Finite Group Databasebeta

← #15625369

Subgroups — #15625369

Order 2816.

2218 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082371C211yesmaximal, characteristic, complemented
2D11×#535C211yesmaximal, characteristic, complemented
3#13079713C212yesmaximal, complemented
4#13079711C212yesmaximal, complemented
5#13079691C212yesmaximal, complemented
6#13079689C212yesmaximal, complemented
7#13079635C212yesmaximal, complemented
8#13079620C212yesmaximal, complemented
9#13079582C212yesmaximal, complemented
10#13079558C212yesmaximal, complemented
11#13079092C211yesmaximal, characteristic, complemented
12#13079088C211yesmaximal, characteristic, complemented
13#13078975C211yesmaximal, characteristic, complemented
14#13078160C211yesmaximal, characteristic, complemented
15#13078154C211yesmaximal, characteristic, complemented
16#13078140C211yesmaximal, characteristic, complemented
17#13078136C211yesmaximal, characteristic, complemented
18#13077877C211yesmaximal, characteristic, complemented
19#13077845C211yesmaximal, characteristic, complemented
20#13077836C211yesmaximal, characteristic, complemented
21C2×#10622389C211yesmaximal, characteristic, complemented
22#13077271C211yesmaximal, characteristic, complemented
23C11×#3136C211yesmaximal, characteristic, complemented
24C2×#41×D11C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C11×#544C2211yescharacteristic, complemented
27C11×#535C2211yescharacteristic
28#10623361C2211yescharacteristic
29C2×#67004C2211yescharacteristic, complemented
30C2×#67003C2211yescharacteristic, complemented
31#10623336C2211yescharacteristic
32C22×#4324C2211yescharacteristic, complemented
33C2×#66985C2211yescharacteristic, complemented
34C2×#66962C2211yescharacteristic, complemented
35C2×#66961C2211yescharacteristic, complemented
36C2×#66957C2211yescharacteristic, complemented
37C22×#4314C2211yescharacteristic, complemented
38#10623264C2212yescomplemented
39#10623263—21no—
40#10623261—21no—
41#10623259C2212yescomplemented
42#10623246C2212yes—
43D11×#127C2212yes—
44#10623228C2212yescomplemented
45#10623225—21no—
46#10623225—21no—
47#10623222C2212yescomplemented
48#10623205C2212yes—
49D11×#124C2212yes—
50#10623173—22no—
51#10623168—22no—
52#10623138—21no—
53#10623138—21no—
54D11×#121—21no—
55D11×#121—21no—
56#10623123—22no—
57D11×#120—22no—
58#10623057C2211yescharacteristic, complemented
59#10623056C2211yescharacteristic
60#10623055C2211yescharacteristic
61D11×#117C2211yescharacteristic
62#10623047C2211yescharacteristic, complemented
63C2×#66950C2211yescharacteristic
64#10623035C2211yescharacteristic, complemented
65C11×#490C2212yescomplemented
66C11×#489C2212yescomplemented
67C11×#488C2212yescomplemented
68C11×#486C2212yescomplemented
69C11×#418C2211yescharacteristic, complemented
70C11×#417C2211yescharacteristic, complemented
71C11×#416C2211yescharacteristic, complemented
72C2×C11×#102C2211yescharacteristic, complemented
73C11×#405C2211yescharacteristic, complemented
74#10622739C2211yescharacteristic
75#10622732C2211yescharacteristic, complemented
76C2×(C2×D11)⋊C8C2211yescharacteristic
77#10622715C2211yescharacteristic, complemented
78#10622702C2212yescomplemented
79#10622701C2212yescomplemented
80#10622689C2212yescomplemented
81#10622687C2212yescomplemented
82#10622681C2212yescomplemented
83#10622680C2212yescomplemented
84#10622673C2212yescomplemented
85#10622672C2212yescomplemented
86#10622615C2211yescharacteristic, complemented
87#10622614C2211yescharacteristic, complemented
88#10622610C2211yescharacteristic, complemented
89#10622579C2211yescharacteristic, complemented
90C2×#66873C2211yescharacteristic, complemented
91#10622432C2212yescomplemented
92#10622424C2211yescharacteristic, complemented
93#10622423C2211yescharacteristic, complemented
94#10622423C2212yescomplemented
95#10622421C2212yescomplemented
96#10622421C2211yescharacteristic, complemented
97#10622419C2211yescharacteristic, complemented
98#10622411C2212yescomplemented
99#10622411C2212yescomplemented
100#10622411C2212yescomplemented
101#10622400C2212yescomplemented
102#10622399C2212yescomplemented
103#10622399C2212yescomplemented
104#10622396C2211yescharacteristic, complemented
105#10622396C2212yescomplemented
106#10622394C2211yescharacteristic, complemented
107#10622389C2212yes—
108#10622389C2212yes—
109#10622389C2212yes—
110#10622389C2212yescomplemented
111#10622389C2212yescomplemented
112#10622389C2212yescomplemented
113#10622389C2211yescharacteristic, complemented
114#10622389C2212yescomplemented
115#10622386C2212yes—
116#10622386C2212yescomplemented
117#10622386C2211yescharacteristic, complemented
118#10622380C2212yescomplemented
119#10622380C2212yescomplemented
120#10622380C2212yescomplemented
121#10622375C2212yescomplemented
122#10622375C2212yescomplemented
123#10622375C2212yescomplemented
124#10622375C2212yescomplemented
125#10622375C2212yescomplemented
126#10622375C2212yescomplemented
127#10622328C2212yescomplemented
128#10622325C2212yescomplemented
129#10622322C2212yescomplemented
130#10622318C2212yescomplemented
131#10622309C2212yescomplemented
132#10622306C2212yescomplemented
133#10622303C2212yescomplemented
134#10622298C2212yescomplemented
135C24×D11—21no—
136C2×C11×#41C2311yescharacteristic
137C22×D4×C11C2311yescharacteristic
138C22×C22⋊D11—21no—
139#41×D11—42no—
140#41×D11—42no—
141C2×#4343C2311yescharacteristic
142C2×Q8×D11C2311yescharacteristic
143C2×#4341—21no—
144C2×#4341C2311yescharacteristic
145C2×D4×D11—21no—
146C2×D4×D11—21no—
147C2×D4×D11—21no—
148C2×D4×D11—22no—
149C2×D4×D11—22no—
150C2×D4×D11—42no—
151C2×D4×D11—42no—
152C2×D4×D11C2311yescharacteristic
153C2×D4×D11C2312yes—
154C2×D4×D11C2312yes—
155C2×#4339—21no—
156C2×#4339C2311yescharacteristic
157C2×#4339C2311yescharacteristic
158C22×D44C2311yescharacteristic
159C22×C4×D11—21no—
160C22×C4×D11C2311yescharacteristic
161C22×Dic22C2311yescharacteristic
162C2×C11×M16C2311yescharacteristic
163C22×C8×C11C2311yescharacteristic
164C11×C4⋊Q8—21no—
165C11×C4⋊Q8C2312yescomplemented
166C11×#127C2312yes—
167C11×#125—21no—
168C11×#125C2312yescomplemented
169C11×#124C2312yes—
170C11×C22⋊Q8—22no—
171C11×#121—21no—
172C11×#121—21no—
173C11×#120—22no—
174C11×#117C2311yescharacteristic
175C11×#117C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177#67006—22no—
178#67004—42no—
179#67003—42no—
180#67000—22no—
181#67000C2312yes—
182#66999—22no—
183#66999—22no—
184Q8×Dic11—22no—
185C2×#4326C2311yescharacteristic, complemented
186C2×#4326C2312yescomplemented
187C2×#4325C2311yescharacteristic, complemented
188#66993—22no—
189#66993—22no—
190#66993C2312yes—
191#66993C2312yes—
192#66992—22no—
193#66992—22no—
194#66991—21no—
195#66991—21no—
196#66990—22no—
197#66990—22no—
198#66990—22no—
199#66989C2312yes—
200C2×#4324—42no—
201C2×#4324C2312yes—
202C2×#4324C2312yes—
203C2×#4324C2312yes—
204C2×#4324C2311yescharacteristic, complemented
205C2×#4324C2312yescomplemented
206#66985—42no—
207C2×#4323C2312yes—
208C2×#4323C2311yescharacteristic, complemented
209#66983—21no—
210#66983—21no—
211C4×C22⋊D11—22no—
212C2×(C2×D11)⋊C4—21no—
213#66979C2311yescharacteristic
214C2×C4⋊Dic11—21no—
215C2×#4318C2311yescharacteristic
216C22×C11⋊C8C2311yescharacteristic
217#66962—42no—
218#66961—42no—
219C2×Dic44C2311yescharacteristic, complemented
220C2×Dic44C2312yescomplemented
221#66957—42no—
222C2×D88C2312yes—
223C2×D88C2311yescharacteristic, complemented
224C2×#4314—42no—
225C2×#4314C2312yes—
226C2×#4314C2312yes—
227C2×#4314C2312yes—
228C2×#4314C2311yescharacteristic, complemented
229C2×#4314C2311yescharacteristic, complemented
230C2×#4314C2312yescomplemented
231#66951—22no—
232#66951—22no—
233#66951—22no—
234#66951—22no—
235#66950—21no—
236#66950—21no—
237#66950—21no—
238#66950—21no—
239#66950C2311yescharacteristic
240#66950C2312yes—
241#66950C2312yes—
242#66950C2311yescharacteristic
243#66948—21no—
244#66948—21no—
245#66948C2311yescharacteristic
246#66948C2311yescharacteristic
247#66947—22no—
248#66947—22no—
249#66946—22no—
250#66946C2312yescomplemented
251#66945—22no—
252#66945—21no—
253#66945—22no—
254#66945D411yescharacteristic
255#66945D411yescharacteristic
256C4⋊C4×D11—21no—
257C4⋊C4×D11D411yescharacteristic
258C4⋊C4×D11D411yescharacteristic
259#66943—22no—
260#66943—22no—
261#66943—22no—
262#66940C2312yescomplemented
263#66940C2312yescomplemented
264#66940C2312yescomplemented
265#66939—21no—
266#66939—22no—
267#66938—22no—
268#66938—22no—
269#66937—22no—
270#66937—22no—
271#66935—21no—
272#66935—22no—
273#66935—22no—
274#66935—22no—
275C22⋊C4×D11—22no—
276C22⋊C4×D11—22no—
277C22⋊C4×D11D412yes—
278#66930—22no—
279#66930D412yes—
280#66928C2312yes—
281#66928C2312yescomplemented
282#66927C2312yes—
283C4×D44—21no—
284C4×D44—21no—
285#66925C2312yes—
286C42×D11C2312yes—
287#66922C2312yescomplemented
288C4×Dic22—21no—
289C4×Dic22—21no—
290C11×#103C2311yescharacteristic, complemented
291C11×#103C2312yescomplemented
292C11×#103C2311yescharacteristic, complemented
293C11×#102C2312yes—
294C11×#102C2312yes—
295C11×#102C2312yes—
296C11×#102C2312yes—
297C11×#102C2311yescharacteristic, complemented
298C11×#102C2312yescomplemented
299C11×#102C2311yescharacteristic, complemented
300C11×#97C2312yescomplemented
301C4×C8×C11C2312yescomplemented
302(C2×D11)⋊C8C2311yescharacteristic
303(C2×D11)⋊C8C2311yescharacteristic
304(C2×D11)⋊C8C2311yescharacteristic
305(C2×D11)⋊C8C2311yescharacteristic
306(C2×D11)⋊C8C2312yes—
307(C2×D11)⋊C8C2312yes—
308Dic11⋊C8C2312yescomplemented
309Dic11⋊C8C2312yescomplemented
310Dic11⋊C8C2312yescomplemented
311Dic11⋊C8C2312yescomplemented
312#66874C2312yescomplemented
313#66874C2311yescharacteristic, complemented
314#66874C2311yescharacteristic, complemented
315#66873C2312yes—
316#66873C2312yes—
317#66873C2312yes—
318#66873C2312yes—
319#66873C2312yescomplemented
320#66873C2311yescharacteristic, complemented
321#66873C2311yescharacteristic, complemented
322#66867C2312yescomplemented
323C4×C11⋊C8C2312yescomplemented
324#60812—111nomaximal, Sylow
325C24×C11—21no—
326C23×D11—21no—
327C23×D11—22no—
328C23×D11—21no—
329C23×D11—22no—
330C23×D11—44no—
331C23×D11—82no—
332C23×D11—82no—
333C23×D11C2×D411yescharacteristic
334C11×#41—22no—
335C11×#41—22no—
336C2×Q8×C11—22no—
337C2×Q8×C11C2411yescharacteristic
338C2×D4×C11—21no—
339C2×D4×C11—21no—
340C2×D4×C11—22no—
341C2×D4×C11—22no—
342C2×D4×C11—22no—
343C2×D4×C11—22no—
344C2×D4×C11C2412yes—
345C2×D4×C11C2411yescharacteristic
346C22×C4×C11—21no—
347C22×C4×C11—21no—
348C22×C4×C11C2411yescharacteristic
349C2×C22⋊D11—22no—
350C2×C22⋊D11—22no—
351C2×C22⋊D11—21no—
352C2×C22⋊D11—22no—
353C2×C22⋊D11—22no—
354C2×C22⋊D11—22no—
355C2×C22⋊D11—22no—
356C2×C22⋊D11—21no—
357C2×C22⋊D11—21no—
358C2×C22⋊D11—21no—
359C2×C22⋊D11—44no—
360C22×Dic11—21no—
361C22×Dic11—21no—
362C22×Dic11C2×D411yescharacteristic
363#4343—41no—
364#4343—41no—
365Q8×D11—41no—
366Q8×D11—41no—
367#4341—41no—
368#4341—41no—
369#4341—44no—
370D4×D11—42no—
371D4×D11—42no—
372D4×D11—42no—
373D4×D11—42no—
374D4×D11—41no—
375D4×D11—41no—
376D4×D11—44no—
377D4×D11—44no—
378D4×D11—44no—
379D4×D11—84no—
380D4×D11—84no—
381#4339—22no—
382#4339—22no—
383#4339—22no—
384#4339—22no—
385#4339—44no—
386C2×D44—21no—
387C2×D44—21no—
388C2×D44—21no—
389C2×D44—21no—
390C2×D44—22no—
391C2×D44—22no—
392C2×D44—22no—
393C2×D44—22no—
394C2×D44C2412yes—
395C2×D44C2411yescharacteristic
396C2×D44C2411yescharacteristic
397C2×C4×D11—21no—
398C2×C4×D11—22no—
399C2×C4×D11—21no—
400C2×C4×D11—21no—
401C2×C4×D11—21no—
402C2×C4×D11—22no—
403C2×C4×D11—22no—
404C2×C4×D11—44no—
405C2×C4×D11C2×D412yes—
406C2×C4×D11C2×D411yescharacteristic
407C2×C4×D11C2×D411yescharacteristic
408C2×C4×D11C2×D412yes—
409C2×C4×D11C2411yescharacteristic
410C2×C4×D11C2411yescharacteristic
411C2×Dic22—21no—
412C2×Dic22—21no—
413C2×Dic22—22no—
414C2×Dic22—22no—
415C2×Dic22C2411yescharacteristic
416C2×Dic22C2411yescharacteristic
417C2×Dic22C2412yes—
418C11×M16—22no—
419C2×C8×C11—22no—
420C2×C8×C11C2411yescharacteristic
421C2×C8×C11C2412yes—
422C2×C8×C11C2411yescharacteristic
423C11×C4⋊C4—22no—
424C11×C4⋊C4—22no—
425C11×C4⋊C4—22no—
426C11×C4⋊C4—21no—
427C11×C4⋊C4C2×D411yescharacteristic
428C11×C4⋊C4C2×D411yescharacteristic
429C11×C4⋊C4C2411yescharacteristic
430C11×C4⋊C4C2411yescharacteristic
431C11×C4⋊C4C2412yes—
432C11×C22⋊C4—21no—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—22no—
435C11×C22⋊C4C2×D412yes—
436C42×C11—21no—
437C42×C11C2412yes—
438C22⋊Dic11—22no—
439C22⋊Dic11—22no—
440C22⋊Dic11C2×D412yes—
441#4326—41no—
442#4326—42no—
443#4325—41no—
444#4324—42no—
445#4324—42no—
446#4324—42no—
447#4324—41no—
448#4324—42no—
449#4323—42no—
450#4323—41no—
451(C2×D11)⋊C4—21no—
452(C2×D11)⋊C4—21no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—22no—
456(C2×D11)⋊C4—21no—
457(C2×D11)⋊C4—21no—
458(C2×D11)⋊C4—22no—
459(C2×D11)⋊C4—22no—
460(C2×D11)⋊C4—22no—
461(C2×D11)⋊C4—22no—
462(C2×D11)⋊C4—22no—
463(C2×D11)⋊C4—22no—
464(C2×D11)⋊C4C2×D412yes—
465(C2×D11)⋊C4C2×D412yes—
466C4⋊Dic11—21no—
467C4⋊Dic11—21no—
468C4⋊Dic11—22no—
469C4⋊Dic11—22no—
470C4⋊Dic11—22no—
471C4⋊Dic11—22no—
472C4⋊Dic11C2×D411yescharacteristic
473C4⋊Dic11C2×D411yescharacteristic
474Dic11⋊C4—22no—
475Dic11⋊C4—22no—
476Dic11⋊C4—22no—
477Dic11⋊C4C2×D412yes—
478Dic11⋊C4C2×D412yes—
479C4×Dic11—22no—
480C4×Dic11—22no—
481C4×Dic11—22no—
482C4×Dic11C2×D412yes—
483C4×Dic11C2×D412yes—
484C4×Dic11C2412yes—
485#4318—22no—
486C2×C11⋊C8—22no—
487C2×C11⋊C8C2411yescharacteristic
488C2×C11⋊C8C2412yes—
489C2×C11⋊C8C2411yescharacteristic
490Dic44—41no—
491Dic44—42no—
492D88—42no—
493D88—41no—
494#4314—42no—
495#4314—42no—
496#4314—42no—
497#4314—41no—
498#4314—41no—
499#4314—42no—
500#3495—111no—
501C2×#535—111no—
502#3224—112no—
503#3224—112no—
504#3222—112no—
505#3222—112no—
506#3217—112no—
507#3215—112no—
508#3211—112no—
509#3208—112no—
510#3154—111no—
511#3154—111no—
512#3136—111no—
513#3136D1111yescharacteristic, complemented
514#3045—111no—
515#3045—111no—
516#3043—111no—
517#3043—111no—
518#3007—111no—
519#3003—111no—
520#3002—111no—
521C2×#450—111no—
522#2924—111no—
523C23×C11—22no—
524C23×C11—21no—
525C23×C11—42no—
526C23×C11—81no—
527C23×C11—81no—
528C23×C11C22×D411yescharacteristic
529C22×D11—22no—
530C22×D11—22no—
531C22×D11—21no—
532C22×D11—22no—
533C22×D11—21no—
534C22×D11—41no—
535C22×D11—42no—
536C22×D11—44no—
537C22×D11—44no—
538C22×D11—42no—
539C22×D11—44no—
540C22×D11—42no—
541C22×D11—42no—
542C22×D11—44no—
543C22×D11—82no—
544C22×D11—82no—
545C22×D11—81no—
546C22×D11—81no—
547C22×D11—816no—
548C22×D11C22×D411yescharacteristic
549C22×D11C22×D411yescharacteristic
550Q8×C11—21no—
551Q8×C11—21no—
552Q8×C11—82no—
553D4×C11—22no—
554D4×C11—21no—
555D4×C11—22no—
556D4×C11—21no—
557D4×C11—42no—
558D4×C11—42no—
559D4×C11—82no—
560D4×C11—82no—
561C2×C4×C11—21no—
562C2×C4×C11—21no—
563C2×C4×C11—22no—
564C2×C4×C11—21no—
565C2×C4×C11—42no—
566C2×C4×C11—81no—
567C2×C4×C11C22×D412yes—
568C2×C4×C11C22×D412yes—
569C2×C4×C11C22×D411yescharacteristic
570C2×C4×C11H(5,𝔽2)12yes—
571C2×C4×C11H(5,𝔽2)12yes—
572C2×C4×C11C2511yescharacteristic
573C22⋊D11—42no—
574C22⋊D11—44no—
575C22⋊D11—44no—
576C22⋊D11—42no—
577C22⋊D11—42no—
578C22⋊D11—42no—
579C22⋊D11—82no—
580C22⋊D11—82no—
581C22⋊D11—82no—
582C22⋊D11—82no—
583C2×Dic11—22no—
584C2×Dic11—21no—
585C2×Dic11—22no—
586C2×Dic11—21no—
587C2×Dic11—42no—
588C2×Dic11—42no—
589C2×Dic11C22×D412yes—
590C2×Dic11C22×D412yes—
591C2×Dic11C22×D411yescharacteristic
592C2×Dic11C22×D411yescharacteristic
593D44—22no—
594D44—21no—
595D44—21no—
596D44—22no—
597D44—21no—
598D44—21no—
599D44—42no—
600D44—42no—
601D44—42no—
602D44—82no—
603D44—82no—
604D44—81no—
605C4×D11—24no—
606C4×D11—22no—
607C4×D11—22no—
608C4×D11—21no—
609C4×D11—21no—
610C4×D11—21no—
611C4×D11—21no—
612C4×D11—42no—
613C4×D11—42no—
614C4×D11—42no—
615C4×D11—42no—
616C4×D11—42no—
617C4×D11—82no—
618Dic22—22no—
619Dic22—21no—
620Dic22—22no—
621Dic22—21no—
622Dic22—21no—
623Dic22—21no—
624Dic22—42no—
625Dic22—42no—
626C8×C11—21no—
627C8×C11—21no—
628C8×C11—22no—
629C11⋊C8—21no—
630C11⋊C8—21no—
631C11⋊C8—22no—
632C22×#41—111no—
633C23×D4—111no—
634C2×#137—111no—
635C2×#137—111no—
636C2×AGL(1,ℤ/8)—111no—
637C2×AGL(1,ℤ/8)—111no—
638C2×#135—111no—
639C2×#135—111no—
640C22×SD16—111no—
641C22×SD16—111no—
642#556—221no—
643#554—221no—
644#552—221no—
645#552—222no—
646#552—221no—
647#551—222no—
648#544C2×D1111yescharacteristic, complemented
649#542—112no—
650#541—112no—
651#536—111no—
652#535—111no—
653#535—111no—
654#535—112no—
655#535—112no—
656#535—111no—
657#535—222no—
658#535—221no—
659#535—221no—
660#535C2×D1111yescharacteristic
661#533—112no—
662C2×#127—112no—
663#529—112no—
664C2×#124—112no—
665#525—111no—
666C2×C22⋊Q8—111no—
667C2×#121—221no—
668C2×#121—221no—
669C2×#120—222no—
670#520—111no—
671#519—111no—
672C2×#117—111no—
673#497—112no—
674#497—112no—
675#496—112no—
676#496—112no—
677#495—112no—
678#495—112no—
679#492—112no—
680#492—112no—
681#490—112no—
682#490C2×D1112yescomplemented
683#489—112no—
684#489C2×D1112yescomplemented
685#488—112no—
686#488C2×D1112yescomplemented
687#486—112no—
688#486C2×D1112yescomplemented
689#464—112no—
690#464—112no—
691#464—112no—
692#464—112no—
693#464—112no—
694#464—112no—
695#463—112no—
696#463—112no—
697#460—112no—
698#460—112no—
699#460—112no—
700#460—112no—
701#460—112no—
702#460—112no—
703#459—112no—
704#459—112no—
705#452—111no—
706#452—112no—
707#452—111no—
708#452—112no—
709#451—112no—
710#451—111no—
711#450—112no—
712#450—112no—
713#450—112no—
714#450—112no—
715#450—112no—
716#450—112no—
717#450—111no—
718#450—112no—
719#449—111no—
720#449—111no—
721#448—111no—
722#447—112no—
723#447—112no—
724#447—111no—
725#433—112no—
726#433—112no—
727#432—112no—
728#431—112no—
729#424—111no—
730#424—111no—
731#418—111no—
732#418C2×D1111yescharacteristic, complemented
733#417—111no—
734#417C2×D1111yescharacteristic, complemented
735#416—111no—
736#416C2×D1111yescharacteristic, complemented
737C2×#102—111no—
738C2×#102C2×D1111yescharacteristic, complemented
739#407—111no—
740C2×C22⋊C8—111no—
741#405—111no—
742#405C2×D1111yescharacteristic, complemented
743C22×C11—21no—
744C22×C11—21no—
745C22×C11—41no—
746C22×C11—42no—
747C22×C11—41no—
748C22×C11—42no—
749C22×C11—41no—
750C22×C11—42no—
751C22×C11—84no—
752C22×C11#53512yes—
753C22×C11C23×D411yescharacteristic
754C2×D11—21no—
755C2×D11—21no—
756C2×D11—21no—
757C2×D11—21no—
758C2×D11—21no—
759C2×D11—44no—
760C2×D11—42no—
761C2×D11—41no—
762C2×D11—41no—
763C2×D11—42no—
764C2×D11—41no—
765C2×D11—41no—
766C2×D11—42no—
767C2×D11—41no—
768C2×D11—41no—
769C2×D11—84no—
770C2×D11—88no—
771C2×D11—88no—
772C2×D11—84no—
773C2×D11#57712yes—
774C4×C11—22no—
775C4×C11—22no—
776C4×C11—42no—
777C4×C11—41no—
778C4×C11—41no—
779C4×C11—41no—
780C4×C11#53512yes—
781C4×C11C2×H(5,𝔽2)11yescharacteristic
782C4×C11C2×H(5,𝔽2)11yescharacteristic
783Dic11—22no—
784Dic11—21no—
785Dic11—21no—
786Dic11—22no—
787Dic11—41no—
788Dic11—42no—
789Dic11—41no—
790C25—221no—
791C2×#41—111no—
792C2×#41—111no—
793C2×#41—111no—
794C2×#41—111no—
795C2×#41—221no—
796C2×#41—221no—
797C2×#41—442no—
798C2×#41—442no—
799C2×#41C22×D1111yescharacteristic
800C22×Q8—111no—
801C22×Q8—111no—
802C22×D4—112no—
803C22×D4—111no—
804C22×D4—112no—
805C22×D4—111no—
806C22×D4—221no—
807C22×D4—221no—
808C22×D4—222no—
809C22×D4—222no—
810C22×D4—221no—
811C22×D4—221no—
812C22×D4—442no—
813C22×D4—442no—
814C22×D4C22×D1111yescharacteristic
815C23×C4—111no—
816C23×C4—221no—
817#137—442no—
818#137—442no—
819AGL(1,ℤ/8)—442no—
820AGL(1,ℤ/8)—442no—
821#135—442no—
822#135—442no—
823C2×Q16—111no—
824C2×Q16—112no—
825C2×Q16—111no—
826C2×Q16—112no—
827C2×SD16—111no—
828C2×SD16—112no—
829C2×SD16—112no—
830C2×SD16—111no—
831C2×SD16—112no—
832C2×SD16—112no—
833C2×SD16—112no—
834C2×SD16—112no—
835C2×SD16—111no—
836C2×SD16—111no—
837C2×SD16—112no—
838C2×SD16—112no—
839C2×SD16—442no—
840C2×SD16—442no—
841C2×D8—111no—
842C2×D8—112no—
843C2×D8—111no—
844C2×D8—112no—
845C2×M16—111no—
846C2×M16C22×D1111yescharacteristic
847C22×C8—111no—
848C22×C8C22×D1111yescharacteristic
849C4⋊Q8—21no—
850C4⋊Q8—112no—
851C4⋊Q8C22×D1112yescomplemented
852#127—112no—
853#127—112no—
854#127—112no—
855#127—222no—
856#127—222no—
857#127C22×D1112yes—
858#126—222no—
859#126—222no—
860#126—222no—
861#126—222no—
862#125—21no—
863#125—222no—
864#125—222no—
865#125—222no—
866#125C22×D1112yescomplemented
867#124—112no—
868#124—112no—
869#124—112no—
870#124—112no—
871#124—222no—
872#124—222no—
873#124—222no—
874#124C22×D1112yes—
875#123—221no—
876#123—222no—
877#123—222no—
878#123—222no—
879C22⋊Q8—22no—
880C22⋊Q8—112no—
881C22⋊Q8—112no—
882C22⋊Q8—111no—
883C22⋊Q8—111no—
884C22⋊Q8—221no—
885C22⋊Q8—221no—
886C22⋊Q8—222no—
887C22⋊Q8—222no—
888C22⋊Q8—221no—
889C22⋊Q8—221no—
890#121—21no—
891#121—21no—
892#121—111no—
893#121—111no—
894#121—222no—
895#121—222no—
896#121—221no—
897#121—221no—
898#121—221no—
899#121—221no—
900#121—222no—
901#121—222no—
902#121—221no—
903#121—221no—
904#120—22no—
905#120—222no—
906#120—222no—
907#120—221no—
908#120—222no—
909#120—222no—
910#120—222no—
911#120—222no—
912#120—222no—
913C4×Q8—112no—
914C4×Q8—112no—
915C4×Q8—112no—
916C4×Q8—221no—
917C4×Q8—221no—
918C4×Q8—222no—
919C4×D4—112no—
920C4×D4—221no—
921C4×D4—221no—
922C4×D4—222no—
923C4×D4—222no—
924#117—111no—
925#117—111no—
926#117—111no—
927#117—112no—
928#117—112no—
929#117—222no—
930#117—222no—
931#117—221no—
932#117—222no—
933#117C22×D1111yescharacteristic
934#117C22×D1111yescharacteristic
935C2×C4⋊C4—111no—
936C2×C4⋊C4—111no—
937C2×C4⋊C4—221no—
938C2×C4⋊C4—221no—
939C2×C4⋊C4C22×D1111yescharacteristic
940C2×C22⋊C4—112no—
941C2×C22⋊C4—222no—
942C2×C22⋊C4—222no—
943C2×C22⋊C4—221no—
944C2×C42—112no—
945C4⋊C8—112no—
946C4⋊C8—112no—
947C4⋊C8—112no—
948C4⋊C8—112no—
949#103—111no—
950#103—111no—
951#103—112no—
952#103C22×D1111yescharacteristic, complemented
953#103C22×D1111yescharacteristic, complemented
954#103C22×D1112yescomplemented
955#102—112no—
956#102—112no—
957#102—112no—
958#102—112no—
959#102—111no—
960#102—111no—
961#102—112no—
962#102C22×D1112yes—
963#102C22×D1112yes—
964#102C22×D1112yes—
965#102C22×D1112yes—
966#102C22×D1111yescharacteristic, complemented
967#102C22×D1111yescharacteristic, complemented
968#102C22×D1112yescomplemented
969C22⋊C8—111no—
970C22⋊C8—111no—
971C22⋊C8—111no—
972C22⋊C8—111no—
973C22⋊C8—112no—
974C22⋊C8—112no—
975#97—112no—
976#97C22×D1112yescomplemented
977C4×C8—112no—
978C4×C8C22×D1112yescomplemented
979C2×C11—22no—
980C2×C11—82no—
981C2×C11—81no—
982C2×C11C2×#53511yescharacteristic
983C2×C11C2×#57711yescharacteristic
984C2×C11#358511yescharacteristic
985D11—22no—
986D11—41no—
987D11—81no—
988D11—81no—
989D11—82no—
990C24—21no—
991C24—111no—
992C24—222no—
993C24—221no—
994C24—222no—
995C24—221no—
996C24—444no—
997C24—882no—
998C24—882no—
999#41—22no—
1000#41—22no—
1001#41—222no—
1002#41—222no—
1003#41—222no—
1004#41—222no—
1005#41—444no—
1006#41—441no—
1007#41—441no—
1008#41—444no—
1009#41—441no—
1010#41—441no—
1011C2×Q8—22no—
1012C2×Q8—111no—
1013C2×Q8—112no—
1014C2×Q8—111no—
1015C2×Q8—221no—
1016C2×Q8—221no—
1017C2×Q8—222no—
1018C2×Q8—222no—
1019C2×Q8—441no—
1020C2×Q8—441no—
1021C2×Q8C23×D1111yescharacteristic
1022C2×D4—21no—
1023C2×D4—21no—
1024C2×D4—22no—
1025C2×D4—22no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C2×D4—112no—
1029C2×D4—111no—
1030C2×D4—111no—
1031C2×D4—221no—
1032C2×D4—221no—
1033C2×D4—221no—
1034C2×D4—222no—
1035C2×D4—222no—
1036C2×D4—221no—
1037C2×D4—222no—
1038C2×D4—222no—
1039C2×D4—222no—
1040C2×D4—222no—
1041C2×D4—221no—
1042C2×D4—221no—
1043C2×D4—221no—
1044C2×D4—221no—
1045C2×D4—222no—
1046C2×D4—222no—
1047C2×D4—222no—
1048C2×D4—222no—
1049C2×D4—442no—
1050C2×D4—442no—
1051C2×D4—442no—
1052C2×D4—442no—
1053C2×D4—441no—
1054C2×D4—441no—
1055C2×D4—444no—
1056C2×D4—444no—
1057C2×D4—444no—
1058C2×D4—444no—
1059C2×D4—884no—
1060C2×D4—884no—
1061C2×D4C23×D1112yes—
1062C2×D4C23×D1111yescharacteristic
1063C22×C4—21no—
1064C22×C4—21no—
1065C22×C4—111no—
1066C22×C4—112no—
1067C22×C4—111no—
1068C22×C4—111no—
1069C22×C4—111no—
1070C22×C4—111no—
1071C22×C4—112no—
1072C22×C4—221no—
1073C22×C4—222no—
1074C22×C4—221no—
1075C22×C4—221no—
1076C22×C4—222no—
1077C22×C4—222no—
1078C22×C4—221no—
1079C22×C4—221no—
1080C22×C4—221no—
1081C22×C4—444no—
1082C22×C4C23×D1111yescharacteristic
1083Q16—441no—
1084Q16—442no—
1085Q16—441no—
1086Q16—442no—
1087SD16—442no—
1088SD16—442no—
1089SD16—441no—
1090SD16—441no—
1091SD16—442no—
1092SD16—442no—
1093SD16—442no—
1094SD16—442no—
1095SD16—441no—
1096SD16—442no—
1097SD16—442no—
1098SD16—441no—
1099D8—441no—
1100D8—442no—
1101D8—441no—
1102D8—442no—
1103M16—22no—
1104M16—222no—
1105C2×C8—22no—
1106C2×C8—111no—
1107C2×C8—112no—
1108C2×C8—111no—
1109C2×C8—222no—
1110C2×C8C23×D1111yescharacteristic
1111C2×C8C23×D1112yes—
1112C2×C8C23×D1111yescharacteristic
1113C4⋊C4—21no—
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—111no—
1118C4⋊C4—111no—
1119C4⋊C4—112no—
1120C4⋊C4—112no—
1121C4⋊C4—222no—
1122C4⋊C4—222no—
1123C4⋊C4—222no—
1124C4⋊C4—222no—
1125C4⋊C4—222no—
1126C4⋊C4—221no—
1127C4⋊C4—221no—
1128C4⋊C4—222no—
1129C4⋊C4—222no—
1130C4⋊C4D4×D1111yescharacteristic
1131C4⋊C4D4×D1111yescharacteristic
1132C4⋊C4C23×D1112yes—
1133C4⋊C4C23×D1111yescharacteristic
1134C4⋊C4C23×D1111yescharacteristic
1135C22⋊C4—21no—
1136C22⋊C4—22no—
1137C22⋊C4—22no—
1138C22⋊C4—112no—
1139C22⋊C4—112no—
1140C22⋊C4—112no—
1141C22⋊C4—222no—
1142C22⋊C4—222no—
1143C22⋊C4—221no—
1144C22⋊C4—222no—
1145C22⋊C4—221no—
1146C22⋊C4—222no—
1147C22⋊C4—222no—
1148C22⋊C4—221no—
1149C22⋊C4—221no—
1150C22⋊C4—222no—
1151C22⋊C4—222no—
1152C22⋊C4—222no—
1153C22⋊C4—222no—
1154C22⋊C4—222no—
1155C22⋊C4—222no—
1156C22⋊C4D4×D1112yes—
1157C42—21no—
1158C42—112no—
1159C42—112no—
1160C42—112no—
1161C42—222no—
1162C42—222no—
1163C42—222no—
1164C42C23×D1112yes—
1165C11#6081211yescharacteristic, complemented, Sylow
1166C23—22no—
1167C23—21no—
1168C23—42no—
1169C23—81no—
1170C23—81no—
1171C23—111no—
1172C23—111no—
1173C23—222no—
1174C23—222no—
1175C23—221no—
1176C23—222no—
1177C23—221no—
1178C23—441no—
1179C23—442no—
1180C23—444no—
1181C23—442no—
1182C23—444no—
1183C23—444no—
1184C23—442no—
1185C23—444no—
1186C23—442no—
1187C23—881no—
1188C23—881no—
1189C23—882no—
1190C23—882no—
1191C23—8816no—
1192C23C2×D4×D1111yescharacteristic
1193Q8—21no—
1194Q8—21no—
1195Q8—82no—
1196Q8—222no—
1197Q8—222no—
1198Q8—221no—
1199Q8—221no—
1200Q8—221no—
1201Q8—221no—
1202Q8—442no—
1203Q8—442no—
1204D4—22no—
1205D4—21no—
1206D4—22no—
1207D4—21no—
1208D4—42no—
1209D4—42no—
1210D4—82no—
1211D4—82no—
1212D4—221no—
1213D4—221no—
1214D4—222no—
1215D4—221no—
1216D4—222no—
1217D4—221no—
1218D4—442no—
1219D4—442no—
1220D4—444no—
1221D4—444no—
1222D4—442no—
1223D4—442no—
1224D4—442no—
1225D4—442no—
1226D4—442no—
1227D4—882no—
1228D4—882no—
1229D4—881no—
1230D4—882no—
1231D4—882no—
1232D4—882no—
1233D4—882no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—42no—
1239C2×C4—81no—
1240C2×C4—111no—
1241C2×C4—112no—
1242C2×C4—112no—
1243C2×C4—111no—
1244C2×C4—224no—
1245C2×C4—222no—
1246C2×C4—221no—
1247C2×C4—221no—
1248C2×C4—221no—
1249C2×C4—221no—
1250C2×C4—222no—
1251C2×C4—222no—
1252C2×C4—222no—
1253C2×C4—221no—
1254C2×C4—221no—
1255C2×C4—442no—
1256C2×C4—442no—
1257C2×C4—442no—
1258C2×C4—442no—
1259C2×C4—442no—
1260C2×C4—442no—
1261C2×C4—442no—
1262C2×C4—882no—
1263C2×C4C2×D4×D1112yes—
1264C2×C4C2×D4×D1112yes—
1265C2×C4C2×D4×D1111yescharacteristic
1266C2×C4#6704212yes—
1267C2×C4#6704212yes—
1268C2×C4C24×D1111yescharacteristic
1269C8—21no—
1270C8—21no—
1271C8—22no—
1272C8—221no—
1273C8—221no—
1274C8—222no—
1275C22—21no—
1276C22—21no—
1277C22—41no—
1278C22—42no—
1279C22—41no—
1280C22—42no—
1281C22—41no—
1282C22—42no—
1283C22—84no—
1284C22—112no—
1285C22—221no—
1286C22—221no—
1287C22—221no—
1288C22—221no—
1289C22—221no—
1290C22—444no—
1291C22—441no—
1292C22—441no—
1293C22—442no—
1294C22—441no—
1295C22—441no—
1296C22—442no—
1297C22—441no—
1298C22—441no—
1299C22—442no—
1300C22—884no—
1301C22—888no—
1302C22—884no—
1303C22—888no—
1304C22#1062320512yes—
1305C22C22×D4×D1111yescharacteristic
1306C4—22no—
1307C4—22no—
1308C4—41no—
1309C4—41no—
1310C4—42no—
1311C4—41no—
1312C4—221no—
1313C4—221no—
1314C4—222no—
1315C4—222no—
1316C4—441no—
1317C4—441no—
1318C4—442no—
1319C4#1062320512yes—
1320C4C2×#6704211yescharacteristic
1321C4C2×#6704211yescharacteristic
1322C2—22no—
1323C2—82no—
1324C2—81no—
1325C2—222no—
1326C2—441no—
1327C2—882no—
1328C2—881no—
1329C2—881no—
1330C2C2×#1062320511yescharacteristic
1331C2D11×#57711yescharacteristic
1332C2#1308339111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3136C2
socleC22×C11C23×D4
hypercenter#3136D11
hypocenterC11#60812
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #3136

Complements

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

NH ≅ G/Ntype
1. #13082371C2semidirect
2. D11×#535C2semidirect
3. #13079713C2semidirect
4. #13079711C2semidirect
5. #13079691C2semidirect
6. #13079689C2semidirect
7. #13079635C2semidirect
8. #13079620C2semidirect
9. #13079582C2semidirect
10. #13079558C2semidirect
11. #13079092C2semidirect
12. #13079088C2semidirect
13. #13078975C2semidirect
14. #13078160C2semidirect
15. #13078154C2semidirect
16. #13078140C2semidirect
17. #13078136C2semidirect
18. #13077877C2semidirect
19. #13077845C2semidirect
20. #13077836C2semidirect
21. C2×#10622389C2semidirect
22. #13077271C2semidirect
23. C11×#3136C2semidirect
26. C11×#544C22semidirect
29. C2×#67004C22semidirect
30. C2×#67003C22semidirect
32. C22×#4324C22semidirect
33. C2×#66985C22semidirect
34. C2×#66962C22semidirect
35. C2×#66961C22semidirect
36. C2×#66957C22semidirect
37. C22×#4314C22semidirect
38. #10623264C22semidirect
41. #10623259C22semidirect
44. #10623228C22semidirect
47. #10623222C22semidirect
58. #10623057C22semidirect
62. #10623047C22semidirect
64. #10623035C22semidirect
65. C11×#490C22semidirect
66. C11×#489C22semidirect
67. C11×#488C22semidirect
68. C11×#486C22semidirect
69. C11×#418C22semidirect
70. C11×#417C22semidirect
71. C11×#416C22semidirect
72. C2×C11×#102C22semidirect
73. C11×#405C22semidirect
75. #10622732C22semidirect
77. #10622715C22semidirect
78. #10622702C22semidirect
79. #10622701C22semidirect
80. #10622689C22semidirect
81. #10622687C22semidirect
82. #10622681C22semidirect
83. #10622680C22semidirect
84. #10622673C22semidirect
85. #10622672C22semidirect
86. #10622615C22semidirect
87. #10622614C22semidirect
88. #10622610C22semidirect
89. #10622579C22semidirect
90. C2×#66873C22semidirect
91. #10622432C22semidirect
92. #10622424C22semidirect
93. #10622423C22semidirect
94. #10622423C22semidirect
95. #10622421C22semidirect
96. #10622421C22semidirect
97. #10622419C22semidirect
98. #10622411C22semidirect
99. #10622411C22semidirect
100. #10622411C22semidirect
101. #10622400C22semidirect
102. #10622399C22semidirect
103. #10622399C22semidirect
104. #10622396C22semidirect
105. #10622396C22semidirect
106. #10622394C22semidirect
110. #10622389C22semidirect
111. #10622389C22semidirect
112. #10622389C22semidirect
113. #10622389C22semidirect
114. #10622389C22semidirect
116. #10622386C22semidirect
117. #10622386C22semidirect
118. #10622380C22semidirect
119. #10622380C22semidirect
120. #10622380C22semidirect
121. #10622375C22semidirect
122. #10622375C22semidirect
123. #10622375C22semidirect
124. #10622375C22semidirect
125. #10622375C22semidirect
126. #10622375C22semidirect
127. #10622328C22semidirect
128. #10622325C22semidirect
129. #10622322C22semidirect
130. #10622318C22semidirect
131. #10622309C22semidirect
132. #10622306C22semidirect
133. #10622303C22semidirect
134. #10622298C22semidirect
165. C11×C4⋊Q8C23semidirect
168. C11×#125C23semidirect
185. C2×#4326C23semidirect
186. C2×#4326C23semidirect
187. C2×#4325C23semidirect
204. C2×#4324C23semidirect
205. C2×#4324C23semidirect
208. C2×#4323C23semidirect
219. C2×Dic44C23semidirect
220. C2×Dic44C23semidirect
223. C2×D88C23semidirect
228. C2×#4314C23semidirect
229. C2×#4314C23semidirect
230. C2×#4314C23semidirect
250. #66946C23semidirect
262. #66940C23semidirect
263. #66940C23semidirect
264. #66940C23semidirect
281. #66928C23semidirect
287. #66922C23semidirect
290. C11×#103C23semidirect
291. C11×#103C23semidirect
292. C11×#103C23semidirect
297. C11×#102C23semidirect
298. C11×#102C23semidirect
299. C11×#102C23semidirect
300. C11×#97C23semidirect
301. C4×C8×C11C23semidirect
308. Dic11⋊C8C23semidirect
309. Dic11⋊C8C23semidirect
310. Dic11⋊C8C23semidirect
311. Dic11⋊C8C23semidirect
312. #66874C23semidirect
313. #66874C23semidirect
314. #66874C23semidirect
319. #66873C23semidirect
320. #66873C23semidirect
321. #66873C23semidirect
322. #66867C23semidirect
323. C4×C11⋊C8C23semidirect
513. #3136D11semidirect
648. #544C2×D11semidirect
682. #490C2×D11semidirect
684. #489C2×D11semidirect
686. #488C2×D11semidirect
688. #486C2×D11semidirect
732. #418C2×D11semidirect
734. #417C2×D11semidirect
736. #416C2×D11semidirect
738. C2×#102C2×D11semidirect
742. #405C2×D11semidirect
851. C4⋊Q8C22×D11semidirect
866. #125C22×D11semidirect
952. #103C22×D11semidirect
953. #103C22×D11semidirect
954. #103C22×D11semidirect
966. #102C22×D11semidirect
967. #102C22×D11semidirect
968. #102C22×D11semidirect
976. #97C22×D11semidirect
978. C4×C8C22×D11semidirect
1165. C11#60812semidirect

Maximal subgroups

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

subgroupindex
#130823712
D11×#5352
#130797132
#130797112
#130796912
#130796892
#130796352
#130796202
#130795822
#130795582
#130790922
#130790882
#130789752
#130781602
#130781542
#130781402
#130781362
#130778772
#130778452
#130778362
C2×#106223892
#130772712
C11×#31362
#6081211