Finite Group Databasebeta

← #15640420

Subgroups — #15640420

Order 2816.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082982C211yesmaximal, characteristic, complemented
2#13082380C211yesmaximal, characteristic, complemented
3#13080918C211yesmaximal, characteristic, complemented
4#13080844C211yesmaximal, characteristic, complemented
5#13080822C212yesmaximal, complemented
6#13080530C211yesmaximal, characteristic, complemented
7#13080471C212yesmaximal, complemented
8#13080426C211yesmaximal, characteristic, complemented
9#13080349C211yesmaximal, characteristic, complemented
10#13080302C212yesmaximal, complemented
11#13080288C211yesmaximal, characteristic, complemented
12#13080239C211yesmaximal, characteristic, complemented
13#13080226C212yesmaximal, complemented
14#13080211C211yesmaximal, characteristic, complemented
15#13079594C211yesmaximal, characteristic, complemented
16#13079545C211yesmaximal, characteristic, complemented
17#13079516C212yesmaximal, complemented
18#13079475C212yesmaximal, complemented
19#13078663C211yesmaximal, characteristic, complemented
20#13077915C212yesmaximal, complemented
21#13077879C212yesmaximal, complemented
22#13077682C211yesmaximal, characteristic, complemented
23C11×#3100C211yesmaximal, characteristic, complemented
24C2×#67037C2212yescomplemented
25C11×#532C2211yescharacteristic, complemented
26C2×C4×D4×C11C2211yescharacteristic, complemented
27#10623365—21no—
28#10623360—21no—
29C2×#66983—21no—
30C2×#66983—21no—
31C2×#66965C2212yescomplemented
32C2×#66964C2212yescomplemented
33C2×#66964C2212yescomplemented
34C2×D8×D11C2212yescomplemented
35#10623263C2211yescharacteristic, complemented
36#10623257C2211yescharacteristic, complemented
37#10623249C2211yescharacteristic, complemented
38#10623248C2211yescharacteristic, complemented
39#10623213—21no—
40#10623205—21no—
41#10623151—22no—
42#10623139C2212yescomplemented
43#10623138C2212yescomplemented
44#10623091—22no—
45#10623089C2212yescomplemented
46#10623086—21no—
47#10623086C2211yescharacteristic
48#10623086C2211yescharacteristic, complemented
49#10623085—22no—
50#10623085C2212yescomplemented
51#10623085C2212yescomplemented
52#10623085C2212yescomplemented
53D4×D44—21no—
54D4×D44C2211yescharacteristic
55D4×D44C2211yescharacteristic, complemented
56#10623041C2212yescomplemented
57#10623024—22no—
58#10623010C2211yescharacteristic, complemented
59#10623008C2211yescharacteristic
60#10623008C2211yescharacteristic, complemented
61C11×#480C2212yescomplemented
62C11×#474C2211yescharacteristic, complemented
63C11×#474C2211yescharacteristic, complemented
64C11×#459C2211yescharacteristic, complemented
65C11×#459C2211yescharacteristic, complemented
66C11×#447C2212yescomplemented
67C4×C11×D8C2212yescomplemented
68C4×C11×D8C2212yescomplemented
69C11×#431C2211yescharacteristic, complemented
70#10622831C2211yescharacteristic, complemented
71#10622830C2211yescharacteristic
72#10622771C2212yescomplemented
73#10622771C2212yescomplemented
74#10622769C2212yescomplemented
75#10622769C2212yescomplemented
76#10622706C2211yescharacteristic, complemented
77#10622701C2211yescharacteristic, complemented
78#10622689C2211yescharacteristic, complemented
79#10622686C2211yescharacteristic, complemented
80#10622650C2212yescomplemented
81#10622650C2212yescomplemented
82C4×#4324C2211yescharacteristic, complemented
83C4×#4324C2211yescharacteristic, complemented
84#10622629C2211yescharacteristic, complemented
85#10622629C2211yescharacteristic, complemented
86#10622629C2212yescomplemented
87#10622629C2212yescomplemented
88C4×#4323C2211yescharacteristic, complemented
89C4×#4323C2211yescharacteristic, complemented
90#10622622C2211yescharacteristic, complemented
91#10622622C2211yescharacteristic, complemented
92#10622583C2211yescharacteristic, complemented
93#10622581C2211yescharacteristic, complemented
94#10622538C2211yescharacteristic, complemented
95#10622501C2212yescomplemented
96#10622500C2212yescomplemented
97#10622499C2212yescomplemented
98#10622499C2212yescomplemented
99#10622498C2212yescomplemented
100#10622497C2212yescomplemented
101#10622496C2212yescomplemented
102#10622495C2212yescomplemented
103#10622462C2211yescharacteristic, complemented
104#10622461C2211yescharacteristic, complemented
105#10622456C2211yescharacteristic, complemented
106#10622454C2211yescharacteristic, complemented
107#10622451C2211yescharacteristic, complemented
108#10622451C2211yescharacteristic, complemented
109#10622447C2211yescharacteristic, complemented
110#10622447C2211yescharacteristic, complemented
111#10622396C2212yescomplemented
112#10622396C2212yescomplemented
113#10622395C2212yescomplemented
114#10622394C2212yescomplemented
115#10622394C2212yescomplemented
116#10622393C2212yescomplemented
117#10622391C2212yescomplemented
118#10622389C2212yescomplemented
119#10622389C2212yescomplemented
120#10622388C2212yescomplemented
121#10622386C2212yescomplemented
122#10622386C2212yescomplemented
123#10622385C2212yescomplemented
124#10622384C2212yescomplemented
125#10622383C2212yescomplemented
126D11×#102C2212yescomplemented
127#10622347C2212yescomplemented
128#10622346C2212yescomplemented
129#10622340C2212yescomplemented
130#10622340C2212yescomplemented
131#10622310C2212yescomplemented
132#10622309C2212yescomplemented
133#10622301C2212yescomplemented
134C8×D44C2212yescomplemented
135C2×C11×#41—21no—
136C22×D4×C11C2311yescharacteristic
137C23×C4×C11—21no—
138C22×C22⋊D11—22no—
139C22×C22⋊D11—22no—
140C2×#4343—21no—
141#67037—44no—
142#67037—44no—
143C2×#4341—22no—
144C2×#4341C2312yes—
145C2×#4341C2312yes—
146C2×#4341C2312yes—
147C2×D4×D11—22no—
148C2×D4×D11—21no—
149C2×D4×D11C2312yes—
150C2×D4×D11C2312yes—
151C2×D4×D11C2312yes—
152C2×#4339C2312yes—
153C2×#4339C2312yes—
154C22×D44—21no—
155C22×D44—21no—
156C2×C11×D8C2312yes—
157C2×C11×D8C2312yes—
158C11×C4⋊Q8C2311yescharacteristic
159C11×#127C2311yescharacteristic
160C11×#124—21no—
161C11×#121—21no—
162C11×#121C2312yes—
163C4×D4×C11—21no—
164C4×D4×C11—21no—
165C4×D4×C11—21no—
166C4×D4×C11C2311yescharacteristic
167C4×D4×C11C2311yescharacteristic
168C4×D4×C11C2311yescharacteristic
169C4×D4×C11C2311yescharacteristic
170C4×D4×C11C2312yes—
171C2×C11×C4⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4—21no—
173C2×C42×C11C2311yescharacteristic
174#67000—21no—
175#66999—21no—
176Q8×Dic11—21no—
177#66993—22no—
178#66993—21no—
179#66992—22no—
180#66992—22no—
181#66991—22no—
182#66991—21no—
183#66991C2312yes—
184#66991C2312yes—
185#66990—22no—
186#66990—22no—
187D4×Dic11—21no—
188C2×#4324C2311yescharacteristic
189C2×#4324C2311yescharacteristic
190C2×#4324C2312yes—
191C2×#4324C2312yes—
192C2×#4323C2311yescharacteristic
193C2×#4323C2311yescharacteristic
194C2×#4323C2312yes—
195C2×#4323C2312yes—
196#66983—21no—
197#66983—21no—
198#66983—22no—
199#66983—22no—
200#66983—21no—
201#66983—21no—
202#66983—22no—
203#66983—22no—
204#66983—22no—
205#66983—21no—
206#66983—21no—
207#66983D412yes—
208#66983D411yescharacteristic
209#66983D411yescharacteristic
210#66983C2311yescharacteristic
211#66982—21no—
212#66982—22no—
213C4×C22⋊D11—21no—
214C4×C22⋊D11—22no—
215C2×(C2×D11)⋊C4—22no—
216C2×(C2×D11)⋊C4—22no—
217C2×(C2×D11)⋊C4—22no—
218C2×C4⋊Dic11—21no—
219C2×C4⋊Dic11—21no—
220#66977C2311yescharacteristic
221#66965—44no—
222#66964—44no—
223#66964—44no—
224D8×D11—44no—
225C2×Dic44C2312yes—
226C2×D88C2312yes—
227C2×#4314C2312yes—
228C2×#4314C2312yes—
229C2×#4313C2312yes—
230C2×#4313C2312yes—
231C2×C8×D11C2312yes—
232C2×C8×D11C2312yes—
233#66951—22no—
234#66950—22no—
235#66950C2312yes—
236#66950C2312yes—
237#66950C2312yes—
238#66948—22no—
239#66948C2312yes—
240#66948C2312yes—
241#66948C2312yes—
242#66947—22no—
243#66945C2312yes—
244C4⋊C4×D11C2312yes—
245#66939—22no—
246#66939—22no—
247#66939—22no—
248#66939—22no—
249#66939—22no—
250#66938—22no—
251#66937—22no—
252#66937—22no—
253#66935—22no—
254#66935—22no—
255#66935—22no—
256#66935—22no—
257#66935—22no—
258#66935—22no—
259#66932—22no—
260#66931—22no—
261#66929—21no—
262#66928D412yes—
263#66928C2312yes—
264#66928C2311yescharacteristic
265#66927D411yescharacteristic
266#66927C2311yescharacteristic
267C4×D44—21no—
268C4×D44—21no—
269C4×D44C2311yescharacteristic
270C4×D44C2311yescharacteristic
271C4×D44C2312yes—
272C4×D44C2311yescharacteristic
273#66925—21no—
274#66923C2311yescharacteristic
275#66922D411yescharacteristic
276#66922C2311yescharacteristic
277C4×Dic22C2311yescharacteristic
278C11×#107C2312yes—
279C11×#107C2312yes—
280C11×C4⋊C8C2311yescharacteristic
281C11×C4⋊C8C2311yescharacteristic
282C11×#102C2312yes—
283C11×#102C2312yes—
284C11×#102C2312yes—
285C11×#102C2312yes—
286C11×C22⋊C8C2312yes—
287C4×C8×C11C2312yes—
288#66896C2311yescharacteristic
289#66896C2311yescharacteristic
290#66896C2311yescharacteristic
291#66896C2311yescharacteristic
292C22⋊(C11⋊C8)C2311yescharacteristic
293C22⋊(C11⋊C8)C2311yescharacteristic
294#66885C2312yes—
295#66885C2312yes—
296(C2×D11)⋊C8C2312yes—
297(C2×D11)⋊C8C2312yes—
298(C2×D11)⋊C8C2312yes—
299(C2×D11)⋊C8C2312yes—
300#66880C2312yes—
301#66880C2312yes—
302#66874C2312yes—
303#66874C2311yescharacteristic
304#66874C2312yes—
305#66874C2311yescharacteristic
306#66873C2312yes—
307#66873C2311yescharacteristic
308#66873C2312yes—
309#66873C2311yescharacteristic
310#66872C2311yescharacteristic
311#66872C2311yescharacteristic
312#66871C2311yescharacteristic
313#66871C2311yescharacteristic
314C4⋊(C11⋊C8)C2311yescharacteristic
315C4⋊(C11⋊C8)C2311yescharacteristic
316C4×C11⋊C8C2311yescharacteristic
317C4×C11⋊C8C2311yescharacteristic
318#61657—111nomaximal, Sylow
319C24×C11—21no—
320C23×D11—22no—
321C23×D11—22no—
322C23×D11—22no—
323C11×#41—82no—
324C2×Q8×C11—21no—
325C2×D4×C11—22no—
326C2×D4×C11—22no—
327C2×D4×C11—22no—
328C2×D4×C11—21no—
329C2×D4×C11—21no—
330C2×D4×C11—21no—
331C2×D4×C11C2412yes—
332C2×D4×C11C2411yescharacteristic
333C2×D4×C11C2411yescharacteristic
334C22×C4×C11—21no—
335C22×C4×C11—21no—
336C22×C4×C11—21no—
337C22×C4×C11—21no—
338C22×C4×C11—21no—
339C22×C4×C11—22no—
340C22×C4×C11—82no—
341C22×C4×C11C2×D411yescharacteristic
342C22×C4×C11C2×D411yescharacteristic
343C22×C4×C11C2411yescharacteristic
344C2×C22⋊D11—22no—
345C2×C22⋊D11—22no—
346C2×C22⋊D11—22no—
347C2×C22⋊D11—22no—
348C2×C22⋊D11—21no—
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—
357C2×C22⋊D11C2×D412yes—
358C22×Dic11—22no—
359C22×Dic11—22no—
360C22×Dic11—22no—
361#4343—82no—
362#4341—24no—
363#4341—24no—
364#4341—42no—
365#4341—42no—
366#4341—42no—
367#4341—42no—
368#4341—48no—
369D4×D11—24no—
370D4×D11—24no—
371D4×D11—42no—
372D4×D11—42no—
373D4×D11—48no—
374D4×D11—42no—
375D4×D11—42no—
376D4×D11—82no—
377#4339—42no—
378#4339—42no—
379#4339—42no—
380#4339—42no—
381C2×D44—22no—
382C2×D44—22no—
383C2×D44—22no—
384C2×D44—21no—
385C2×D44—21no—
386C2×D44—82no—
387C2×D44—82no—
388C2×D44C2×D411yescharacteristic
389C2×D44C2×D411yescharacteristic
390C2×D44C2×D412yes—
391C2×D44C2×D412yes—
392C2×D44C2412yes—
393C2×D44C2411yescharacteristic
394C2×C4×D11—22no—
395C2×C4×D11—21no—
396C2×C4×D11—22no—
397C2×C4×D11C2412yes—
398C2×C4×D11C2412yes—
399C2×Dic22C2×D412yes—
400C2×Dic22C2412yes—
401C2×Dic22C2411yescharacteristic
402C11×D8—24no—
403C11×D8—24no—
404C2×C8×C11C2412yes—
405C2×C8×C11C2412yes—
406C11×C4⋊C4—21no—
407C11×C4⋊C4—21no—
408C11×C4⋊C4C2411yescharacteristic
409C11×C4⋊C4C2411yescharacteristic
410C11×C4⋊C4C2412yes—
411C11×C22⋊C4—22no—
412C11×C22⋊C4—22no—
413C11×C22⋊C4—21no—
414C11×C22⋊C4—21no—
415C11×C22⋊C4—21no—
416C11×C22⋊C4—21no—
417C42×C11C2×D411yescharacteristic
418C42×C11C2×D411yescharacteristic
419C42×C11C2411yescharacteristic
420C42×C11C2411yescharacteristic
421C22⋊Dic11—22no—
422C22⋊Dic11—22no—
423C22⋊Dic11—21no—
424#4324—22no—
425#4324—22no—
426#4324—42no—
427#4324—42no—
428#4323—22no—
429#4323—22no—
430#4323—42no—
431#4323—42no—
432(C2×D11)⋊C4—22no—
433(C2×D11)⋊C4—22no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—21no—
440(C2×D11)⋊C4—21no—
441(C2×D11)⋊C4—22no—
442(C2×D11)⋊C4—22no—
443(C2×D11)⋊C4—21no—
444(C2×D11)⋊C4—21no—
445(C2×D11)⋊C4C2×D412yes—
446(C2×D11)⋊C4C2×D412yes—
447(C2×D11)⋊C4C2×D412yes—
448(C2×D11)⋊C4C2×D412yes—
449C4⋊Dic11—22no—
450C4⋊Dic11—22no—
451C4⋊Dic11—22no—
452C4⋊Dic11—21no—
453C4⋊Dic11—21no—
454C4⋊Dic11C2×D412yes—
455C4⋊Dic11C2×D411yescharacteristic
456C4⋊Dic11C2×D411yescharacteristic
457C4⋊Dic11C2411yescharacteristic
458C4⋊Dic11C2411yescharacteristic
459Dic11⋊C4—22no—
460Dic11⋊C4—21no—
461Dic11⋊C4—21no—
462Dic11⋊C4—21no—
463Dic11⋊C4—21no—
464C4×Dic11—22no—
465C4×Dic11—21no—
466C2×C11⋊C8C2411yescharacteristic
467C2×C11⋊C8C2411yescharacteristic
468C2×C11⋊C8C2411yescharacteristic
469C2×C11⋊C8C2411yescharacteristic
470Dic44—42no—
471D88—42no—
472#4314—42no—
473#4314—42no—
474#4313—42no—
475#4313—42no—
476C8×D11—42no—
477C8×D11—42no—
478#3546—111no—
479#3496—111no—
480#3330—111no—
481#3324—111no—
482#3322—112no—
483#3302—111no—
484#3297—112no—
485#3294—111no—
486#3284—111no—
487#3280—112no—
488D4×D8—111no—
489#3274—111no—
490#3273—112no—
491#3272—111no—
492#3212—111no—
493#3207—111no—
494#3203—112no—
495#3198—112no—
496#3105—111no—
497#3100D1111yescharacteristic, complemented
498#3012—112no—
499#3008—112no—
500#2979—111no—
501C23×C11—24no—
502C23×C11—21no—
503C23×C11—21no—
504C23×C11—22no—
505C23×C11—81no—
506C23×C11—81no—
507C23×C11C22×D411yescharacteristic
508C22×D11—21no—
509C22×D11—22no—
510C22×D11—44no—
511C22×D11—44no—
512C22×D11—82no—
513C22×D11—82no—
514C22×D11—82no—
515C22×D11—82no—
516C22×D11—82no—
517C22×D11—82no—
518C22×D11—82no—
519C22×D11C22×D412yes—
520C22×D11C22×D412yes—
521Q8×C11—42no—
522D4×C11—24no—
523D4×C11—21no—
524D4×C11—21no—
525D4×C11—22no—
526D4×C11—22no—
527D4×C11—42no—
528D4×C11—81no—
529D4×C11—82no—
530D4×C11H(5,𝔽2)12yes—
531D4×C11H(5,𝔽2)12yes—
532C2×C4×C11—22no—
533C2×C4×C11—21no—
534C2×C4×C11—21no—
535C2×C4×C11—22no—
536C2×C4×C11—21no—
537C2×C4×C11—21no—
538C2×C4×C11—41no—
539C2×C4×C11—42no—
540C2×C4×C11—42no—
541C2×C4×C11—81no—
542C2×C4×C11—81no—
543C2×C4×C11—82no—
544C2×C4×C11—81no—
545C2×C4×C11C22×D411yescharacteristic
546C2×C4×C11C22×D411yescharacteristic
547C2×C4×C11C22×D411yescharacteristic
548C2×C4×C11C22×D411yescharacteristic
549C2×C4×C11C22×D411yescharacteristic
550C2×C4×C11C2511yescharacteristic
551C22⋊D11—42no—
552C22⋊D11—42no—
553C22⋊D11—44no—
554C22⋊D11—44no—
555C22⋊D11—44no—
556C22⋊D11—44no—
557C22⋊D11—44no—
558C22⋊D11—82no—
559C22⋊D11—82no—
560C22⋊D11—82no—
561C22⋊D11—82no—
562C22⋊D11—81no—
563C2×Dic11—21no—
564C2×Dic11—21no—
565C2×Dic11—21no—
566C2×Dic11—22no—
567C2×Dic11—44no—
568C2×Dic11—44no—
569C2×Dic11—82no—
570C2×Dic11C22×D412yes—
571C2×Dic11C22×D412yes—
572D44—22no—
573D44—22no—
574D44—21no—
575D44—22no—
576D44—21no—
577D44—22no—
578D44—42no—
579D44—42no—
580D44—42no—
581D44—81no—
582D44—82no—
583D44—82no—
584D44—82no—
585C4×D11—22no—
586C4×D11—22no—
587C4×D11—22no—
588C4×D11—22no—
589C4×D11—44no—
590C4×D11—42no—
591C4×D11—82no—
592Dic22—21no—
593Dic22—22no—
594Dic22—21no—
595Dic22—22no—
596Dic22—42no—
597C8×C11—22no—
598C8×C11—22no—
599C11⋊C8—21no—
600C11⋊C8—21no—
601C11⋊C8—21no—
602C11⋊C8—21no—
603C2×H(5,𝔽2)—112no—
604C2×AGL(1,ℤ/8)—112no—
605C2×AGL(1,ℤ/8)—112no—
606C2×#135—112no—
607C22×D8—112no—
608#560—222no—
609#556—111no—
610#553—112no—
611#550—111no—
612#550—221no—
613#547—111no—
614#547—111no—
615#547—111no—
616#547—221no—
617#546—112no—
618#546—112no—
619#546—112no—
620#546—222no—
621#546—221no—
622D42—111no—
623D42—111no—
624D42—111no—
625D42—221no—
626#542—221no—
627#538—222no—
628#537—112no—
629#537—112no—
630#535—112no—
631#535—221no—
632#534—222no—
633#532—111no—
634#532—111no—
635#532C2×D1111yescharacteristic, complemented
636#529—111no—
637C2×#121—221no—
638C2×#121—221no—
639C2×C4×D4C2×D1111yescharacteristic, complemented
640#495—112no—
641#493—111no—
642#492—111no—
643#488—112no—
644#487—111no—
645#486—111no—
646#485—112no—
647#484—111no—
648#484—112no—
649#482—112no—
650#481—111no—
651#480—112no—
652#480C2×D1112yescomplemented
653#478—111no—
654#478—111no—
655#474C2×D1111yescharacteristic, complemented
656#474C2×D1111yescharacteristic, complemented
657#469—112no—
658#468—112no—
659#468—112no—
660#468—112no—
661#467—112no—
662#466—112no—
663#466—112no—
664#465—112no—
665#463—111no—
666#463—111no—
667#463—112no—
668#463—112no—
669#462—111no—
670#461—111no—
671#460—111no—
672#459—111no—
673#459C2×D1111yescharacteristic, complemented
674#459C2×D1111yescharacteristic, complemented
675#452—112no—
676#452—112no—
677#452—112no—
678#450—111no—
679#450—112no—
680#450—112no—
681#449—112no—
682#449—112no—
683#449—112no—
684#449—112no—
685#449—112no—
686#449—112no—
687#449—112no—
688#447—111no—
689#447—112no—
690#447—112no—
691#447—112no—
692#447—112no—
693#447C2×D1112yescomplemented
694C4×SD16—111no—
695C4×SD16—111no—
696C4×D8—111no—
697C4×D8—111no—
698C4×D8C2×D1112yescomplemented
699C4×D8C2×D1112yescomplemented
700#436—111no—
701#436—111no—
702#436—112no—
703C8×D4—111no—
704C8×D4—111no—
705C8×D4—112no—
706#431—111no—
707#431C2×D1111yescharacteristic, complemented
708#418—112no—
709#417—112no—
710#416—112no—
711C2×#102—112no—
712#408—112no—
713#408—112no—
714C22×C11—21no—
715C22×C11—21no—
716C22×C11—22no—
717C22×C11—22no—
718C22×C11—21no—
719C22×C11—41no—
720C22×C11—41no—
721C22×C11—41no—
722C22×C11—41no—
723C22×C11—42no—
724C22×C11—42no—
725C22×C11—42no—
726C22×C11—84no—
727C22×C11C23×D411yescharacteristic
728C2×D11—22no—
729C2×D11—22no—
730C2×D11—22no—
731C2×D11—22no—
732C2×D11—22no—
733C2×D11—22no—
734C2×D11—42no—
735C2×D11—41no—
736C2×D11—42no—
737C2×D11—41no—
738C2×D11—41no—
739C2×D11—42no—
740C2×D11—164no—
741C2×D11—164no—
742C2×D11—164no—
743C4×C11—21no—
744C4×C11—21no—
745C4×C11—21no—
746C4×C11—21no—
747C4×C11—41no—
748C4×C11—41no—
749C4×C11—42no—
750C4×C11#57612yes—
751C4×C11C2×H(5,𝔽2)11yescharacteristic
752C4×C11C2×H(5,𝔽2)11yescharacteristic
753Dic11—22no—
754Dic11—22no—
755Dic11—41no—
756Dic11—42no—
757Dic11—41no—
758Dic11—41no—
759H(5,𝔽2)—444no—
760H(5,𝔽2)—444no—
761C2×#41—21no—
762C2×#41—112no—
763C2×#41—112no—
764C2×#41—112no—
765C2×#41—112no—
766C2×#41—112no—
767C2×#41—222no—
768C2×#41—221no—
769C22×D4—112no—
770C22×D4—112no—
771C22×D4—112no—
772C22×D4—221no—
773C22×D4—221no—
774C22×D4—222no—
775C22×D4—221no—
776C22×D4—222no—
777C22×D4—222no—
778C22×D4C22×D1111yescharacteristic
779C23×C4—21no—
780AGL(1,ℤ/8)—444no—
781AGL(1,ℤ/8)—444no—
782#135—444no—
783C2×Q16—112no—
784C2×SD16—111no—
785C2×SD16—111no—
786C2×SD16—112no—
787C2×SD16—112no—
788C2×SD16—112no—
789C2×SD16—112no—
790C2×D8—111no—
791C2×D8—111no—
792C2×D8—112no—
793C2×D8—112no—
794C2×D8—112no—
795C2×D8—444no—
796C2×D8C22×D1112yes—
797C2×D8C22×D1112yes—
798C2×M16—112no—
799C2×M16—112no—
800C22×C8—112no—
801C22×C8—112no—
802C4⋊Q8—111no—
803C4⋊Q8—111no—
804C4⋊Q8C22×D1111yescharacteristic
805#127—111no—
806#127—111no—
807#127—222no—
808#127—221no—
809#127C22×D1111yescharacteristic
810#126—222no—
811#126—222no—
812#126—221no—
813#125—111no—
814#124—21no—
815#124—112no—
816#124—111no—
817#124—112no—
818#124—222no—
819#124—221no—
820#123—222no—
821#123—222no—
822#123—222no—
823#123—222no—
824#123—222no—
825#123—222no—
826#123—222no—
827#123—221no—
828C22⋊Q8—111no—
829C22⋊Q8—112no—
830C22⋊Q8—112no—
831C22⋊Q8—112no—
832C22⋊Q8—222no—
833C22⋊Q8—222no—
834C22⋊Q8—221no—
835#121—21no—
836#121—111no—
837#121—111no—
838#121—112no—
839#121—112no—
840#121—112no—
841#121—111no—
842#121—112no—
843#121—112no—
844#121—112no—
845#121—222no—
846#121—222no—
847#121—222no—
848#121—222no—
849#121—222no—
850#121—222no—
851#121—222no—
852#121—221no—
853#121—221no—
854#121—221no—
855#121—222no—
856#121—222no—
857#121—221no—
858#121—221no—
859#121—222no—
860#121—222no—
861#121—221no—
862#121—221no—
863#121C22×D1112yes—
864#120—222no—
865#120—222no—
866#120—222no—
867#120—222no—
868#120—222no—
869#120—222no—
870#120—222no—
871#120—222no—
872C4×Q8—111no—
873C4×Q8—221no—
874C4×D4—21no—
875C4×D4—21no—
876C4×D4—21no—
877C4×D4—111no—
878C4×D4—111no—
879C4×D4—112no—
880C4×D4—111no—
881C4×D4—222no—
882C4×D4—221no—
883C4×D4—221no—
884C4×D4—221no—
885C4×D4—221no—
886C4×D4C22×D1111yescharacteristic
887C4×D4C22×D1111yescharacteristic
888C4×D4C22×D1111yescharacteristic
889C4×D4C22×D1111yescharacteristic
890C4×D4C22×D1112yes—
891#117—112no—
892#117—221no—
893C2×C4⋊C4—112no—
894C2×C4⋊C4—221no—
895C2×C4⋊C4—221no—
896C2×C4⋊C4C22×D1111yescharacteristic
897C2×C22⋊C4—21no—
898C2×C22⋊C4—222no—
899C2×C22⋊C4—222no—
900C2×C22⋊C4—222no—
901C2×C42C22×D1111yescharacteristic
902#107—111no—
903#107—111no—
904#107C22×D1112yes—
905#107C22×D1112yes—
906#106—111no—
907#106—111no—
908C4⋊C8—111no—
909C4⋊C8—111no—
910C4⋊C8C22×D1111yescharacteristic
911C4⋊C8C22×D1111yescharacteristic
912#103—112no—
913#103—112no—
914#103—112no—
915#103—112no—
916#103—111no—
917#103—111no—
918#102—111no—
919#102—111no—
920#102—111no—
921#102—111no—
922#102—112no—
923#102—112no—
924#102—112no—
925#102—112no—
926#102—111no—
927#102—111no—
928#102C22×D1112yes—
929#102C22×D1112yes—
930#102C22×D1112yes—
931#102C22×D1112yes—
932C22⋊C8—111no—
933C22⋊C8—111no—
934C22⋊C8—112no—
935C22⋊C8—112no—
936C22⋊C8—112no—
937C22⋊C8—112no—
938C22⋊C8C22×D1112yes—
939C4×C8—111no—
940C4×C8—111no—
941C4×C8C22×D1112yes—
942C2×C11—42no—
943C2×C11—42no—
944C2×C11—41no—
945C2×C11—82no—
946C2×C11#348411yescharacteristic
947C2×C11C2×#57611yescharacteristic
948C2×C11#358411yescharacteristic
949D11—42no—
950D11—42no—
951D11—82no—
952D11—81no—
953C24—21no—
954C24—222no—
955C24—222no—
956C24—222no—
957#41—82no—
958#41—224no—
959#41—224no—
960#41—442no—
961#41—442no—
962#41—442no—
963#41—442no—
964#41—442no—
965#41—442no—
966#41—442no—
967#41—442no—
968#41—448no—
969#41—882no—
970C2×Q8—21no—
971C2×Q8—112no—
972C2×Q8—112no—
973C2×Q8—111no—
974C2×D4—22no—
975C2×D4—22no—
976C2×D4—22no—
977C2×D4—21no—
978C2×D4—21no—
979C2×D4—21no—
980C2×D4—112no—
981C2×D4—112no—
982C2×D4—111no—
983C2×D4—111no—
984C2×D4—112no—
985C2×D4—112no—
986C2×D4—112no—
987C2×D4—111no—
988C2×D4—222no—
989C2×D4—222no—
990C2×D4—222no—
991C2×D4—222no—
992C2×D4—222no—
993C2×D4—222no—
994C2×D4—224no—
995C2×D4—224no—
996C2×D4—222no—
997C2×D4—222no—
998C2×D4—222no—
999C2×D4—222no—
1000C2×D4—222no—
1001C2×D4—222no—
1002C2×D4—221no—
1003C2×D4—221no—
1004C2×D4—221no—
1005C2×D4—442no—
1006C2×D4—442no—
1007C2×D4—442no—
1008C2×D4—442no—
1009C2×D4—448no—
1010C2×D4—448no—
1011C2×D4—448no—
1012C2×D4—882no—
1013C2×D4—882no—
1014C2×D4—882no—
1015C2×D4C23×D1112yes—
1016C2×D4C23×D1111yescharacteristic
1017C2×D4C23×D1111yescharacteristic
1018C22×C4—21no—
1019C22×C4—21no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—22no—
1024C22×C4—82no—
1025C22×C4—112no—
1026C22×C4—112no—
1027C22×C4—222no—
1028C22×C4—222no—
1029C22×C4—222no—
1030C22×C4—222no—
1031C22×C4—221no—
1032C22×C4—222no—
1033C22×C4D4×D1111yescharacteristic
1034C22×C4D4×D1111yescharacteristic
1035C22×C4C23×D1111yescharacteristic
1036Q16—442no—
1037SD16—222no—
1038SD16—222no—
1039SD16—442no—
1040SD16—442no—
1041SD16—442no—
1042SD16—442no—
1043D8—24no—
1044D8—24no—
1045D8—222no—
1046D8—222no—
1047D8—442no—
1048D8—442no—
1049D8—442no—
1050M16—442no—
1051M16—442no—
1052C2×C8—111no—
1053C2×C8—111no—
1054C2×C8—111no—
1055C2×C8—111no—
1056C2×C8—442no—
1057C2×C8—442no—
1058C2×C8C23×D1112yes—
1059C2×C8C23×D1112yes—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—111no—
1063C4⋊C4—111no—
1064C4⋊C4—112no—
1065C4⋊C4—111no—
1066C4⋊C4—111no—
1067C4⋊C4—222no—
1068C4⋊C4—222no—
1069C4⋊C4—222no—
1070C4⋊C4—222no—
1071C4⋊C4—221no—
1072C4⋊C4—221no—
1073C4⋊C4—221no—
1074C4⋊C4—221no—
1075C4⋊C4—221no—
1076C4⋊C4—221no—
1077C4⋊C4C23×D1112yes—
1078C4⋊C4C23×D1111yescharacteristic
1079C4⋊C4C23×D1111yescharacteristic
1080C22⋊C4—21no—
1081C22⋊C4—21no—
1082C22⋊C4—21no—
1083C22⋊C4—21no—
1084C22⋊C4—22no—
1085C22⋊C4—22no—
1086C22⋊C4—112no—
1087C22⋊C4—112no—
1088C22⋊C4—112no—
1089C22⋊C4—112no—
1090C22⋊C4—222no—
1091C22⋊C4—222no—
1092C22⋊C4—222no—
1093C22⋊C4—222no—
1094C22⋊C4—222no—
1095C22⋊C4—222no—
1096C22⋊C4—222no—
1097C22⋊C4—222no—
1098C22⋊C4—222no—
1099C22⋊C4—221no—
1100C22⋊C4—222no—
1101C22⋊C4—221no—
1102C22⋊C4—221no—
1103C22⋊C4—221no—
1104C22⋊C4—221no—
1105C22⋊C4—222no—
1106C42—222no—
1107C42—221no—
1108C42D4×D1111yescharacteristic
1109C42D4×D1111yescharacteristic
1110C42C23×D1111yescharacteristic
1111C42C23×D1111yescharacteristic
1112C11#6165711yescharacteristic, complemented, Sylow
1113C23—24no—
1114C23—21no—
1115C23—21no—
1116C23—22no—
1117C23—81no—
1118C23—81no—
1119C23—112no—
1120C23—112no—
1121C23—221no—
1122C23—222no—
1123C23—444no—
1124C23—444no—
1125C23—882no—
1126C23—882no—
1127C23—882no—
1128C23—882no—
1129C23—882no—
1130C23—882no—
1131C23—882no—
1132C23C2×D4×D1111yescharacteristic
1133Q8—42no—
1134Q8—221no—
1135Q8—221no—
1136Q8—222no—
1137Q8—222no—
1138Q8—442no—
1139D4—24no—
1140D4—21no—
1141D4—21no—
1142D4—22no—
1143D4—22no—
1144D4—42no—
1145D4—81no—
1146D4—82no—
1147D4—222no—
1148D4—222no—
1149D4—221no—
1150D4—221no—
1151D4—222no—
1152D4—222no—
1153D4—442no—
1154D4—442no—
1155D4—442no—
1156D4—442no—
1157D4—444no—
1158D4—444no—
1159D4—444no—
1160D4—444no—
1161D4—444no—
1162D4—442no—
1163D4—881no—
1164D4—882no—
1165D4—882no—
1166D4—882no—
1167D4—882no—
1168D4—881no—
1169D4—882no—
1170D4—882no—
1171D4—882no—
1172D4#6704212yes—
1173D4#6704212yes—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—81no—
1184C2×C4—81no—
1185C2×C4—82no—
1186C2×C4—81no—
1187C2×C4—112no—
1188C2×C4—112no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—221no—
1194C2×C4—221no—
1195C2×C4—221no—
1196C2×C4—222no—
1197C2×C4—444no—
1198C2×C4—444no—
1199C2×C4—444no—
1200C2×C4—442no—
1201C2×C4—882no—
1202C2×C4—882no—
1203C2×C4C2×D4×D1111yescharacteristic
1204C2×C4C2×D4×D1111yescharacteristic
1205C2×C4C2×D4×D1111yescharacteristic
1206C2×C4C2×D4×D1111yescharacteristic
1207C2×C4C2×D4×D1111yescharacteristic
1208C2×C4C24×D1111yescharacteristic
1209C8—22no—
1210C8—22no—
1211C8—221no—
1212C8—221no—
1213C8—221no—
1214C8—221no—
1215C22—21no—
1216C22—22no—
1217C22—22no—
1218C22—21no—
1219C22—21no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—84no—
1228C22—222no—
1229C22—222no—
1230C22—222no—
1231C22—222no—
1232C22—222no—
1233C22—222no—
1234C22—442no—
1235C22—441no—
1236C22—441no—
1237C22—442no—
1238C22—442no—
1239C22—441no—
1240C22—1764no—
1241C22—1764no—
1242C22—1764no—
1243C22C22×D4×D1111yescharacteristic
1244C4—21no—
1245C4—21no—
1246C4—21no—
1247C4—21no—
1248C4—41no—
1249C4—41no—
1250C4—42no—
1251C4—222no—
1252C4—222no—
1253C4—442no—
1254C4—441no—
1255C4—441no—
1256C4—441no—
1257C4#1062328812yes—
1258C4C2×#6704211yescharacteristic
1259C4C2×#6704211yescharacteristic
1260C2—41no—
1261C2—42no—
1262C2—42no—
1263C2—82no—
1264C2—442no—
1265C2—442no—
1266C2—882no—
1267C2—881no—
1268C2#1308224911yescharacteristic
1269C2C2×#1062328811yescharacteristic
1270C2#1308338911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3100C2
socleC22×C11C23×D4
hypercenter#3100D11
hypocenterC11#61657
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13082982C2semidirect
2. #13082380C2semidirect
3. #13080918C2semidirect
4. #13080844C2semidirect
5. #13080822C2semidirect
6. #13080530C2semidirect
7. #13080471C2semidirect
8. #13080426C2semidirect
9. #13080349C2semidirect
10. #13080302C2semidirect
11. #13080288C2semidirect
12. #13080239C2semidirect
13. #13080226C2semidirect
14. #13080211C2semidirect
15. #13079594C2semidirect
16. #13079545C2semidirect
17. #13079516C2semidirect
18. #13079475C2semidirect
19. #13078663C2semidirect
20. #13077915C2semidirect
21. #13077879C2semidirect
22. #13077682C2semidirect
23. C11×#3100C2semidirect
24. C2×#67037C22semidirect
25. C11×#532C22semidirect
26. C2×C4×D4×C11C22semidirect
31. C2×#66965C22semidirect
32. C2×#66964C22semidirect
33. C2×#66964C22semidirect
34. C2×D8×D11C22semidirect
35. #10623263C22semidirect
36. #10623257C22semidirect
37. #10623249C22semidirect
38. #10623248C22semidirect
42. #10623139C22semidirect
43. #10623138C22semidirect
45. #10623089C22semidirect
48. #10623086C22semidirect
50. #10623085C22semidirect
51. #10623085C22semidirect
52. #10623085C22semidirect
55. D4×D44C22semidirect
56. #10623041C22semidirect
58. #10623010C22semidirect
60. #10623008C22semidirect
61. C11×#480C22semidirect
62. C11×#474C22semidirect
63. C11×#474C22semidirect
64. C11×#459C22semidirect
65. C11×#459C22semidirect
66. C11×#447C22semidirect
67. C4×C11×D8C22semidirect
68. C4×C11×D8C22semidirect
69. C11×#431C22semidirect
70. #10622831C22semidirect
72. #10622771C22semidirect
73. #10622771C22semidirect
74. #10622769C22semidirect
75. #10622769C22semidirect
76. #10622706C22semidirect
77. #10622701C22semidirect
78. #10622689C22semidirect
79. #10622686C22semidirect
80. #10622650C22semidirect
81. #10622650C22semidirect
82. C4×#4324C22semidirect
83. C4×#4324C22semidirect
84. #10622629C22semidirect
85. #10622629C22semidirect
86. #10622629C22semidirect
87. #10622629C22semidirect
88. C4×#4323C22semidirect
89. C4×#4323C22semidirect
90. #10622622C22semidirect
91. #10622622C22semidirect
92. #10622583C22semidirect
93. #10622581C22semidirect
94. #10622538C22semidirect
95. #10622501C22semidirect
96. #10622500C22semidirect
97. #10622499C22semidirect
98. #10622499C22semidirect
99. #10622498C22semidirect
100. #10622497C22semidirect
101. #10622496C22semidirect
102. #10622495C22semidirect
103. #10622462C22semidirect
104. #10622461C22semidirect
105. #10622456C22semidirect
106. #10622454C22semidirect
107. #10622451C22semidirect
108. #10622451C22semidirect
109. #10622447C22semidirect
110. #10622447C22semidirect
111. #10622396C22semidirect
112. #10622396C22semidirect
113. #10622395C22semidirect
114. #10622394C22semidirect
115. #10622394C22semidirect
116. #10622393C22semidirect
117. #10622391C22semidirect
118. #10622389C22semidirect
119. #10622389C22semidirect
120. #10622388C22semidirect
121. #10622386C22semidirect
122. #10622386C22semidirect
123. #10622385C22semidirect
124. #10622384C22semidirect
125. #10622383C22semidirect
126. D11×#102C22semidirect
127. #10622347C22semidirect
128. #10622346C22semidirect
129. #10622340C22semidirect
130. #10622340C22semidirect
131. #10622310C22semidirect
132. #10622309C22semidirect
133. #10622301C22semidirect
134. C8×D44C22semidirect
497. #3100D11semidirect
635. #532C2×D11semidirect
639. C2×C4×D4C2×D11semidirect
652. #480C2×D11semidirect
655. #474C2×D11semidirect
656. #474C2×D11semidirect
673. #459C2×D11semidirect
674. #459C2×D11semidirect
693. #447C2×D11semidirect
698. C4×D8C2×D11semidirect
699. C4×D8C2×D11semidirect
707. #431C2×D11semidirect
1112. C11#61657semidirect

Maximal subgroups

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

subgroupindex
#130829822
#130823802
#130809182
#130808442
#130808222
#130805302
#130804712
#130804262
#130803492
#130803022
#130802882
#130802392
#130802262
#130802112
#130795942
#130795452
#130795162
#130794752
#130786632
#130779152
#130778792
#130776822
C11×#31002
#6165711