Finite Group Databasebeta

← #14722241

Subgroups — #14722241

Order 2816.

1004 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082485C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic, complemented
3#13077277C211yesmaximal, characteristic, complemented
4#13067319C211yesmaximal, characteristic, complemented
5#13067318C211yesmaximal, characteristic, complemented
6#13067311C211yesmaximal, characteristic, complemented
7#13067310C211yesmaximal, characteristic, complemented
8#13067303C211yesmaximal, characteristic, complemented
9#13067282C211yesmaximal, characteristic, complemented
10#13067277C211yesmaximal, characteristic, complemented
11#13067270C211yesmaximal, characteristic, complemented
12#13067263C211yesmaximal, characteristic, complemented
13#13067262C211yesmaximal, characteristic, complemented
14D11×#331C211yesmaximal, characteristic, complemented
15C11×#1543C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17#10623365C412yes—
18#10623360C412yes—
19#10623259C2211yescharacteristic
20#10623256C2211yescharacteristic
21#10623247C2211yescharacteristic
22D11×#127C2211yescharacteristic
23#10623212C412yes—
24#10623207C412yes—
25#10623150—21no—
26#10623143—21no—
27#10623138—21no—
28#10623130—21no—
29#10623093—21no—
30#10623090—21no—
31#10623085—21no—
32#10623076—21no—
33#10623008C2211yescharacteristic
34C4×#4339C2211yescharacteristic
35C11×#431C2211yescharacteristic, complemented
36C11×#431C2211yescharacteristic, complemented
37#10622539C2211yescharacteristic, complemented
38C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
39#10622450C2211yescharacteristic
40#10622448C2211yescharacteristic, complemented
41#10622446C2211yescharacteristic
42#10622446C2211yescharacteristic, complemented
43#10622446C2211yescharacteristic, complemented
44D11×C4⋊C8C2211yescharacteristic
45D11×C4⋊C8C2211yescharacteristic
46D11×C4⋊C8C2211yescharacteristic, complemented
47#10622340—21no—
48(C22⋊D11)⋊C8—21no—
49(C22⋊D11)⋊C8—21no—
50#10622333—21no—
51#10622303—21no—
52#10622302—21no—
53C8×D44—21no—
54C8×Dic22—21no—
55C11×#333C2211yescharacteristic, complemented
56C11×#333C2211yescharacteristic, complemented
57C11×#331C2211yescharacteristic
58C11×#331C2211yescharacteristic
59#10622184C2211yescharacteristic, complemented
60#10622184C2211yescharacteristic, complemented
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622124C2211yescharacteristic, complemented
64#10622124C2211yescharacteristic, complemented
65#10622123C2211yescharacteristic
66#10622123C2211yescharacteristic
67#10622123C2211yescharacteristic
68#10622123C2211yescharacteristic
69#10622120C2211yescharacteristic, complemented
70#10622120C2211yescharacteristic, complemented
71C2×C11×#41C2×C412yes—
72C2×#4343C2×C412yes—
73C2×#4341—21no—
74C2×D4×D11—21no—
75C2×D4×D11—21no—
76C2×D4×D11C2×C412yes—
77C2×#4339—21no—
78C2×#4339D411yescharacteristic
79C11×C4⋊Q8C2311yescharacteristic
80C11×#127C2311yescharacteristic
81C11×#124C2×C412yes—
82C11×#121—21no—
83C11×#121—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C2×C42×C11C2311yescharacteristic
87#67000C2×C412yes—
88#66999C2×C412yes—
89Q8×Dic11C2×C412yes—
90#66993—22no—
91#66993—21no—
92#66993—21no—
93#66993C2×C412yes—
94#66992—22no—
95#66991—21no—
96#66991—22no—
97#66991C2×C412yes—
98#66990—22no—
99#66989—21no—
100D4×Dic11—21no—
101D4×Dic11C2×C412yes—
102#66983—21no—
103#66983—22no—
104#66983C2×C412yes—
105#66982—22no—
106C4×C22⋊D11—22no—
107C4×C22⋊D11C2×C411yescharacteristic
108C4×C22⋊D11C2×C411yescharacteristic
109C4×C22⋊D11D411yescharacteristic
110C4×C22⋊D11D411yescharacteristic
111C2×(C2×D11)⋊C4—22no—
112#66979D411yescharacteristic
113C22×C11⋊C8—21no—
114C2×#4313—21no—
115C2×C8×D11—21no—
116C2×C8×D11—21no—
117C2×C8×D11—21no—
118#66950—21no—
119#66948—21no—
120#66948—21no—
121#66946—21no—
122#66946—21no—
123#66945—21no—
124#66943—21no—
125#66940—21no—
126#66939—22no—
127#66938—22no—
128#66937—22no—
129#66936—22no—
130#66936—22no—
131#66935—22no—
132(C22⋊D11)⋊C4—22no—
133C22⋊C4×D11—22no—
134#66928—21no—
135#66927C2311yescharacteristic
136C4×D44—21no—
137C4×D44C2×C411yescharacteristic
138C4×D44C2×C412yes—
139C4×D44D411yescharacteristic
140#66925D411yescharacteristic
141#66925D411yescharacteristic
142C42×D11C2311yescharacteristic
143C42×D11C2311yescharacteristic
144#66922C2311yescharacteristic
145C4×Dic22C2×C411yescharacteristic
146C4×Dic22D411yescharacteristic
147C11×C4⋊C8C2311yescharacteristic
148C11×C4⋊C8C2311yescharacteristic
149C11×C4⋊C8C2311yescharacteristic
150C11×C4⋊C8C2311yescharacteristic
151C11×C22⋊C8—21no—
152C11×C22⋊C8—21no—
153C4×C8×C11—21no—
154C4×C8×C11—21no—
155C22⋊(C11⋊C8)—21no—
156(C2×D11)⋊C8—21no—
157(C2×D11)⋊C8—21no—
158(C2×D11)⋊C8—21no—
159(C2×D11)⋊C8—21no—
160#66879—21no—
161Dic11⋊C8—21no—
162Dic11⋊C8—21no—
163Dic11⋊C8—21no—
164Dic11⋊C8—21no—
165C8×Dic11—21no—
166C8×Dic11—21no—
167C8×Dic11—21no—
168C4⋊(C11⋊C8)—21no—
169C4⋊(C11⋊C8)C2311yescharacteristic
170C4⋊(C11⋊C8)C2311yescharacteristic
171C4⋊(C11⋊C8)C2311yescharacteristic
172C4⋊(C11⋊C8)C2311yescharacteristic
173#66867—21no—
174#17724—111nomaximal, Sylow
175C23×D11—22no—
176C11×#41—82no—
177C2×Q8×C11C22×C412yes—
178C2×D4×C11—22no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11C22×C412yes—
182C22×C4×C11—22no—
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C2×C22⋊D11—22no—
187C2×C22⋊D11—22no—
188C2×C22⋊D11—22no—
189C2×C22⋊D11—22no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11C22⋊C411yescharacteristic
192C2×C22⋊D11C22⋊C411yescharacteristic
193C22×Dic11—22no—
194#4343—82no—
195#4341—81no—
196#4341—81no—
197D4×D11—42no—
198D4×D11—42no—
199D4×D11—81no—
200D4×D11—81no—
201D4×D11—82no—
202#4339—22no—
203#4339—22no—
204#4339—81no—
205#4339—81no—
206C2×D44—22no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44C22⋊C411yescharacteristic
210C2×D44C22×C412yes—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11C22×C411yescharacteristic
214C2×C4×D11C22×C411yescharacteristic
215C2×C4×D11C2×D411yescharacteristic
216C2×C4×D11C2×D411yescharacteristic
217C2×C4×D11C2×D411yescharacteristic
218C2×C4×D11C2×D411yescharacteristic
219C2×Dic22—21no—
220C2×Dic22C22⋊C411yescharacteristic
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C22⋊C4—22no—
228C11×C22⋊C4—22no—
229C42×C11C22×C411yescharacteristic
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2411yescharacteristic
233C22⋊Dic11—22no—
234C22⋊Dic11—22no—
235C22⋊Dic11C22⋊C411yescharacteristic
236C22⋊Dic11C22⋊C411yescharacteristic
237(C2×D11)⋊C4—22no—
238(C2×D11)⋊C4—22no—
239(C2×D11)⋊C4—22no—
240(C2×D11)⋊C4—22no—
241(C2×D11)⋊C4—22no—
242(C2×D11)⋊C4C22⋊C411yescharacteristic
243(C2×D11)⋊C4C22⋊C411yescharacteristic
244(C2×D11)⋊C4C22⋊C411yescharacteristic
245(C2×D11)⋊C4C22⋊C411yescharacteristic
246C4⋊Dic11—22no—
247C4⋊Dic11—21no—
248C4⋊Dic11C22⋊C411yescharacteristic
249C4⋊Dic11C22⋊C411yescharacteristic
250C4⋊Dic11C22×C412yes—
251Dic11⋊C4—22no—
252Dic11⋊C4C22⋊C411yescharacteristic
253Dic11⋊C4C22⋊C411yescharacteristic
254Dic11⋊C4C22⋊C411yescharacteristic
255Dic11⋊C4C22⋊C411yescharacteristic
256C4×Dic11—22no—
257C4×Dic11C22×C411yescharacteristic
258C4×Dic11C22×C411yescharacteristic
259C4×Dic11C2×D411yescharacteristic
260C4×Dic11C2×D411yescharacteristic
261C4×Dic11C2×D411yescharacteristic
262C4×Dic11C2×D411yescharacteristic
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—81no—
268#4313—42no—
269C8×D11—42no—
270C8×D11—81no—
271C8×D11—81no—
272#3508—111no—
273#2988—111no—
274#2925—111no—
275#1553—111no—
276#1553—111no—
277#1551—111no—
278#1551—111no—
279#1550—111no—
280#1545—111no—
281#1543—111no—
282#1543D1111yescharacteristic, complemented
283#1542—111no—
284#1540—111no—
285#1540—111no—
286C2×#331—111no—
287C23×C11—22no—
288C23×C11C2×C22⋊C411yescharacteristic
289C22×D11—22no—
290C22×D11—44no—
291C22×D11—82no—
292C22×D11—82no—
293C22×D11C2×C22⋊C411yescharacteristic
294C22×D11C2×C22⋊C411yescharacteristic
295Q8×C11—42no—
296D4×C11—42no—
297D4×C11—41no—
298D4×C11—41no—
299D4×C11—41no—
300D4×C11—41no—
301D4×C11—82no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—22no—
307C2×C4×C11—41no—
308C2×C4×C11—82no—
309C2×C4×C11C2×C22⋊C411yescharacteristic
310C2×C4×C11C2×C22⋊C411yescharacteristic
311C2×C4×C11C2×C22⋊C411yescharacteristic
312C2×C4×C11C23×C411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C22⋊D11—22no—
316C22⋊D11—22no—
317C22⋊D11—44no—
318C22⋊D11—82no—
319C22⋊D11—82no—
320C22⋊D11—82no—
321C22⋊D11—82no—
322C2×Dic11—22no—
323C2×Dic11—82no—
324C2×Dic11C2×C22⋊C411yescharacteristic
325C2×Dic11C2×C22⋊C411yescharacteristic
326C2×Dic11C2×C22⋊C411yescharacteristic
327C2×Dic11C2×C22⋊C411yescharacteristic
328C2×Dic11C2×C22⋊C411yescharacteristic
329C2×Dic11C2×C22⋊C411yescharacteristic
330D44—22no—
331D44—42no—
332D44—41no—
333D44—41no—
334D44—41no—
335D44—41no—
336D44—82no—
337C4×D11—21no—
338C4×D11—21no—
339C4×D11—21no—
340C4×D11—21no—
341C4×D11—21no—
342C4×D11—21no—
343C4×D11—41no—
344C4×D11—41no—
345C4×D11—82no—
346C4×D11—82no—
347C4×D11#13512yes—
348C4×D11#13512yes—
349Dic22—22no—
350Dic22—41no—
351Dic22—41no—
352C8×C11—41no—
353C8×C11—41no—
354C8×C11—41no—
355C8×C11—41no—
356C11⋊C8—41no—
357C11⋊C8—41no—
358C11⋊C8—41no—
359C11⋊C8—41no—
360#559—112no—
361#559—221no—
362#550—112no—
363#550—221no—
364#546—112no—
365#546—112no—
366#546—221no—
367#546—221no—
368#540—221no—
369#540—221no—
370#535—221no—
371#533—111no—
372#532—111no—
373#532—111no—
374#532—111no—
375#532C2×D1111yescharacteristic
376C2×#127—111no—
377#518—221no—
378C4×#41—111no—
379C8×Q8—221no—
380C8×D4—221no—
381C8×D4—221no—
382C8×D4—221no—
383#433—221no—
384#433—221no—
385#432—111no—
386#432—111no—
387#431—111no—
388#431—111no—
389#431—111no—
390#431C2×D1111yescharacteristic, complemented
391#431C2×D1111yescharacteristic, complemented
392#423—111no—
393C2×C4⋊C8—111no—
394C2×C4⋊C8—111no—
395C2×C4⋊C8—111no—
396C2×C4⋊C8—111no—
397#408—221no—
398#405—221no—
399#333—111no—
400#333—111no—
401#333C2×D1111yescharacteristic, complemented
402#333C2×D1111yescharacteristic, complemented
403#332—111no—
404#332—111no—
405#332—111no—
406#332—111no—
407#331—111no—
408#331—111no—
409#331—111no—
410#331—111no—
411#331—111no—
412#331—111no—
413#331C2×D1111yescharacteristic
414#331C2×D1111yescharacteristic
415C22×C11—21no—
416C22×C11—21no—
417C22×C11—21no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11C22×C22⋊C411yescharacteristic
422C2×D11—21no—
423C2×D11—21no—
424C2×D11—21no—
425C2×D11—21no—
426C2×D11—21no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—164no—
431C2×D11#41612yes—
432C4×C11—21no—
433C4×C11—21no—
434C4×C11—21no—
435C4×C11—21no—
436C4×C11—42no—
437C4×C11C2×#13511yescharacteristic
438C4×C11C2×#13511yescharacteristic
439C4×C11#57611yescharacteristic
440C4×C11#57711yescharacteristic
441Dic11—21no—
442Dic11—21no—
443Dic11—21no—
444Dic11—21no—
445Dic11—21no—
446Dic11—42no—
447Dic11#41612yes—
448C2×#41—111no—
449C2×#41—112no—
450C2×#41—221no—
451C2×#41—221no—
452C2×#41C4×D1112yes—
453C22×D4—112no—
454C22×D4—221no—
455C22×D4—221no—
456C2×M16—221no—
457C22×C8—221no—
458C22×C8—221no—
459C22×C8—221no—
460C22×C8—221no—
461C4⋊Q8—111no—
462C4⋊Q8C22×D1111yescharacteristic
463#127—112no—
464#127—111no—
465#127—221no—
466#127—221no—
467#127—222no—
468#127C22×D1111yescharacteristic
469#125—221no—
470#124—112no—
471#124—221no—
472#124—222no—
473#124—221no—
474#124C4×D1112yes—
475#123—222no—
476#123—222no—
477#123—222no—
478#123—222no—
479C22⋊Q8—112no—
480C22⋊Q8—221no—
481#121—21no—
482#121—21no—
483#121—112no—
484#121—112no—
485#121—222no—
486#121—222no—
487#121—222no—
488#121—222no—
489#121—221no—
490#121—221no—
491#121—221no—
492#121—221no—
493#120—222no—
494#120—222no—
495C4×Q8—111no—
496C4×Q8—111no—
497C4×Q8—112no—
498C4×Q8—221no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—111no—
502C4×D4—111no—
503C4×D4—111no—
504C4×D4—111no—
505C4×D4—112no—
506C4×D4—111no—
507C4×D4—112no—
508C4×D4—111no—
509C4×D4—221no—
510C4×D4—221no—
511C4×D4—221no—
512C4×D4—222no—
513C4×D4—222no—
514C4×D4—221no—
515#117—111no—
516#117—111no—
517#117—111no—
518#117—221no—
519C2×C22⋊C4—222no—
520C2×C22⋊C4—222no—
521C2×C42—111no—
522C2×C42—111no—
523C2×C42C22×D1111yescharacteristic
524C4⋊C8—111no—
525C4⋊C8—111no—
526C4⋊C8—111no—
527C4⋊C8—111no—
528C4⋊C8—221no—
529C4⋊C8—221no—
530C4⋊C8—221no—
531C4⋊C8—221no—
532C4⋊C8—221no—
533C4⋊C8C22×D1111yescharacteristic
534C4⋊C8C22×D1111yescharacteristic
535C4⋊C8C22×D1111yescharacteristic
536C4⋊C8C22×D1111yescharacteristic
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8—221no—
540C22⋊C8—221no—
541C22⋊C8—221no—
542C22⋊C8—221no—
543C22⋊C8—221no—
544#97—221no—
545#97—221no—
546C4×C8—21no—
547C4×C8—21no—
548C4×C8—221no—
549C4×C8—221no—
550C4×C8—221no—
551C2×C11—41no—
552C2×C11—82no—
553C2×C11#288811yescharacteristic
554C2×C11C2×#41611yescharacteristic
555C2×C11#289711yescharacteristic
556D11—22no—
557D11—41no—
558D11—82no—
559C24—222no—
560#41—82no—
561#41—222no—
562#41—222no—
563#41—881no—
564#41—881no—
565#41—881no—
566#41—881no—
567#41—882no—
568C2×Q8—111no—
569C2×Q8—221no—
570C2×Q8C2×C4×D1112yes—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—111no—
575C2×D4—111no—
576C2×D4—111no—
577C2×D4—112no—
578C2×D4—222no—
579C2×D4—222no—
580C2×D4—222no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—221no—
585C2×D4—221no—
586C2×D4—442no—
587C2×D4—442no—
588C2×D4—881no—
589C2×D4—881no—
590C2×D4—882no—
591C2×D4C2×C4×D1112yes—
592C22×C4—22no—
593C22×C4—111no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4C2×C4×D1111yescharacteristic
603C22×C4D4×D1111yescharacteristic
604C22×C4D4×D1111yescharacteristic
605M16—442no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—221no—
611C2×C8—221no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—442no—
615C2×C8—881no—
616C2×C8—881no—
617C2×C8—881no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—111no—
621C4⋊C4—111no—
622C4⋊C4—111no—
623C4⋊C4—111no—
624C4⋊C4—111no—
625C4⋊C4—111no—
626C4⋊C4—112no—
627C4⋊C4—222no—
628C4⋊C4—222no—
629C4⋊C4—221no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—111no—
633C22⋊C4—111no—
634C22⋊C4—111no—
635C22⋊C4—111no—
636C22⋊C4—111no—
637C22⋊C4—111no—
638C22⋊C4—222no—
639C22⋊C4—222no—
640C22⋊C4—222no—
641C22⋊C4—222no—
642C22⋊C4—222no—
643C22⋊C4—222no—
644C22⋊C4—222no—
645C42—111no—
646C42—111no—
647C42—111no—
648C42—111no—
649C42—111no—
650C42—111no—
651C42—222no—
652C42C2×C4×D1111yescharacteristic
653C42D4×D1111yescharacteristic
654C42D4×D1111yescharacteristic
655C42C23×D1111yescharacteristic
656C11#1772411yescharacteristic, complemented, Sylow
657C23—22no—
658C23—111no—
659C23—111no—
660C23—222no—
661C23—444no—
662C23—882no—
663C23—882no—
664C23C22⋊C4×D1111yescharacteristic
665Q8—42no—
666Q8—222no—
667Q8—441no—
668Q8—441no—
669D4—42no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—82no—
675D4—222no—
676D4—222no—
677D4—222no—
678D4—442no—
679D4—444no—
680D4—441no—
681D4—441no—
682D4—441no—
683D4—441no—
684D4—882no—
685D4—882no—
686D4—882no—
687D4—882no—
688D4—882no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—82no—
696C2×C4—111no—
697C2×C4—112no—
698C2×C4—112no—
699C2×C4—111no—
700C2×C4—111no—
701C2×C4—111no—
702C2×C4—111no—
703C2×C4—111no—
704C2×C4—221no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—221no—
709C2×C4—221no—
710C2×C4—222no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—882no—
714C2×C4—882no—
715C2×C4—882no—
716C2×C4C22⋊C4×D1111yescharacteristic
717C2×C4C22⋊C4×D1111yescharacteristic
718C2×C4C22⋊C4×D1111yescharacteristic
719C2×C4C22×C4×D1111yescharacteristic
720C2×C4C2×D4×D1111yescharacteristic
721C2×C4C2×D4×D1111yescharacteristic
722C8—41no—
723C8—41no—
724C8—41no—
725C8—41no—
726C8—441no—
727C8—441no—
728C8—441no—
729C8—441no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—112no—
737C22—221no—
738C22—221no—
739C22—221no—
740C22—221no—
741C22—221no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—1764no—
746C22C2×C22⋊C4×D1111yescharacteristic
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—42no—
752C4—112no—
753C4—221no—
754C4—221no—
755C4—221no—
756C4—221no—
757C4—221no—
758C4—442no—
759C4D11×#13511yescharacteristic
760C4D11×#13511yescharacteristic
761C4#1062330011yescharacteristic
762C4#1062330111yescharacteristic
763C2—41no—
764C2—82no—
765C2—222no—
766C2—441no—
767C2—882no—
768C2#1307709211yescharacteristic
769C2D11×#41611yescharacteristic
770C2#1307713811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1543C2
socleC22×C11C22×C22⋊C4
prime radical#13082485C2
cosocleC42×C11C24
hypercenter#1543D11
hypocenterC11#17724
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
2. #13077724C2semidirect
3. #13077277C2semidirect
4. #13067319C2semidirect
5. #13067318C2semidirect
6. #13067311C2semidirect
7. #13067310C2semidirect
8. #13067303C2semidirect
9. #13067282C2semidirect
10. #13067277C2semidirect
11. #13067270C2semidirect
12. #13067263C2semidirect
13. #13067262C2semidirect
14. D11×#331C2semidirect
15. C11×#1543C2semidirect
35. C11×#431C22semidirect
36. C11×#431C22semidirect
37. #10622539C22semidirect
38. C2×C4⋊(C11⋊C8)C22semidirect
40. #10622448C22semidirect
42. #10622446C22semidirect
43. #10622446C22semidirect
46. D11×C4⋊C8C22semidirect
55. C11×#333C22semidirect
56. C11×#333C22semidirect
59. #10622184C22semidirect
60. #10622184C22semidirect
63. #10622124C22semidirect
64. #10622124C22semidirect
69. #10622120C22semidirect
70. #10622120C22semidirect
282. #1543D11semidirect
390. #431C2×D11semidirect
391. #431C2×D11semidirect
401. #333C2×D11semidirect
402. #333C2×D11semidirect
656. C11#17724semidirect

Maximal subgroups

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

subgroupindex
#130824852
#130777242
#130772772
#130673192
#130673182
#130673112
#130673102
#130673032
#130672822
#130672772
#130672702
#130672632
#130672622
D11×#3312
C11×#15432
#1772411