Finite Group Databasebeta

← #15622681

Subgroups — #15622681

Order 2816.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082351C211yesmaximal, characteristic, complemented
2#13078907C212yesmaximal, complemented
3#13078859C212yesmaximal, complemented
4#13078845C212yesmaximal, complemented
5#13078800C212yesmaximal, complemented
6#13078767C212yesmaximal, complemented
7#13078725C212yesmaximal, complemented
8#13078676C212yesmaximal, complemented
9#13078634C212yesmaximal, complemented
10#13078547C211yesmaximal, characteristic, complemented
11C2×#10622616C211yesmaximal, characteristic, complemented
12#13078478C211yesmaximal, characteristic, complemented
13#13078467C211yesmaximal, characteristic, complemented
14#13078155C211yesmaximal, characteristic, complemented
15#13078155C211yesmaximal, characteristic, complemented
16#13077868C211yesmaximal, characteristic, complemented
17#13077834C211yesmaximal, characteristic, complemented
18#13077497C211yesmaximal, characteristic, complemented
19#13077489C211yesmaximal, characteristic, complemented
20#13077444C211yesmaximal, characteristic, complemented
21#13077444C211yesmaximal, characteristic, complemented
22#13077274C211yesmaximal, characteristic, complemented
23C11×#3428C211yesmaximal, characteristic, complemented
24C22×C11×#41C2211yescharacteristic
25C11×#520—21no—
26C11×#520—21no—
27C11×#520C2211yescharacteristic
28C11×#520C2211yescharacteristic
29C11×#520C2211yescharacteristic
30C11×#520C2211yescharacteristic
31C11×#519C2212yescomplemented
32C11×#518—22no—
33C11×#518C2212yescomplemented
34C4×C11×#41—22no—
35C4×C11×#41C2212yescomplemented
36C4×C11×#41C2212yescomplemented
37C2×C11×#117—21no—
38C2×C11×#117—21no—
39C2×C11×#117C2211yescharacteristic
40C2×C11×#117C2211yescharacteristic
41C2×#67003C2211yescharacteristic
42C2×#67003C2211yescharacteristic
43C2×#67002C2211yescharacteristic
44C2×#67002C2211yescharacteristic
45#10623322C2211yescharacteristic
46C2×#66983C2211yescharacteristic
47#10623066C2212yes—
48#10623065C2212yes—
49#10623063—21no—
50#10623061—21no—
51#10623058—22no—
52#10623056C2211yescharacteristic, complemented
53#10623054C2211yescharacteristic, complemented
54#10623052C2211yescharacteristic, complemented
55#10623050C2211yescharacteristic, complemented
56#10623045—21no—
57#10623038—21no—
58#10623021—22no—
59#10623010C2212yescomplemented
60#10623008C2212yescomplemented
61#10622852C2211yescharacteristic, complemented
62#10622852C2211yescharacteristic, complemented
63#10622851C2212yes—
64#10622851C2212yes—
65#10622851C2211yescharacteristic, complemented
66#10622851C2211yescharacteristic, complemented
67#10622846C2211yescharacteristic
68#10622846C2211yescharacteristic
69#10622845C2211yescharacteristic
70#10622845C2211yescharacteristic
71#10622841C2211yescharacteristic, complemented
72#10622840C2212yes—
73#10622840C2211yescharacteristic, complemented
74#10622831C2211yescharacteristic, complemented
75#10622830C2212yes—
76#10622830C2211yescharacteristic, complemented
77#10622820C2211yescharacteristic
78C2×C22⋊(C11⋊C8)C2211yescharacteristic
79#10622643C2212yescomplemented
80C4×#4326C2212yescomplemented
81#10622641C2212yescomplemented
82#10622641C2212yescomplemented
83#10622640C2212yescomplemented
84#10622640C2212yescomplemented
85#10622639C2212yescomplemented
86#10622639C2212yescomplemented
87#10622639C2212yescomplemented
88C4×#4325C2212yescomplemented
89C4×#4325C2212yescomplemented
90C4×#4325C2212yescomplemented
91#10622635C2212yescomplemented
92#10622635C2212yescomplemented
93#10622634C2212yescomplemented
94#10622633C2212yescomplemented
95#10622631C2212yescomplemented
96C4×#4324C2212yescomplemented
97#10622629C2212yescomplemented
98#10622629C2212yescomplemented
99#10622628C2212yescomplemented
100#10622628C2212yescomplemented
101#10622627C2212yescomplemented
102#10622627C2212yescomplemented
103#10622627C2212yescomplemented
104C4×#4323C2212yescomplemented
105C4×#4323C2212yescomplemented
106C4×#4323C2212yescomplemented
107#10622622C2212yescomplemented
108#10622622C2212yescomplemented
109#10622621C2212yescomplemented
110#10622620C2212yescomplemented
111#10622616C2212yes—
112#10622616C2212yes—
113#10622616C2212yescomplemented
114#10622616C2212yescomplemented
115#10622616C2212yescomplemented
116#10622616C2212yescomplemented
117#10622613C2212yescomplemented
118#10622613C2212yescomplemented
119#10622612C2211yescharacteristic, complemented
120#10622612C2211yescharacteristic, complemented
121#10622610C2211yescharacteristic, complemented
122#10622610C2211yescharacteristic, complemented
123#10622609C2212yescomplemented
124#10622609C2212yescomplemented
125#10622579C2211yescharacteristic, complemented
126#10622579C2211yescharacteristic, complemented
127C2×#66873C2211yescharacteristic, complemented
128C2×#66873C2211yescharacteristic, complemented
129#10622577C2211yescharacteristic, complemented
130#10622577C2211yescharacteristic, complemented
131C2×#66872C2211yescharacteristic, complemented
132C2×#66871C2211yescharacteristic, complemented
133#10622539C2212yescomplemented
134#10622538C2212yescomplemented
135C2×C11×#41—24no—
136C2×C11×#41—24no—
137C2×C11×#41—21no—
138C2×C11×#41—21no—
139C2×C11×#41C2311yescharacteristic
140C2×C11×#41C2311yescharacteristic
141C2×C11×#41C2311yescharacteristic
142C2×C11×#41C2311yescharacteristic
143C22×Q8×C11C2311yescharacteristic
144C22×D4×C11—21no—
145C22×D4×C11C2311yescharacteristic
146C23×C4×C11—21no—
147C23×C4×C11C2311yescharacteristic
148C22×C22⋊D11—21no—
149C2×#4339—22no—
150C2×#4339C2311yescharacteristic
151C22×D44C2311yescharacteristic
152C4×Q8×C11—22no—
153C4×Q8×C11—22no—
154C4×Q8×C11C2312yes—
155C4×Q8×C11C2312yes—
156C4×Q8×C11C2312yes—
157C4×Q8×C11C2312yes—
158C4×D4×C11—22no—
159C4×D4×C11—22no—
160C4×D4×C11—22no—
161C4×D4×C11—22no—
162C4×D4×C11—22no—
163C4×D4×C11—22no—
164C4×D4×C11—22no—
165C4×D4×C11—22no—
166C4×D4×C11—22no—
167C4×D4×C11—22no—
168C4×D4×C11C2312yes—
169C4×D4×C11C2312yes—
170C4×D4×C11C2312yes—
171C4×D4×C11C2312yes—
172C11×#117—21no—
173C11×#117—21no—
174C11×#117—21no—
175C11×#117—21no—
176C11×#117—21no—
177C11×#117—21no—
178C11×#117—22no—
179C11×#117—22no—
180C11×#117—22no—
181C11×#117—22no—
182C11×#117D412yes—
183C11×#117D411yescharacteristic
184C11×#117D411yescharacteristic
185C11×#117C2312yes—
186C11×#117C2312yes—
187C11×#117C2311yescharacteristic
188C11×#117C2311yescharacteristic
189C11×#117C2312yes—
190C2×C11×C4⋊C4—21no—
191C2×C11×C4⋊C4—21no—
192C2×C11×C4⋊C4—21no—
193C2×C11×C4⋊C4—21no—
194C2×C11×C4⋊C4D411yescharacteristic
195C2×C11×C4⋊C4D411yescharacteristic
196C2×C11×C4⋊C4C2311yescharacteristic
197C2×C11×C4⋊C4C2311yescharacteristic
198C2×C11×C22⋊C4—21no—
199C2×C11×C22⋊C4—22no—
200C2×C11×C22⋊C4—22no—
201C2×C11×C22⋊C4D412yes—
202C2×C42×C11—21no—
203C2×C42×C11—22no—
204C2×C42×C11—22no—
205C2×C42×C11C2312yes—
206#67006—21no—
207#67003—24no—
208#67003—24no—
209#67002—24no—
210#67002—24no—
211C2×#4326C2311yescharacteristic
212C2×#4326C2311yescharacteristic
213C2×#4325C2312yes—
214C2×#4325C2312yes—
215C2×#4325C2311yescharacteristic
216C2×#4325C2311yescharacteristic
217C2×#4324C2311yescharacteristic
218C2×#4324C2311yescharacteristic
219C2×#4323C2312yes—
220C2×#4323C2312yes—
221C2×#4323C2311yescharacteristic
222C2×#4323C2311yescharacteristic
223#66983—22no—
224#66983—21no—
225#66983—21no—
226#66983C2311yescharacteristic
227#66983C2312yes—
228#66983C2312yes—
229#66983C2311yescharacteristic
230#66982—22no—
231#66982—21no—
232C4×C22⋊D11—22no—
233C4×C22⋊D11—21no—
234C4×C22⋊D11—21no—
235C2×(C2×D11)⋊C4—21no—
236#66979C2311yescharacteristic
237C2×C4⋊Dic11C2311yescharacteristic
238#66977C2311yescharacteristic
239#66977C2311yescharacteristic
240C2×#4318C2311yescharacteristic
241C2×#4318C2311yescharacteristic
242C22×C11⋊C8C2311yescharacteristic
243C22×C11⋊C8C2311yescharacteristic
244#66951—22no—
245#66949—22no—
246#66948—21no—
247#66948—21no—
248#66947—22no—
249#66947—22no—
250#66946—21no—
251#66946—21no—
252#66945—21no—
253C4⋊C4×D11—21no—
254#66943—21no—
255#66941—21no—
256#66938—22no—
257#66937—22no—
258#66937—22no—
259#66936—22no—
260#66935—22no—
261(C22⋊D11)⋊C4—22no—
262C22⋊C4×D11—22no—
263#66931—22no—
264#66929—22no—
265#66928—22no—
266#66928C2312yes—
267#66927C2312yes—
268C4×D44—22no—
269C4×D44C2312yes—
270C4×D44C2312yes—
271C4×D44C2312yes—
272#66925—22no—
273#66923C2312yes—
274#66922C2312yes—
275C4×Dic22C2312yes—
276#66899C2312yes—
277#66899C2312yes—
278#66899C2311yescharacteristic
279#66899C2311yescharacteristic
280#66899C2311yescharacteristic
281#66899C2311yescharacteristic
282#66896C2312yes—
283#66896C2312yes—
284#66896C2311yescharacteristic
285#66896C2311yescharacteristic
286#66896C2311yescharacteristic
287#66896C2311yescharacteristic
288C22⋊(C11⋊C8)C2311yescharacteristic
289C22⋊(C11⋊C8)C2312yes—
290C22⋊(C11⋊C8)C2311yescharacteristic
291C22⋊(C11⋊C8)C2311yescharacteristic
292C22⋊(C11⋊C8)C2311yescharacteristic
293C22⋊(C11⋊C8)C2312yes—
294#66874C2312yes—
295#66874C2312yes—
296#66873C2312yes—
297#66873C2312yes—
298#66873C2312yes—
299#66873C2312yes—
300#66873C2312yes—
301#66873C2312yes—
302#66872C2312yes—
303#66872C2312yes—
304#66872C2312yes—
305#66872C2312yes—
306#66871C2312yes—
307#66871C2312yes—
308#66871C2312yes—
309#66871C2312yes—
310C4⋊(C11⋊C8)C2312yes—
311C4⋊(C11⋊C8)C2312yes—
312C4⋊(C11⋊C8)C2312yes—
313C4⋊(C11⋊C8)C2312yes—
314#66867C2312yes—
315#66867C2312yes—
316C4×C11⋊C8C2312yes—
317C4×C11⋊C8C2312yes—
318#60587—111nomaximal, Sylow
319C24×C11—21no—
320C24×C11C2×D411yescharacteristic
321C23×D11—21no—
322C11×#41—28no—
323C11×#41—28no—
324C11×#41—22no—
325C11×#41—22no—
326C11×#41—22no—
327C11×#41—22no—
328C11×#41—22no—
329C11×#41—22no—
330C11×#41#4114yescomplemented
331C11×#41#4114yescomplemented
332C2×Q8×C11—22no—
333C2×Q8×C11—22no—
334C2×Q8×C11—21no—
335C2×Q8×C11C2411yescharacteristic
336C2×Q8×C11C2411yescharacteristic
337C2×D4×C11—28no—
338C2×D4×C11—21no—
339C2×D4×C11—21no—
340C2×D4×C11—21no—
341C2×D4×C11—21no—
342C2×D4×C11—22no—
343C2×D4×C11—22no—
344C2×D4×C11—21no—
345C2×D4×C11C2411yescharacteristic
346C2×D4×C11C2411yescharacteristic
347C22×C4×C11—28no—
348C22×C4×C11—21no—
349C22×C4×C11—21no—
350C22×C4×C11—21no—
351C22×C4×C11—21no—
352C22×C4×C11—21no—
353C22×C4×C11—22no—
354C22×C4×C11—22no—
355C22×C4×C11—21no—
356C22×C4×C11—21no—
357C22×C4×C11—22no—
358C22×C4×C11—22no—
359C22×C4×C11—22no—
360C22×C4×C11—22no—
361C22×C4×C11C2×D411yescharacteristic
362C22×C4×C11C2×D411yescharacteristic
363C22×C4×C11C2×D411yescharacteristic
364C22×C4×C11C2×D412yes—
365C22×C4×C11C2×D412yes—
366C22×C4×C11C2411yescharacteristic
367C22×C4×C11C2411yescharacteristic
368C22×C4×C11C2411yescharacteristic
369C2×C22⋊D11—21no—
370C2×C22⋊D11—22no—
371C2×C22⋊D11—21no—
372C2×C22⋊D11—22no—
373C2×C22⋊D11—21no—
374C2×C22⋊D11—82no—
375C22×Dic11—21no—
376#4339—22no—
377#4339—22no—
378#4339—84no—
379C2×D44—21no—
380C2×D44—22no—
381C2×D44—22no—
382C2×D44—22no—
383C2×D44—22no—
384C2×D44C2411yescharacteristic
385C2×D44C2412yes—
386C2×C4×D11—21no—
387C2×C4×D11—22no—
388C2×C4×D11—22no—
389C2×C4×D11—22no—
390C2×Dic22—22no—
391C2×Dic22C2411yescharacteristic
392C11×C4⋊C4—21no—
393C11×C4⋊C4—21no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—22no—
397C11×C4⋊C4—22no—
398C11×C4⋊C4C2×D411yescharacteristic
399C11×C4⋊C4C2×D411yescharacteristic
400C11×C4⋊C4C2×D411yescharacteristic
401C11×C4⋊C4C2×D411yescharacteristic
402C11×C4⋊C4C2×D412yes—
403C11×C4⋊C4C2×D412yes—
404C11×C4⋊C4C2412yes—
405C11×C4⋊C4C2412yes—
406C11×C22⋊C4—22no—
407C11×C22⋊C4—22no—
408C11×C22⋊C4—22no—
409C11×C22⋊C4—22no—
410C11×C22⋊C4—22no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4C2×D412yes—
413C11×C22⋊C4C2×D412yes—
414C11×C22⋊C4C2×D412yes—
415C11×C22⋊C4C2×D412yes—
416C42×C11—22no—
417C42×C11—22no—
418C42×C11—22no—
419C42×C11—22no—
420C42×C11—22no—
421C42×C11—22no—
422C42×C11C2×D412yes—
423C42×C11C2×D412yes—
424C42×C11C2412yes—
425C42×C11C2412yes—
426C22⋊Dic11—21no—
427C22⋊Dic11—21no—
428C22⋊Dic11—21no—
429#4326—22no—
430#4326—22no—
431#4325—24no—
432#4325—24no—
433#4325—22no—
434#4325—22no—
435#4324—22no—
436#4324—22no—
437#4323—24no—
438#4323—24no—
439#4323—22no—
440#4323—22no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—21no—
444(C2×D11)⋊C4—22no—
445(C2×D11)⋊C4—22no—
446(C2×D11)⋊C4—22no—
447(C2×D11)⋊C4—22no—
448(C2×D11)⋊C4—21no—
449(C2×D11)⋊C4—22no—
450C4⋊Dic11—22no—
451C4⋊Dic11—21no—
452C4⋊Dic11C2412yes—
453C4⋊Dic11C2411yescharacteristic
454C4⋊Dic11C2411yescharacteristic
455Dic11⋊C4—22no—
456Dic11⋊C4—22no—
457Dic11⋊C4—22no—
458Dic11⋊C4—21no—
459Dic11⋊C4—21no—
460C4×Dic11—22no—
461C4×Dic11—21no—
462#4318—22no—
463#4318—22no—
464C2×C11⋊C8—22no—
465C2×C11⋊C8—22no—
466C2×C11⋊C8C2411yescharacteristic
467C2×C11⋊C8C2411yescharacteristic
468C2×C11⋊C8C2412yes—
469C2×C11⋊C8C2412yes—
470C2×C11⋊C8C2411yescharacteristic
471C2×C11⋊C8C2411yescharacteristic
472#3494—111no—
473#3428D1111yescharacteristic, complemented
474#3126—112no—
475#3122—112no—
476#3121—112no—
477#3118—112no—
478#3115—112no—
479#3111—112no—
480#3106—112no—
481#3102—112no—
482#3093—111no—
483C2×#482—111no—
484#3084—111no—
485#3083—111no—
486#3045—111no—
487#3045—111no—
488#3006—111no—
489#3002—111no—
490#2952—111no—
491#2951—111no—
492#2946—111no—
493#2946—111no—
494#2924—111no—
495C23×C11—24no—
496C23×C11—21no—
497C23×C11—21no—
498C23×C11—22no—
499C23×C11—41no—
500C23×C11—41no—
501C23×C11—81no—
502C23×C11—81no—
503C23×C11C22×D411yescharacteristic
504C23×C11C22×D411yescharacteristic
505C23×C11C22×D411yescharacteristic
506C22×D11—22no—
507C22×D11—21no—
508C22×D11—42no—
509C22×D11—81no—
510C22×D11—81no—
511Q8×C11—24no—
512Q8×C11—21no—
513Q8×C11—21no—
514Q8×C11C2×#4112yes—
515Q8×C11C2×#4112yes—
516D4×C11—24no—
517D4×C11—24no—
518D4×C11—24no—
519D4×C11—24no—
520D4×C11—24no—
521D4×C11—21no—
522D4×C11—21no—
523D4×C11C2×#4112yes—
524D4×C11C2×#4112yes—
525C2×C4×C11—24no—
526C2×C4×C11—24no—
527C2×C4×C11—24no—
528C2×C4×C11—22no—
529C2×C4×C11—21no—
530C2×C4×C11—21no—
531C2×C4×C11—22no—
532C2×C4×C11—24no—
533C2×C4×C11—24no—
534C2×C4×C11—22no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—21no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—42no—
542C2×C4×C11—42no—
543C2×C4×C11—82no—
544C2×C4×C11—82no—
545C2×C4×C11—82no—
546C2×C4×C11—82no—
547C2×C4×C11—81no—
548C2×C4×C11—81no—
549C2×C4×C11C22×D412yes—
550C2×C4×C11C22×D412yes—
551C2×C4×C11C22×D411yescharacteristic
552C2×C4×C11C22×D411yescharacteristic
553C2×C4×C11C22×D412yes—
554C2×C4×C11C22×D412yes—
555C2×C4×C11C22×D411yescharacteristic
556C2×C4×C11C2×#4112yes—
557C2×C4×C11C2×#4112yes—
558C2×C4×C11C2511yescharacteristic
559C22⋊D11—42no—
560C22⋊D11—44no—
561C22⋊D11—42no—
562C22⋊D11—81no—
563C22⋊D11—82no—
564C2×Dic11—21no—
565C2×Dic11—21no—
566C2×Dic11—22no—
567C2×Dic11—21no—
568C2×Dic11—81no—
569D44—22no—
570D44—22no—
571D44—21no—
572D44—21no—
573D44—42no—
574D44—82no—
575D44—82no—
576C4×D11—42no—
577C4×D11—82no—
578C4×D11—82no—
579C4×D11—82no—
580Dic22—21no—
581Dic22—21no—
582Dic22—82no—
583C11⋊C8—21no—
584C11⋊C8—21no—
585C11⋊C8—21no—
586C11⋊C8—21no—
587C11⋊C8—22no—
588C11⋊C8—22no—
589C22×#41C2×D1111yescharacteristic
590C2×AGL(1,ℤ/8)—111no—
591C2×AGL(1,ℤ/8)—111no—
592C2×#135—111no—
593C2×#135—111no—
594#555—221no—
595#553—221no—
596#553—221no—
597#551—222no—
598#547—221no—
599#546—222no—
600#544—111no—
601#542—112no—
602#540—112no—
603#535—111no—
604#532—112no—
605#529—112no—
606#525—111no—
607C2×#121—111no—
608#520—21no—
609#520—21no—
610#520—111no—
611#520C2×D1111yescharacteristic
612#520C2×D1111yescharacteristic
613#520C2×D1111yescharacteristic
614#520C2×D1111yescharacteristic
615#519C2×D1112yescomplemented
616#518—22no—
617#518—111no—
618#518C2×D1112yescomplemented
619C4×#41—22no—
620C4×#41C2×D1112yescomplemented
621C4×#41C2×D1112yescomplemented
622C2×#117—21no—
623C2×#117—21no—
624C2×#117C2×D1111yescharacteristic
625C2×#117C2×D1111yescharacteristic
626#485—112no—
627#485—112no—
628#482—112no—
629#482—112no—
630#482—112no—
631#482—112no—
632#482—112no—
633#482—112no—
634#479—112no—
635#479—112no—
636#478—112no—
637#478—112no—
638#477—112no—
639#476—112no—
640#475—112no—
641#474—112no—
642#464—112no—
643#464—112no—
644#463—112no—
645#463—112no—
646#460—112no—
647#460—112no—
648#459—112no—
649#459—112no—
650#452—111no—
651#452—111no—
652#451—111no—
653#450—111no—
654#449—112no—
655#449—111no—
656#449—112no—
657#449—111no—
658#448—112no—
659#448—111no—
660#447—112no—
661#447—111no—
662#442—112no—
663#442—112no—
664#442—112no—
665#441—112no—
666#440—112no—
667#440—112no—
668#440—112no—
669#440—112no—
670C4×Q16—112no—
671C4×SD16—112no—
672C4×SD16—112no—
673C4×SD16—112no—
674C4×SD16—112no—
675C4×D8—112no—
676C4×D8—112no—
677C4×D8—112no—
678#433—112no—
679#433—112no—
680#432—112no—
681#431—112no—
682#428—111no—
683#428—111no—
684C2×#107—111no—
685C2×#106—111no—
686#424—111no—
687#424—111no—
688#417—111no—
689#417—111no—
690#417—111no—
691#417—111no—
692#416—111no—
693#416—111no—
694C2×#102—111no—
695C2×#102—111no—
696#407—111no—
697C2×C22⋊C8—111no—
698#405—111no—
699#405—111no—
700C22×C11—21no—
701C22×C11—21no—
702C22×C11—21no—
703C22×C11—21no—
704C22×C11—21no—
705C22×C11—21no—
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—22no—
709C22×C11—22no—
710C22×C11—41no—
711C22×C11—41no—
712C22×C11—41no—
713C22×C11—41no—
714C22×C11—82no—
715C22×C11—84no—
716C22×C11#52512yes—
717C22×C11C23×D411yescharacteristic
718C2×D11—42no—
719C2×D11—41no—
720C2×D11—42no—
721C2×D11—41no—
722C2×D11—42no—
723C2×D11—41no—
724C2×D11—162no—
725C4×C11—22no—
726C4×C11—22no—
727C4×C11—22no—
728C4×C11—22no—
729C4×C11—21no—
730C4×C11—22no—
731C4×C11—22no—
732C4×C11—21no—
733C4×C11—42no—
734C4×C11—42no—
735C4×C11#52512yes—
736C4×C11C22×#4111yescharacteristic
737C4×C11C22×#4111yescharacteristic
738Dic11—41no—
739Dic11—41no—
740Dic11—42no—
741Dic11—41no—
742C2×#41—24no—
743C2×#41—24no—
744C2×#41—21no—
745C2×#41—21no—
746C2×#41—111no—
747C2×#41—222no—
748C2×#41C22×D1111yescharacteristic
749C2×#41C22×D1111yescharacteristic
750C2×#41C22×D1111yescharacteristic
751C2×#41C22×D1111yescharacteristic
752C22×Q8C22×D1111yescharacteristic
753C22×D4—21no—
754C22×D4—111no—
755C22×D4—221no—
756C22×D4C22×D1111yescharacteristic
757C23×C4—21no—
758C23×C4C22×D1111yescharacteristic
759AGL(1,ℤ/8)—224no—
760AGL(1,ℤ/8)—224no—
761#135—224no—
762#135—224no—
763C2×Q16—111no—
764C2×Q16—111no—
765C2×SD16—111no—
766C2×SD16—111no—
767C2×SD16—112no—
768C2×SD16—112no—
769C2×SD16—111no—
770C2×SD16—111no—
771C2×D8—111no—
772C2×D8—111no—
773C2×D8—112no—
774C2×D8—112no—
775C2×M16—111no—
776C2×M16—111no—
777C22×C8—111no—
778C22×C8—111no—
779C4⋊Q8—112no—
780C4⋊Q8—221no—
781#127—112no—
782#126—222no—
783#126—222no—
784#125—112no—
785#125—221no—
786#124—112no—
787#124—222no—
788#124—222no—
789#123—221no—
790#123—222no—
791#123—222no—
792#123—222no—
793#123—222no—
794C22⋊Q8—111no—
795C22⋊Q8—111no—
796C22⋊Q8—222no—
797C22⋊Q8—222no—
798#121—112no—
799#121—112no—
800#121—111no—
801#121—111no—
802#121—221no—
803#121—221no—
804#121—222no—
805#121—221no—
806#121—221no—
807#121—222no—
808#121—222no—
809#120—221no—
810#120—222no—
811C4×Q8—22no—
812C4×Q8—22no—
813C4×Q8—112no—
814C4×Q8C22×D1112yes—
815C4×Q8C22×D1112yes—
816C4×Q8C22×D1112yes—
817C4×Q8C22×D1112yes—
818C4×D4—22no—
819C4×D4—22no—
820C4×D4—22no—
821C4×D4—22no—
822C4×D4—22no—
823C4×D4—22no—
824C4×D4—22no—
825C4×D4—22no—
826C4×D4—22no—
827C4×D4—22no—
828C4×D4—112no—
829C4×D4—112no—
830C4×D4—112no—
831C4×D4—221no—
832C4×D4—221no—
833C4×D4—222no—
834C4×D4—221no—
835C4×D4—221no—
836C4×D4—222no—
837C4×D4—222no—
838C4×D4C22×D1112yes—
839C4×D4C22×D1112yes—
840C4×D4C22×D1112yes—
841C4×D4C22×D1112yes—
842#117—21no—
843#117—21no—
844#117—21no—
845#117—21no—
846#117—21no—
847#117—21no—
848#117—22no—
849#117—22no—
850#117—22no—
851#117—22no—
852#117—111no—
853#117—221no—
854#117—222no—
855#117C22⋊D1111yescharacteristic
856#117C22⋊D1111yescharacteristic
857#117C22⋊D1112yes—
858#117C22×D1112yes—
859#117C22×D1112yes—
860#117C22×D1111yescharacteristic
861#117C22×D1112yes—
862#117C22×D1111yescharacteristic
863C2×C4⋊C4—21no—
864C2×C4⋊C4—21no—
865C2×C4⋊C4—21no—
866C2×C4⋊C4—21no—
867C2×C4⋊C4—111no—
868C2×C4⋊C4—221no—
869C2×C4⋊C4C22⋊D1111yescharacteristic
870C2×C4⋊C4C22⋊D1111yescharacteristic
871C2×C4⋊C4C22×D1111yescharacteristic
872C2×C4⋊C4C22×D1111yescharacteristic
873C2×C22⋊C4—21no—
874C2×C22⋊C4—22no—
875C2×C22⋊C4—22no—
876C2×C22⋊C4—221no—
877C2×C22⋊C4—222no—
878C2×C22⋊C4C22⋊D1112yes—
879C2×C42—21no—
880C2×C42—22no—
881C2×C42—22no—
882C2×C42C22×D1112yes—
883#107—112no—
884#107—112no—
885#107—112no—
886#107—112no—
887#106—112no—
888#106—112no—
889#106—112no—
890#106—112no—
891C4⋊C8—112no—
892C4⋊C8—112no—
893C4⋊C8—112no—
894C4⋊C8—112no—
895#103—111no—
896#103—111no—
897#103—111no—
898#103—111no—
899#103—112no—
900#103—112no—
901#103—112no—
902#103—112no—
903#102—111no—
904#102—111no—
905#102—111no—
906#102—111no—
907#102—112no—
908#102—112no—
909#102—112no—
910#102—112no—
911#102—112no—
912#102—112no—
913#102—112no—
914#102—112no—
915C22⋊C8—111no—
916C22⋊C8—111no—
917C22⋊C8—111no—
918C22⋊C8—111no—
919C22⋊C8—112no—
920C22⋊C8—112no—
921#97—112no—
922#97—112no—
923C4×C8—112no—
924C4×C8—112no—
925C2×C11—22no—
926C2×C11—41no—
927C2×C11—41no—
928C2×C11—42no—
929C2×C11—42no—
930C2×C11C2×#52511yescharacteristic
931C2×C11#358411yescharacteristic
932C2×C11#358511yescharacteristic
933D11—81no—
934D11—82no—
935C24—21no—
936C24—221no—
937C24C2×C22⋊D1111yescharacteristic
938#41—28no—
939#41—28no—
940#41—22no—
941#41—22no—
942#41—22no—
943#41—22no—
944#41—22no—
945#41—22no—
946#41—222no—
947#41—222no—
948#41—884no—
949#41#433914yescomplemented
950#41#433914yescomplemented
951C2×Q8—22no—
952C2×Q8—22no—
953C2×Q8—21no—
954C2×Q8—111no—
955C2×Q8—222no—
956C2×Q8C23×D1111yescharacteristic
957C2×Q8C23×D1111yescharacteristic
958C2×D4—28no—
959C2×D4—21no—
960C2×D4—21no—
961C2×D4—21no—
962C2×D4—21no—
963C2×D4—22no—
964C2×D4—22no—
965C2×D4—21no—
966C2×D4—112no—
967C2×D4—111no—
968C2×D4—221no—
969C2×D4—221no—
970C2×D4—222no—
971C2×D4—221no—
972C2×D4—222no—
973C2×D4—222no—
974C2×D4—222no—
975C2×D4—221no—
976C2×D4—222no—
977C2×D4—222no—
978C2×D4—882no—
979C2×D4C23×D1111yescharacteristic
980C2×D4C23×D1111yescharacteristic
981C22×C4—28no—
982C22×C4—21no—
983C22×C4—22no—
984C22×C4—22no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—221no—
996C22×C4—221no—
997C22×C4—222no—
998C22×C4—222no—
999C22×C4—222no—
1000C22×C4C2×C22⋊D1111yescharacteristic
1001C22×C4C2×C22⋊D1111yescharacteristic
1002C22×C4C2×C22⋊D1111yescharacteristic
1003C22×C4C2×C22⋊D1112yes—
1004C22×C4C2×C22⋊D1112yes—
1005C22×C4C23×D1111yescharacteristic
1006C22×C4C23×D1111yescharacteristic
1007C22×C4C23×D1111yescharacteristic
1008Q16—222no—
1009Q16—222no—
1010SD16—222no—
1011SD16—222no—
1012SD16—224no—
1013SD16—224no—
1014SD16—222no—
1015SD16—222no—
1016D8—222no—
1017D8—222no—
1018D8—224no—
1019D8—224no—
1020M16—222no—
1021M16—222no—
1022C2×C8—111no—
1023C2×C8—111no—
1024C2×C8—112no—
1025C2×C8—112no—
1026C2×C8—111no—
1027C2×C8—111no—
1028C2×C8—222no—
1029C2×C8—222no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—112no—
1037C4⋊C4—111no—
1038C4⋊C4—111no—
1039C4⋊C4—221no—
1040C4⋊C4—222no—
1041C4⋊C4—221no—
1042C4⋊C4—222no—
1043C4⋊C4—222no—
1044C4⋊C4—222no—
1045C4⋊C4—221no—
1046C4⋊C4C2×C22⋊D1111yescharacteristic
1047C4⋊C4C2×C22⋊D1111yescharacteristic
1048C4⋊C4C2×C22⋊D1111yescharacteristic
1049C4⋊C4C2×C22⋊D1111yescharacteristic
1050C4⋊C4C2×C22⋊D1112yes—
1051C4⋊C4C2×C22⋊D1112yes—
1052C4⋊C4C23×D1112yes—
1053C4⋊C4C23×D1112yes—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—221no—
1061C22⋊C4—221no—
1062C22⋊C4—221no—
1063C22⋊C4—222no—
1064C22⋊C4—222no—
1065C22⋊C4—222no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—221no—
1070C22⋊C4—222no—
1071C22⋊C4—221no—
1072C22⋊C4C2×C22⋊D1112yes—
1073C22⋊C4C2×C22⋊D1112yes—
1074C22⋊C4C2×C22⋊D1112yes—
1075C22⋊C4C2×C22⋊D1112yes—
1076C42—22no—
1077C42—22no—
1078C42—22no—
1079C42—22no—
1080C42—22no—
1081C42—22no—
1082C42—221no—
1083C42—222no—
1084C42C2×C22⋊D1112yes—
1085C42C2×C22⋊D1112yes—
1086C42C23×D1112yes—
1087C42C23×D1112yes—
1088C11#6058711yescharacteristic, complemented, Sylow
1089C23—24no—
1090C23—21no—
1091C23—21no—
1092C23—22no—
1093C23—41no—
1094C23—41no—
1095C23—81no—
1096C23—81no—
1097C23—222no—
1098C23—221no—
1099C23—442no—
1100C23—881no—
1101C23—881no—
1102C23C22×C22⋊D1111yescharacteristic
1103C23C22×C22⋊D1111yescharacteristic
1104C23C22×C22⋊D1111yescharacteristic
1105Q8—24no—
1106Q8—21no—
1107Q8—21no—
1108Q8—221no—
1109Q8—221no—
1110Q8—882no—
1111Q8C2×#433912yes—
1112Q8C2×#433912yes—
1113D4—24no—
1114D4—24no—
1115D4—24no—
1116D4—24no—
1117D4—24no—
1118D4—21no—
1119D4—21no—
1120D4—222no—
1121D4—222no—
1122D4—221no—
1123D4—221no—
1124D4—444no—
1125D4—442no—
1126D4—442no—
1127D4—442no—
1128D4—882no—
1129D4—882no—
1130D4—882no—
1131D4—881no—
1132D4C2×#433912yes—
1133D4C2×#433912yes—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—82no—
1153C2×C4—82no—
1154C2×C4—82no—
1155C2×C4—82no—
1156C2×C4—81no—
1157C2×C4—81no—
1158C2×C4—221no—
1159C2×C4—221no—
1160C2×C4—221no—
1161C2×C4—222no—
1162C2×C4—442no—
1163C2×C4—882no—
1164C2×C4—882no—
1165C2×C4—882no—
1166C2×C4—881no—
1167C2×C4C2×#433912yes—
1168C2×C4C2×#433912yes—
1169C2×C4C22×C22⋊D1111yescharacteristic
1170C2×C4C22×C22⋊D1111yescharacteristic
1171C2×C4C22×C22⋊D1112yes—
1172C2×C4C22×C22⋊D1112yes—
1173C2×C4C22×C22⋊D1112yes—
1174C2×C4C22×C22⋊D1112yes—
1175C2×C4C22×C22⋊D1111yescharacteristic
1176C2×C4C24×D1111yescharacteristic
1177C8—221no—
1178C8—221no—
1179C8—221no—
1180C8—221no—
1181C8—222no—
1182C8—222no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—22no—
1188C22—22no—
1189C22—21no—
1190C22—21no—
1191C22—21no—
1192C22—21no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—82no—
1198C22—84no—
1199C22—441no—
1200C22—442no—
1201C22—441no—
1202C22—442no—
1203C22—442no—
1204C22—441no—
1205C22—1762no—
1206C22#1062332212yes—
1207C22C23×C22⋊D1111yescharacteristic
1208C4—21no—
1209C4—22no—
1210C4—22no—
1211C4—21no—
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—42no—
1217C4—42no—
1218C4—441no—
1219C4—442no—
1220C4—441no—
1221C4—441no—
1222C4#1062332212yes—
1223C4C22×#433911yescharacteristic
1224C4C22×#433911yescharacteristic
1225C2—22no—
1226C2—41no—
1227C2—41no—
1228C2—42no—
1229C2—42no—
1230C2—882no—
1231C2—881no—
1232C2C2×#1062332211yescharacteristic
1233C2#1308338711yescharacteristic
1234C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3428C2
socleC22×C11C23×D4
hypercenter#3428D11
hypocenterC11#60587
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. #13082351C2semidirect
2. #13078907C2semidirect
3. #13078859C2semidirect
4. #13078845C2semidirect
5. #13078800C2semidirect
6. #13078767C2semidirect
7. #13078725C2semidirect
8. #13078676C2semidirect
9. #13078634C2semidirect
10. #13078547C2semidirect
11. C2×#10622616C2semidirect
12. #13078478C2semidirect
13. #13078467C2semidirect
14. #13078155C2semidirect
15. #13078155C2semidirect
16. #13077868C2semidirect
17. #13077834C2semidirect
18. #13077497C2semidirect
19. #13077489C2semidirect
20. #13077444C2semidirect
21. #13077444C2semidirect
22. #13077274C2semidirect
23. C11×#3428C2semidirect
31. C11×#519C22semidirect
33. C11×#518C22semidirect
35. C4×C11×#41C22semidirect
36. C4×C11×#41C22semidirect
52. #10623056C22semidirect
53. #10623054C22semidirect
54. #10623052C22semidirect
55. #10623050C22semidirect
59. #10623010C22semidirect
60. #10623008C22semidirect
61. #10622852C22semidirect
62. #10622852C22semidirect
65. #10622851C22semidirect
66. #10622851C22semidirect
71. #10622841C22semidirect
73. #10622840C22semidirect
74. #10622831C22semidirect
76. #10622830C22semidirect
79. #10622643C22semidirect
80. C4×#4326C22semidirect
81. #10622641C22semidirect
82. #10622641C22semidirect
83. #10622640C22semidirect
84. #10622640C22semidirect
85. #10622639C22semidirect
86. #10622639C22semidirect
87. #10622639C22semidirect
88. C4×#4325C22semidirect
89. C4×#4325C22semidirect
90. C4×#4325C22semidirect
91. #10622635C22semidirect
92. #10622635C22semidirect
93. #10622634C22semidirect
94. #10622633C22semidirect
95. #10622631C22semidirect
96. C4×#4324C22semidirect
97. #10622629C22semidirect
98. #10622629C22semidirect
99. #10622628C22semidirect
100. #10622628C22semidirect
101. #10622627C22semidirect
102. #10622627C22semidirect
103. #10622627C22semidirect
104. C4×#4323C22semidirect
105. C4×#4323C22semidirect
106. C4×#4323C22semidirect
107. #10622622C22semidirect
108. #10622622C22semidirect
109. #10622621C22semidirect
110. #10622620C22semidirect
113. #10622616C22semidirect
114. #10622616C22semidirect
115. #10622616C22semidirect
116. #10622616C22semidirect
117. #10622613C22semidirect
118. #10622613C22semidirect
119. #10622612C22semidirect
120. #10622612C22semidirect
121. #10622610C22semidirect
122. #10622610C22semidirect
123. #10622609C22semidirect
124. #10622609C22semidirect
125. #10622579C22semidirect
126. #10622579C22semidirect
127. C2×#66873C22semidirect
128. C2×#66873C22semidirect
129. #10622577C22semidirect
130. #10622577C22semidirect
131. C2×#66872C22semidirect
132. C2×#66871C22semidirect
133. #10622539C22semidirect
134. #10622538C22semidirect
330. C11×#41#41semidirect
331. C11×#41#41semidirect
473. #3428D11semidirect
615. #519C2×D11semidirect
618. #518C2×D11semidirect
620. C4×#41C2×D11semidirect
621. C4×#41C2×D11semidirect
949. #41#4339semidirect
950. #41#4339semidirect
1088. C11#60587semidirect

Maximal subgroups

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

subgroupindex
#130823512
#130789072
#130788592
#130788452
#130788002
#130787672
#130787252
#130786762
#130786342
#130785472
C2×#106226162
#130784782
#130784672
#130781552
#130778682
#130778342
#130774972
#130774892
#130774442
#130772742
C11×#34282
#6058711