Finite Group Databasebeta

← #14800940

Subgroups — #14800940

Order 2816.

1068 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×#10622665C211yesmaximal, characteristic, complemented
2C2×#10622841C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic
4C2×#10622838C211yesmaximal, characteristic, complemented
5#13072045C211yesmaximal, characteristic
6#13069997C211yesmaximal, characteristic, complemented
7#13069938C211yesmaximal, characteristic, complemented
8#13069816C211yesmaximal, characteristic, complemented
9#13069624C211yesmaximal, characteristic, complemented
10#13069476C211yesmaximal, characteristic, complemented
11#13069295C211yesmaximal, characteristic, complemented
12#13069050C211yesmaximal, characteristic, complemented
13#13069047C211yesmaximal, characteristic, complemented
14#13068813C211yesmaximal, characteristic, complemented
15C11×#2409C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C22×#4318C2211yescharacteristic
27C11×#395—21no—
28C11×#393—21no—
29C11×#391C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#386—21no—
32C11×#385—21no—
33C11×#380C2211yescharacteristic
34#10622841—24no—
35#10622838—24no—
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42#10622835—21no—
43#10622825C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622665—24no—
47#10622625—24no—
48#10622585—21no—
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622565—21no—
54#10622558—21no—
55#10622542C2211yescharacteristic
56#10622541C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11—21no—
64C22×Q8×C11—22no—
65C22×Q8×C11—22no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11D411yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C22×Dic22C2311yescharacteristic
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—41no—
80C11×C22⋊Q8—41no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4D411yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4D411yescharacteristic
92C2×C11×C22⋊C4D411yescharacteristic
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×#4326—22no—
99C2×#4326—22no—
100C2×#4326—22no—
101C2×#4326—22no—
102C2×#4326—41no—
103C2×#4326—41no—
104#66979—22no—
105#66979—41no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109#66977—22no—
110#66977—22no—
111#66977—22no—
112#66977—41no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×C4×Dic11—21no—
117C2×#4318—22no—
118C2×#4318—22no—
119C2×#4318—22no—
120C2×#4318—22no—
121C2×#4318—41no—
122C2×#4318—41no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132#66899—22no—
133#66899—22no—
134#66899—22no—
135#66899—22no—
136#66899—22no—
137#66899D414yescomplemented
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)D414yes—
144#66874—22no—
145#66874—41no—
146#66872—22no—
147#66871—41no—
148C4⋊(C11⋊C8)—22no—
149C4×C11⋊C8—22no—
150#25134—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C24×C11C2×D411yescharacteristic
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—28no—
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×C11—42no—
165C2×Q8×C11—42no—
166C2×Q8×C11—44no—
167C2×Q8×C11—44no—
168C2×Q8×C11—44no—
169C2×Q8×C11—42no—
170C2×Q8×C11C2×D412yes—
171C2×Q8×C11#4112yes—
172C2×D4×C11—22no—
173C2×D4×C11—22no—
174C2×D4×C11—41no—
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—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11#4112yes—
198C22×C4×C11C2411yescharacteristic
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—42no—
215C11×C4⋊C4—42no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C11×C22⋊C4—42no—
221C42×C11—21no—
222C42×C11—21no—
223C22⋊Dic11—42no—
224C22⋊Dic11—42no—
225C22⋊Dic11—42no—
226C22⋊Dic11—42no—
227#4326—44no—
228#4326—44no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11C2×D412yes—
235Dic11⋊C4—42no—
236Dic11⋊C4—42no—
237Dic11⋊C4—42no—
238C4×Dic11—42no—
239#4318—44no—
240#4318—44no—
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⋊C8C2×D412yes—
251C2×C11⋊C8C2×D412yes—
252C2×C11⋊C8C2×D412yes—
253C2×#470—111no—
254C2×#451—111no—
255C2×#436—111no—
256C2×#419—111no—
257#2415—111no—
258#2409D1111yescharacteristic
259#2066—111no—
260#2056—111no—
261#2036—111no—
262#2001—111no—
263#1969—111no—
264#1933—111no—
265#1894—111no—
266#1894—111no—
267#1854—111no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11—21no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11#12112yes—
282C23×C11C22×D411yescharacteristic
283Q8×C11—22no—
284Q8×C11—22no—
285Q8×C11—22no—
286Q8×C11—22no—
287Q8×C11—48no—
288Q8×C11—41no—
289Q8×C11—41no—
290Q8×C11—41no—
291Q8×C11—41no—
292D4×C11—44no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
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—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11#12112yes—
325C2×C4×C11#13712yes—
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×Dic11—22no—
333C2×Dic11—41no—
334C2×Dic11—41no—
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—
344Dic22—41no—
345Dic22—41no—
346Dic22—41no—
347Dic22—41no—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C11⋊C8—22no—
351C11⋊C8—41no—
352C23×Q8C2×D1111yescharacteristic
353C22×Q16—111no—
354C22×Q16—111no—
355C22×M16—111no—
356C22×M16—111no—
357C2×C22⋊Q8—111no—
358C2×C22⋊Q8—111no—
359C2×C22⋊Q8C2×D1111yescharacteristic
360C2×C22⋊Q8C2×D1111yescharacteristic
361C2×C4×D4C2×D1111yescharacteristic
362C2×#117—111no—
363#470—224no—
364#451—224no—
365#436—224no—
366C2×#107—111no—
367C2×#106—111no—
368C2×C4⋊C8—111no—
369#419—224no—
370C2×#103—111no—
371C2×#103—111no—
372C2×#103—111no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#103—111no—
376C2×#103—111no—
377C2×#103—111no—
378C2×C22⋊C8—111no—
379C2×C22⋊C8—111no—
380C2×C4×C8—111no—
381#397—221no—
382#395—21no—
383#394—221no—
384#393—21no—
385#391—111no—
386#391C2×D1111yescharacteristic
387#391C2×D1111yescharacteristic
388#389—111no—
389#389—221no—
390#388—221no—
391#386—21no—
392#385—21no—
393#380—111no—
394#380C2×D1111yescharacteristic
395#340—111no—
396#340—111no—
397#340—111no—
398#340—111no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—22no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11—41no—
410C22×C11—41no—
411C22×C11—41no—
412C22×C11—41no—
413C22×C11C2×#12111yescharacteristic
414C22×C11D4211yescharacteristic
415C22×C11#54611yescharacteristic
416C22×C11C2×#13711yescharacteristic
417C22×C11#57511yescharacteristic
418C22×C11#57811yescharacteristic
419C22×C11#57811yescharacteristic
420C4×C11—22no—
421C4×C11—22no—
422C4×C11—41no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—41no—
426C4×C11—81no—
427C4×C11—81no—
428C4×C11#52511yescharacteristic
429C4×C11#53811yescharacteristic
430C4×C11D4211yescharacteristic
431C4×C11#54611yescharacteristic
432Dic11—42no—
433Dic11—81no—
434Dic11—81no—
435Dic11—81no—
436C22×Q8—21no—
437C22×Q8—22no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—22no—
441C22×Q8—41no—
442C22×Q8—41no—
443C22×Q8—111no—
444C22×Q8C22×D1111yescharacteristic
445C22×Q8C22×D1111yescharacteristic
446C22×D4C22⋊D1111yescharacteristic
447C23×C4—21no—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C2×Q16—222no—
451C2×Q16—222no—
452C2×Q16—222no—
453C2×Q16—222no—
454C2×Q16—441no—
455C2×Q16—441no—
456C2×M16—222no—
457C2×M16—222no—
458C2×M16—222no—
459C2×M16—222no—
460C2×M16—441no—
461C2×M16—441no—
462C22×C8—111no—
463C22×C8—111no—
464C22×C8—111no—
465C22×C8—111no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—41no—
469C22⋊Q8—41no—
470C22⋊Q8—222no—
471C22⋊Q8—222no—
472C22⋊Q8—222no—
473C22⋊Q8—441no—
474C4×D4—22no—
475C4×D4—22no—
476#117—222no—
477#117—441no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4C22⋊D1111yescharacteristic
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
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—221no—
499C2×C42C22×D1111yescharacteristic
500#107—441no—
501#106—222no—
502C4⋊C8—222no—
503#103—114no—
504#103—222no—
505#103—222no—
506#103—222no—
507#103—222no—
508#103—222no—
509#103—222no—
510#103—441no—
511C22⋊C8—114no—
512C22⋊C8—222no—
513C4×C8—222no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—221no—
520#95—221no—
521#95—221no—
522#95—221no—
523C2×C11—42no—
524C2×C11—81no—
525C2×C11#242411yescharacteristic
526C2×C11#305611yescharacteristic
527C2×C11#305911yescharacteristic
528C2×C11#327611yescharacteristic
529C2×C11#327711yescharacteristic
530C2×C11#332711yescharacteristic
531C2×C11#332811yescharacteristic
532C24C2×C22⋊D1111yescharacteristic
533C24C2×C22⋊D1111yescharacteristic
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—28no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—42no—
546C2×Q8—42no—
547C2×Q8—44no—
548C2×Q8—44no—
549C2×Q8—44no—
550C2×Q8—42no—
551C2×Q8—221no—
552C2×Q8—221no—
553C2×Q8—221no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—221no—
557C2×Q8D4×D1112yes—
558C2×Q8#434112yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—41no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
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—21no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4D4×D1112yes—
584C22×C4#434112yes—
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C23×D1111yescharacteristic
590Q16—444no—
591Q16—444no—
592M16—444no—
593M16—444no—
594C2×C8—112no—
595C2×C8—112no—
596C2×C8—112no—
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—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—112no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—442no—
620C4⋊C4—442no—
621C4⋊C4—442no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—442no—
628C22⋊C4—442no—
629C22⋊C4—442no—
630C22⋊C4—442no—
631C42—21no—
632C42—21no—
633C42—442no—
634C11#2513411yescharacteristic, complemented, Sylow
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23#6699212yes—
649C23C22×C22⋊D1111yescharacteristic
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—22no—
654Q8—48no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—441no—
660Q8—441no—
661Q8—441no—
662Q8—441no—
663D4—44no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—48no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
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—222no—
696C2×C4—441no—
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#6699212yes—
708C2×C4#6699512yes—
709C2×C4C2×D4×D1111yescharacteristic
710C2×C4C2×D4×D1111yescharacteristic
711C2×C4C2×#434111yescharacteristic
712C2×C4C2×#434111yescharacteristic
713C2×C4#6703711yescharacteristic
714C2×C4#6703711yescharacteristic
715C8—222no—
716C8—222no—
717C8—222no—
718C8—441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22D4×C22⋊D1111yescharacteristic
734C22C2×#6699211yescharacteristic
735C22#1062333711yescharacteristic
736C22C2×#6699511yescharacteristic
737C22#1062335311yescharacteristic
738C22#1062336911yescharacteristic
739C22#1062336911yescharacteristic
740C4—22no—
741C4—22no—
742C4—41no—
743C4—42no—
744C4—42no—
745C4—41no—
746C4—81no—
747C4—81no—
748C4—442no—
749C4—881no—
750C4—881no—
751C4—881no—
752C4#1062311711yescharacteristic
753C4#1062312111yescharacteristic
754C4#1062312211yescharacteristic
755C4#1062312411yescharacteristic
756C2—42no—
757C2—81no—
758C2#1307215611yescharacteristic
759C2#1307824211yescharacteristic
760C2#1307826811yescharacteristic
761C2#1308026211yescharacteristic
762C2#1308026911yescharacteristic
763C2#1308088411yescharacteristic
764C2#1308089911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2409C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2409D11
hypocenterC11#25134
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
1. C2×#10622665C2semidirect
2. C2×#10622841C2semidirect
4. C2×#10622838C2semidirect
6. #13069997C2semidirect
7. #13069938C2semidirect
8. #13069816C2semidirect
9. #13069624C2semidirect
10. #13069476C2semidirect
11. #13069295C2semidirect
12. #13069050C2semidirect
13. #13069047C2semidirect
14. #13068813C2semidirect
137. #66899D4semidirect
634. C11#25134semidirect

Maximal subgroups

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

subgroupindex
C2×#106226652
C2×#106228412
C2×#106226252
C2×#106228382
#130720452
#130699972
#130699382
#130698162
#130696242
#130694762
#130692952
#130690502
#130690472
#130688132
C11×#24092
#2513411