Finite Group Databasebeta

← C2×#13080664 #15630376

Subgroups — C2×#13080664 #15630376

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623225C211yesmaximal, characteristic
2C2×Q8×D44C211yesmaximal, characteristic
3#13080664C2116yesmaximal, direct product factor
4C2×#10622682C211yesmaximal, characteristic, complemented
5C2×#10622501C211yesmaximal, characteristic, complemented
6C2×#10622475C211yesmaximal, characteristic, complemented
7C2×#10622481C211yesmaximal, characteristic, complemented
8C2×#10622500C211yesmaximal, characteristic, complemented
9C2×#10622462C211yesmaximal, characteristic, complemented
10C2×#10622421C211yesmaximal, characteristic, complemented
11C2×#10622421C211yesmaximal, characteristic, complemented
12C2×#10622643C211yesmaximal, characteristic, complemented
13C2×#10622449C211yesmaximal, characteristic
14C2×#10622415C211yesmaximal, characteristic, complemented
15C2×D11×#103C211yesmaximal, characteristic, complemented
16C2×C11×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×Dic44C2211yescharacteristic
23C22×Dic44C2211yescharacteristic
24C22×#4313C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26#10623225—24no—
27#10623225C2218yes—
28Q8×D44—24no—
29Q8×D44C2218yes—
30C2×#66951—21no—
31C2×#66950—21no—
32C2×#66950—21no—
33C2×#66950C2211yescharacteristic
34C2×#66950C2211yescharacteristic
35C2×#66950C2211yescharacteristic
36C2×#66950C2211yescharacteristic
37C2×#66947—21no—
38C2×#66945—21no—
39C2×#66945C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66943—21no—
42C2×C4×D44—21no—
43C2×C4×D44C2211yescharacteristic
44C2×#66922—21no—
45C2×#66922C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47C11×#479C2218yescomplemented
48C2×C11×#107C2211yescharacteristic
49C2×C11×#106C2211yescharacteristic
50C2×C11×C4⋊C8C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×(C2×D11)⋊C8C2211yescharacteristic
56C2×#66880C2211yescharacteristic
57C2×#66880C2211yescharacteristic
58#10622682C2218yescomplemented
59#10622643C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622501C2218yescomplemented
68#10622500C2218yescomplemented
69#10622481C2218yescomplemented
70#10622475C2218yescomplemented
71#10622462C2218yescomplemented
72#10622449C2218yes—
73#10622421C2218yescomplemented
74#10622421C2218yescomplemented
75#10622415C2218yescomplemented
76D11×#103C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C2×Q8×D11—22no—
79C2×Q8×D11—22no—
80C2×Q8×D11—24no—
81C2×Q8×D11—24no—
82C2×Q8×D11—42no—
83C2×Q8×D11—42no—
84C2×Q8×D11C2314yes—
85C2×Q8×D11C2314yes—
86C22×D44D411yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C22×Dic22—21no—
93C22×Dic22—21no—
94C22×Dic22C2311yescharacteristic
95C22×Dic22C2311yescharacteristic
96C22×Dic22C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C11×#125—22no—
100C11×#125C2314yes—
101C4×Q8×C11—22no—
102C4×Q8×C11C2314yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C2×#4326—24no—
112C2×#4326C2314yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4D411yescharacteristic
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11D411yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11—21no—
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C2×Dic44—42no—
135C2×Dic44—42no—
136C2×Dic44C2314yes—
137C2×Dic44C2314yes—
138C2×#4313—42no—
139C2×#4313C2314yes—
140C2×C8×D11—42no—
141C2×C8×D11C2314yes—
142#66951—28no—
143#66950—22no—
144#66950—22no—
145#66950—22no—
146#66950—22no—
147#66950—28no—
148#66950—28no—
149#66950C2314yes—
150#66950C2314yes—
151#66950C2314yes—
152#66950C2314yes—
153#66947—28no—
154#66945—22no—
155#66945—28no—
156#66945C2314yes—
157C4⋊C4×D11—22no—
158C4⋊C4×D11C2314yes—
159#66943—28no—
160C4×D44—28no—
161C4×D44D414yes—
162C4×D44C2314yes—
163#66922—22no—
164#66922—28no—
165#66922C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168C11×#107C2314yes—
169C11×#106C2314yes—
170C11×C4⋊C8C2314yes—
171C11×#103C2314yes—
172C11×#103C2314yes—
173#66899C2314yes—
174(C2×D11)⋊C8C2314yes—
175(C2×D11)⋊C8C2314yes—
176#66880C2314yes—
177#66880C2314yes—
178#66874C2314yes—
179#66874C2314yes—
180#66874C2314yes—
181#66874C2314yes—
182#66874C2314yes—
183#66872C2314yes—
184#66867C2314yes—
185C2×#3312—111nomaximal, Sylow
186C23×D11C2×D411yescharacteristic
187C23×D11C2×D411yescharacteristic
188C2×Q8×C11—21no—
189C2×Q8×C11—22no—
190C2×Q8×C11#4114yes—
191C2×Q8×C11C2412yes—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205Q8×D11—28no—
206Q8×D11—28no—
207Q8×D11—44no—
208Q8×D11—44no—
209Q8×D11—48no—
210Q8×D11—48no—
211C2×D44—24no—
212C2×D44C2×D414yes—
213C2×C4×D11—24no—
214C2×C4×D11—24no—
215C2×C4×D11—24no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C2×C4×D11C2×D412yes—
224C2×C4×D11C2×D412yes—
225C2×C4×D11C2412yes—
226C2×C4×D11C2412yes—
227C2×Dic22—24no—
228C2×Dic22—24no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22—22no—
235C2×Dic22—22no—
236C2×Dic22—22no—
237C2×Dic22—22no—
238C2×Dic22—44no—
239C2×Dic22—44no—
240C2×Dic22C2412yes—
241C2×Dic22C2412yes—
242C2×Dic22C2412yes—
243C2×C8×C11—22no—
244C2×C8×C11—22no—
245C2×C8×C11C2412yes—
246C2×C8×C11C2412yes—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4C2412yes—
254C11×C4⋊C4C2412yes—
255C11×C4⋊C4C2412yes—
256C42×C11—24no—
257C42×C11C2×D412yes—
258C42×C11C2412yes—
259#4326—28no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4C2×D414yes—
266(C2×D11)⋊C4C2×D414yes—
267C4⋊Dic11—24no—
268C4⋊Dic11—24no—
269C4⋊Dic11—24no—
270C4⋊Dic11—24no—
271C4⋊Dic11—21no—
272C4⋊Dic11—24no—
273C4⋊Dic11—24no—
274C4⋊Dic11C2×D414yes—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8C2412yes—
283C2×C11⋊C8C2412yes—
284Dic44—44no—
285Dic44—44no—
286#4313—44no—
287C8×D11—44no—
288C2×#552—111no—
289C2×D4×Q8—111no—
290#3312—1116no—
291C2×#491—111no—
292C2×#485—111no—
293C2×#483—111no—
294C2×#479D1111yescharacteristic, complemented
295C2×#470—111no—
296C2×#467—111no—
297C2×#462—111no—
298C2×#451—111no—
299C2×#451—111no—
300C2×#441—111no—
301C2×#435—111no—
302C2×#419—111no—
303C22×#103—111no—
304C23×C11C22×D411yescharacteristic
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11#13714yes—
311C22×D11C22×D412yes—
312C22×D11C22×D412yes—
313Q8×C11—24no—
314Q8×C11—22no—
315Q8×C11C2×#4114yes—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4112yes—
330C2×C4×C11H(5,𝔽2)12yes—
331C2×C4×C11C2511yescharacteristic
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344D44—28no—
345C4×D11—24no—
346C4×D11—24no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—48no—
352C4×D11—48no—
353C4×D11—48no—
354Dic22—22no—
355Dic22—22no—
356Dic22—22no—
357Dic22—22no—
358Dic22—22no—
359Dic22—22no—
360Dic22—48no—
361Dic22—48no—
362Dic22—42no—
363Dic22—42no—
364Dic22—42no—
365C8×C11—22no—
366C8×C11—22no—
367C11⋊C8—22no—
368C11⋊C8—22no—
369C23×Q8—111no—
370C23×Q8—111no—
371C22×Q16—111no—
372C22×Q16—111no—
373C22×Q16—111no—
374C22×M16—111no—
375C23×C8—111no—
376#552—118no—
377#552—224no—
378D4×Q8—118no—
379D4×Q8—224no—
380C2×C4⋊Q8—111no—
381C2×C4⋊Q8—221no—
382C2×#126—221no—
383C2×#125—221no—
384C2×#125C2×D1111yescharacteristic
385C2×#123—221no—
386C2×C22⋊Q8—111no—
387C2×C22⋊Q8—111no—
388C2×C22⋊Q8—111no—
389C2×C22⋊Q8—111no—
390C2×C22⋊Q8—221no—
391C2×C22⋊Q8—221no—
392C2×C4×Q8—111no—
393C2×C4×Q8C2×D1111yescharacteristic
394C2×C4×D4—111no—
395C2×C4×D4—221no—
396C2×#117—111no—
397C2×#117—221no—
398C22×C4⋊C4—111no—
399#491—118no—
400#485—118no—
401#483—118no—
402#479C2×D1118yescomplemented
403#470—118no—
404#467—118no—
405#462—118no—
406#451—118no—
407#451—118no—
408#441—118no—
409#435—118no—
410C2×#107C2×D1111yescharacteristic
411C2×#106—111no—
412C2×#106C2×D1111yescharacteristic
413C2×C4⋊C8C2×D1111yescharacteristic
414#419—118no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—118no—
424C2×#103C2×D1111yescharacteristic
425C2×#103C2×D1111yescharacteristic
426C2×C22⋊C8—111no—
427C2×C22⋊C8—111no—
428C2×#97—111no—
429C22×C11#54612yes—
430C22×C11C2×#13712yes—
431C22×C11#57812yes—
432C22×C11C23×D411yescharacteristic
433C2×D11—22no—
434C2×D11—28no—
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—44no—
440C2×D11C2×#13714yes—
441C4×C11—24no—
442C4×C11—22no—
443C4×C11—22no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11#54612yes—
448C4×C11C22×#4111yescharacteristic
449C4×C11C2×H(5,𝔽2)11yescharacteristic
450Dic11—22no—
451Dic11—22no—
452Dic11—42no—
453Dic11—42no—
454Dic11—42no—
455Dic11—42no—
456C22×Q8—114no—
457C22×Q8—114no—
458C22×Q8—111no—
459C22×Q8—111no—
460C22×Q8—111no—
461C22×Q8—221no—
462C22×Q8—221no—
463C22×Q8—222no—
464C22×Q8—222no—
465C22×Q8—224no—
466C22×Q8—224no—
467C22×Q8—442no—
468C22×Q8—442no—
469C22×Q8C22×D1111yescharacteristic
470C22×D4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—221no—
474C23×C4—221no—
475C23×C4—221no—
476C2×Q16—114no—
477C2×Q16—114no—
478C2×Q16—114no—
479C2×Q16—224no—
480C2×Q16—442no—
481C2×Q16—442no—
482C2×M16—114no—
483C2×M16—442no—
484C22×C8—111no—
485C22×C8—111no—
486C22×C8—114no—
487C22×C8—442no—
488C22×C8C22×D1111yescharacteristic
489C22×C8C22×D1111yescharacteristic
490C4⋊Q8—114no—
491C4⋊Q8—228no—
492C4⋊Q8—222no—
493#126—228no—
494#125—22no—
495#125—228no—
496#125C22×D1114yes—
497#123—228no—
498C22⋊Q8—114no—
499C22⋊Q8—114no—
500C22⋊Q8—114no—
501C22⋊Q8—114no—
502C22⋊Q8—228no—
503C22⋊Q8—228no—
504C22⋊Q8—222no—
505C22⋊Q8—222no—
506C22⋊Q8—222no—
507C22⋊Q8—222no—
508C4×Q8—22no—
509C4×Q8—114no—
510C4×Q8—222no—
511C4×Q8C22×D1114yes—
512C4×D4—114no—
513C4×D4—114no—
514C4×D4—228no—
515#117—114no—
516#117—228no—
517#117—222no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—222no—
525C2×C4⋊C4—221no—
526C2×C4⋊C4—221no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—221no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C22⋊C4—111no—
537C2×C22⋊C4—111no—
538C2×C22⋊C4—221no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C42—21no—
544C2×C42—221no—
545C2×C42—221no—
546C2×C42C22×D1111yescharacteristic
547#107C22×D1114yes—
548#106—114no—
549#106C22×D1114yes—
550C4⋊C8C22×D1114yes—
551#103—114no—
552#103—114no—
553#103—114no—
554#103—114no—
555#103—114no—
556#103—114no—
557#103—114no—
558#103—114no—
559#103C22×D1114yes—
560#103C22×D1114yes—
561C22⋊C8—114no—
562C22⋊C8—114no—
563#97—114no—
564C2×C11#331214yescomplemented
565C2×C11C2×#54611yescharacteristic
566C2×C11C22×#13711yescharacteristic
567C2×C11C2×#57811yescharacteristic
568D11—24no—
569D11—42no—
570C24—111no—
571C24—111no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—112no—
575C2×Q8—112no—
576C2×Q8—112no—
577C2×Q8—224no—
578C2×Q8—224no—
579C2×Q8—221no—
580C2×Q8—221no—
581C2×Q8—221no—
582C2×Q8—228no—
583C2×Q8—228no—
584C2×Q8—222no—
585C2×Q8—222no—
586C2×Q8—222no—
587C2×Q8—222no—
588C2×Q8—222no—
589C2×Q8—222no—
590C2×Q8—444no—
591C2×Q8—444no—
592C2×Q8—444no—
593C2×Q8—444no—
594C2×Q8—448no—
595C2×Q8—448no—
596C2×Q8#434314yes—
597C2×Q8C23×D1112yes—
598C2×D4—114no—
599C2×D4—224no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—112no—
607C22×C4—112no—
608C22×C4—112no—
609C22×C4—112no—
610C22×C4—224no—
611C22×C4—224no—
612C22×C4—224no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—444no—
622C22×C4—444no—
623C22×C4—444no—
624C22×C4D4×D1111yescharacteristic
625C22×C4D4×D1111yescharacteristic
626C22×C4C23×D1111yescharacteristic
627Q16—228no—
628Q16—444no—
629Q16—444no—
630M16—444no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—112no—
634C2×C8—112no—
635C2×C8—222no—
636C2×C8—222no—
637C2×C8—444no—
638C2×C8C23×D1112yes—
639C2×C8C23×D1112yes—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—114no—
647C4⋊C4—112no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4—224no—
653C4⋊C4—221no—
654C4⋊C4—224no—
655C4⋊C4—224no—
656C4⋊C4—224no—
657C4⋊C4C23×D1112yes—
658C4⋊C4C23×D1112yes—
659C4⋊C4C23×D1112yes—
660C22⋊C4—114no—
661C22⋊C4—114no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C22⋊C4—224no—
666C22⋊C4—224no—
667C42—24no—
668C42—224no—
669C42—224no—
670C42D4×D1112yes—
671C42C23×D1112yes—
672C11C2×#331211yescharacteristic, complemented, Sylow
673C23—114no—
674C23—112no—
675C23—112no—
676C23—222no—
677C23—222no—
678C23—222no—
679C23—222no—
680C23—222no—
681C23C2×D4×D1111yescharacteristic
682Q8—24no—
683Q8—22no—
684Q8—222no—
685Q8—222no—
686Q8—222no—
687Q8—222no—
688Q8—222no—
689Q8—222no—
690Q8—448no—
691Q8—448no—
692Q8—442no—
693Q8—442no—
694Q8—442no—
695Q8C2×#434314yes—
696D4—228no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—112no—
708C2×C4—112no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—448no—
722C2×C4—448no—
723C2×C4—448no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4C2×D4×D1112yes—
729C2×C4C2×D4×D1112yes—
730C2×C4C2×D4×D1111yescharacteristic
731C2×C4C2×#434312yes—
732C2×C4#6704212yes—
733C2×C4C24×D1111yescharacteristic
734C8—22no—
735C8—22no—
736C8—222no—
737C8—222no—
738C22—114no—
739C22—228no—
740C22—222no—
741C22—222no—
742C22—222no—
743C22—222no—
744C22—222no—
745C22—444no—
746C22#1062316112yes—
747C22#1062330212yes—
748C22D11×#13712yes—
749C22C22×D4×D1111yescharacteristic
750C4—24no—
751C4—22no—
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—222no—
757C4—222no—
758C4—442no—
759C4—442no—
760C4—442no—
761C4—442no—
762C4#1062316112yes—
763C4C22×#434311yescharacteristic
764C4C2×#6704211yescharacteristic
765C2—224no—
766C2—442no—
767C2#1308066414yesdirect product factor
768C2C2×#1062316111yescharacteristic
769C2C2×D11×#13711yescharacteristic
770C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#479D11
hypocenterC11C2×#3312
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #13080664C2direct (N × H)
4. C2×#10622682C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622475C2semidirect
7. C2×#10622481C2semidirect
8. C2×#10622500C2semidirect
9. C2×#10622462C2semidirect
10. C2×#10622421C2semidirect
11. C2×#10622421C2semidirect
12. C2×#10622643C2semidirect
14. C2×#10622415C2semidirect
15. C2×D11×#103C2semidirect
16. C2×C11×#479C2semidirect
47. C11×#479C22semidirect
58. #10622682C22semidirect
59. #10622643C22semidirect
67. #10622501C22semidirect
68. #10622500C22semidirect
69. #10622481C22semidirect
70. #10622475C22semidirect
71. #10622462C22semidirect
73. #10622421C22semidirect
74. #10622421C22semidirect
75. #10622415C22semidirect
76. D11×#103C22semidirect
294. C2×#479D11semidirect
402. #479C2×D11semidirect
564. C2×C11#3312semidirect
672. C11C2×#3312semidirect
767. C2#13080664direct (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×Q8×D442
#130806642
C2×#106226822
C2×#106225012
C2×#106224752
C2×#106224812
C2×#106225002
C2×#106224622
C2×#106224212
C2×#106226432
C2×#106224492
C2×#106224152
C2×D11×#1032
C2×C11×#4792
C2×#331211