Finite Group Databasebeta

← #15631084

Subgroups — #15631084

Order 2816.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082345C211yesmaximal, characteristic, complemented
2#13082285C211yesmaximal, characteristic, complemented
3#13080776C212yesmaximal, complemented
4#13080761C212yesmaximal, complemented
5#13080626C212yesmaximal, complemented
6#13080611C212yesmaximal, complemented
7#13080559C212yesmaximal, complemented
8#13080522C212yesmaximal, complemented
9#13080459C212yesmaximal, complemented
10#13080422C212yesmaximal, complemented
11#13078973C211yesmaximal, characteristic, complemented
12#13078593C211yesmaximal, characteristic, complemented
13#13078557C211yesmaximal, characteristic, complemented
14#13078471C211yesmaximal, characteristic, complemented
15#13078290C211yesmaximal, characteristic, complemented
16C2×#10622651C211yesmaximal, characteristic, complemented
17#13078121C211yesmaximal, characteristic, complemented
18#13077883C211yesmaximal, characteristic, complemented
19#13077449C211yesmaximal, characteristic, complemented
20#13077306C211yesmaximal, characteristic, complemented
21#13077140C211yesmaximal, characteristic, complemented
22C2×#10622846C211yesmaximal, characteristic, complemented
23C11×#3006C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C2×#67042C2211yescharacteristic
26C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
27C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
28C2×C11×#121C2211yescharacteristic, complemented
29#10623365C2212yescomplemented
30#10623364—21no—
31#10623364C2211yescharacteristic
32#10623361—21no—
33#10623361C2211yescharacteristic
34#10623360—22no—
35#10623360C2212yescomplemented
36#10623358C2211yescharacteristic
37#10623348C2212yescomplemented
38#10623337—22no—
39#10623336C2211yescharacteristic, complemented
40D4×C22⋊D11—22no—
41D4×C22⋊D11C2212yescomplemented
42#10623329C2211yescharacteristic, complemented
43C22×#4323C2211yescharacteristic, complemented
44#10623322—21no—
45#10623322C2211yescharacteristic
46C2×#66983—21no—
47C2×#66983C2211yescharacteristic
48C2×#66979C2211yescharacteristic, complemented
49C23×C11⋊C8C2211yescharacteristic, complemented
50C2×#66960C2211yescharacteristic, complemented
51#10623150—21no—
52#10623149C2212yescomplemented
53#10623147C2212yescomplemented
54#10623145C2212yescomplemented
55#10623142C2212yescomplemented
56#10623134—21no—
57#10623131—21no—
58#10623127—21no—
59#10623035C2211yescharacteristic, complemented
60#10623031C2211yescharacteristic, complemented
61#10623026—22no—
62C11×#449C2212yescomplemented
63C11×#449C2212yescomplemented
64C11×#448C2212yescomplemented
65C11×#447C2212yescomplemented
66C11×#417C2211yescharacteristic
67C11×#417C2211yescharacteristic, complemented
68C11×#407C2211yescharacteristic, complemented
69#10622846C2211yescharacteristic
70#10622846C2211yescharacteristic
71#10622846C2211yescharacteristic, complemented
72#10622846C2211yescharacteristic, complemented
73#10622846C2211yescharacteristic, complemented
74#10622846C2211yescharacteristic, complemented
75#10622846C2211yescharacteristic, complemented
76#10622846C2211yescharacteristic, complemented
77C2×#66899C2211yescharacteristic, complemented
78C2×#66899C2211yescharacteristic, complemented
79C2×#66896C2211yescharacteristic, complemented
80C2×#66896C2211yescharacteristic, complemented
81C2×#66896C2211yescharacteristic, complemented
82#10622787C2212yescomplemented
83#10622785C2212yescomplemented
84#10622785C2212yescomplemented
85#10622784C2212yescomplemented
86#10622778C2212yescomplemented
87#10622778C2212yescomplemented
88#10622777C2212yescomplemented
89SD16×Dic11C2212yescomplemented
90#10622772C2212yescomplemented
91#10622770C2212yescomplemented
92#10622769C2212yescomplemented
93#10622769C2212yescomplemented
94#10622765C2212yescomplemented
95#10622763C2212yescomplemented
96#10622763C2212yescomplemented
97D8×Dic11C2212yescomplemented
98#10622744C2211yescharacteristic, complemented
99#10622744C2211yescharacteristic, complemented
100#10622742C2211yescharacteristic, complemented
101#10622735C2211yescharacteristic, complemented
102#10622734C2211yescharacteristic, complemented
103#10622734C2211yescharacteristic, complemented
104#10622732C2211yescharacteristic, complemented
105#10622651C2212yescomplemented
106#10622651C2212yescomplemented
107#10622651C2212yescomplemented
108#10622651C2212yescomplemented
109C2×#66873C2211yescharacteristic, complemented
110C2×#66871C2211yescharacteristic, complemented
111#10622428C2212yescomplemented
112#10622422C2212yescomplemented
113#10622417C2212yescomplemented
114#10622416C2212yescomplemented
115#10622413C2212yescomplemented
116#10622412C2212yescomplemented
117#10622408C2212yescomplemented
118#10622407C2212yescomplemented
119#10622392C2212yescomplemented
120#10622387C2212yescomplemented
121#10622383C2212yescomplemented
122D11×#102C2212yescomplemented
123#10622377C2212yescomplemented
124#10622376C2212yescomplemented
125#10622373C2212yescomplemented
126#10622372C2212yescomplemented
127#10622350C2212yescomplemented
128#10622350C2212yescomplemented
129#10622349C2212yescomplemented
130#10622348C2212yescomplemented
131#10622343C2212yescomplemented
132#10622343C2212yescomplemented
133(C22⋊D11)⋊C8C2212yescomplemented
134(C22⋊D11)⋊C8C2212yescomplemented
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×C11—21no—
146C22×D4×C11C2311yescharacteristic
147C22×D4×C11C2311yescharacteristic
148C23×C4×C11—21no—
149C23×C4×C11C2311yescharacteristic
150C22×C22⋊D11—21no—
151C22×C22⋊D11—22no—
152#67042—24no—
153#67042—42no—
154C2×#4343C2312yes—
155C2×#4341—22no—
156C2×D4×D11—22no—
157C2×D4×D11C2312yes—
158C2×#4339—21no—
159C2×#4339C2311yescharacteristic
160C22×D44—21no—
161C22×D44C2311yescharacteristic
162C11×AGL(1,ℤ/8)—24no—
163C11×AGL(1,ℤ/8)—42no—
164C2×C11×SD16C2312yes—
165C2×C11×SD16C2312yes—
166C2×C11×D8C2312yes—
167C2×C11×D8C2312yes—
168C2×C11×M16C2311yescharacteristic
169C2×C11×M16C2311yescharacteristic
170C11×#121—21no—
171C11×#121—21no—
172C11×#121C2312yes—
173C11×#121C2312yes—
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4—21no—
176#67006—22no—
177#67006—22no—
178#67006D412yes—
179C2×C22⋊Dic11—21no—
180C2×C22⋊Dic11—22no—
181#67000—22no—
182#67000C2312yes—
183#66999—22no—
184#66999C2312yes—
185Q8×Dic11C2312yes—
186#66993—22no—
187#66993—21no—
188#66993C2312yes—
189#66992—22no—
190#66992—22no—
191#66992—22no—
192#66992—22no—
193#66992—22no—
194#66991—22no—
195#66991—22no—
196#66991C2312yes—
197#66991C2312yes—
198#66991C2312yes—
199#66990—22no—
200#66990—22no—
201#66990—22no—
202#66989—21no—
203#66989—22no—
204#66988—22no—
205#66988—22no—
206D4×Dic11—22no—
207D4×Dic11—22no—
208D4×Dic11—21no—
209D4×Dic11—21no—
210D4×Dic11C2312yes—
211D4×Dic11C2312yes—
212D4×Dic11C2312yes—
213C2×#4323—42no—
214C2×#4323C2312yes—
215C2×#4323C2312yes—
216#66983—21no—
217#66983—21no—
218#66983—22no—
219#66983—21no—
220#66983—22no—
221#66983—21no—
222#66983—21no—
223#66983D411yescharacteristic
224#66983D411yescharacteristic
225#66983C2312yes—
226#66983C2312yes—
227#66982—22no—
228#66982D412yes—
229C4×C22⋊D11—22no—
230C4×C22⋊D11—22no—
231C4×C22⋊D11—22no—
232C4×C22⋊D11C2312yes—
233C4×C22⋊D11C2312yes—
234C2×(C2×D11)⋊C4—21no—
235C2×(C2×D11)⋊C4—22no—
236#66979—21no—
237#66979—21no—
238#66979—21no—
239#66979C2311yescharacteristic
240#66979C2311yescharacteristic
241#66979C2311yescharacteristic
242#66979C2311yescharacteristic
243#66979C2311yescharacteristic
244C2×C4⋊Dic11—21no—
245C2×C4⋊Dic11C2311yescharacteristic
246C2×C4⋊Dic11C2311yescharacteristic
247C2×C4⋊Dic11C2311yescharacteristic
248#66977—21no—
249#66977—22no—
250#66977D411yescharacteristic
251#66977D411yescharacteristic
252C2×C4×Dic11—21no—
253C22×C11⋊C8—42no—
254C22×C11⋊C8C2311yescharacteristic
255C22×C11⋊C8C2311yescharacteristic
256C22×C11⋊C8C2311yescharacteristic
257C22×C11⋊C8C2311yescharacteristic
258C22×C11⋊C8C2311yescharacteristic
259C22×C11⋊C8C2311yescharacteristic
260#66960—42no—
261C2×#4313C2312yes—
262C2×C8×D11C2312yes—
263#66946—21no—
264#66945C2312yes—
265C4⋊C4×D11C2312yes—
266#66943—21no—
267#66943C2312yes—
268#66941—21no—
269#66941C2312yes—
270#66940—21no—
271#66939—22no—
272#66938—22no—
273#66936—22no—
274(C22⋊D11)⋊C4—22no—
275#66932—22no—
276#66932—22no—
277#66931—22no—
278#66930—22no—
279C11×#103C2312yes—
280C11×#103C2312yes—
281C11×#102C2312yes—
282C11×#102C2312yes—
283C11×C22⋊C8C2312yes—
284C11×C22⋊C8C2312yes—
285#66899C2311yescharacteristic
286#66899C2311yescharacteristic
287#66899C2311yescharacteristic
288#66899C2311yescharacteristic
289#66899C2311yescharacteristic
290#66899C2311yescharacteristic
291#66899C2311yescharacteristic
292#66899C2311yescharacteristic
293#66896C2311yescharacteristic
294#66896C2312yes—
295#66896C2311yescharacteristic
296#66896C2311yescharacteristic
297#66896C2311yescharacteristic
298#66896C2312yes—
299#66896C2311yescharacteristic
300#66896C2311yescharacteristic
301#66896C2311yescharacteristic
302#66896C2311yescharacteristic
303#66885C2312yes—
304#66885C2312yes—
305#66885C2312yes—
306#66885C2312yes—
307(C2×D11)⋊C8C2312yes—
308(C2×D11)⋊C8C2312yes—
309#66882C2312yes—
310#66882C2312yes—
311#66881C2312yes—
312#66881C2312yes—
313#66879C2312yes—
314Dic11⋊C8C2312yes—
315Dic11⋊C8C2312yes—
316C8×Dic11C2312yes—
317#66873C2312yes—
318#66873C2312yes—
319#66871C2312yes—
320#66871C2312yes—
321#61171—111nomaximal, Sylow
322C24×C11—21no—
323C24×C11—21no—
324C24×C11C2×D411yescharacteristic
325C23×D11—21no—
326C23×D11—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41—22no—
331C11×#41—22no—
332C11×#41—44no—
333C11×#41—41no—
334C11×#41—41no—
335C11×#41—44no—
336C11×#41#4114yescomplemented
337C2×Q8×C11—21no—
338C2×Q8×C11—22no—
339C2×Q8×C11—41no—
340C2×Q8×C11C2411yescharacteristic
341C2×Q8×C11C2411yescharacteristic
342C2×D4×C11—21no—
343C2×D4×C11—22no—
344C2×D4×C11—22no—
345C2×D4×C11—21no—
346C2×D4×C11—21no—
347C2×D4×C11—21no—
348C2×D4×C11—22no—
349C2×D4×C11—21no—
350C2×D4×C11—21no—
351C2×D4×C11—22no—
352C2×D4×C11—22no—
353C2×D4×C11—41no—
354C2×D4×C11—44no—
355C2×D4×C11—82no—
356C2×D4×C11C2411yescharacteristic
357C2×D4×C11C2412yes—
358C2×D4×C11C2411yescharacteristic
359C22×C4×C11—21no—
360C22×C4×C11—22no—
361C22×C4×C11—22no—
362C22×C4×C11—21no—
363C22×C4×C11—21no—
364C22×C4×C11—21no—
365C22×C4×C11—21no—
366C22×C4×C11—21no—
367C22×C4×C11—44no—
368C22×C4×C11C2×D411yescharacteristic
369C22×C4×C11C2×D411yescharacteristic
370C22×C4×C11C2×D411yescharacteristic
371C22×C4×C11C2411yescharacteristic
372C22×C4×C11C2411yescharacteristic
373C22×C4×C11C2411yescharacteristic
374C2×C22⋊D11—22no—
375C2×C22⋊D11—22no—
376C2×C22⋊D11—22no—
377C2×C22⋊D11—22no—
378C2×C22⋊D11—22no—
379C2×C22⋊D11—22no—
380C2×C22⋊D11—22no—
381C2×C22⋊D11—22no—
382C2×C22⋊D11—82no—
383C2×C22⋊D11—84no—
384C2×C22⋊D11C2×D412yes—
385C2×C22⋊D11C2×D412yes—
386C2×C22⋊D11C2×D412yes—
387C22×Dic11—22no—
388C22×Dic11—22no—
389C22×Dic11—22no—
390C22×Dic11—21no—
391C22×Dic11—21no—
392C22×Dic11—21no—
393#4343—24no—
394#4343—42no—
395#4341—84no—
396D4×D11—24no—
397D4×D11—42no—
398D4×D11—48no—
399#4339—22no—
400#4339—22no—
401#4339—44no—
402C2×D44—22no—
403C2×D44—21no—
404C2×D44—22no—
405C2×D44—22no—
406C2×D44—44no—
407C2×D44C2×D411yescharacteristic
408C2×D44C2412yes—
409C2×C4×D11—22no—
410C2×C4×D11—22no—
411C2×C4×D11C2412yes—
412C2×Dic22—22no—
413C2×Dic22C2×D411yescharacteristic
414C11×SD16—24no—
415C11×SD16—42no—
416C11×D8—24no—
417C11×D8—42no—
418C11×M16—22no—
419C11×M16—22no—
420C2×C8×C11C2412yes—
421C2×C8×C11C2412yes—
422C11×C4⋊C4—21no—
423C11×C4⋊C4C2412yes—
424C11×C22⋊C4—22no—
425C11×C22⋊C4—22no—
426C22⋊Dic11—22no—
427C22⋊Dic11—22no—
428C22⋊Dic11—22no—
429C22⋊Dic11—22no—
430C22⋊Dic11—22no—
431C22⋊Dic11—22no—
432C22⋊Dic11—21no—
433C22⋊Dic11—21no—
434C22⋊Dic11—21no—
435C22⋊Dic11—21no—
436C22⋊Dic11C2×D412yes—
437C22⋊Dic11C2×D412yes—
438C22⋊Dic11C2×D412yes—
439#4323—42no—
440#4323—42no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—22no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—22no—
447(C2×D11)⋊C4C2×D412yes—
448(C2×D11)⋊C4C2×D412yes—
449C4⋊Dic11—22no—
450C4⋊Dic11—22no—
451C4⋊Dic11—21no—
452C4⋊Dic11—21no—
453C4⋊Dic11—21no—
454C4⋊Dic11C2×D411yescharacteristic
455C4⋊Dic11C2×D411yescharacteristic
456C4⋊Dic11C2412yes—
457C4⋊Dic11C2411yescharacteristic
458C4⋊Dic11C2411yescharacteristic
459C4⋊Dic11C2411yescharacteristic
460C4⋊Dic11C2411yescharacteristic
461Dic11⋊C4—22no—
462Dic11⋊C4—22no—
463Dic11⋊C4—22no—
464Dic11⋊C4—22no—
465Dic11⋊C4C2×D412yes—
466Dic11⋊C4C2×D412yes—
467C4×Dic11—22no—
468C4×Dic11—22no—
469C4×Dic11—21no—
470C4×Dic11—21no—
471C4×Dic11—21no—
472C4×Dic11—21no—
473C4×Dic11C2412yes—
474C2×C11⋊C8—22no—
475C2×C11⋊C8—22no—
476C2×C11⋊C8—41no—
477C2×C11⋊C8—41no—
478C2×C11⋊C8—41no—
479C2×C11⋊C8—41no—
480C2×C11⋊C8C2411yescharacteristic
481C2×C11⋊C8C2411yescharacteristic
482C2×C11⋊C8C2411yescharacteristic
483C2×C11⋊C8C2411yescharacteristic
484#4313—42no—
485C8×D11—42no—
486#3494—111no—
487#3488—111no—
488#3319—112no—
489#3318—112no—
490#3309—112no—
491#3308—112no—
492#3305—112no—
493#3301—112no—
494#3297—112no—
495#3294—112no—
496#3136—111no—
497#3098—111no—
498#3094—111no—
499#3083—111no—
500#3062—111no—
501C2×#466—111no—
502#3041—111no—
503#3008—111no—
504#3006D1111yescharacteristic, complemented
505#2946—111no—
506#2929—111no—
507#2897—111no—
508C2×#416—111no—
509C23×C11—22no—
510C23×C11—22no—
511C23×C11—21no—
512C23×C11—22no—
513C23×C11—21no—
514C23×C11—41no—
515C23×C11—42no—
516C23×C11—42no—
517C23×C11—42no—
518C23×C11—81no—
519C23×C11—81no—
520C23×C11—81no—
521C23×C11C22×D411yescharacteristic
522C23×C11C22×D411yescharacteristic
523C23×C11C22×D411yescharacteristic
524C22×D11—22no—
525C22×D11—44no—
526C22×D11—42no—
527C22×D11—82no—
528C22×D11—82no—
529C22×D11—81no—
530C22×D11—81no—
531C22×D11C22×D412yes—
532Q8×C11—21no—
533Q8×C11—21no—
534Q8×C11—21no—
535Q8×C11—42no—
536Q8×C11C2×#4112yes—
537D4×C11—24no—
538D4×C11—22no—
539D4×C11—21no—
540D4×C11—21no—
541D4×C11—22no—
542D4×C11—21no—
543D4×C11—42no—
544D4×C11—42no—
545D4×C11—42no—
546D4×C11—42no—
547D4×C11—44no—
548D4×C11—42no—
549D4×C11—82no—
550D4×C11C2×#4112yes—
551C2×C4×C11—22no—
552C2×C4×C11—21no—
553C2×C4×C11—24no—
554C2×C4×C11—22no—
555C2×C4×C11—22no—
556C2×C4×C11—21no—
557C2×C4×C11—21no—
558C2×C4×C11—21no—
559C2×C4×C11—21no—
560C2×C4×C11—22no—
561C2×C4×C11—21no—
562C2×C4×C11—42no—
563C2×C4×C11—42no—
564C2×C4×C11—42no—
565C2×C4×C11—42no—
566C2×C4×C11—81no—
567C2×C4×C11C22×D411yescharacteristic
568C2×C4×C11C22×D411yescharacteristic
569C2×C4×C11C22×D411yescharacteristic
570C2×C4×C11C2×#4112yes—
571C2×C4×C11H(5,𝔽2)12yes—
572C2×C4×C11C2511yescharacteristic
573C22⋊D11—24no—
574C22⋊D11—24no—
575C22⋊D11—42no—
576C22⋊D11—44no—
577C22⋊D11—44no—
578C22⋊D11—82no—
579C22⋊D11—82no—
580C22⋊D11—82no—
581C22⋊D11—82no—
582C22⋊D11—82no—
583C22⋊D11—82no—
584C2×Dic11—21no—
585C2×Dic11—21no—
586C2×Dic11—21no—
587C2×Dic11—21no—
588C2×Dic11—22no—
589C2×Dic11—42no—
590C2×Dic11—82no—
591C2×Dic11—82no—
592C2×Dic11—82no—
593C2×Dic11—81no—
594C2×Dic11—81no—
595C2×Dic11C22×D412yes—
596C2×Dic11C22×D412yes—
597C2×Dic11C22×D412yes—
598D44—22no—
599D44—22no—
600D44—22no—
601D44—44no—
602D44—42no—
603C4×D11—22no—
604C4×D11—22no—
605C4×D11—44no—
606C4×D11—82no—
607Dic22—22no—
608Dic22—82no—
609C8×C11—22no—
610C8×C11—22no—
611C11⋊C8—21no—
612C11⋊C8—21no—
613C11⋊C8—21no—
614C11⋊C8—21no—
615C2×H(5,𝔽2)—111no—
616C22×#41C2×D1111yescharacteristic
617C2×AGL(1,ℤ/8)C2×D1111yescharacteristic
618C2×AGL(1,ℤ/8)C2×D1111yescharacteristic, complemented
619C22×D8—111no—
620C2×#131—111no—
621C23×C8—111no—
622#555—112no—
623#553—112no—
624#553—112no—
625#551—222no—
626#550—112no—
627#548—112no—
628#547—112no—
629#546—112no—
630#546—222no—
631#546—222no—
632D42—112no—
633D42—222no—
634#544—111no—
635#542—221no—
636#540—221no—
637#537—111no—
638#537—221no—
639#535—111no—
640#535—111no—
641#535—221no—
642#532—221no—
643#529—221no—
644#525—111no—
645#525—221no—
646C2×#121—111no—
647C2×#121—221no—
648C2×#121C2×D1111yescharacteristic, complemented
649#520—111no—
650#520—111no—
651#518—111no—
652C2×#117—111no—
653#490—112no—
654#489—112no—
655#488—112no—
656#486—112no—
657#485—112no—
658#484—112no—
659#482—112no—
660#482—112no—
661#482—112no—
662#481—112no—
663#480—112no—
664#480—112no—
665#479—112no—
666#478—112no—
667#477—112no—
668#474—112no—
669#469—112no—
670#468—112no—
671#466—112no—
672#466—112no—
673#466—112no—
674#466—112no—
675#466—112no—
676#465—112no—
677#463—112no—
678#463—112no—
679#459—112no—
680#459—112no—
681#449—112no—
682#449—112no—
683#449C2×D1112yescomplemented
684#449C2×D1112yescomplemented
685#448C2×D1112yescomplemented
686#447—112no—
687#447—112no—
688#447C2×D1112yescomplemented
689#442—112no—
690#440—112no—
691C4×SD16—112no—
692C4×D8—112no—
693#435—112no—
694#435—112no—
695C8×D4—112no—
696C8×D4—112no—
697#428—111no—
698#428—111no—
699C2×#107—111no—
700#424—111no—
701#418—111no—
702#418—111no—
703#418—112no—
704#417—112no—
705#417C2×D1111yescharacteristic
706#417C2×D1111yescharacteristic, complemented
707#416—111no—
708#416—111no—
709#416—111no—
710#416—111no—
711#416—111no—
712#416—111no—
713#416—111no—
714#416—111no—
715#416—112no—
716C2×#103—111no—
717C2×#103—111no—
718C2×#102—111no—
719C2×#102—111no—
720C2×#102—111no—
721C2×#102—111no—
722C2×#102—112no—
723#408—111no—
724#407C2×D1111yescharacteristic, complemented
725#405—111no—
726C22×C11—21no—
727C22×C11—21no—
728C22×C11—21no—
729C22×C11—21no—
730C22×C11—21no—
731C22×C11—21no—
732C22×C11—22no—
733C22×C11—21no—
734C22×C11—44no—
735C22×C11—41no—
736C22×C11—41no—
737C22×C11—42no—
738C22×C11—41no—
739C22×C11—41no—
740C22×C11—42no—
741C22×C11—42no—
742C22×C11—41no—
743C22×C11—84no—
744C22×C11—162no—
745C22×C11#54612yes—
746C22×C11#57612yes—
747C22×C11C23×D411yescharacteristic
748C2×D11—22no—
749C2×D11—22no—
750C2×D11—22no—
751C2×D11—42no—
752C2×D11—42no—
753C2×D11—42no—
754C2×D11—164no—
755C2×D11—162no—
756C4×C11—21no—
757C4×C11—21no—
758C4×C11—22no—
759C4×C11—41no—
760C4×C11—42no—
761C4×C11#54612yes—
762C4×C11C22×#4111yescharacteristic
763C4×C11C2×H(5,𝔽2)11yescharacteristic
764Dic11—22no—
765Dic11—22no—
766Dic11—22no—
767Dic11—41no—
768Dic11—41no—
769Dic11—41no—
770Dic11—41no—
771Dic11—42no—
772H(5,𝔽2)—224no—
773H(5,𝔽2)—442no—
774C2×#41—21no—
775C2×#41—21no—
776C2×#41—24no—
777C2×#41—42no—
778C2×#41—111no—
779C2×#41—112no—
780C2×#41—221no—
781C2×#41—222no—
782C2×#41C22×D1111yescharacteristic
783C2×#41C22×D1111yescharacteristic
784C2×#41C22×D1111yescharacteristic
785C2×#41C22×D1111yescharacteristic
786C22×Q8C22×D1111yescharacteristic
787C22×D4—21no—
788C22×D4—21no—
789C22×D4—112no—
790C22×D4—111no—
791C22×D4—221no—
792C22×D4—222no—
793C22×D4—222no—
794C22×D4—221no—
795C22×D4C22×D1111yescharacteristic
796C22×D4C22×D1111yescharacteristic
797C23×C4—21no—
798C23×C4C22×D1111yescharacteristic
799AGL(1,ℤ/8)—24no—
800AGL(1,ℤ/8)—42no—
801C2×SD16C22×D1112yes—
802C2×SD16C22×D1112yes—
803C2×D8—112no—
804C2×D8—112no—
805C2×D8—442no—
806C2×D8C22×D1112yes—
807C2×D8C22×D1112yes—
808#131—442no—
809C2×M16—112no—
810C2×M16C22×D1111yescharacteristic
811C2×M16C22×D1111yescharacteristic
812C22×C8—111no—
813C22×C8—111no—
814C22×C8—111no—
815C22×C8—111no—
816C22×C8—111no—
817C22×C8—111no—
818C22×C8—112no—
819C22×C8—442no—
820C4⋊Q8—112no—
821C4⋊Q8—221no—
822#127—112no—
823#127—221no—
824#127—222no—
825#126—222no—
826#126—222no—
827#125—112no—
828#125—221no—
829#124—112no—
830#124—222no—
831#124—222no—
832#124—222no—
833#124—221no—
834#123—112no—
835#123—222no—
836#123—222no—
837#123—222no—
838#123—222no—
839#123—222no—
840C22⋊Q8—111no—
841C22⋊Q8—111no—
842C22⋊Q8—112no—
843C22⋊Q8—222no—
844C22⋊Q8—222no—
845C22⋊Q8—222no—
846C22⋊Q8—221no—
847#121—21no—
848#121—21no—
849#121—111no—
850#121—111no—
851#121—112no—
852#121—112no—
853#121—112no—
854#121—112no—
855#121—112no—
856#121—222no—
857#121—222no—
858#121—222no—
859#121—221no—
860#121—221no—
861#121—222no—
862#121—221no—
863#121—222no—
864#121—222no—
865#121—222no—
866#121—222no—
867#121—222no—
868#121—221no—
869#121—221no—
870#121C22×D1112yes—
871#121C22×D1112yes—
872#120—112no—
873#120—222no—
874#120—222no—
875#120—222no—
876#120—222no—
877#120—222no—
878C4×Q8—112no—
879C4×Q8—221no—
880C4×D4—112no—
881C4×D4—112no—
882C4×D4—112no—
883C4×D4—112no—
884C4×D4—112no—
885C4×D4—222no—
886C4×D4—222no—
887C4×D4—222no—
888C4×D4—222no—
889C4×D4—221no—
890C4×D4—222no—
891C4×D4—221no—
892C4×D4—221no—
893C4×D4—222no—
894#117—111no—
895#117—111no—
896#117—111no—
897#117—111no—
898#117—111no—
899#117—112no—
900#117—222no—
901#117—221no—
902#117—221no—
903#117—221no—
904C2×C4⋊C4—111no—
905C2×C4⋊C4—111no—
906C2×C4⋊C4—111no—
907C2×C4⋊C4—112no—
908C2×C4⋊C4—221no—
909C2×C4⋊C4C22×D1111yescharacteristic
910C2×C22⋊C4—21no—
911C2×C22⋊C4—222no—
912C2×C22⋊C4—222no—
913C2×C22⋊C4—221no—
914C2×C22⋊C4—221no—
915C2×C42—221no—
916#107—112no—
917#107—112no—
918#107—112no—
919#107—112no—
920#106—112no—
921#106—112no—
922C4⋊C8—112no—
923C4⋊C8—112no—
924#103—111no—
925#103—111no—
926#103—111no—
927#103—111no—
928#103—111no—
929#103—111no—
930#103—111no—
931#103—111no—
932#103C22×D1112yes—
933#103C22×D1112yes—
934#102—111no—
935#102—111no—
936#102—111no—
937#102—111no—
938#102—111no—
939#102—111no—
940#102—111no—
941#102—111no—
942#102—112no—
943#102—112no—
944#102—112no—
945#102—112no—
946#102—112no—
947#102—112no—
948#102—112no—
949#102—112no—
950#102C22×D1112yes—
951#102C22×D1112yes—
952C22⋊C8—112no—
953C22⋊C8—112no—
954C22⋊C8C22×D1112yes—
955C22⋊C8C22×D1112yes—
956#97—112no—
957C4×C8—112no—
958C2×C11—22no—
959C2×C11—22no—
960C2×C11—42no—
961C2×C11—41no—
962C2×C11—81no—
963C2×C11—82no—
964C2×C11C2×#54611yescharacteristic
965C2×C11C2×#57611yescharacteristic
966C2×C11#358411yescharacteristic
967D11—42no—
968D11—82no—
969C24—21no—
970C24—21no—
971C24—222no—
972C24—221no—
973C24D4×D1111yescharacteristic
974#41—22no—
975#41—22no—
976#41—22no—
977#41—22no—
978#41—22no—
979#41—44no—
980#41—41no—
981#41—41no—
982#41—44no—
983#41—222no—
984#41—222no—
985#41—224no—
986#41—444no—
987#41—442no—
988#41—884no—
989#41#434114yescomplemented
990C2×Q8—21no—
991C2×Q8—22no—
992C2×Q8—41no—
993C2×Q8—111no—
994C2×Q8—222no—
995C2×Q8C23×D1111yescharacteristic
996C2×Q8C23×D1111yescharacteristic
997C2×D4—21no—
998C2×D4—22no—
999C2×D4—22no—
1000C2×D4—21no—
1001C2×D4—21no—
1002C2×D4—21no—
1003C2×D4—22no—
1004C2×D4—21no—
1005C2×D4—21no—
1006C2×D4—22no—
1007C2×D4—22no—
1008C2×D4—41no—
1009C2×D4—44no—
1010C2×D4—82no—
1011C2×D4—112no—
1012C2×D4—112no—
1013C2×D4—112no—
1014C2×D4—111no—
1015C2×D4—112no—
1016C2×D4—222no—
1017C2×D4—222no—
1018C2×D4—222no—
1019C2×D4—222no—
1020C2×D4—224no—
1021C2×D4—222no—
1022C2×D4—222no—
1023C2×D4—222no—
1024C2×D4—222no—
1025C2×D4—222no—
1026C2×D4—221no—
1027C2×D4—222no—
1028C2×D4—222no—
1029C2×D4—444no—
1030C2×D4—442no—
1031C2×D4—448no—
1032C2×D4—884no—
1033C2×D4—882no—
1034C2×D4C23×D1111yescharacteristic
1035C2×D4C23×D1112yes—
1036C2×D4C23×D1111yescharacteristic
1037C22×C4—21no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—21no—
1041C22×C4—21no—
1042C22×C4—21no—
1043C22×C4—21no—
1044C22×C4—21no—
1045C22×C4—44no—
1046C22×C4—112no—
1047C22×C4—222no—
1048C22×C4—222no—
1049C22×C4—222no—
1050C22×C4—222no—
1051C22×C4—222no—
1052C22×C4—221no—
1053C22×C4—221no—
1054C22×C4—221no—
1055C22×C4D4×D1111yescharacteristic
1056C22×C4D4×D1111yescharacteristic
1057C22×C4D4×D1111yescharacteristic
1058C22×C4C23×D1111yescharacteristic
1059C22×C4C23×D1111yescharacteristic
1060C22×C4C23×D1111yescharacteristic
1061SD16—24no—
1062SD16—42no—
1063D8—24no—
1064D8—42no—
1065D8—442no—
1066D8—442no—
1067M16—22no—
1068M16—22no—
1069M16—442no—
1070C2×C8—111no—
1071C2×C8—111no—
1072C2×C8—111no—
1073C2×C8—111no—
1074C2×C8—222no—
1075C2×C8—222no—
1076C2×C8—442no—
1077C2×C8—441no—
1078C2×C8—441no—
1079C2×C8—441no—
1080C2×C8—441no—
1081C2×C8C23×D1112yes—
1082C2×C8C23×D1112yes—
1083C4⋊C4—21no—
1084C4⋊C4—111no—
1085C4⋊C4—111no—
1086C4⋊C4—112no—
1087C4⋊C4—112no—
1088C4⋊C4—111no—
1089C4⋊C4—111no—
1090C4⋊C4—111no—
1091C4⋊C4—111no—
1092C4⋊C4—112no—
1093C4⋊C4—222no—
1094C4⋊C4—222no—
1095C4⋊C4—222no—
1096C4⋊C4—222no—
1097C4⋊C4—222no—
1098C4⋊C4—222no—
1099C4⋊C4—221no—
1100C4⋊C4—221no—
1101C4⋊C4—221no—
1102C4⋊C4C23×D1112yes—
1103C22⋊C4—22no—
1104C22⋊C4—22no—
1105C22⋊C4—112no—
1106C22⋊C4—112no—
1107C22⋊C4—112no—
1108C22⋊C4—112no—
1109C22⋊C4—112no—
1110C22⋊C4—222no—
1111C22⋊C4—222no—
1112C22⋊C4—222no—
1113C22⋊C4—222no—
1114C22⋊C4—222no—
1115C22⋊C4—222no—
1116C22⋊C4—222no—
1117C22⋊C4—222no—
1118C22⋊C4—222no—
1119C22⋊C4—222no—
1120C22⋊C4—221no—
1121C22⋊C4—221no—
1122C22⋊C4—221no—
1123C22⋊C4—221no—
1124C22⋊C4—222no—
1125C22⋊C4—222no—
1126C42—112no—
1127C42—222no—
1128C42—222no—
1129C42—221no—
1130C42—221no—
1131C42—221no—
1132C42—221no—
1133C11#6117111yescharacteristic, complemented, Sylow
1134C23—22no—
1135C23—22no—
1136C23—21no—
1137C23—22no—
1138C23—21no—
1139C23—41no—
1140C23—42no—
1141C23—42no—
1142C23—42no—
1143C23—81no—
1144C23—81no—
1145C23—81no—
1146C23—112no—
1147C23—222no—
1148C23—444no—
1149C23—442no—
1150C23—881no—
1151C23—881no—
1152C23—882no—
1153C23—882no—
1154C23C2×D4×D1111yescharacteristic
1155C23C2×D4×D1111yescharacteristic
1156C23C2×D4×D1111yescharacteristic
1157Q8—21no—
1158Q8—21no—
1159Q8—21no—
1160Q8—42no—
1161Q8—222no—
1162Q8—882no—
1163Q8C2×#434112yes—
1164D4—24no—
1165D4—22no—
1166D4—21no—
1167D4—21no—
1168D4—21no—
1169D4—22no—
1170D4—42no—
1171D4—42no—
1172D4—42no—
1173D4—44no—
1174D4—42no—
1175D4—42no—
1176D4—82no—
1177D4—224no—
1178D4—224no—
1179D4—222no—
1180D4—222no—
1181D4—222no—
1182D4—444no—
1183D4—442no—
1184D4—444no—
1185D4—444no—
1186D4—442no—
1187D4—882no—
1188D4—882no—
1189D4—882no—
1190D4—882no—
1191D4—882no—
1192D4—882no—
1193D4C2×#434112yes—
1194C2×C4—22no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—81no—
1210C2×C4—112no—
1211C2×C4—112no—
1212C2×C4—112no—
1213C2×C4—222no—
1214C2×C4—222no—
1215C2×C4—221no—
1216C2×C4—221no—
1217C2×C4—221no—
1218C2×C4—221no—
1219C2×C4—222no—
1220C2×C4—444no—
1221C2×C4—442no—
1222C2×C4—882no—
1223C2×C4—882no—
1224C2×C4—882no—
1225C2×C4—882no—
1226C2×C4—881no—
1227C2×C4—881no—
1228C2×C4C2×D4×D1111yescharacteristic
1229C2×C4C2×D4×D1111yescharacteristic
1230C2×C4C2×D4×D1111yescharacteristic
1231C2×C4C2×#434112yes—
1232C2×C4#6703712yes—
1233C2×C4C24×D1111yescharacteristic
1234C8—22no—
1235C8—22no—
1236C8—221no—
1237C8—221no—
1238C8—221no—
1239C8—221no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—22no—
1246C22—21no—
1247C22—21no—
1248C22—44no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—42no—
1253C22—42no—
1254C22—41no—
1255C22—42no—
1256C22—41no—
1257C22—84no—
1258C22—162no—
1259C22—222no—
1260C22—222no—
1261C22—222no—
1262C22—442no—
1263C22—442no—
1264C22—442no—
1265C22—1762no—
1266C22—1764no—
1267C22#1062312212yes—
1268C22#1062330512yes—
1269C22C22×D4×D1111yescharacteristic
1270C4—21no—
1271C4—21no—
1272C4—22no—
1273C4—41no—
1274C4—42no—
1275C4—222no—
1276C4—222no—
1277C4—222no—
1278C4—441no—
1279C4—441no—
1280C4—442no—
1281C4—441no—
1282C4—441no—
1283C4#1062312212yes—
1284C4C22×#434111yescharacteristic
1285C4C2×#6703711yescharacteristic
1286C2—22no—
1287C2—22no—
1288C2—41no—
1289C2—42no—
1290C2—81no—
1291C2—82no—
1292C2—442no—
1293C2—882no—
1294C2C2×#1062312211yescharacteristic
1295C2C2×#1062330511yescharacteristic
1296C2#1308338911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3006C2
socleC22×C11C23×D4
hypercenter#3006D11
hypocenterC11#61171
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. #13082345C2semidirect
2. #13082285C2semidirect
3. #13080776C2semidirect
4. #13080761C2semidirect
5. #13080626C2semidirect
6. #13080611C2semidirect
7. #13080559C2semidirect
8. #13080522C2semidirect
9. #13080459C2semidirect
10. #13080422C2semidirect
11. #13078973C2semidirect
12. #13078593C2semidirect
13. #13078557C2semidirect
14. #13078471C2semidirect
15. #13078290C2semidirect
16. C2×#10622651C2semidirect
17. #13078121C2semidirect
18. #13077883C2semidirect
19. #13077449C2semidirect
20. #13077306C2semidirect
21. #13077140C2semidirect
22. C2×#10622846C2semidirect
23. C11×#3006C2semidirect
27. C2×C11×AGL(1,ℤ/8)C22semidirect
28. C2×C11×#121C22semidirect
29. #10623365C22semidirect
35. #10623360C22semidirect
37. #10623348C22semidirect
39. #10623336C22semidirect
41. D4×C22⋊D11C22semidirect
42. #10623329C22semidirect
43. C22×#4323C22semidirect
48. C2×#66979C22semidirect
49. C23×C11⋊C8C22semidirect
50. C2×#66960C22semidirect
52. #10623149C22semidirect
53. #10623147C22semidirect
54. #10623145C22semidirect
55. #10623142C22semidirect
59. #10623035C22semidirect
60. #10623031C22semidirect
62. C11×#449C22semidirect
63. C11×#449C22semidirect
64. C11×#448C22semidirect
65. C11×#447C22semidirect
67. C11×#417C22semidirect
68. C11×#407C22semidirect
71. #10622846C22semidirect
72. #10622846C22semidirect
73. #10622846C22semidirect
74. #10622846C22semidirect
75. #10622846C22semidirect
76. #10622846C22semidirect
77. C2×#66899C22semidirect
78. C2×#66899C22semidirect
79. C2×#66896C22semidirect
80. C2×#66896C22semidirect
81. C2×#66896C22semidirect
82. #10622787C22semidirect
83. #10622785C22semidirect
84. #10622785C22semidirect
85. #10622784C22semidirect
86. #10622778C22semidirect
87. #10622778C22semidirect
88. #10622777C22semidirect
89. SD16×Dic11C22semidirect
90. #10622772C22semidirect
91. #10622770C22semidirect
92. #10622769C22semidirect
93. #10622769C22semidirect
94. #10622765C22semidirect
95. #10622763C22semidirect
96. #10622763C22semidirect
97. D8×Dic11C22semidirect
98. #10622744C22semidirect
99. #10622744C22semidirect
100. #10622742C22semidirect
101. #10622735C22semidirect
102. #10622734C22semidirect
103. #10622734C22semidirect
104. #10622732C22semidirect
105. #10622651C22semidirect
106. #10622651C22semidirect
107. #10622651C22semidirect
108. #10622651C22semidirect
109. C2×#66873C22semidirect
110. C2×#66871C22semidirect
111. #10622428C22semidirect
112. #10622422C22semidirect
113. #10622417C22semidirect
114. #10622416C22semidirect
115. #10622413C22semidirect
116. #10622412C22semidirect
117. #10622408C22semidirect
118. #10622407C22semidirect
119. #10622392C22semidirect
120. #10622387C22semidirect
121. #10622383C22semidirect
122. D11×#102C22semidirect
123. #10622377C22semidirect
124. #10622376C22semidirect
125. #10622373C22semidirect
126. #10622372C22semidirect
127. #10622350C22semidirect
128. #10622350C22semidirect
129. #10622349C22semidirect
130. #10622348C22semidirect
131. #10622343C22semidirect
132. #10622343C22semidirect
133. (C22⋊D11)⋊C8C22semidirect
134. (C22⋊D11)⋊C8C22semidirect
336. C11×#41#41semidirect
504. #3006D11semidirect
618. C2×AGL(1,ℤ/8)C2×D11semidirect
648. C2×#121C2×D11semidirect
683. #449C2×D11semidirect
684. #449C2×D11semidirect
685. #448C2×D11semidirect
688. #447C2×D11semidirect
706. #417C2×D11semidirect
724. #407C2×D11semidirect
989. #41#4341semidirect
1133. C11#61171semidirect

Maximal subgroups

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

subgroupindex
#130823452
#130822852
#130807762
#130807612
#130806262
#130806112
#130805592
#130805222
#130804592
#130804222
#130789732
#130785932
#130785572
#130784712
#130782902
C2×#106226512
#130781212
#130778832
#130774492
#130773062
#130771402
C2×#106228462
C11×#30062
#6117111