Finite Group Databasebeta

← C2×#13080711 #15630426

Subgroups — C2×#13080711 #15630426

Order 2816.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623225C211yesmaximal, characteristic, complemented
2C2×#10623257C211yesmaximal, characteristic
3#13080711C2116yesmaximal, direct product factor
4C2×#10622422C211yesmaximal, characteristic, complemented
5C2×#10622427C211yesmaximal, characteristic, complemented
6C2×#10622679C211yesmaximal, characteristic, complemented
7C2×#10622429C211yesmaximal, characteristic, complemented
8C2×#10622426C211yesmaximal, characteristic, complemented
9C2×#10622703C211yesmaximal, characteristic, complemented
10C2×#10622423C211yesmaximal, characteristic, complemented
11C2×#10622423C211yesmaximal, characteristic, complemented
12C2×#10622323C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#491C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#125C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C2×#66999C2211yescharacteristic
23C22×#4326C2211yescharacteristic
24C22×#4326C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26C22×#4313C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28#10623257—24no—
29#10623257C2218yes—
30#10623225—24no—
31#10623225C2218yescomplemented
32C2×#66951—21no—
33C2×#66950C2211yescharacteristic
34C2×#66950C2211yescharacteristic
35C2×#66948—21no—
36C2×#66947—21no—
37C2×#66947—21no—
38C2×#66947—21no—
39C2×#66945—21no—
40C2×#66945C2211yescharacteristic
41C2×C4⋊C4×D11—21no—
42C2×C4⋊C4×D11C2211yescharacteristic
43C2×#66943—21no—
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C11×#491C2218yescomplemented
48C2×C11×#103C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×C11×#97C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60#10622703C2218yescomplemented
61#10622679C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622429C2218yescomplemented
68#10622427C2218yescomplemented
69#10622426C2218yescomplemented
70#10622423C2218yescomplemented
71#10622423C2218yescomplemented
72#10622422C2218yescomplemented
73#10622417C2218yescomplemented
74#10622416C2218yescomplemented
75#10622323C2218yescomplemented
76#10622319C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C2×#4343—22no—
80C2×#4343—22no—
81C2×#4343—24no—
82C2×#4343—24no—
83C2×#4343—42no—
84C2×#4343—42no—
85C2×#4343C2314yes—
86C2×#4343C2314yes—
87C22×D44—21no—
88C22×D44—21no—
89C22×D44D411yescharacteristic
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×C4×D11C2311yescharacteristic
96C22×C4×D11C2311yescharacteristic
97C22×Dic22C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×C4⋊Q8—22no—
101C11×C4⋊Q8C2314yes—
102C11×#125—22no—
103C11×#125C2314yes—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111#66999—22no—
112#66999—22no—
113#66999C2314yes—
114#66999C2314yes—
115C2×#4326—42no—
116C2×#4326—42no—
117C2×#4326C2314yes—
118C2×#4326C2314yes—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125C2×(C2×D11)⋊C4D411yescharacteristic
126C2×(C2×D11)⋊C4D411yescharacteristic
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11D411yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×#4314—24no—
141C2×#4314C2314yes—
142C2×#4313—42no—
143C2×#4313C2314yes—
144C2×C8×D11—42no—
145C2×C8×D11C2314yes—
146#66951—28no—
147#66950—22no—
148#66950—22no—
149#66950C2314yes—
150#66950C2314yes—
151#66948—28no—
152#66947—28no—
153#66947—28no—
154#66947—28no—
155#66945—22no—
156#66945—28no—
157#66945C2314yes—
158C4⋊C4×D11—22no—
159C4⋊C4×D11—28no—
160C4⋊C4×D11C2314yes—
161#66943—28no—
162C4×D44—22no—
163C4×D44D414yes—
164C4×D44C2314yes—
165C4×D44C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168C11×#103C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171C11×#103C2314yes—
172C11×#97C2314yes—
173#66899C2314yes—
174#66899C2314yes—
175#66885C2314yes—
176(C2×D11)⋊C8C2314yes—
177(C2×D11)⋊C8C2314yes—
178#66882C2314yes—
179#66880C2314yes—
180#66873C2314yes—
181#66873C2314yes—
182#66872C2314yes—
183#66871C2314yes—
184C4⋊(C11⋊C8)C2314yes—
185C2×#3315—111nomaximal, Sylow
186C23×D11—21no—
187C23×D11C2×D411yescharacteristic
188C23×D11C2×D411yescharacteristic
189C2×Q8×C11—21no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11—22no—
195C2×Q8×C11C2412yes—
196C2×Q8×C11C2412yes—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2411yescharacteristic
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209#4343—28no—
210#4343—28no—
211#4343—44no—
212#4343—44no—
213#4343—48no—
214#4343—48no—
215C2×D44—24no—
216C2×D44—24no—
217C2×D44—21no—
218C2×D44—22no—
219C2×D44—42no—
220C2×D44—44no—
221C2×D44—44no—
222C2×D44C2×D414yes—
223C2×D44#4114yes—
224C2×D44C2412yes—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×C4×D11—22no—
230C2×C4×D11—22no—
231C2×C4×D11—22no—
232C2×C4×D11—22no—
233C2×C4×D11—44no—
234C2×C4×D11—44no—
235C2×C4×D11—44no—
236C2×C4×D11—44no—
237C2×C4×D11C2×D412yes—
238C2×C4×D11C2×D412yes—
239C2×C4×D11C2412yes—
240C2×C4×D11C2412yes—
241C2×Dic22—21no—
242C2×Dic22—22no—
243C2×Dic22—22no—
244C2×Dic22C2412yes—
245C2×C8×C11—22no—
246C2×C8×C11—22no—
247C2×C8×C11C2412yes—
248C2×C8×C11C2412yes—
249C11×C4⋊C4—24no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—24no—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C42×C11C2×D412yes—
258C42×C11C2412yes—
259#4326—44no—
260#4326—44no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4C2×D414yes—
268(C2×D11)⋊C4C2×D414yes—
269C4⋊Dic11—24no—
270C4⋊Dic11—24no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11C2×D414yes—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280C4×Dic11—24no—
281C4×Dic11—24no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8C2412yes—
285C2×C11⋊C8C2412yes—
286#4314—28no—
287#4313—44no—
288C8×D11—44no—
289C2×#552—111no—
290C2×#547—111no—
291#3315—1116no—
292C2×#491D1111yescharacteristic, complemented
293C2×#484—111no—
294C2×#485—111no—
295C2×#478—111no—
296C2×#470—111no—
297C2×#467—111no—
298C2×#462—111no—
299C2×#452—111no—
300C2×#452—111no—
301C2×#440—111no—
302C2×#435—111no—
303C2×#417—111no—
304C2×#416—111no—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—24no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—42no—
315C22×D11—42no—
316C22×D11C22×D412yes—
317C22×D11C22×D412yes—
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—42no—
323Q8×C11—42no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4112yes—
338C2×C4×C11H(5,𝔽2)12yes—
339C2×C4×C11C2511yescharacteristic
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11C22×D412yes—
349C2×Dic11C22×D412yes—
350D44—24no—
351D44—22no—
352D44—44no—
353D44—48no—
354D44—48no—
355D44C2×#4114yes—
356C4×D11—24no—
357C4×D11—24no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—48no—
363C4×D11—48no—
364C4×D11—48no—
365C4×D11—48no—
366Dic22—22no—
367Dic22—22no—
368Dic22—42no—
369C8×C11—22no—
370C8×C11—22no—
371C11⋊C8—22no—
372C11⋊C8—22no—
373C22×#41—111no—
374C22×#41—111no—
375C22×Q16—111no—
376C22×Q16—111no—
377C22×SD16—111no—
378C22×M16—111no—
379C23×C8—111no—
380#552—118no—
381#552—224no—
382#547—118no—
383#547—224no—
384C2×C4⋊Q8C2×D1111yescharacteristic
385C2×#126—221no—
386C2×#125—221no—
387C2×#125C2×D1111yescharacteristic
388C2×#123—221no—
389C2×#123—221no—
390C2×#123—221no—
391C2×C22⋊Q8—111no—
392C2×C22⋊Q8—111no—
393C2×C22⋊Q8—111no—
394C2×C22⋊Q8—111no—
395C2×#121—221no—
396C2×C4×Q8—111no—
397C2×C4×D4—111no—
398C2×C4×D4—111no—
399C2×#117—111no—
400C2×#117—221no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—221no—
403#491C2×D1118yescomplemented
404#485—118no—
405#484—118no—
406#478—118no—
407#470—118no—
408#467—118no—
409#462—118no—
410#452—118no—
411#452—118no—
412#440—118no—
413#435—118no—
414C2×#107—111no—
415C2×#107—111no—
416C2×#106—111no—
417C2×C4⋊C8—111no—
418#417—118no—
419#416—118no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103C2×D1111yescharacteristic
424C2×#103C2×D1111yescharacteristic
425C2×#103C2×D1111yescharacteristic
426C2×#103C2×D1111yescharacteristic
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×C22⋊C8—111no—
431C2×C22⋊C8—111no—
432C2×#97C2×D1111yescharacteristic
433C22×C11#54612yes—
434C22×C11#57512yes—
435C22×C11#57812yes—
436C22×C11C23×D411yescharacteristic
437C2×D11—24no—
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—22no—
441C2×D11—22no—
442C2×D11—22no—
443C2×D11—22no—
444C2×D11—44no—
445C2×D11—44no—
446C2×D11—48no—
447C2×D11—42no—
448C2×D11—42no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11#54612yes—
456C4×C11C22×#4111yescharacteristic
457C4×C11C2×H(5,𝔽2)11yescharacteristic
458Dic11—22no—
459Dic11—22no—
460Dic11—42no—
461Dic11—42no—
462Dic11—42no—
463C2×#41—114no—
464C2×#41—114no—
465C2×#41—222no—
466C2×#41—222no—
467C2×#41—224no—
468C2×#41—224no—
469C2×#41—442no—
470C2×#41—442no—
471C22×Q8—111no—
472C22×Q8C22×D1111yescharacteristic
473C22×Q8C22×D1111yescharacteristic
474C22×D4—111no—
475C22×D4—111no—
476C22×D4—221no—
477C22×D4—221no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—221no—
481C23×C4—221no—
482C23×C4—221no—
483C23×C4—221no—
484C2×Q16—114no—
485C2×Q16—114no—
486C2×Q16—442no—
487C2×Q16—442no—
488C2×SD16—114no—
489C2×SD16—224no—
490C2×M16—114no—
491C2×M16—442no—
492C22×C8—111no—
493C22×C8—111no—
494C22×C8—114no—
495C22×C8—442no—
496C22×C8C22×D1111yescharacteristic
497C22×C8C22×D1111yescharacteristic
498C4⋊Q8—22no—
499C4⋊Q8C22×D1114yes—
500#126—228no—
501#125—22no—
502#125—228no—
503#125C22×D1114yes—
504#123—228no—
505#123—228no—
506#123—228no—
507C22⋊Q8—114no—
508C22⋊Q8—114no—
509C22⋊Q8—114no—
510C22⋊Q8—114no—
511C22⋊Q8—222no—
512C22⋊Q8—222no—
513C22⋊Q8—222no—
514C22⋊Q8—222no—
515#121—228no—
516C4×Q8—114no—
517C4×Q8—222no—
518C4×D4—114no—
519C4×D4—114no—
520C4×D4—114no—
521C4×D4—222no—
522#117—114no—
523#117—228no—
524#117—222no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—111no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—228no—
534C2×C4⋊C4—222no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4C22×D1111yescharacteristic
542C2×C4⋊C4C22×D1111yescharacteristic
543C2×C22⋊C4—111no—
544C2×C22⋊C4—111no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C42—221no—
552C2×C42—221no—
553C2×C42C22×D1111yescharacteristic
554#107—114no—
555#107—114no—
556#106—114no—
557C4⋊C8—114no—
558#103—114no—
559#103—114no—
560#103—114no—
561#103C22×D1114yes—
562#103C22×D1114yes—
563#103C22×D1114yes—
564#103C22×D1114yes—
565#102—114no—
566#102—114no—
567#102—114no—
568C22⋊C8—114no—
569C22⋊C8—114no—
570#97C22×D1114yes—
571C2×C11#331514yescomplemented
572C2×C11C2×#54611yescharacteristic
573C2×C11C2×#57511yescharacteristic
574C2×C11C2×#57811yescharacteristic
575D11—42no—
576D11—42no—
577D11—44no—
578C24—111no—
579C24—111no—
580C24—221no—
581#41—228no—
582#41—228no—
583#41—444no—
584#41—444no—
585#41—448no—
586#41—448no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—112no—
594C2×Q8—221no—
595C2×Q8—222no—
596C2×Q8—222no—
597C2×Q8C23×D1112yes—
598C2×Q8C23×D1112yes—
599C2×D4—114no—
600C2×D4—114no—
601C2×D4—112no—
602C2×D4—224no—
603C2×D4—224no—
604C2×D4—221no—
605C2×D4—222no—
606C2×D4—442no—
607C2×D4—444no—
608C2×D4—444no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—111no—
614C22×C4—111no—
615C22×C4—112no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—224no—
620C22×C4—224no—
621C22×C4—224no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—221no—
627C22×C4—221no—
628C22×C4—221no—
629C22×C4—224no—
630C22×C4—444no—
631C22×C4—444no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4D4×D1111yescharacteristic
635C22×C4D4×D1111yescharacteristic
636C22×C4C23×D1111yescharacteristic
637Q16—444no—
638Q16—444no—
639SD16—228no—
640M16—444no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—112no—
644C2×C8—112no—
645C2×C8—222no—
646C2×C8—222no—
647C2×C8—444no—
648C2×C8C23×D1112yes—
649C2×C8C23×D1112yes—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—114no—
657C4⋊C4—112no—
658C4⋊C4—112no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—221no—
665C4⋊C4—221no—
666C4⋊C4—224no—
667C4⋊C4C23×D1112yes—
668C4⋊C4C23×D1112yes—
669C22⋊C4—114no—
670C22⋊C4—114no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C42—224no—
678C42—224no—
679C42D4×D1112yes—
680C42C23×D1112yes—
681C11C2×#331511yescharacteristic, complemented, Sylow
682C23—112no—
683C23—112no—
684C23—222no—
685C23—222no—
686C23—222no—
687C23—222no—
688C23—222no—
689C23—222no—
690C23—222no—
691C23—224no—
692C23—442no—
693C23—442no—
694C23C2×D4×D1111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—222no—
702Q8—222no—
703Q8—442no—
704D4—114no—
705D4—222no—
706D4—224no—
707D4—444no—
708D4—448no—
709D4—448no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—112no—
721C2×C4—112no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—448no—
734C2×C4—448no—
735C2×C4—448no—
736C2×C4—448no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4C2×D4×D1112yes—
741C2×C4C2×D4×D1112yes—
742C2×C4C2×D4×D1111yescharacteristic
743C2×C4#41×D1112yes—
744C2×C4#6704212yes—
745C2×C4C24×D1111yescharacteristic
746C8—22no—
747C8—22no—
748C8—222no—
749C8—222no—
750C22—222no—
751C22—222no—
752C22—224no—
753C22—222no—
754C22—222no—
755C22—222no—
756C22—222no—
757C22—444no—
758C22—444no—
759C22—448no—
760C22—442no—
761C22—442no—
762C22#1062320712yes—
763C22#1062330812yes—
764C22#1062331012yes—
765C22C22×D4×D1111yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—222no—
773C4—222no—
774C4—442no—
775C4—442no—
776C4—442no—
777C4#1062320712yes—
778C4C2×#41×D1111yescharacteristic
779C4C2×#6704211yescharacteristic
780C2—442no—
781C2—442no—
782C2—444no—
783C2#1308071114yesdirect product factor
784C2C2×#1062320711yescharacteristic
785C2C2×#1062330811yescharacteristic
786C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#491C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
hypercenterC2×#491D11
hypocenterC11C2×#3315
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
1. C2×#10623225C2semidirect
3. #13080711C2direct (N × H)
4. C2×#10622422C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622679C2semidirect
7. C2×#10622429C2semidirect
8. C2×#10622426C2semidirect
9. C2×#10622703C2semidirect
10. C2×#10622423C2semidirect
11. C2×#10622423C2semidirect
12. C2×#10622323C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622416C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#491C2semidirect
31. #10623225C22semidirect
47. C11×#491C22semidirect
60. #10622703C22semidirect
61. #10622679C22semidirect
67. #10622429C22semidirect
68. #10622427C22semidirect
69. #10622426C22semidirect
70. #10622423C22semidirect
71. #10622423C22semidirect
72. #10622422C22semidirect
73. #10622417C22semidirect
74. #10622416C22semidirect
75. #10622323C22semidirect
76. #10622319C22semidirect
292. C2×#491D11semidirect
403. #491C2×D11semidirect
571. C2×C11#3315semidirect
681. C11C2×#3315semidirect
783. C2#13080711direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232252
C2×#106232572
#130807112
C2×#106224222
C2×#106224272
C2×#106226792
C2×#106224292
C2×#106224262
C2×#106227032
C2×#106224232
C2×#106223232
C2×#106223192
C2×#106224162
C2×#106224172
C2×C11×#4912
C2×#331511