Finite Group Databasebeta

← #15638811

Subgroups — #15638811

Order 2816.

2570 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082469C211yesmaximal, characteristic, complemented
2D42×D11C211yesmaximal, characteristic, complemented
3#13080856C212yesmaximal, complemented
4#13080854C212yesmaximal, complemented
5#13080846C211yesmaximal, characteristic, complemented
6#13080844C211yesmaximal, characteristic, complemented
7#13080841C211yesmaximal, characteristic, complemented
8#13080238C211yesmaximal, characteristic, complemented
9#13080237C211yesmaximal, characteristic, complemented
10#13080232C211yesmaximal, characteristic, complemented
11#13080231C211yesmaximal, characteristic, complemented
12#13080214C212yesmaximal, complemented
13#13080213C212yesmaximal, complemented
14#13079556C211yesmaximal, characteristic, complemented
15#13079535C211yesmaximal, characteristic, complemented
16#13079434C212yesmaximal, complemented
17#13079431C212yesmaximal, complemented
18#13078622C211yesmaximal, characteristic, complemented
19#13078618C211yesmaximal, characteristic, complemented
20#13077845C212yesmaximal, complemented
21#13077844C212yesmaximal, complemented
22#13077654C211yesmaximal, characteristic, complemented
23C11×#3324C211yesmaximal, characteristic, complemented
24C22×D4×D11—21no—
25C22×D4×D11C2212yes—
26C11×#556C2211yescharacteristic, complemented
27D42×C11C2211yescharacteristic
28D4×C22⋊D11—21no—
29D4×C22⋊D11C2212yes—
30C2×#66985C2212yescomplemented
31C2×#66967C2212yescomplemented
32C2×#66967C2212yescomplemented
33C2×#66961C2212yescomplemented
34#10623263C2211yescharacteristic, complemented
35#10623256C2211yescharacteristic, complemented
36#10623248C2211yescharacteristic
37D11×#127C2211yescharacteristic
38#10623240—22no—
39#10623235—22no—
40#10623212—21no—
41#10623205—21no—
42#10623162C2212yescomplemented
43#10623158C2212yescomplemented
44#10623140—21no—
45#10623140C2212yes—
46D11×#121—21no—
47D11×#121C2212yes—
48#10623121—22no—
49D11×#120—22no—
50#10623116—21no—
51#10623109C2211yescharacteristic, complemented
52#10623108C2211yescharacteristic, complemented
53#10623105—21no—
54#10623084C2211yescharacteristic, complemented
55D4×D44C2211yescharacteristic
56D4×D44C2211yescharacteristic
57C4×D4×D11C2211yescharacteristic
58C4×D4×D11C2211yescharacteristic
59#10623063C2212yescomplemented
60#10623055C2212yescomplemented
61C11×#486C2211yescharacteristic, complemented
62C11×#482C2212yescomplemented
63C11×#474C2211yescharacteristic, complemented
64C11×#468C2212yescomplemented
65C11×#460C2211yescharacteristic, complemented
66C11×#450C2212yescomplemented
67C4×C11×SD16C2211yescharacteristic, complemented
68C11×#436C2211yescharacteristic, complemented
69C11×#418C2212yescomplemented
70#10622830C2212yescomplemented
71#10622788C2212yescomplemented
72#10622785C2212yescomplemented
73#10622782C2211yescharacteristic
74#10622782C2212yescomplemented
75#10622775C2211yescharacteristic, complemented
76#10622748C2212yescomplemented
77#10622741C2212yescomplemented
78#10622739C2212yescomplemented
79#10622701C2211yescharacteristic, complemented
80#10622700C2211yescharacteristic, complemented
81#10622688C2211yescharacteristic, complemented
82#10622686C2211yescharacteristic, complemented
83#10622662C2212yescomplemented
84#10622659C2212yescomplemented
85#10622652C2212yescomplemented
86#10622650C2212yescomplemented
87#10622640C2211yescharacteristic, complemented
88C4×#4325C2211yescharacteristic, complemented
89C4×#4324C2211yescharacteristic, complemented
90#10622628C2211yescharacteristic, complemented
91#10622625C2211yescharacteristic, complemented
92#10622616C2212yescomplemented
93#10622614C2212yescomplemented
94#10622499C2212yescomplemented
95#10622498C2212yescomplemented
96#10622495C2212yescomplemented
97#10622485C2212yescomplemented
98#10622483C2211yescharacteristic, complemented
99#10622478C2212yescomplemented
100#10622475C2211yescharacteristic, complemented
101#10622461C2211yescharacteristic, complemented
102#10622456C2211yescharacteristic, complemented
103#10622451C2211yescharacteristic, complemented
104#10622446C2211yescharacteristic, complemented
105#10622431C2211yescharacteristic, complemented
106#10622424C2212yescomplemented
107#10622418C2211yescharacteristic, complemented
108#10622399C2212yescomplemented
109#10622399C2212yescomplemented
110#10622395C2212yescomplemented
111#10622393C2212yescomplemented
112#10622392C2212yescomplemented
113#10622389C2211yescharacteristic
114#10622389C2212yescomplemented
115#10622389C2212yescomplemented
116#10622389C2212yescomplemented
117#10622386C2212yes—
118#10622386C2212yescomplemented
119#10622386C2212yescomplemented
120#10622386C2212yescomplemented
121#10622386C2212yescomplemented
122#10622383C2212yescomplemented
123#10622383C2212yescomplemented
124#10622374C2211yescharacteristic, complemented
125#10622373C2212yescomplemented
126#10622369C2212yescomplemented
127#10622347C2212yescomplemented
128#10622345C2212yescomplemented
129#10622342C2212yescomplemented
130#10622339C2212yescomplemented
131#10622308C2211yescharacteristic, complemented
132C4×#4314C2211yescharacteristic, complemented
133#10622301C2211yescharacteristic, complemented
134#10622298C2211yescharacteristic, complemented
135C24×D11—22no—
136C22×D4×C11—21no—
137C22×D4×C11C2312yes—
138C22×C22⋊D11—22no—
139C22×C22⋊D11—22no—
140C2×#4343—21no—
141C2×#4343C2312yescomplemented
142C2×D4×D11—22no—
143C2×D4×D11—21no—
144C2×D4×D11—22no—
145C2×D4×D11—21no—
146C2×D4×D11—21no—
147C2×D4×D11—22no—
148C2×D4×D11—22no—
149C2×D4×D11—21no—
150C2×D4×D11—44no—
151C2×D4×D11—44no—
152C2×D4×D11—48no—
153C2×D4×D11D411yescharacteristic
154C2×D4×D11C2311yescharacteristic
155C2×D4×D11C2312yes—
156C2×D4×D11C2312yes—
157C2×D4×D11C2312yes—
158C2×#4339C2312yescomplemented
159C22×D44—21no—
160C22×D44C2312yes—
161C22×C4×D11—21no—
162C22×C4×D11C2312yes—
163C2×C11×SD16C2311yescharacteristic
164C2×C11×SD16C2312yescomplemented
165C2×C11×M16C2312yescomplemented
166C11×C4⋊Q8C2311yescharacteristic, complemented
167C11×#127C2311yescharacteristic
168C11×#126—22no—
169C11×#124—21no—
170C11×C22⋊Q8C2312yescomplemented
171C11×#121—21no—
172C11×#121C2312yes—
173C11×#120—22no—
174C4×Q8×C11—21no—
175C4×Q8×C11C2311yescharacteristic, complemented
176C4×D4×C11C2311yescharacteristic
177C4×D4×C11C2311yescharacteristic
178C11×#117C2312yescomplemented
179#67006—22no—
180#67000—21no—
181#67000—21no—
182#66999C2311yescharacteristic
183Q8×Dic11—21no—
184#66997C2311yescharacteristic, complemented
185C2×#4325C2311yescharacteristic
186C2×#4325C2312yescomplemented
187#66993—21no—
188#66993—21no—
189#66993—21no—
190#66993C2312yes—
191#66992—22no—
192#66992—22no—
193#66991—21no—
194#66991C2312yes—
195#66990—22no—
196#66990—22no—
197#66990—22no—
198D4×Dic11D411yescharacteristic
199D4×Dic11C2311yescharacteristic
200C2×#4324C2311yescharacteristic
201C2×#4324C2312yescomplemented
202#66985—44no—
203C2×#4323C2312yes—
204C2×#4323C2312yescomplemented
205C2×#4323C2312yescomplemented
206#66983—21no—
207#66983C2312yes—
208#66983C2312yescomplemented
209C4×C22⋊D11—21no—
210C4×C22⋊D11C2312yes—
211C2×#4318C2312yescomplemented
212#66967—44no—
213#66967—44no—
214#66961—44no—
215C2×D88C2312yes—
216C2×D88C2312yescomplemented
217C2×D88C2312yescomplemented
218C2×#4314C2311yescharacteristic
219C2×#4314C2312yescomplemented
220C2×#4313C2312yescomplemented
221C2×#4313C2312yescomplemented
222#66951—22no—
223#66950C2311yescharacteristic
224#66950C2312yescomplemented
225#66949—21no—
226#66948—21no—
227#66948—21no—
228#66948—22no—
229#66948C2312yes—
230#66948C2312yes—
231#66948C2312yescomplemented
232#66947—22no—
233#66947—22no—
234#66946—22no—
235#66946—21no—
236#66946—21no—
237#66946D411yescharacteristic
238#66946C2311yescharacteristic
239#66946C2312yescomplemented
240#66945C2312yescomplemented
241C4⋊C4×D11—22no—
242C4⋊C4×D11D411yescharacteristic
243C4⋊C4×D11C2311yescharacteristic
244#66942—21no—
245#66941C2311yescharacteristic, complemented
246#66939—22no—
247#66938—22no—
248#66937—22no—
249#66937—22no—
250#66937—22no—
251#66937—22no—
252#66937—22no—
253#66936—22no—
254#66935—22no—
255#66935—22no—
256#66935—22no—
257#66935—22no—
258#66935—22no—
259(C22⋊D11)⋊C4—22no—
260(C22⋊D11)⋊C4—21no—
261(C22⋊D11)⋊C4D412yes—
262C22⋊C4×D11—21no—
263C22⋊C4×D11—22no—
264C22⋊C4×D11D412yes—
265#66928—22no—
266#66927—21no—
267#66927C2311yescharacteristic
268#66927C2311yescharacteristic, complemented
269C4×D44—22no—
270C4×D44—22no—
271C4×D44—21no—
272C4×D44C2311yescharacteristic
273C4×D44C2311yescharacteristic
274#66925—21no—
275#66925—22no—
276C42×D11C2311yescharacteristic
277C4×Dic22—21no—
278C4×Dic22C2311yescharacteristic, complemented
279C11×#107C2312yescomplemented
280C11×#106C2311yescharacteristic, complemented
281C11×C4⋊C8C2311yescharacteristic, complemented
282C11×#103C2311yescharacteristic, complemented
283C11×#102C2312yes—
284C11×#102C2311yescharacteristic
285C11×#102C2312yescomplemented
286C11×#102C2312yescomplemented
287C11×#102C2312yescomplemented
288C11×C22⋊C8C2312yescomplemented
289C4×C8×C11C2311yescharacteristic, complemented
290#66899C2311yescharacteristic, complemented
291#66896C2311yescharacteristic
292#66896C2312yescomplemented
293C22⋊(C11⋊C8)C2312yescomplemented
294#66885C2311yescharacteristic
295#66885C2312yescomplemented
296#66885C2312yescomplemented
297(C2×D11)⋊C8C2311yescharacteristic
298(C2×D11)⋊C8C2311yescharacteristic
299(C2×D11)⋊C8C2312yes—
300(C2×D11)⋊C8C2312yescomplemented
301(C2×D11)⋊C8C2312yescomplemented
302#66881C2311yescharacteristic, complemented
303#66880C2311yescharacteristic, complemented
304Dic11⋊C8C2311yescharacteristic, complemented
305Dic11⋊C8C2311yescharacteristic, complemented
306C8×Dic11C2312yescomplemented
307#66874C2311yescharacteristic, complemented
308#66873C2311yescharacteristic
309#66873C2312yes—
310#66873C2312yescomplemented
311#66873C2312yescomplemented
312#66873C2312yescomplemented
313#66873C2312yescomplemented
314#66872C2311yescharacteristic, complemented
315#66872C2311yescharacteristic, complemented
316#66871C2312yescomplemented
317C4⋊(C11⋊C8)C2311yescharacteristic, complemented
318C4×C11⋊C8C2311yescharacteristic, complemented
319#61582—111nomaximal, Sylow
320C24×C11—22no—
321C23×D11—21no—
322C23×D11—22no—
323C23×D11—22no—
324C23×D11—22no—
325C23×D11—22no—
326C23×D11—48no—
327C23×D11—48no—
328C23×D11—84no—
329C23×D11C2×D412yes—
330C2×Q8×C11—21no—
331C2×Q8×C11C2411yescharacteristic
332C2×D4×C11—24no—
333C2×D4×C11—22no—
334C2×D4×C11—22no—
335C2×D4×C11—21no—
336C2×D4×C11—21no—
337C2×D4×C11—42no—
338C2×D4×C11—44no—
339C2×D4×C11C2×D411yescharacteristic
340C2×D4×C11C2412yes—
341C2×D4×C11C2411yescharacteristic
342C22×C4×C11—21no—
343C22×C4×C11C2412yes—
344C2×C22⋊D11—21no—
345C2×C22⋊D11—22no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—22no—
349C2×C22⋊D11—22no—
350C2×C22⋊D11—22no—
351C2×C22⋊D11—22no—
352C2×C22⋊D11—22no—
353C2×C22⋊D11—22no—
354C2×C22⋊D11—48no—
355C2×C22⋊D11—48no—
356C2×C22⋊D11C2×D412yes—
357C22×Dic11—21no—
358C22×Dic11C2×D412yes—
359#4343—42no—
360#4343—42no—
361#4343—44no—
362D4×D11—22no—
363D4×D11—24no—
364D4×D11—24no—
365D4×D11—22no—
366D4×D11—24no—
367D4×D11—42no—
368D4×D11—42no—
369D4×D11—42no—
370D4×D11—42no—
371D4×D11—44no—
372D4×D11—48no—
373D4×D11—48no—
374D4×D11—44no—
375D4×D11—48no—
376D4×D11—48no—
377D4×D11—44no—
378D4×D11—82no—
379#4339—42no—
380#4339—42no—
381C2×D44—22no—
382C2×D44—22no—
383C2×D44—22no—
384C2×D44—22no—
385C2×D44—24no—
386C2×D44—21no—
387C2×D44—21no—
388C2×D44—22no—
389C2×D44—21no—
390C2×D44—21no—
391C2×D44—42no—
392C2×D44—44no—
393C2×D44C2×D411yescharacteristic
394C2×D44C2412yes—
395C2×D44C2412yes—
396C2×D44C2411yescharacteristic
397C2×C4×D11—22no—
398C2×C4×D11—21no—
399C2×C4×D11—22no—
400C2×C4×D11—21no—
401C2×C4×D11—21no—
402C2×C4×D11—22no—
403C2×C4×D11—42no—
404C2×C4×D11—42no—
405C2×C4×D11—44no—
406C2×C4×D11C2×D411yescharacteristic
407C2×C4×D11C2×D412yes—
408C2×C4×D11C2×D412yes—
409C2×C4×D11C2×D411yescharacteristic
410C2×C4×D11C2411yescharacteristic
411C2×C4×D11C2412yes—
412C2×Dic22—21no—
413C2×Dic22C2411yescharacteristic
414C11×SD16—22no—
415C11×SD16—42no—
416C11×M16—42no—
417C2×C8×C11C2412yes—
418C2×C8×C11C2411yescharacteristic
419C2×C8×C11C2411yescharacteristic
420C11×C4⋊C4—21no—
421C11×C4⋊C4—22no—
422C11×C4⋊C4—21no—
423C11×C4⋊C4C2×D411yescharacteristic
424C11×C4⋊C4C2412yes—
425C11×C4⋊C4C2411yescharacteristic
426C11×C4⋊C4C2411yescharacteristic
427C11×C22⋊C4—22no—
428C11×C22⋊C4—22no—
429C11×C22⋊C4—21no—
430C11×C22⋊C4—22no—
431C11×C22⋊C4C2×D412yes—
432C42×C11—21no—
433C42×C11—22no—
434C42×C11C2411yescharacteristic
435C22⋊Dic11—21no—
436C22⋊Dic11—22no—
437C22⋊Dic11C2×D412yes—
438#4325—22no—
439#4325—42no—
440#4324—22no—
441#4324—42no—
442#4323—24no—
443#4323—42no—
444#4323—42no—
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—
450(C2×D11)⋊C4—21no—
451(C2×D11)⋊C4—21no—
452(C2×D11)⋊C4—22no—
453(C2×D11)⋊C4—22no—
454(C2×D11)⋊C4—22no—
455(C2×D11)⋊C4—21no—
456(C2×D11)⋊C4—22no—
457(C2×D11)⋊C4C2×D412yes—
458(C2×D11)⋊C4C2×D412yes—
459C4⋊Dic11—21no—
460C4⋊Dic11—22no—
461C4⋊Dic11C2×D411yescharacteristic
462C4⋊Dic11C2411yescharacteristic
463C4⋊Dic11C2411yescharacteristic
464Dic11⋊C4—21no—
465Dic11⋊C4—21no—
466Dic11⋊C4—21no—
467Dic11⋊C4—21no—
468Dic11⋊C4—21no—
469Dic11⋊C4—21no—
470Dic11⋊C4C2×D412yes—
471C4×Dic11—22no—
472C4×Dic11—21no—
473C4×Dic11C2×D411yescharacteristic
474C4×Dic11C2×D411yescharacteristic
475C4×Dic11C2411yescharacteristic
476#4318—42no—
477C2×C11⋊C8C2411yescharacteristic
478C2×C11⋊C8C2411yescharacteristic
479C2×C11⋊C8C2412yes—
480D88—24no—
481D88—42no—
482D88—42no—
483#4314—22no—
484#4314—42no—
485#4313—42no—
486#4313—42no—
487#3506—111no—
488C2×D42—111no—
489#3325—112no—
490#3325—112no—
491#3324—111no—
492#3324—111no—
493#3324—111no—
494#3324D1111yescharacteristic, complemented
495#3274—111no—
496#3274—111no—
497#3274—111no—
498#3274—111no—
499#3272—112no—
500#3272—112no—
501#3208—111no—
502#3205—111no—
503#3194—112no—
504#3194—112no—
505#3101—111no—
506#3100—111no—
507#3003—112no—
508#3003—112no—
509#2975—111no—
510C23×C11—21no—
511C23×C11—22no—
512C23×C11—44no—
513C23×C11—44no—
514C23×C11—82no—
515C23×C11C22×D412yes—
516C22×D11—24no—
517C22×D11—21no—
518C22×D11—24no—
519C22×D11—22no—
520C22×D11—22no—
521C22×D11—42no—
522C22×D11—42no—
523C22×D11—44no—
524C22×D11—42no—
525C22×D11—44no—
526C22×D11—44no—
527C22×D11—44no—
528C22×D11—44no—
529C22×D11—44no—
530C22×D11—44no—
531C22×D11—42no—
532C22×D11—44no—
533C22×D11—44no—
534C22×D11—82no—
535C22×D11—82no—
536C22×D11—82no—
537C22×D11—832no—
538C22×D11C22×D412yes—
539C22×D11C22×D411yescharacteristic
540Q8×C11—21no—
541Q8×C11—21no—
542Q8×C11—42no—
543D4×C11—22no—
544D4×C11—21no—
545D4×C11—22no—
546D4×C11—22no—
547D4×C11—44no—
548D4×C11—44no—
549D4×C11—42no—
550D4×C11—81no—
551D4×C11H(5,𝔽2)12yes—
552C2×C4×C11—22no—
553C2×C4×C11—22no—
554C2×C4×C11—22no—
555C2×C4×C11—21no—
556C2×C4×C11—21no—
557C2×C4×C11—21no—
558C2×C4×C11—42no—
559C2×C4×C11C22×D411yescharacteristic
560C2×C4×C11C22×D412yes—
561C2×C4×C11C22×D411yescharacteristic
562C2×C4×C11C2511yescharacteristic
563C22⋊D11—24no—
564C22⋊D11—24no—
565C22⋊D11—44no—
566C22⋊D11—44no—
567C22⋊D11—44no—
568C22⋊D11—44no—
569C22⋊D11—44no—
570C22⋊D11—44no—
571C22⋊D11—82no—
572C22⋊D11—82no—
573C22⋊D11—82no—
574C2×Dic11—21no—
575C2×Dic11—21no—
576C2×Dic11—21no—
577C2×Dic11—42no—
578C2×Dic11—42no—
579C2×Dic11C22×D412yes—
580C2×Dic11C22×D411yescharacteristic
581C2×Dic11C22×D411yescharacteristic
582C2×Dic11C22×D411yescharacteristic
583D44—22no—
584D44—21no—
585D44—22no—
586D44—22no—
587D44—22no—
588D44—22no—
589D44—44no—
590D44—44no—
591D44—44no—
592D44—42no—
593D44—42no—
594D44—81no—
595D44—81no—
596D44—82no—
597D44—82no—
598D44H(5,𝔽2)12yes—
599C4×D11—22no—
600C4×D11—22no—
601C4×D11—21no—
602C4×D11—21no—
603C4×D11—42no—
604C4×D11—42no—
605C4×D11—41no—
606C4×D11—42no—
607C4×D11—42no—
608C4×D11—42no—
609C4×D11—44no—
610C4×D11—82no—
611C4×D11—82no—
612C4×D11AGL(1,ℤ/8)14yescomplemented
613Dic22—21no—
614Dic22—21no—
615Dic22—81no—
616C8×C11—21no—
617C8×C11—22no—
618C8×C11—21no—
619C11⋊C8—21no—
620C11⋊C8—22no—
621C11⋊C8—21no—
622C23×D4—112no—
623C23×D4—221no—
624C2×AGL(1,ℤ/8)—112no—
625C2×AGL(1,ℤ/8)—112no—
626C2×AGL(1,ℤ/8)—112no—
627C2×AGL(1,ℤ/8)—112no—
628#559—221no—
629#559—221no—
630#556—111no—
631#556C2×D1111yescharacteristic, complemented
632#555—112no—
633#553—222no—
634#550—111no—
635#550—111no—
636#547—112no—
637D42—112no—
638D42—111no—
639D42—112no—
640D42—111no—
641D42—111no—
642D42—222no—
643D42—221no—
644D42—221no—
645D42C2×D1111yescharacteristic
646#538—222no—
647#535—221no—
648#533—111no—
649#532—111no—
650C2×#127—111no—
651#525—112no—
652#525—112no—
653C2×#121—112no—
654C2×#121—221no—
655C2×#120—222no—
656#520—221no—
657C2×C4×D4—111no—
658C2×C4×D4—111no—
659#493—111no—
660#493—111no—
661#492—112no—
662#486—111no—
663#486—112no—
664#486C2×D1111yescharacteristic, complemented
665#483—111no—
666#483—111no—
667#482—112no—
668#482—112no—
669#482—112no—
670#482C2×D1112yescomplemented
671#480—112no—
672#476—111no—
673#476—111no—
674#474—111no—
675#474C2×D1111yescharacteristic, complemented
676#469—112no—
677#469—112no—
678#469—112no—
679#469—112no—
680#468—112no—
681#468—112no—
682#468—112no—
683#468C2×D1112yescomplemented
684#461—111no—
685#461—111no—
686#460—111no—
687#460—111no—
688#460—111no—
689#460C2×D1111yescharacteristic, complemented
690#459—111no—
691#459—111no—
692#459—112no—
693#459—112no—
694#450—111no—
695#450—112no—
696#450—112no—
697#450—111no—
698#450—112no—
699#450—112no—
700#450—112no—
701#450C2×D1112yescomplemented
702#449—112no—
703#449—112no—
704#449—112no—
705#449—112no—
706#447—112no—
707#447—112no—
708#447—112no—
709#447—112no—
710#447—112no—
711#447—112no—
712#447—112no—
713C4×SD16—111no—
714C4×SD16—111no—
715C4×SD16—111no—
716C4×SD16C2×D1111yescharacteristic, complemented
717C4×D8—112no—
718C4×D8—112no—
719#436—112no—
720#436—111no—
721#436—111no—
722#436—112no—
723#436—111no—
724#436C2×D1111yescharacteristic, complemented
725#431—111no—
726#431—111no—
727#418—112no—
728#418—112no—
729#418—112no—
730#418C2×D1112yescomplemented
731#407—112no—
732#407—112no—
733C22×C11—22no—
734C22×C11—22no—
735C22×C11—22no—
736C22×C11—22no—
737C22×C11—41no—
738C22×C11—41no—
739C22×C11—42no—
740C22×C11—42no—
741C22×C11—42no—
742C22×C11—88no—
743C22×C11C23×D411yescharacteristic
744C2×D11—21no—
745C2×D11—21no—
746C2×D11—22no—
747C2×D11—22no—
748C2×D11—22no—
749C2×D11—22no—
750C2×D11—48no—
751C2×D11—48no—
752C2×D11—41no—
753C2×D11—41no—
754C2×D11—42no—
755C2×D11—42no—
756C2×D11—42no—
757C2×D11—42no—
758C2×D11—42no—
759C2×D11—42no—
760C2×D11—88no—
761C2×D11—88no—
762C2×D11—88no—
763C2×D11—88no—
764C2×D11C2×AGL(1,ℤ/8)12yes—
765C4×C11—21no—
766C4×C11—22no—
767C4×C11—41no—
768C4×C11—41no—
769C4×C11—41no—
770C4×C11—42no—
771C4×C11C2×AGL(1,ℤ/8)12yes—
772C4×C11C2×H(5,𝔽2)11yescharacteristic
773C4×C11C2×H(5,𝔽2)11yescharacteristic
774Dic11—21no—
775Dic11—21no—
776Dic11—22no—
777Dic11—41no—
778Dic11—41no—
779Dic11—41no—
780Dic11C2×AGL(1,ℤ/8)12yes—
781C25—222no—
782C2×#41—112no—
783C2×#41—112no—
784C2×#41—221no—
785C22×D4—21no—
786C22×D4—111no—
787C22×D4—111no—
788C22×D4—112no—
789C22×D4—112no—
790C22×D4—112no—
791C22×D4—112no—
792C22×D4—221no—
793C22×D4—222no—
794C22×D4—221no—
795C22×D4—222no—
796C22×D4—221no—
797C22×D4—222no—
798C22×D4—222no—
799C22×D4—221no—
800C22×D4—222no—
801C22×D4—222no—
802C22×D4—221no—
803C22×D4—444no—
804C22×D4—444no—
805C22×D4—448no—
806C22×D4C22×D1112yes—
807C23×C4—112no—
808C23×C4—221no—
809AGL(1,ℤ/8)—444no—
810AGL(1,ℤ/8)—444no—
811AGL(1,ℤ/8)—444no—
812AGL(1,ℤ/8)—444no—
813C2×SD16—111no—
814C2×SD16—111no—
815C2×SD16—112no—
816C2×SD16—112no—
817C2×SD16—111no—
818C2×SD16—112no—
819C2×SD16C22×D1111yescharacteristic
820C2×SD16C22×D1112yescomplemented
821C2×D8—112no—
822C2×D8—112no—
823C2×D8—112no—
824C2×D8—112no—
825C2×D8—112no—
826C2×D8—112no—
827C2×M16—112no—
828C2×M16—112no—
829C2×M16—112no—
830C2×M16C22×D1112yescomplemented
831C4⋊Q8—111no—
832C4⋊Q8—111no—
833C4⋊Q8C22×D1111yescharacteristic, complemented
834#127—112no—
835#127—111no—
836#127—111no—
837#127—221no—
838#127—221no—
839#127—221no—
840#127—221no—
841#127C22×D1111yescharacteristic
842#126—22no—
843#126—222no—
844#125—221no—
845#124—21no—
846#124—222no—
847#124—221no—
848#124—222no—
849#124—221no—
850#123—222no—
851#123—222no—
852#123—222no—
853#123—222no—
854C22⋊Q8—111no—
855C22⋊Q8—111no—
856C22⋊Q8—112no—
857C22⋊Q8—221no—
858C22⋊Q8C22×D1112yescomplemented
859#121—21no—
860#121—112no—
861#121—112no—
862#121—112no—
863#121—112no—
864#121—112no—
865#121—112no—
866#121—222no—
867#121—222no—
868#121—222no—
869#121—222no—
870#121—222no—
871#121—221no—
872#121—221no—
873#121—221no—
874#121—222no—
875#121—222no—
876#121—221no—
877#121—222no—
878#121C22×D1112yes—
879#120—22no—
880#120—222no—
881#120—222no—
882#120—222no—
883#120—222no—
884#120—222no—
885#120—222no—
886#120—222no—
887#120—222no—
888#120—222no—
889C4×Q8—21no—
890C4×Q8—111no—
891C4×Q8—221no—
892C4×Q8—221no—
893C4×Q8C22×D1111yescharacteristic, complemented
894C4×D4—111no—
895C4×D4—112no—
896C4×D4—111no—
897C4×D4—112no—
898C4×D4—111no—
899C4×D4—111no—
900C4×D4—112no—
901C4×D4—111no—
902C4×D4—111no—
903C4×D4—221no—
904C4×D4—222no—
905C4×D4—222no—
906C4×D4—221no—
907C4×D4—221no—
908C4×D4—221no—
909C4×D4—222no—
910C4×D4—222no—
911C4×D4—221no—
912C4×D4C22×D1111yescharacteristic
913C4×D4C22×D1111yescharacteristic
914#117—112no—
915#117—222no—
916#117—221no—
917#117C22×D1112yescomplemented
918C2×C4⋊C4—111no—
919C2×C4⋊C4—111no—
920C2×C4⋊C4—222no—
921C2×C22⋊C4—112no—
922C2×C22⋊C4—221no—
923C2×C22⋊C4—222no—
924C2×C42—111no—
925#107—112no—
926#107C22×D1112yescomplemented
927#106—111no—
928#106—111no—
929#106—111no—
930#106C22×D1111yescharacteristic, complemented
931C4⋊C8—111no—
932C4⋊C8—111no—
933C4⋊C8—111no—
934C4⋊C8C22×D1111yescharacteristic, complemented
935#103—111no—
936#103—111no—
937#103—111no—
938#103C22×D1111yescharacteristic, complemented
939#102—111no—
940#102—112no—
941#102—111no—
942#102—112no—
943#102—112no—
944#102—112no—
945#102—111no—
946#102—112no—
947#102—112no—
948#102—112no—
949#102—112no—
950#102C22×D1112yes—
951#102C22×D1111yescharacteristic
952#102C22×D1112yescomplemented
953#102C22×D1112yescomplemented
954#102C22×D1112yescomplemented
955C22⋊C8—112no—
956C22⋊C8—111no—
957C22⋊C8—111no—
958C22⋊C8—112no—
959C22⋊C8—112no—
960C22⋊C8—112no—
961C22⋊C8C22×D1112yescomplemented
962C4×C8—112no—
963C4×C8—111no—
964C4×C8C22×D1111yescharacteristic, complemented
965C2×C11—42no—
966C2×C11—42no—
967C2×C11—82no—
968C2×C11#348411yescharacteristic
969C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
970C2×C11#358511yescharacteristic
971D11—22no—
972D11—42no—
973D11—42no—
974D11—82no—
975D11—82no—
976C24—22no—
977C24—112no—
978C24—221no—
979C24—222no—
980C24—222no—
981C24—222no—
982C24—222no—
983C24—448no—
984C24—448no—
985C24—884no—
986#41—442no—
987#41—442no—
988#41—444no—
989#41—442no—
990#41—442no—
991C2×Q8—21no—
992C2×Q8—111no—
993C2×Q8—221no—
994C2×Q8C23×D1111yescharacteristic
995C2×D4—24no—
996C2×D4—22no—
997C2×D4—22no—
998C2×D4—21no—
999C2×D4—21no—
1000C2×D4—42no—
1001C2×D4—44no—
1002C2×D4—112no—
1003C2×D4—111no—
1004C2×D4—111no—
1005C2×D4—112no—
1006C2×D4—112no—
1007C2×D4—224no—
1008C2×D4—222no—
1009C2×D4—222no—
1010C2×D4—222no—
1011C2×D4—222no—
1012C2×D4—224no—
1013C2×D4—221no—
1014C2×D4—222no—
1015C2×D4—222no—
1016C2×D4—222no—
1017C2×D4—222no—
1018C2×D4—222no—
1019C2×D4—222no—
1020C2×D4—224no—
1021C2×D4—222no—
1022C2×D4—224no—
1023C2×D4—222no—
1024C2×D4—222no—
1025C2×D4—222no—
1026C2×D4—222no—
1027C2×D4—221no—
1028C2×D4—222no—
1029C2×D4—221no—
1030C2×D4—221no—
1031C2×D4—221no—
1032C2×D4—442no—
1033C2×D4—444no—
1034C2×D4—444no—
1035C2×D4—442no—
1036C2×D4—442no—
1037C2×D4—442no—
1038C2×D4—442no—
1039C2×D4—444no—
1040C2×D4—448no—
1041C2×D4—448no—
1042C2×D4—444no—
1043C2×D4—448no—
1044C2×D4—448no—
1045C2×D4—448no—
1046C2×D4—448no—
1047C2×D4—882no—
1048C2×D4D4×D1111yescharacteristic
1049C2×D4C23×D1112yes—
1050C2×D4C23×D1111yescharacteristic
1051C22×C4—21no—
1052C22×C4—111no—
1053C22×C4—112no—
1054C22×C4—111no—
1055C22×C4—112no—
1056C22×C4—111no—
1057C22×C4—112no—
1058C22×C4—112no—
1059C22×C4—222no—
1060C22×C4—221no—
1061C22×C4—222no—
1062C22×C4—221no—
1063C22×C4—221no—
1064C22×C4—221no—
1065C22×C4—222no—
1066C22×C4—442no—
1067C22×C4—442no—
1068C22×C4—444no—
1069C22×C4C23×D1112yes—
1070SD16—22no—
1071SD16—42no—
1072SD16—222no—
1073SD16—222no—
1074SD16—222no—
1075SD16—442no—
1076SD16—442no—
1077SD16—442no—
1078D8—224no—
1079D8—224no—
1080D8—442no—
1081D8—442no—
1082D8—442no—
1083D8—442no—
1084M16—42no—
1085M16—442no—
1086M16—442no—
1087M16—442no—
1088C2×C8—112no—
1089C2×C8—111no—
1090C2×C8—111no—
1091C2×C8C23×D1112yes—
1092C2×C8C23×D1111yescharacteristic
1093C2×C8C23×D1111yescharacteristic
1094C4⋊C4—22no—
1095C4⋊C4—21no—
1096C4⋊C4—21no—
1097C4⋊C4—112no—
1098C4⋊C4—111no—
1099C4⋊C4—111no—
1100C4⋊C4—111no—
1101C4⋊C4—221no—
1102C4⋊C4—221no—
1103C4⋊C4—222no—
1104C4⋊C4—221no—
1105C4⋊C4—221no—
1106C4⋊C4—221no—
1107C4⋊C4—221no—
1108C4⋊C4—221no—
1109C4⋊C4D4×D1111yescharacteristic
1110C4⋊C4C23×D1111yescharacteristic
1111C4⋊C4C23×D1112yes—
1112C4⋊C4C23×D1111yescharacteristic
1113C22⋊C4—22no—
1114C22⋊C4—22no—
1115C22⋊C4—21no—
1116C22⋊C4—22no—
1117C22⋊C4—112no—
1118C22⋊C4—112no—
1119C22⋊C4—112no—
1120C22⋊C4—221no—
1121C22⋊C4—222no—
1122C22⋊C4—222no—
1123C22⋊C4—222no—
1124C22⋊C4—222no—
1125C22⋊C4—222no—
1126C22⋊C4—221no—
1127C22⋊C4—221no—
1128C22⋊C4—222no—
1129C22⋊C4—221no—
1130C22⋊C4—222no—
1131C22⋊C4—221no—
1132C22⋊C4—222no—
1133C22⋊C4—222no—
1134C22⋊C4D4×D1112yes—
1135C42—22no—
1136C42—21no—
1137C42—111no—
1138C42—111no—
1139C42—111no—
1140C42—222no—
1141C42—221no—
1142C42C23×D1111yescharacteristic
1143C11#6158211yescharacteristic, complemented, Sylow
1144C23—21no—
1145C23—22no—
1146C23—44no—
1147C23—44no—
1148C23—82no—
1149C23—111no—
1150C23—112no—
1151C23—224no—
1152C23—224no—
1153C23—221no—
1154C23—222no—
1155C23—222no—
1156C23—442no—
1157C23—442no—
1158C23—444no—
1159C23—444no—
1160C23—444no—
1161C23—442no—
1162C23—444no—
1163C23—444no—
1164C23—442no—
1165C23—444no—
1166C23—444no—
1167C23—444no—
1168C23—444no—
1169C23—882no—
1170C23—882no—
1171C23—882no—
1172C23—8832no—
1173C23C2×D4×D1112yes—
1174Q8—21no—
1175Q8—21no—
1176Q8—42no—
1177Q8—221no—
1178Q8—221no—
1179Q8—881no—
1180D4—22no—
1181D4—22no—
1182D4—21no—
1183D4—22no—
1184D4—44no—
1185D4—44no—
1186D4—42no—
1187D4—81no—
1188D4—112no—
1189D4—224no—
1190D4—224no—
1191D4—222no—
1192D4—221no—
1193D4—222no—
1194D4—222no—
1195D4—222no—
1196D4—222no—
1197D4—444no—
1198D4—444no—
1199D4—444no—
1200D4—444no—
1201D4—444no—
1202D4—444no—
1203D4—444no—
1204D4—444no—
1205D4—444no—
1206D4—442no—
1207D4—442no—
1208D4—881no—
1209D4—881no—
1210D4—882no—
1211D4—882no—
1212D4—882no—
1213D4—882no—
1214D4—882no—
1215D4#6704212yes—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—42no—
1223C2×C4—111no—
1224C2×C4—114no—
1225C2×C4—111no—
1226C2×C4—111no—
1227C2×C4—112no—
1228C2×C4—222no—
1229C2×C4—221no—
1230C2×C4—222no—
1231C2×C4—221no—
1232C2×C4—221no—
1233C2×C4—221no—
1234C2×C4—221no—
1235C2×C4—442no—
1236C2×C4—442no—
1237C2×C4—441no—
1238C2×C4—442no—
1239C2×C4—444no—
1240C2×C4—442no—
1241C2×C4—442no—
1242C2×C4—442no—
1243C2×C4—442no—
1244C2×C4—882no—
1245C2×C4—882no—
1246C2×C4C2×D4×D1112yes—
1247C2×C4C2×D4×D1111yescharacteristic
1248C2×C4C2×D4×D1111yescharacteristic
1249C2×C4C24×D1111yescharacteristic
1250C8—21no—
1251C8—21no—
1252C8—22no—
1253C8—222no—
1254C8—221no—
1255C8—221no—
1256C22—22no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—41no—
1261C22—41no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—88no—
1266C22—112no—
1267C22—221no—
1268C22—221no—
1269C22—222no—
1270C22—222no—
1271C22—222no—
1272C22—222no—
1273C22—448no—
1274C22—448no—
1275C22—441no—
1276C22—441no—
1277C22—442no—
1278C22—442no—
1279C22—442no—
1280C22—442no—
1281C22—442no—
1282C22—442no—
1283C22—888no—
1284C22—888no—
1285C22—888no—
1286C22—888no—
1287C22C22×D4×D1111yescharacteristic
1288C4—21no—
1289C4—22no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—42no—
1294C4—112no—
1295C4—221no—
1296C4—221no—
1297C4—222no—
1298C4—441no—
1299C4—441no—
1300C4—441no—
1301C4D11×AGL(1,ℤ/8)12yes—
1302C4C2×#6704211yescharacteristic
1303C4D11×H(5,𝔽2)11yescharacteristic
1304C2—42no—
1305C2—42no—
1306C2—82no—
1307C2—222no—
1308C2—442no—
1309C2—442no—
1310C2—882no—
1311C2—882no—
1312C2#1308224611yescharacteristic
1313C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1314C2#1308339411yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3324C2
socleC22×C11C23×D4
hypercenter#3324D11
hypocenterC11#61582
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3324

Complements

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

NH ≅ G/Ntype
1. #13082469C2semidirect
2. D42×D11C2semidirect
3. #13080856C2semidirect
4. #13080854C2semidirect
5. #13080846C2semidirect
6. #13080844C2semidirect
7. #13080841C2semidirect
8. #13080238C2semidirect
9. #13080237C2semidirect
10. #13080232C2semidirect
11. #13080231C2semidirect
12. #13080214C2semidirect
13. #13080213C2semidirect
14. #13079556C2semidirect
15. #13079535C2semidirect
16. #13079434C2semidirect
17. #13079431C2semidirect
18. #13078622C2semidirect
19. #13078618C2semidirect
20. #13077845C2semidirect
21. #13077844C2semidirect
22. #13077654C2semidirect
23. C11×#3324C2semidirect
26. C11×#556C22semidirect
30. C2×#66985C22semidirect
31. C2×#66967C22semidirect
32. C2×#66967C22semidirect
33. C2×#66961C22semidirect
34. #10623263C22semidirect
35. #10623256C22semidirect
42. #10623162C22semidirect
43. #10623158C22semidirect
51. #10623109C22semidirect
52. #10623108C22semidirect
54. #10623084C22semidirect
59. #10623063C22semidirect
60. #10623055C22semidirect
61. C11×#486C22semidirect
62. C11×#482C22semidirect
63. C11×#474C22semidirect
64. C11×#468C22semidirect
65. C11×#460C22semidirect
66. C11×#450C22semidirect
67. C4×C11×SD16C22semidirect
68. C11×#436C22semidirect
69. C11×#418C22semidirect
70. #10622830C22semidirect
71. #10622788C22semidirect
72. #10622785C22semidirect
74. #10622782C22semidirect
75. #10622775C22semidirect
76. #10622748C22semidirect
77. #10622741C22semidirect
78. #10622739C22semidirect
79. #10622701C22semidirect
80. #10622700C22semidirect
81. #10622688C22semidirect
82. #10622686C22semidirect
83. #10622662C22semidirect
84. #10622659C22semidirect
85. #10622652C22semidirect
86. #10622650C22semidirect
87. #10622640C22semidirect
88. C4×#4325C22semidirect
89. C4×#4324C22semidirect
90. #10622628C22semidirect
91. #10622625C22semidirect
92. #10622616C22semidirect
93. #10622614C22semidirect
94. #10622499C22semidirect
95. #10622498C22semidirect
96. #10622495C22semidirect
97. #10622485C22semidirect
98. #10622483C22semidirect
99. #10622478C22semidirect
100. #10622475C22semidirect
101. #10622461C22semidirect
102. #10622456C22semidirect
103. #10622451C22semidirect
104. #10622446C22semidirect
105. #10622431C22semidirect
106. #10622424C22semidirect
107. #10622418C22semidirect
108. #10622399C22semidirect
109. #10622399C22semidirect
110. #10622395C22semidirect
111. #10622393C22semidirect
112. #10622392C22semidirect
114. #10622389C22semidirect
115. #10622389C22semidirect
116. #10622389C22semidirect
118. #10622386C22semidirect
119. #10622386C22semidirect
120. #10622386C22semidirect
121. #10622386C22semidirect
122. #10622383C22semidirect
123. #10622383C22semidirect
124. #10622374C22semidirect
125. #10622373C22semidirect
126. #10622369C22semidirect
127. #10622347C22semidirect
128. #10622345C22semidirect
129. #10622342C22semidirect
130. #10622339C22semidirect
131. #10622308C22semidirect
132. C4×#4314C22semidirect
133. #10622301C22semidirect
134. #10622298C22semidirect
141. C2×#4343C23semidirect
158. C2×#4339C23semidirect
164. C2×C11×SD16C23semidirect
165. C2×C11×M16C23semidirect
166. C11×C4⋊Q8C23semidirect
170. C11×C22⋊Q8C23semidirect
175. C4×Q8×C11C23semidirect
178. C11×#117C23semidirect
184. #66997C23semidirect
186. C2×#4325C23semidirect
201. C2×#4324C23semidirect
204. C2×#4323C23semidirect
205. C2×#4323C23semidirect
208. #66983C23semidirect
211. C2×#4318C23semidirect
216. C2×D88C23semidirect
217. C2×D88C23semidirect
219. C2×#4314C23semidirect
220. C2×#4313C23semidirect
221. C2×#4313C23semidirect
224. #66950C23semidirect
231. #66948C23semidirect
239. #66946C23semidirect
240. #66945C23semidirect
245. #66941C23semidirect
268. #66927C23semidirect
278. C4×Dic22C23semidirect
279. C11×#107C23semidirect
280. C11×#106C23semidirect
281. C11×C4⋊C8C23semidirect
282. C11×#103C23semidirect
285. C11×#102C23semidirect
286. C11×#102C23semidirect
287. C11×#102C23semidirect
288. C11×C22⋊C8C23semidirect
289. C4×C8×C11C23semidirect
290. #66899C23semidirect
292. #66896C23semidirect
293. C22⋊(C11⋊C8)C23semidirect
295. #66885C23semidirect
296. #66885C23semidirect
300. (C2×D11)⋊C8C23semidirect
301. (C2×D11)⋊C8C23semidirect
302. #66881C23semidirect
303. #66880C23semidirect
304. Dic11⋊C8C23semidirect
305. Dic11⋊C8C23semidirect
306. C8×Dic11C23semidirect
307. #66874C23semidirect
310. #66873C23semidirect
311. #66873C23semidirect
312. #66873C23semidirect
313. #66873C23semidirect
314. #66872C23semidirect
315. #66872C23semidirect
316. #66871C23semidirect
317. C4⋊(C11⋊C8)C23semidirect
318. C4×C11⋊C8C23semidirect
494. #3324D11semidirect
612. C4×D11AGL(1,ℤ/8)semidirect
631. #556C2×D11semidirect
664. #486C2×D11semidirect
670. #482C2×D11semidirect
675. #474C2×D11semidirect
683. #468C2×D11semidirect
689. #460C2×D11semidirect
701. #450C2×D11semidirect
716. C4×SD16C2×D11semidirect
724. #436C2×D11semidirect
730. #418C2×D11semidirect
820. C2×SD16C22×D11semidirect
830. C2×M16C22×D11semidirect
833. C4⋊Q8C22×D11semidirect
858. C22⋊Q8C22×D11semidirect
893. C4×Q8C22×D11semidirect
917. #117C22×D11semidirect
926. #107C22×D11semidirect
930. #106C22×D11semidirect
934. C4⋊C8C22×D11semidirect
938. #103C22×D11semidirect
952. #102C22×D11semidirect
953. #102C22×D11semidirect
954. #102C22×D11semidirect
961. C22⋊C8C22×D11semidirect
964. C4×C8C22×D11semidirect
1143. C11#61582semidirect

Maximal subgroups

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

subgroupindex
#130824692
D42×D112
#130808562
#130808542
#130808462
#130808442
#130808412
#130802382
#130802372
#130802322
#130802312
#130802142
#130802132
#130795562
#130795352
#130794342
#130794312
#130786222
#130786182
#130778452
#130778442
#130776542
C11×#33242
#6158211