Finite Group Databasebeta

← #15631038

Subgroups — #15631038

Order 2816.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082333C211yesmaximal, characteristic, complemented
2#13082260C211yesmaximal, characteristic, complemented
3#13080776C212yesmaximal, complemented
4#13080716C212yesmaximal, complemented
5#13080656C212yesmaximal, complemented
6#13080596C212yesmaximal, complemented
7#13080537C212yesmaximal, complemented
8#13080526C212yesmaximal, complemented
9#13080459C212yesmaximal, complemented
10#13080444C212yesmaximal, complemented
11#13078977C211yesmaximal, characteristic, complemented
12#13078583C211yesmaximal, characteristic, complemented
13#13078549C211yesmaximal, characteristic, complemented
14#13078449C211yesmaximal, characteristic, complemented
15#13078301C211yesmaximal, characteristic, complemented
16#13078194C211yesmaximal, characteristic, complemented
17#13078170C211yesmaximal, characteristic, complemented
18#13077919C211yesmaximal, characteristic, complemented
19#13077449C211yesmaximal, characteristic, complemented
20#13077306C211yesmaximal, characteristic, complemented
21#13077141C211yesmaximal, characteristic, complemented
22C2×#10622846C211yesmaximal, characteristic, complemented
23C11×#3005C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C2×#67037C2211yescharacteristic
26C2×C11×#137C2211yescharacteristic, complemented
27C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
28C11×#525C2211yescharacteristic, complemented
29#10623364C2211yescharacteristic
30#10623360—21no—
31#10623360—21no—
32#10623360C2212yes—
33#10623360C2212yes—
34#10623358C2211yescharacteristic, complemented
35#10623355—21no—
36#10623355—21no—
37#10623355C2212yes—
38#10623355C2212yes—
39C2×#67003C2211yescharacteristic
40#10623347C2211yescharacteristic
41#10623347C2211yescharacteristic
42#10623335—22no—
43#10623329C2211yescharacteristic
44#10623322C2211yescharacteristic
45#10623322C2211yescharacteristic
46C2×#66982—22no—
47C2×#66979C2211yescharacteristic, complemented
48C23×C11⋊C8C2211yescharacteristic, complemented
49C2×#66960C2211yescharacteristic
50#10623180—22no—
51#10623172C2212yescomplemented
52#10623170C2212yescomplemented
53#10623147C2212yescomplemented
54#10623145C2212yescomplemented
55#10623124—22no—
56#10623096—21no—
57#10623094—21no—
58#10623073—21no—
59#10623072—21no—
60#10623054C2211yescharacteristic
61#10623050C2211yescharacteristic, complemented
62C11×#452C2212yescomplemented
63C11×#452C2212yescomplemented
64C11×#449C2212yescomplemented
65C11×#449C2212yescomplemented
66C11×#419C2211yescharacteristic, complemented
67C11×#418C2211yescharacteristic
68C11×#407C2211yescharacteristic, complemented
69#10622846C2212yescomplemented
70#10622846C2211yescharacteristic, complemented
71#10622846C2212yescomplemented
72#10622846C2212yescomplemented
73#10622846C2212yescomplemented
74C2×#66899C2211yescharacteristic, complemented
75C2×#66899C2211yescharacteristic, complemented
76C2×#66896C2211yescharacteristic
77C2×#66896C2211yescharacteristic
78#10622802C2212yescomplemented
79#10622801C2212yescomplemented
80#10622798C2212yescomplemented
81#10622795C2212yescomplemented
82#10622787C2212yescomplemented
83#10622786C2212yescomplemented
84#10622784C2212yescomplemented
85#10622782C2212yescomplemented
86#10622778C2212yescomplemented
87#10622777C2212yescomplemented
88#10622775C2212yescomplemented
89SD16×Dic11C2212yescomplemented
90#10622771C2212yescomplemented
91#10622769C2212yescomplemented
92#10622765C2212yescomplemented
93D8×Dic11C2212yescomplemented
94#10622746C2211yescharacteristic
95#10622746C2211yescharacteristic
96#10622742C2211yescharacteristic
97#10622735C2211yescharacteristic, complemented
98#10622734C2211yescharacteristic, complemented
99#10622734C2211yescharacteristic, complemented
100#10622732C2211yescharacteristic, complemented
101#10622664C2211yescharacteristic, complemented
102#10622664C2211yescharacteristic, complemented
103#10622661C2211yescharacteristic, complemented
104#10622661C2211yescharacteristic, complemented
105#10622654C2211yescharacteristic, complemented
106#10622654C2211yescharacteristic, complemented
107#10622651C2211yescharacteristic, complemented
108#10622651C2211yescharacteristic, complemented
109#10622615C2211yescharacteristic
110#10622611C2211yescharacteristic, complemented
111#10622428C2212yescomplemented
112#10622427C2212yescomplemented
113#10622422C2212yescomplemented
114#10622418C2212yescomplemented
115#10622413C2212yescomplemented
116#10622410C2212yescomplemented
117#10622408C2212yescomplemented
118#10622405C2212yescomplemented
119#10622385C2212yescomplemented
120#10622384C2212yescomplemented
121#10622383C2212yescomplemented
122D11×#102C2212yescomplemented
123#10622379C2212yescomplemented
124#10622376C2212yescomplemented
125#10622374C2212yescomplemented
126#10622372C2212yescomplemented
127#10622350C2212yescomplemented
128#10622350C2212yescomplemented
129#10622343C2212yescomplemented
130#10622343C2212yescomplemented
131(C22⋊D11)⋊C8C2212yescomplemented
132(C22⋊D11)⋊C8C2212yescomplemented
133#10622336C2212yescomplemented
134#10622336C2212yescomplemented
135C2×C11×#41—21no—
136C2×C11×#41—21no—
137C2×C11×#41—24no—
138C2×C11×#41—42no—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2312yes—
141C2×C11×#41C2312yes—
142C22×Q8×C11C2311yescharacteristic
143C22×D4×C11—21no—
144C22×D4×C11C2311yescharacteristic
145C23×C4×C11—21no—
146C23×C4×C11C2311yescharacteristic
147C22×C22⋊D11—22no—
148#67037—24no—
149#67037—42no—
150C2×#4341—21no—
151C2×#4341C2312yes—
152C2×D4×D11—21no—
153C2×D4×D11C2312yes—
154C2×#4339C2311yescharacteristic
155C2×#4339C2311yescharacteristic
156C11×#137—42no—
157C11×AGL(1,ℤ/8)—24no—
158C2×C11×Q16C2312yes—
159C2×C11×SD16C2312yes—
160C2×C11×SD16C2312yes—
161C2×C11×D8C2312yes—
162C2×C11×M16C2311yescharacteristic
163C2×C11×M16C2311yescharacteristic
164C11×#123—21no—
165C11×C22⋊Q8C2311yescharacteristic
166C11×C22⋊Q8C2311yescharacteristic
167C11×#121C2311yescharacteristic
168C11×#121C2311yescharacteristic
169C11×#120—21no—
170C4×D4×C11—21no—
171C4×D4×C11—21no—
172C11×#117C2311yescharacteristic
173#67006—21no—
174#67006D412yes—
175C2×C22⋊Dic11—21no—
176C2×C22⋊Dic11—22no—
177#67003—42no—
178#67000—21no—
179#67000C2312yes—
180#66999—21no—
181#66999—21no—
182#66999C2312yes—
183#66999C2312yes—
184#66999C2312yes—
185Q8×Dic11C2312yes—
186#66997—21no—
187#66997C2312yes—
188C2×#4326C2311yescharacteristic
189C2×#4325C2311yescharacteristic
190#66992—22no—
191#66992—22no—
192#66992—22no—
193#66992—22no—
194#66992—22no—
195#66992—22no—
196#66991—22no—
197#66991C2312yes—
198#66990—22no—
199#66990—22no—
200#66989—22no—
201#66988—22no—
202#66988—22no—
203#66988—22no—
204D4×Dic11—22no—
205D4×Dic11—21no—
206D4×Dic11—21no—
207D4×Dic11C2312yes—
208D4×Dic11C2312yes—
209D4×Dic11C2312yes—
210C2×#4324C2311yescharacteristic
211C2×#4323C2311yescharacteristic
212#66983—21no—
213#66983D411yescharacteristic
214#66983D411yescharacteristic
215#66983C2311yescharacteristic
216#66983C2311yescharacteristic
217#66982—21no—
218#66982—22no—
219#66982—22no—
220#66982—22no—
221#66982—22no—
222#66982—22no—
223#66982—22no—
224#66982D412yes—
225C4×C22⋊D11—21no—
226C4×C22⋊D11—21no—
227C4×C22⋊D11C2312yes—
228C4×C22⋊D11C2312yes—
229C2×(C2×D11)⋊C4—22no—
230C2×(C2×D11)⋊C4—22no—
231#66979—21no—
232#66979—21no—
233#66979—21no—
234#66979C2311yescharacteristic
235#66979C2312yes—
236#66979C2312yes—
237#66979C2311yescharacteristic
238C2×C4⋊Dic11—21no—
239C2×C4⋊Dic11C2311yescharacteristic
240C2×C4⋊Dic11C2311yescharacteristic
241#66977—21no—
242#66977D411yescharacteristic
243#66977D411yescharacteristic
244#66977C2311yescharacteristic
245#66977C2311yescharacteristic
246C2×Dic11⋊C4—22no—
247C2×Dic11⋊C4—22no—
248C2×C4×Dic11—21no—
249C22×C11⋊C8—42no—
250C22×C11⋊C8C2311yescharacteristic
251C22×C11⋊C8C2311yescharacteristic
252C22×C11⋊C8C2311yescharacteristic
253C22×C11⋊C8C2311yescharacteristic
254C22×C11⋊C8C2311yescharacteristic
255C22×C11⋊C8C2311yescharacteristic
256#66960—42no—
257C2×#4313C2312yes—
258C2×C8×D11C2312yes—
259#66951—22no—
260#66945—22no—
261#66945C2312yes—
262C4⋊C4×D11C2312yes—
263#66943C2312yes—
264#66942—22no—
265#66941C2312yes—
266#66940—22no—
267#66938—22no—
268#66938—22no—
269#66936—22no—
270(C22⋊D11)⋊C4—22no—
271(C22⋊D11)⋊C4—22no—
272#66932—22no—
273#66932—22no—
274#66932—22no—
275#66931—22no—
276#66930—22no—
277C4×D44—21no—
278#66923—21no—
279#66922—21no—
280C4×Dic22—21no—
281C11×#103C2312yes—
282C11×#103C2312yes—
283C11×#102C2312yes—
284C11×#102C2312yes—
285C11×C22⋊C8C2312yes—
286C11×C22⋊C8C2312yes—
287#66899C2311yescharacteristic
288#66899C2312yes—
289#66899C2311yescharacteristic
290#66899C2312yes—
291#66899C2312yes—
292#66899C2312yes—
293#66896C2311yescharacteristic
294#66896C2312yes—
295#66896C2311yescharacteristic
296#66896C2312yes—
297#66896C2312yes—
298#66896C2312yes—
299#66885C2312yes—
300#66885C2312yes—
301(C2×D11)⋊C8C2312yes—
302(C2×D11)⋊C8C2312yes—
303#66882C2312yes—
304#66882C2312yes—
305#66881C2312yes—
306#66881C2312yes—
307#66880C2312yes—
308#66880C2312yes—
309#66879C2312yes—
310Dic11⋊C8C2312yes—
311Dic11⋊C8C2312yes—
312C8×Dic11C2312yes—
313#66874C2311yescharacteristic
314#66874C2311yescharacteristic
315#66873C2311yescharacteristic
316#66873C2311yescharacteristic
317#66872C2311yescharacteristic
318#66872C2311yescharacteristic
319#66871C2311yescharacteristic
320#66871C2311yescharacteristic
321#61169—111nomaximal, Sylow
322C24×C11—21no—
323C24×C11C2×D411yescharacteristic
324C23×D11—22no—
325C11×#41—24no—
326C11×#41—24no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—42no—
330C11×#41—42no—
331C11×#41—44no—
332C11×#41—44no—
333C2×Q8×C11—21no—
334C2×Q8×C11—22no—
335C2×Q8×C11—22no—
336C2×Q8×C11C2412yes—
337C2×Q8×C11C2411yescharacteristic
338C2×D4×C11—21no—
339C2×D4×C11—22no—
340C2×D4×C11—22no—
341C2×D4×C11—21no—
342C2×D4×C11—21no—
343C2×D4×C11—21no—
344C2×D4×C11—22no—
345C2×D4×C11—44no—
346C2×D4×C11#4114yes—
347C2×D4×C11C2411yescharacteristic
348C2×D4×C11C2412yes—
349C22×C4×C11—22no—
350C22×C4×C11—22no—
351C22×C4×C11—21no—
352C22×C4×C11—22no—
353C22×C4×C11—22no—
354C22×C4×C11—21no—
355C22×C4×C11—44no—
356C22×C4×C11C2×D411yescharacteristic
357C22×C4×C11C2×D411yescharacteristic
358C22×C4×C11C2×D411yescharacteristic
359C22×C4×C11C2411yescharacteristic
360C22×C4×C11C2411yescharacteristic
361C22×C4×C11C2411yescharacteristic
362C2×C22⋊D11—22no—
363C2×C22⋊D11—21no—
364C2×C22⋊D11—21no—
365C2×C22⋊D11—21no—
366C2×C22⋊D11—22no—
367C2×C22⋊D11—22no—
368C2×C22⋊D11—48no—
369C2×C22⋊D11C2×D412yes—
370C2×C22⋊D11C2×D412yes—
371C2×C22⋊D11C2×D412yes—
372C22×Dic11—22no—
373C22×Dic11—22no—
374C22×Dic11—22no—
375C22×Dic11—22no—
376C22×Dic11—21no—
377C22×Dic11—21no—
378#4341—24no—
379#4341—42no—
380#4341—44no—
381D4×D11—24no—
382D4×D11—42no—
383D4×D11—44no—
384#4339—22no—
385#4339—22no—
386#4339—22no—
387#4339—22no—
388C2×D44C2×D411yescharacteristic
389C2×D44C2411yescharacteristic
390C2×C4×D11—22no—
391C2×C4×D11—21no—
392C2×C4×D11C2412yes—
393C2×Dic22—22no—
394C2×Dic22C2×D411yescharacteristic
395C2×Dic22C2411yescharacteristic
396C11×Q16—42no—
397C11×SD16—24no—
398C11×SD16—42no—
399C11×D8—24no—
400C11×M16—22no—
401C11×M16—22no—
402C2×C8×C11C2412yes—
403C2×C8×C11C2412yes—
404C11×C4⋊C4—21no—
405C11×C4⋊C4—21no—
406C11×C4⋊C4C2411yescharacteristic
407C11×C4⋊C4C2411yescharacteristic
408C11×C22⋊C4—21no—
409C11×C22⋊C4—21no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—21no—
412C11×C22⋊C4—21no—
413C42×C11—21no—
414C22⋊Dic11—22no—
415C22⋊Dic11—22no—
416C22⋊Dic11—22no—
417C22⋊Dic11—22no—
418C22⋊Dic11—22no—
419C22⋊Dic11—22no—
420C22⋊Dic11—21no—
421C22⋊Dic11—21no—
422C22⋊Dic11—21no—
423C22⋊Dic11C2×D412yes—
424C22⋊Dic11C2×D412yes—
425C22⋊Dic11C2×D412yes—
426#4326—41no—
427#4325—41no—
428#4324—41no—
429#4323—41no—
430(C2×D11)⋊C4—22no—
431(C2×D11)⋊C4—22no—
432(C2×D11)⋊C4—22no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—21no—
437(C2×D11)⋊C4—21no—
438(C2×D11)⋊C4C2×D412yes—
439(C2×D11)⋊C4C2×D412yes—
440C4⋊Dic11—22no—
441C4⋊Dic11—22no—
442C4⋊Dic11—21no—
443C4⋊Dic11—21no—
444C4⋊Dic11C2×D411yescharacteristic
445C4⋊Dic11C2×D411yescharacteristic
446C4⋊Dic11C2411yescharacteristic
447C4⋊Dic11C2411yescharacteristic
448C4⋊Dic11C2412yes—
449C4⋊Dic11C2412yes—
450Dic11⋊C4—22no—
451Dic11⋊C4—22no—
452Dic11⋊C4—22no—
453Dic11⋊C4—22no—
454Dic11⋊C4—22no—
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—21no—
459Dic11⋊C4—21no—
460Dic11⋊C4C2×D412yes—
461Dic11⋊C4C2×D412yes—
462C4×Dic11—22no—
463C4×Dic11—22no—
464C4×Dic11—22no—
465C4×Dic11—22no—
466C4×Dic11—21no—
467C4×Dic11C2412yes—
468C2×C11⋊C8—22no—
469C2×C11⋊C8—22no—
470C2×C11⋊C8—41no—
471C2×C11⋊C8—41no—
472C2×C11⋊C8—41no—
473C2×C11⋊C8—41no—
474C2×C11⋊C8C2411yescharacteristic
475C2×C11⋊C8C2411yescharacteristic
476C2×C11⋊C8C2411yescharacteristic
477C2×C11⋊C8C2411yescharacteristic
478#4313—42no—
479C8×D11—42no—
480#3493—111no—
481#3485—111no—
482#3319—112no—
483#3315—112no—
484#3311—112no—
485#3307—112no—
486#3303—112no—
487#3302—112no—
488#3297—112no—
489#3296—112no—
490#3137—111no—
491#3097—111no—
492#3093—111no—
493#3081—111no—
494#3063—111no—
495#3050—111no—
496#3046—111no—
497#3012—111no—
498#3005D1111yescharacteristic, complemented
499#2946—111no—
500#2929—111no—
501#2897—111no—
502C2×#416—111no—
503C23×C11—22no—
504C23×C11—22no—
505C23×C11—24no—
506C23×C11—21no—
507C23×C11—41no—
508C23×C11—41no—
509C23×C11—81no—
510C23×C11—81no—
511C23×C11C22×D411yescharacteristic
512C23×C11C22×D411yescharacteristic
513C23×C11C22×D411yescharacteristic
514C22×D11—21no—
515C22×D11—44no—
516C22×D11—82no—
517C22×D11—82no—
518C22×D11C22×D412yes—
519Q8×C11—21no—
520Q8×C11—22no—
521Q8×C11—21no—
522Q8×C11—22no—
523Q8×C11—42no—
524D4×C11—24no—
525D4×C11—21no—
526D4×C11—22no—
527D4×C11—21no—
528D4×C11—44no—
529D4×C11—44no—
530D4×C11—42no—
531D4×C11—81no—
532D4×C11—81no—
533D4×C11C2×#4114yes—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—21no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—22no—
545C2×C4×C11—44no—
546C2×C4×C11—44no—
547C2×C4×C11—42no—
548C2×C4×C11—42no—
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C2×#4112yes—
553C2×C4×C11H(5,𝔽2)12yes—
554C2×C4×C11C2511yescharacteristic
555C22⋊D11—24no—
556C22⋊D11—42no—
557C22⋊D11—42no—
558C22⋊D11—44no—
559C22⋊D11—44no—
560C22⋊D11—42no—
561C22⋊D11—82no—
562C22⋊D11—81no—
563C22⋊D11—81no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—21no—
567C2×Dic11—21no—
568C2×Dic11—21no—
569C2×Dic11—44no—
570C2×Dic11—82no—
571C2×Dic11—82no—
572C2×Dic11—82no—
573C2×Dic11—81no—
574C2×Dic11—81no—
575C2×Dic11C22×D412yes—
576C2×Dic11C22×D412yes—
577C2×Dic11C22×D412yes—
578D44—22no—
579D44—21no—
580D44—21no—
581C4×D11—22no—
582C4×D11—22no—
583C4×D11—42no—
584C4×D11—82no—
585Dic22—22no—
586Dic22—21no—
587Dic22—21no—
588Dic22—82no—
589C8×C11—22no—
590C8×C11—22no—
591C11⋊C8—21no—
592C11⋊C8—21no—
593C11⋊C8—21no—
594C11⋊C8—21no—
595C2×H(5,𝔽2)—111no—
596C22×#41C2×D1111yescharacteristic
597C2×#137C2×D1111yescharacteristic, complemented
598C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
599C2×#135—111no—
600C2×#131—111no—
601C23×C8—111no—
602#556—112no—
603#556—221no—
604#555—112no—
605#555—221no—
606#553—112no—
607#553—221no—
608#552—112no—
609#552—221no—
610#547—112no—
611#547—112no—
612#547—221no—
613#547—221no—
614#546—112no—
615#546—112no—
616#546—221no—
617#546—221no—
618#544—111no—
619#538—222no—
620#537—111no—
621#536—111no—
622#536—111no—
623#534—222no—
624#529—222no—
625#525—111no—
626#525—111no—
627#525C2×D1111yescharacteristic, complemented
628C2×#123—222no—
629#520—111no—
630#520—111no—
631#518—111no—
632C2×#117—111no—
633#491—112no—
634#489—112no—
635#488—112no—
636#487—112no—
637#485—112no—
638#485—112no—
639#485—112no—
640#485—112no—
641#484—112no—
642#483—112no—
643#482—112no—
644#482—112no—
645#478—112no—
646#478—112no—
647#476—112no—
648#474—112no—
649#470—112no—
650#468—112no—
651#467—112no—
652#467—111no—
653#467—111no—
654#466—111no—
655#466—111no—
656#465—112no—
657#465—111no—
658#465—111no—
659#465—111no—
660#465—111no—
661#464—112no—
662#463—112no—
663#462—112no—
664#461—112no—
665#452—112no—
666#452C2×D1112yescomplemented
667#452C2×D1112yescomplemented
668#450—112no—
669#449—112no—
670#449C2×D1112yescomplemented
671#449C2×D1112yescomplemented
672#447—112no—
673#442—112no—
674#440—112no—
675C4×SD16—112no—
676C4×D8—112no—
677#435—112no—
678#435—112no—
679C8×D4—112no—
680C8×D4—112no—
681#428—111no—
682#428—111no—
683#427—111no—
684#424—111no—
685#419C2×D1111yescharacteristic, complemented
686#418—112no—
687#418C2×D1111yescharacteristic
688#417—111no—
689#417—111no—
690#417—112no—
691#416—112no—
692#416—112no—
693#416—112no—
694#416—112no—
695#416—111no—
696#416—111no—
697#416—112no—
698C2×#103—111no—
699C2×#103—111no—
700C2×#102—111no—
701C2×#102—111no—
702C2×#102—112no—
703#408—111no—
704#407C2×D1111yescharacteristic, complemented
705#405—111no—
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—21no—
709C22×C11—21no—
710C22×C11—21no—
711C22×C11—21no—
712C22×C11—21no—
713C22×C11—21no—
714C22×C11—24no—
715C22×C11—44no—
716C22×C11—42no—
717C22×C11—42no—
718C22×C11—41no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11—84no—
722C22×C11#54612yes—
723C22×C11C23×D411yescharacteristic
724C2×D11—22no—
725C2×D11—22no—
726C2×D11—22no—
727C2×D11—41no—
728C2×D11—41no—
729C2×D11—41no—
730C2×D11—164no—
731C4×C11—21no—
732C4×C11—21no—
733C4×C11—41no—
734C4×C11—41no—
735C4×C11—42no—
736C4×C11—41no—
737C4×C11#54612yes—
738C4×C11C22×#4111yescharacteristic
739C4×C11C2×H(5,𝔽2)11yescharacteristic
740Dic11—22no—
741Dic11—22no—
742Dic11—22no—
743Dic11—42no—
744Dic11—42no—
745Dic11—41no—
746Dic11—41no—
747Dic11—41no—
748H(5,𝔽2)—224no—
749H(5,𝔽2)—442no—
750C2×#41—21no—
751C2×#41—21no—
752C2×#41—24no—
753C2×#41—42no—
754C2×#41—111no—
755C2×#41—112no—
756C2×#41—111no—
757C2×#41—221no—
758C2×#41C22×D1111yescharacteristic
759C2×#41C22×D1112yes—
760C2×#41C22×D1112yes—
761C22×Q8C22×D1111yescharacteristic
762C22×D4—21no—
763C22×D4—112no—
764C22×D4—221no—
765C22×D4—222no—
766C22×D4C22×D1111yescharacteristic
767C23×C4—21no—
768C23×C4C22×D1111yescharacteristic
769#137—42no—
770AGL(1,ℤ/8)—24no—
771#135—442no—
772C2×Q16—111no—
773C2×Q16C22×D1112yes—
774C2×SD16—111no—
775C2×SD16—111no—
776C2×SD16C22×D1112yes—
777C2×SD16C22×D1112yes—
778C2×D8—111no—
779C2×D8C22×D1112yes—
780#131—442no—
781C2×M16—112no—
782C2×M16C22×D1111yescharacteristic
783C2×M16C22×D1111yescharacteristic
784C22×C8—111no—
785C22×C8—111no—
786C22×C8—111no—
787C22×C8—111no—
788C22×C8—111no—
789C22×C8—111no—
790C22×C8—112no—
791C22×C8—442no—
792C4⋊Q8—112no—
793C4⋊Q8—112no—
794C4⋊Q8—221no—
795C4⋊Q8—221no—
796#126—222no—
797#126—222no—
798#126—222no—
799#126—222no—
800#125—112no—
801#125—221no—
802#125—222no—
803#124—112no—
804#124—222no—
805#124—222no—
806#124—222no—
807#124—221no—
808#123—21no—
809#123—112no—
810#123—222no—
811#123—222no—
812#123—222no—
813#123—222no—
814#123—222no—
815#123—222no—
816#123—222no—
817#123—222no—
818#123—222no—
819#123—222no—
820#123—221no—
821C22⋊Q8—111no—
822C22⋊Q8—111no—
823C22⋊Q8—112no—
824C22⋊Q8—112no—
825C22⋊Q8—112no—
826C22⋊Q8—111no—
827C22⋊Q8—111no—
828C22⋊Q8—222no—
829C22⋊Q8—221no—
830C22⋊Q8—221no—
831C22⋊Q8—221no—
832C22⋊Q8C22×D1111yescharacteristic
833C22⋊Q8C22×D1111yescharacteristic
834#121—111no—
835#121—111no—
836#121—112no—
837#121—111no—
838#121—111no—
839#121—222no—
840#121—222no—
841#121—221no—
842#121—222no—
843#121—222no—
844#121—222no—
845#121—222no—
846#121—222no—
847#121C22×D1111yescharacteristic
848#121C22×D1111yescharacteristic
849#120—21no—
850#120—112no—
851#120—222no—
852#120—222no—
853#120—221no—
854C4×Q8—112no—
855C4×Q8—221no—
856C4×Q8—222no—
857C4×D4—21no—
858C4×D4—21no—
859C4×D4—112no—
860C4×D4—112no—
861C4×D4—112no—
862C4×D4—112no—
863C4×D4—112no—
864C4×D4—221no—
865C4×D4—222no—
866C4×D4—222no—
867C4×D4—222no—
868C4×D4—221no—
869C4×D4—221no—
870C4×D4—221no—
871C4×D4—221no—
872#117—111no—
873#117—112no—
874#117—112no—
875#117—111no—
876#117—112no—
877#117—222no—
878#117—222no—
879#117—221no—
880#117—221no—
881#117—221no—
882#117C22×D1111yescharacteristic
883C2×C4⋊C4—111no—
884C2×C4⋊C4—111no—
885C2×C4⋊C4—112no—
886C2×C4⋊C4—221no—
887C2×C4⋊C4—222no—
888C2×C4⋊C4—222no—
889C2×C22⋊C4—222no—
890C2×C22⋊C4—222no—
891C2×C22⋊C4—222no—
892C2×C22⋊C4—221no—
893C2×C42—221no—
894#107—112no—
895#107—112no—
896#107—111no—
897#107—111no—
898#106—112no—
899#106—112no—
900#106—111no—
901#106—111no—
902C4⋊C8—112no—
903C4⋊C8—112no—
904#103—112no—
905#103—112no—
906#103—112no—
907#103—112no—
908#103—111no—
909#103—111no—
910#103—112no—
911#103—112no—
912#103—111no—
913#103—111no—
914#103C22×D1112yes—
915#103C22×D1112yes—
916#102—112no—
917#102—112no—
918#102—112no—
919#102—112no—
920#102—111no—
921#102—111no—
922#102—112no—
923#102—112no—
924#102—111no—
925#102—111no—
926#102C22×D1112yes—
927#102C22×D1112yes—
928C22⋊C8—112no—
929C22⋊C8—112no—
930C22⋊C8C22×D1112yes—
931C22⋊C8C22×D1112yes—
932#97—112no—
933C4×C8—112no—
934C2×C11—22no—
935C2×C11—44no—
936C2×C11—41no—
937C2×C11—41no—
938C2×C11—81no—
939C2×C11C2×#54611yescharacteristic
940C2×C11#358411yescharacteristic
941C2×C11#358411yescharacteristic
942D11—42no—
943D11—81no—
944C24—21no—
945C24—222no—
946C24D4×D1111yescharacteristic
947#41—24no—
948#41—24no—
949#41—22no—
950#41—22no—
951#41—42no—
952#41—42no—
953#41—44no—
954#41—44no—
955#41—222no—
956#41—222no—
957#41—224no—
958#41—222no—
959#41—222no—
960#41—442no—
961#41—444no—
962C2×Q8—21no—
963C2×Q8—22no—
964C2×Q8—22no—
965C2×Q8—111no—
966C2×Q8—111no—
967C2×Q8—222no—
968C2×Q8C23×D1112yes—
969C2×Q8C23×D1111yescharacteristic
970C2×D4—21no—
971C2×D4—22no—
972C2×D4—22no—
973C2×D4—21no—
974C2×D4—21no—
975C2×D4—21no—
976C2×D4—22no—
977C2×D4—44no—
978C2×D4—112no—
979C2×D4—112no—
980C2×D4—112no—
981C2×D4—111no—
982C2×D4—111no—
983C2×D4—222no—
984C2×D4—224no—
985C2×D4—222no—
986C2×D4—221no—
987C2×D4—222no—
988C2×D4—221no—
989C2×D4—221no—
990C2×D4—442no—
991C2×D4—444no—
992C2×D4—448no—
993C2×D4#434114yes—
994C2×D4C23×D1111yescharacteristic
995C2×D4C23×D1112yes—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—21no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—21no—
1002C22×C4—44no—
1003C22×C4—112no—
1004C22×C4—222no—
1005C22×C4—222no—
1006C22×C4—222no—
1007C22×C4—222no—
1008C22×C4—222no—
1009C22×C4—221no—
1010C22×C4—221no—
1011C22×C4—221no—
1012C22×C4D4×D1111yescharacteristic
1013C22×C4D4×D1111yescharacteristic
1014C22×C4D4×D1111yescharacteristic
1015C22×C4C23×D1111yescharacteristic
1016C22×C4C23×D1111yescharacteristic
1017C22×C4C23×D1111yescharacteristic
1018Q16—42no—
1019Q16—441no—
1020SD16—24no—
1021SD16—42no—
1022SD16—441no—
1023SD16—441no—
1024D8—24no—
1025D8—441no—
1026M16—22no—
1027M16—22no—
1028M16—442no—
1029C2×C8—111no—
1030C2×C8—111no—
1031C2×C8—111no—
1032C2×C8—111no—
1033C2×C8—222no—
1034C2×C8—222no—
1035C2×C8—442no—
1036C2×C8—441no—
1037C2×C8—441no—
1038C2×C8—441no—
1039C2×C8—441no—
1040C2×C8C23×D1112yes—
1041C2×C8C23×D1112yes—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—111no—
1045C4⋊C4—112no—
1046C4⋊C4—112no—
1047C4⋊C4—111no—
1048C4⋊C4—112no—
1049C4⋊C4—112no—
1050C4⋊C4—111no—
1051C4⋊C4—111no—
1052C4⋊C4—222no—
1053C4⋊C4—222no—
1054C4⋊C4—222no—
1055C4⋊C4—222no—
1056C4⋊C4—222no—
1057C4⋊C4—222no—
1058C4⋊C4—222no—
1059C4⋊C4—222no—
1060C4⋊C4—222no—
1061C4⋊C4—222no—
1062C4⋊C4—221no—
1063C4⋊C4—221no—
1064C4⋊C4—221no—
1065C4⋊C4—221no—
1066C4⋊C4C23×D1111yescharacteristic
1067C4⋊C4C23×D1111yescharacteristic
1068C22⋊C4—21no—
1069C22⋊C4—21no—
1070C22⋊C4—21no—
1071C22⋊C4—21no—
1072C22⋊C4—21no—
1073C22⋊C4—112no—
1074C22⋊C4—112no—
1075C22⋊C4—112no—
1076C22⋊C4—112no—
1077C22⋊C4—112no—
1078C22⋊C4—222no—
1079C22⋊C4—222no—
1080C22⋊C4—222no—
1081C22⋊C4—222no—
1082C22⋊C4—222no—
1083C22⋊C4—222no—
1084C22⋊C4—222no—
1085C22⋊C4—222no—
1086C22⋊C4—222no—
1087C22⋊C4—222no—
1088C22⋊C4—221no—
1089C22⋊C4—222no—
1090C22⋊C4—222no—
1091C22⋊C4—221no—
1092C22⋊C4—221no—
1093C22⋊C4—221no—
1094C22⋊C4—221no—
1095C42—21no—
1096C42—112no—
1097C42—222no—
1098C42—222no—
1099C42—222no—
1100C42—222no—
1101C42—221no—
1102C11#6116911yescharacteristic, complemented, Sylow
1103C23—22no—
1104C23—22no—
1105C23—24no—
1106C23—21no—
1107C23—41no—
1108C23—41no—
1109C23—81no—
1110C23—81no—
1111C23—112no—
1112C23—221no—
1113C23—444no—
1114C23—882no—
1115C23—882no—
1116C23C2×D4×D1111yescharacteristic
1117C23C2×D4×D1111yescharacteristic
1118C23C2×D4×D1111yescharacteristic
1119Q8—21no—
1120Q8—22no—
1121Q8—22no—
1122Q8—21no—
1123Q8—42no—
1124Q8—222no—
1125Q8—221no—
1126Q8—221no—
1127Q8—882no—
1128D4—24no—
1129D4—21no—
1130D4—22no—
1131D4—21no—
1132D4—44no—
1133D4—44no—
1134D4—42no—
1135D4—81no—
1136D4—81no—
1137D4—224no—
1138D4—222no—
1139D4—221no—
1140D4—221no—
1141D4—442no—
1142D4—442no—
1143D4—444no—
1144D4—444no—
1145D4—442no—
1146D4—881no—
1147D4—881no—
1148D4—882no—
1149D4C2×#434114yes—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—22no—
1161C2×C4—44no—
1162C2×C4—44no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—112no—
1166C2×C4—112no—
1167C2×C4—112no—
1168C2×C4—222no—
1169C2×C4—222no—
1170C2×C4—222no—
1171C2×C4—222no—
1172C2×C4—221no—
1173C2×C4—221no—
1174C2×C4—221no—
1175C2×C4—444no—
1176C2×C4—442no—
1177C2×C4—882no—
1178C2×C4—882no—
1179C2×C4—882no—
1180C2×C4—882no—
1181C2×C4—881no—
1182C2×C4—881no—
1183C2×C4C2×D4×D1111yescharacteristic
1184C2×C4C2×D4×D1111yescharacteristic
1185C2×C4C2×D4×D1111yescharacteristic
1186C2×C4C2×#434112yes—
1187C2×C4#6703712yes—
1188C2×C4C24×D1111yescharacteristic
1189C8—22no—
1190C8—22no—
1191C8—221no—
1192C8—221no—
1193C8—221no—
1194C8—221no—
1195C22—21no—
1196C22—21no—
1197C22—21no—
1198C22—21no—
1199C22—24no—
1200C22—21no—
1201C22—21no—
1202C22—21no—
1203C22—21no—
1204C22—44no—
1205C22—42no—
1206C22—42no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—84no—
1211C22—222no—
1212C22—222no—
1213C22—222no—
1214C22—441no—
1215C22—441no—
1216C22—441no—
1217C22—1764no—
1218C22#1062312212yes—
1219C22C22×D4×D1111yescharacteristic
1220C4—21no—
1221C4—21no—
1222C4—42no—
1223C4—41no—
1224C4—41no—
1225C4—41no—
1226C4—222no—
1227C4—222no—
1228C4—222no—
1229C4—441no—
1230C4—442no—
1231C4—441no—
1232C4—441no—
1233C4—442no—
1234C4#1062312212yes—
1235C4C22×#434111yescharacteristic
1236C4C2×#6703711yescharacteristic
1237C2—22no—
1238C2—41no—
1239C2—41no—
1240C2—44no—
1241C2—81no—
1242C2—442no—
1243C2—881no—
1244C2C2×#1062312211yescharacteristic
1245C2#1308338911yescharacteristic
1246C2#1308338911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3005C2
socleC22×C11C23×D4
hypercenter#3005D11
hypocenterC11#61169
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3005

Complements

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

NH ≅ G/Ntype
1. #13082333C2semidirect
2. #13082260C2semidirect
3. #13080776C2semidirect
4. #13080716C2semidirect
5. #13080656C2semidirect
6. #13080596C2semidirect
7. #13080537C2semidirect
8. #13080526C2semidirect
9. #13080459C2semidirect
10. #13080444C2semidirect
11. #13078977C2semidirect
12. #13078583C2semidirect
13. #13078549C2semidirect
14. #13078449C2semidirect
15. #13078301C2semidirect
16. #13078194C2semidirect
17. #13078170C2semidirect
18. #13077919C2semidirect
19. #13077449C2semidirect
20. #13077306C2semidirect
21. #13077141C2semidirect
22. C2×#10622846C2semidirect
23. C11×#3005C2semidirect
26. C2×C11×#137C22semidirect
28. C11×#525C22semidirect
34. #10623358C22semidirect
47. C2×#66979C22semidirect
48. C23×C11⋊C8C22semidirect
51. #10623172C22semidirect
52. #10623170C22semidirect
53. #10623147C22semidirect
54. #10623145C22semidirect
61. #10623050C22semidirect
62. C11×#452C22semidirect
63. C11×#452C22semidirect
64. C11×#449C22semidirect
65. C11×#449C22semidirect
66. C11×#419C22semidirect
68. C11×#407C22semidirect
69. #10622846C22semidirect
70. #10622846C22semidirect
71. #10622846C22semidirect
72. #10622846C22semidirect
73. #10622846C22semidirect
74. C2×#66899C22semidirect
75. C2×#66899C22semidirect
78. #10622802C22semidirect
79. #10622801C22semidirect
80. #10622798C22semidirect
81. #10622795C22semidirect
82. #10622787C22semidirect
83. #10622786C22semidirect
84. #10622784C22semidirect
85. #10622782C22semidirect
86. #10622778C22semidirect
87. #10622777C22semidirect
88. #10622775C22semidirect
89. SD16×Dic11C22semidirect
90. #10622771C22semidirect
91. #10622769C22semidirect
92. #10622765C22semidirect
93. D8×Dic11C22semidirect
97. #10622735C22semidirect
98. #10622734C22semidirect
99. #10622734C22semidirect
100. #10622732C22semidirect
101. #10622664C22semidirect
102. #10622664C22semidirect
103. #10622661C22semidirect
104. #10622661C22semidirect
105. #10622654C22semidirect
106. #10622654C22semidirect
107. #10622651C22semidirect
108. #10622651C22semidirect
110. #10622611C22semidirect
111. #10622428C22semidirect
112. #10622427C22semidirect
113. #10622422C22semidirect
114. #10622418C22semidirect
115. #10622413C22semidirect
116. #10622410C22semidirect
117. #10622408C22semidirect
118. #10622405C22semidirect
119. #10622385C22semidirect
120. #10622384C22semidirect
121. #10622383C22semidirect
122. D11×#102C22semidirect
123. #10622379C22semidirect
124. #10622376C22semidirect
125. #10622374C22semidirect
126. #10622372C22semidirect
127. #10622350C22semidirect
128. #10622350C22semidirect
129. #10622343C22semidirect
130. #10622343C22semidirect
131. (C22⋊D11)⋊C8C22semidirect
132. (C22⋊D11)⋊C8C22semidirect
133. #10622336C22semidirect
134. #10622336C22semidirect
498. #3005D11semidirect
597. C2×#137C2×D11semidirect
627. #525C2×D11semidirect
666. #452C2×D11semidirect
667. #452C2×D11semidirect
670. #449C2×D11semidirect
671. #449C2×D11semidirect
685. #419C2×D11semidirect
704. #407C2×D11semidirect
1102. C11#61169semidirect

Maximal subgroups

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

subgroupindex
#130823332
#130822602
#130807762
#130807162
#130806562
#130805962
#130805372
#130805262
#130804592
#130804442
#130789772
#130785832
#130785492
#130784492
#130783012
#130781942
#130781702
#130779192
#130774492
#130773062
#130771412
C2×#106228462
C11×#30052
#6116911