Finite Group Databasebeta

← #15624691

Subgroups — #15624691

Order 2816.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082292C211yesmaximal, characteristic, complemented
2#13081949C211yesmaximal, characteristic, complemented
3#13079526C212yesmaximal, complemented
4#13079520C212yesmaximal, complemented
5#13079505C212yesmaximal, complemented
6#13079503C212yesmaximal, complemented
7#13079460C212yesmaximal, complemented
8#13079450C212yesmaximal, complemented
9#13079411C212yesmaximal, complemented
10#13079401C212yesmaximal, complemented
11#13078587C211yesmaximal, characteristic, complemented
12#13078576C211yesmaximal, characteristic, complemented
13#13078529C211yesmaximal, characteristic, complemented
14#13078308C211yesmaximal, characteristic, complemented
15#13078297C211yesmaximal, characteristic, complemented
16#13078270C211yesmaximal, characteristic, complemented
17#13078258C211yesmaximal, characteristic, complemented
18#13077912C211yesmaximal, characteristic, complemented
19#13077903C211yesmaximal, characteristic, complemented
20#13077861C211yesmaximal, characteristic, complemented
21C2×#10622660C211yesmaximal, characteristic, complemented
22#13077066C211yesmaximal, characteristic, complemented
23C11×#3095C211yesmaximal, characteristic, complemented
24C2×#67040C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C22×#4339C2211yescharacteristic
27C2×C11×C22⋊Q8C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29#10623347C2211yescharacteristic
30C22×#4326C2211yescharacteristic, complemented
31C22×#4325C2211yescharacteristic, complemented
32#10623322C2211yescharacteristic
33C2×#66962C2211yescharacteristic, complemented
34C2×#66961C2211yescharacteristic, complemented
35C2×#66960C2211yescharacteristic
36C2×#66960C2211yescharacteristic
37#10623164—21no—
38#10623163—21no—
39#10623162—21no—
40#10623161—21no—
41#10623160C2212yescomplemented
42#10623159C2212yescomplemented
43#10623158C2212yescomplemented
44D11×C22⋊Q8C2212yescomplemented
45#10623057—21no—
46#10623057C2211yescharacteristic
47#10623057C2211yescharacteristic
48#10623056—21no—
49#10623056C2211yescharacteristic
50#10623056C2211yescharacteristic
51#10623055—22no—
52#10623055C2212yes—
53#10623055C2212yes—
54#10623041C2211yescharacteristic
55#10623041C2212yes—
56#10623041C2212yes—
57#10623038—22no—
58#10623035C2211yescharacteristic
59#10623024—22no—
60#10623021—22no—
61#10623008—21no—
62#10623008—21no—
63C11×#485C2212yescomplemented
64C11×#485C2212yescomplemented
65C11×#484C2212yescomplemented
66C11×#483C2212yescomplemented
67C11×#428C2211yescharacteristic, complemented
68C11×#428C2211yescharacteristic, complemented
69C11×#419C2211yescharacteristic, complemented
70C11×#419C2211yescharacteristic, complemented
71C11×#407C2211yescharacteristic
72C2×C22⋊(C11⋊C8)C2211yescharacteristic
73#10622744C2211yescharacteristic, complemented
74#10622742C2211yescharacteristic
75#10622742C2211yescharacteristic
76#10622733C2211yescharacteristic, complemented
77#10622660C2212yes—
78#10622660C2212yes—
79#10622660C2212yescomplemented
80#10622660C2212yescomplemented
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#10622429C2212yescomplemented
112#10622429C2212yescomplemented
113#10622426C2212yescomplemented
114#10622426C2212yescomplemented
115#10622425C2212yescomplemented
116#10622425C2212yescomplemented
117#10622424C2212yescomplemented
118#10622424C2212yescomplemented
119#10622423C2212yescomplemented
120#10622423C2212yescomplemented
121#10622421C2212yescomplemented
122#10622421C2212yescomplemented
123#10622420C2212yescomplemented
124#10622420C2212yescomplemented
125#10622419C2212yescomplemented
126#10622419C2212yescomplemented
127#10622347C2212yes—
128#10622347C2212yescomplemented
129#10622346C2212yes—
130#10622346C2212yescomplemented
131#10622340C2212yescomplemented
132#10622340C2212yescomplemented
133#10622339C2212yescomplemented
134D11×C22⋊C8C2212yescomplemented
135C22×Q8×C11C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C22×C22⋊D11—21no—
138C22×C22⋊D11D412yes—
139#67040—42no—
140#67040—42no—
141C2×#4343—21no—
142C2×#4343C2312yes—
143C2×Q8×D11—21no—
144C2×Q8×D11C2312yes—
145C2×#4339—21no—
146C2×#4339—21no—
147C2×#4339—22no—
148C2×#4339—42no—
149C2×#4339—42no—
150C2×#4339—42no—
151C2×#4339—42no—
152C2×#4339D411yescharacteristic
153C2×#4339D411yescharacteristic
154C2×#4339D412yes—
155C2×#4339C2311yescharacteristic
156C2×#4339C2311yescharacteristic
157C2×#4339C2312yes—
158C2×#4339C2311yescharacteristic
159C2×#4339C2312yes—
160C2×#4339C2312yes—
161C22×D44D411yescharacteristic
162C22×D44C2311yescharacteristic
163C22×C4×D11—21no—
164C22×C4×D11C2312yes—
165C22×Dic22D411yescharacteristic
166C22×Dic22C2311yescharacteristic
167C2×C11×M16C2311yescharacteristic
168C2×C11×M16C2311yescharacteristic
169C11×C22⋊Q8—21no—
170C11×C22⋊Q8—21no—
171C11×C22⋊Q8C2312yes—
172C11×C22⋊Q8C2312yes—
173C11×#117—21no—
174C11×#117—21no—
175C11×#117C2311yescharacteristic
176C11×#117C2311yescharacteristic
177C11×#117C2311yescharacteristic
178C11×#117C2311yescharacteristic
179C2×C11×C4⋊C4—21no—
180C2×C11×C4⋊C4C2311yescharacteristic
181C2×C11×C4⋊C4C2311yescharacteristic
182C2×C11×C4⋊C4C2311yescharacteristic
183C2×C11×C22⋊C4—21no—
184C2×C11×C22⋊C4—21no—
185C2×C42×C11—21no—
186#67006—21no—
187#67000—21no—
188#66999C2312yes—
189#66999C2312yes—
190#66997—21no—
191C2×#4326—42no—
192C2×#4326C2312yes—
193C2×#4326C2312yes—
194C2×#4325—42no—
195C2×#4325C2312yes—
196C2×#4325C2312yes—
197#66983—22no—
198#66983—22no—
199#66983—22no—
200#66983—22no—
201#66983—22no—
202#66983C2311yescharacteristic
203#66983C2311yescharacteristic
204#66982—21no—
205#66982—22no—
206C4×C22⋊D11—21no—
207C4×C22⋊D11—21no—
208C4×C22⋊D11—22no—
209#66979C2311yescharacteristic
210#66977C2311yescharacteristic
211#66977C2311yescharacteristic
212C22×C11⋊C8C2311yescharacteristic
213C22×C11⋊C8C2311yescharacteristic
214#66962—42no—
215#66961—42no—
216#66960—42no—
217#66960—42no—
218C2×Dic44C2312yes—
219C2×D88C2312yes—
220C2×#4314C2312yes—
221C2×#4314C2312yes—
222C2×#4313C2312yes—
223C2×#4313C2312yes—
224C2×C8×D11C2312yes—
225C2×C8×D11C2312yes—
226#66950—22no—
227#66950—22no—
228#66950—21no—
229#66950C2312yes—
230#66950C2312yes—
231#66950C2312yes—
232#66950C2312yes—
233#66950C2312yes—
234#66949—22no—
235#66949—22no—
236#66948—22no—
237#66948—22no—
238#66948—22no—
239#66948—21no—
240#66948C2312yes—
241#66948C2312yes—
242#66948C2312yes—
243#66948C2312yes—
244#66948C2312yes—
245#66947—22no—
246#66947—22no—
247#66946—21no—
248#66946—22no—
249#66945C2312yes—
250C4⋊C4×D11—22no—
251C4⋊C4×D11C2312yes—
252#66941—22no—
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×#103C2312yes—
287C11×#103C2312yes—
288C11×#103C2312yes—
289C11×#103C2312yes—
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#66873C2312yes—
313#66873C2311yescharacteristic
314#66873C2311yescharacteristic
315#66873C2311yescharacteristic
316#66872C2311yescharacteristic
317#66872C2311yescharacteristic
318#66872C2311yescharacteristic
319#66872C2311yescharacteristic
320#66871C2311yescharacteristic
321#66871C2311yescharacteristic
322#66871C2311yescharacteristic
323#66871C2311yescharacteristic
324#60761—111nomaximal, Sylow
325C24×C11C2×D411yescharacteristic
326C23×D11—21no—
327C23×D11C2×D412yes—
328C2×Q8×C11—21no—
329C2×Q8×C11—22no—
330C2×Q8×C11—22no—
331C2×Q8×C11C2412yes—
332C22×C4×C11—22no—
333C22×C4×C11—22no—
334C22×C4×C11—21no—
335C22×C4×C11—21no—
336C22×C4×C11—21no—
337C22×C4×C11—21no—
338C22×C4×C11C2×D411yescharacteristic
339C22×C4×C11C2×D411yescharacteristic
340C22×C4×C11C2×D411yescharacteristic
341C22×C4×C11C2411yescharacteristic
342C22×C4×C11C2411yescharacteristic
343C22×C4×C11C2411yescharacteristic
344C2×C22⋊D11—21no—
345C2×C22⋊D11—22no—
346C2×C22⋊D11—21no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—21no—
349C2×C22⋊D11—44no—
350C2×C22⋊D11—44no—
351C2×C22⋊D11C2×D412yes—
352C2×C22⋊D11C2×D412yes—
353C2×C22⋊D11C2×D412yes—
354C2×C22⋊D11C2×D412yes—
355C22×Dic11—21no—
356C22×Dic11C2×D412yes—
357#4343—42no—
358#4343—42no—
359#4343—44no—
360Q8×D11—42no—
361Q8×D11—42no—
362Q8×D11—44no—
363#4339—22no—
364#4339—22no—
365#4339—22no—
366#4339—22no—
367#4339—22no—
368#4339—22no—
369#4339—42no—
370#4339—42no—
371#4339—42no—
372#4339—42no—
373#4339—42no—
374#4339—42no—
375#4339—42no—
376#4339—42no—
377#4339—44no—
378#4339—44no—
379#4339—44no—
380#4339—48no—
381C2×D44—22no—
382C2×D44—22no—
383C2×D44—22no—
384C2×D44—22no—
385C2×D44—22no—
386C2×D44—22no—
387C2×D44—21no—
388C2×D44—22no—
389C2×D44—22no—
390C2×D44—42no—
391C2×D44C2×D411yescharacteristic
392C2×D44C2×D411yescharacteristic
393C2×D44C2×D412yes—
394C2×D44C2411yescharacteristic
395C2×D44C2412yes—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—22no—
399C2×C4×D11—22no—
400C2×C4×D11—22no—
401C2×C4×D11—21no—
402C2×C4×D11—42no—
403C2×C4×D11—42no—
404C2×C4×D11—44no—
405C2×C4×D11C2×D412yes—
406C2×C4×D11C2×D412yes—
407C2×C4×D11C2412yes—
408C2×C4×D11C2412yes—
409C2×Dic22—22no—
410C2×Dic22—21no—
411C2×Dic22—22no—
412C2×Dic22—22no—
413C2×Dic22—42no—
414C2×Dic22C2×D411yescharacteristic
415C2×Dic22C2×D411yescharacteristic
416C2×Dic22C2×D412yes—
417C2×Dic22C2411yescharacteristic
418C2×Dic22C2412yes—
419C11×M16—22no—
420C11×M16—22no—
421C2×C8×C11C2412yes—
422C2×C8×C11C2412yes—
423C11×C4⋊C4—21no—
424C11×C4⋊C4—22no—
425C11×C4⋊C4—22no—
426C11×C4⋊C4—21no—
427C11×C4⋊C4—21no—
428C11×C4⋊C4C2411yescharacteristic
429C11×C4⋊C4C2411yescharacteristic
430C11×C4⋊C4C2411yescharacteristic
431C11×C4⋊C4C2411yescharacteristic
432C11×C4⋊C4C2412yes—
433C11×C22⋊C4—22no—
434C11×C22⋊C4—21no—
435C11×C22⋊C4—21no—
436C11×C22⋊C4—21no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—22no—
439C42×C11—21no—
440C42×C11—21no—
441C42×C11—21no—
442C42×C11—21no—
443C22⋊Dic11—21no—
444C22⋊Dic11—21no—
445C22⋊Dic11—21no—
446#4326—42no—
447#4326—42no—
448#4325—42no—
449#4325—42no—
450(C2×D11)⋊C4—22no—
451(C2×D11)⋊C4—22no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—22no—
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—21no—
464(C2×D11)⋊C4—21no—
465C4⋊Dic11—22no—
466C4⋊Dic11—22no—
467C4⋊Dic11—22no—
468C4⋊Dic11—22no—
469C4⋊Dic11—22no—
470C4⋊Dic11C2411yescharacteristic
471C4⋊Dic11C2411yescharacteristic
472Dic11⋊C4—22no—
473Dic11⋊C4—22no—
474Dic11⋊C4—22no—
475Dic11⋊C4—21no—
476Dic11⋊C4—21no—
477C4×Dic11—22no—
478C4×Dic11—21no—
479C2×C11⋊C8—22no—
480C2×C11⋊C8—22no—
481C2×C11⋊C8C2411yescharacteristic
482C2×C11⋊C8C2411yescharacteristic
483C2×C11⋊C8C2411yescharacteristic
484C2×C11⋊C8C2411yescharacteristic
485Dic44—42no—
486D88—42no—
487#4314—42no—
488#4314—42no—
489#4313—42no—
490#4313—42no—
491C8×D11—42no—
492C8×D11—42no—
493#3489—111no—
494#3449—111no—
495#3204—112no—
496#3203—112no—
497#3201—112no—
498#3201—112no—
499#3197—112no—
500#3196—112no—
501#3191—112no—
502#3190—112no—
503#3097—111no—
504#3096—111no—
505#3095D1111yescharacteristic, complemented
506#3091—111no—
507#3063—111no—
508#3062—111no—
509#3059—111no—
510#3057—111no—
511#3011—111no—
512#3010—111no—
513#3005—111no—
514C2×#452—111no—
515#2880—111no—
516C23×C11—22no—
517C23×C11—41no—
518C23×C11—41no—
519C23×C11C22×D411yescharacteristic
520C23×C11C22×D411yescharacteristic
521C23×C11C22×D411yescharacteristic
522C22×D11—21no—
523C22×D11—22no—
524C22×D11—42no—
525C22×D11—42no—
526C22×D11—42no—
527C22×D11—42no—
528C22×D11—81no—
529C22×D11—81no—
530C22×D11C22×D412yes—
531C22×D11C22×D412yes—
532Q8×C11—22no—
533Q8×C11—22no—
534Q8×C11—42no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—21no—
541C2×C4×C11—21no—
542C2×C4×C11—22no—
543C2×C4×C11—22no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—42no—
549C2×C4×C11—81no—
550C2×C4×C11—81no—
551C2×C4×C11—81no—
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C22×D411yescharacteristic
554C2×C4×C11C22×D411yescharacteristic
555C2×C4×C11H(5,𝔽2)12yes—
556C2×C4×C11H(5,𝔽2)12yes—
557C2×C4×C11C2511yescharacteristic
558C22⋊D11—24no—
559C22⋊D11—24no—
560C22⋊D11—42no—
561C22⋊D11—42no—
562C22⋊D11—44no—
563C22⋊D11—44no—
564C22⋊D11—42no—
565C22⋊D11—42no—
566C22⋊D11—81no—
567C2×Dic11—21no—
568C2×Dic11—21no—
569C2×Dic11—21no—
570C2×Dic11—22no—
571C2×Dic11—42no—
572C2×Dic11—42no—
573C2×Dic11C22×D412yes—
574C2×Dic11C22×D412yes—
575D44—22no—
576D44—22no—
577D44—21no—
578D44—22no—
579D44—21no—
580D44—22no—
581D44—42no—
582D44—44no—
583D44—42no—
584D44—82no—
585D44—82no—
586D44—82no—
587D44—82no—
588D44—82no—
589C4×D11—22no—
590C4×D11—22no—
591C4×D11—22no—
592C4×D11—22no—
593C4×D11—42no—
594C4×D11—42no—
595C4×D11—44no—
596C4×D11—44no—
597C4×D11—44no—
598C4×D11—44no—
599C4×D11—42no—
600C4×D11—82no—
601Dic22—22no—
602Dic22—22no—
603Dic22—21no—
604Dic22—22no—
605Dic22—21no—
606Dic22—22no—
607Dic22—42no—
608Dic22—44no—
609Dic22—42no—
610C8×C11—22no—
611C8×C11—22no—
612C11⋊C8—21no—
613C11⋊C8—21no—
614C11⋊C8—21no—
615C11⋊C8—21no—
616C2×2−1+4—111no—
617C22×#41—111no—
618C22×#41—111no—
619C2×#137—111no—
620C2×AGL(1,ℤ/8)—111no—
621C22×Q16—111no—
622C22×SD16—111no—
623C2×#131—111no—
624C2×#131—111no—
625D4×Q8—221no—
626#548—221no—
627#547—222no—
628#547—221no—
629#546—222no—
630#546—221no—
631#537—112no—
632#537—112no—
633#537—112no—
634#537—111no—
635#536—111no—
636#536—112no—
637#536—111no—
638#536—111no—
639#536—221no—
640#535—111no—
641#535—111no—
642#535—221no—
643#534—222no—
644#532—221no—
645#532—221no—
646#525—111no—
647#525—112no—
648#525—112no—
649#525—112no—
650#525—222no—
651C2×C22⋊Q8—112no—
652C2×C22⋊Q8C2×D1111yescharacteristic
653#520—111no—
654C2×#117C2×D1111yescharacteristic
655#485—111no—
656#485—111no—
657#485—112no—
658#485—112no—
659#485C2×D1112yescomplemented
660#485C2×D1112yescomplemented
661#484—111no—
662#484—112no—
663#484C2×D1112yescomplemented
664#483—111no—
665#483—112no—
666#483C2×D1112yescomplemented
667#482—111no—
668#482—111no—
669#482—112no—
670#482—112no—
671#481—111no—
672#481—112no—
673#480—111no—
674#480—112no—
675#470—112no—
676#470—112no—
677#470—112no—
678#469—112no—
679#468—112no—
680#468—112no—
681#468—112no—
682#468—112no—
683#467—112no—
684#467—112no—
685#467—112no—
686#466—112no—
687#465—112no—
688#465—112no—
689#465—112no—
690#465—112no—
691#452—112no—
692#452—112no—
693#452—112no—
694#452—112no—
695#452—112no—
696#452—112no—
697#452—112no—
698#452—112no—
699#451—112no—
700#451—112no—
701#449—112no—
702#449—112no—
703#449—112no—
704#449—112no—
705#448—112no—
706#448—112no—
707#428C2×D1111yescharacteristic, complemented
708#428C2×D1111yescharacteristic, complemented
709#427—111no—
710#427—111no—
711#419—111no—
712#419C2×D1111yescharacteristic, complemented
713#419C2×D1111yescharacteristic, complemented
714#418—111no—
715#416—111no—
716#416—111no—
717C2×#103—111no—
718C2×#102—111no—
719#408—111no—
720#408—111no—
721#408—112no—
722#408—112no—
723#407—112no—
724#407C2×D1111yescharacteristic
725C2×C22⋊C8—111no—
726C2×C22⋊C8—112no—
727C22×C11—21no—
728C22×C11—21no—
729C22×C11—21no—
730C22×C11—21no—
731C22×C11—21no—
732C22×C11—21no—
733C22×C11—21no—
734C22×C11—21no—
735C22×C11—82no—
736C22×C11#53412yes—
737C22×C11C23×D411yescharacteristic
738C2×D11—22no—
739C2×D11—22no—
740C2×D11—22no—
741C2×D11—22no—
742C2×D11—22no—
743C2×D11—22no—
744C2×D11—42no—
745C2×D11—41no—
746C2×D11—42no—
747C2×D11—41no—
748C2×D11—42no—
749C2×D11—41no—
750C2×D11—84no—
751C2×D11—84no—
752C4×C11—21no—
753C4×C11—21no—
754C4×C11—42no—
755C4×C11—41no—
756C4×C11—41no—
757C4×C11—41no—
758C4×C11—41no—
759C4×C11—42no—
760C4×C11#53412yes—
761C4×C11C2×H(5,𝔽2)11yescharacteristic
762C4×C11C2×H(5,𝔽2)11yescharacteristic
763Dic11—22no—
764Dic11—22no—
765Dic11—41no—
766Dic11—41no—
767Dic11—41no—
768Dic11—42no—
7692−1+4—442no—
7702−1+4—442no—
771C2×#41—112no—
772C2×#41—111no—
773C2×#41—111no—
774C2×#41—111no—
775C2×#41—111no—
776C2×#41—112no—
777C2×#41—112no—
778C2×#41—111no—
779C2×#41—112no—
780C2×#41—112no—
781C2×#41—222no—
782C2×#41—221no—
783C2×#41—221no—
784C2×#41—221no—
785C2×#41—442no—
786C2×#41—442no—
787C2×#41—442no—
788C2×#41—442no—
789C22×Q8—111no—
790C22×Q8—112no—
791C22×Q8—111no—
792C22×Q8—221no—
793C22×Q8C22×D1111yescharacteristic
794C22×D4—112no—
795C22×D4—111no—
796C22×D4—111no—
797C22×D4—221no—
798C23×C4—112no—
799C23×C4—221no—
800C23×C4C22×D1111yescharacteristic
801#137—442no—
802AGL(1,ℤ/8)—442no—
803C2×Q16—112no—
804C2×Q16—112no—
805C2×Q16—112no—
806C2×Q16—442no—
807C2×SD16—112no—
808C2×SD16—112no—
809C2×SD16—112no—
810C2×SD16—112no—
811C2×SD16—442no—
812C2×D8—112no—
813#131—442no—
814#131—442no—
815C2×M16—112no—
816C2×M16—112no—
817C2×M16C22×D1111yescharacteristic
818C2×M16C22×D1111yescharacteristic
819C22×C8—111no—
820C22×C8—111no—
821C22×C8—112no—
822C22×C8—112no—
823C4⋊Q8—221no—
824C4⋊Q8—221no—
825C4⋊Q8—222no—
826C4⋊Q8—221no—
827#127—221no—
828#127—221no—
829#124—221no—
830#124—221no—
831#124—221no—
832#124—221no—
833#124—222no—
834#124—221no—
835#123—222no—
836#123—222no—
837#123—222no—
838#123—222no—
839#123—222no—
840#123—222no—
841#123—222no—
842#123—222no—
843#123—221no—
844C22⋊Q8—21no—
845C22⋊Q8—21no—
846C22⋊Q8—112no—
847C22⋊Q8—112no—
848C22⋊Q8—111no—
849C22⋊Q8—111no—
850C22⋊Q8—112no—
851C22⋊Q8—112no—
852C22⋊Q8—112no—
853C22⋊Q8—112no—
854C22⋊Q8—112no—
855C22⋊Q8—222no—
856C22⋊Q8—222no—
857C22⋊Q8—222no—
858C22⋊Q8—222no—
859C22⋊Q8—222no—
860C22⋊Q8—221no—
861C22⋊Q8C22×D1112yes—
862C22⋊Q8C22×D1112yes—
863#121—111no—
864#121—111no—
865#121—112no—
866#121—112no—
867#121—112no—
868#121—112no—
869#121—112no—
870#121—222no—
871#121—222no—
872#121—222no—
873#121—222no—
874#121—222no—
875#121—221no—
876#121—222no—
877#121—222no—
878#121—222no—
879#121—222no—
880#121—222no—
881#120—222no—
882#120—222no—
883#120—222no—
884#120—222no—
885#120—222no—
886#120—221no—
887C4×Q8—221no—
888C4×D4—222no—
889C4×D4—222no—
890C4×D4—222no—
891C4×D4—222no—
892C4×D4—222no—
893C4×D4—222no—
894C4×D4—221no—
895C4×D4—222no—
896C4×D4—221no—
897C4×D4—221no—
898#117—21no—
899#117—21no—
900#117—111no—
901#117—112no—
902#117C22×D1111yescharacteristic
903#117C22×D1111yescharacteristic
904#117C22×D1111yescharacteristic
905#117C22×D1111yescharacteristic
906C2×C4⋊C4—21no—
907C2×C4⋊C4—112no—
908C2×C4⋊C4—222no—
909C2×C4⋊C4C22×D1111yescharacteristic
910C2×C4⋊C4C22×D1111yescharacteristic
911C2×C4⋊C4C22×D1111yescharacteristic
912C2×C22⋊C4—21no—
913C2×C22⋊C4—21no—
914C2×C22⋊C4—222no—
915C2×C42—21no—
916#107—111no—
917#107—111no—
918#107—111no—
919#107—111no—
920#107C22×D1112yes—
921#107C22×D1112yes—
922#106—111no—
923#106—111no—
924#106—111no—
925#106—111no—
926#106C22×D1112yes—
927#106C22×D1112yes—
928#103—112no—
929#103—112no—
930#103—112no—
931#103—112no—
932#103—111no—
933#103—111no—
934#103—111no—
935#103—111no—
936#103C22×D1112yes—
937#103C22×D1112yes—
938#103C22×D1112yes—
939#103C22×D1112yes—
940#102—112no—
941#102—112no—
942#102—112no—
943#102—112no—
944#102—111no—
945#102—111no—
946#102—111no—
947#102—111no—
948C22⋊C8—111no—
949C22⋊C8—111no—
950C22⋊C8—111no—
951C22⋊C8—111no—
952C22⋊C8—112no—
953C22⋊C8—112no—
954C22⋊C8—112no—
955C22⋊C8—112no—
956C22⋊C8C22×D1112yes—
957C22⋊C8C22×D1112yes—
958C2×C11—22no—
959C2×C11—41no—
960C2×C11—41no—
961C2×C11C2×#53411yescharacteristic
962C2×C11#358411yescharacteristic
963C2×C11#358611yescharacteristic
964D11—42no—
965D11—42no—
966D11—81no—
967D11—82no—
968C24—112no—
969C24—221no—
970C24D4×D1111yescharacteristic
971#41—222no—
972#41—222no—
973#41—222no—
974#41—222no—
975#41—222no—
976#41—222no—
977#41—442no—
978#41—442no—
979#41—444no—
980#41—442no—
981#41—442no—
982#41—442no—
983#41—442no—
984#41—442no—
985#41—442no—
986#41—444no—
987#41—444no—
988#41—448no—
989#41—442no—
990#41—442no—
991#41—444no—
992C2×Q8—21no—
993C2×Q8—22no—
994C2×Q8—22no—
995C2×Q8—111no—
996C2×Q8—111no—
997C2×Q8—112no—
998C2×Q8—111no—
999C2×Q8—112no—
1000C2×Q8—222no—
1001C2×Q8—221no—
1002C2×Q8—222no—
1003C2×Q8—222no—
1004C2×Q8—442no—
1005C2×Q8—442no—
1006C2×Q8—442no—
1007C2×Q8—444no—
1008C2×Q8C23×D1112yes—
1009C2×D4—112no—
1010C2×D4—112no—
1011C2×D4—112no—
1012C2×D4—112no—
1013C2×D4—111no—
1014C2×D4—111no—
1015C2×D4—112no—
1016C2×D4—111no—
1017C2×D4—112no—
1018C2×D4—222no—
1019C2×D4—222no—
1020C2×D4—222no—
1021C2×D4—222no—
1022C2×D4—222no—
1023C2×D4—222no—
1024C2×D4—221no—
1025C2×D4—222no—
1026C2×D4—221no—
1027C2×D4—222no—
1028C2×D4—221no—
1029C2×D4—221no—
1030C2×D4—222no—
1031C2×D4—222no—
1032C2×D4—442no—
1033C2×D4—444no—
1034C2×D4—444no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—21no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—21no—
1041C22×C4—112no—
1042C22×C4—112no—
1043C22×C4—112no—
1044C22×C4—112no—
1045C22×C4—112no—
1046C22×C4—222no—
1047C22×C4—222no—
1048C22×C4—222no—
1049C22×C4—221no—
1050C22×C4—222no—
1051C22×C4—221no—
1052C22×C4—222no—
1053C22×C4—442no—
1054C22×C4—442no—
1055C22×C4—444no—
1056C22×C4D4×D1111yescharacteristic
1057C22×C4D4×D1111yescharacteristic
1058C22×C4D4×D1111yescharacteristic
1059C22×C4C23×D1111yescharacteristic
1060C22×C4C23×D1111yescharacteristic
1061C22×C4C23×D1111yescharacteristic
1062Q16—442no—
1063Q16—442no—
1064Q16—442no—
1065SD16—442no—
1066SD16—442no—
1067SD16—442no—
1068SD16—442no—
1069D8—442no—
1070M16—22no—
1071M16—22no—
1072M16—442no—
1073M16—442no—
1074C2×C8—111no—
1075C2×C8—111no—
1076C2×C8—111no—
1077C2×C8—111no—
1078C2×C8—222no—
1079C2×C8—222no—
1080C2×C8—442no—
1081C2×C8—442no—
1082C2×C8C23×D1112yes—
1083C2×C8C23×D1112yes—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—21no—
1087C4⋊C4—21no—
1088C4⋊C4—21no—
1089C4⋊C4—111no—
1090C4⋊C4—111no—
1091C4⋊C4—222no—
1092C4⋊C4—222no—
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⋊C4C23×D1112yes—
1102C4⋊C4C23×D1111yescharacteristic
1103C4⋊C4C23×D1111yescharacteristic
1104C4⋊C4C23×D1111yescharacteristic
1105C4⋊C4C23×D1111yescharacteristic
1106C22⋊C4—22no—
1107C22⋊C4—21no—
1108C22⋊C4—21no—
1109C22⋊C4—21no—
1110C22⋊C4—21no—
1111C22⋊C4—22no—
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—222no—
1121C22⋊C4—222no—
1122C22⋊C4—222no—
1123C22⋊C4—222no—
1124C22⋊C4—222no—
1125C22⋊C4—221no—
1126C22⋊C4—221no—
1127C22⋊C4—221no—
1128C22⋊C4—221no—
1129C22⋊C4—221no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—222no—
1135C42—221no—
1136C11#6076111yescharacteristic, complemented, Sylow
1137C23—22no—
1138C23—41no—
1139C23—41no—
1140C23—112no—
1141C23—112no—
1142C23—221no—
1143C23—222no—
1144C23—442no—
1145C23—442no—
1146C23—442no—
1147C23—442no—
1148C23—881no—
1149C23—881no—
1150C23C2×D4×D1111yescharacteristic
1151C23C2×D4×D1111yescharacteristic
1152C23C2×D4×D1111yescharacteristic
1153Q8—22no—
1154Q8—22no—
1155Q8—42no—
1156Q8—222no—
1157Q8—222no—
1158Q8—221no—
1159Q8—222no—
1160Q8—222no—
1161Q8—221no—
1162Q8—442no—
1163Q8—444no—
1164Q8—442no—
1165D4—224no—
1166D4—224no—
1167D4—222no—
1168D4—222no—
1169D4—221no—
1170D4—222no—
1171D4—222no—
1172D4—221no—
1173D4—442no—
1174D4—444no—
1175D4—442no—
1176D4—442no—
1177D4—444no—
1178D4—444no—
1179D4—442no—
1180D4—442no—
1181D4—442no—
1182D4—882no—
1183D4—882no—
1184D4—882no—
1185D4—882no—
1186D4—882no—
1187D4—881no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—42no—
1202C2×C4—81no—
1203C2×C4—81no—
1204C2×C4—81no—
1205C2×C4—112no—
1206C2×C4—112no—
1207C2×C4—222no—
1208C2×C4—222no—
1209C2×C4—222no—
1210C2×C4—222no—
1211C2×C4—221no—
1212C2×C4—221no—
1213C2×C4—222no—
1214C2×C4—221no—
1215C2×C4—442no—
1216C2×C4—442no—
1217C2×C4—444no—
1218C2×C4—444no—
1219C2×C4—444no—
1220C2×C4—444no—
1221C2×C4—442no—
1222C2×C4—442no—
1223C2×C4—442no—
1224C2×C4—882no—
1225C2×C4C2×D4×D1111yescharacteristic
1226C2×C4C2×D4×D1111yescharacteristic
1227C2×C4C2×D4×D1111yescharacteristic
1228C2×C4#6704212yes—
1229C2×C4#6704212yes—
1230C2×C4C24×D1111yescharacteristic
1231C8—22no—
1232C8—22no—
1233C8—221no—
1234C8—221no—
1235C8—221no—
1236C8—221no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—82no—
1246C22—222no—
1247C22—222no—
1248C22—222no—
1249C22—222no—
1250C22—222no—
1251C22—222no—
1252C22—441no—
1253C22—442no—
1254C22—441no—
1255C22—442no—
1256C22—441no—
1257C22—442no—
1258C22—884no—
1259C22—884no—
1260C22#1062318412yes—
1261C22C22×D4×D1111yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—41no—
1265C4—41no—
1266C4—42no—
1267C4—42no—
1268C4—41no—
1269C4—41no—
1270C4—222no—
1271C4—222no—
1272C4—441no—
1273C4—442no—
1274C4—441no—
1275C4—441no—
1276C4#1062318412yes—
1277C4C2×#6704211yescharacteristic
1278C4C2×#6704211yescharacteristic
1279C2—22no—
1280C2—41no—
1281C2—41no—
1282C2—442no—
1283C2—442no—
1284C2—882no—
1285C2—881no—
1286C2C2×#1062318411yescharacteristic
1287C2#1308338911yescharacteristic
1288C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3095C2
socleC22×C11C23×D4
hypercenter#3095D11
hypocenterC11#60761
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
1. #13082292C2semidirect
2. #13081949C2semidirect
3. #13079526C2semidirect
4. #13079520C2semidirect
5. #13079505C2semidirect
6. #13079503C2semidirect
7. #13079460C2semidirect
8. #13079450C2semidirect
9. #13079411C2semidirect
10. #13079401C2semidirect
11. #13078587C2semidirect
12. #13078576C2semidirect
13. #13078529C2semidirect
14. #13078308C2semidirect
15. #13078297C2semidirect
16. #13078270C2semidirect
17. #13078258C2semidirect
18. #13077912C2semidirect
19. #13077903C2semidirect
20. #13077861C2semidirect
21. C2×#10622660C2semidirect
22. #13077066C2semidirect
23. C11×#3095C2semidirect
30. C22×#4326C22semidirect
31. C22×#4325C22semidirect
33. C2×#66962C22semidirect
34. C2×#66961C22semidirect
41. #10623160C22semidirect
42. #10623159C22semidirect
43. #10623158C22semidirect
44. D11×C22⋊Q8C22semidirect
63. C11×#485C22semidirect
64. C11×#485C22semidirect
65. C11×#484C22semidirect
66. C11×#483C22semidirect
67. C11×#428C22semidirect
68. C11×#428C22semidirect
69. C11×#419C22semidirect
70. C11×#419C22semidirect
73. #10622744C22semidirect
76. #10622733C22semidirect
79. #10622660C22semidirect
80. #10622660C22semidirect
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. #10622429C22semidirect
112. #10622429C22semidirect
113. #10622426C22semidirect
114. #10622426C22semidirect
115. #10622425C22semidirect
116. #10622425C22semidirect
117. #10622424C22semidirect
118. #10622424C22semidirect
119. #10622423C22semidirect
120. #10622423C22semidirect
121. #10622421C22semidirect
122. #10622421C22semidirect
123. #10622420C22semidirect
124. #10622420C22semidirect
125. #10622419C22semidirect
126. #10622419C22semidirect
128. #10622347C22semidirect
130. #10622346C22semidirect
131. #10622340C22semidirect
132. #10622340C22semidirect
133. #10622339C22semidirect
134. D11×C22⋊C8C22semidirect
505. #3095D11semidirect
659. #485C2×D11semidirect
660. #485C2×D11semidirect
663. #484C2×D11semidirect
666. #483C2×D11semidirect
707. #428C2×D11semidirect
708. #428C2×D11semidirect
712. #419C2×D11semidirect
713. #419C2×D11semidirect
1136. C11#60761semidirect

Maximal subgroups

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

subgroupindex
#130822922
#130819492
#130795262
#130795202
#130795052
#130795032
#130794602
#130794502
#130794112
#130794012
#130785872
#130785762
#130785292
#130783082
#130782972
#130782702
#130782582
#130779122
#130779032
#130778612
C2×#106226602
#130770662
C11×#30952
#6076111