Finite Group Databasebeta

← #15624668

Subgroups — #15624668

Order 2816.

2208 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082281C211yesmaximal, characteristic, complemented
2#13081949C211yesmaximal, characteristic, complemented
3#13079529C212yesmaximal, complemented
4#13079516C212yesmaximal, complemented
5#13079475C212yesmaximal, complemented
6#13079473C212yesmaximal, complemented
7#13079456C212yesmaximal, complemented
8#13079434C212yesmaximal, complemented
9#13079407C212yesmaximal, complemented
10#13079385C212yesmaximal, complemented
11#13078587C211yesmaximal, characteristic, complemented
12#13078576C211yesmaximal, characteristic, complemented
13#13078529C211yesmaximal, characteristic, complemented
14#13078308C211yesmaximal, characteristic, complemented
15#13078297C211yesmaximal, characteristic, complemented
16#13078263C211yesmaximal, characteristic, complemented
17#13078254C211yesmaximal, characteristic, complemented
18#13077894C211yesmaximal, characteristic, complemented
19#13077885C211yesmaximal, characteristic, complemented
20#13077861C211yesmaximal, characteristic, complemented
21C2×#10622650C211yesmaximal, characteristic, complemented
22#13077066C211yesmaximal, characteristic, complemented
23C11×#3094C211yesmaximal, characteristic, complemented
24C2×#67037C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C22×#4339C2211yescharacteristic, complemented
27C2×C11×#121C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic, complemented
29#10623336C2211yescharacteristic
30D4×C22⋊D11—22no—
31C22×#4324C2211yescharacteristic, complemented
32C22×#4323C2211yescharacteristic, complemented
33#10623322C2211yescharacteristic
34C2×#66962C2211yescharacteristic, complemented
35C2×#66961C2211yescharacteristic, complemented
36C2×#66960C2211yescharacteristic, complemented
37C2×#66960C2211yescharacteristic, complemented
38#10623143—21no—
39#10623140—21no—
40#10623139C2212yescomplemented
41#10623138C2212yescomplemented
42#10623137C2212yescomplemented
43D11×#121C2212yescomplemented
44#10623130—21no—
45#10623129—21no—
46#10623057—21no—
47#10623057C2211yescharacteristic
48#10623057C2211yescharacteristic, complemented
49#10623056—21no—
50#10623056C2211yescharacteristic
51#10623056C2211yescharacteristic, complemented
52#10623055—22no—
53#10623055C2212yescomplemented
54#10623055C2212yescomplemented
55#10623041C2211yescharacteristic
56#10623041C2212yescomplemented
57#10623041C2212yescomplemented
58#10623035C2211yescharacteristic
59#10623024—22no—
60#10623021—22no—
61#10623008—21no—
62#10623008—21no—
63C11×#482C2212yescomplemented
64C11×#482C2212yescomplemented
65C11×#481C2212yescomplemented
66C11×#480C2212yescomplemented
67C11×#428C2211yescharacteristic, complemented
68C11×#428C2211yescharacteristic, complemented
69C11×#418C2211yescharacteristic, complemented
70C11×#418C2211yescharacteristic, complemented
71C11×#407C2211yescharacteristic, complemented
72C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
73#10622744C2211yescharacteristic, complemented
74#10622742C2211yescharacteristic
75#10622742C2211yescharacteristic
76#10622733C2211yescharacteristic, complemented
77#10622650C2212yescomplemented
78#10622650C2212yescomplemented
79#10622650C2212yescomplemented
80#10622650C2212yescomplemented
81#10622616C2211yescharacteristic, complemented
82#10622616C2211yescharacteristic, complemented
83#10622615C2211yescharacteristic, complemented
84#10622615C2211yescharacteristic, complemented
85#10622611C2211yescharacteristic, complemented
86#10622611C2211yescharacteristic, complemented
87#10622609C2211yescharacteristic, complemented
88#10622609C2211yescharacteristic, complemented
89#10622584C2211yescharacteristic, complemented
90#10622583C2211yescharacteristic, complemented
91C2×#66874C2211yescharacteristic, complemented
92#10622581C2211yescharacteristic, complemented
93#10622580C2211yescharacteristic, complemented
94C2×#66873C2211yescharacteristic, complemented
95#10622501C2212yescomplemented
96#10622500C2212yescomplemented
97#10622499C2212yescomplemented
98#10622499C2212yescomplemented
99#10622498C2212yescomplemented
100#10622497C2212yescomplemented
101#10622496C2212yescomplemented
102#10622495C2212yescomplemented
103#10622481C2212yescomplemented
104#10622480C2212yescomplemented
105#10622479C2212yescomplemented
106#10622478C2212yescomplemented
107#10622477C2212yescomplemented
108#10622477C2212yescomplemented
109#10622476C2212yescomplemented
110#10622475C2212yescomplemented
111#10622396C2212yescomplemented
112#10622396C2212yescomplemented
113#10622395C2212yescomplemented
114#10622395C2212yescomplemented
115#10622394C2212yescomplemented
116#10622394C2212yescomplemented
117#10622393C2212yescomplemented
118#10622393C2212yescomplemented
119#10622391C2212yescomplemented
120#10622391C2212yescomplemented
121#10622389C2212yescomplemented
122#10622389C2212yescomplemented
123#10622388C2212yescomplemented
124#10622388C2212yescomplemented
125#10622386C2212yescomplemented
126#10622386C2212yescomplemented
127#10622347C2212yescomplemented
128#10622347C2212yescomplemented
129#10622346C2212yescomplemented
130#10622346C2212yescomplemented
131#10622340C2212yescomplemented
132#10622340C2212yescomplemented
133#10622339C2212yescomplemented
134D11×C22⋊C8C2212yescomplemented
135C22×D4×C11—21no—
136C22×D4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11—21no—
139C22×C22⋊D11—22no—
140C22×C22⋊D11D412yes—
141#67037—42no—
142#67037—42no—
143C2×#4341—21no—
144C2×#4341C2312yes—
145C2×D4×D11—22no—
146C2×D4×D11—21no—
147C2×D4×D11C2312yes—
148C2×#4339—21no—
149C2×#4339—21no—
150C2×#4339—42no—
151C2×#4339—42no—
152C2×#4339—42no—
153C2×#4339—42no—
154C2×#4339D411yescharacteristic
155C2×#4339D411yescharacteristic
156C2×#4339D412yes—
157C2×#4339C2311yescharacteristic
158C2×#4339C2311yescharacteristic
159C2×#4339C2312yes—
160C2×#4339C2311yescharacteristic
161C2×#4339C2312yes—
162C2×#4339C2312yes—
163C22×D44D411yescharacteristic
164C22×D44C2311yescharacteristic
165C22×C4×D11—21no—
166C22×C4×D11C2312yes—
167C22×Dic22D411yescharacteristic
168C22×Dic22C2311yescharacteristic
169C2×C11×M16C2311yescharacteristic
170C2×C11×M16C2311yescharacteristic
171C11×#121—21no—
172C11×#121—21no—
173C11×#121C2312yes—
174C11×#121C2312yes—
175C11×#117—21no—
176C11×#117—21no—
177C11×#117C2311yescharacteristic
178C11×#117C2311yescharacteristic
179C11×#117C2311yescharacteristic
180C11×#117C2311yescharacteristic
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C4⋊C4C2311yescharacteristic
183C2×C11×C4⋊C4C2311yescharacteristic
184C2×C11×C22⋊C4—21no—
185C2×C11×C22⋊C4—21no—
186C2×C42×C11—21no—
187#67006—21no—
188#67006—22no—
189#66993—22no—
190#66993—21no—
191#66992—22no—
192#66992—22no—
193#66991—22no—
194#66991C2312yes—
195#66991C2312yes—
196#66990—22no—
197#66990—22no—
198#66989—21no—
199D4×Dic11—22no—
200C2×#4324—42no—
201C2×#4324C2312yes—
202C2×#4324C2312yes—
203C2×#4323—42no—
204C2×#4323C2312yes—
205C2×#4323C2312yes—
206#66983—22no—
207#66983—22no—
208#66983—22no—
209#66983—22no—
210#66983—22no—
211#66983C2311yescharacteristic
212#66983C2311yescharacteristic
213#66982—21no—
214C4×C22⋊D11—21no—
215C4×C22⋊D11—21no—
216C4×C22⋊D11—22no—
217#66979C2311yescharacteristic
218#66977C2311yescharacteristic
219#66977C2311yescharacteristic
220C22×C11⋊C8C2311yescharacteristic
221C22×C11⋊C8C2311yescharacteristic
222#66962—42no—
223#66961—42no—
224#66960—42no—
225#66960—42no—
226C2×Dic44C2312yes—
227C2×D88C2312yes—
228C2×#4314C2312yes—
229C2×#4314C2312yes—
230C2×#4313C2312yes—
231C2×#4313C2312yes—
232C2×C8×D11C2312yes—
233C2×C8×D11C2312yes—
234#66950—21no—
235#66950—22no—
236#66950—22no—
237#66950C2312yes—
238#66950C2312yes—
239#66950C2312yes—
240#66950C2312yes—
241#66950C2312yes—
242#66948—21no—
243#66948—22no—
244#66948—22no—
245#66948C2312yes—
246#66948C2312yes—
247#66948C2312yes—
248#66948C2312yes—
249#66948C2312yes—
250#66946—21no—
251#66945C2312yes—
252C4⋊C4×D11C2312yes—
253#66940—21no—
254#66939—22no—
255#66939—22no—
256#66939—22no—
257#66939—22no—
258#66938—22no—
259#66937—22no—
260#66937—22no—
261#66936—22no—
262#66935—22no—
263#66935—22no—
264#66935—22no—
265#66935—22no—
266#66935—22no—
267(C22⋊D11)⋊C4—22no—
268C22⋊C4×D11—22no—
269#66931—22no—
270#66928—21no—
271#66928—21no—
272#66928—21no—
273#66928—21no—
274#66927—21no—
275#66927—21no—
276C4×D44—22no—
277C4×D44—22no—
278C4×D44—22no—
279C4×D44—22no—
280#66922—21no—
281#66922—21no—
282C11×#107C2312yes—
283C11×#107C2312yes—
284C11×#106C2312yes—
285C11×#106C2312yes—
286C11×#102C2312yes—
287C11×#102C2312yes—
288C11×#102C2312yes—
289C11×#102C2312yes—
290C11×C22⋊C8C2312yes—
291C11×C22⋊C8C2312yes—
292C22⋊(C11⋊C8)C2311yescharacteristic
293C22⋊(C11⋊C8)C2311yescharacteristic
294C22⋊(C11⋊C8)C2311yescharacteristic
295C22⋊(C11⋊C8)C2311yescharacteristic
296#66885C2312yes—
297#66885C2312yes—
298(C2×D11)⋊C8C2312yes—
299(C2×D11)⋊C8C2312yes—
300(C2×D11)⋊C8C2312yes—
301(C2×D11)⋊C8C2312yes—
302#66880C2312yes—
303#66880C2312yes—
304#66874C2312yes—
305#66874C2311yescharacteristic
306#66874C2312yes—
307#66874C2311yescharacteristic
308#66874C2311yescharacteristic
309#66874C2311yescharacteristic
310#66873C2312yes—
311#66873C2311yescharacteristic
312#66873C2311yescharacteristic
313#66873C2312yes—
314#66873C2311yescharacteristic
315#66873C2311yescharacteristic
316#66872C2311yescharacteristic
317#66872C2311yescharacteristic
318#66872C2311yescharacteristic
319#66872C2311yescharacteristic
320#66871C2311yescharacteristic
321#66871C2311yescharacteristic
322#66871C2311yescharacteristic
323#66871C2311yescharacteristic
324#60760—111nomaximal, Sylow
325C24×C11—21no—
326C24×C11C2×D411yescharacteristic
327C23×D11—21no—
328C23×D11—22no—
329C23×D11C2×D412yes—
330C2×D4×C11—22no—
331C2×D4×C11—22no—
332C2×D4×C11—21no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—82no—
336C2×D4×C11C2412yes—
337C22×C4×C11—22no—
338C22×C4×C11—22no—
339C22×C4×C11—21no—
340C22×C4×C11—21no—
341C22×C4×C11—21no—
342C22×C4×C11C2×D411yescharacteristic
343C22×C4×C11C2×D411yescharacteristic
344C22×C4×C11C2×D411yescharacteristic
345C22×C4×C11C2411yescharacteristic
346C22×C4×C11C2411yescharacteristic
347C22×C4×C11C2411yescharacteristic
348C2×C22⋊D11—22no—
349C2×C22⋊D11—22no—
350C2×C22⋊D11—21no—
351C2×C22⋊D11—21no—
352C2×C22⋊D11—22no—
353C2×C22⋊D11—21no—
354C2×C22⋊D11—22no—
355C2×C22⋊D11—22no—
356C2×C22⋊D11—22no—
357C2×C22⋊D11—44no—
358C2×C22⋊D11—44no—
359C2×C22⋊D11—48no—
360C2×C22⋊D11C2×D412yes—
361C2×C22⋊D11C2×D412yes—
362C2×C22⋊D11C2×D412yes—
363C2×C22⋊D11C2×D412yes—
364C22×Dic11—22no—
365C22×Dic11—21no—
366C22×Dic11C2×D412yes—
367#4341—42no—
368#4341—42no—
369#4341—44no—
370D4×D11—42no—
371D4×D11—42no—
372D4×D11—44no—
373D4×D11—84no—
374#4339—22no—
375#4339—22no—
376#4339—22no—
377#4339—22no—
378#4339—22no—
379#4339—22no—
380#4339—42no—
381#4339—42no—
382#4339—42no—
383#4339—42no—
384#4339—42no—
385#4339—42no—
386#4339—42no—
387#4339—42no—
388#4339—44no—
389#4339—44no—
390#4339—44no—
391C2×D44—22no—
392C2×D44—22no—
393C2×D44—22no—
394C2×D44—22no—
395C2×D44—22no—
396C2×D44—21no—
397C2×D44—22no—
398C2×D44—22no—
399C2×D44—42no—
400C2×D44C2×D411yescharacteristic
401C2×D44C2×D411yescharacteristic
402C2×D44C2×D412yes—
403C2×D44C2411yescharacteristic
404C2×D44C2412yes—
405C2×C4×D11—22no—
406C2×C4×D11—22no—
407C2×C4×D11—22no—
408C2×C4×D11—21no—
409C2×C4×D11—42no—
410C2×C4×D11—42no—
411C2×C4×D11—44no—
412C2×C4×D11C2×D412yes—
413C2×C4×D11C2×D412yes—
414C2×C4×D11C2412yes—
415C2×C4×D11C2412yes—
416C2×Dic22—21no—
417C2×Dic22—22no—
418C2×Dic22—22no—
419C2×Dic22—42no—
420C2×Dic22C2×D411yescharacteristic
421C2×Dic22C2×D411yescharacteristic
422C2×Dic22C2×D412yes—
423C2×Dic22C2411yescharacteristic
424C2×Dic22C2412yes—
425C11×M16—22no—
426C11×M16—22no—
427C2×C8×C11C2412yes—
428C2×C8×C11C2412yes—
429C11×C4⋊C4—21no—
430C11×C4⋊C4—21no—
431C11×C4⋊C4—21no—
432C11×C4⋊C4C2411yescharacteristic
433C11×C4⋊C4C2411yescharacteristic
434C11×C4⋊C4C2411yescharacteristic
435C11×C4⋊C4C2411yescharacteristic
436C11×C4⋊C4C2412yes—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—21no—
439C11×C22⋊C4—21no—
440C11×C22⋊C4—21no—
441C11×C22⋊C4—22no—
442C11×C22⋊C4—22no—
443C42×C11—21no—
444C42×C11—21no—
445C42×C11—21no—
446C42×C11—21no—
447C22⋊Dic11—22no—
448C22⋊Dic11—22no—
449C22⋊Dic11—21no—
450C22⋊Dic11—21no—
451C22⋊Dic11—21no—
452#4324—42no—
453#4324—42no—
454#4323—42no—
455#4323—42no—
456(C2×D11)⋊C4—22no—
457(C2×D11)⋊C4—22no—
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)⋊C4—22no—
465(C2×D11)⋊C4—22no—
466(C2×D11)⋊C4—22no—
467(C2×D11)⋊C4—21no—
468(C2×D11)⋊C4—21no—
469C4⋊Dic11—22no—
470C4⋊Dic11—22no—
471C4⋊Dic11—22no—
472C4⋊Dic11—22no—
473C4⋊Dic11—22no—
474C4⋊Dic11C2411yescharacteristic
475C4⋊Dic11C2411yescharacteristic
476Dic11⋊C4—22no—
477Dic11⋊C4—21no—
478Dic11⋊C4—21no—
479C4×Dic11—22no—
480C4×Dic11—21no—
481C2×C11⋊C8—22no—
482C2×C11⋊C8—22no—
483C2×C11⋊C8C2411yescharacteristic
484C2×C11⋊C8C2411yescharacteristic
485C2×C11⋊C8C2411yescharacteristic
486C2×C11⋊C8C2411yescharacteristic
487Dic44—42no—
488D88—42no—
489#4314—42no—
490#4314—42no—
491#4313—42no—
492#4313—42no—
493C8×D11—42no—
494C8×D11—42no—
495#3488—111no—
496#3449—111no—
497#3204—112no—
498#3203—112no—
499#3198—112no—
500#3198—112no—
501#3197—112no—
502#3194—112no—
503#3191—112no—
504#3188—112no—
505#3097—111no—
506#3096—111no—
507#3094D1111yescharacteristic, complemented
508#3091—111no—
509#3063—111no—
510#3062—111no—
511#3058—111no—
512#3057—111no—
513#3009—111no—
514#3008—111no—
515#3005—111no—
516C2×#449—111no—
517#2880—111no—
518C23×C11—22no—
519C23×C11—22no—
520C23×C11—41no—
521C23×C11—41no—
522C23×C11—42no—
523C23×C11—81no—
524C23×C11—81no—
525C23×C11C22×D411yescharacteristic
526C23×C11C22×D411yescharacteristic
527C23×C11C22×D411yescharacteristic
528C22×D11—22no—
529C22×D11—21no—
530C22×D11—42no—
531C22×D11—42no—
532C22×D11—42no—
533C22×D11—44no—
534C22×D11—42no—
535C22×D11—82no—
536C22×D11—82no—
537C22×D11—81no—
538C22×D11—81no—
539C22×D11C22×D412yes—
540C22×D11C22×D412yes—
541D4×C11—22no—
542D4×C11—22no—
543D4×C11—44no—
544D4×C11—42no—
545D4×C11—82no—
546C2×C4×C11—22no—
547C2×C4×C11—22no—
548C2×C4×C11—22no—
549C2×C4×C11—21no—
550C2×C4×C11—21no—
551C2×C4×C11—21no—
552C2×C4×C11—21no—
553C2×C4×C11—22no—
554C2×C4×C11—21no—
555C2×C4×C11—21no—
556C2×C4×C11—21no—
557C2×C4×C11—21no—
558C2×C4×C11—81no—
559C2×C4×C11—81no—
560C2×C4×C11—81no—
561C2×C4×C11C22×D411yescharacteristic
562C2×C4×C11C22×D411yescharacteristic
563C2×C4×C11C22×D411yescharacteristic
564C2×C4×C11H(5,𝔽2)12yes—
565C2×C4×C11H(5,𝔽2)12yes—
566C2×C4×C11C2511yescharacteristic
567C22⋊D11—24no—
568C22⋊D11—24no—
569C22⋊D11—42no—
570C22⋊D11—42no—
571C22⋊D11—44no—
572C22⋊D11—44no—
573C22⋊D11—44no—
574C22⋊D11—44no—
575C22⋊D11—42no—
576C22⋊D11—42no—
577C22⋊D11—82no—
578C22⋊D11—82no—
579C22⋊D11—81no—
580C2×Dic11—21no—
581C2×Dic11—21no—
582C2×Dic11—21no—
583C2×Dic11—22no—
584C2×Dic11—42no—
585C2×Dic11—44no—
586C2×Dic11—42no—
587C2×Dic11C22×D412yes—
588C2×Dic11C22×D412yes—
589D44—22no—
590D44—22no—
591D44—21no—
592D44—22no—
593D44—21no—
594D44—22no—
595D44—42no—
596D44—42no—
597D44—82no—
598D44—82no—
599D44—82no—
600D44—82no—
601D44—82no—
602C4×D11—22no—
603C4×D11—22no—
604C4×D11—22no—
605C4×D11—22no—
606C4×D11—42no—
607C4×D11—42no—
608C4×D11—44no—
609C4×D11—44no—
610C4×D11—42no—
611C4×D11—82no—
612Dic22—22no—
613Dic22—22no—
614Dic22—21no—
615Dic22—22no—
616Dic22—21no—
617Dic22—22no—
618Dic22—42no—
619Dic22—42no—
620C8×C11—22no—
621C8×C11—22no—
622C11⋊C8—21no—
623C11⋊C8—21no—
624C11⋊C8—21no—
625C11⋊C8—21no—
626C2×H(5,𝔽2)—111no—
627C22×#41—111no—
628C22×#41—111no—
629C2×#137—111no—
630C2×AGL(1,ℤ/8)—111no—
631C22×SD16—111no—
632C22×D8—111no—
633C2×#131—111no—
634C2×#131—111no—
635#550—221no—
636#548—221no—
637#546—222no—
638#546—221no—
639D42—221no—
640D42—222no—
641#537—112no—
642#537—111no—
643#537—112no—
644#537—112no—
645#536—111no—
646#536—111no—
647#536—221no—
648#535—111no—
649#535—112no—
650#535—111no—
651#535—111no—
652#535—221no—
653#534—222no—
654#532—221no—
655#532—221no—
656#525—111no—
657#525—112no—
658#525—112no—
659#525—112no—
660#525—222no—
661C2×#121—112no—
662C2×#121C2×D1111yescharacteristic
663#520—111no—
664C2×#117C2×D1111yescharacteristic, complemented
665#485—111no—
666#485—111no—
667#485—112no—
668#485—112no—
669#484—111no—
670#484—112no—
671#483—111no—
672#483—112no—
673#482—111no—
674#482—111no—
675#482—112no—
676#482—112no—
677#482C2×D1112yescomplemented
678#482C2×D1112yescomplemented
679#481—111no—
680#481—112no—
681#481C2×D1112yescomplemented
682#480—111no—
683#480—112no—
684#480C2×D1112yescomplemented
685#470—112no—
686#469—112no—
687#469—112no—
688#469—112no—
689#468—112no—
690#468—112no—
691#468—112no—
692#468—112no—
693#467—112no—
694#466—112no—
695#466—112no—
696#466—112no—
697#465—112no—
698#465—112no—
699#465—112no—
700#465—112no—
701#452—112no—
702#452—112no—
703#452—112no—
704#452—112no—
705#450—112no—
706#450—112no—
707#449—112no—
708#449—112no—
709#449—112no—
710#449—112no—
711#449—112no—
712#449—112no—
713#449—112no—
714#449—112no—
715#447—112no—
716#447—112no—
717#428C2×D1111yescharacteristic, complemented
718#428C2×D1111yescharacteristic, complemented
719#427—111no—
720#427—111no—
721#419—111no—
722#418—111no—
723#418C2×D1111yescharacteristic, complemented
724#418C2×D1111yescharacteristic, complemented
725#416—111no—
726#416—111no—
727C2×#103—111no—
728C2×#102—111no—
729#408—111no—
730#408—111no—
731#408—112no—
732#408—112no—
733#407—112no—
734#407C2×D1111yescharacteristic, complemented
735C2×C22⋊C8—111no—
736C2×C22⋊C8—112no—
737C22×C11—21no—
738C22×C11—21no—
739C22×C11—21no—
740C22×C11—21no—
741C22×C11—21no—
742C22×C11—21no—
743C22×C11—21no—
744C22×C11—21no—
745C22×C11—42no—
746C22×C11—42no—
747C22×C11—42no—
748C22×C11—82no—
749C22×C11—162no—
750C22×C11#53412yes—
751C22×C11C23×D411yescharacteristic
752C2×D11—22no—
753C2×D11—22no—
754C2×D11—22no—
755C2×D11—22no—
756C2×D11—22no—
757C2×D11—22no—
758C2×D11—41no—
759C2×D11—42no—
760C2×D11—41no—
761C2×D11—42no—
762C2×D11—41no—
763C2×D11—42no—
764C2×D11—84no—
765C2×D11—84no—
766C2×D11—164no—
767C4×C11—21no—
768C4×C11—21no—
769C4×C11—41no—
770C4×C11—41no—
771C4×C11—42no—
772C4×C11—41no—
773C4×C11—41no—
774C4×C11#53412yes—
775C4×C11C2×H(5,𝔽2)11yescharacteristic
776C4×C11C2×H(5,𝔽2)11yescharacteristic
777Dic11—22no—
778Dic11—22no—
779Dic11—41no—
780Dic11—41no—
781Dic11—42no—
782Dic11—41no—
783H(5,𝔽2)—442no—
784H(5,𝔽2)—442no—
785C2×#41—112no—
786C2×#41—111no—
787C2×#41—111no—
788C2×#41—111no—
789C2×#41—111no—
790C2×#41—112no—
791C2×#41—112no—
792C2×#41—111no—
793C2×#41—112no—
794C2×#41—112no—
795C2×#41—221no—
796C2×#41—221no—
797C2×#41—221no—
798C2×#41—442no—
799C2×#41—442no—
800C2×#41—442no—
801C2×#41—442no—
802C22×Q8—111no—
803C22×Q8—111no—
804C22×D4—21no—
805C22×D4—112no—
806C22×D4—112no—
807C22×D4—111no—
808C22×D4—111no—
809C22×D4—221no—
810C22×D4—222no—
811C22×D4—222no—
812C22×D4—221no—
813C22×D4C22×D1111yescharacteristic
814C23×C4—112no—
815C23×C4—221no—
816C23×C4C22×D1111yescharacteristic
817#137—442no—
818AGL(1,ℤ/8)—442no—
819C2×Q16—112no—
820C2×SD16—112no—
821C2×SD16—112no—
822C2×SD16—112no—
823C2×SD16—112no—
824C2×SD16—442no—
825C2×D8—112no—
826C2×D8—112no—
827C2×D8—112no—
828C2×D8—442no—
829#131—442no—
830#131—442no—
831C2×M16—112no—
832C2×M16—112no—
833C2×M16C22×D1111yescharacteristic
834C2×M16C22×D1111yescharacteristic
835C22×C8—111no—
836C22×C8—111no—
837C22×C8—112no—
838C22×C8—112no—
839C4⋊Q8—221no—
840C4⋊Q8—221no—
841#127—221no—
842#127—221no—
843#127—222no—
844#127—221no—
845#124—221no—
846#124—221no—
847#124—221no—
848#124—221no—
849#124—222no—
850#124—221no—
851#123—222no—
852#123—222no—
853#123—222no—
854#123—222no—
855#123—222no—
856#123—221no—
857C22⋊Q8—111no—
858C22⋊Q8—111no—
859C22⋊Q8—112no—
860C22⋊Q8—112no—
861C22⋊Q8—112no—
862C22⋊Q8—112no—
863C22⋊Q8—112no—
864C22⋊Q8—222no—
865C22⋊Q8—222no—
866C22⋊Q8—222no—
867C22⋊Q8—221no—
868#121—21no—
869#121—21no—
870#121—112no—
871#121—112no—
872#121—111no—
873#121—111no—
874#121—112no—
875#121—112no—
876#121—112no—
877#121—112no—
878#121—112no—
879#121—222no—
880#121—222no—
881#121—222no—
882#121—222no—
883#121—221no—
884#121—222no—
885#121—222no—
886#121—222no—
887#121—222no—
888#121—222no—
889#121—222no—
890#121—222no—
891#121—222no—
892#121C22×D1112yes—
893#121C22×D1112yes—
894#120—222no—
895#120—222no—
896#120—222no—
897#120—222no—
898#120—222no—
899#120—222no—
900#120—222no—
901#120—222no—
902#120—221no—
903C4×Q8—221no—
904C4×D4—222no—
905C4×D4—222no—
906C4×D4—222no—
907C4×D4—222no—
908C4×D4—222no—
909C4×D4—221no—
910C4×D4—222no—
911C4×D4—222no—
912C4×D4—221no—
913C4×D4—221no—
914#117—21no—
915#117—21no—
916#117—111no—
917#117—112no—
918#117C22×D1111yescharacteristic
919#117C22×D1111yescharacteristic
920#117C22×D1111yescharacteristic
921#117C22×D1111yescharacteristic
922C2×C4⋊C4—112no—
923C2×C4⋊C4C22×D1111yescharacteristic
924C2×C4⋊C4C22×D1111yescharacteristic
925C2×C4⋊C4C22×D1111yescharacteristic
926C2×C22⋊C4—21no—
927C2×C22⋊C4—21no—
928C2×C22⋊C4—222no—
929C2×C42—21no—
930#107—111no—
931#107—111no—
932#107—111no—
933#107—111no—
934#107C22×D1112yes—
935#107C22×D1112yes—
936#106—111no—
937#106—111no—
938#106—111no—
939#106—111no—
940#106C22×D1112yes—
941#106C22×D1112yes—
942#103—112no—
943#103—112no—
944#103—112no—
945#103—112no—
946#103—111no—
947#103—111no—
948#103—111no—
949#103—111no—
950#102—112no—
951#102—112no—
952#102—112no—
953#102—112no—
954#102—111no—
955#102—111no—
956#102—111no—
957#102—111no—
958#102C22×D1112yes—
959#102C22×D1112yes—
960#102C22×D1112yes—
961#102C22×D1112yes—
962C22⋊C8—111no—
963C22⋊C8—111no—
964C22⋊C8—111no—
965C22⋊C8—111no—
966C22⋊C8—112no—
967C22⋊C8—112no—
968C22⋊C8—112no—
969C22⋊C8—112no—
970C22⋊C8C22×D1112yes—
971C22⋊C8C22×D1112yes—
972C2×C11—22no—
973C2×C11—41no—
974C2×C11—41no—
975C2×C11—82no—
976C2×C11C2×#53411yescharacteristic
977C2×C11#358411yescharacteristic
978C2×C11#358511yescharacteristic
979D11—42no—
980D11—42no—
981D11—82no—
982D11—81no—
983C24—21no—
984C24—112no—
985C24—222no—
986C24—221no—
987C24D4×D1111yescharacteristic
988#41—222no—
989#41—222no—
990#41—222no—
991#41—222no—
992#41—222no—
993#41—222no—
994#41—442no—
995#41—442no—
996#41—444no—
997#41—442no—
998#41—442no—
999#41—442no—
1000#41—442no—
1001#41—442no—
1002#41—442no—
1003#41—444no—
1004#41—444no—
1005#41—442no—
1006#41—442no—
1007#41—444no—
1008C2×Q8—111no—
1009C2×Q8—111no—
1010C2×Q8—112no—
1011C2×Q8—112no—
1012C2×Q8—111no—
1013C2×Q8—221no—
1014C2×Q8—222no—
1015C2×Q8—222no—
1016C2×Q8—442no—
1017C2×D4—22no—
1018C2×D4—22no—
1019C2×D4—21no—
1020C2×D4—22no—
1021C2×D4—22no—
1022C2×D4—82no—
1023C2×D4—112no—
1024C2×D4—112no—
1025C2×D4—112no—
1026C2×D4—112no—
1027C2×D4—111no—
1028C2×D4—111no—
1029C2×D4—112no—
1030C2×D4—112no—
1031C2×D4—111no—
1032C2×D4—222no—
1033C2×D4—222no—
1034C2×D4—222no—
1035C2×D4—222no—
1036C2×D4—222no—
1037C2×D4—222no—
1038C2×D4—222no—
1039C2×D4—221no—
1040C2×D4—222no—
1041C2×D4—221no—
1042C2×D4—222no—
1043C2×D4—222no—
1044C2×D4—222no—
1045C2×D4—221no—
1046C2×D4—221no—
1047C2×D4—222no—
1048C2×D4—222no—
1049C2×D4—442no—
1050C2×D4—442no—
1051C2×D4—442no—
1052C2×D4—444no—
1053C2×D4—444no—
1054C2×D4—448no—
1055C2×D4—444no—
1056C2×D4—884no—
1057C2×D4C23×D1112yes—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—21no—
1063C22×C4—112no—
1064C22×C4—112no—
1065C22×C4—112no—
1066C22×C4—112no—
1067C22×C4—112no—
1068C22×C4—222no—
1069C22×C4—222no—
1070C22×C4—221no—
1071C22×C4—222no—
1072C22×C4—221no—
1073C22×C4—222no—
1074C22×C4—442no—
1075C22×C4—442no—
1076C22×C4—444no—
1077C22×C4D4×D1111yescharacteristic
1078C22×C4D4×D1111yescharacteristic
1079C22×C4D4×D1111yescharacteristic
1080C22×C4C23×D1111yescharacteristic
1081C22×C4C23×D1111yescharacteristic
1082C22×C4C23×D1111yescharacteristic
1083Q16—442no—
1084SD16—442no—
1085SD16—442no—
1086SD16—442no—
1087SD16—442no—
1088D8—442no—
1089D8—442no—
1090D8—442no—
1091M16—22no—
1092M16—22no—
1093M16—442no—
1094M16—442no—
1095C2×C8—111no—
1096C2×C8—111no—
1097C2×C8—111no—
1098C2×C8—111no—
1099C2×C8—222no—
1100C2×C8—222no—
1101C2×C8—442no—
1102C2×C8—442no—
1103C2×C8C23×D1112yes—
1104C2×C8C23×D1112yes—
1105C4⋊C4—21no—
1106C4⋊C4—21no—
1107C4⋊C4—21no—
1108C4⋊C4—111no—
1109C4⋊C4—111no—
1110C4⋊C4—222no—
1111C4⋊C4—222no—
1112C4⋊C4—222no—
1113C4⋊C4—222no—
1114C4⋊C4—222no—
1115C4⋊C4—222no—
1116C4⋊C4—221no—
1117C4⋊C4—221no—
1118C4⋊C4C23×D1112yes—
1119C4⋊C4C23×D1111yescharacteristic
1120C4⋊C4C23×D1111yescharacteristic
1121C4⋊C4C23×D1111yescharacteristic
1122C4⋊C4C23×D1111yescharacteristic
1123C22⋊C4—21no—
1124C22⋊C4—21no—
1125C22⋊C4—21no—
1126C22⋊C4—21no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—222no—
1130C22⋊C4—222no—
1131C22⋊C4—222no—
1132C22⋊C4—222no—
1133C22⋊C4—222no—
1134C22⋊C4—222no—
1135C22⋊C4—222no—
1136C22⋊C4—222no—
1137C22⋊C4—222no—
1138C22⋊C4—222no—
1139C22⋊C4—222no—
1140C22⋊C4—222no—
1141C22⋊C4—222no—
1142C22⋊C4—221no—
1143C22⋊C4—221no—
1144C22⋊C4—221no—
1145C22⋊C4—221no—
1146C22⋊C4—221no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—222no—
1152C42—221no—
1153C11#6076011yescharacteristic, complemented, Sylow
1154C23—22no—
1155C23—22no—
1156C23—41no—
1157C23—41no—
1158C23—42no—
1159C23—81no—
1160C23—81no—
1161C23—112no—
1162C23—112no—
1163C23—222no—
1164C23—221no—
1165C23—442no—
1166C23—442no—
1167C23—442no—
1168C23—444no—
1169C23—442no—
1170C23—881no—
1171C23—881no—
1172C23—882no—
1173C23—882no—
1174C23C2×D4×D1111yescharacteristic
1175C23C2×D4×D1111yescharacteristic
1176C23C2×D4×D1111yescharacteristic
1177Q8—222no—
1178Q8—222no—
1179Q8—222no—
1180Q8—221no—
1181Q8—222no—
1182Q8—221no—
1183Q8—442no—
1184Q8—442no—
1185D4—22no—
1186D4—22no—
1187D4—44no—
1188D4—42no—
1189D4—82no—
1190D4—224no—
1191D4—224no—
1192D4—222no—
1193D4—222no—
1194D4—222no—
1195D4—221no—
1196D4—222no—
1197D4—221no—
1198D4—442no—
1199D4—442no—
1200D4—442no—
1201D4—444no—
1202D4—444no—
1203D4—444no—
1204D4—442no—
1205D4—444no—
1206D4—442no—
1207D4—442no—
1208D4—882no—
1209D4—882no—
1210D4—882no—
1211D4—882no—
1212D4—882no—
1213D4—881no—
1214D4—882no—
1215D4—882no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—81no—
1229C2×C4—81no—
1230C2×C4—81no—
1231C2×C4—112no—
1232C2×C4—112no—
1233C2×C4—222no—
1234C2×C4—222no—
1235C2×C4—222no—
1236C2×C4—222no—
1237C2×C4—221no—
1238C2×C4—221no—
1239C2×C4—221no—
1240C2×C4—222no—
1241C2×C4—442no—
1242C2×C4—442no—
1243C2×C4—444no—
1244C2×C4—444no—
1245C2×C4—442no—
1246C2×C4—444no—
1247C2×C4—442no—
1248C2×C4—442no—
1249C2×C4—882no—
1250C2×C4C2×D4×D1111yescharacteristic
1251C2×C4C2×D4×D1111yescharacteristic
1252C2×C4C2×D4×D1111yescharacteristic
1253C2×C4#6704212yes—
1254C2×C4#6704212yes—
1255C2×C4C24×D1111yescharacteristic
1256C8—22no—
1257C8—22no—
1258C8—221no—
1259C8—221no—
1260C8—221no—
1261C8—221no—
1262C22—21no—
1263C22—21no—
1264C22—21no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—82no—
1274C22—162no—
1275C22—222no—
1276C22—222no—
1277C22—222no—
1278C22—222no—
1279C22—222no—
1280C22—222no—
1281C22—441no—
1282C22—442no—
1283C22—442no—
1284C22—441no—
1285C22—442no—
1286C22—441no—
1287C22—884no—
1288C22—884no—
1289C22—1764no—
1290C22#1062318412yes—
1291C22C22×D4×D1111yescharacteristic
1292C4—21no—
1293C4—21no—
1294C4—42no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—222no—
1300C4—222no—
1301C4—441no—
1302C4—441no—
1303C4—442no—
1304C4—441no—
1305C4#1062318412yes—
1306C4C2×#6704211yescharacteristic
1307C4C2×#6704211yescharacteristic
1308C2—22no—
1309C2—41no—
1310C2—41no—
1311C2—82no—
1312C2—442no—
1313C2—442no—
1314C2—882no—
1315C2—881no—
1316C2C2×#1062318411yescharacteristic
1317C2#1308338911yescharacteristic
1318C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3094C2
socleC22×C11C23×D4
hypercenter#3094D11
hypocenterC11#60760
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. #13082281C2semidirect
2. #13081949C2semidirect
3. #13079529C2semidirect
4. #13079516C2semidirect
5. #13079475C2semidirect
6. #13079473C2semidirect
7. #13079456C2semidirect
8. #13079434C2semidirect
9. #13079407C2semidirect
10. #13079385C2semidirect
11. #13078587C2semidirect
12. #13078576C2semidirect
13. #13078529C2semidirect
14. #13078308C2semidirect
15. #13078297C2semidirect
16. #13078263C2semidirect
17. #13078254C2semidirect
18. #13077894C2semidirect
19. #13077885C2semidirect
20. #13077861C2semidirect
21. C2×#10622650C2semidirect
22. #13077066C2semidirect
23. C11×#3094C2semidirect
26. C22×#4339C22semidirect
28. C2×C11×#117C22semidirect
31. C22×#4324C22semidirect
32. C22×#4323C22semidirect
34. C2×#66962C22semidirect
35. C2×#66961C22semidirect
36. C2×#66960C22semidirect
37. C2×#66960C22semidirect
40. #10623139C22semidirect
41. #10623138C22semidirect
42. #10623137C22semidirect
43. D11×#121C22semidirect
48. #10623057C22semidirect
51. #10623056C22semidirect
53. #10623055C22semidirect
54. #10623055C22semidirect
56. #10623041C22semidirect
57. #10623041C22semidirect
63. C11×#482C22semidirect
64. C11×#482C22semidirect
65. C11×#481C22semidirect
66. C11×#480C22semidirect
67. C11×#428C22semidirect
68. C11×#428C22semidirect
69. C11×#418C22semidirect
70. C11×#418C22semidirect
71. C11×#407C22semidirect
72. C2×C22⋊(C11⋊C8)C22semidirect
73. #10622744C22semidirect
76. #10622733C22semidirect
77. #10622650C22semidirect
78. #10622650C22semidirect
79. #10622650C22semidirect
80. #10622650C22semidirect
81. #10622616C22semidirect
82. #10622616C22semidirect
83. #10622615C22semidirect
84. #10622615C22semidirect
85. #10622611C22semidirect
86. #10622611C22semidirect
87. #10622609C22semidirect
88. #10622609C22semidirect
89. #10622584C22semidirect
90. #10622583C22semidirect
91. C2×#66874C22semidirect
92. #10622581C22semidirect
93. #10622580C22semidirect
94. C2×#66873C22semidirect
95. #10622501C22semidirect
96. #10622500C22semidirect
97. #10622499C22semidirect
98. #10622499C22semidirect
99. #10622498C22semidirect
100. #10622497C22semidirect
101. #10622496C22semidirect
102. #10622495C22semidirect
103. #10622481C22semidirect
104. #10622480C22semidirect
105. #10622479C22semidirect
106. #10622478C22semidirect
107. #10622477C22semidirect
108. #10622477C22semidirect
109. #10622476C22semidirect
110. #10622475C22semidirect
111. #10622396C22semidirect
112. #10622396C22semidirect
113. #10622395C22semidirect
114. #10622395C22semidirect
115. #10622394C22semidirect
116. #10622394C22semidirect
117. #10622393C22semidirect
118. #10622393C22semidirect
119. #10622391C22semidirect
120. #10622391C22semidirect
121. #10622389C22semidirect
122. #10622389C22semidirect
123. #10622388C22semidirect
124. #10622388C22semidirect
125. #10622386C22semidirect
126. #10622386C22semidirect
127. #10622347C22semidirect
128. #10622347C22semidirect
129. #10622346C22semidirect
130. #10622346C22semidirect
131. #10622340C22semidirect
132. #10622340C22semidirect
133. #10622339C22semidirect
134. D11×C22⋊C8C22semidirect
507. #3094D11semidirect
664. C2×#117C2×D11semidirect
677. #482C2×D11semidirect
678. #482C2×D11semidirect
681. #481C2×D11semidirect
684. #480C2×D11semidirect
717. #428C2×D11semidirect
718. #428C2×D11semidirect
723. #418C2×D11semidirect
724. #418C2×D11semidirect
734. #407C2×D11semidirect
1153. C11#60760semidirect

Maximal subgroups

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

subgroupindex
#130822812
#130819492
#130795292
#130795162
#130794752
#130794732
#130794562
#130794342
#130794072
#130793852
#130785872
#130785762
#130785292
#130783082
#130782972
#130782632
#130782542
#130778942
#130778852
#130778612
C2×#106226502
#130770662
C11×#30942
#6076011