Finite Group Databasebeta

← #15639287

Subgroups — #15639287

Order 2816.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4339C211yesmaximal, characteristic, complemented
2#13080893C211yesmaximal, characteristic, complemented
3#13080841C211yesmaximal, characteristic, complemented
4#13080796C212yesmaximal, complemented
5#13080766C212yesmaximal, complemented
6#13080549C211yesmaximal, characteristic, complemented
7#13080527C211yesmaximal, characteristic, complemented
8#13080372C211yesmaximal, characteristic, complemented
9#13080346C211yesmaximal, characteristic, complemented
10#13080282C211yesmaximal, characteristic, complemented
11#13080236C211yesmaximal, characteristic, complemented
12#13080167C212yesmaximal, complemented
13#13080142C212yesmaximal, complemented
14#13079623C211yesmaximal, characteristic, complemented
15#13079545C211yesmaximal, characteristic, complemented
16#13079453C212yesmaximal, complemented
17#13079404C212yesmaximal, complemented
18#13078761C211yesmaximal, characteristic, complemented
19#13078681C211yesmaximal, characteristic, complemented
20#13077856C212yesmaximal, complemented
21#13077832C212yesmaximal, complemented
22#13077651C211yesmaximal, characteristic, complemented
23C11×#3506C211yesmaximal, characteristic, complemented
24C22×#4339C2212yes—
25C11×#559—21no—
26C11×#559—21no—
27C11×#556C2211yescharacteristic
28C11×#556C2211yescharacteristic, complemented
29C11×#555C2212yescomplemented
30C11×#553—22no—
31C11×#550C2211yescharacteristic
32C11×#550C2211yescharacteristic, complemented
33C11×#547C2212yescomplemented
34C11×#538—22no—
35C11×#535—21no—
36C11×#533C2211yescharacteristic, complemented
37C11×#532C2211yescharacteristic, complemented
38C11×#525C2212yescomplemented
39C11×#525C2212yescomplemented
40C11×#520—21no—
41C2×C4×D4×C11C2211yescharacteristic
42C2×#67004C2212yescomplemented
43C2×#67003C2212yescomplemented
44C2×#67003C2212yescomplemented
45C2×#67002C2212yescomplemented
46D4×C22⋊D11—21no—
47#10623322C2212yes—
48#10623084C2211yescharacteristic
49#10623083C2212yes—
50#10623082C2211yescharacteristic
51#10623081C2212yes—
52D4×D44C2211yescharacteristic
53#10623079—21no—
54#10623078—22no—
55C4×D4×D11—21no—
56D4×Dic22C2211yescharacteristic
57#10623038—21no—
58#10623021—22no—
59#10623008C2211yescharacteristic
60C4×#4339C2211yescharacteristic
61#10622852C2212yescomplemented
62#10622852C2212yescomplemented
63#10622851C2212yescomplemented
64#10622851C2212yescomplemented
65#10622820C2212yescomplemented
66C2×C22⋊(C11⋊C8)C2212yescomplemented
67#10622707C2211yescharacteristic, complemented
68#10622707C2211yescharacteristic, complemented
69#10622706C2211yescharacteristic, complemented
70#10622703C2211yescharacteristic, complemented
71#10622702C2212yescomplemented
72#10622701C2211yescharacteristic, complemented
73#10622700C2211yescharacteristic, complemented
74#10622700C2211yescharacteristic, complemented
75#10622699C2212yescomplemented
76#10622696C2211yescharacteristic, complemented
77#10622689C2211yescharacteristic, complemented
78#10622688C2211yescharacteristic, complemented
79#10622686C2211yescharacteristic, complemented
80#10622685C2211yescharacteristic, complemented
81#10622665C2212yescomplemented
82#10622664C2212yescomplemented
83#10622663C2212yescomplemented
84#10622662C2212yescomplemented
85#10622661C2212yescomplemented
86#10622660C2211yescharacteristic
87#10622660C2211yescharacteristic
88#10622660C2212yescomplemented
89#10622660C2212yescomplemented
90#10622660C2212yescomplemented
91#10622660C2212yescomplemented
92#10622659C2212yescomplemented
93#10622658C2211yescharacteristic, complemented
94#10622658C2211yescharacteristic, complemented
95#10622655C2212yescomplemented
96#10622654C2212yescomplemented
97#10622653C2212yescomplemented
98#10622652C2212yescomplemented
99#10622651C2212yescomplemented
100#10622650C2212yes—
101#10622650C2212yescomplemented
102#10622650C2212yescomplemented
103#10622650C2212yescomplemented
104#10622650C2212yescomplemented
105#10622649C2212yescomplemented
106#10622648C2212yescomplemented
107#10622644C2211yescharacteristic, complemented
108#10622644C2211yescharacteristic, complemented
109C4×#4326C2211yescharacteristic, complemented
110C4×#4326C2211yescharacteristic, complemented
111#10622640C2211yescharacteristic, complemented
112#10622640C2211yescharacteristic, complemented
113C4×#4325C2211yescharacteristic, complemented
114C4×#4325C2211yescharacteristic, complemented
115#10622631C2212yescomplemented
116#10622629C2212yescomplemented
117#10622629C2212yescomplemented
118#10622627C2212yescomplemented
119#10622625C2211yescharacteristic
120#10622625C2211yescharacteristic
121#10622624C2212yescomplemented
122#10622624C2212yescomplemented
123D4×C11⋊C8C2211yescharacteristic, complemented
124D4×C11⋊C8C2211yescharacteristic, complemented
125#10622617C2212yescomplemented
126#10622616C2212yescomplemented
127#10622616C2212yescomplemented
128#10622615C2212yescomplemented
129#10622615C2212yescomplemented
130#10622614C2212yescomplemented
131#10622609C2212yescomplemented
132#10622609C2212yescomplemented
133#10622539C2211yescharacteristic, complemented
134#10622538C2211yescharacteristic, complemented
135C2×C11×#41—21no—
136C2×C11×#41C2312yes—
137C2×C11×#41C2312yes—
138C22×D4×C11D411yescharacteristic
139C23×C4×C11C2312yes—
140C22×C22⋊D11—22no—
141C2×D4×D11—21no—
142C2×#4339—22no—
143C2×#4339—22no—
144C2×#4339—44no—
145C2×#4339—44no—
146C2×#4339C2311yescharacteristic
147C2×#4339C2312yes—
148C2×#4339C2312yes—
149C2×#4339C2312yes—
150C22×D44C2312yes—
151C22×C4×D11—22no—
152C22×Dic22C2312yes—
153C11×C4⋊Q8C2311yescharacteristic
154C11×C4⋊Q8C2311yescharacteristic
155C11×C4⋊Q8C2311yescharacteristic
156C11×#127—21no—
157C11×#127—21no—
158C11×#127C2311yescharacteristic
159C11×#126—22no—
160C11×#126—22no—
161C11×#125—21no—
162C11×#124—21no—
163C11×#124—21no—
164C11×#124—22no—
165C11×#124—22no—
166C11×#124—21no—
167C11×#123—22no—
168C11×#123—22no—
169C11×#123—22no—
170C11×#123—22no—
171C11×C22⋊Q8—21no—
172C11×C22⋊Q8C2311yescharacteristic
173C11×C22⋊Q8C2311yescharacteristic
174C11×C22⋊Q8C2312yes—
175C11×C22⋊Q8C2312yes—
176C11×#121—22no—
177C11×#121—22no—
178C11×#121—21no—
179C11×#121—22no—
180C11×#121—22no—
181C11×#121C2312yes—
182C11×#121C2312yes—
183C11×#121C2312yes—
184C11×#120—22no—
185C11×#120—22no—
186C4×Q8×C11—21no—
187C4×Q8×C11—21no—
188C4×Q8×C11—21no—
189C4×Q8×C11C2311yescharacteristic
190C4×Q8×C11C2311yescharacteristic
191C4×D4×C11—22no—
192C4×D4×C11—22no—
193C4×D4×C11—22no—
194C4×D4×C11—22no—
195C4×D4×C11—21no—
196C4×D4×C11—21no—
197C4×D4×C11—21no—
198C4×D4×C11D411yescharacteristic
199C4×D4×C11D412yes—
200C4×D4×C11D411yescharacteristic
201C4×D4×C11C2312yes—
202C4×D4×C11C2311yescharacteristic
203C4×D4×C11C2312yes—
204C4×D4×C11C2311yescharacteristic
205C11×#117—21no—
206C11×#117—22no—
207C11×#117C2312yes—
208C11×#117C2312yes—
209C2×C11×C4⋊C4—22no—
210C2×C11×C4⋊C4D411yescharacteristic
211C2×C11×C22⋊C4D412yes—
212C2×C42×C11C2311yescharacteristic
213#67006—22no—
214#67004—44no—
215#67003—44no—
216#67003—44no—
217#67002—44no—
218C2×#4326C2311yescharacteristic
219C2×#4326C2311yescharacteristic
220C2×#4326C2312yes—
221C2×#4326C2312yes—
222C2×#4325C2311yescharacteristic
223C2×#4325C2311yescharacteristic
224C2×#4325C2312yes—
225C2×#4325C2312yes—
226#66993—21no—
227#66992—22no—
228#66991—21no—
229#66990—22no—
230D4×Dic11—21no—
231C2×#4324C2312yes—
232C2×#4324C2312yes—
233C2×#4324C2312yes—
234C2×#4323C2312yes—
235C2×#4323C2312yes—
236C2×#4323C2312yes—
237#66983—21no—
238#66983—21no—
239#66983C2312yes—
240#66983C2312yes—
241#66982—22no—
242C4×C22⋊D11—21no—
243C4×C22⋊D11—21no—
244C4×C22⋊D11—22no—
245C4×C22⋊D11—22no—
246#66979C2311yescharacteristic
247#66977C2312yes—
248#66977C2312yes—
249C2×#4318C2312yes—
250C2×#4318C2312yes—
251C22×C11⋊C8C2312yes—
252C22×C11⋊C8C2312yes—
253#66949—22no—
254#66948—21no—
255#66947—22no—
256#66946—21no—
257C4⋊C4×D11—21no—
258#66941—21no—
259#66938—22no—
260#66937—22no—
261#66937—22no—
262#66936—22no—
263#66935—22no—
264(C22⋊D11)⋊C4—22no—
265C22⋊C4×D11—22no—
266#66931—22no—
267#66928C2312yes—
268#66927C2311yescharacteristic
269C4×D44—21no—
270C4×D44—21no—
271C4×D44C2311yescharacteristic
272C4×D44C2311yescharacteristic
273#66925—21no—
274C42×D11—21no—
275#66922C2311yescharacteristic
276C4×Dic22C2311yescharacteristic
277C4×Dic22C2311yescharacteristic
278#66899C2311yescharacteristic
279#66899C2311yescharacteristic
280#66899C2311yescharacteristic
281#66899C2311yescharacteristic
282#66896C2312yes—
283#66896C2312yes—
284C22⋊(C11⋊C8)C2311yescharacteristic
285C22⋊(C11⋊C8)C2311yescharacteristic
286C22⋊(C11⋊C8)C2312yes—
287C22⋊(C11⋊C8)C2312yes—
288C22⋊(C11⋊C8)C2312yes—
289C22⋊(C11⋊C8)C2312yes—
290C22⋊(C11⋊C8)C2312yes—
291#66874C2312yes—
292#66874C2312yes—
293#66874C2312yes—
294#66874C2312yes—
295#66874C2311yescharacteristic
296#66874C2312yes—
297#66874C2311yescharacteristic
298#66873C2311yescharacteristic
299#66873C2312yes—
300#66873C2312yes—
301#66873C2312yes—
302#66873C2311yescharacteristic
303#66873C2312yes—
304#66873C2312yes—
305#66872C2311yescharacteristic
306#66872C2312yes—
307#66872C2311yescharacteristic
308#66871C2311yescharacteristic
309#66871C2312yes—
310#66871C2311yescharacteristic
311C4⋊(C11⋊C8)C2311yescharacteristic
312C4⋊(C11⋊C8)C2311yescharacteristic
313C4⋊(C11⋊C8)C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315#66867C2312yes—
316C4×C11⋊C8C2311yescharacteristic
317C4×C11⋊C8C2311yescharacteristic
318#61608—111nomaximal, Sylow
319C24×C11C2×D412yes—
320C23×D11—22no—
321C11×#41—44no—
322C11×#41—42no—
323C11×#41—42no—
324C11×#41—42no—
325C11×#41—42no—
326C2×Q8×C11—21no—
327C2×Q8×C11—21no—
328C2×Q8×C11C2411yescharacteristic
329C2×Q8×C11C2411yescharacteristic
330C2×D4×C11—22no—
331C2×D4×C11—22no—
332C2×D4×C11—22no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—21no—
336C2×D4×C11—21no—
337C2×D4×C11—42no—
338C2×D4×C11C2×D411yescharacteristic
339C2×D4×C11C2×D411yescharacteristic
340C2×D4×C11C2×D412yes—
341C2×D4×C11C2412yes—
342C22×C4×C11—22no—
343C22×C4×C11—22no—
344C22×C4×C11—22no—
345C22×C4×C11—42no—
346C22×C4×C11—42no—
347C22×C4×C11C2×D411yescharacteristic
348C22×C4×C11C2×D411yescharacteristic
349C22×C4×C11C2×D412yes—
350C22×C4×C11C2×D412yes—
351C22×C4×C11C2×D412yes—
352C22×C4×C11C2411yescharacteristic
353C22×C4×C11C2412yes—
354C22×C4×C11C2412yes—
355C2×C22⋊D11—21no—
356C2×C22⋊D11—22no—
357C2×C22⋊D11—22no—
358C2×C22⋊D11—22no—
359C2×C22⋊D11—22no—
360C2×C22⋊D11—22no—
361C2×C22⋊D11—48no—
362C22×Dic11—22no—
363D4×D11—44no—
364#4339—22no—
365#4339—24no—
366#4339—22no—
367#4339—24no—
368#4339—42no—
369#4339—42no—
370#4339—42no—
371#4339—42no—
372#4339—48no—
373#4339—48no—
374C2×D44—24no—
375C2×D44—21no—
376C2×D44—22no—
377C2×D44—21no—
378C2×D44—42no—
379C2×D44C2412yes—
380C2×D44C2411yescharacteristic
381C2×C4×D11—21no—
382C2×C4×D11—21no—
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—22no—
386C2×C4×D11—21no—
387C2×C4×D11—48no—
388C2×Dic22—24no—
389C2×Dic22—22no—
390C2×Dic22—42no—
391C2×Dic22C2412yes—
392C2×Dic22C2411yescharacteristic
393C11×C4⋊C4—21no—
394C11×C4⋊C4—22no—
395C11×C4⋊C4—22no—
396C11×C4⋊C4—21no—
397C11×C4⋊C4—21no—
398C11×C4⋊C4—21no—
399C11×C4⋊C4—21no—
400C11×C4⋊C4—21no—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4C2×D411yescharacteristic
404C11×C4⋊C4C2×D411yescharacteristic
405C11×C4⋊C4C2×D412yes—
406C11×C4⋊C4C2412yes—
407C11×C4⋊C4C2411yescharacteristic
408C11×C4⋊C4C2411yescharacteristic
409C11×C22⋊C4—21no—
410C11×C22⋊C4—21no—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—22no—
414C11×C22⋊C4—22no—
415C11×C22⋊C4—22no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4—22no—
418C11×C22⋊C4—22no—
419C11×C22⋊C4C2×D412yes—
420C11×C22⋊C4C2×D412yes—
421C11×C22⋊C4C2×D412yes—
422C11×C22⋊C4C2×D412yes—
423C42×C11—22no—
424C42×C11—22no—
425C42×C11—21no—
426C42×C11—21no—
427C42×C11C2×D411yescharacteristic
428C42×C11C2×D411yescharacteristic
429C42×C11C2411yescharacteristic
430C42×C11C2411yescharacteristic
431C22⋊Dic11—22no—
432C22⋊Dic11—22no—
433C22⋊Dic11—21no—
434#4326—22no—
435#4326—22no—
436#4326—42no—
437#4326—42no—
438#4325—22no—
439#4325—22no—
440#4325—42no—
441#4325—42no—
442#4324—24no—
443#4324—42no—
444#4324—42no—
445#4323—24no—
446#4323—42no—
447#4323—42no—
448(C2×D11)⋊C4—21no—
449(C2×D11)⋊C4—21no—
450(C2×D11)⋊C4—22no—
451(C2×D11)⋊C4—22no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4—22no—
454C4⋊Dic11—21no—
455C4⋊Dic11—21no—
456C4⋊Dic11C2411yescharacteristic
457C4⋊Dic11C2411yescharacteristic
458Dic11⋊C4—21no—
459Dic11⋊C4—21no—
460Dic11⋊C4—22no—
461Dic11⋊C4—22no—
462C4×Dic11—21no—
463C4×Dic11—21no—
464C4×Dic11—21no—
465#4318—42no—
466#4318—42no—
467C2×C11⋊C8—42no—
468C2×C11⋊C8—42no—
469C2×C11⋊C8C2411yescharacteristic
470C2×C11⋊C8C2411yescharacteristic
471C2×C11⋊C8C2411yescharacteristic
472C2×C11⋊C8C2411yescharacteristic
473C2×C11⋊C8C2412yes—
474C2×C11⋊C8C2412yes—
475#3506D1111yescharacteristic, complemented
476D4×#41—111no—
477#3328—111no—
478#3324—111no—
479#3321—112no—
480#3319—112no—
481#3304—111no—
482#3302—111no—
483#3287—111no—
484#3284—111no—
485#3278—111no—
486#3274—111no—
487#3269—112no—
488#3267—112no—
489#3216—111no—
490#3207—111no—
491#3197—112no—
492#3191—112no—
493#3115—111no—
494#3107—111no—
495#3005—112no—
496#3002—112no—
497#2974—111no—
498C23×C11—22no—
499C23×C11—42no—
500C23×C11—42no—
501C23×C11—42no—
502C23×C11C22×D412yes—
503C23×C11C22×D412yes—
504C23×C11C22×D411yescharacteristic
505C22×D11—21no—
506C22×D11—22no—
507C22×D11—44no—
508C22×D11—44no—
509C22×D11—82no—
510Q8×C11—21no—
511Q8×C11—21no—
512Q8×C11—21no—
513Q8×C11—21no—
514Q8×C11—42no—
515Q8×C11—81no—
516D4×C11—22no—
517D4×C11—22no—
518D4×C11—22no—
519D4×C11—22no—
520D4×C11—42no—
521D4×C11—44no—
522D4×C11—42no—
523D4×C11—81no—
524D4×C11—82no—
525D4×C11—82no—
526D4×C11—82no—
527D4×C11—82no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—21no—
536C2×C4×C11—21no—
537C2×C4×C11—22no—
538C2×C4×C11—21no—
539C2×C4×C11—21no—
540C2×C4×C11—42no—
541C2×C4×C11—42no—
542C2×C4×C11—42no—
543C2×C4×C11—41no—
544C2×C4×C11—44no—
545C2×C4×C11—82no—
546C2×C4×C11—82no—
547C2×C4×C11C22×D411yescharacteristic
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C22×D411yescharacteristic
551C2×C4×C11C22×D412yes—
552C2×C4×C11C22×D412yes—
553C2×C4×C11C22×D411yescharacteristic
554C2×C4×C11C2511yescharacteristic
555C22⋊D11—24no—
556C22⋊D11—44no—
557C22⋊D11—44no—
558C22⋊D11—44no—
559C22⋊D11—44no—
560C22⋊D11—82no—
561C2×Dic11—21no—
562C2×Dic11—21no—
563C2×Dic11—21no—
564C2×Dic11—22no—
565C2×Dic11—44no—
566D44—21no—
567D44—22no—
568D44—22no—
569D44—44no—
570D44—42no—
571D44—81no—
572D44H(5,𝔽2)12yes—
573C4×D11—24no—
574C4×D11—44no—
575C4×D11—44no—
576C4×D11—44no—
577C4×D11—42no—
578C4×D11—81no—
579Dic22—21no—
580Dic22—22no—
581Dic22—22no—
582Dic22—44no—
583Dic22H(5,𝔽2)12yes—
584C11⋊C8—21no—
585C11⋊C8—21no—
586C11⋊C8—22no—
587C11⋊C8—22no—
588C11⋊C8—21no—
589C11⋊C8—21no—
590C22×#41—112no—
591C2×#137—112no—
592C2×AGL(1,ℤ/8)—112no—
593C2×#135—112no—
594C2×#135—112no—
595#559—21no—
596#559—21no—
597#556C2×D1111yescharacteristic
598#556C2×D1111yescharacteristic, complemented
599#555C2×D1112yescomplemented
600#553—22no—
601#550—111no—
602#550C2×D1111yescharacteristic
603#550C2×D1111yescharacteristic, complemented
604D4×Q8—111no—
605#548—112no—
606#547—111no—
607#547—221no—
608#547C2×D1112yescomplemented
609#546—112no—
610#546—222no—
611D42—111no—
612D42—221no—
613#538—22no—
614#535—21no—
615#533C2×D1111yescharacteristic, complemented
616#532—111no—
617#532—221no—
618#532C2×D1111yescharacteristic, complemented
619#525—112no—
620#525—222no—
621#525C2×D1112yescomplemented
622#525C2×D1112yescomplemented
623#520—21no—
624C4×#41—111no—
625C2×C4×D4—221no—
626C2×C4×D4C2×D1111yescharacteristic
627#497—112no—
628#493—111no—
629#492—111no—
630#489—112no—
631#487—111no—
632#486—111no—
633#485—111no—
634#485—111no—
635#485—112no—
636#485—112no—
637#482—112no—
638#482—112no—
639#482—112no—
640#475—111no—
641#475—111no—
642#474—111no—
643#474—111no—
644#470—112no—
645#469—112no—
646#468—112no—
647#468—112no—
648#467—112no—
649#466—112no—
650#465—112no—
651#465—112no—
652#463—112no—
653#463—112no—
654#462—111no—
655#462—111no—
656#462—111no—
657#461—111no—
658#460—111no—
659#460—111no—
660#460—111no—
661#459—111no—
662#452—112no—
663#452—112no—
664#452—111no—
665#452—111no—
666#452—112no—
667#452—112no—
668#452—112no—
669#452—112no—
670#451—112no—
671#450—112no—
672#449—112no—
673#449—112no—
674#449—112no—
675#449—112no—
676#449—112no—
677#449—112no—
678#449—112no—
679#448—112no—
680#447—112no—
681#442—112no—
682#440—112no—
683C4×Q16—111no—
684C4×Q16—111no—
685C4×SD16—111no—
686C4×SD16—111no—
687#436—111no—
688#436—111no—
689#435—112no—
690#435—112no—
691C8×D4—111no—
692C8×D4—111no—
693#432—111no—
694#431—111no—
695#419—112no—
696#418—112no—
697#416—112no—
698#416—112no—
699#407—112no—
700C2×C22⋊C8—112no—
701C22×C11—21no—
702C22×C11—22no—
703C22×C11—22no—
704C22×C11—21no—
705C22×C11—22no—
706C22×C11—22no—
707C22×C11—21no—
708C22×C11—22no—
709C22×C11—22no—
710C22×C11—42no—
711C22×C11—42no—
712C22×C11—42no—
713C22×C11—84no—
714C22×C11C23×D411yescharacteristic
715C2×D11—22no—
716C2×D11—41no—
717C2×D11—41no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—88no—
722C4×C11—21no—
723C4×C11—21no—
724C4×C11—21no—
725C4×C11—22no—
726C4×C11—22no—
727C4×C11—21no—
728C4×C11—41no—
729C4×C11—41no—
730C4×C11—41no—
731C4×C11—41no—
732C4×C11—42no—
733C4×C11#57512yes—
734C4×C11C2×H(5,𝔽2)11yescharacteristic
735C4×C11C2×H(5,𝔽2)11yescharacteristic
736Dic11—22no—
737Dic11—41no—
738Dic11—42no—
739Dic11—41no—
740C2×#41—21no—
741C2×#41—111no—
742C2×#41—112no—
743C2×#41—112no—
744C2×#41—112no—
745C2×#41—222no—
746C2×#41—222no—
747C2×#41—444no—
748C2×#41—444no—
749C2×#41C22×D1112yes—
750C2×#41C22×D1112yes—
751C22×Q8—112no—
752C22×D4—112no—
753C22×D4—222no—
754C22×D4—221no—
755C22×D4C22⋊D1111yescharacteristic
756C23×C4—222no—
757C23×C4C22×D1112yes—
758#137—444no—
759AGL(1,ℤ/8)—444no—
760#135—444no—
761#135—444no—
762C2×Q16—111no—
763C2×Q16—111no—
764C2×Q16—112no—
765C2×Q16—112no—
766C2×SD16—111no—
767C2×SD16—111no—
768C2×SD16—112no—
769C2×SD16—112no—
770C2×SD16—112no—
771C2×SD16—112no—
772C2×SD16—112no—
773C2×D8—112no—
774C2×D8—112no—
775C2×D8—112no—
776C2×M16—112no—
777C2×M16—112no—
778C22×C8—112no—
779C22×C8—112no—
780C4⋊Q8—111no—
781C4⋊Q8—221no—
782C4⋊Q8C22×D1111yescharacteristic
783C4⋊Q8C22×D1111yescharacteristic
784C4⋊Q8C22×D1111yescharacteristic
785#127—21no—
786#127—21no—
787#127—111no—
788#127—221no—
789#127C22×D1111yescharacteristic
790#126—22no—
791#126—22no—
792#125—21no—
793#124—21no—
794#124—21no—
795#124—22no—
796#124—22no—
797#124—21no—
798#124—112no—
799#124—222no—
800#123—22no—
801#123—22no—
802#123—22no—
803#123—22no—
804#123—222no—
805#123—222no—
806#123—222no—
807C22⋊Q8—21no—
808C22⋊Q8—112no—
809C22⋊Q8—112no—
810C22⋊Q8—222no—
811C22⋊Q8—222no—
812C22⋊Q8C22×D1111yescharacteristic
813C22⋊Q8C22×D1111yescharacteristic
814C22⋊Q8C22×D1112yes—
815C22⋊Q8C22×D1112yes—
816#121—22no—
817#121—22no—
818#121—21no—
819#121—22no—
820#121—22no—
821#121—112no—
822#121—112no—
823#121—222no—
824#121—221no—
825#121—221no—
826#121—221no—
827#121—221no—
828#121—222no—
829#121—222no—
830#121C22×D1112yes—
831#121C22×D1112yes—
832#121C22×D1112yes—
833#120—22no—
834#120—22no—
835#120—222no—
836#120—222no—
837#120—222no—
838C4×Q8—21no—
839C4×Q8—21no—
840C4×Q8—21no—
841C4×Q8—111no—
842C4×Q8—111no—
843C4×Q8C22×D1111yescharacteristic
844C4×Q8C22×D1111yescharacteristic
845C4×D4—22no—
846C4×D4—22no—
847C4×D4—22no—
848C4×D4—22no—
849C4×D4—21no—
850C4×D4—21no—
851C4×D4—21no—
852C4×D4—111no—
853C4×D4—111no—
854C4×D4—221no—
855C4×D4—222no—
856C4×D4—221no—
857C4×D4—221no—
858C4×D4—222no—
859C4×D4—221no—
860C4×D4—222no—
861C4×D4—221no—
862C4×D4—221no—
863C4×D4C22⋊D1111yescharacteristic
864C4×D4C22⋊D1112yes—
865C4×D4C22⋊D1111yescharacteristic
866C4×D4C22×D1112yes—
867C4×D4C22×D1111yescharacteristic
868C4×D4C22×D1112yes—
869C4×D4C22×D1111yescharacteristic
870#117—21no—
871#117—22no—
872#117—111no—
873#117—221no—
874#117C22×D1112yes—
875#117C22×D1112yes—
876C2×C4⋊C4—22no—
877C2×C4⋊C4—221no—
878C2×C4⋊C4C22⋊D1111yescharacteristic
879C2×C22⋊C4—222no—
880C2×C22⋊C4C22⋊D1112yes—
881C2×C42—221no—
882C2×C42C22×D1111yescharacteristic
883#107—111no—
884#107—111no—
885#107—112no—
886#106—111no—
887#106—111no—
888#106—112no—
889C4⋊C8—111no—
890C4⋊C8—111no—
891C4⋊C8—111no—
892C4⋊C8—111no—
893#103—111no—
894#103—111no—
895#103—111no—
896#103—111no—
897#103—111no—
898#103—112no—
899#103—112no—
900#103—112no—
901#103—111no—
902#103—112no—
903#103—112no—
904#102—112no—
905#102—112no—
906#102—111no—
907#102—112no—
908#102—112no—
909#102—112no—
910#102—111no—
911#102—112no—
912#102—112no—
913C22⋊C8—111no—
914C22⋊C8—112no—
915C22⋊C8—112no—
916C22⋊C8—112no—
917C22⋊C8—111no—
918C22⋊C8—112no—
919C22⋊C8—112no—
920#97—112no—
921C4×C8—111no—
922C4×C8—111no—
923C2×C11—42no—
924C2×C11—42no—
925C2×C11—41no—
926C2×C11—82no—
927C2×C11#348411yescharacteristic
928C2×C11C2×#57511yescharacteristic
929C2×C11#358411yescharacteristic
930D11—42no—
931D11—82no—
932C24—222no—
933C24C2×C22⋊D1112yes—
934#41—44no—
935#41—42no—
936#41—42no—
937#41—42no—
938#41—42no—
939#41—222no—
940#41—222no—
941#41—224no—
942#41—224no—
943#41—442no—
944#41—442no—
945#41—442no—
946#41—442no—
947#41—448no—
948#41—448no—
949C2×Q8—21no—
950C2×Q8—21no—
951C2×Q8—111no—
952C2×Q8—112no—
953C2×Q8—224no—
954C2×Q8—222no—
955C2×Q8—442no—
956C2×Q8C23×D1111yescharacteristic
957C2×Q8C23×D1111yescharacteristic
958C2×D4—22no—
959C2×D4—22no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—22no—
963C2×D4—21no—
964C2×D4—21no—
965C2×D4—42no—
966C2×D4—111no—
967C2×D4—112no—
968C2×D4—224no—
969C2×D4—221no—
970C2×D4—222no—
971C2×D4—222no—
972C2×D4—222no—
973C2×D4—222no—
974C2×D4—222no—
975C2×D4—221no—
976C2×D4—222no—
977C2×D4—221no—
978C2×D4—442no—
979C2×D4—444no—
980C2×D4—448no—
981C2×D4C2×C22⋊D1111yescharacteristic
982C2×D4C2×C22⋊D1111yescharacteristic
983C2×D4C2×C22⋊D1112yes—
984C2×D4C23×D1112yes—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—22no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—221no—
991C22×C4—222no—
992C22×C4—221no—
993C22×C4—222no—
994C22×C4—222no—
995C22×C4—222no—
996C22×C4—221no—
997C22×C4—448no—
998C22×C4C2×C22⋊D1111yescharacteristic
999C22×C4C2×C22⋊D1111yescharacteristic
1000C22×C4C2×C22⋊D1112yes—
1001C22×C4C2×C22⋊D1112yes—
1002C22×C4C2×C22⋊D1112yes—
1003C22×C4C23×D1111yescharacteristic
1004C22×C4C23×D1112yes—
1005C22×C4C23×D1112yes—
1006Q16—222no—
1007Q16—222no—
1008Q16—442no—
1009Q16—442no—
1010SD16—224no—
1011SD16—222no—
1012SD16—222no—
1013SD16—442no—
1014SD16—442no—
1015SD16—442no—
1016SD16—442no—
1017D8—224no—
1018D8—442no—
1019D8—442no—
1020M16—442no—
1021M16—442no—
1022C2×C8—111no—
1023C2×C8—111no—
1024C2×C8—111no—
1025C2×C8—111no—
1026C2×C8—112no—
1027C2×C8—112no—
1028C2×C8—442no—
1029C2×C8—442no—
1030C4⋊C4—21no—
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—111no—
1041C4⋊C4—111no—
1042C4⋊C4—221no—
1043C4⋊C4—222no—
1044C4⋊C4—221no—
1045C4⋊C4—221no—
1046C4⋊C4—222no—
1047C4⋊C4—221no—
1048C4⋊C4C2×C22⋊D1112yes—
1049C4⋊C4C2×C22⋊D1111yescharacteristic
1050C4⋊C4C2×C22⋊D1111yescharacteristic
1051C4⋊C4C23×D1112yes—
1052C4⋊C4C23×D1111yescharacteristic
1053C4⋊C4C23×D1111yescharacteristic
1054C22⋊C4—21no—
1055C22⋊C4—21no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—222no—
1065C22⋊C4—221no—
1066C22⋊C4—222no—
1067C22⋊C4—222no—
1068C22⋊C4—222no—
1069C22⋊C4—221no—
1070C22⋊C4—221no—
1071C22⋊C4—222no—
1072C22⋊C4—222no—
1073C22⋊C4C2×C22⋊D1112yes—
1074C22⋊C4C2×C22⋊D1112yes—
1075C22⋊C4C2×C22⋊D1112yes—
1076C22⋊C4C2×C22⋊D1112yes—
1077C42—22no—
1078C42—22no—
1079C42—21no—
1080C42—21no—
1081C42—221no—
1082C42—221no—
1083C42—221no—
1084C42C2×C22⋊D1111yescharacteristic
1085C42C2×C22⋊D1111yescharacteristic
1086C42C23×D1111yescharacteristic
1087C42C23×D1111yescharacteristic
1088C11#6160811yescharacteristic, complemented, Sylow
1089C23—22no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—221no—
1094C23—222no—
1095C23—444no—
1096C23—444no—
1097C23—882no—
1098C23C22×C22⋊D1112yes—
1099C23C22×C22⋊D1112yes—
1100C23C22×C22⋊D1111yescharacteristic
1101Q8—21no—
1102Q8—21no—
1103Q8—21no—
1104Q8—21no—
1105Q8—42no—
1106Q8—81no—
1107Q8—112no—
1108Q8—221no—
1109Q8—222no—
1110Q8—222no—
1111Q8—444no—
1112D4—22no—
1113D4—22no—
1114D4—22no—
1115D4—22no—
1116D4—42no—
1117D4—44no—
1118D4—42no—
1119D4—81no—
1120D4—82no—
1121D4—82no—
1122D4—82no—
1123D4—82no—
1124D4—112no—
1125D4—224no—
1126D4—221no—
1127D4—222no—
1128D4—222no—
1129D4—444no—
1130D4—444no—
1131D4—444no—
1132D4—444no—
1133D4—444no—
1134D4—442no—
1135D4—881no—
1136D4—882no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—44no—
1154C2×C4—82no—
1155C2×C4—82no—
1156C2×C4—224no—
1157C2×C4—221no—
1158C2×C4—221no—
1159C2×C4—221no—
1160C2×C4—222no—
1161C2×C4—444no—
1162C2×C4—444no—
1163C2×C4—444no—
1164C2×C4—444no—
1165C2×C4—442no—
1166C2×C4—881no—
1167C2×C4C22×C22⋊D1112yes—
1168C2×C4C22×C22⋊D1112yes—
1169C2×C4C22×C22⋊D1111yescharacteristic
1170C2×C4C22×C22⋊D1111yescharacteristic
1171C2×C4C22×C22⋊D1111yescharacteristic
1172C2×C4C22×C22⋊D1111yescharacteristic
1173C2×C4C22×C22⋊D1111yescharacteristic
1174C2×C4C24×D1111yescharacteristic
1175C8—221no—
1176C8—221no—
1177C8—222no—
1178C8—222no—
1179C8—221no—
1180C8—221no—
1181C22—21no—
1182C22—22no—
1183C22—22no—
1184C22—21no—
1185C22—22no—
1186C22—22no—
1187C22—21no—
1188C22—22no—
1189C22—22no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—84no—
1194C22—222no—
1195C22—441no—
1196C22—441no—
1197C22—442no—
1198C22—442no—
1199C22—442no—
1200C22—888no—
1201C22C23×C22⋊D1111yescharacteristic
1202C4—21no—
1203C4—22no—
1204C4—22no—
1205C4—21no—
1206C4—21no—
1207C4—21no—
1208C4—41no—
1209C4—41no—
1210C4—42no—
1211C4—41no—
1212C4—41no—
1213C4—222no—
1214C4—442no—
1215C4—441no—
1216C4—441no—
1217C4#1062335312yes—
1218C4D11×H(5,𝔽2)11yescharacteristic
1219C4D11×H(5,𝔽2)11yescharacteristic
1220C2—41no—
1221C2—42no—
1222C2—42no—
1223C2—82no—
1224C2—442no—
1225C2—882no—
1226C2#1308224711yescharacteristic
1227C2C2×#1062335311yescharacteristic
1228C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3506C2
socleC22×C11C23×D4
hypercenter#3506D11
hypocenterC11#61608
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. D4×#4339C2semidirect
2. #13080893C2semidirect
3. #13080841C2semidirect
4. #13080796C2semidirect
5. #13080766C2semidirect
6. #13080549C2semidirect
7. #13080527C2semidirect
8. #13080372C2semidirect
9. #13080346C2semidirect
10. #13080282C2semidirect
11. #13080236C2semidirect
12. #13080167C2semidirect
13. #13080142C2semidirect
14. #13079623C2semidirect
15. #13079545C2semidirect
16. #13079453C2semidirect
17. #13079404C2semidirect
18. #13078761C2semidirect
19. #13078681C2semidirect
20. #13077856C2semidirect
21. #13077832C2semidirect
22. #13077651C2semidirect
23. C11×#3506C2semidirect
28. C11×#556C22semidirect
29. C11×#555C22semidirect
32. C11×#550C22semidirect
33. C11×#547C22semidirect
36. C11×#533C22semidirect
37. C11×#532C22semidirect
38. C11×#525C22semidirect
39. C11×#525C22semidirect
42. C2×#67004C22semidirect
43. C2×#67003C22semidirect
44. C2×#67003C22semidirect
45. C2×#67002C22semidirect
61. #10622852C22semidirect
62. #10622852C22semidirect
63. #10622851C22semidirect
64. #10622851C22semidirect
65. #10622820C22semidirect
66. C2×C22⋊(C11⋊C8)C22semidirect
67. #10622707C22semidirect
68. #10622707C22semidirect
69. #10622706C22semidirect
70. #10622703C22semidirect
71. #10622702C22semidirect
72. #10622701C22semidirect
73. #10622700C22semidirect
74. #10622700C22semidirect
75. #10622699C22semidirect
76. #10622696C22semidirect
77. #10622689C22semidirect
78. #10622688C22semidirect
79. #10622686C22semidirect
80. #10622685C22semidirect
81. #10622665C22semidirect
82. #10622664C22semidirect
83. #10622663C22semidirect
84. #10622662C22semidirect
85. #10622661C22semidirect
88. #10622660C22semidirect
89. #10622660C22semidirect
90. #10622660C22semidirect
91. #10622660C22semidirect
92. #10622659C22semidirect
93. #10622658C22semidirect
94. #10622658C22semidirect
95. #10622655C22semidirect
96. #10622654C22semidirect
97. #10622653C22semidirect
98. #10622652C22semidirect
99. #10622651C22semidirect
101. #10622650C22semidirect
102. #10622650C22semidirect
103. #10622650C22semidirect
104. #10622650C22semidirect
105. #10622649C22semidirect
106. #10622648C22semidirect
107. #10622644C22semidirect
108. #10622644C22semidirect
109. C4×#4326C22semidirect
110. C4×#4326C22semidirect
111. #10622640C22semidirect
112. #10622640C22semidirect
113. C4×#4325C22semidirect
114. C4×#4325C22semidirect
115. #10622631C22semidirect
116. #10622629C22semidirect
117. #10622629C22semidirect
118. #10622627C22semidirect
121. #10622624C22semidirect
122. #10622624C22semidirect
123. D4×C11⋊C8C22semidirect
124. D4×C11⋊C8C22semidirect
125. #10622617C22semidirect
126. #10622616C22semidirect
127. #10622616C22semidirect
128. #10622615C22semidirect
129. #10622615C22semidirect
130. #10622614C22semidirect
131. #10622609C22semidirect
132. #10622609C22semidirect
133. #10622539C22semidirect
134. #10622538C22semidirect
475. #3506D11semidirect
598. #556C2×D11semidirect
599. #555C2×D11semidirect
603. #550C2×D11semidirect
608. #547C2×D11semidirect
615. #533C2×D11semidirect
618. #532C2×D11semidirect
621. #525C2×D11semidirect
622. #525C2×D11semidirect
1088. C11#61608semidirect

Maximal subgroups

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

subgroupindex
D4×#43392
#130808932
#130808412
#130807962
#130807662
#130805492
#130805272
#130803722
#130803462
#130802822
#130802362
#130801672
#130801422
#130796232
#130795452
#130794532
#130794042
#130787612
#130786812
#130778562
#130778322
#130776512
C11×#35062
#6160811