Finite Group Databasebeta

← #14788252

Subgroups — #14788252

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622676C211yesmaximal, characteristic, complemented
2C2×#10622688C211yesmaximal, characteristic, complemented
3#13071298C211yesmaximal, characteristic, complemented
4#13069802C211yesmaximal, characteristic, complemented
5#13069795C211yesmaximal, characteristic, complemented
6#13069619C211yesmaximal, characteristic, complemented
7#13069619C211yesmaximal, characteristic, complemented
8#13069574C211yesmaximal, characteristic, complemented
9#13069544C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068877C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068600C211yesmaximal, characteristic, complemented
15C2×C11×#540C211yesmaximal, characteristic
16C11×#540—24no—
17C11×#540—24no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C11×#123—21no—
21C2×C11×#123—21no—
22C2×C11×#121—21no—
23C2×C11×#121—21no—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622688—24no—
43#10622676—24no—
44#10622591—21no—
45#10622585—21no—
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622558—21no—
51#10622557—21no—
52C4×C4⋊Dic11C2211yescharacteristic
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C11×#127—22no—
74C11×#127D414yes—
75C11×#125—22no—
76C11×#125D414yes—
77C11×#123—28no—
78C11×#123—28no—
79C11×#121—28no—
80C11×#121—28no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C11×#117—22no—
90C11×#117—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×#4324—22no—
108C2×#4324—22no—
109C2×#4324—22no—
110C2×#4324—22no—
111C2×#4324—41no—
112C2×#4324—41no—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116#66977—22no—
117#66977—22no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×C4×Dic11—21no—
122C2×C4×Dic11—21no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C4×Dic22—22no—
128C4×Dic22—22no—
129#66896—22no—
130#66896—22no—
131#66896—22no—
132#66896—22no—
133#66896—41no—
134#66896—41no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—41no—
141C22⋊(C11⋊C8)—41no—
142#66874—22no—
143#66874—22no—
144#66872—22no—
145#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4⋊(C11⋊C8)—22no—
148#24164—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11—21no—
151C24×C11C2×D411yescharacteristic
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—24no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—81no—
167C2×D4×C11—81no—
168C2×D4×C11—81no—
169C2×D4×C11—81no—
170C2×D4×C11—81no—
171C2×D4×C11—81no—
172C2×D4×C11—81no—
173C2×D4×C11—81no—
174C2×D4×C11C2×D412yes—
175C2×D4×C11C2×D412yes—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—81no—
187C22×C4×C11—81no—
188C22×C4×C11—81no—
189C22×C4×C11—81no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22#4112yes—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4C2×D412yes—
213C11×C4⋊C4C2×D412yes—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11C2×D412yes—
223C42×C11C2×D412yes—
224C22⋊Dic11—24no—
225C22⋊Dic11—81no—
226#4324—44no—
227#4324—44no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11#4112yes—
234Dic11⋊C4—24no—
235Dic11⋊C4—42no—
236Dic11⋊C4—81no—
237C4×Dic11—42no—
238C4×Dic11—81no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×#540D1111yescharacteristic
252C2×#479—111no—
253C2×#460—111no—
254#2323—111no—
255#2034—111no—
256#2033—111no—
257#2000—111no—
258#2000—111no—
259#1989—111no—
260#1982—111no—
261#1877—111no—
262#1877—111no—
263#1864—111no—
264#1862—111no—
265#1798—111no—
266C23×C11—21no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11C22×D411yescharacteristic
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—22no—
292D4×C11—41no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11—41no—
296D4×C11—84no—
297D4×C11—84no—
298D4×C11—84no—
299D4×C11—84no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—84no—
324C2×C4×C11—84no—
325C2×C4×C11#12012yes—
326C2×C4×C11#12012yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11C2×#4111yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C112−1+411yescharacteristic
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345Dic22—22no—
346Dic22—22no—
347Dic22—41no—
348Dic22—41no—
349C11⋊C8—41no—
350C11⋊C8—41no—
351C11⋊C8—41no—
352C11⋊C8—41no—
353C22×SD16—111no—
354C22×SD16—111no—
355#540—24no—
356#540—24no—
357C2×#127C2×D1111yescharacteristic
358C2×#125C2×D1111yescharacteristic
359C2×#123—21no—
360C2×#123—21no—
361C2×C22⋊Q8—111no—
362C2×#121—21no—
363C2×#121—21no—
364C2×#121C2×D1111yescharacteristic
365C2×#121C2×D1111yescharacteristic
366C2×C4×Q8—111no—
367C2×C4×D4C2×D1111yescharacteristic
368C2×C4×D4C2×D1111yescharacteristic
369C2×#117C2×D1111yescharacteristic
370#479—224no—
371#460—224no—
372C2×#107—111no—
373C2×#106—111no—
374C2×C4⋊C8—111no—
375C2×C4⋊C8—111no—
376C2×#103—111no—
377C2×#103—111no—
378C2×#102—111no—
379C2×#102—111no—
380C2×#102—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×#102—111no—
384C2×C22⋊C8—111no—
385C2×C22⋊C8—111no—
386#391—111no—
387#389—111no—
388#389—221no—
389#388—221no—
390#388—221no—
391#387—221no—
392#380—111no—
393C4×C4⋊C4—111no—
394#340—111no—
395#340—111no—
396#340—111no—
397#340—111no—
398#336—111no—
399#336—111no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—42no—
408C22×C11—41no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—41no—
412C22×C11—42no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11—81no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11C2×#12011yescharacteristic
422C22×C11#52511yescharacteristic
423C22×C11#53711yescharacteristic
424C22×C11#57611yescharacteristic
425C22×C11#57711yescharacteristic
426C22×C11#57711yescharacteristic
427C22×C11#57711yescharacteristic
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—42no—
433C4×C11—41no—
434C4×C11—42no—
435C4×C11#54611yescharacteristic
436C4×C11#54711yescharacteristic
437C4×C11#54811yescharacteristic
438C4×C11#55011yescharacteristic
439Dic11—42no—
440Dic11—42no—
441Dic11—81no—
442Dic11—81no—
443C22×Q8—111no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22×D1111yescharacteristic
449C22×D4C22×D1111yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4C22×D1111yescharacteristic
453C2×SD16—222no—
454C2×SD16—222no—
455C2×SD16—222no—
456C2×SD16—222no—
457C2×SD16—441no—
458C2×SD16—441no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—111no—
463#127—22no—
464#127C22⋊D1114yes—
465#125—22no—
466#125C22⋊D1114yes—
467#123—28no—
468#123—28no—
469C22⋊Q8—222no—
470C22⋊Q8—222no—
471#121—28no—
472#121—28no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—22no—
477C4×Q8—222no—
478C4×Q8—222no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4—22no—
483#117—22no—
484#117—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4C22⋊D1111yescharacteristic
494C2×C4⋊C4C22⋊D1111yescharacteristic
495C2×C4⋊C4C22×D1111yescharacteristic
496C2×C4⋊C4C22×D1111yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4C22⋊D1111yescharacteristic
504C2×C22⋊C4C22⋊D1111yescharacteristic
505C2×C42—221no—
506C2×C42—221no—
507C2×C42C22×D1111yescharacteristic
508C2×C42C22×D1111yescharacteristic
509#107—222no—
510#106—222no—
511C4⋊C8—222no—
512C4⋊C8—222no—
513#103—222no—
514#103—222no—
515#102—222no—
516#102—222no—
517#102—222no—
518#102—222no—
519#102—441no—
520#102—441no—
521C22⋊C8—441no—
522C22⋊C8—441no—
523#95—221no—
524#95—221no—
525#95—221no—
526#95—221no—
527#95—221no—
528C2×C11—81no—
529C2×C11—82no—
530C2×C11—82no—
531C2×C11#240711yescharacteristic
532C2×C11#300911yescharacteristic
533C2×C11#301211yescharacteristic
534C2×C11#311911yescharacteristic
535C2×C11#312611yescharacteristic
536C2×C11#325711yescharacteristic
537C2×C11#326011yescharacteristic
538C24—21no—
539C24—21no—
540C24C2×C22⋊D1111yescharacteristic
541C2×Q8—112no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×Q8—221no—
546C2×Q8—221no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—81no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4C2×C22⋊D1112yes—
570C2×D4C2×C22⋊D1112yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C23×D1111yescharacteristic
595SD16—444no—
596SD16—444no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—112no—
616C4⋊C4—224no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—442no—
623C4⋊C4—881no—
624C4⋊C4C2×C22⋊D1112yes—
625C4⋊C4C2×C22⋊D1112yes—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—224no—
633C22⋊C4—881no—
634C42—21no—
635C42—21no—
636C42—442no—
637C42—881no—
638C42C2×C22⋊D1112yes—
639C42C2×C22⋊D1112yes—
640C11#2416411yescharacteristic, complemented, Sylow
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23C22×C22⋊D1111yescharacteristic
663Q8—222no—
664Q8—222no—
665Q8—441no—
666Q8—441no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—22no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677D4—84no—
678D4—84no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—84no—
703C2×C4—84no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—441no—
716C2×C4#6700612yes—
717C2×C4#6700612yes—
718C2×C4#41×D1111yescharacteristic
719C2×C4#41×D1111yescharacteristic
720C2×C4#6704211yescharacteristic
721C2×C4#6704311yescharacteristic
722C2×C4C22×C22⋊D1111yescharacteristic
723C2×C4C22×C22⋊D1111yescharacteristic
724C8—441no—
725C8—441no—
726C8—441no—
727C8—441no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22—41no—
740C22—41no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22#1062335911yescharacteristic
750C22#1062336411yescharacteristic
751C22#1062336611yescharacteristic
752C22#1062336711yescharacteristic
753C22#1062336711yescharacteristic
754C22#1062336711yescharacteristic
755C22C2×#6700611yescharacteristic
756C4—22no—
757C4—22no—
758C4—41no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—442no—
764C4—442no—
765C4—881no—
766C4—881no—
767C4#1062335511yescharacteristic
768C4#1062336011yescharacteristic
769C4#1062336211yescharacteristic
770C4#1062336511yescharacteristic
771C2—81no—
772C2—82no—
773C2—82no—
774C2#1307195511yescharacteristic
775C2#1307789311yescharacteristic
776C2#1307792011yescharacteristic
777C2#1307880911yescharacteristic
778C2#1307890211yescharacteristic
779C2#1308002111yescharacteristic
780C2#1308006211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#540C2
socleC23×C11C22×D4
hypercenterC2×#540D11
hypocenterC11#24164
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
2. C2×#10622688C2semidirect
3. #13071298C2semidirect
4. #13069802C2semidirect
5. #13069795C2semidirect
6. #13069619C2semidirect
7. #13069619C2semidirect
8. #13069574C2semidirect
9. #13069544C2semidirect
10. #13068950C2semidirect
11. #13068950C2semidirect
12. #13068877C2semidirect
13. #13068863C2semidirect
14. #13068600C2semidirect
640. C11#24164semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C2×#106226882
#130712982
#130698022
#130697952
#130696192
#130695742
#130695442
#130689502
#130688772
#130688632
#130686002
C2×C11×#5402
#2416411