Finite Group Databasebeta

← #14788297

Subgroups — #14788297

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×#10622670C211yesmaximal, characteristic, complemented
3#13071309C211yesmaximal, characteristic, complemented
4#13069816C211yesmaximal, characteristic, complemented
5#13069795C211yesmaximal, characteristic, complemented
6#13069617C211yesmaximal, characteristic, complemented
7#13069612C211yesmaximal, characteristic
8#13069565C211yesmaximal, characteristic, complemented
9#13069549C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068870C211yesmaximal, characteristic, complemented
13#13068863C211yesmaximal, characteristic, complemented
14#13068600C211yesmaximal, characteristic, complemented
15C2×C11×#542C211yesmaximal, characteristic, complemented
16C11×#542—24no—
17C11×#542—24no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C11×#126—21no—
20C2×C11×#124—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×C22⋊Q8—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39#10622825C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42#10622700—24no—
43#10622670—24no—
44#10622603—21no—
45#10622602—21no—
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622570—21no—
51#10622569—21no—
52#10622552C2211yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic
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×Q8×C11—21no—
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8D414yescomplemented
74C11×#126—28no—
75C11×#124—28no—
76C11×#124—22no—
77C11×#124D414yescomplemented
78C11×#123—28no—
79C11×C22⋊Q8—28no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×#121—22no—
83C11×#121—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C11×#117—22no—
89C11×#117—22no—
90C2×C11×C4⋊C4—21no—
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⋊C4—21no—
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×#4325—22no—
109C2×#4325—22no—
110C2×#4325—41no—
111C2×#4323—22no—
112C2×#4323—22no—
113C2×#4323—41no—
114#66983—22no—
115#66983—22no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C22×C11⋊C8C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C4×D44—22no—
130C4×D44—22no—
131#66899—22no—
132#66899—22no—
133#66899—41no—
134#66896—22no—
135#66896—22no—
136#66896—41no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C22⋊(C11⋊C8)—41no—
141C22⋊(C11⋊C8)—41no—
142#66873—22no—
143#66873—22no—
144#66871—22no—
145#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4⋊(C11⋊C8)—22no—
148#24167—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C23×D11—21no—
152C2×Q8×C11—24no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—81no—
159C2×Q8×C11—81no—
160C2×Q8×C11C2×D412yes—
161C2×D4×C11—24no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—81no—
168C2×D4×C11—81no—
169C2×D4×C11C2×D412yes—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
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—81no—
181C22×C4×C11—81no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C2×C22⋊D11—24no—
189C2×C22⋊D11—81no—
190C2×C22⋊D11—81no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44#4112yes—
200C2×C4×D11—42no—
201C2×C4×D11—81no—
202C2×C4×D11—81no—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—24no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4C2×D412yes—
211C11×C4⋊C4C2×D412yes—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C42×C11—24no—
220C42×C11—21no—
221C42×C11—21no—
222C42×C11C2×D412yes—
223C42×C11C2×D412yes—
224C22⋊Dic11—81no—
225#4325—44no—
226#4323—44no—
227(C2×D11)⋊C4—24no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—81no—
230(C2×D11)⋊C4—81no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11#4112yes—
237Dic11⋊C4—81no—
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×#542D1111yescharacteristic, complemented
252C2×#474—111no—
253C2×#463—111no—
254#2324—111no—
255#2036—111no—
256#2033—111no—
257#2000—111no—
258#1999—111no—
259#1987—111no—
260#1983—111no—
261#1880—111no—
262#1879—111no—
263#1863—111no—
264#1862—111no—
265#1798—111no—
266C23×C11—21no—
267C23×C11—22no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—21no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—41no—
280C23×C11C22×D411yescharacteristic
281C22×D11—22no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288Q8×C11—22no—
289Q8×C11—22no—
290Q8×C11—41no—
291Q8×C11—41no—
292Q8×C11—84no—
293D4×C11—22no—
294D4×C11—22no—
295D4×C11—41no—
296D4×C11—41no—
297D4×C11—84no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—22no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
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—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
333C22⋊D11—84no—
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—
343D44—22no—
344D44—22no—
345D44—41no—
346D44—41no—
347C4×D11—84no—
348C11⋊C8—41no—
349C11⋊C8—41no—
350C11⋊C8—41no—
351C11⋊C8—41no—
352C22×SD16—111no—
353C22×D8—111no—
354#542—24no—
355#542—24no—
356C2×C4⋊Q8C2×D1111yescharacteristic
357C2×#126—21no—
358C2×#124—21no—
359C2×#124C2×D1111yescharacteristic
360C2×#123—21no—
361C2×C22⋊Q8—21no—
362C2×C22⋊Q8C2×D1111yescharacteristic
363C2×#121—111no—
364C2×#121C2×D1111yescharacteristic
365C2×C4×Q8C2×D1111yescharacteristic
366C2×C4×D4—111no—
367C2×C4×D4C2×D1111yescharacteristic
368C2×#117C2×D1111yescharacteristic
369#474—224no—
370#463—224no—
371C2×#107—111no—
372C2×#107—111no—
373C2×C4⋊C8—111no—
374C2×C4⋊C8—111no—
375C2×#103—111no—
376C2×#103—111no—
377C2×#103—111no—
378C2×#102—111no—
379C2×#102—111no—
380C2×#102—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×C22⋊C8—111no—
384C2×C22⋊C8—111no—
385#390—111no—
386#390—221no—
387#389—111no—
388#388—221no—
389#386—221no—
390#385—221no—
391#380—111no—
392C4×C4⋊C4—111no—
393#340—111no—
394#340—111no—
395#340—111no—
396#340—111no—
397#336—111no—
398#336—111no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—42no—
403C22×C11—41no—
404C22×C11—41no—
405C22×C11—42no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—42no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11C2×#12011yescharacteristic
414C22×C11#52511yescharacteristic
415C22×C11#53711yescharacteristic
416C22×C11#57611yescharacteristic
417C22×C11#57611yescharacteristic
418C22×C11#57711yescharacteristic
419C22×C11#57811yescharacteristic
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—81no—
424C2×D11—81no—
425C2×D11—81no—
426C2×D11—81no—
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—41no—
430C4×C11—42no—
431C4×C11—41no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—41no—
435C4×C11#54611yescharacteristic
436C4×C11#54711yescharacteristic
437C4×C11#54811yescharacteristic
438C4×C11#55011yescharacteristic
439Dic11—42no—
440Dic11—81no—
441Dic11—81no—
442C22×Q8—21no—
443C22×Q8C22×D1111yescharacteristic
444C22×D4—21no—
445C22×D4—111no—
446C22×D4—221no—
447C22×D4C22×D1111yescharacteristic
448C23×C4—21no—
449C23×C4—221no—
450C23×C4C22×D1111yescharacteristic
451C2×SD16—222no—
452C2×SD16—222no—
453C2×SD16—441no—
454C2×D8—222no—
455C2×D8—222no—
456C2×D8—441no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—111no—
460C22×C8—111no—
461C4⋊Q8—22no—
462C4⋊Q8C22⋊D1114yescomplemented
463#126—28no—
464#124—28no—
465#124—22no—
466#124C22⋊D1114yescomplemented
467#123—28no—
468C22⋊Q8—28no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471#121—22no—
472#121—22no—
473#121—222no—
474#121—222no—
475C4×Q8—22no—
476C4×Q8—22no—
477C4×D4—22no—
478C4×D4—22no—
479C4×D4—222no—
480C4×D4—222no—
481#117—22no—
482#117—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4C22⋊D1111yescharacteristic
491C2×C4⋊C4C22⋊D1111yescharacteristic
492C2×C4⋊C4C22×D1111yescharacteristic
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4C22⋊D1111yescharacteristic
505C2×C22⋊C4C22⋊D1111yescharacteristic
506C2×C42—21no—
507C2×C42—221no—
508C2×C42C22×D1111yescharacteristic
509C2×C42C22×D1111yescharacteristic
510#107—222no—
511#107—222no—
512C4⋊C8—222no—
513C4⋊C8—222no—
514#103—222no—
515#103—222no—
516#103—441no—
517#102—222no—
518#102—222no—
519#102—222no—
520#102—222no—
521#102—441no—
522C22⋊C8—441no—
523C22⋊C8—441no—
524#95—221no—
525#95—221no—
526#95—221no—
527C2×C11—81no—
528C2×C11—82no—
529C2×C11#240711yescharacteristic
530C2×C11#300811yescharacteristic
531C2×C11#301311yescharacteristic
532C2×C11#311811yescharacteristic
533C2×C11#312411yescharacteristic
534C2×C11#325711yescharacteristic
535C2×C11#326211yescharacteristic
536D11—82no—
537C24—21no—
538C24—221no—
539C24C2×C22⋊D1111yescharacteristic
540C2×Q8—24no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—81no—
547C2×Q8—81no—
548C2×Q8C2×C22⋊D1112yes—
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4—112no—
558C2×D4—224no—
559C2×D4—221no—
560C2×D4—221no—
561C2×D4—221no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—881no—
565C2×D4—881no—
566C2×D4C2×C22⋊D1112yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—81no—
578C22×C4—81no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—442no—
583C22×C4—881no—
584C22×C4—881no—
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C23×D1111yescharacteristic
591SD16—444no—
592D8—444no—
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—
603C2×C8—221no—
604C2×C8—221no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—112no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—881no—
619C4⋊C4C2×C22⋊D1112yes—
620C4⋊C4C2×C22⋊D1112yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—224no—
629C22⋊C4—442no—
630C22⋊C4—881no—
631C22⋊C4—881no—
632C22⋊C4—881no—
633C42—24no—
634C42—21no—
635C42—21no—
636C42—881no—
637C42C2×C22⋊D1112yes—
638C42C2×C22⋊D1112yes—
639C11#2416711yescharacteristic, complemented, Sylow
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—222no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23—441no—
660C23—441no—
661C23C22×C22⋊D1111yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666Q8—84no—
667D4—22no—
668D4—22no—
669D4—41no—
670D4—41no—
671D4—84no—
672D4—222no—
673D4—222no—
674D4—441no—
675D4—441no—
676D4—884no—
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—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
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—41no—
703C2×C4—84no—
704C2×C4—222no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—884no—
714C2×C4#6700612yes—
715C2×C4#6700612yes—
716C2×C4#41×D1111yescharacteristic
717C2×C4#41×D1111yescharacteristic
718C2×C4#6704211yescharacteristic
719C2×C4#6704311yescharacteristic
720C2×C4C22×C22⋊D1111yescharacteristic
721C2×C4C22×C22⋊D1111yescharacteristic
722C8—441no—
723C8—441no—
724C8—441no—
725C8—441no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22—881no—
744C22—881no—
745C22—881no—
746C22—881no—
747C22#1062335911yescharacteristic
748C22#1062336411yescharacteristic
749C22#1062336611yescharacteristic
750C22#1062336611yescharacteristic
751C22#1062336811yescharacteristic
752C22#1062336911yescharacteristic
753C22C2×#6700611yescharacteristic
754C4—22no—
755C4—22no—
756C4—41no—
757C4—42no—
758C4—41no—
759C4—42no—
760C4—42no—
761C4—41no—
762C4—442no—
763C4—881no—
764C4—881no—
765C4#1062335511yescharacteristic
766C4#1062336011yescharacteristic
767C4#1062336211yescharacteristic
768C4#1062336511yescharacteristic
769C2—81no—
770C2—82no—
771C2—882no—
772C2#1307195511yescharacteristic
773C2#1307788411yescharacteristic
774C2#1307793111yescharacteristic
775C2#1307879411yescharacteristic
776C2#1307887211yescharacteristic
777C2#1308002711yescharacteristic
778C2#1308007211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
prime radical#13069612C2
hypercenterC2×#542D11
hypocenterC11#24167
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
2. C2×#10622670C2semidirect
3. #13071309C2semidirect
4. #13069816C2semidirect
5. #13069795C2semidirect
6. #13069617C2semidirect
8. #13069565C2semidirect
9. #13069549C2semidirect
10. #13068971C2semidirect
11. #13068964C2semidirect
12. #13068870C2semidirect
13. #13068863C2semidirect
14. #13068600C2semidirect
15. C2×C11×#542C2semidirect
73. C11×C4⋊Q8D4semidirect
77. C11×#124D4semidirect
251. C2×#542D11semidirect
462. C4⋊Q8C22⋊D11semidirect
466. #124C22⋊D11semidirect
639. C11#24167semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×#106226702
#130713092
#130698162
#130697952
#130696172
#130696122
#130695652
#130695492
#130689712
#130689642
#130688702
#130688632
#130686002
C2×C11×#5422
#2416711