
925C2×Q8—21no—
926C2×Q8—22no—
927C2×Q8—41no—
928C2×Q8—112no—
929C2×Q8—221no—
930C2×Q8—222no—
931C2×Q8—441no—
932C2×Q8—441no—
933C2×Q8C2×C22⋊D1111yescharacteristic
934C2×Q8C23×D1111yescharacteristic
935C2×Q8C23×D1111yescharacteristic
936C2×D4—21no—
937C2×D4—22no—
938C2×D4—24no—
939C2×D4—22no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—22no—
943C2×D4—21no—
944C2×D4—22no—
945C2×D4—22no—
946C2×D4—21no—
947C2×D4—22no—
948C2×D4—21no—
949C2×D4—22no—
950C2×D4—22no—
951C2×D4—41no—
952C2×D4—42no—
953C2×D4—41no—
954C2×D4—41no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—48no—
958C2×D4—84no—
959C2×D4—82no—
960C2×D4—112no—
961C2×D4—222no—
962C2×D4—222no—
963C2×D4—222no—
964C2×D4—222no—
965C2×D4—221no—
966C2×D4—441no—
967C2×D4—441no—
968C2×D4—882no—
969C2×D4C2×C22⋊D1112yes—
970C2×D4C2×C22⋊D1112yes—
971C2×D4C2×C22⋊D1112yes—
972C2×D4C2×C22⋊D1111yescharacteristic
973C2×D4C23×D1112yes—
974C2×D4C23×D1111yescharacteristic
975C2×D4C23×D1111yescharacteristic
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—22no—
982C22×C4—21no—
983C22×C4—22no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—44no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—222no—
991C22×C4—222no—
992C22×C4—222no—
993C22×C4C2×C22⋊D1111yescharacteristic
994C22×C4C2×C22⋊D1111yescharacteristic
995C22×C4C2×C22⋊D1111yescharacteristic
996C22×C4C23×D1111yescharacteristic
997C22×C4C23×D1111yescharacteristic
998C22×C4C23×D1112yes—
999C22×C4C23×D1111yescharacteristic
1000Q16—224no—
1001Q16—442no—
1002SD16—224no—
1003SD16—224no—
1004SD16—442no—
1005SD16—442no—
1006SD16—442no—
1007SD16—442no—
1008D8—224no—
1009D8—442no—
1010D8—442no—
1011D8—442no—
1012M16—441no—
1013M16—442no—
1014M16—441no—
1015C2×C8—112no—
1016C2×C8—112no—
1017C2×C8—112no—
1018C2×C8—112no—
1019C2×C8—441no—
1020C2×C8—441no—
1021C2×C8—442no—
1022C4⋊C4—21no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—112no—
1026C4⋊C4—112no—
1027C4⋊C4—221no—
1028C4⋊C4—222no—
1029C4⋊C4—221no—
1030C4⋊C4—222no—
1031C4⋊C4—222no—
1032C4⋊C4—222no—
1033C4⋊C4—222no—
1034C4⋊C4—222no—
1035C4⋊C4C2×C22⋊D1111yescharacteristic
1036C4⋊C4C2×C22⋊D1111yescharacteristic
1037C4⋊C4C2×C22⋊D1112yes—
1038C4⋊C4C2×C22⋊D1112yes—
1039C4⋊C4C23×D1112yes—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—222no—
1048C22⋊C4—222no—
1049C22⋊C4—222no—
1050C22⋊C4—222no—
1051C22⋊C4—222no—
1052C22⋊C4—222no—
1053C22⋊C4—222no—
1054C22⋊C4—222no—
1055C22⋊C4—222no—
1056C22⋊C4C2×C22⋊D1112yes—
1057C22⋊C4C2×C22⋊D1112yes—
1058C22⋊C4C2×C22⋊D1112yes—
1059C22⋊C4C2×C22⋊D1112yes—
1060C22⋊C4C2×C22⋊D1112yes—
1061C42—22no—
1062C42—222no—
1063C42C23×D1112yes—
1064C11#6162411yescharacteristic, complemented, Sylow
1065C23—21no—
1066C23—22no—
1067C23—22no—
1068C23—21no—
1069C23—41no—
1070C23—41no—
1071C23—42no—
1072C23—44no—
1073C23—42no—
1074C23—42no—
1075C23—81no—
1076C23—81no—
1077C23—82no—
1078C23—82no—
1079C23—81no—
1080C23—222no—
1081C23—442no—
1082C23—881no—
1083C23—881no—
1084C23C22×C22⋊D1112yes—
1085C23C22×C22⋊D1111yescharacteristic
1086C23C22×C22⋊D1111yescharacteristic
1087C23C22×C22⋊D1111yescharacteristic
1088Q8—21no—
1089Q8—21no—
1090Q8—21no—
1091Q8—41no—
1092Q8—42no—
1093Q8—222no—
1094Q8—222no—
1095Q8—881no—
1096Q8—882no—
1097Q8#6703712yes—
1098D4—24no—
1099D4—24no—
1100D4—21no—
1101D4—21no—
1102D4—22no—
1103D4—22no—
1104D4—21no—
1105D4—41no—
1106D4—42no—
1107D4—42no—
1108D4—44no—
1109D4—42no—
1110D4—44no—
1111D4—42no—
1112D4—42no—
1113D4—42no—
1114D4—42no—
1115D4—44no—
1116D4—82no—
1117D4—82no—
1118D4—82no—
1119D4—82no—
1120D4—222no—
1121D4—222no—
1122D4—444no—
1123D4—881no—
1124D4—882no—
1125D4—882no—
1126D4—882no—
1127D4#6703712yes—
1128C2×C4—24no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—44no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—82no—
1149C2×C4—81no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—222no—
1153C2×C4—442no—
1154C2×C4—882no—
1155C2×C4—882no—
1156C2×C4—881no—
1157C2×C4—881no—
1158C2×C4—882no—
1159C2×C4C22×C22⋊D1112yes—
1160C2×C4C22×C22⋊D1112yes—
1161C2×C4C22×C22⋊D1111yescharacteristic
1162C2×C4C22×C22⋊D1111yescharacteristic
1163C2×C4C22×C22⋊D1112yes—
1164C2×C4C22×C22⋊D1111yescharacteristic
1165C2×C4C24×D1111yescharacteristic
1166C8—222no—
1167C8—222no—
1168C8—222no—
1169C8—222no—
1170C22—21no—
1171C22—21no—
1172C22—21no—
1173C22—22no—
1174C22—21no—
1175C22—21no—
1176C22—22no—
1177C22—21no—
1178C22—22no—
1179C22—21no—
1180C22—22no—
1181C22—21no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—42no—
1186C22—41no—
1187C22—42no—
1188C22—42no—
1189C22—41no—
1190C22—82no—
1191C22—84no—
1192C22—164no—
1193C22—162no—
1194C22—442no—
1195C22—442no—
1196C22—442no—
1197C22—1762no—
1198C22#1062336612yes—
1199C22C23×C22⋊D1111yescharacteristic
1200C4—22no—
1201C4—21no—
1202C4—22no—
1203C4—21no—
1204C4—22no—
1205C4—21no—
1206C4—22no—
1207C4—41no—
1208C4—42no—
1209C4—442no—
1210C4—442no—
1211C4—442no—
1212C4C2×#6703711yescharacteristic
1213C4C2×#6703711yescharacteristic
1214C2—22no—
1215C2—41no—
1216C2—41no—
1217C2—42no—
1218C2—42no—
1219C2—81no—
1220C2—82no—
1221C2—882no—
1222C2#1308225111yescharacteristic
1223C2C2×#1062336611yescharacteristic
1224C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3488C2
socleC22×C11C23×D4
hypercenter#3488D11
hypocenterC11#61624
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #525 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #13082843C2semidirect
2. #13080954C2semidirect
3. #13080697C2semidirect
4. #13080607C2semidirect
5. #13080429C2semidirect
6. #13080353C2semidirect
7. #13080223C2semidirect
8. #13080157C2semidirect
9. #13080107C2semidirect
10. #13079710C2semidirect
11. #13079513C2semidirect
12. #13079422C2semidirect
13. #13079364C2semidirect
14. #13078878C2semidirect
15. #13077920C2semidirect
16. #13077868C2semidirect
17. C2×#10622852C2semidirect
18. #13077664C2semidirect
19. C11×#3488C2semidirect
20. C2×C11×H(5,𝔽2)C22semidirect
23. C11×#548C22semidirect
27. D42×C11C22semidirect
29. C11×#537C22semidirect
31. C11×#535C22semidirect
36. C11×#520C22semidirect
37. #10623364C22semidirect
38. C2×#67003C22semidirect
39. C2×#67002C22semidirect
40. C2×#67002C22semidirect
41. C22×#4326C22semidirect
42. C22×#4324C22semidirect
43. C2×#66985C22semidirect
44. C2×#66983C22semidirect
45. C2×#66977C22semidirect
52. #10623086C22semidirect
53. #10623083C22semidirect
54. #10623081C22semidirect
55. #10623074C22semidirect
56. #10623065C22semidirect
57. #10622852C22semidirect
58. #10622852C22semidirect
59. #10622852C22semidirect
60. #10622852C22semidirect
61. #10622852C22semidirect
63. #10622851C22semidirect
64. #10622851C22semidirect
65. #10622847C22semidirect
66. #10622845C22semidirect
67. #10622845C22semidirect
68. #10622845C22semidirect
69. #10622840C22semidirect
70. C2×#66899C22semidirect
71. #10622831C22semidirect
72. #10622831C22semidirect
73. #10622830C22semidirect
74. #10622830C22semidirect
75. #10622830C22semidirect
76. C2×#66896C22semidirect
77. C2×#66896C22semidirect
78. #10622820C22semidirect
79. C2×C22⋊(C11⋊C8)C22semidirect
80. #10622688C22semidirect
81. #10622687C22semidirect
82. #10622685C22semidirect
83. #10622683C22semidirect
84. #10622672C22semidirect
85. #10622670C22semidirect
86. #10622668C22semidirect
87. #10622667C22semidirect
88. #10622664C22semidirect
89. #10622662C22semidirect
90. #10622660C22semidirect
91. #10622657C22semidirect
92. #10622655C22semidirect
93. #10622655C22semidirect
94. #10622655C22semidirect
95. #10622653C22semidirect
96. #10622651C22semidirect
97. #10622651C22semidirect
98. #10622651C22semidirect
99. #10622650C22semidirect
100. #10622649C22semidirect
101. #10622646C22semidirect
102. #10622646C22semidirect
103. #10622646C22semidirect
104. C4×#4326C22semidirect
105. #10622641C22semidirect
106. #10622639C22semidirect
107. #10622634C22semidirect
108. #10622631C22semidirect
109. #10622629C22semidirect
110. C4×#4323C22semidirect
111. #10622625C22semidirect
112. #10622624C22semidirect
113. #10622624C22semidirect
114. D4×C11⋊C8C22semidirect
115. #10622620C22semidirect
116. #10622613C22semidirect
117. #10622583C22semidirect
118. #10622580C22semidirect
454. #3488D11semidirect
577. C2×H(5,𝔽2)C2×D11semidirect
589. #548C2×D11semidirect
596. D42C2×D11semidirect
604. #537C2×D11semidirect
606. #535C2×D11semidirect
613. #520C2×D11semidirect
1064. C11#61624semidirect

Maximal subgroups

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

subgroupindex
#130828432
#130809542
#130806972
#130806072
#130804292
#130803532
#130802232
#130801572
#130801072
#130797102
#130795132
#130794222
#130793642
#130788782
#130779202
#130778682
C2×#106228522
#130776642
C11×#34882
#6162411