Finite Group Databasebeta

← #14801281

Subgroups — #14801281

Order 2816.

1100 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622641C211yesmaximal, characteristic, complemented
2C2×#10622841C211yesmaximal, characteristic, complemented
3C2×#10622840C211yesmaximal, characteristic
4C2×C4×#4325C211yesmaximal, characteristic, complemented
5#13072193C211yesmaximal, characteristic
6#13069997C211yesmaximal, characteristic, complemented
7#13069812C211yesmaximal, characteristic, complemented
8#13069798C211yesmaximal, characteristic
9#13069709C211yesmaximal, characteristic, complemented
10#13069476C211yesmaximal, characteristic, complemented
11#13069224C211yesmaximal, characteristic, complemented
12#13068957C211yesmaximal, characteristic, complemented
13#13068953C211yesmaximal, characteristic, complemented
14#13068870C211yesmaximal, characteristic, complemented
15Q8×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C2×#66928C2211yescharacteristic
26C2×C4×D44C2211yescharacteristic
27C11×#391—21no—
28C11×#391—21no—
29C11×#391C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#380—21no—
32C11×#380C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C4×C11×C22⋊C4C2211yescharacteristic
35#10622841—24no—
36#10622840—24no—
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622641—24no—
44C4×#4325—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622572—21no—
52#10622569—21no—
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622288—21no—
58#10622280—21no—
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—21no—
66C22×Q8×C11—22no—
67C22×Q8×C11—22no—
68C22×Q8×C11—41no—
69C22×Q8×C11—41no—
70C22×Q8×C11C2311yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11—21no—
75C22×D44C2311yescharacteristic
76C22×C4×D11—21no—
77C22×Dic22C2311yescharacteristic
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—41no—
81C4×Q8×C11—41no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C42×C11—21no—
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2311yescharacteristic
93C2×C22⋊Dic11—21no—
94C2×#4326—22no—
95C2×#4326—22no—
96C2×#4326—22no—
97C2×#4326—22no—
98C2×#4326—22no—
99C2×#4326—41no—
100C2×#4325—22no—
101C2×#4325—22no—
102C2×#4325—22no—
103C2×#4325—22no—
104C2×#4325—41no—
105C2×#4325D414yes—
106#66983—22no—
107#66983—41no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114#66977—22no—
115#66977—41no—
116C2×Dic11⋊C4—21no—
117C2×Dic11⋊C4—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122#66928—22no—
123#66928—41no—
124C4×D44—22no—
125C4×D44—41no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95D411yescharacteristic
132C11×#95D411yescharacteristic
133#66899—22no—
134#66899—22no—
135#66899—22no—
136#66899D414yescomplemented
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—22no—
141C22⋊(C11⋊C8)—22no—
142#66874—22no—
143#66874—41no—
144#66873—22no—
145#66873—22no—
146#66872—22no—
147#66871—41no—
148C4⋊(C11⋊C8)—22no—
149C4×C11⋊C8—22no—
150#25157—111nomaximal, Sylow
151C24×C11C2×D411yescharacteristic
152C23×D11—21no—
153C2×Q8×C11—24no—
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—42no—
163C2×Q8×C11—42no—
164C2×Q8×C11—44no—
165C2×Q8×C11—44no—
166C2×Q8×C11—44no—
167C2×Q8×C11—44no—
168C2×Q8×C11C2×D412yes—
169C2×Q8×C11C2×D412yes—
170C2×Q8×C11#4112yes—
171C2×Q8×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—21no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2411yescharacteristic
191C2×C22⋊D11—42no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—81no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44C2×D412yes—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11—81no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—42no—
217C11×C4⋊C4—42no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—42no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—42no—
226C42×C11—42no—
227C22⋊Dic11—42no—
228#4326—44no—
229#4326—44no—
230#4325—28no—
231#4325—44no—
232(C2×D11)⋊C4—42no—
233(C2×D11)⋊C4—42no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—42no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11C2×D412yes—
240Dic11⋊C4—42no—
241Dic11⋊C4—81no—
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×#464—111no—
255C2×#451—111no—
256C2×#448—111no—
257C2×C4×SD16—111no—
258#2427—111no—
259Q8×C22⋊C4D1111yescharacteristic, complemented
260#2066—111no—
261#2035—111no—
262#2033—111no—
263#2015—111no—
264#1969—111no—
265#1923—111no—
266#1878—111no—
267#1877—111no—
268#1863—111no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—21no—
275C23×C11#13512yes—
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—22no—
287Q8×C11—22no—
288Q8×C11—22no—
289Q8×C11—48no—
290Q8×C11—41no—
291Q8×C11—41no—
292Q8×C11#12114yes—
293C2×C4×C11—22no—
294C2×C4×C11—21no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
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—21no—
310C2×C4×C11—21no—
311C2×C4×C11—48no—
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#13712yes—
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C2×#4111yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C22⋊D11—84no—
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—
341D44—22no—
342D44—22no—
343D44—41no—
344D44—41no—
345C4×D11—84no—
346Dic22—41no—
347Dic22—41no—
348Dic22—41no—
349Dic22—41no—
350C11⋊C8—22no—
351C11⋊C8—22no—
352C11⋊C8—41no—
353C11⋊C8—41no—
354C23×Q8C2×D1111yescharacteristic
355C22×Q16—111no—
356C22×Q16—111no—
357C22×SD16—111no—
358C22×SD16—111no—
359C2×#124—111no—
360C2×C22⋊Q8—111no—
361C2×#121—111no—
362C2×C4×Q8C2×D1111yescharacteristic
363C2×C4×Q8C2×D1111yescharacteristic
364C2×C4×D4—111no—
365#464—224no—
366#451—224no—
367#448—224no—
368C4×SD16—224no—
369C2×#107—111no—
370C2×#106—111no—
371C2×C4⋊C8—111no—
372C2×#103—111no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#103—111no—
376C2×#103—111no—
377C2×#103—111no—
378C2×#102—111no—
379C2×#102—111no—
380C2×C22⋊C8—111no—
381C2×C22⋊C8—111no—
382C2×C4×C8—111no—
383#397—221no—
384#394—221no—
385#391—21no—
386#391—21no—
387#391—111no—
388#391C2×D1111yescharacteristic
389#391C2×D1111yescharacteristic
390#389—111no—
391#386—221no—
392#380—21no—
393#380—221no—
394#380C2×D1111yescharacteristic
395C4×C22⋊C4—21no—
396C4×C22⋊C4C2×D1111yescharacteristic
397#340—111no—
398#340—111no—
399#336—111no—
400#336—111no—
401C22×C11—22no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—41no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11#52511yescharacteristic
409C22×C11D4211yescharacteristic
410C22×C11D4211yescharacteristic
411C22×C11C2×#13511yescharacteristic
412C22×C11C2×#13711yescharacteristic
413C22×C11#57711yescharacteristic
414C22×C11#57811yescharacteristic
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—81no—
419C2×D11—81no—
420C2×D11—81no—
421C2×D11—81no—
422C4×C11—24no—
423C4×C11—22no—
424C4×C11—41no—
425C4×C11—42no—
426C4×C11—41no—
427C4×C11—41no—
428C4×C11—41no—
429C4×C11—81no—
430C4×C11—81no—
431C4×C11C2×#12111yescharacteristic
432C4×C11#53811yescharacteristic
433C4×C11#54611yescharacteristic
434C4×C11#54611yescharacteristic
435Dic11—42no—
436Dic11—81no—
437Dic11—81no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—21no—
441C22×Q8—22no—
442C22×Q8—22no—
443C22×Q8—41no—
444C22×Q8—41no—
445C22×Q8—111no—
446C22×Q8C22×D1111yescharacteristic
447C22×Q8C22×D1111yescharacteristic
448C22×D4—111no—
449C22×D4—221no—
450C23×C4—21no—
451C23×C4—221no—
452C23×C4C22×D1111yescharacteristic
453C2×Q16—222no—
454C2×Q16—222no—
455C2×Q16—222no—
456C2×Q16—222no—
457C2×Q16—222no—
458C2×Q16—441no—
459C2×SD16—114no—
460C2×SD16—222no—
461C2×SD16—222no—
462C2×SD16—222no—
463C2×SD16—222no—
464C2×SD16—441no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—111no—
468C22×C8—111no—
469#124—222no—
470#124—441no—
471C22⋊Q8—222no—
472C22⋊Q8—441no—
473#121—222no—
474#121—441no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×Q8—41no—
479C4×D4—222no—
480C4×D4—441no—
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—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4C22⋊D1111yescharacteristic
496C2×C22⋊C4C22⋊D1111yescharacteristic
497C2×C42—21no—
498C2×C42—21no—
499C2×C42C22×D1111yescharacteristic
500C2×C42C22×D1111yescharacteristic
501#107—441no—
502#106—222no—
503C4⋊C8—222no—
504#103—114no—
505#103—222no—
506#103—222no—
507#103—222no—
508#103—222no—
509#103—441no—
510#102—222no—
511#102—222no—
512C22⋊C8—222no—
513C22⋊C8—222no—
514C4×C8—222no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—221no—
521#95—221no—
522#95—221no—
523#95C22⋊D1111yescharacteristic
524#95C22⋊D1111yescharacteristic
525C2×C11—42no—
526C2×C11#242411yescharacteristic
527C2×C11#310811yescharacteristic
528C2×C11#312111yescharacteristic
529C2×C11#326611yescharacteristic
530C2×C11#327611yescharacteristic
531C2×C11#328211yescharacteristic
532C2×C11#328511yescharacteristic
533D11—82no—
534C24—221no—
535C24C2×C22⋊D1111yescharacteristic
536C2×Q8—24no—
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—44no—
551C2×Q8—221no—
552C2×Q8—221no—
553C2×Q8—221no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—221no—
557C2×Q8#433912yes—
558C2×Q8#433912yes—
559C2×Q8D4×D1112yes—
560C2×Q8D4×D1112yes—
561C2×D4—112no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—221no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—442no—
568C2×D4—442no—
569C2×D4—881no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—442no—
587C22×C4—442no—
588C22×C4—881no—
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C23×D1111yescharacteristic
595Q16—444no—
596Q16—444no—
597SD16—228no—
598SD16—444no—
599C2×C8—112no—
600C2×C8—112no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C2×C8—221no—
606C2×C8—221no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—112no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—442no—
622C4⋊C4—881no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—42no—
626C22⋊C4—442no—
627C22⋊C4—442no—
628C22⋊C4—442no—
629C22⋊C4—442no—
630C22⋊C4—442no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—42no—
636C42—42no—
637C11#2515711yescharacteristic, complemented, Sylow
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—222no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23#6700312yes—
652C23C22×C22⋊D1111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—48no—
659Q8—41no—
660Q8—41no—
661Q8—441no—
662Q8—441no—
663Q8—441no—
664Q8—441no—
665Q8#6693714yes—
666D4—222no—
667D4—222no—
668D4—441no—
669D4—441no—
670D4—884no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
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—48no—
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—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—222no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—884no—
712C2×C4#6699512yes—
713C2×C4C2×#433911yescharacteristic
714C2×C4C2×#433911yescharacteristic
715C2×C4C2×D4×D1111yescharacteristic
716C2×C4C2×D4×D1111yescharacteristic
717C2×C4#6703711yescharacteristic
718C2×C4#6703711yescharacteristic
719C8—222no—
720C8—222no—
721C8—441no—
722C8—441no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—881no—
734C22—881no—
735C22—881no—
736C22—881no—
737C22#1062332211yescharacteristic
738C22D4×C22⋊D1111yescharacteristic
739C22D4×C22⋊D1111yescharacteristic
740C22C2×#6699511yescharacteristic
741C22C2×#6700311yescharacteristic
742C22#1062336811yescharacteristic
743C22#1062336911yescharacteristic
744C4—24no—
745C4—22no—
746C4—41no—
747C4—41no—
748C4—42no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—442no—
754C4—881no—
755C4—881no—
756C4C2×#6693711yescharacteristic
757C4#1062302111yescharacteristic
758C4#1062302111yescharacteristic
759C4#1062302511yescharacteristic
760C2—42no—
761C2—882no—
762C2#1307215211yescharacteristic
763C2#1307869611yescharacteristic
764C2#1307884511yescharacteristic
765C2#1308012711yescharacteristic
766C2#1308026211yescharacteristic
767C2#1308032411yescharacteristic
768C2#1308035311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterQ8×C22⋊C4D11
hypocenterC11#25157
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622641C2semidirect
2. C2×#10622841C2semidirect
4. C2×C4×#4325C2semidirect
6. #13069997C2semidirect
7. #13069812C2semidirect
9. #13069709C2semidirect
10. #13069476C2semidirect
11. #13069224C2semidirect
12. #13068957C2semidirect
13. #13068953C2semidirect
14. #13068870C2semidirect
15. Q8×C11×C22⋊C4C2semidirect
136. #66899D4semidirect
259. Q8×C22⋊C4D11semidirect
637. C11#25157semidirect

Maximal subgroups

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

subgroupindex
C2×#106226412
C2×#106228412
C2×#106228402
C2×C4×#43252
#130721932
#130699972
#130698122
#130697982
#130697092
#130694762
#130692242
#130689572
#130689532
#130688702
Q8×C11×C22⋊C42
#2515711