Finite Group Databasebeta

← #14801488

Subgroups — #14801488

Order 2816.

1072 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×#10622703C211yesmaximal, characteristic, complemented
2C2×#10622660C211yesmaximal, characteristic
3C2×#10622660C211yesmaximal, characteristic
4C2×#10622643C211yesmaximal, characteristic, complemented
5#13071456C211yesmaximal, characteristic
6#13069987C211yesmaximal, characteristic, complemented
7#13069816C211yesmaximal, characteristic, complemented
8#13069809C211yesmaximal, characteristic, complemented
9#13069699C211yesmaximal, characteristic, complemented
10#13069500C211yesmaximal, characteristic, complemented
11#13069231C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic, complemented
13#13068960C211yesmaximal, characteristic, complemented
14#13068869C211yesmaximal, characteristic, complemented
15C11×#2429C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#398—21no—
28C11×#396—21no—
29C11×#391C2211yescharacteristic
30C11×#389—21no—
31C11×#389C2211yescharacteristic
32C11×#388—21no—
33C4×C11×C22⋊C4C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622825C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41#10622703—24no—
42#10622660—24no—
43#10622660—24no—
44#10622643—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622570—21no—
52#10622570—21no—
53#10622552C2211yescharacteristic
54#10622552C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622280—21no—
58#10622279—21no—
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339—41no—
72C2×#4339—41no—
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×Dic22C2311yescharacteristic
76C11×C4⋊Q8—22no—
77C11×C4⋊Q8—41no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—41no—
81C11×C22⋊Q8—41no—
82C4×Q8×C11—22no—
83C4×Q8×C11—41no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C22⋊Dic11—21no—
100C2×#4326—22no—
101C2×#4326—22no—
102C2×#4326—22no—
103C2×#4326—22no—
104C2×#4326—22no—
105C2×#4326D414yes—
106C2×#4325—22no—
107C2×#4325—22no—
108C2×#4325—22no—
109C2×#4325—22no—
110C2×#4325—41no—
111C2×#4325—41no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C2×C4×Dic11—21no—
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C4×Dic22—22no—
127C4×Dic22—22no—
128C4×Dic22—41no—
129C4×Dic22—41no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95D411yescharacteristic
134C11×#95D411yescharacteristic
135#66899—22no—
136#66899—22no—
137#66899—22no—
138#66899—41no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142#66874—22no—
143#66874D414yes—
144#66873—22no—
145#66873—22no—
146#66872—22no—
147#66871—41no—
148C4⋊(C11⋊C8)—22no—
149#66867—22no—
150#25171—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C23×D11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11C2×D412yes—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—24no—
182C2×C22⋊D11—42no—
183C2×C22⋊D11—42no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187#4339—44no—
188#4339—44no—
189#4339—44no—
190#4339—44no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44#4112yes—
197C2×C4×D11—24no—
198C2×C4×D11—42no—
199C2×C4×D11—42no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22C2×D412yes—
204C2×Dic22C2×D412yes—
205C2×Dic22#4112yes—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—42no—
210C11×C4⋊C4—42no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4—42no—
214C11×C4⋊C4—42no—
215C11×C4⋊C4C2×D412yes—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—41no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—42no—
225C22⋊Dic11—81no—
226#4326—28no—
227#4326—44no—
228#4325—44no—
229#4325—44no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—81no—
233(C2×D11)⋊C4—81no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238Dic11⋊C4—42no—
239Dic11⋊C4—42no—
240C4×Dic11—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×#441—111no—
258#2429D1111yescharacteristic, complemented
259#2341—111no—
260#2065—111no—
261#2036—111no—
262#2035—111no—
263#2013—111no—
264#1973—111no—
265#1924—111no—
266#1880—111no—
267#1878—111no—
268#1863—111no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11C22×D411yescharacteristic
277C22×D11—22no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284Q8×C11—22no—
285Q8×C11—22no—
286Q8×C11—41no—
287Q8×C11—41no—
288Q8×C11—41no—
289Q8×C11—41no—
290Q8×C11—41no—
291Q8×C11—41no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
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—41no—
309C2×C4×C11—41no—
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—41no—
321C2×C4×C11—41no—
322C2×C4×C11#13712yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C22⋊D11—48no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339D44—22no—
340D44—22no—
341D44—41no—
342D44—41no—
343C4×D11—48no—
344Dic22—22no—
345Dic22—22no—
346Dic22—22no—
347Dic22#12114yes—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C11⋊C8—41no—
351C11⋊C8—41no—
352C22×#41—111no—
353C22×Q16—111no—
354C22×Q16—111no—
355C22×SD16—111no—
356C22×SD16—111no—
357C2×C4⋊Q8C2×D1111yescharacteristic
358C2×C22⋊Q8C2×D1111yescharacteristic
359C2×C22⋊Q8C2×D1111yescharacteristic
360C2×C4×Q8—111no—
361C2×C4×Q8—111no—
362C2×C4×Q8C2×D1111yescharacteristic
363#462—224no—
364#452—224no—
365#452—224no—
366#441—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×#97—111no—
381#398—21no—
382#396—21no—
383#391C2×D1111yescharacteristic
384#390—111no—
385#390—111no—
386#390—221no—
387#390—221no—
388#389—21no—
389#389C2×D1111yescharacteristic
390#388—21no—
391#380—111no—
392#380—221no—
393C4×C22⋊C4—221no—
394C4×C22⋊C4C2×D1111yescharacteristic
395#340—111no—
396#340—111no—
397#336—111no—
398#336—111no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11#52511yescharacteristic
407C22×C11D4211yescharacteristic
408C22×C11D4211yescharacteristic
409C22×C11C2×#13711yescharacteristic
410C22×C11#57511yescharacteristic
411C22×C11#57711yescharacteristic
412C22×C11#57811yescharacteristic
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—81no—
417C2×D11—81no—
418C2×D11—81no—
419C2×D11—81no—
420C4×C11—22no—
421C4×C11—41no—
422C4×C11—42no—
423C4×C11—41no—
424C4×C11—42no—
425C4×C11—41no—
426C4×C11—41no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11C2×#12111yescharacteristic
430C4×C11#53811yescharacteristic
431C4×C11#54611yescharacteristic
432C4×C11#54611yescharacteristic
433Dic11—24no—
434Dic11—81no—
435Dic11—81no—
436C2×#41—222no—
437C2×#41—222no—
438C2×#41—222no—
439C2×#41—222no—
440C2×#41—441no—
441C2×#41—441no—
442C22×Q8—111no—
443C22×Q8C22×D1111yescharacteristic
444C22×Q8C22×D1111yescharacteristic
445C22×D4—111no—
446C22×D4—221no—
447C23×C4—221no—
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—22no—
466C4⋊Q8—41no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—41no—
470C22⋊Q8—41no—
471C4×Q8—22no—
472C4×Q8—41no—
473C4×Q8—222no—
474C4×Q8—222no—
475C4×Q8—441no—
476C4×Q8—441no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
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—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4C22⋊D1111yescharacteristic
497C2×C22⋊C4C22⋊D1111yescharacteristic
498C2×C42—21no—
499C2×C42—221no—
500C2×C42—221no—
501C2×C42C22×D1111yescharacteristic
502C2×C42C22×D1111yescharacteristic
503#107—441no—
504#106—222no—
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—
516#97—222no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—221no—
521#95C22⋊D1111yescharacteristic
522#95C22⋊D1111yescharacteristic
523C2×C11—81no—
524C2×C11#242411yescharacteristic
525C2×C11#311611yescharacteristic
526C2×C11#312011yescharacteristic
527C2×C11#326911yescharacteristic
528C2×C11#327011yescharacteristic
529C2×C11#327111yescharacteristic
530C2×C11#327811yescharacteristic
531D11—82no—
532C24—221no—
533C24C2×C22⋊D1111yescharacteristic
534#41—444no—
535#41—444no—
536#41—444no—
537#41—444no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—112no—
550C2×Q8—112no—
551C2×Q8—112no—
552C2×Q8—221no—
553C2×Q8—221no—
554C2×Q8—221no—
555C2×Q8D4×D1112yes—
556C2×D4—112no—
557C2×D4—224no—
558C2×D4—221no—
559C2×D4—221no—
560C2×D4—221no—
561C2×D4—221no—
562C2×D4—221no—
563C2×D4—442no—
564C2×D4—442no—
565C22×C4—21no—
566C22×C4—21no—
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—224no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—442no—
580C22×C4—442no—
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—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—442no—
617C4⋊C4—442no—
618C4⋊C4D4×D1112yes—
619C22⋊C4—22no—
620C22⋊C4—41no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—442no—
624C22⋊C4—442no—
625C22⋊C4—881no—
626C22⋊C4—881no—
627C22⋊C4—881no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—42no—
633C42—442no—
634C42—442no—
635C11#2517111yescharacteristic, complemented, Sylow
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—222no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23C22×C22⋊D1111yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—114no—
660Q8—222no—
661Q8—222no—
662Q8—222no—
663D4—222no—
664D4—222no—
665D4—448no—
666D4—441no—
667D4—441no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
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—41no—
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—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—448no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4#6699512yes—
709C2×C4C2×D4×D1111yescharacteristic
710C2×C4C2×D4×D1111yescharacteristic
711C2×C4#6703711yescharacteristic
712C2×C4#6703711yescharacteristic
713C2×C4#41×D1111yescharacteristic
714C2×C4#41×D1111yescharacteristic
715C8—222no—
716C8—222no—
717C8—441no—
718C8—441no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—881no—
730C22—881no—
731C22—881no—
732C22—881no—
733C22D4×C22⋊D1111yescharacteristic
734C22D4×C22⋊D1111yescharacteristic
735C22C2×#6699511yescharacteristic
736C22#1062335311yescharacteristic
737C22#1062335911yescharacteristic
738C22#1062336811yescharacteristic
739C22#1062336911yescharacteristic
740C4—22no—
741C4—41no—
742C4—42no—
743C4—41no—
744C4—42no—
745C4—41no—
746C4—41no—
747C4—81no—
748C4—81no—
749C4—224no—
750C4—881no—
751C4—881no—
752C4D11×#12111yescharacteristic
753C4#1062314111yescharacteristic
754C4#1062314311yescharacteristic
755C4#1062314411yescharacteristic
756C2—81no—
757C2—882no—
758C2#1307214911yescharacteristic
759C2#1307877211yescharacteristic
760C2#1307882411yescharacteristic
761C2#1308016711yescharacteristic
762C2#1308018711yescharacteristic
763C2#1308020211yescharacteristic
764C2#1308027811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2429C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenter#2429D11
hypocenterC11#25171
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2429

Complements

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

NH ≅ G/Ntype
1. C2×#10622703C2semidirect
4. C2×#10622643C2semidirect
6. #13069987C2semidirect
7. #13069816C2semidirect
8. #13069809C2semidirect
9. #13069699C2semidirect
10. #13069500C2semidirect
11. #13069231C2semidirect
12. #13068971C2semidirect
13. #13068960C2semidirect
14. #13068869C2semidirect
15. C11×#2429C2semidirect
258. #2429D11semidirect
635. C11#25171semidirect

Maximal subgroups

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

subgroupindex
C2×#106227032
C2×#106226602
C2×#106226432
#130714562
#130699872
#130698162
#130698092
#130696992
#130695002
#130692312
#130689712
#130689602
#130688692
C11×#24292
#2517111