Finite Group Databasebeta

← #14770119

Subgroups — #14770119

Order 2816.

1390 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×#10623142C211yesmaximal, characteristic
2C2×#10622343C211yesmaximal, characteristic, complemented
3#13071541C211yesmaximal, characteristic, complemented
4#13069587C211yesmaximal, characteristic, complemented
5#13069562C211yesmaximal, characteristic, complemented
6#13069051C211yesmaximal, characteristic, complemented
7#13069045C211yesmaximal, characteristic, complemented
8#13068935C211yesmaximal, characteristic, complemented
9#13068705C211yesmaximal, characteristic, complemented
10#13068703C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068334C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic, complemented
15C11×#1874C211yesmaximal, characteristic, complemented
16C22×#4341—21no—
17C2×C11×#121C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C2×#66988—21no—
21C2×D4×Dic11C2211yescharacteristic
22C2×C4×C22⋊D11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26#10623142—24no—
27#10623142C418yescomplemented
28C2×#66945C2211yescharacteristic
29C2×C4⋊C4×D11C2211yescharacteristic
30C2×#66941C2211yescharacteristic
31C2×#66936—21no—
32C2×#66931—21no—
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38#10622826—21no—
39#10622825C2211yescharacteristic
40C4×C22⋊Dic11—21no—
41C2×(C2×D11)⋊C8C2211yescharacteristic
42C2×#66879C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44#10622603—21no—
45#10622600C2211yescharacteristic
46#10622591—21no—
47#10622590C2211yescharacteristic
48C4⋊C4×Dic11C2211yescharacteristic
49#10622343—24no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C22×C22⋊D11D411yescharacteristic
68C23×Dic11—21no—
69C23×Dic11—21no—
70C2×#4341—28no—
71C2×#4341—44no—
72C2×#4341—44no—
73C22×C4×D11—21no—
74C22×C4×D11C2311yescharacteristic
75C22×Dic22—21no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#121—22no—
79C11×#121C2×C414yes—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—41no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11D411yescharacteristic
91#66991—22no—
92#66991C2×C414yescomplemented
93#66988—28no—
94D4×Dic11—22no—
95D4×Dic11C2×C414yescomplemented
96C4×C22⋊D11C2×C414yes—
97C4×C22⋊D11D414yes—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4D411yescharacteristic
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11C2×C414yes—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4D411yescharacteristic
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8—22no—
115C22×C11⋊C8—22no—
116C22×C11⋊C8—41no—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C2×#4313—22no—
120C2×#4313—22no—
121C2×#4313—41no—
122#66945—22no—
123#66945—41no—
124C4⋊C4×D11—22no—
125C4⋊C4×D11C2×C414yescomplemented
126#66941—22no—
127#66941C2×C414yescomplemented
128#66936—28no—
129#66931—28no—
130C11×#102—22no—
131C11×#102—41no—
132C11×C22⋊C8—22no—
133#66896—22no—
134#66896—41no—
135C11⋊#95—21no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140(C2×D11)⋊C8—22no—
141#66879—22no—
142Dic11⋊C8—22no—
143#22495—111nomaximal, Sylow
144C24×C11—21no—
145C24×C11C2×D411yescharacteristic
146C23×D11C2×D411yescharacteristic
147C2×D4×C11—24no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11C22×C412yes—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—81no—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—22no—
171C2×C22⋊D11—22no—
172C2×C22⋊D11—24no—
173C2×C22⋊D11—42no—
174C2×C22⋊D11—42no—
175C2×C22⋊D11C22⋊C414yes—
176C22×Dic11—24no—
177C22×Dic11—24no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11—42no—
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
189#4341—432no—
190C2×C4×D11—24no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×C4×D11C22×C412yes—
198C2×C4×D11C2×D412yes—
199C2×Dic22—24no—
200C2×Dic22—42no—
201C2×Dic22—42no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4C22×C412yes—
214C11×C4⋊C4#4112yescomplemented
215C11×C22⋊C4—24no—
216C22⋊Dic11—24no—
217C22⋊Dic11—24no—
218C22⋊Dic11—42no—
219C22⋊Dic11C22⋊C414yes—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—81no—
222(C2×D11)⋊C4C22⋊C414yes—
223C4⋊Dic11—24no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11C22×C412yes—
231C4⋊Dic11C22×C412yes—
232Dic11⋊C4—24no—
233Dic11⋊C4—24no—
234Dic11⋊C4C22⋊C414yes—
235C4×Dic11—42no—
236C4×Dic11—81no—
237C4×Dic11C22×C412yes—
238C4×Dic11C2×D412yes—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—44no—
245C2×C11⋊C8#4112yescomplemented
246#4313—44no—
247C2×#547—111no—
248C2×#435—111no—
249#2352—111no—
250#1993—111no—
251#1987—111no—
252#1895—111no—
253#1893—111no—
254#1875—111no—
255#1874D1111yescharacteristic, complemented
256#1824—111no—
257#1823—111no—
258#1804—111no—
259#1762—111no—
260#1736—111no—
261C2×#340—111no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—22no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11C2×C22⋊C412yes—
274C23×C11AGL(1,ℤ/8)12yes—
275C23×C11AGL(1,ℤ/8)12yes—
276C23×C11C22×D411yescharacteristic
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11C2×C22⋊C412yes—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—48no—
287D4×C11—41no—
288D4×C11—41no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
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×C11—41no—
304C2×C4×C11—84no—
305C2×C4×C11C2×C22⋊C412yes—
306C2×C4×C11C23×C411yescharacteristic
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11C2×#4111yescharacteristic
310C2×C4×C11H(5,𝔽2)11yescharacteristic
311C2×C4×C112−1+411yescharacteristic
312C22⋊D11—28no—
313C22⋊D11—48no—
314C2×Dic11—21no—
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—48no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—48no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11C2×C22⋊C412yes—
335C2×Dic11C2×C22⋊C412yes—
336C2×Dic11C2×C22⋊C412yes—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—48no—
342Dic22—48no—
343C8×C11—41no—
344C8×C11—41no—
345C11⋊C8—22no—
346C11⋊C8—41no—
347C22×#41—221no—
348C22×M16—111no—
349C23×C8—111no—
350#547—118no—
351#547—224no—
352C2×C4⋊Q8—111no—
353C2×#123—221no—
354C2×#123—221no—
355C2×C22⋊Q8—221no—
356C2×#121—111no—
357C2×#121C2×D1111yescharacteristic
358C2×C4×D4—111no—
359C2×C4×D4—111no—
360C2×#117—111no—
361C22×C4⋊C4—111no—
362C22×C4⋊C4—111no—
363C22×C4⋊C4C2×D1111yescharacteristic
364#435—224no—
365C2×C4⋊C8—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102C2×D1111yescharacteristic
369C2×#102C2×D1111yescharacteristic
370C2×C22⋊C8—111no—
371C2×C22⋊C8C2×D1111yescharacteristic
372C2×#97—111no—
373#388—221no—
374#387—221no—
375#386—221no—
376#382—111no—
377#380—111no—
378#380—111no—
379C4×C4⋊C4—111no—
380C4×C22⋊C4—221no—
381#340—111no—
382#340—111no—
383#340—111no—
384#340—111no—
385#340—111no—
386#340—111no—
387#340—111no—
388#340—111no—
389#340—111no—
390#340—111no—
391#340C2×D1111yescharacteristic
392#340C2×D1111yescharacteristic
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—42no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11#41814yes—
407C22×C11C22×C22⋊C411yescharacteristic
408C22×C11#54611yescharacteristic
409C22×C11#54711yescharacteristic
410C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
411C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
412C22×C11#57711yescharacteristic
413C22×C11#57811yescharacteristic
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—41no—
420C2×D11—41no—
421C4×C11—22no—
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—22no—
432Dic11—42no—
433Dic11—42no—
434Dic11—81no—
435Dic11—81no—
436C2×#41—228no—
437C2×#41—444no—
438C2×#41—444no—
439C22×Q8—221no—
440C22×D4—21no—
441C22×D4—111no—
442C22×D4—221no—
443C22×D4C22×D1111yescharacteristic
444C23×C4—21no—
445C23×C4—111no—
446C23×C4—221no—
447C23×C4—221no—
448C23×C4—221no—
449C23×C4C22×D1111yescharacteristic
450C2×M16—222no—
451C2×M16—222no—
452C2×M16—441no—
453C22×C8—111no—
454C22×C8—111no—
455C22×C8—222no—
456C22×C8—222no—
457C22×C8—441no—
458C22×C8C22×D1111yescharacteristic
459C22×C8C22×D1111yescharacteristic
460C4⋊Q8—114no—
461C4⋊Q8—222no—
462#123—228no—
463#123—228no—
464C22⋊Q8—228no—
465#121—22no—
466#121—114no—
467#121—222no—
468#121C4×D1114yes—
469C4×D4—114no—
470C4×D4—114no—
471C4×D4—114no—
472C4×D4—222no—
473#117—222no—
474#117—441no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—41no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—114no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—222no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4—221no—
489C2×C4⋊C4—222no—
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C4⋊C4C22×D1111yescharacteristic
492C2×C4⋊C4C22×D1111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—111no—
495C2×C22⋊C4—111no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C42—111no—
502C2×C42—221no—
503C2×C42—221no—
504C4⋊C8—222no—
505#102—22no—
506#102—41no—
507#102—222no—
508#102—441no—
509C22⋊C8—22no—
510C22⋊C8—222no—
511#97—222no—
512#95—221no—
513#95—221no—
514#95—221no—
515#95—221no—
516#95—221no—
517C2×C11—24no—
518C2×C11—82no—
519C2×C11#233911yescharacteristic
520C2×C11C2×#41811yescharacteristic
521C2×C11#289811yescharacteristic
522C2×C11#330611yescharacteristic
523C2×C11#330811yescharacteristic
524C2×C11#334311yescharacteristic
525C2×C11#334511yescharacteristic
526D11—42no—
527C24—21no—
528C24—111no—
529C24D4×D1111yescharacteristic
530#41—4432no—
531C2×Q8—224no—
532C2×Q8—442no—
533C2×Q8—442no—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—114no—
543C2×D4—222no—
544C2×D4—222no—
545C2×D4—224no—
546C2×D4—442no—
547C2×D4—442no—
548C2×D4C2×C4×D1112yes—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
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—224no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—442no—
576C22×C4—442no—
577C22×C4—442no—
578C22×C4—442no—
579C22×C4—442no—
580C22×C4—442no—
581C22×C4C2×C4×D1112yes—
582C22×C4D4×D1111yescharacteristic
583C22×C4D4×D1112yes—
584C22×C4C23×D1111yescharacteristic
585M16—444no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—112no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—444no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—114no—
605C4⋊C4—112no—
606C4⋊C4—112no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4—221no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4C2×C4×D1112yes—
617C4⋊C4#434112yescomplemented
618C22⋊C4—24no—
619C22⋊C4—114no—
620C22⋊C4—114no—
621C22⋊C4—224no—
622C22⋊C4—224no—
623C22⋊C4—442no—
624C22⋊C4—442no—
625C22⋊C4—881no—
626C42—112no—
627C42—112no—
628C42—442no—
629C42—881no—
630C11#2249511yescharacteristic, complemented, Sylow
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—112no—
643C23—221no—
644C23—221no—
645C23—221no—
646C23—221no—
647C23—221no—
648C23—221no—
649C23C22⋊C4×D1112yes—
650C23#6696412yes—
651C23#6696712yes—
652C23C2×D4×D1111yescharacteristic
653Q8—448no—
654D4—22no—
655D4—22no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—228no—
660D4—448no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—84no—
677C2×C4—112no—
678C2×C4—112no—
679C2×C4—112no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—448no—
693C2×C4—448no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4—448no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4C22⋊C4×D1112yes—
706C2×C4C22×C4×D1111yescharacteristic
707C2×C4C2×D4×D1111yescharacteristic
708C2×C4C2×#434111yescharacteristic
709C2×C4#6703711yescharacteristic
710C2×C4#41×D1111yescharacteristic
711C2×C4#6704311yescharacteristic
712C8—41no—
713C8—41no—
714C8—222no—
715C8—441no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—222no—
730C22—222no—
731C22—222no—
732C22—441no—
733C22—441no—
734C22—441no—
735C22—441no—
736C22#1062238314yes—
737C22C2×C22⋊C4×D1111yescharacteristic
738C22#1062312211yescharacteristic
739C22#1062318611yescharacteristic
740C22C2×#6696411yescharacteristic
741C22C2×#6696711yescharacteristic
742C22#1062330611yescharacteristic
743C22#1062331011yescharacteristic
744C4—22no—
745C4—42no—
746C4—42no—
747C4—81no—
748C4—222no—
749C4—222no—
750C4—222no—
751C4—442no—
752C4—442no—
753C4—881no—
754C4—881no—
755C4C4×#434111yescharacteristic
756C4#1062307711yescharacteristic
757C4#1062314111yescharacteristic
758C4#1062314211yescharacteristic
759C2—24no—
760C2—82no—
761C2—442no—
762C2#1307144211yescharacteristic
763C2C2×#1062238311yescharacteristic
764C2#1307714711yescharacteristic
765C2#1308058111yescharacteristic
766C2#1308061111yescharacteristic
767C2#1308106011yescharacteristic
768C2#1308108411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×#10623142C2
cosocleC22×C4×C11C24
hypercenter#1874D11
hypocenterC11#22495
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#10622343C2semidirect
3. #13071541C2semidirect
4. #13069587C2semidirect
5. #13069562C2semidirect
6. #13069051C2semidirect
7. #13069045C2semidirect
8. #13068935C2semidirect
9. #13068705C2semidirect
10. #13068703C2semidirect
11. #13068624C2semidirect
12. #13068443C2semidirect
13. #13068334C2semidirect
14. C2×#10622167C2semidirect
15. C11×#1874C2semidirect
27. #10623142C4semidirect
92. #66991C2×C4semidirect
95. D4×Dic11C2×C4semidirect
125. C4⋊C4×D11C2×C4semidirect
127. #66941C2×C4semidirect
214. C11×C4⋊C4#41semidirect
245. C2×C11⋊C8#41semidirect
255. #1874D11semidirect
617. C4⋊C4#4341semidirect
630. C11#22495semidirect

Maximal subgroups

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

subgroupindex
C2×#106231422
C2×#106223432
#130715412
#130695872
#130695622
#130690512
#130690452
#130689352
#130687052
#130687032
#130686242
#130684432
#130683342
C2×#106221672
C11×#18742
#2249511