Finite Group Databasebeta

← #15631750

Subgroups — #15631750

Order 2816.

2116 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082533C211yesmaximal, characteristic, complemented
2#13082375C211yesmaximal, characteristic, complemented
3#13080833C212yesmaximal, complemented
4#13080813C212yesmaximal, complemented
5#13080753C212yesmaximal, complemented
6#13080708C212yesmaximal, complemented
7#13080638C212yesmaximal, complemented
8#13080593C212yesmaximal, complemented
9#13080467C212yesmaximal, complemented
10#13080447C212yesmaximal, complemented
11#13079014C211yesmaximal, characteristic, complemented
12#13078605C211yesmaximal, characteristic, complemented
13#13078592C211yesmaximal, characteristic, complemented
14C2×#10622379C211yesmaximal, characteristic, complemented
15#13078286C211yesmaximal, characteristic, complemented
16#13078277C211yesmaximal, characteristic, complemented
17#13078069C211yesmaximal, characteristic, complemented
18#13077925C211yesmaximal, characteristic, complemented
19#13077920C211yesmaximal, characteristic, complemented
20#13077420C211yesmaximal, characteristic, complemented
21#13077358C211yesmaximal, characteristic, complemented
22#13077141C211yesmaximal, characteristic, complemented
23C11×#2897C211yesmaximal, characteristic, complemented
24C2×C11×H(5,𝔽2)C2211yescharacteristic
25C2×#67037C2211yescharacteristic
26C2×C11×#131C2211yescharacteristic, complemented
27C11×#520C2211yescharacteristic, complemented
28#10623364C2211yescharacteristic
29#10623364C2211yescharacteristic
30#10623364C2211yescharacteristic, complemented
31#10623363C2211yescharacteristic
32#10623363C2211yescharacteristic
33#10623360—21no—
34#10623360C2212yes—
35#10623355—21no—
36#10623355C2212yes—
37C2×#67003C2211yescharacteristic, complemented
38#10623337—21no—
39#10623337C2212yes—
40#10623335—22no—
41C2×#66992—22no—
42D4×C22⋊D11—21no—
43D4×C22⋊D11C2212yes—
44C2×D4×Dic11C2211yescharacteristic
45C2×#66985C2211yescharacteristic
46C2×#66960C2211yescharacteristic, complemented
47C2×#66957C2211yescharacteristic, complemented
48#10623114—21no—
49#10623111—21no—
50#10623096—22no—
51#10623093—21no—
52#10623088—21no—
53#10623071—22no—
54#10623061C2212yescomplemented
55#10623060C2212yescomplemented
56#10623054C2211yescharacteristic, complemented
57#10623053C2211yescharacteristic, complemented
58#10623045C2212yescomplemented
59#10623044C2212yescomplemented
60#10623041C2211yescharacteristic, complemented
61C2×#66943C2211yescharacteristic, complemented
62C11×#418C2211yescharacteristic
63C11×#418C2212yescomplemented
64C11×#417C2212yescomplemented
65C11×#417C2211yescharacteristic, complemented
66C11×#416C2211yescharacteristic, complemented
67C11×#416C2212yescomplemented
68C2×C11×#102C2211yescharacteristic
69C2×C11×#102C2212yescomplemented
70#10622852C2212yescomplemented
71#10622851C2212yescomplemented
72#10622847C2211yescharacteristic, complemented
73#10622845C2211yescharacteristic, complemented
74#10622831C2212yescomplemented
75#10622830C2212yescomplemented
76C2×#66896C2211yescharacteristic
77#10622747C2212yescomplemented
78#10622747C2212yescomplemented
79#10622746C2211yescharacteristic, complemented
80#10622746C2211yescharacteristic, complemented
81#10622741C2212yescomplemented
82#10622740C2212yescomplemented
83M16×Dic11C2211yescharacteristic, complemented
84#10622729C2212yescomplemented
85#10622728C2212yescomplemented
86#10622724C2212yescomplemented
87#10622723C2211yescharacteristic, complemented
88C8×C22⋊D11C2212yescomplemented
89C2×#66882C2211yescharacteristic, complemented
90C2×Dic11⋊C8C2211yescharacteristic, complemented
91#10622616C2212yescomplemented
92#10622615C2211yescharacteristic, complemented
93#10622609C2212yescomplemented
94#10622608C2211yescharacteristic, complemented
95#10622584C2212yescomplemented
96#10622581C2212yescomplemented
97#10622579C2211yescharacteristic, complemented
98C2×#66872C2211yescharacteristic, complemented
99#10622432C2211yescharacteristic, complemented
100#10622431C2211yescharacteristic, complemented
101#10622429C2212yescomplemented
102#10622427C2212yescomplemented
103#10622422C2212yescomplemented
104#10622420C2212yescomplemented
105#10622413C2212yescomplemented
106#10622411C2211yescharacteristic, complemented
107#10622410C2212yescomplemented
108#10622406C2211yescharacteristic, complemented
109#10622400C2211yescharacteristic, complemented
110#10622399C2211yescharacteristic, complemented
111#10622398C2212yescomplemented
112#10622397C2212yescomplemented
113#10622396C2212yescomplemented
114#10622395C2212yescomplemented
115#10622394C2212yescomplemented
116#10622391C2212yescomplemented
117#10622389C2212yescomplemented
118#10622387C2212yescomplemented
119#10622386C2212yescomplemented
120#10622385C2212yescomplemented
121#10622384C2212yescomplemented
122#10622383C2212yescomplemented
123D11×#102C2212yescomplemented
124#10622381C2212yescomplemented
125#10622380C2211yescharacteristic, complemented
126#10622379C2212yescomplemented
127#10622379C2212yescomplemented
128#10622379C2212yescomplemented
129#10622379C2212yescomplemented
130#10622377C2212yescomplemented
131#10622375C2211yescharacteristic, complemented
132#10622371C2212yescomplemented
133#10622370C2212yescomplemented
134#10622369C2212yescomplemented
135C11×H(5,𝔽2)—24no—
136C11×H(5,𝔽2)—42no—
137C2×C11×#41—21no—
138C2×C11×#41C2311yescharacteristic
139C2×C11×#41C2312yes—
140C2×C11×#41C2311yescharacteristic
141C22×D4×C11—21no—
142C22×D4×C11—22no—
143C22×D4×C11C2312yes—
144C22×D4×C11C2311yescharacteristic
145C22×C22⋊D11—22no—
146C22×C22⋊D11—22no—
147C23×Dic11—21no—
148#67037—24no—
149#67037—42no—
150C2×#4341—21no—
151C2×#4341C2312yes—
152C2×D4×D11—21no—
153C2×D4×D11C2312yes—
154C2×#4339C2311yescharacteristic
155C2×#4339C2311yescharacteristic
156C2×#4339C2311yescharacteristic
157C11×#131—42no—
158C2×C11×M16C2311yescharacteristic
159C2×C11×M16C2312yes—
160C22×C8×C11C2311yescharacteristic
161C22×C8×C11C2312yes—
162C4×Q8×C11—21no—
163C4×D4×C11—22no—
164C4×D4×C11—21no—
165C11×#117C2311yescharacteristic
166C11×#117C2312yes—
167C2×C11×C4⋊C4C2311yescharacteristic
168C2×C11×C4⋊C4C2312yes—
169#67006—22no—
170#67006—22no—
171C2×C22⋊Dic11—21no—
172C2×C22⋊Dic11—22no—
173#67003—42no—
174#67000D411yescharacteristic
175#67000C2311yescharacteristic
176#66999—21no—
177#66999—21no—
178#66999C2312yes—
179#66997D411yescharacteristic
180#66997C2311yescharacteristic
181C2×#4326C2311yescharacteristic
182C2×#4325C2311yescharacteristic
183#66993D411yescharacteristic
184#66993C2311yescharacteristic
185#66992—22no—
186#66992—22no—
187#66992—22no—
188#66992—22no—
189#66992—21no—
190#66992—21no—
191#66992—22no—
192#66992—22no—
193#66992—22no—
194#66992D412yes—
195#66992D412yes—
196#66991—21no—
197#66991—21no—
198#66991C2312yes—
199#66990—22no—
200#66990—22no—
201#66989D411yescharacteristic
202#66989C2311yescharacteristic
203#66988—22no—
204#66988—22no—
205D4×Dic11—21no—
206D4×Dic11—21no—
207D4×Dic11C2312yes—
208D4×Dic11C2312yes—
209C2×#4324C2312yes—
210C2×#4324C2311yescharacteristic
211#66985—24no—
212C2×#4323C2312yes—
213C2×#4323C2311yescharacteristic
214#66983—22no—
215#66983—22no—
216#66983—21no—
217#66983C2312yes—
218#66983C2312yes—
219#66982—22no—
220#66982—22no—
221#66982—22no—
222C4×C22⋊D11—22no—
223C4×C22⋊D11—21no—
224C4×C22⋊D11—21no—
225C4×C22⋊D11C2312yes—
226C4×C22⋊D11C2312yes—
227C2×(C2×D11)⋊C4—22no—
228#66979—22no—
229C2×C4⋊Dic11—21no—
230C2×C4⋊Dic11C2311yescharacteristic
231C2×C4⋊Dic11C2311yescharacteristic
232#66977—21no—
233#66977C2312yes—
234#66977C2312yes—
235C2×Dic11⋊C4—21no—
236C2×Dic11⋊C4—22no—
237C2×C4×Dic11C2311yescharacteristic
238C2×#4318C2311yescharacteristic
239C22×C11⋊C8C2311yescharacteristic
240#66960—42no—
241C2×Dic44C2311yescharacteristic
242#66957—42no—
243C2×D88C2311yescharacteristic
244C2×#4314C2311yescharacteristic
245C2×#4314C2311yescharacteristic
246C2×#4313C2312yes—
247C2×C8×D11C2312yes—
248#66951—22no—
249#66951—22no—
250#66950—21no—
251#66950C2312yes—
252#66948—21no—
253#66948C2312yes—
254#66947—22no—
255#66946C2311yescharacteristic
256#66946C2311yescharacteristic
257#66945C2312yes—
258C4⋊C4×D11C2312yes—
259#66943—21no—
260#66943—21no—
261#66943C2312yes—
262#66943C2312yes—
263#66942—22no—
264#66940C2311yescharacteristic
265#66940C2311yescharacteristic
266#66937—22no—
267#66936—22no—
268#66936—22no—
269(C22⋊D11)⋊C4—22no—
270(C22⋊D11)⋊C4—21no—
271(C22⋊D11)⋊C4—21no—
272#66932—22no—
273#66929—22no—
274C4×D44—21no—
275C4×D44—22no—
276#66925—22no—
277#66925—21no—
278C42×D11—21no—
279#66923—22no—
280C4×Dic22—21no—
281C11×#103C2311yescharacteristic
282C11×#103C2312yes—
283C11×#103C2311yescharacteristic
284C11×#102C2312yes—
285C11×#102C2312yes—
286C11×#102C2311yescharacteristic
287C11×#102C2312yes—
288C11×#102C2312yes—
289C11×#102C2312yes—
290C11×#102C2311yescharacteristic
291#66899C2312yes—
292#66896C2312yes—
293#66896C2312yes—
294#66896C2312yes—
295C22⋊(C11⋊C8)C2312yes—
296C22⋊(C11⋊C8)C2312yes—
297#66885C2312yes—
298#66885C2312yes—
299(C2×D11)⋊C8C2312yes—
300(C2×D11)⋊C8C2312yes—
301#66882C2312yes—
302#66882C2312yes—
303#66880C2312yes—
304#66880C2312yes—
305#66879C2312yes—
306Dic11⋊C8C2311yescharacteristic
307Dic11⋊C8C2311yescharacteristic
308Dic11⋊C8C2311yescharacteristic
309Dic11⋊C8C2311yescharacteristic
310C8×Dic11C2312yes—
311#66874C2312yes—
312#66874C2311yescharacteristic
313#66874C2311yescharacteristic
314#66873C2312yes—
315#66873C2311yescharacteristic
316#66873C2311yescharacteristic
317#66872C2312yes—
318#66872C2312yes—
319#66872C2312yes—
320#66871C2312yes—
321#61201—111nomaximal, Sylow
322C24×C11—21no—
323C24×C11—22no—
324C23×D11—22no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—24no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—42no—
331C11×#41—44no—
332C2×Q8×C11C2×D411yescharacteristic
333C2×Q8×C11C2411yescharacteristic
334C2×D4×C11—24no—
335C2×D4×C11—22no—
336C2×D4×C11—21no—
337C2×D4×C11—21no—
338C2×D4×C11—22no—
339C2×D4×C11—22no—
340C2×D4×C11—42no—
341C2×D4×C11—44no—
342C2×D4×C11—48no—
343C2×D4×C11C2×D411yescharacteristic
344C2×D4×C11C2×D412yes—
345C2×D4×C11#4114yes—
346C2×D4×C11C2411yescharacteristic
347C2×D4×C11C2412yes—
348C22×C4×C11—21no—
349C22×C4×C11—22no—
350C22×C4×C11—22no—
351C22×C4×C11—21no—
352C22×C4×C11C2412yes—
353C22×C4×C11C2411yescharacteristic
354C2×C22⋊D11—21no—
355C2×C22⋊D11—22no—
356C2×C22⋊D11—21no—
357C2×C22⋊D11—21no—
358C2×C22⋊D11—21no—
359C2×C22⋊D11—22no—
360C2×C22⋊D11—22no—
361C2×C22⋊D11—22no—
362C2×C22⋊D11—22no—
363C2×C22⋊D11—48no—
364C2×C22⋊D11—84no—
365C2×C22⋊D11C2×D412yes—
366C2×C22⋊D11C2×D412yes—
367C2×C22⋊D11C2×D412yes—
368C22×Dic11—22no—
369C22×Dic11—22no—
370C22×Dic11—22no—
371C22×Dic11—21no—
372C22×Dic11—21no—
373C22×Dic11—82no—
374C22×Dic11C2×D411yescharacteristic
375C22×Dic11C2×D411yescharacteristic
376#4341—24no—
377#4341—42no—
378#4341—44no—
379D4×D11—24no—
380D4×D11—42no—
381D4×D11—44no—
382#4339—22no—
383#4339—22no—
384#4339—22no—
385#4339—22no—
386#4339—22no—
387#4339—22no—
388C2×D44—22no—
389C2×D44C2×D411yescharacteristic
390C2×D44C2411yescharacteristic
391C2×D44C2411yescharacteristic
392C2×C4×D11—21no—
393C2×C4×D11—21no—
394C2×C4×D11—22no—
395C2×C4×D11—21no—
396C2×C4×D11—21no—
397C2×C4×D11C2412yes—
398C2×Dic22C2×D411yescharacteristic
399C2×Dic22C2411yescharacteristic
400C2×Dic22C2411yescharacteristic
401C11×M16—22no—
402C11×M16—42no—
403C2×C8×C11—22no—
404C2×C8×C11—42no—
405C2×C8×C11C2412yes—
406C2×C8×C11C2411yescharacteristic
407C2×C8×C11C2411yescharacteristic
408C11×C4⋊C4—22no—
409C11×C4⋊C4—21no—
410C11×C4⋊C4C2411yescharacteristic
411C11×C4⋊C4C2411yescharacteristic
412C11×C4⋊C4C2412yes—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—21no—
415C42×C11—21no—
416C42×C11—22no—
417C22⋊Dic11—22no—
418C22⋊Dic11—21no—
419C22⋊Dic11—21no—
420C22⋊Dic11—22no—
421C22⋊Dic11—22no—
422C22⋊Dic11—22no—
423C22⋊Dic11—22no—
424C22⋊Dic11C2×D412yes—
425C22⋊Dic11C2×D412yes—
426#4326—41no—
427#4325—41no—
428#4324—24no—
429#4324—41no—
430#4323—24no—
431#4323—41no—
432(C2×D11)⋊C4—21no—
433(C2×D11)⋊C4—21no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—21no—
436(C2×D11)⋊C4—21no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—22no—
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4C2×D412yes—
443(C2×D11)⋊C4C2×D412yes—
444C4⋊Dic11—22no—
445C4⋊Dic11—22no—
446C4⋊Dic11—22no—
447C4⋊Dic11—21no—
448C4⋊Dic11—21no—
449C4⋊Dic11C2412yes—
450C4⋊Dic11C2412yes—
451Dic11⋊C4—22no—
452Dic11⋊C4—21no—
453Dic11⋊C4—22no—
454Dic11⋊C4—21no—
455Dic11⋊C4—22no—
456Dic11⋊C4—21no—
457Dic11⋊C4—22no—
458Dic11⋊C4—21no—
459Dic11⋊C4—22no—
460Dic11⋊C4—22no—
461Dic11⋊C4C2×D412yes—
462Dic11⋊C4C2×D412yes—
463C4×Dic11—22no—
464C4×Dic11—21no—
465C4×Dic11—21no—
466C4×Dic11C2×D411yescharacteristic
467C4×Dic11C2×D411yescharacteristic
468C4×Dic11C2411yescharacteristic
469C4×Dic11C2411yescharacteristic
470#4318—22no—
471C2×C11⋊C8—22no—
472C2×C11⋊C8C2412yes—
473C2×C11⋊C8C2411yescharacteristic
474C2×C11⋊C8C2411yescharacteristic
475Dic44—41no—
476D88—41no—
477#4314—41no—
478#4314—41no—
479#4313—42no—
480C8×D11—42no—
481#3512—111no—
482#3496—111no—
483#3323—112no—
484#3322—112no—
485#3318—112no—
486#3315—112no—
487#3310—112no—
488#3307—112no—
489#3297—112no—
490#3296—112no—
491#3142—111no—
492#3099—111no—
493#3098—111no—
494C2×#478—111no—
495#3061—111no—
496#3060—111no—
497#3035—111no—
498#3012—111no—
499#3012—111no—
500C4×AGL(1,ℤ/8)—111no—
501#2935—111no—
502#2897—111no—
503#2897D1111yescharacteristic, complemented
504C23×C11—22no—
505C23×C11—24no—
506C23×C11—21no—
507C23×C11—44no—
508C23×C11—81no—
509C23×C11—81no—
510C23×C11—82no—
511C23×C11—82no—
512C23×C11C22×D412yes—
513C23×C11C22×D411yescharacteristic
514C22×D11—21no—
515C22×D11—21no—
516C22×D11—44no—
517C22×D11—82no—
518C22×D11—82no—
519C22×D11C22×D412yes—
520Q8×C11—22no—
521Q8×C11—21no—
522Q8×C11—21no—
523D4×C11—24no—
524D4×C11—24no—
525D4×C11—22no—
526D4×C11—21no—
527D4×C11—22no—
528D4×C11—21no—
529D4×C11—44no—
530D4×C11—44no—
531D4×C11—42no—
532D4×C11C2×#4114yes—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—22no—
539C2×C4×C11—44no—
540C2×C4×C11—42no—
541C2×C4×C11—82no—
542C2×C4×C11—81no—
543C2×C4×C11C22×D412yes—
544C2×C4×C11C22×D411yescharacteristic
545C2×C4×C11C2×#4112yes—
546C2×C4×C11H(5,𝔽2)12yes—
547C2×C4×C11C2511yescharacteristic
548C22⋊D11—24no—
549C22⋊D11—42no—
550C22⋊D11—42no—
551C22⋊D11—44no—
552C22⋊D11—42no—
553C22⋊D11—44no—
554C22⋊D11—42no—
555C22⋊D11—42no—
556C22⋊D11—81no—
557C22⋊D11—82no—
558C22⋊D11—82no—
559C22⋊D11—82no—
560C2×Dic11—21no—
561C2×Dic11—22no—
562C2×Dic11—21no—
563C2×Dic11—22no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—44no—
567C2×Dic11—44no—
568C2×Dic11—82no—
569C2×Dic11—81no—
570C2×Dic11—81no—
571C2×Dic11C22×D411yescharacteristic
572C2×Dic11C22×D411yescharacteristic
573C2×Dic11C22×D412yes—
574C2×Dic11C22×D411yescharacteristic
575C2×Dic11C22×D411yescharacteristic
576D44—22no—
577D44—21no—
578D44—21no—
579D44—21no—
580D44—21no—
581D44—82no—
582C4×D11—22no—
583C4×D11—22no—
584C4×D11—42no—
585C4×D11—42no—
586C4×D11—81no—
587C4×D11—81no—
588C4×D11—82no—
589Dic22—22no—
590Dic22—21no—
591Dic22—21no—
592Dic22—21no—
593Dic22—21no—
594C8×C11—22no—
595C8×C11—21no—
596C8×C11—21no—
597C11⋊C8—22no—
598C11⋊C8—21no—
599C11⋊C8—21no—
600C2×H(5,𝔽2)—111no—
601C2×H(5,𝔽2)C2×D1111yescharacteristic
602C2×AGL(1,ℤ/8)—111no—
603C2×#135—111no—
604C2×#135—111no—
605C2×#131—111no—
606C2×#131C2×D1111yescharacteristic, complemented
607#553—112no—
608#553—112no—
609#553—222no—
610#553—222no—
611#552—112no—
612#552—112no—
613#547—112no—
614#547—221no—
615#546—112no—
616#546—112no—
617#546—221no—
618#546—221no—
619D42—112no—
620D42—221no—
621#541—221no—
622#540—221no—
623#537—111no—
624#537—111no—
625#537—111no—
626#537—111no—
627#534—222no—
628#532—111no—
629#532—111no—
630#529—221no—
631#529—221no—
632C2×#125—111no—
633C2×#121—222no—
634#520—111no—
635#520C2×D1111yescharacteristic, complemented
636C4×#41—111no—
637C2×C4×D4—111no—
638#491—112no—
639#490—112no—
640#488—112no—
641#488—112no—
642#485—112no—
643#485—112no—
644#484—112no—
645#483—112no—
646#482—112no—
647#482—112no—
648#481—112no—
649#480—112no—
650#478—112no—
651#478—112no—
652#478—112no—
653#478—112no—
654#470—112no—
655#469—112no—
656#468—112no—
657#468—112no—
658#467—112no—
659#466—112no—
660#465—112no—
661#465—112no—
662#464—111no—
663#464—111no—
664#463—111no—
665#463—111no—
666#462—111no—
667#461—111no—
668#460—111no—
669#459—111no—
670#452—112no—
671#452—112no—
672#450—112no—
673#450—112no—
674#449—112no—
675#449—112no—
676#447—112no—
677#447—112no—
678#442—112no—
679#440—112no—
680C4×SD16—112no—
681C4×D8—112no—
682#436—112no—
683#435—112no—
684#435—112no—
685C8×D4—112no—
686#428—111no—
687C2×#107—111no—
688C2×#106—111no—
689C2×C4⋊C8—111no—
690#418—112no—
691#418C2×D1111yescharacteristic
692#418C2×D1112yescomplemented
693#417—111no—
694#417—111no—
695#417—111no—
696#417—111no—
697#417—112no—
698#417C2×D1111yescharacteristic, complemented
699#417C2×D1112yescomplemented
700#416—111no—
701#416—112no—
702#416C2×D1111yescharacteristic, complemented
703#416C2×D1112yescomplemented
704C2×#102—111no—
705C2×#102—112no—
706C2×#102C2×D1111yescharacteristic
707C2×#102C2×D1112yescomplemented
708#408—111no—
709#408—111no—
710C4×M16—111no—
711C22×C11—21no—
712C22×C11—21no—
713C22×C11—22no—
714C22×C11—22no—
715C22×C11—22no—
716C22×C11—24no—
717C22×C11—42no—
718C22×C11—42no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11—41no—
722C22×C11—84no—
723C22×C11—164no—
724C22×C11#54612yes—
725C22×C11C23×D411yescharacteristic
726C2×D11—22no—
727C2×D11—22no—
728C2×D11—22no—
729C2×D11—41no—
730C2×D11—41no—
731C2×D11—41no—
732C2×D11—41no—
733C2×D11—41no—
734C2×D11—41no—
735C2×D11—164no—
736C4×C11—22no—
737C4×C11—41no—
738C4×C11—42no—
739C4×C11—41no—
740C4×C11—41no—
741C4×C11#54612yes—
742C4×C11C22×#4111yescharacteristic
743C4×C11C2×H(5,𝔽2)11yescharacteristic
744Dic11—21no—
745Dic11—21no—
746Dic11—21no—
747Dic11—21no—
748Dic11—22no—
749Dic11—42no—
750Dic11—42no—
751Dic11—41no—
752Dic11—41no—
753H(5,𝔽2)—24no—
754H(5,𝔽2)—42no—
755H(5,𝔽2)—224no—
756H(5,𝔽2)—442no—
757C2×#41—21no—
758C2×#41—111no—
759C2×#41—112no—
760C2×#41—111no—
761C2×#41—111no—
762C2×#41—221no—
763C2×#41C22×D1111yescharacteristic
764C2×#41C22×D1112yes—
765C2×#41C22×D1111yescharacteristic
766C22×D4—22no—
767C22×D4—21no—
768C22×D4—112no—
769C22×D4—221no—
770C22×D4—222no—
771C22×D4—222no—
772C22×D4C22×D1112yes—
773C22×D4C22×D1111yescharacteristic
774C23×C4—221no—
775AGL(1,ℤ/8)—224no—
776#135—442no—
777#135—442no—
778C2×Q16—111no—
779C2×Q16—111no—
780C2×SD16—112no—
781C2×SD16—111no—
782C2×SD16—111no—
783C2×SD16—111no—
784C2×SD16—111no—
785C2×D8—112no—
786C2×D8—111no—
787C2×D8—111no—
788#131—42no—
789#131—442no—
790C2×M16—111no—
791C2×M16—112no—
792C2×M16C22×D1111yescharacteristic
793C2×M16C22×D1112yes—
794C22×C8—111no—
795C22×C8—112no—
796C22×C8C22×D1111yescharacteristic
797C22×C8C22×D1112yes—
798C4⋊Q8—111no—
799C4⋊Q8—111no—
800#127—111no—
801#127—111no—
802#126—222no—
803#126—222no—
804#126—222no—
805#126—222no—
806#125—112no—
807#125—112no—
808#125—222no—
809#125—221no—
810#125—221no—
811#125—222no—
812#124—111no—
813#124—111no—
814#124—111no—
815#124—111no—
816#123—222no—
817#123—222no—
818#123—222no—
819#123—222no—
820#123—222no—
821#123—222no—
822#123—222no—
823#123—222no—
824C22⋊Q8—112no—
825C22⋊Q8—112no—
826C22⋊Q8—112no—
827C22⋊Q8—112no—
828C22⋊Q8—221no—
829C22⋊Q8—221no—
830C22⋊Q8—221no—
831C22⋊Q8—221no—
832#121—112no—
833#121—112no—
834#121—112no—
835#121—112no—
836#121—112no—
837#121—112no—
838#121—222no—
839#121—222no—
840#121—222no—
841#121—221no—
842#121—222no—
843#121—221no—
844#121—222no—
845#121—222no—
846#121—221no—
847#121—221no—
848#121—222no—
849#121—222no—
850#121—222no—
851#121—221no—
852#121—221no—
853#121—222no—
854#120—222no—
855#120—222no—
856#120—222no—
857#120—222no—
858C4×Q8—21no—
859C4×Q8—111no—
860C4×Q8—111no—
861C4×Q8—221no—
862C4×D4—21no—
863C4×D4—22no—
864C4×D4—112no—
865C4×D4—112no—
866C4×D4—112no—
867C4×D4—112no—
868C4×D4—111no—
869C4×D4—111no—
870C4×D4—222no—
871C4×D4—221no—
872C4×D4—221no—
873C4×D4—221no—
874C4×D4—221no—
875C4×D4—221no—
876C4×D4—221no—
877C4×D4—221no—
878C4×D4—222no—
879C4×D4—222no—
880#117—112no—
881#117—221no—
882#117—222no—
883#117—222no—
884#117C22×D1111yescharacteristic
885#117C22×D1112yes—
886C2×C4⋊C4—111no—
887C2×C4⋊C4—111no—
888C2×C4⋊C4—112no—
889C2×C4⋊C4—222no—
890C2×C4⋊C4—221no—
891C2×C4⋊C4—221no—
892C2×C4⋊C4C22×D1111yescharacteristic
893C2×C4⋊C4C22×D1112yes—
894C2×C22⋊C4—222no—
895C2×C22⋊C4—222no—
896C2×C22⋊C4—221no—
897C2×C42—111no—
898C2×C42—221no—
899#107—112no—
900#107—112no—
901#107—112no—
902#106—112no—
903#106—112no—
904#106—112no—
905C4⋊C8—111no—
906C4⋊C8—111no—
907C4⋊C8—111no—
908C4⋊C8—111no—
909#103—112no—
910#103—112no—
911#103—112no—
912#103—111no—
913#103—111no—
914#103—112no—
915#103C22×D1111yescharacteristic
916#103C22×D1111yescharacteristic
917#103C22×D1112yes—
918#102—112no—
919#102—112no—
920#102—112no—
921#102—112no—
922#102—112no—
923#102—111no—
924#102—111no—
925#102—112no—
926#102C22×D1112yes—
927#102C22×D1112yes—
928#102C22×D1112yes—
929#102C22×D1111yescharacteristic
930#102C22×D1112yes—
931#102C22×D1112yes—
932#102C22×D1111yescharacteristic
933C22⋊C8—112no—
934C22⋊C8—112no—
935C22⋊C8—112no—
936C22⋊C8—112no—
937#97—112no—
938C4×C8—112no—
939C2×C11—22no—
940C2×C11—44no—
941C2×C11—42no—
942C2×C11—81no—
943C2×C11C2×#54611yescharacteristic
944C2×C11#358411yescharacteristic
945C2×C11#358511yescharacteristic
946D11—42no—
947D11—81no—
948D11—81no—
949C24—21no—
950C24—22no—
951C24—222no—
952#41—22no—
953#41—22no—
954#41—24no—
955#41—22no—
956#41—22no—
957#41—42no—
958#41—44no—
959#41—222no—
960#41—222no—
961#41—224no—
962#41—222no—
963#41—222no—
964#41—222no—
965#41—222no—
966#41—442no—
967#41—444no—
968C2×Q8—111no—
969C2×Q8—111no—
970C2×Q8—111no—
971C2×Q8D4×D1111yescharacteristic
972C2×Q8C23×D1111yescharacteristic
973C2×D4—24no—
974C2×D4—22no—
975C2×D4—21no—
976C2×D4—21no—
977C2×D4—22no—
978C2×D4—22no—
979C2×D4—42no—
980C2×D4—44no—
981C2×D4—48no—
982C2×D4—112no—
983C2×D4—112no—
984C2×D4—112no—
985C2×D4—111no—
986C2×D4—111no—
987C2×D4—111no—
988C2×D4—222no—
989C2×D4—221no—
990C2×D4—222no—
991C2×D4—221no—
992C2×D4—224no—
993C2×D4—222no—
994C2×D4—221no—
995C2×D4—221no—
996C2×D4—222no—
997C2×D4—222no—
998C2×D4—222no—
999C2×D4—442no—
1000C2×D4—444no—
1001C2×D4—448no—
1002C2×D4—884no—
1003C2×D4#433914yes—
1004C2×D4D4×D1112yes—
1005C2×D4D4×D1111yescharacteristic
1006C2×D4C23×D1111yescharacteristic
1007C2×D4C23×D1112yes—
1008C22×C4—21no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—21no—
1012C22×C4—111no—
1013C22×C4—111no—
1014C22×C4—112no—
1015C22×C4—221no—
1016C22×C4—221no—
1017C22×C4—222no—
1018C22×C4—222no—
1019C22×C4—222no—
1020C22×C4—222no—
1021C22×C4—221no—
1022C22×C4—221no—
1023C22×C4—221no—
1024C22×C4—221no—
1025C22×C4—882no—
1026C22×C4C23×D1112yes—
1027C22×C4C23×D1111yescharacteristic
1028Q16—441no—
1029Q16—441no—
1030SD16—224no—
1031SD16—441no—
1032SD16—441no—
1033SD16—441no—
1034SD16—441no—
1035D8—224no—
1036D8—441no—
1037D8—441no—
1038M16—22no—
1039M16—42no—
1040M16—222no—
1041M16—442no—
1042C2×C8—22no—
1043C2×C8—42no—
1044C2×C8—112no—
1045C2×C8—111no—
1046C2×C8—111no—
1047C2×C8—222no—
1048C2×C8—442no—
1049C2×C8C23×D1112yes—
1050C2×C8C23×D1111yescharacteristic
1051C2×C8C23×D1111yescharacteristic
1052C4⋊C4—21no—
1053C4⋊C4—22no—
1054C4⋊C4—112no—
1055C4⋊C4—112no—
1056C4⋊C4—112no—
1057C4⋊C4—112no—
1058C4⋊C4—222no—
1059C4⋊C4—221no—
1060C4⋊C4—222no—
1061C4⋊C4—222no—
1062C4⋊C4—222no—
1063C4⋊C4—222no—
1064C4⋊C4—222no—
1065C4⋊C4—221no—
1066C4⋊C4—221no—
1067C4⋊C4—222no—
1068C4⋊C4—221no—
1069C4⋊C4—221no—
1070C4⋊C4—221no—
1071C4⋊C4—222no—
1072C4⋊C4—222no—
1073C4⋊C4C23×D1111yescharacteristic
1074C4⋊C4C23×D1112yes—
1075C4⋊C4C23×D1111yescharacteristic
1076C22⋊C4—21no—
1077C22⋊C4—22no—
1078C22⋊C4—112no—
1079C22⋊C4—112no—
1080C22⋊C4—112no—
1081C22⋊C4—112no—
1082C22⋊C4—221no—
1083C22⋊C4—221no—
1084C22⋊C4—221no—
1085C22⋊C4—221no—
1086C22⋊C4—222no—
1087C22⋊C4—222no—
1088C22⋊C4—222no—
1089C22⋊C4—222no—
1090C22⋊C4—221no—
1091C22⋊C4—222no—
1092C22⋊C4—222no—
1093C22⋊C4—222no—
1094C22⋊C4—221no—
1095C22⋊C4—222no—
1096C22⋊C4—222no—
1097C22⋊C4—222no—
1098C22⋊C4—222no—
1099C42—21no—
1100C42—22no—
1101C42—111no—
1102C42—111no—
1103C42—111no—
1104C42—111no—
1105C42—221no—
1106C42—221no—
1107C42—222no—
1108C11#6120111yescharacteristic, complemented, Sylow
1109C23—22no—
1110C23—24no—
1111C23—21no—
1112C23—44no—
1113C23—81no—
1114C23—81no—
1115C23—82no—
1116C23—82no—
1117C23—112no—
1118C23—221no—
1119C23—221no—
1120C23—444no—
1121C23—882no—
1122C23—882no—
1123C23C2×D4×D1112yes—
1124C23C2×D4×D1111yescharacteristic
1125Q8—22no—
1126Q8—21no—
1127Q8—21no—
1128Q8—222no—
1129Q8—221no—
1130Q8—221no—
1131Q8—221no—
1132Q8—221no—
1133D4—24no—
1134D4—24no—
1135D4—22no—
1136D4—21no—
1137D4—22no—
1138D4—21no—
1139D4—44no—
1140D4—44no—
1141D4—42no—
1142D4—224no—
1143D4—222no—
1144D4—221no—
1145D4—221no—
1146D4—221no—
1147D4—221no—
1148D4—442no—
1149D4—442no—
1150D4—444no—
1151D4—442no—
1152D4—444no—
1153D4—442no—
1154D4—442no—
1155D4—882no—
1156D4—881no—
1157D4—882no—
1158D4—882no—
1159D4—882no—
1160D4C2×#433914yes—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—44no—
1168C2×C4—42no—
1169C2×C4—82no—
1170C2×C4—81no—
1171C2×C4—111no—
1172C2×C4—111no—
1173C2×C4—111no—
1174C2×C4—111no—
1175C2×C4—112no—
1176C2×C4—222no—
1177C2×C4—222no—
1178C2×C4—221no—
1179C2×C4—222no—
1180C2×C4—222no—
1181C2×C4—221no—
1182C2×C4—441no—
1183C2×C4—441no—
1184C2×C4—444no—
1185C2×C4—444no—
1186C2×C4—442no—
1187C2×C4—442no—
1188C2×C4—881no—
1189C2×C4—881no—
1190C2×C4—882no—
1191C2×C4—882no—
1192C2×C4—881no—
1193C2×C4—881no—
1194C2×C4C2×#433912yes—
1195C2×C4C2×D4×D1112yes—
1196C2×C4C2×D4×D1111yescharacteristic
1197C2×C4#6703712yes—
1198C2×C4C24×D1111yescharacteristic
1199C8—21no—
1200C8—21no—
1201C8—22no—
1202C8—222no—
1203C8—221no—
1204C8—221no—
1205C22—21no—
1206C22—21no—
1207C22—22no—
1208C22—22no—
1209C22—24no—
1210C22—22no—
1211C22—42no—
1212C22—42no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—84no—
1217C22—164no—
1218C22—222no—
1219C22—222no—
1220C22—222no—
1221C22—441no—
1222C22—441no—
1223C22—441no—
1224C22—441no—
1225C22—441no—
1226C22—441no—
1227C22—1764no—
1228C22#1062302112yes—
1229C22C22×D4×D1111yescharacteristic
1230C4—22no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—42no—
1235C4—221no—
1236C4—221no—
1237C4—222no—
1238C4—221no—
1239C4—221no—
1240C4—442no—
1241C4—442no—
1242C4—441no—
1243C4—441no—
1244C4#1062302112yes—
1245C4C22×#433911yescharacteristic
1246C4C2×#6703711yescharacteristic
1247C2—22no—
1248C2—42no—
1249C2—44no—
1250C2—81no—
1251C2—442no—
1252C2—881no—
1253C2—881no—
1254C2C2×#1062302111yescharacteristic
1255C2#1308338411yescharacteristic
1256C2#1308339411yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2897C2
socleC22×C11C23×D4
hypercenter#2897D11
hypocenterC11#61201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2897

Complements

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

NH ≅ G/Ntype
1. #13082533C2semidirect
2. #13082375C2semidirect
3. #13080833C2semidirect
4. #13080813C2semidirect
5. #13080753C2semidirect
6. #13080708C2semidirect
7. #13080638C2semidirect
8. #13080593C2semidirect
9. #13080467C2semidirect
10. #13080447C2semidirect
11. #13079014C2semidirect
12. #13078605C2semidirect
13. #13078592C2semidirect
14. C2×#10622379C2semidirect
15. #13078286C2semidirect
16. #13078277C2semidirect
17. #13078069C2semidirect
18. #13077925C2semidirect
19. #13077920C2semidirect
20. #13077420C2semidirect
21. #13077358C2semidirect
22. #13077141C2semidirect
23. C11×#2897C2semidirect
26. C2×C11×#131C22semidirect
27. C11×#520C22semidirect
30. #10623364C22semidirect
37. C2×#67003C22semidirect
46. C2×#66960C22semidirect
47. C2×#66957C22semidirect
54. #10623061C22semidirect
55. #10623060C22semidirect
56. #10623054C22semidirect
57. #10623053C22semidirect
58. #10623045C22semidirect
59. #10623044C22semidirect
60. #10623041C22semidirect
61. C2×#66943C22semidirect
63. C11×#418C22semidirect
64. C11×#417C22semidirect
65. C11×#417C22semidirect
66. C11×#416C22semidirect
67. C11×#416C22semidirect
69. C2×C11×#102C22semidirect
70. #10622852C22semidirect
71. #10622851C22semidirect
72. #10622847C22semidirect
73. #10622845C22semidirect
74. #10622831C22semidirect
75. #10622830C22semidirect
77. #10622747C22semidirect
78. #10622747C22semidirect
79. #10622746C22semidirect
80. #10622746C22semidirect
81. #10622741C22semidirect
82. #10622740C22semidirect
83. M16×Dic11C22semidirect
84. #10622729C22semidirect
85. #10622728C22semidirect
86. #10622724C22semidirect
87. #10622723C22semidirect
88. C8×C22⋊D11C22semidirect
89. C2×#66882C22semidirect
90. C2×Dic11⋊C8C22semidirect
91. #10622616C22semidirect
92. #10622615C22semidirect
93. #10622609C22semidirect
94. #10622608C22semidirect
95. #10622584C22semidirect
96. #10622581C22semidirect
97. #10622579C22semidirect
98. C2×#66872C22semidirect
99. #10622432C22semidirect
100. #10622431C22semidirect
101. #10622429C22semidirect
102. #10622427C22semidirect
103. #10622422C22semidirect
104. #10622420C22semidirect
105. #10622413C22semidirect
106. #10622411C22semidirect
107. #10622410C22semidirect
108. #10622406C22semidirect
109. #10622400C22semidirect
110. #10622399C22semidirect
111. #10622398C22semidirect
112. #10622397C22semidirect
113. #10622396C22semidirect
114. #10622395C22semidirect
115. #10622394C22semidirect
116. #10622391C22semidirect
117. #10622389C22semidirect
118. #10622387C22semidirect
119. #10622386C22semidirect
120. #10622385C22semidirect
121. #10622384C22semidirect
122. #10622383C22semidirect
123. D11×#102C22semidirect
124. #10622381C22semidirect
125. #10622380C22semidirect
126. #10622379C22semidirect
127. #10622379C22semidirect
128. #10622379C22semidirect
129. #10622379C22semidirect
130. #10622377C22semidirect
131. #10622375C22semidirect
132. #10622371C22semidirect
133. #10622370C22semidirect
134. #10622369C22semidirect
503. #2897D11semidirect
606. C2×#131C2×D11semidirect
635. #520C2×D11semidirect
692. #418C2×D11semidirect
698. #417C2×D11semidirect
699. #417C2×D11semidirect
702. #416C2×D11semidirect
703. #416C2×D11semidirect
707. C2×#102C2×D11semidirect
1108. C11#61201semidirect

Maximal subgroups

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

subgroupindex
#130825332
#130823752
#130808332
#130808132
#130807532
#130807082
#130806382
#130805932
#130804672
#130804472
#130790142
#130786052
#130785922
C2×#106223792
#130782862
#130782772
#130780692
#130779252
#130779202
#130774202
#130773582
#130771412
C11×#28972
#6120111