Finite Group Databasebeta

← #14770192

Subgroups — #14770192

Order 2816.

1370 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623038C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3#13071566C211yesmaximal, characteristic, complemented
4#13069575C211yesmaximal, characteristic, complemented
5#13069566C211yesmaximal, characteristic, complemented
6#13069054C211yesmaximal, characteristic, complemented
7#13069053C211yesmaximal, characteristic, complemented
8#13068938C211yesmaximal, characteristic, complemented
9#13068937C211yesmaximal, characteristic, complemented
10#13068706C211yesmaximal, characteristic, complemented
11#13068705C211yesmaximal, characteristic, complemented
12#13068615C211yesmaximal, characteristic, complemented
13#13068430C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×#4339—21no—
17C22×C11×M16C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66982—21no—
22C2×C4×C22⋊D11C2211yescharacteristic
23C22×#4313C2211yescharacteristic
24C2×#66949—21no—
25#10623038—24no—
26#10623038C418yescomplemented
27C2×#66948C2211yescharacteristic
28C2×#66947—21no—
29C2×#66946C2211yescharacteristic
30C2×#66945C2211yescharacteristic
31C2×C4⋊C4×D11C2211yescharacteristic
32C2×#66941C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622741—24no—
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622589C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46#10622570—21no—
47#10622557—21no—
48#10622553—21no—
49C4×Dic11⋊C4—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11D411yescharacteristic
66C2×#4339—28no—
67C2×#4339—44no—
68C2×#4339—44no—
69C22×D44—21no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11C2311yescharacteristic
74C22×Dic22—21no—
75C2×C11×M16—22no—
76C2×C11×M16—22no—
77C2×C11×M16—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C11×#117—22no—
81C11×#117—41no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4C2×C414yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11D411yescharacteristic
93#66983—22no—
94#66983C2×C414yes—
95#66982—28no—
96C4×C22⋊D11C2×C414yes—
97C4×C22⋊D11D414yes—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4D411yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4D411yescharacteristic
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C2×#4313—22no—
118C2×#4313—22no—
119C2×#4313—41no—
120#66949—28no—
121#66948—22no—
122#66948C2×C414yes—
123#66947—28no—
124#66946—22no—
125#66946C2×C414yes—
126#66945—22no—
127#66945—41no—
128C4⋊C4×D11—22no—
129C4⋊C4×D11C2×C414yes—
130#66941—22no—
131#66941C2×C414yes—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C22⋊(C11⋊C8)—22no—
136#66885—22no—
137#66885—41no—
138(C2×D11)⋊C8—22no—
139Dic11⋊C8—22no—
140C8×Dic11—22no—
141#66873—22no—
142#66873—41no—
143#22500—111nomaximal, Sylow
144C24×C11C2×D411yescharacteristic
145C23×D11—21no—
146C23×D11C2×D411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—24no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—22no—
163C2×C22⋊D11—22no—
164C2×C22⋊D11—24no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—42no—
167C2×C22⋊D11C22⋊C414yes—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174#4339—432no—
175C2×D44—24no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—42no—
182C2×D44—42no—
183C2×D44C22×C412yes—
184C2×C4×D11—24no—
185C2×C4×D11—24no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×C4×D11C22×C412yes—
195C2×C4×D11C2×D412yes—
196C2×Dic22—24no—
197C2×Dic22—42no—
198C2×Dic22—42no—
199C11×M16—44no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11#4112yescomplemented
206C11×C4⋊C4—24no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4C22×C412yes—
213C11×C4⋊C4C22×C412yes—
214C11×C4⋊C4#4112yescomplemented
215C11×C22⋊C4—42no—
216C42×C11—42no—
217C22⋊Dic11—81no—
218C22⋊Dic11C22⋊C414yes—
219(C2×D11)⋊C4—24no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—81no—
224(C2×D11)⋊C4C22⋊C414yes—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11C22×C412yes—
231Dic11⋊C4—24no—
232Dic11⋊C4—24no—
233Dic11⋊C4—42no—
234Dic11⋊C4—81no—
235Dic11⋊C4C22⋊C414yes—
236C4×Dic11—42no—
237C4×Dic11—42no—
238C4×Dic11C22×C412yes—
239C4×Dic11C2×D412yes—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246#4313—44no—
247C2×#547—111no—
248C2×#436—111no—
249#2354—111no—
250#1990—111no—
251#1988—111no—
252#1895—111no—
253#1895—111no—
254#1875—111no—
255#1875—111no—
256#1824—111no—
257#1824—111no—
258#1802—111no—
259C4×#102—111no—
260#1736—111no—
261#1736D1111yescharacteristic, complemented
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11C2×C22⋊C412yes—
269C23×C11C22×D411yescharacteristic
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—22no—
277C22×D11—41no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11C2×C22⋊C412yes—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—48no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11C2×C22⋊C412yes—
304C2×C4×C11C23×C411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C112−1+411yescharacteristic
310C22⋊D11—28no—
311C22⋊D11—48no—
312C2×Dic11—21no—
313C2×Dic11—21no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11C2×C22⋊C412yes—
326C2×Dic11C2×C22⋊C412yes—
327C2×Dic11C2×C22⋊C412yes—
328C2×Dic11AGL(1,ℤ/8)12yes—
329C2×Dic11AGL(1,ℤ/8)12yes—
330D44—22no—
331D44—22no—
332D44—48no—
333D44—41no—
334D44—41no—
335C4×D11—22no—
336C4×D11—22no—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—48no—
340C4×D11—48no—
341Dic22—48no—
342C8×C11—22no—
343C8×C11—41no—
344C11⋊C8—41no—
345C11⋊C8—41no—
346C22×#41—221no—
347C22×M16—111no—
348C22×M16C2×D1111yescharacteristic
349#547—118no—
350#547—224no—
351C2×C4⋊Q8—111no—
352C2×#123—221no—
353C2×#123—221no—
354C2×C22⋊Q8—221no—
355C2×#121—111no—
356C2×#121—111no—
357C2×C4×D4—111no—
358C2×C4×D4—111no—
359C2×#117—111no—
360C2×#117C2×D1111yescharacteristic
361C22×C4⋊C4—111no—
362C22×C4⋊C4C2×D1111yescharacteristic
363#436—224no—
364C2×C4⋊C8—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×C22⋊C8—111no—
370C2×C22⋊C8—111no—
371C2×C4×C8—111no—
372#390—221no—
373#388—221no—
374#388—221no—
375#384—111no—
376#380—111no—
377#380—111no—
378C4×C4⋊C4—111no—
379C4×C4⋊C4—221no—
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#340—111no—
388#340C2×D1111yescharacteristic
389#340C2×D1111yescharacteristic
390#340C2×D1111yescharacteristic
391#340C2×D1111yescharacteristic
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—41no—
396C22×C11—41no—
397C22×C11—41no—
398C22×C11—41no—
399C22×C11C22×C22⋊C411yescharacteristic
400C22×C11#54611yescharacteristic
401C22×C11#54711yescharacteristic
402C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
403C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
404C22×C11#57711yescharacteristic
405C22×C11#57811yescharacteristic
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—41no—
412C2×D11—41no—
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—42no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—81no—
425C4×C11C4×#4111yescharacteristic
426C4×C11#52011yescharacteristic
427C4×C11#54611yescharacteristic
428C4×C11#54711yescharacteristic
429Dic11—22no—
430Dic11—22no—
431Dic11—42no—
432Dic11—81no—
433Dic11—81no—
434Dic11#41814yes—
435C2×#41—228no—
436C2×#41—444no—
437C2×#41—444no—
438C22×Q8—221no—
439C22×D4—111no—
440C22×D4—111no—
441C22×D4—221no—
442C22×D4—221no—
443C23×C4—21no—
444C23×C4—111no—
445C23×C4—221no—
446C23×C4—221no—
447C23×C4C22×D1111yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—41no—
451C2×M16—222no—
452C2×M16—222no—
453C2×M16—441no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458C4⋊Q8—114no—
459C4⋊Q8—222no—
460#123—228no—
461#123—228no—
462C22⋊Q8—228no—
463#121—114no—
464#121—114no—
465#121—222no—
466#121—222no—
467C4×D4—114no—
468C4×D4—114no—
469C4×D4—114no—
470C4×D4—222no—
471#117—22no—
472#117—41no—
473#117—222no—
474#117—441no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—114no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—222no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4C4×D1114yes—
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C4⋊C4C22×D1111yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—111no—
494C2×C22⋊C4—111no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C42—21no—
502C2×C42—111no—
503C2×C42—221no—
504C2×C42—221no—
505C4⋊C8—222no—
506#102—222no—
507#102—222no—
508#102—441no—
509#102—441no—
510C22⋊C8—222no—
511C22⋊C8—222no—
512C4×C8—222no—
513#95—221no—
514#95—221no—
515#95—221no—
516C2×C11—42no—
517C2×C11#233911yescharacteristic
518C2×C11C2×#41811yescharacteristic
519C2×C11#289811yescharacteristic
520C2×C11#333011yescharacteristic
521C2×C11#333211yescharacteristic
522C2×C11#335311yescharacteristic
523C2×C11#335411yescharacteristic
524D11—42no—
525D11—82no—
526C24—111no—
527C24—221no—
528C24D4×D1111yescharacteristic
529#41—4432no—
530C2×Q8—224no—
531C2×Q8—442no—
532C2×Q8—442no—
533C2×D4—114no—
534C2×D4—112no—
535C2×D4—224no—
536C2×D4—222no—
537C2×D4—222no—
538C2×D4—224no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—442no—
545C2×D4—442no—
546C2×D4—442no—
547C2×D4—442no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—111no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—224no—
565C22×C4—224no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—442no—
574C22×C4—442no—
575C22×C4—442no—
576C22×C4—442no—
577C22×C4C2×C4×D1112yes—
578C22×C4D4×D1111yescharacteristic
579C22×C4D4×D1112yes—
580C22×C4C23×D1111yescharacteristic
581M16—44no—
582M16—444no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8#433912yescomplemented
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—114no—
602C4⋊C4—112no—
603C4⋊C4—224no—
604C4⋊C4—224no—
605C4⋊C4—221no—
606C4⋊C4—221no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—442no—
611C4⋊C4—881no—
612C4⋊C4C2×C4×D1112yes—
613C4⋊C4C2×C4×D1112yes—
614C4⋊C4#433912yescomplemented
615C22⋊C4—42no—
616C22⋊C4—114no—
617C22⋊C4—114no—
618C22⋊C4—224no—
619C22⋊C4—224no—
620C22⋊C4—224no—
621C22⋊C4—442no—
622C22⋊C4—881no—
623C22⋊C4—881no—
624C42—42no—
625C42—112no—
626C42—112no—
627C42—442no—
628C42—442no—
629C11#2250011yescharacteristic, complemented, Sylow
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—112no—
637C23—221no—
638C23—221no—
639C23—221no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—222no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23C22⋊C4×D1112yes—
651C23C2×D4×D1111yescharacteristic
652Q8—448no—
653D4—228no—
654D4—222no—
655D4—222no—
656D4—448no—
657D4—448no—
658D4—441no—
659D4—441no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—48no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—112no—
682C2×C4—112no—
683C2×C4—112no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—448no—
694C2×C4—448no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4C22⋊C4×D1112yes—
704C2×C4C22×C4×D1111yescharacteristic
705C2×C4C2×#433911yescharacteristic
706C2×C4C2×#433911yescharacteristic
707C2×C4C2×D4×D1111yescharacteristic
708C2×C4#6703711yescharacteristic
709C2×C4#6704011yescharacteristic
710C8—22no—
711C8—41no—
712C8—441no—
713C8—441no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—222no—
722C22—222no—
723C22—222no—
724C22—441no—
725C22—441no—
726C22—441no—
727C22—441no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—881no—
732C22—881no—
733C22—881no—
734C22—881no—
735C22C2×C22⋊C4×D1111yescharacteristic
736C22#1062302111yescharacteristic
737C22#1062303811yescharacteristic
738C22D11×AGL(1,ℤ/8)11yescharacteristic
739C22D11×AGL(1,ℤ/8)11yescharacteristic
740C22#1062330911yescharacteristic
741C22#1062331011yescharacteristic
742C4—22no—
743C4—42no—
744C4—42no—
745C4—42no—
746C4—81no—
747C4—114no—
748C4—222no—
749C4—222no—
750C4—442no—
751C4—881no—
752C4—881no—
753C4C4×#433911yescharacteristic
754C4#1062302111yescharacteristic
755C4#1062303511yescharacteristic
756C4#1062303811yescharacteristic
757C2—42no—
758C2—442no—
759C2—882no—
760C2#1307144311yescharacteristic
761C2D11×#41811yescharacteristic
762C2#1307714811yescharacteristic
763C2#1308091711yescharacteristic
764C2#1308093911yescharacteristic
765C2#1308119611yescharacteristic
766C2#1308120711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC2×#10623038C2
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#22500
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. #13071566C2semidirect
4. #13069575C2semidirect
5. #13069566C2semidirect
6. #13069054C2semidirect
7. #13069053C2semidirect
8. #13068938C2semidirect
9. #13068937C2semidirect
10. #13068706C2semidirect
11. #13068705C2semidirect
12. #13068615C2semidirect
13. #13068430C2semidirect
14. #13068334C2semidirect
15. C11×#1736C2semidirect
26. #10623038C4semidirect
205. C2×C8×C11#41semidirect
214. C11×C4⋊C4#41semidirect
261. #1736D11semidirect
594. C2×C8#4339semidirect
614. C4⋊C4#4339semidirect
629. C11#22500semidirect

Maximal subgroups

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

subgroupindex
C2×#106230382
C2×#106227412
#130715662
#130695752
#130695662
#130690542
#130690532
#130689382
#130689372
#130687062
#130687052
#130686152
#130684302
#130683342
C11×#17362
#2250011