Finite Group Databasebeta

← #15624701

Subgroups — #15624701

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#13082288C211yesmaximal, characteristic, complemented
2#13081949C211yesmaximal, characteristic, complemented
3#13079529C212yesmaximal, complemented
4#13079516C212yesmaximal, complemented
5#13079505C212yesmaximal, complemented
6#13079503C212yesmaximal, complemented
7#13079456C212yesmaximal, complemented
8#13079450C212yesmaximal, complemented
9#13079407C212yesmaximal, complemented
10#13079401C212yesmaximal, complemented
11#13078588C211yesmaximal, characteristic, complemented
12#13078577C211yesmaximal, characteristic, complemented
13#13078564C211yesmaximal, characteristic, complemented
14#13078310C211yesmaximal, characteristic, complemented
15#13078299C211yesmaximal, characteristic, complemented
16#13078272C211yesmaximal, characteristic, complemented
17#13078256C211yesmaximal, characteristic, complemented
18#13077914C211yesmaximal, characteristic, complemented
19#13077905C211yesmaximal, characteristic, complemented
20#13077856C211yesmaximal, characteristic, complemented
21C2×#10622346C211yesmaximal, characteristic, complemented
22#13077062C211yesmaximal, characteristic, complemented
23C11×#3091C211yesmaximal, characteristic, complemented
24C2×#67043C2211yescharacteristic
25C22×#4339C2211yescharacteristic
26C22×#4339C2211yescharacteristic
27C11×#525C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29#10623364C2211yescharacteristic
30C2×#67004C2211yescharacteristic, complemented
31C2×#67002C2211yescharacteristic, complemented
32C2×#66977C2211yescharacteristic
33C22×Dic44C2211yescharacteristic, complemented
34C22×#4314C2211yescharacteristic, complemented
35C2×#66954C2211yescharacteristic
36C2×#66954C2211yescharacteristic
37#10623186—22no—
38#10623159C2212yescomplemented
39D11×C22⋊Q8C2212yescomplemented
40#10623139C2212yescomplemented
41#10623137C2212yescomplemented
42#10623122—22no—
43#10623083—21no—
44#10623082—21no—
45#10623081—21no—
46D4×Dic22—21no—
47#10623057—21no—
48#10623057C2211yescharacteristic
49#10623057C2211yescharacteristic
50#10623057C2211yescharacteristic
51#10623056—21no—
52#10623056C2211yescharacteristic
53#10623056C2211yescharacteristic
54#10623055—22no—
55#10623055C2212yes—
56#10623055C2212yes—
57#10623054C2211yescharacteristic
58#10623041C2212yes—
59#10623041C2212yes—
60#10623024—22no—
61#10623008—21no—
62#10623008—21no—
63C11×#485C2211yescharacteristic, complemented
64C11×#485C2211yescharacteristic, complemented
65C11×#484C2211yescharacteristic, complemented
66C11×#483C2211yescharacteristic, complemented
67C11×#482C2211yescharacteristic, complemented
68C11×#482C2211yescharacteristic, complemented
69C11×#481C2211yescharacteristic, complemented
70C11×#480C2211yescharacteristic, complemented
71C11×#427C2211yescharacteristic, complemented
72C11×#427C2211yescharacteristic, complemented
73C11×#416C2211yescharacteristic, complemented
74C11×#416C2211yescharacteristic, complemented
75C2×C11×C22⋊C8C2211yescharacteristic
76#10622820C2211yescharacteristic
77C2×#66885C2211yescharacteristic, complemented
78#10622723C2211yescharacteristic
79#10622723C2211yescharacteristic
80C2×#66880C2211yescharacteristic, complemented
81#10622660C2212yes—
82#10622660C2212yescomplemented
83#10622650C2212yes—
84#10622650C2212yescomplemented
85#10622617C2211yescharacteristic, complemented
86#10622617C2211yescharacteristic, complemented
87#10622617C2211yescharacteristic, complemented
88#10622614C2211yescharacteristic, complemented
89#10622609C2212yescomplemented
90#10622609C2212yescomplemented
91#10622608C2211yescharacteristic, complemented
92#10622608C2211yescharacteristic, complemented
93#10622584C2212yescomplemented
94#10622583C2212yescomplemented
95#10622501C2212yescomplemented
96#10622500C2212yescomplemented
97#10622500C2212yescomplemented
98#10622499C2212yescomplemented
99#10622499C2212yescomplemented
100#10622498C2212yescomplemented
101#10622497C2212yescomplemented
102#10622495C2212yescomplemented
103#10622481C2212yescomplemented
104#10622481C2212yescomplemented
105#10622480C2212yescomplemented
106#10622479C2212yescomplemented
107#10622477C2212yescomplemented
108#10622477C2212yescomplemented
109#10622476C2212yescomplemented
110#10622475C2212yescomplemented
111#10622429C2212yescomplemented
112#10622426C2212yescomplemented
113#10622425C2212yescomplemented
114#10622421C2212yescomplemented
115#10622421C2212yescomplemented
116#10622420C2212yescomplemented
117#10622419C2212yescomplemented
118#10622419C2212yescomplemented
119#10622396C2212yescomplemented
120#10622396C2212yescomplemented
121#10622395C2212yescomplemented
122#10622394C2212yescomplemented
123#10622394C2212yescomplemented
124#10622393C2212yescomplemented
125#10622391C2212yescomplemented
126#10622388C2212yescomplemented
127#10622346C2212yes—
128#10622346C2212yes—
129#10622346C2212yescomplemented
130#10622346C2212yescomplemented
131#10622340C2212yescomplemented
132#10622340C2212yescomplemented
133#10622339C2212yescomplemented
134D11×C22⋊C8C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C22×C22⋊D11—21no—
138C22×C22⋊D11D412yes—
139#67043—42no—
140#67043—42no—
141C2×Q8×D11C2312yes—
142C2×#4341—22no—
143C2×#4341C2312yes—
144C2×#4339—21no—
145C2×#4339—21no—
146C2×#4339—21no—
147C2×#4339—42no—
148C2×#4339—42no—
149C2×#4339—42no—
150C2×#4339—42no—
151C2×#4339D411yescharacteristic
152C2×#4339D411yescharacteristic
153C2×#4339D412yes—
154C2×#4339C2311yescharacteristic
155C2×#4339C2311yescharacteristic
156C2×#4339C2312yes—
157C2×#4339C2312yes—
158C2×#4339C2312yes—
159C22×D44D411yescharacteristic
160C22×D44C2311yescharacteristic
161C22×C4×D11—21no—
162C22×C4×D11C2312yes—
163C22×Dic22—21no—
164C22×Dic22D411yescharacteristic
165C22×Dic22C2311yescharacteristic
166C22×Dic22C2311yescharacteristic
167C22×C8×C11C2311yescharacteristic
168C22×C8×C11C2311yescharacteristic
169C11×#123—21no—
170C11×C22⋊Q8C2311yescharacteristic
171C11×C22⋊Q8C2311yescharacteristic
172C11×#121C2311yescharacteristic
173C11×#121C2311yescharacteristic
174C11×#120—21no—
175C4×D4×C11—21no—
176C4×D4×C11—21no—
177C11×#117—21no—
178C11×#117—21no—
179C11×#117C2311yescharacteristic
180C11×#117C2311yescharacteristic
181C11×#117C2311yescharacteristic
182C11×#117C2311yescharacteristic
183C11×#117C2311yescharacteristic
184C2×C11×C4⋊C4C2311yescharacteristic
185C2×C11×C4⋊C4C2311yescharacteristic
186C2×C11×C22⋊C4—21no—
187C2×C42×C11—21no—
188C2×C22⋊Dic11—21no—
189#67004—42no—
190#67002—42no—
191#66999C2312yes—
192C2×#4326C2312yes—
193C2×#4325C2312yes—
194#66992—22no—
195#66992—22no—
196#66991—22no—
197#66991C2312yes—
198#66990—22no—
199D4×Dic11—22no—
200C2×#4324C2312yes—
201C2×#4323C2312yes—
202#66983—22no—
203#66983—22no—
204#66983—22no—
205#66983—22no—
206#66983—21no—
207C2×C4⋊Dic11C2311yescharacteristic
208#66977—21no—
209#66977—21no—
210#66977—21no—
211#66977C2312yes—
212#66977C2312yes—
213C2×Dic11⋊C4—21no—
214C2×#4318C2311yescharacteristic
215C2×#4318C2311yescharacteristic
216C2×Dic44—42no—
217C2×Dic44C2312yes—
218C2×Dic44C2312yes—
219C2×#4314—42no—
220C2×#4314C2312yes—
221C2×#4314C2312yes—
222#66954—42no—
223#66954—42no—
224C2×#4313C2312yes—
225C2×#4313C2312yes—
226C2×C8×D11C2312yes—
227C2×C8×D11C2312yes—
228#66950—22no—
229#66950—22no—
230#66950C2312yes—
231#66950C2312yes—
232#66950C2312yes—
233#66950C2312yes—
234#66950C2312yes—
235#66950C2312yes—
236#66949—22no—
237#66948—22no—
238#66948—22no—
239#66948C2312yes—
240#66948C2312yes—
241#66948C2312yes—
242#66948C2312yes—
243#66947—22no—
244#66945C2312yes—
245C4⋊C4×D11—22no—
246C4⋊C4×D11C2312yes—
247#66941—22no—
248#66939—22no—
249#66939—22no—
250#66939—22no—
251#66939—22no—
252#66939—22no—
253#66938—22no—
254#66937—22no—
255#66936—22no—
256#66936—22no—
257#66935—22no—
258#66935—22no—
259#66935—22no—
260#66935—22no—
261(C22⋊D11)⋊C4—22no—
262(C22⋊D11)⋊C4—22no—
263C22⋊C4×D11—22no—
264#66931—22no—
265#66931—22no—
266#66928—21no—
267#66928—21no—
268#66928—21no—
269#66928—21no—
270#66928—21no—
271#66927—21no—
272#66927—21no—
273C4×D44—21no—
274C4×D44—22no—
275C4×D44—22no—
276C4×D44—22no—
277C4×D44—22no—
278#66922—21no—
279#66922—21no—
280#66922—21no—
281C4×Dic22—21no—
282C11×#107C2311yescharacteristic
283C11×#107C2311yescharacteristic
284C11×#107C2311yescharacteristic
285C11×#107C2311yescharacteristic
286C11×#106C2311yescharacteristic
287C11×#106C2311yescharacteristic
288C11×#106C2311yescharacteristic
289C11×#106C2311yescharacteristic
290C11×#103C2311yescharacteristic
291C11×#103C2311yescharacteristic
292C11×#103C2311yescharacteristic
293C11×#103C2311yescharacteristic
294C11×#102C2311yescharacteristic
295C11×#102C2311yescharacteristic
296C11×#102C2311yescharacteristic
297C11×#102C2311yescharacteristic
298C11×C22⋊C8C2311yescharacteristic
299C11×C22⋊C8C2311yescharacteristic
300C11×C22⋊C8C2311yescharacteristic
301C11×C22⋊C8C2311yescharacteristic
302C22⋊(C11⋊C8)C2312yes—
303C22⋊(C11⋊C8)C2312yes—
304#66885C2312yes—
305#66885C2312yes—
306(C2×D11)⋊C8C2312yes—
307(C2×D11)⋊C8C2312yes—
308(C2×D11)⋊C8C2312yes—
309(C2×D11)⋊C8C2312yes—
310#66880C2312yes—
311#66880C2312yes—
312#66874C2312yes—
313#66874C2312yes—
314#66874C2312yes—
315#66874C2312yes—
316#66874C2312yes—
317#66874C2312yes—
318#66873C2312yes—
319#66873C2312yes—
320#66872C2312yes—
321#66872C2312yes—
322#66871C2312yes—
323#66871C2312yes—
324#60761—111nomaximal, Sylow
325C24×C11C2×D411yescharacteristic
326C23×D11—21no—
327C23×D11C2×D412yes—
328C11×#41—22no—
329C11×#41—22no—
330C2×Q8×C11C2411yescharacteristic
331C2×D4×C11—21no—
332C2×D4×C11—21no—
333C2×D4×C11—21no—
334C2×D4×C11C2411yescharacteristic
335C22×C4×C11—22no—
336C22×C4×C11—22no—
337C22×C4×C11—21no—
338C22×C4×C11—21no—
339C22×C4×C11—21no—
340C22×C4×C11C2×D411yescharacteristic
341C22×C4×C11C2×D411yescharacteristic
342C22×C4×C11C2×D411yescharacteristic
343C22×C4×C11C2411yescharacteristic
344C22×C4×C11C2411yescharacteristic
345C22×C4×C11C2411yescharacteristic
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—22no—
350C2×C22⋊D11—44no—
351C2×C22⋊D11—44no—
352C2×C22⋊D11C2×D412yes—
353C2×C22⋊D11C2×D412yes—
354C2×C22⋊D11C2×D412yes—
355C2×C22⋊D11C2×D412yes—
356C22×Dic11—22no—
357C22×Dic11—21no—
358C22×Dic11—21no—
359C22×Dic11—21no—
360C22×Dic11C2×D412yes—
361Q8×D11—42no—
362Q8×D11—42no—
363#4341—42no—
364#4341—42no—
365#4341—48no—
366#4339—22no—
367#4339—22no—
368#4339—22no—
369#4339—22no—
370#4339—42no—
371#4339—42no—
372#4339—42no—
373#4339—42no—
374#4339—42no—
375#4339—42no—
376#4339—42no—
377#4339—42no—
378#4339—44no—
379#4339—44no—
380#4339—44no—
381#4339—44no—
382C2×D44—22no—
383C2×D44—22no—
384C2×D44—22no—
385C2×D44—22no—
386C2×D44—21no—
387C2×D44—22no—
388C2×D44—22no—
389C2×D44—42no—
390C2×D44C2×D411yescharacteristic
391C2×D44C2×D411yescharacteristic
392C2×D44C2×D412yes—
393C2×D44C2412yes—
394C2×C4×D11—22no—
395C2×C4×D11—22no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—42no—
399C2×C4×D11—42no—
400C2×C4×D11—44no—
401C2×C4×D11C2×D412yes—
402C2×C4×D11C2×D412yes—
403C2×C4×D11C2412yes—
404C2×C4×D11C2412yes—
405C2×Dic22—22no—
406C2×Dic22—21no—
407C2×Dic22—21no—
408C2×Dic22—22no—
409C2×Dic22—22no—
410C2×Dic22—22no—
411C2×Dic22—22no—
412C2×Dic22—42no—
413C2×Dic22—44no—
414C2×Dic22C2×D411yescharacteristic
415C2×Dic22C2×D411yescharacteristic
416C2×Dic22C2×D412yes—
417C2×Dic22C2412yes—
418C2×Dic22C2412yes—
419C2×C8×C11—22no—
420C2×C8×C11—22no—
421C2×C8×C11C2411yescharacteristic
422C2×C8×C11C2411yescharacteristic
423C2×C8×C11C2411yescharacteristic
424C2×C8×C11C2411yescharacteristic
425C11×C4⋊C4—21no—
426C11×C4⋊C4—21no—
427C11×C4⋊C4—21no—
428C11×C4⋊C4—21no—
429C11×C4⋊C4C2411yescharacteristic
430C11×C4⋊C4C2411yescharacteristic
431C11×C4⋊C4C2411yescharacteristic
432C11×C4⋊C4C2411yescharacteristic
433C11×C4⋊C4C2411yescharacteristic
434C11×C4⋊C4C2411yescharacteristic
435C11×C22⋊C4—21no—
436C11×C22⋊C4—21no—
437C11×C22⋊C4—21no—
438C11×C22⋊C4—21no—
439C11×C22⋊C4—21no—
440C11×C22⋊C4—21no—
441C11×C22⋊C4—21no—
442C11×C22⋊C4—21no—
443C11×C22⋊C4—21no—
444C42×C11—21no—
445C42×C11—21no—
446C42×C11—21no—
447C42×C11—21no—
448C42×C11—21no—
449C22⋊Dic11—22no—
450C22⋊Dic11—22no—
451C22⋊Dic11—22no—
452#4326—42no—
453#4325—42no—
454#4324—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—22no—
468C4⋊Dic11—22no—
469C4⋊Dic11—22no—
470C4⋊Dic11—22no—
471C4⋊Dic11—22no—
472C4⋊Dic11—22no—
473C4⋊Dic11—22no—
474C4⋊Dic11—21no—
475C4⋊Dic11C2412yes—
476Dic11⋊C4—22no—
477Dic11⋊C4—22no—
478Dic11⋊C4—22no—
479Dic11⋊C4—22no—
480C4×Dic11—22no—
481#4318—22no—
482#4318—22no—
483C2×C11⋊C8C2412yes—
484C2×C11⋊C8C2412yes—
485Dic44—42no—
486Dic44—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#3095—111no—
506#3091D1111yescharacteristic, complemented
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—21no—
518C23×C11—41no—
519C23×C11—41no—
520C23×C11C22×D411yescharacteristic
521C23×C11C22×D411yescharacteristic
522C23×C11C22×D411yescharacteristic
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—21no—
533Q8×C11—21no—
534D4×C11—21no—
535D4×C11—21no—
536D4×C11—42no—
537D4×C11—42no—
538D4×C11—81no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—21no—
543C2×C4×C11—21no—
544C2×C4×C11—21no—
545C2×C4×C11—21no—
546C2×C4×C11—21no—
547C2×C4×C11—21no—
548C2×C4×C11—21no—
549C2×C4×C11—21no—
550C2×C4×C11—21no—
551C2×C4×C11—21no—
552C2×C4×C11—21no—
553C2×C4×C11—42no—
554C2×C4×C11—81no—
555C2×C4×C11—81no—
556C2×C4×C11C22×D411yescharacteristic
557C2×C4×C11C22×D411yescharacteristic
558C2×C4×C11C22×D411yescharacteristic
559C2×C4×C11H(5,𝔽2)12yes—
560C2×C4×C11H(5,𝔽2)12yes—
561C2×C4×C11C2511yescharacteristic
562C22⋊D11—24no—
563C22⋊D11—24no—
564C22⋊D11—42no—
565C22⋊D11—42no—
566C22⋊D11—44no—
567C22⋊D11—44no—
568C22⋊D11—44no—
569C22⋊D11—82no—
570C2×Dic11—22no—
571C2×Dic11—22no—
572C2×Dic11—22no—
573C2×Dic11—42no—
574C2×Dic11—44no—
575C2×Dic11—42no—
576C2×Dic11—42no—
577C2×Dic11—81no—
578C2×Dic11C22×D412yes—
579C2×Dic11C22×D412yes—
580D44—22no—
581D44—22no—
582D44—22no—
583D44—22no—
584D44—42no—
585D44—42no—
586D44—82no—
587D44—82no—
588D44—82no—
589D44—82no—
590C4×D11—22no—
591C4×D11—22no—
592C4×D11—22no—
593C4×D11—22no—
594C4×D11—42no—
595C4×D11—42no—
596C4×D11—44no—
597C4×D11—44no—
598C4×D11—44no—
599C4×D11—82no—
600Dic22—22no—
601Dic22—22no—
602Dic22—22no—
603Dic22—22no—
604Dic22—22no—
605Dic22—22no—
606Dic22—42no—
607Dic22—44no—
608Dic22—42no—
609Dic22—42no—
610C8×C11—21no—
611C8×C11—21no—
612C8×C11—21no—
613C8×C11—21no—
614C11⋊C8—22no—
615C11⋊C8—22no—
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—221no—
628#547—222no—
629#546—221no—
630#546—222no—
631#537—111no—
632#537—112no—
633#537—112no—
634#537—112no—
635#536—112no—
636#536—111no—
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—112no—
647#525—112no—
648#525—112no—
649#525—222no—
650#525C2×D1111yescharacteristic
651C2×C22⋊Q8—111no—
652C2×C22⋊Q8—112no—
653#520—111no—
654C2×#117C2×D1111yescharacteristic
655#485—112no—
656#485—112no—
657#485—112no—
658#485—112no—
659#485C2×D1111yescharacteristic, complemented
660#485C2×D1111yescharacteristic, complemented
661#484—112no—
662#484—112no—
663#484C2×D1111yescharacteristic, complemented
664#483—112no—
665#483—112no—
666#483C2×D1111yescharacteristic, complemented
667#482—112no—
668#482—112no—
669#482C2×D1111yescharacteristic, complemented
670#482C2×D1111yescharacteristic, complemented
671#481—112no—
672#481C2×D1111yescharacteristic, complemented
673#480—112no—
674#480C2×D1111yescharacteristic, complemented
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#428—111no—
708#428—111no—
709#427C2×D1111yescharacteristic, complemented
710#427C2×D1111yescharacteristic, complemented
711#419—111no—
712#419—111no—
713#419—111no—
714#418—111no—
715#416C2×D1111yescharacteristic, complemented
716#416C2×D1111yescharacteristic, complemented
717C2×#103—111no—
718C2×#102—111no—
719#408—111no—
720#408—111no—
721#408—112no—
722#408—112no—
723#407—111no—
724#407—112no—
725C2×C22⋊C8—112no—
726C2×C22⋊C8C2×D1111yescharacteristic
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—41no—
736C22×C11—41no—
737C22×C11—41no—
738C22×C11—82no—
739C22×C11#53412yes—
740C22×C11C23×D411yescharacteristic
741C2×D11—22no—
742C2×D11—22no—
743C2×D11—22no—
744C2×D11—22no—
745C2×D11—22no—
746C2×D11—22no—
747C2×D11—42no—
748C2×D11—42no—
749C2×D11—42no—
750C2×D11—84no—
751C2×D11—84no—
752C4×C11—21no—
753C4×C11—21no—
754C4×C11—41no—
755C4×C11—41no—
756C4×C11—41no—
757C4×C11—41no—
758C4×C11—41no—
759C4×C11—41no—
760C4×C11—41no—
761C4×C11#53412yes—
762C4×C11C2×H(5,𝔽2)11yescharacteristic
763C4×C11C2×H(5,𝔽2)11yescharacteristic
764Dic11—22no—
765Dic11—22no—
766Dic11—42no—
767Dic11—42no—
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—112no—
779C2×#41—112no—
780C2×#41—221no—
781C2×#41—222no—
782C2×#41—221no—
783C2×#41—221no—
784C2×#41—442no—
785C2×#41—442no—
786C2×#41—442no—
787C2×#41—442no—
788C2×#41C22×D1111yescharacteristic
789C22×Q8—111no—
790C22×Q8—112no—
791C22×Q8—111no—
792C22×Q8—111no—
793C22×Q8—221no—
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—111no—
816C2×M16—111no—
817C2×M16—112no—
818C2×M16—112no—
819C22×C8—112no—
820C22×C8—112no—
821C22×C8C22×D1111yescharacteristic
822C22×C8C22×D1111yescharacteristic
823C4⋊Q8—221no—
824C4⋊Q8—221no—
825C4⋊Q8—221no—
826C4⋊Q8—222no—
827#127—221no—
828#127—221no—
829#124—221no—
830#124—221no—
831#124—221no—
832#124—221no—
833#124—221no—
834#124—222no—
835#123—21no—
836#123—222no—
837#123—222no—
838#123—222no—
839#123—222no—
840#123—222no—
841#123—222no—
842#123—222no—
843#123—222no—
844C22⋊Q8—112no—
845C22⋊Q8—112no—
846C22⋊Q8—112no—
847C22⋊Q8—112no—
848C22⋊Q8—112no—
849C22⋊Q8—112no—
850C22⋊Q8—112no—
851C22⋊Q8—112no—
852C22⋊Q8—112no—
853C22⋊Q8—222no—
854C22⋊Q8—222no—
855C22⋊Q8—222no—
856C22⋊Q8—222no—
857C22⋊Q8—222no—
858C22⋊Q8—221no—
859C22⋊Q8—221no—
860C22⋊Q8—221no—
861C22⋊Q8C22×D1111yescharacteristic
862C22⋊Q8C22×D1111yescharacteristic
863#121—112no—
864#121—112no—
865#121—112no—
866#121—112no—
867#121—112no—
868#121—222no—
869#121—222no—
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#121C22×D1111yescharacteristic
880#121C22×D1111yescharacteristic
881#120—21no—
882#120—222no—
883#120—222no—
884#120—222no—
885#120—222no—
886#120—222no—
887C4×Q8—221no—
888C4×D4—21no—
889C4×D4—21no—
890C4×D4—222no—
891C4×D4—222no—
892C4×D4—222no—
893C4×D4—222no—
894C4×D4—221no—
895C4×D4—222no—
896C4×D4—222no—
897C4×D4—222no—
898#117—21no—
899#117—21no—
900#117—112no—
901#117C22×D1111yescharacteristic
902#117C22×D1111yescharacteristic
903#117C22×D1111yescharacteristic
904#117C22×D1111yescharacteristic
905#117C22×D1111yescharacteristic
906C2×C4⋊C4—111no—
907C2×C4⋊C4—112no—
908C2×C4⋊C4—222no—
909C2×C4⋊C4—221no—
910C2×C4⋊C4C22×D1111yescharacteristic
911C2×C4⋊C4C22×D1111yescharacteristic
912C2×C22⋊C4—21no—
913C2×C22⋊C4—222no—
914C2×C22⋊C4—221no—
915C2×C42—21no—
916#107—112no—
917#107—112no—
918#107C22×D1111yescharacteristic
919#107C22×D1111yescharacteristic
920#107C22×D1111yescharacteristic
921#107C22×D1111yescharacteristic
922#106—112no—
923#106—112no—
924#106C22×D1111yescharacteristic
925#106C22×D1111yescharacteristic
926#106C22×D1111yescharacteristic
927#106C22×D1111yescharacteristic
928#103—112no—
929#103—112no—
930#103—112no—
931#103—112no—
932#103—112no—
933#103—112no—
934#103—112no—
935#103—112no—
936#103C22×D1111yescharacteristic
937#103C22×D1111yescharacteristic
938#103C22×D1111yescharacteristic
939#103C22×D1111yescharacteristic
940#102—112no—
941#102—112no—
942#102—112no—
943#102—112no—
944#102C22×D1111yescharacteristic
945#102C22×D1111yescharacteristic
946#102C22×D1111yescharacteristic
947#102C22×D1111yescharacteristic
948C22⋊C8—112no—
949C22⋊C8—112no—
950C22⋊C8—112no—
951C22⋊C8—112no—
952C22⋊C8—112no—
953C22⋊C8—112no—
954C22⋊C8C22×D1111yescharacteristic
955C22⋊C8C22×D1111yescharacteristic
956C22⋊C8C22×D1111yescharacteristic
957C22⋊C8C22×D1111yescharacteristic
958C2×C11—22no—
959C2×C11—41no—
960C2×C11—41no—
961C2×C11—81no—
962C2×C11C2×#53411yescharacteristic
963C2×C11#358411yescharacteristic
964C2×C11#358611yescharacteristic
965D11—42no—
966D11—42no—
967D11—82no—
968C24—112no—
969C24—221no—
970C24D4×D1111yescharacteristic
971#41—22no—
972#41—22no—
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—444no—
989#41—442no—
990#41—442no—
991#41—448no—
992C2×Q8—111no—
993C2×Q8—111no—
994C2×Q8—112no—
995C2×Q8—112no—
996C2×Q8—112no—
997C2×Q8—222no—
998C2×Q8—221no—
999C2×Q8—221no—
1000C2×Q8—222no—
1001C2×Q8—222no—
1002C2×Q8—222no—
1003C2×Q8—222no—
1004C2×Q8—442no—
1005C2×Q8—444no—
1006C2×Q8—442no—
1007C2×Q8—442no—
1008C2×Q8C23×D1111yescharacteristic
1009C2×D4—21no—
1010C2×D4—21no—
1011C2×D4—21no—
1012C2×D4—112no—
1013C2×D4—112no—
1014C2×D4—112no—
1015C2×D4—112no—
1016C2×D4—111no—
1017C2×D4—111no—
1018C2×D4—112no—
1019C2×D4—112no—
1020C2×D4—222no—
1021C2×D4—222no—
1022C2×D4—222no—
1023C2×D4—222no—
1024C2×D4—222no—
1025C2×D4—222no—
1026C2×D4—222no—
1027C2×D4—222no—
1028C2×D4—221no—
1029C2×D4—222no—
1030C2×D4—222no—
1031C2×D4—442no—
1032C2×D4—444no—
1033C2×D4—444no—
1034C2×D4C23×D1111yescharacteristic
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—21no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—112no—
1041C22×C4—112no—
1042C22×C4—112no—
1043C22×C4—112no—
1044C22×C4—112no—
1045C22×C4—222no—
1046C22×C4—222no—
1047C22×C4—222no—
1048C22×C4—221no—
1049C22×C4—221no—
1050C22×C4—221no—
1051C22×C4—222no—
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—222no—
1071M16—222no—
1072M16—442no—
1073M16—442no—
1074C2×C8—22no—
1075C2×C8—22no—
1076C2×C8—112no—
1077C2×C8—112no—
1078C2×C8—442no—
1079C2×C8—442no—
1080C2×C8C23×D1111yescharacteristic
1081C2×C8C23×D1111yescharacteristic
1082C2×C8C23×D1111yescharacteristic
1083C2×C8C23×D1111yescharacteristic
1084C4⋊C4—21no—
1085C4⋊C4—21no—
1086C4⋊C4—21no—
1087C4⋊C4—21no—
1088C4⋊C4—112no—
1089C4⋊C4—222no—
1090C4⋊C4—222no—
1091C4⋊C4—222no—
1092C4⋊C4—222no—
1093C4⋊C4—222no—
1094C4⋊C4—222no—
1095C4⋊C4—222no—
1096C4⋊C4—222no—
1097C4⋊C4—221no—
1098C4⋊C4—222no—
1099C4⋊C4—222no—
1100C4⋊C4C23×D1111yescharacteristic
1101C4⋊C4C23×D1111yescharacteristic
1102C4⋊C4C23×D1111yescharacteristic
1103C4⋊C4C23×D1111yescharacteristic
1104C4⋊C4C23×D1111yescharacteristic
1105C4⋊C4C23×D1111yescharacteristic
1106C22⋊C4—21no—
1107C22⋊C4—21no—
1108C22⋊C4—21no—
1109C22⋊C4—21no—
1110C22⋊C4—21no—
1111C22⋊C4—21no—
1112C22⋊C4—21no—
1113C22⋊C4—21no—
1114C22⋊C4—21no—
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—222no—
1126C22⋊C4—222no—
1127C22⋊C4—222no—
1128C22⋊C4—222no—
1129C22⋊C4—222no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—222no—
1136C11#6076111yescharacteristic, complemented, Sylow
1137C23—22no—
1138C23—21no—
1139C23—41no—
1140C23—41no—
1141C23—112no—
1142C23—112no—
1143C23—222no—
1144C23—442no—
1145C23—442no—
1146C23—442no—
1147C23—442no—
1148C23—881no—
1149C23—881no—
1150C23C2×D4×D1111yescharacteristic
1151C23C2×D4×D1111yescharacteristic
1152C23C2×D4×D1111yescharacteristic
1153Q8—21no—
1154Q8—21no—
1155Q8—222no—
1156Q8—222no—
1157Q8—222no—
1158Q8—222no—
1159Q8—222no—
1160Q8—222no—
1161Q8—442no—
1162Q8—444no—
1163Q8—442no—
1164Q8—442no—
1165D4—21no—
1166D4—21no—
1167D4—42no—
1168D4—42no—
1169D4—81no—
1170D4—224no—
1171D4—224no—
1172D4—222no—
1173D4—222no—
1174D4—222no—
1175D4—222no—
1176D4—442no—
1177D4—442no—
1178D4—442no—
1179D4—444no—
1180D4—444no—
1181D4—444no—
1182D4—442no—
1183D4—882no—
1184D4—882no—
1185D4—882no—
1186D4—882no—
1187D4—882no—
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—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—42no—
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—222no—
1212C2×C4—222no—
1213C2×C4—222no—
1214C2×C4—442no—
1215C2×C4—442no—
1216C2×C4—444no—
1217C2×C4—444no—
1218C2×C4—444no—
1219C2×C4—442no—
1220C2×C4—444no—
1221C2×C4—442no—
1222C2×C4—442no—
1223C2×C4—882no—
1224C2×C4—881no—
1225C2×C4C2×D4×D1111yescharacteristic
1226C2×C4C2×D4×D1111yescharacteristic
1227C2×C4C2×D4×D1111yescharacteristic
1228C2×C4#6704212yes—
1229C2×C4#6704212yes—
1230C2×C4C24×D1111yescharacteristic
1231C8—21no—
1232C8—21no—
1233C8—21no—
1234C8—21no—
1235C8—222no—
1236C8—222no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—82no—
1249C22—222no—
1250C22—222no—
1251C22—222no—
1252C22—222no—
1253C22—222no—
1254C22—222no—
1255C22—442no—
1256C22—442no—
1257C22—442no—
1258C22—884no—
1259C22—884no—
1260C22#1062318412yes—
1261C22C22×D4×D1111yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—222no—
1272C4—222no—
1273C4—442no—
1274C4—442no—
1275C4—442no—
1276C4#1062318412yes—
1277C4C2×#6704211yescharacteristic
1278C4C2×#6704211yescharacteristic
1279C2—22no—
1280C2—41no—
1281C2—41no—
1282C2—81no—
1283C2—442no—
1284C2—442no—
1285C2—882no—
1286C2C2×#1062318411yescharacteristic
1287C2#1308338511yescharacteristic
1288C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3091C2
socleC22×C11C23×D4
hypercenter#3091D11
hypocenterC11#60761
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3091

Complements

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

NH ≅ G/Ntype
1. #13082288C2semidirect
2. #13081949C2semidirect
3. #13079529C2semidirect
4. #13079516C2semidirect
5. #13079505C2semidirect
6. #13079503C2semidirect
7. #13079456C2semidirect
8. #13079450C2semidirect
9. #13079407C2semidirect
10. #13079401C2semidirect
11. #13078588C2semidirect
12. #13078577C2semidirect
13. #13078564C2semidirect
14. #13078310C2semidirect
15. #13078299C2semidirect
16. #13078272C2semidirect
17. #13078256C2semidirect
18. #13077914C2semidirect
19. #13077905C2semidirect
20. #13077856C2semidirect
21. C2×#10622346C2semidirect
22. #13077062C2semidirect
23. C11×#3091C2semidirect
30. C2×#67004C22semidirect
31. C2×#67002C22semidirect
33. C22×Dic44C22semidirect
34. C22×#4314C22semidirect
38. #10623159C22semidirect
39. D11×C22⋊Q8C22semidirect
40. #10623139C22semidirect
41. #10623137C22semidirect
63. C11×#485C22semidirect
64. C11×#485C22semidirect
65. C11×#484C22semidirect
66. C11×#483C22semidirect
67. C11×#482C22semidirect
68. C11×#482C22semidirect
69. C11×#481C22semidirect
70. C11×#480C22semidirect
71. C11×#427C22semidirect
72. C11×#427C22semidirect
73. C11×#416C22semidirect
74. C11×#416C22semidirect
77. C2×#66885C22semidirect
80. C2×#66880C22semidirect
82. #10622660C22semidirect
84. #10622650C22semidirect
85. #10622617C22semidirect
86. #10622617C22semidirect
87. #10622617C22semidirect
88. #10622614C22semidirect
89. #10622609C22semidirect
90. #10622609C22semidirect
91. #10622608C22semidirect
92. #10622608C22semidirect
93. #10622584C22semidirect
94. #10622583C22semidirect
95. #10622501C22semidirect
96. #10622500C22semidirect
97. #10622500C22semidirect
98. #10622499C22semidirect
99. #10622499C22semidirect
100. #10622498C22semidirect
101. #10622497C22semidirect
102. #10622495C22semidirect
103. #10622481C22semidirect
104. #10622481C22semidirect
105. #10622480C22semidirect
106. #10622479C22semidirect
107. #10622477C22semidirect
108. #10622477C22semidirect
109. #10622476C22semidirect
110. #10622475C22semidirect
111. #10622429C22semidirect
112. #10622426C22semidirect
113. #10622425C22semidirect
114. #10622421C22semidirect
115. #10622421C22semidirect
116. #10622420C22semidirect
117. #10622419C22semidirect
118. #10622419C22semidirect
119. #10622396C22semidirect
120. #10622396C22semidirect
121. #10622395C22semidirect
122. #10622394C22semidirect
123. #10622394C22semidirect
124. #10622393C22semidirect
125. #10622391C22semidirect
126. #10622388C22semidirect
129. #10622346C22semidirect
130. #10622346C22semidirect
131. #10622340C22semidirect
132. #10622340C22semidirect
133. #10622339C22semidirect
134. D11×C22⋊C8C22semidirect
506. #3091D11semidirect
659. #485C2×D11semidirect
660. #485C2×D11semidirect
663. #484C2×D11semidirect
666. #483C2×D11semidirect
669. #482C2×D11semidirect
670. #482C2×D11semidirect
672. #481C2×D11semidirect
674. #480C2×D11semidirect
709. #427C2×D11semidirect
710. #427C2×D11semidirect
715. #416C2×D11semidirect
716. #416C2×D11semidirect
1136. C11#60761semidirect

Maximal subgroups

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

subgroupindex
#130822882
#130819492
#130795292
#130795162
#130795052
#130795032
#130794562
#130794502
#130794072
#130794012
#130785882
#130785772
#130785642
#130783102
#130782992
#130782722
#130782562
#130779142
#130779052
#130778562
C2×#106223462
#130770622
C11×#30912
#6076111