Finite Group Databasebeta

← #14801191

Subgroups — #14801191

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622644C211yesmaximal, characteristic, complemented
2C2×#10622852C211yesmaximal, characteristic
3C2×#10622852C211yesmaximal, characteristic
4C2×C4×#4326C211yesmaximal, characteristic, complemented
5#13072215C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13069819C211yesmaximal, characteristic, complemented
8#13069812C211yesmaximal, characteristic, complemented
9#13069698C211yesmaximal, characteristic, complemented
10#13069469C211yesmaximal, characteristic, complemented
11#13069224C211yesmaximal, characteristic, complemented
12#13068974C211yesmaximal, characteristic, complemented
13#13068957C211yesmaximal, characteristic, complemented
14#13068884C211yesmaximal, characteristic, complemented
15C11×#2341C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#390—21no—
28C11×#390—21no—
29C11×#390C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#380—21no—
32C11×#380C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35#10622852—24no—
36#10622852—24no—
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622644—24no—
44C4×#4326—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622564—21no—
52#10622561—21no—
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622270—21no—
58#10622260—21no—
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×Dic22C2311yescharacteristic
75C22×Dic22C2311yescharacteristic
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11—41no—
79C4×Q8×C11—41no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C11×C22⋊C4D411yescharacteristic
91C2×C42×C11—21no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×#4326—22no—
98C2×#4326—22no—
99C2×#4326—22no—
100C2×#4326—22no—
101C2×#4326—22no—
102C2×#4326D414yes—
103C2×#4324—22no—
104C2×#4324—22no—
105C2×#4324—22no—
106C2×#4324—22no—
107C2×#4324—41no—
108C2×#4324—41no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113#66977—22no—
114#66977—22no—
115#66977—41no—
116#66977—41no—
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×C4×Dic11—21no—
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126#66922—22no—
127#66922—41no—
128C4×Dic22—22no—
129C4×Dic22—41no—
130C11×#95—21no—
131C11×#95D411yescharacteristic
132C11×#95D411yescharacteristic
133#66899—22no—
134#66899D414yes—
135#66896—22no—
136#66896—22no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142#66874—22no—
143#66874—22no—
144#66874—22no—
145#66874—41no—
146#66872—41no—
147#66871—22no—
148C4⋊(C11⋊C8)—22no—
149C4×C11⋊C8—22no—
150#25151—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C11×#41—44no—
154C11×#41—44no—
155C11×#41—44no—
156C11×#41—44no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C2×D412yes—
161C2×Q8×C11C2×D412yes—
162C2×Q8×C11#4112yes—
163C2×D4×C11—24no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11#4112yes—
172C22×C4×C11—21no—
173C22×C4×C11—24no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22C2×D412yes—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—81no—
217C11×C22⋊C4—81no—
218C11×C22⋊C4—81no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—42no—
224C42×C11—42no—
225C22⋊Dic11—42no—
226C22⋊Dic11—42no—
227#4326—28no—
228#4326—44no—
229#4324—44no—
230#4324—44no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—42no—
235C4⋊Dic11—42no—
236C4⋊Dic11C2×D412yes—
237Dic11⋊C4—42no—
238Dic11⋊C4—42no—
239Dic11⋊C4—42no—
240Dic11⋊C4—42no—
241C4×Dic11—42no—
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×C11⋊C8—21no—
252C2×C11⋊C8C2×D412yes—
253C2×C11⋊C8C2×D412yes—
254C2×#462—111no—
255C2×#452—111no—
256C2×#452—111no—
257C2×C4×Q16—111no—
258#2429—111no—
259#2341D1111yescharacteristic
260#2067—111no—
261#2036—111no—
262#2035—111no—
263#2013—111no—
264#1968—111no—
265#1923—111no—
266#1880—111no—
267#1878—111no—
268#1865—111no—
269C23×C11—21no—
270C23×C11—22no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11—41no—
281C23×C11—41no—
282C23×C11—41no—
283C23×C11C22×D411yescharacteristic
284Q8×C11—22no—
285Q8×C11—22no—
286Q8×C11—22no—
287Q8×C11#12114yes—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—48no—
291D4×C11—41no—
292D4×C11—41no—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
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—21no—
308C2×C4×C11—21no—
309C2×C4×C11—48no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11#13512yes—
321C2×C4×C11#13712yes—
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340Dic22—22no—
341Dic22—22no—
342Dic22—41no—
343Dic22—41no—
344Dic22—41no—
345Dic22—41no—
346Dic22—41no—
347Dic22—41no—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C11⋊C8—41no—
351C11⋊C8—41no—
352C22×#41C2×D1111yescharacteristic
353C22×Q16—111no—
354C22×Q16—111no—
355C22×SD16—111no—
356C22×SD16—111no—
357C2×C4⋊Q8—111no—
358C2×C22⋊Q8—111no—
359C2×C22⋊Q8—111no—
360C2×C4×Q8—111no—
361C2×C4×Q8C2×D1111yescharacteristic
362C2×C4×Q8C2×D1111yescharacteristic
363#462—224no—
364#452—224no—
365#452—224no—
366C4×Q16—224no—
367C2×#107—111no—
368C2×#106—111no—
369C2×C4⋊C8—111no—
370C2×#103—111no—
371C2×#103—111no—
372C2×#103—111no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#103—111no—
376C2×#102—111no—
377C2×#102—111no—
378C2×C22⋊C8—111no—
379C2×C22⋊C8—111no—
380C2×C4×C8—111no—
381#398—221no—
382#396—221no—
383#391—111no—
384#390—21no—
385#390—21no—
386#390C2×D1111yescharacteristic
387#390C2×D1111yescharacteristic
388#389—111no—
389#389—221no—
390#388—221no—
391#380—21no—
392#380C2×D1111yescharacteristic
393C4×C22⋊C4—21no—
394C4×C22⋊C4C2×D1111yescharacteristic
395#340—111no—
396#340—111no—
397#336—111no—
398#336—111no—
399C22×C11—41no—
400C22×C11—42no—
401C22×C11—41no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11#52511yescharacteristic
414C22×C11D4211yescharacteristic
415C22×C11D4211yescharacteristic
416C22×C11C2×#13511yescharacteristic
417C22×C11C2×#13711yescharacteristic
418C22×C11#57711yescharacteristic
419C22×C11#57811yescharacteristic
420C4×C11—24no—
421C4×C11—22no—
422C4×C11—22no—
423C4×C11—41no—
424C4×C11—41no—
425C4×C11—41no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11C2×#12111yescharacteristic
429C4×C11#53811yescharacteristic
430C4×C11#54611yescharacteristic
431C4×C11#54611yescharacteristic
432Dic11—42no—
433Dic11—42no—
434Dic11—81no—
435Dic11—81no—
436C2×#41—22no—
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—41no—
441C2×#41—41no—
442C22×Q8—111no—
443C22×Q8—111no—
444C22×Q8C22×D1111yescharacteristic
445C22×D4—21no—
446C22×D4C22×D1111yescharacteristic
447C23×C4—21no—
448C23×C4C22×D1111yescharacteristic
449C2×Q16—114no—
450C2×Q16—222no—
451C2×Q16—222no—
452C2×Q16—222no—
453C2×Q16—222no—
454C2×Q16—222no—
455C2×SD16—222no—
456C2×SD16—222no—
457C2×SD16—222no—
458C2×SD16—222no—
459C2×SD16—441no—
460C2×SD16—441no—
461C22×C8—111no—
462C22×C8—111no—
463C22×C8—111no—
464C22×C8—111no—
465C4⋊Q8—222no—
466C4⋊Q8—441no—
467C22⋊Q8—222no—
468C22⋊Q8—222no—
469C22⋊Q8—441no—
470C22⋊Q8—441no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—41no—
474C4×Q8—41no—
475C4×Q8—222no—
476C4×Q8—441no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4C22⋊D1111yescharacteristic
497C2×C22⋊C4C22⋊D1111yescharacteristic
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—221no—
501C2×C42C22×D1111yescharacteristic
502C2×C42C22×D1111yescharacteristic
503#107—222no—
504#106—441no—
505C4⋊C8—222no—
506#103—114no—
507#103—222no—
508#103—222no—
509#103—222no—
510#103—222no—
511#103—441no—
512#102—222no—
513#102—222no—
514C22⋊C8—222no—
515C22⋊C8—222no—
516C4×C8—222no—
517#95—21no—
518#95—221no—
519#95—221no—
520#95—221no—
521#95C22⋊D1111yescharacteristic
522#95C22⋊D1111yescharacteristic
523C2×C11—81no—
524C2×C11—82no—
525C2×C11#242411yescharacteristic
526C2×C11#310711yescharacteristic
527C2×C11#312011yescharacteristic
528C2×C11#327011yescharacteristic
529C2×C11#327811yescharacteristic
530C2×C11#328411yescharacteristic
531C2×C11#328511yescharacteristic
532C24—21no—
533C24C2×C22⋊D1111yescharacteristic
534#41—44no—
535#41—44no—
536#41—44no—
537#41—44no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—112no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×Q8—221no—
546C2×Q8—221no—
547C2×Q8—221no—
548C2×Q8—221no—
549C2×Q8—221no—
550C2×Q8—221no—
551C2×Q8—221no—
552C2×Q8—221no—
553C2×Q8#433912yes—
554C2×Q8D4×D1112yes—
555C2×Q8D4×D1112yes—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4#433912yes—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4C2×C22⋊D1111yescharacteristic
582C22×C4C2×C22⋊D1111yescharacteristic
583C22×C4C2×C22⋊D1111yescharacteristic
584C22×C4C2×C22⋊D1111yescharacteristic
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C23×D1111yescharacteristic
587Q16—228no—
588Q16—444no—
589SD16—444no—
590SD16—444no—
591C2×C8—112no—
592C2×C8—112no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—112no—
610C4⋊C4—221no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—442no—
614C4⋊C4—442no—
615C4⋊C4—442no—
616C4⋊C4—442no—
617C4⋊C4—442no—
618C4⋊C4—442no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—442no—
627C22⋊C4—442no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—42no—
633C42—42no—
634C42—442no—
635C11#2515111yescharacteristic, complemented, Sylow
636C23—21no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C22×C22⋊D1111yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—222no—
655Q8—222no—
656Q8—441no—
657Q8—441no—
658Q8—441no—
659Q8—441no—
660Q8—441no—
661Q8—441no—
662Q8#6693714yes—
663D4—22no—
664D4—22no—
665D4—48no—
666D4—41no—
667D4—41no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—48no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4#6700312yes—
708C2×C4#6700412yes—
709C2×C4C2×#433911yescharacteristic
710C2×C4C2×#433911yescharacteristic
711C2×C4C2×D4×D1111yescharacteristic
712C2×C4C2×D4×D1111yescharacteristic
713C2×C4#6703711yescharacteristic
714C2×C4#6703711yescharacteristic
715C8—222no—
716C8—222no—
717C8—441no—
718C8—441no—
719C22—42no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22#1062332211yescharacteristic
734C22D4×C22⋊D1111yescharacteristic
735C22D4×C22⋊D1111yescharacteristic
736C22C2×#6700311yescharacteristic
737C22C2×#6700411yescharacteristic
738C22#1062336711yescharacteristic
739C22#1062336911yescharacteristic
740C4—24no—
741C4—22no—
742C4—22no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—81no—
747C4—81no—
748C4—442no—
749C4—442no—
750C4—881no—
751C4—881no—
752C4C2×#6693711yescharacteristic
753C4#1062302111yescharacteristic
754C4#1062302111yescharacteristic
755C4#1062302511yescharacteristic
756C2—81no—
757C2—82no—
758C2#1307215211yescharacteristic
759C2#1307868711yescharacteristic
760C2#1307883011yescharacteristic
761C2#1308018211yescharacteristic
762C2#1308028211yescharacteristic
763C2#1308034611yescharacteristic
764C2#1308035311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2341C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenter#2341D11
hypocenterC11#25151
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
1. C2×#10622644C2semidirect
4. C2×C4×#4326C2semidirect
5. #13072215C2semidirect
6. #13070004C2semidirect
7. #13069819C2semidirect
8. #13069812C2semidirect
9. #13069698C2semidirect
10. #13069469C2semidirect
11. #13069224C2semidirect
12. #13068974C2semidirect
13. #13068957C2semidirect
14. #13068884C2semidirect
635. C11#25151semidirect

Maximal subgroups

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

subgroupindex
C2×#106226442
C2×#106228522
C2×C4×#43262
#130722152
#130700042
#130698192
#130698122
#130696982
#130694692
#130692242
#130689742
#130689572
#130688842
C11×#23412
#2515111