Finite Group Databasebeta

← #15631141

Subgroups — #15631141

Order 2816.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082351C211yesmaximal, characteristic, complemented
2#13082296C211yesmaximal, characteristic, complemented
3#13080798C212yesmaximal, complemented
4#13080783C212yesmaximal, complemented
5#13080588C212yesmaximal, complemented
6#13080573C212yesmaximal, complemented
7#13080540C212yesmaximal, complemented
8#13080519C212yesmaximal, complemented
9#13080477C212yesmaximal, complemented
10#13080462C212yesmaximal, complemented
11#13078985C211yesmaximal, characteristic, complemented
12#13078603C211yesmaximal, characteristic, complemented
13#13078564C211yesmaximal, characteristic, complemented
14#13078476C211yesmaximal, characteristic, complemented
15#13078299C211yesmaximal, characteristic, complemented
16C2×#10622727C211yesmaximal, characteristic, complemented
17#13078131C211yesmaximal, characteristic, complemented
18#13077905C211yesmaximal, characteristic, complemented
19#13077868C211yesmaximal, characteristic, complemented
20#13077451C211yesmaximal, characteristic, complemented
21#13077310C211yesmaximal, characteristic, complemented
22#13077145C211yesmaximal, characteristic, complemented
23C2×C11×#416C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C2×#67043C2211yescharacteristic
26C23×C8×C11C2211yescharacteristic
27C2×C11×#117C2211yescharacteristic
28#10623364—21no—
29#10623364C2211yescharacteristic
30#10623362C2212yescomplemented
31#10623358C2211yescharacteristic
32#10623356—21no—
33#10623356C2211yescharacteristic
34#10623355—22no—
35#10623355C2212yescomplemented
36C2×#67002C2211yescharacteristic
37C2×#67002C2211yescharacteristic
38Q8×C22⋊D11C2212yescomplemented
39#10623337—22no—
40#10623337C2212yescomplemented
41#10623322—21no—
42#10623322C2211yescharacteristic
43C2×#66983C2211yescharacteristic
44C2×#66977—21no—
45C2×#66977C2211yescharacteristic
46C22×#4314C2211yescharacteristic, complemented
47C2×#66954C2211yescharacteristic, complemented
48#10623066—21no—
49#10623065—21no—
50#10623063C2212yescomplemented
51#10623061C2212yescomplemented
52#10623058—22no—
53#10623056C2211yescharacteristic, complemented
54#10623054C2211yescharacteristic, complemented
55#10623052C2211yescharacteristic, complemented
56#10623050C2211yescharacteristic, complemented
57#10623045C2212yes—
58#10623038C2212yes—
59#10623021—22no—
60#10623010—21no—
61#10623008—21no—
62C11×#416C2211yescharacteristic
63C11×#416C2211yescharacteristic
64C11×#416C2211yescharacteristic
65C11×#416C2211yescharacteristic
66C11×#416C2211yescharacteristic, complemented
67C11×#416C2211yescharacteristic, complemented
68C11×#416C2211yescharacteristic, complemented
69C11×#416C2211yescharacteristic, complemented
70C2×C11×#103C2211yescharacteristic, complemented
71C2×C11×#103C2211yescharacteristic, complemented
72C2×C11×#102C2211yescharacteristic, complemented
73C2×C11×#102C2211yescharacteristic, complemented
74#10622851C2212yes—
75#10622851C2212yes—
76#10622845C2211yescharacteristic
77#10622845C2211yescharacteristic
78#10622840C2212yes—
79#10622830C2212yes—
80#10622820C2211yescharacteristic
81#10622727C2212yes—
82#10622727C2212yes—
83#10622727C2212yescomplemented
84#10622727C2212yescomplemented
85C2×#66885C2211yescharacteristic, complemented
86#10622724C2212yescomplemented
87#10622724C2212yescomplemented
88#10622723C2211yescharacteristic, complemented
89C8×C22⋊D11C2212yescomplemented
90C8×C22⋊D11C2212yescomplemented
91C2×#66881C2211yescharacteristic, complemented
92C2×#66880C2211yescharacteristic, complemented
93#10622715C2211yescharacteristic, complemented
94#10622714C2211yescharacteristic, complemented
95#10622617C2211yescharacteristic, complemented
96#10622617C2211yescharacteristic, complemented
97#10622609C2212yescomplemented
98#10622609C2212yescomplemented
99#10622608C2211yescharacteristic, complemented
100#10622608C2211yescharacteristic, complemented
101#10622584C2212yescomplemented
102#10622583C2212yescomplemented
103#10622431C2212yescomplemented
104#10622431C2212yescomplemented
105#10622430C2212yescomplemented
106#10622428C2212yescomplemented
107#10622425C2212yescomplemented
108#10622420C2212yescomplemented
109#10622419C2212yescomplemented
110#10622419C2212yescomplemented
111#10622418C2212yescomplemented
112#10622415C2212yescomplemented
113D11×#103C2212yescomplemented
114#10622412C2212yescomplemented
115#10622410C2212yescomplemented
116#10622405C2212yescomplemented
117#10622404C2212yescomplemented
118#10622401C2212yescomplemented
119#10622400C2212yescomplemented
120#10622400C2212yescomplemented
121#10622398C2212yescomplemented
122#10622395C2212yescomplemented
123#10622394C2212yescomplemented
124#10622394C2212yescomplemented
125#10622392C2212yescomplemented
126#10622390C2212yescomplemented
127#10622388C2212yescomplemented
128#10622385C2212yescomplemented
129#10622384C2212yescomplemented
130#10622381C2212yescomplemented
131#10622378C2212yescomplemented
132#10622376C2212yescomplemented
133#10622374C2212yescomplemented
134#10622369C2212yescomplemented
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41—24no—
138C2×C11×#41—42no—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2311yescharacteristic
141C2×C11×#41C2311yescharacteristic
142C2×C11×#41C2311yescharacteristic
143C22×Q8×C11C2311yescharacteristic
144C22×D4×C11—21no—
145C22×D4×C11C2311yescharacteristic
146C23×C4×C11—21no—
147C23×C4×C11C2311yescharacteristic
148C22×C22⋊D11—21no—
149#67043—24no—
150#67043—42no—
151C2×Q8×D11C2312yes—
152C2×#4341—22no—
153C2×#4341C2312yes—
154C2×#4339—22no—
155C2×#4339—21no—
156C2×#4339C2311yescharacteristic
157C22×D44C2311yescharacteristic
158C22×Dic22—21no—
159C22×Dic22C2311yescharacteristic
160C22×C8×C11—42no—
161C22×C8×C11C2311yescharacteristic
162C22×C8×C11C2311yescharacteristic
163C22×C8×C11C2311yescharacteristic
164C22×C8×C11C2311yescharacteristic
165C22×C8×C11C2311yescharacteristic
166C22×C8×C11C2311yescharacteristic
167C11×#117—21no—
168C11×#117—21no—
169C11×#117C2311yescharacteristic
170C11×#117C2311yescharacteristic
171C11×#117C2311yescharacteristic
172C11×#117C2311yescharacteristic
173C2×C11×C4⋊C4C2311yescharacteristic
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4—21no—
176C2×C42×C11—21no—
177#67006—22no—
178#67006D412yes—
179C2×C22⋊Dic11—21no—
180C2×C22⋊Dic11—22no—
181#67002—24no—
182#67002—42no—
183#66999—22no—
184#66999C2312yes—
185Q8×Dic11C2312yes—
186#66997—22no—
187#66997C2312yes—
188C2×#4325C2312yes—
189C2×#4325C2312yes—
190#66992—22no—
191#66992—22no—
192#66992—22no—
193#66991—22no—
194#66991C2312yes—
195#66989—22no—
196#66989C2312yes—
197#66988—22no—
198#66988—22no—
199#66988—22no—
200D4×Dic11—22no—
201D4×Dic11C2312yes—
202C2×#4323C2312yes—
203C2×#4323C2312yes—
204#66983—21no—
205#66983—21no—
206#66983—22no—
207#66983—21no—
208#66983D411yescharacteristic
209#66983D411yescharacteristic
210#66983C2312yes—
211#66983C2312yes—
212#66982—22no—
213#66982—22no—
214#66982D412yes—
215C4×C22⋊D11—22no—
216C4×C22⋊D11—22no—
217C4×C22⋊D11—22no—
218C4×C22⋊D11C2312yes—
219C4×C22⋊D11C2312yes—
220C2×(C2×D11)⋊C4—21no—
221#66979—21no—
222#66979C2311yescharacteristic
223C2×C4⋊Dic11—21no—
224C2×C4⋊Dic11C2311yescharacteristic
225C2×C4⋊Dic11C2311yescharacteristic
226#66977—21no—
227#66977—21no—
228#66977—21no—
229#66977—22no—
230#66977—21no—
231#66977—21no—
232#66977—22no—
233#66977D411yescharacteristic
234#66977D411yescharacteristic
235#66977C2312yes—
236#66977C2312yes—
237C2×Dic11⋊C4—21no—
238C2×Dic11⋊C4—22no—
239C2×#4318C2311yescharacteristic
240C2×#4318C2311yescharacteristic
241C2×#4314—42no—
242C2×#4314C2312yes—
243C2×#4314C2312yes—
244#66954—42no—
245C2×#4313C2312yes—
246C2×C8×D11C2312yes—
247#66951—22no—
248#66949—22no—
249#66948C2312yes—
250#66948C2312yes—
251#66947—22no—
252#66947—22no—
253#66946C2312yes—
254#66946C2312yes—
255#66945C2312yes—
256C4⋊C4×D11C2312yes—
257#66943C2312yes—
258#66941C2312yes—
259#66938—22no—
260#66937—22no—
261#66937—22no—
262#66936—22no—
263#66935—22no—
264(C22⋊D11)⋊C4—22no—
265C22⋊C4×D11—22no—
266#66931—22no—
267#66929—22no—
268#66928—21no—
269#66928—22no—
270#66927—21no—
271C4×D44—21no—
272C4×D44—22no—
273C4×D44—21no—
274C4×D44—21no—
275#66925—22no—
276#66923—21no—
277#66922—21no—
278C4×Dic22—21no—
279C11×#103C2311yescharacteristic
280C11×#103C2311yescharacteristic
281C11×#103C2311yescharacteristic
282C11×#103C2311yescharacteristic
283C11×#103C2311yescharacteristic
284C11×#103C2311yescharacteristic
285C11×#103C2311yescharacteristic
286C11×#103C2311yescharacteristic
287C11×#102C2311yescharacteristic
288C11×#102C2311yescharacteristic
289C11×#102C2311yescharacteristic
290C11×#102C2311yescharacteristic
291C11×#102C2311yescharacteristic
292C11×#102C2311yescharacteristic
293C11×#102C2311yescharacteristic
294C11×#102C2311yescharacteristic
295#66899C2312yes—
296#66899C2312yes—
297#66896C2312yes—
298#66896C2312yes—
299C22⋊(C11⋊C8)C2312yes—
300C22⋊(C11⋊C8)C2312yes—
301#66885C2312yes—
302#66885C2312yes—
303(C2×D11)⋊C8C2312yes—
304(C2×D11)⋊C8C2312yes—
305#66881C2312yes—
306#66881C2312yes—
307#66880C2312yes—
308#66880C2312yes—
309#66879C2312yes—
310Dic11⋊C8C2312yes—
311Dic11⋊C8C2312yes—
312C8×Dic11C2312yes—
313#66874C2312yes—
314#66874C2312yes—
315#66874C2312yes—
316#66874C2312yes—
317#66872C2312yes—
318#66872C2312yes—
319#66871C2312yes—
320#66871C2312yes—
321#61174—111nomaximal, Sylow
322C24×C11—21no—
323C24×C11C2×D411yescharacteristic
324C23×D11—21no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—44no—
331C11×#41—41no—
332C11×#41—41no—
333C11×#41—44no—
334C11×#41#4114yescomplemented
335C2×Q8×C11—21no—
336C2×Q8×C11—22no—
337C2×Q8×C11—41no—
338C2×Q8×C11C2411yescharacteristic
339C2×Q8×C11C2411yescharacteristic
340C2×D4×C11—21no—
341C2×D4×C11—22no—
342C2×D4×C11—21no—
343C2×D4×C11—21no—
344C2×D4×C11—21no—
345C2×D4×C11—21no—
346C2×D4×C11—41no—
347C2×D4×C11—44no—
348C2×D4×C11C2411yescharacteristic
349C2×D4×C11C2411yescharacteristic
350C22×C4×C11—21no—
351C22×C4×C11—22no—
352C22×C4×C11—22no—
353C22×C4×C11—21no—
354C22×C4×C11—21no—
355C22×C4×C11—21no—
356C22×C4×C11—21no—
357C22×C4×C11—21no—
358C22×C4×C11—21no—
359C22×C4×C11—44no—
360C22×C4×C11C2×D411yescharacteristic
361C22×C4×C11C2×D411yescharacteristic
362C22×C4×C11C2×D411yescharacteristic
363C22×C4×C11C2411yescharacteristic
364C22×C4×C11C2411yescharacteristic
365C22×C4×C11C2411yescharacteristic
366C2×C22⋊D11—22no—
367C2×C22⋊D11—22no—
368C2×C22⋊D11—22no—
369C2×C22⋊D11—22no—
370C2×C22⋊D11—82no—
371C2×C22⋊D11C2×D412yes—
372C2×C22⋊D11C2×D412yes—
373C2×C22⋊D11C2×D412yes—
374C22×Dic11—22no—
375C22×Dic11—22no—
376C22×Dic11—21no—
377C22×Dic11—21no—
378C22×Dic11—21no—
379Q8×D11—24no—
380Q8×D11—42no—
381#4341—24no—
382#4341—42no—
383#4341—48no—
384#4339—22no—
385#4339—22no—
386#4339—44no—
387#4339—84no—
388C2×D44—22no—
389C2×D44—22no—
390C2×D44—21no—
391C2×D44—22no—
392C2×D44—22no—
393C2×D44C2×D411yescharacteristic
394C2×D44C2412yes—
395C2×C4×D11—22no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—22no—
399C2×C4×D11C2412yes—
400C2×Dic22—22no—
401C2×Dic22—22no—
402C2×Dic22—21no—
403C2×Dic22—22no—
404C2×Dic22—22no—
405C2×Dic22—44no—
406C2×Dic22C2×D411yescharacteristic
407C2×Dic22C2412yes—
408C2×C8×C11—22no—
409C2×C8×C11—22no—
410C2×C8×C11—41no—
411C2×C8×C11—41no—
412C2×C8×C11—41no—
413C2×C8×C11—41no—
414C2×C8×C11C2411yescharacteristic
415C2×C8×C11C2411yescharacteristic
416C2×C8×C11C2411yescharacteristic
417C2×C8×C11C2411yescharacteristic
418C11×C4⋊C4—21no—
419C11×C4⋊C4—21no—
420C11×C4⋊C4C2411yescharacteristic
421C11×C4⋊C4C2411yescharacteristic
422C11×C4⋊C4C2411yescharacteristic
423C11×C4⋊C4C2411yescharacteristic
424C11×C22⋊C4—21no—
425C11×C22⋊C4—21no—
426C11×C22⋊C4—21no—
427C11×C22⋊C4—21no—
428C42×C11—21no—
429C42×C11—21no—
430C42×C11—21no—
431C42×C11—21no—
432C22⋊Dic11—22no—
433C22⋊Dic11—22no—
434C22⋊Dic11—22no—
435C22⋊Dic11—22no—
436C22⋊Dic11—22no—
437C22⋊Dic11—22no—
438C22⋊Dic11C2×D412yes—
439C22⋊Dic11C2×D412yes—
440C22⋊Dic11C2×D412yes—
441#4325—24no—
442#4325—42no—
443#4323—24no—
444#4323—42no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—22no—
447(C2×D11)⋊C4—22no—
448(C2×D11)⋊C4—22no—
449(C2×D11)⋊C4—22no—
450(C2×D11)⋊C4—22no—
451(C2×D11)⋊C4—22no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4C2×D412yes—
454(C2×D11)⋊C4C2×D412yes—
455C4⋊Dic11—22no—
456C4⋊Dic11—22no—
457C4⋊Dic11—21no—
458C4⋊Dic11—21no—
459C4⋊Dic11C2×D411yescharacteristic
460C4⋊Dic11C2×D411yescharacteristic
461C4⋊Dic11C2412yes—
462C4⋊Dic11C2412yes—
463Dic11⋊C4—22no—
464Dic11⋊C4—22no—
465Dic11⋊C4—22no—
466Dic11⋊C4—22no—
467Dic11⋊C4—22no—
468Dic11⋊C4—22no—
469Dic11⋊C4—22no—
470Dic11⋊C4—22no—
471Dic11⋊C4C2×D412yes—
472Dic11⋊C4C2×D412yes—
473C4×Dic11—22no—
474C4×Dic11—22no—
475C4×Dic11C2412yes—
476#4318—22no—
477#4318—22no—
478C2×C11⋊C8C2412yes—
479C2×C11⋊C8C2412yes—
480#4314—42no—
481#4314—42no—
482#4313—42no—
483C8×D11—42no—
484#3494—111no—
485#3489—111no—
486#3321—112no—
487#3320—112no—
488#3307—112no—
489#3306—112no—
490#3303—112no—
491#3301—112no—
492#3298—112no—
493#3297—112no—
494#3137—111no—
495#3099—111no—
496#3095—111no—
497#3084—111no—
498#3062—111no—
499C2×#465—111no—
500#3042—111no—
501#3010—111no—
502#3006—111no—
503#2946—111no—
504#2929—111no—
505#2898—111no—
506C2×#416D1111yescharacteristic, complemented
507C23×C11—22no—
508C23×C11—22no—
509C23×C11—21no—
510C23×C11—21no—
511C23×C11—41no—
512C23×C11—42no—
513C23×C11—42no—
514C23×C11—81no—
515C23×C11C22×D411yescharacteristic
516C23×C11C22×D411yescharacteristic
517C23×C11C22×D411yescharacteristic
518C22×D11—22no—
519C22×D11—42no—
520C22×D11—81no—
521C22×D11—81no—
522C22×D11C22×D412yes—
523Q8×C11—21no—
524Q8×C11—21no—
525Q8×C11—21no—
526Q8×C11—42no—
527Q8×C11C2×#4112yes—
528D4×C11—24no—
529D4×C11—21no—
530D4×C11—21no—
531D4×C11—21no—
532D4×C11—42no—
533D4×C11—42no—
534D4×C11—42no—
535D4×C11—42no—
536D4×C11C2×#4112yes—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—24no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—21no—
550C2×C4×C11—21no—
551C2×C4×C11—42no—
552C2×C4×C11—42no—
553C2×C4×C11—42no—
554C2×C4×C11—42no—
555C2×C4×C11—42no—
556C2×C4×C11—81no—
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C22×D411yescharacteristic
559C2×C4×C11C22×D411yescharacteristic
560C2×C4×C11C2×#4112yes—
561C2×C4×C11H(5,𝔽2)12yes—
562C2×C4×C11C2511yescharacteristic
563C22⋊D11—24no—
564C22⋊D11—24no—
565C22⋊D11—42no—
566C22⋊D11—44no—
567C22⋊D11—44no—
568C22⋊D11—82no—
569C22⋊D11—82no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—44no—
574C2×Dic11—42no—
575C2×Dic11—82no—
576C2×Dic11—81no—
577C2×Dic11—81no—
578C2×Dic11C22×D412yes—
579C2×Dic11C22×D412yes—
580C2×Dic11C22×D412yes—
581D44—22no—
582D44—22no—
583D44—22no—
584D44—42no—
585D44—82no—
586D44—82no—
587C4×D11—22no—
588C4×D11—22no—
589C4×D11—44no—
590C4×D11—82no—
591C4×D11—82no—
592C4×D11—82no—
593Dic22—22no—
594Dic22—22no—
595Dic22—22no—
596Dic22—44no—
597Dic22—42no—
598Dic22—82no—
599C8×C11—21no—
600C8×C11—21no—
601C8×C11—21no—
602C8×C11—21no—
603C11⋊C8—22no—
604C11⋊C8—22no—
605C2×2−1+4—111no—
606C22×#41C2×D1111yescharacteristic
607C2×AGL(1,ℤ/8)—111no—
608C2×AGL(1,ℤ/8)—111no—
609C22×SD16—111no—
610C2×#131—111no—
611C23×C8C2×D1111yescharacteristic
612#555—112no—
613#553—112no—
614#553—112no—
615#551—222no—
616D4×Q8—112no—
617#548—112no—
618#547—112no—
619#547—112no—
620#547—222no—
621#546—112no—
622#546—222no—
623#546—222no—
624#544—111no—
625#542—221no—
626#540—221no—
627#537—111no—
628#537—221no—
629#536—111no—
630#536—221no—
631#535—111no—
632#532—221no—
633#529—221no—
634#525—111no—
635#525—221no—
636C2×C22⋊Q8—111no—
637C2×C22⋊Q8—221no—
638C2×#121—111no—
639#520—111no—
640#520—111no—
641#518—111no—
642C2×#117C2×D1111yescharacteristic
643#491—112no—
644#489—112no—
645#488—112no—
646#487—112no—
647#485—112no—
648#485—112no—
649#485—112no—
650#484—112no—
651#483—112no—
652#483—112no—
653#482—112no—
654#481—112no—
655#479—112no—
656#478—112no—
657#476—112no—
658#475—112no—
659#469—112no—
660#468—112no—
661#466—112no—
662#465—112no—
663#465—112no—
664#465—112no—
665#465—112no—
666#465—112no—
667#463—112no—
668#463—112no—
669#461—112no—
670#461—112no—
671#449—112no—
672#449—112no—
673#449—112no—
674#449—112no—
675#448—112no—
676#448—112no—
677#448—112no—
678#447—112no—
679#442—112no—
680#440—112no—
681C4×SD16—112no—
682C4×D8—112no—
683#435—112no—
684#435—112no—
685C8×D4—112no—
686C8×D4—112no—
687#428—111no—
688#428—111no—
689C2×#106—111no—
690#424—111no—
691#419—111no—
692#419—111no—
693#419—112no—
694#417—111no—
695#417—111no—
696#417—112no—
697#416—112no—
698#416C2×D1111yescharacteristic
699#416C2×D1111yescharacteristic
700#416C2×D1111yescharacteristic
701#416C2×D1111yescharacteristic
702#416C2×D1111yescharacteristic, complemented
703#416C2×D1111yescharacteristic, complemented
704#416C2×D1111yescharacteristic, complemented
705#416C2×D1111yescharacteristic, complemented
706C2×#103—111no—
707C2×#103—112no—
708C2×#103C2×D1111yescharacteristic, complemented
709C2×#103C2×D1111yescharacteristic, complemented
710C2×#102—111no—
711C2×#102C2×D1111yescharacteristic, complemented
712C2×#102C2×D1111yescharacteristic, complemented
713#408—111no—
714#407—111no—
715#405—111no—
716C22×C11—21no—
717C22×C11—21no—
718C22×C11—21no—
719C22×C11—21no—
720C22×C11—21no—
721C22×C11—21no—
722C22×C11—22no—
723C22×C11—21no—
724C22×C11—44no—
725C22×C11—41no—
726C22×C11—41no—
727C22×C11—41no—
728C22×C11—41no—
729C22×C11—41no—
730C22×C11—84no—
731C22×C11#54612yes—
732C22×C11#57712yes—
733C22×C11C23×D411yescharacteristic
734C2×D11—22no—
735C2×D11—22no—
736C2×D11—22no—
737C2×D11—42no—
738C2×D11—42no—
739C2×D11—42no—
740C2×D11—162no—
741C4×C11—21no—
742C4×C11—21no—
743C4×C11—22no—
744C4×C11—41no—
745C4×C11—41no—
746C4×C11—41no—
747C4×C11—41no—
748C4×C11—41no—
749C4×C11#54612yes—
750C4×C11C22×#4111yescharacteristic
751C4×C11C2×H(5,𝔽2)11yescharacteristic
752Dic11—22no—
753Dic11—22no—
754Dic11—22no—
755Dic11—42no—
756Dic11—42no—
757Dic11—42no—
7582−1+4—224no—
7592−1+4—442no—
760C2×#41—21no—
761C2×#41—21no—
762C2×#41—24no—
763C2×#41—42no—
764C2×#41—111no—
765C2×#41—112no—
766C2×#41—221no—
767C2×#41—222no—
768C2×#41—222no—
769C2×#41C22×D1111yescharacteristic
770C2×#41C22×D1111yescharacteristic
771C2×#41C22×D1111yescharacteristic
772C2×#41C22×D1111yescharacteristic
773C22×Q8—112no—
774C22×Q8—111no—
775C22×Q8—221no—
776C22×Q8C22×D1111yescharacteristic
777C22×D4—21no—
778C22×D4—111no—
779C22×D4—221no—
780C22×D4C22×D1111yescharacteristic
781C23×C4—21no—
782C23×C4C22×D1111yescharacteristic
783AGL(1,ℤ/8)—224no—
784AGL(1,ℤ/8)—442no—
785C2×SD16—112no—
786C2×SD16—112no—
787C2×SD16—112no—
788C2×SD16—112no—
789C2×SD16—442no—
790C2×D8—112no—
791C2×D8—112no—
792#131—442no—
793C2×M16—111no—
794C2×M16—111no—
795C2×M16—112no—
796C22×C8—42no—
797C22×C8—112no—
798C22×C8C22×D1111yescharacteristic
799C22×C8C22×D1111yescharacteristic
800C22×C8C22×D1111yescharacteristic
801C22×C8C22×D1111yescharacteristic
802C22×C8C22×D1111yescharacteristic
803C22×C8C22×D1111yescharacteristic
804C4⋊Q8—112no—
805C4⋊Q8—112no—
806C4⋊Q8—221no—
807C4⋊Q8—222no—
808#127—221no—
809#126—222no—
810#126—222no—
811#125—112no—
812#125—221no—
813#124—112no—
814#124—222no—
815#124—221no—
816#124—222no—
817#124—222no—
818#123—112no—
819#123—222no—
820#123—222no—
821#123—222no—
822#123—222no—
823#123—222no—
824#123—222no—
825#123—222no—
826#123—222no—
827C22⋊Q8—111no—
828C22⋊Q8—111no—
829C22⋊Q8—112no—
830C22⋊Q8—112no—
831C22⋊Q8—112no—
832C22⋊Q8—222no—
833C22⋊Q8—222no—
834C22⋊Q8—222no—
835C22⋊Q8—222no—
836C22⋊Q8—221no—
837C22⋊Q8—222no—
838C22⋊Q8—221no—
839C22⋊Q8—221no—
840C22⋊Q8—221no—
841C22⋊Q8—221no—
842#121—111no—
843#121—111no—
844#121—112no—
845#121—112no—
846#121—112no—
847#121—112no—
848#121—112no—
849#121—222no—
850#121—222no—
851#121—222no—
852#121—221no—
853#121—222no—
854#121—222no—
855#121—222no—
856#121—222no—
857#121—221no—
858#121—221no—
859#120—112no—
860#120—222no—
861#120—222no—
862C4×Q8—112no—
863C4×Q8—221no—
864C4×D4—112no—
865C4×D4—112no—
866C4×D4—112no—
867C4×D4—112no—
868C4×D4—112no—
869C4×D4—222no—
870C4×D4—221no—
871C4×D4—221no—
872C4×D4—221no—
873C4×D4—222no—
874C4×D4—222no—
875C4×D4—222no—
876C4×D4—222no—
877C4×D4—222no—
878#117—21no—
879#117—21no—
880#117—111no—
881#117—112no—
882#117—222no—
883#117—221no—
884#117C22×D1111yescharacteristic
885#117C22×D1111yescharacteristic
886#117C22×D1111yescharacteristic
887#117C22×D1111yescharacteristic
888C2×C4⋊C4—111no—
889C2×C4⋊C4—111no—
890C2×C4⋊C4—112no—
891C2×C4⋊C4—221no—
892C2×C4⋊C4—222no—
893C2×C4⋊C4—221no—
894C2×C4⋊C4C22×D1111yescharacteristic
895C2×C4⋊C4C22×D1111yescharacteristic
896C2×C22⋊C4—21no—
897C2×C22⋊C4—222no—
898C2×C22⋊C4—222no—
899C2×C22⋊C4—221no—
900C2×C22⋊C4—221no—
901C2×C42—21no—
902#107—112no—
903#107—112no—
904#106—112no—
905#106—112no—
906#106—112no—
907#106—112no—
908C4⋊C8—112no—
909C4⋊C8—112no—
910#103—112no—
911#103—112no—
912#103—112no—
913#103—112no—
914#103—112no—
915#103—112no—
916#103—112no—
917#103—112no—
918#103C22×D1111yescharacteristic
919#103C22×D1111yescharacteristic
920#103C22×D1111yescharacteristic
921#103C22×D1111yescharacteristic
922#103C22×D1111yescharacteristic
923#103C22×D1111yescharacteristic
924#103C22×D1111yescharacteristic
925#103C22×D1111yescharacteristic
926#102—112no—
927#102—112no—
928#102—112no—
929#102—112no—
930#102C22×D1111yescharacteristic
931#102C22×D1111yescharacteristic
932#102C22×D1111yescharacteristic
933#102C22×D1111yescharacteristic
934#102C22×D1111yescharacteristic
935#102C22×D1111yescharacteristic
936#102C22×D1111yescharacteristic
937#102C22×D1111yescharacteristic
938C22⋊C8—112no—
939C22⋊C8—112no—
940C22⋊C8—112no—
941C22⋊C8—112no—
942#97—112no—
943C4×C8—112no—
944C2×C11—22no—
945C2×C11—22no—
946C2×C11—41no—
947C2×C11—42no—
948C2×C11—81no—
949C2×C11C2×#54611yescharacteristic
950C2×C11C2×#57711yescharacteristic
951C2×C11#358411yescharacteristic
952D11—42no—
953D11—82no—
954C24—21no—
955C24—221no—
956C24D4×D1111yescharacteristic
957#41—22no—
958#41—22no—
959#41—22no—
960#41—22no—
961#41—22no—
962#41—44no—
963#41—41no—
964#41—41no—
965#41—44no—
966#41—222no—
967#41—222no—
968#41—224no—
969#41—444no—
970#41—442no—
971#41—448no—
972#41—884no—
973#41#433914yescomplemented
974C2×Q8—21no—
975C2×Q8—22no—
976C2×Q8—41no—
977C2×Q8—111no—
978C2×Q8—112no—
979C2×Q8—222no—
980C2×Q8—222no—
981C2×Q8—221no—
982C2×Q8—224no—
983C2×Q8—222no—
984C2×Q8—222no—
985C2×Q8—444no—
986C2×Q8—442no—
987C2×Q8C23×D1111yescharacteristic
988C2×Q8C23×D1111yescharacteristic
989C2×D4—21no—
990C2×D4—22no—
991C2×D4—21no—
992C2×D4—21no—
993C2×D4—21no—
994C2×D4—21no—
995C2×D4—41no—
996C2×D4—44no—
997C2×D4—112no—
998C2×D4—112no—
999C2×D4—112no—
1000C2×D4—111no—
1001C2×D4—112no—
1002C2×D4—222no—
1003C2×D4—222no—
1004C2×D4—222no—
1005C2×D4—222no—
1006C2×D4—222no—
1007C2×D4—222no—
1008C2×D4—222no—
1009C2×D4—221no—
1010C2×D4—222no—
1011C2×D4—882no—
1012C2×D4C23×D1111yescharacteristic
1013C2×D4C23×D1111yescharacteristic
1014C22×C4—22no—
1015C22×C4—21no—
1016C22×C4—22no—
1017C22×C4—21no—
1018C22×C4—21no—
1019C22×C4—21no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—44no—
1024C22×C4—112no—
1025C22×C4—222no—
1026C22×C4—222no—
1027C22×C4—222no—
1028C22×C4—222no—
1029C22×C4—222no—
1030C22×C4—222no—
1031C22×C4—221no—
1032C22×C4—221no—
1033C22×C4—221no—
1034C22×C4D4×D1111yescharacteristic
1035C22×C4D4×D1111yescharacteristic
1036C22×C4D4×D1111yescharacteristic
1037C22×C4C23×D1111yescharacteristic
1038C22×C4C23×D1111yescharacteristic
1039C22×C4C23×D1111yescharacteristic
1040SD16—224no—
1041SD16—442no—
1042SD16—442no—
1043SD16—442no—
1044D8—224no—
1045D8—442no—
1046M16—222no—
1047M16—222no—
1048M16—442no—
1049C2×C8—22no—
1050C2×C8—22no—
1051C2×C8—41no—
1052C2×C8—41no—
1053C2×C8—41no—
1054C2×C8—41no—
1055C2×C8—112no—
1056C2×C8—112no—
1057C2×C8—442no—
1058C2×C8C23×D1111yescharacteristic
1059C2×C8C23×D1111yescharacteristic
1060C2×C8C23×D1111yescharacteristic
1061C2×C8C23×D1111yescharacteristic
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—111no—
1065C4⋊C4—112no—
1066C4⋊C4—111no—
1067C4⋊C4—112no—
1068C4⋊C4—112no—
1069C4⋊C4—112no—
1070C4⋊C4—222no—
1071C4⋊C4—222no—
1072C4⋊C4—222no—
1073C4⋊C4—222no—
1074C4⋊C4—222no—
1075C4⋊C4—222no—
1076C4⋊C4—222no—
1077C4⋊C4—222no—
1078C4⋊C4—221no—
1079C4⋊C4—221no—
1080C4⋊C4—222no—
1081C4⋊C4—222no—
1082C4⋊C4C23×D1111yescharacteristic
1083C4⋊C4C23×D1111yescharacteristic
1084C4⋊C4C23×D1111yescharacteristic
1085C4⋊C4C23×D1111yescharacteristic
1086C22⋊C4—21no—
1087C22⋊C4—21no—
1088C22⋊C4—21no—
1089C22⋊C4—21no—
1090C22⋊C4—112no—
1091C22⋊C4—112no—
1092C22⋊C4—112no—
1093C22⋊C4—112no—
1094C22⋊C4—112no—
1095C22⋊C4—222no—
1096C22⋊C4—222no—
1097C22⋊C4—222no—
1098C22⋊C4—222no—
1099C22⋊C4—222no—
1100C22⋊C4—222no—
1101C22⋊C4—222no—
1102C22⋊C4—222no—
1103C22⋊C4—222no—
1104C22⋊C4—222no—
1105C22⋊C4—222no—
1106C22⋊C4—222no—
1107C22⋊C4—222no—
1108C22⋊C4—222no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—112no—
1114C42—222no—
1115C42—222no—
1116C11#6117411yescharacteristic, complemented, Sylow
1117C23—22no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—41no—
1122C23—42no—
1123C23—42no—
1124C23—81no—
1125C23—112no—
1126C23—222no—
1127C23—442no—
1128C23—881no—
1129C23—881no—
1130C23C2×D4×D1111yescharacteristic
1131C23C2×D4×D1111yescharacteristic
1132C23C2×D4×D1111yescharacteristic
1133Q8—21no—
1134Q8—21no—
1135Q8—21no—
1136Q8—42no—
1137Q8—222no—
1138Q8—222no—
1139Q8—222no—
1140Q8—444no—
1141Q8—442no—
1142Q8—882no—
1143Q8C2×#433912yes—
1144D4—24no—
1145D4—21no—
1146D4—21no—
1147D4—21no—
1148D4—42no—
1149D4—42no—
1150D4—42no—
1151D4—42no—
1152D4—224no—
1153D4—224no—
1154D4—222no—
1155D4—222no—
1156D4—222no—
1157D4—442no—
1158D4—444no—
1159D4—444no—
1160D4—442no—
1161D4—882no—
1162D4—882no—
1163D4—882no—
1164D4—882no—
1165D4C2×#433912yes—
1166C2×C4—22no—
1167C2×C4—21no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—81no—
1186C2×C4—112no—
1187C2×C4—112no—
1188C2×C4—112no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—444no—
1195C2×C4—444no—
1196C2×C4—442no—
1197C2×C4—882no—
1198C2×C4—882no—
1199C2×C4—882no—
1200C2×C4—882no—
1201C2×C4—881no—
1202C2×C4—881no—
1203C2×C4C2×#433912yes—
1204C2×C4C2×D4×D1111yescharacteristic
1205C2×C4C2×D4×D1111yescharacteristic
1206C2×C4C2×D4×D1111yescharacteristic
1207C2×C4#6703712yes—
1208C2×C4C24×D1111yescharacteristic
1209C8—21no—
1210C8—21no—
1211C8—21no—
1212C8—21no—
1213C8—222no—
1214C8—222no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—22no—
1221C22—21no—
1222C22—21no—
1223C22—44no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—84no—
1230C22—222no—
1231C22—222no—
1232C22—222no—
1233C22—442no—
1234C22—442no—
1235C22—442no—
1236C22—1762no—
1237C22#1062302112yes—
1238C22#1062330112yes—
1239C22C22×D4×D1111yescharacteristic
1240C4—21no—
1241C4—21no—
1242C4—22no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—222no—
1249C4—222no—
1250C4—222no—
1251C4—442no—
1252C4—442no—
1253C4—442no—
1254C4#1062302112yes—
1255C4C22×#433911yescharacteristic
1256C4C2×#6703711yescharacteristic
1257C2—22no—
1258C2—22no—
1259C2—41no—
1260C2—42no—
1261C2—81no—
1262C2—442no—
1263C2—882no—
1264C2C2×#1062302111yescharacteristic
1265C2C2×#1062330111yescharacteristic
1266C2#1308338511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#416C2
socleC22×C11C23×D4
hypercenterC2×#416D11
hypocenterC11#61174
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. #13082351C2semidirect
2. #13082296C2semidirect
3. #13080798C2semidirect
4. #13080783C2semidirect
5. #13080588C2semidirect
6. #13080573C2semidirect
7. #13080540C2semidirect
8. #13080519C2semidirect
9. #13080477C2semidirect
10. #13080462C2semidirect
11. #13078985C2semidirect
12. #13078603C2semidirect
13. #13078564C2semidirect
14. #13078476C2semidirect
15. #13078299C2semidirect
16. C2×#10622727C2semidirect
17. #13078131C2semidirect
18. #13077905C2semidirect
19. #13077868C2semidirect
20. #13077451C2semidirect
21. #13077310C2semidirect
22. #13077145C2semidirect
23. C2×C11×#416C2semidirect
30. #10623362C22semidirect
35. #10623355C22semidirect
38. Q8×C22⋊D11C22semidirect
40. #10623337C22semidirect
46. C22×#4314C22semidirect
47. C2×#66954C22semidirect
50. #10623063C22semidirect
51. #10623061C22semidirect
53. #10623056C22semidirect
54. #10623054C22semidirect
55. #10623052C22semidirect
56. #10623050C22semidirect
66. C11×#416C22semidirect
67. C11×#416C22semidirect
68. C11×#416C22semidirect
69. C11×#416C22semidirect
70. C2×C11×#103C22semidirect
71. C2×C11×#103C22semidirect
72. C2×C11×#102C22semidirect
73. C2×C11×#102C22semidirect
83. #10622727C22semidirect
84. #10622727C22semidirect
85. C2×#66885C22semidirect
86. #10622724C22semidirect
87. #10622724C22semidirect
88. #10622723C22semidirect
89. C8×C22⋊D11C22semidirect
90. C8×C22⋊D11C22semidirect
91. C2×#66881C22semidirect
92. C2×#66880C22semidirect
93. #10622715C22semidirect
94. #10622714C22semidirect
95. #10622617C22semidirect
96. #10622617C22semidirect
97. #10622609C22semidirect
98. #10622609C22semidirect
99. #10622608C22semidirect
100. #10622608C22semidirect
101. #10622584C22semidirect
102. #10622583C22semidirect
103. #10622431C22semidirect
104. #10622431C22semidirect
105. #10622430C22semidirect
106. #10622428C22semidirect
107. #10622425C22semidirect
108. #10622420C22semidirect
109. #10622419C22semidirect
110. #10622419C22semidirect
111. #10622418C22semidirect
112. #10622415C22semidirect
113. D11×#103C22semidirect
114. #10622412C22semidirect
115. #10622410C22semidirect
116. #10622405C22semidirect
117. #10622404C22semidirect
118. #10622401C22semidirect
119. #10622400C22semidirect
120. #10622400C22semidirect
121. #10622398C22semidirect
122. #10622395C22semidirect
123. #10622394C22semidirect
124. #10622394C22semidirect
125. #10622392C22semidirect
126. #10622390C22semidirect
127. #10622388C22semidirect
128. #10622385C22semidirect
129. #10622384C22semidirect
130. #10622381C22semidirect
131. #10622378C22semidirect
132. #10622376C22semidirect
133. #10622374C22semidirect
134. #10622369C22semidirect
334. C11×#41#41semidirect
506. C2×#416D11semidirect
702. #416C2×D11semidirect
703. #416C2×D11semidirect
704. #416C2×D11semidirect
705. #416C2×D11semidirect
708. C2×#103C2×D11semidirect
709. C2×#103C2×D11semidirect
711. C2×#102C2×D11semidirect
712. C2×#102C2×D11semidirect
973. #41#4339semidirect
1116. C11#61174semidirect

Maximal subgroups

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

subgroupindex
#130823512
#130822962
#130807982
#130807832
#130805882
#130805732
#130805402
#130805192
#130804772
#130804622
#130789852
#130786032
#130785642
#130784762
#130782992
C2×#106227272
#130781312
#130779052
#130778682
#130774512
#130773102
#130771452
C2×C11×#4162
#6117411