Finite Group Databasebeta

← C2×#13080673 #15630385

Subgroups — C2×#13080673 #15630385

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×#10623173C211yesmaximal, characteristic
2C2×#10623163C211yesmaximal, characteristic
3#13080673C2116yesmaximal, direct product factor
4C2×#10622410C211yesmaximal, characteristic, complemented
5C2×#10622501C211yesmaximal, characteristic, complemented
6C2×#10622656C211yesmaximal, characteristic, complemented
7C2×#10622490C211yesmaximal, characteristic, complemented
8C2×#10622429C211yesmaximal, characteristic, complemented
9C2×#10622795C211yesmaximal, characteristic, complemented
10C2×#10622663C211yesmaximal, characteristic, complemented
11C2×#10622799C211yesmaximal, characteristic, complemented
12C2×#10622402C211yesmaximal, characteristic, complemented
13C2×#10622724C211yesmaximal, characteristic
14C2×#10622415C211yesmaximal, characteristic, complemented
15C22×#66880C211yesmaximal, characteristic, complemented
16C2×C11×#467C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×Q16C2211yescharacteristic
20C23×C8×C11C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×Q8×Dic11C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C22×#4326C2211yescharacteristic
28C2×C4×C22⋊D11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×#4313C2211yescharacteristic
31#10623173—24no—
32#10623173C2218yes—
33#10623163—24no—
34#10623163C2218yes—
35C2×#66951—21no—
36C2×#66950C2211yescharacteristic
37C2×#66949—21no—
38C2×#66945C2211yescharacteristic
39C2×#66943—21no—
40C2×#66943C2211yescharacteristic
41C2×#66941—21no—
42C2×#66940C2211yescharacteristic
43C2×#66939—21no—
44C2×(C22⋊D11)⋊C4—21no—
45C2×#66931—21no—
46C2×#66930—21no—
47C11×#467C2218yescomplemented
48C2×C11×#107C2211yescharacteristic
49C2×C11×#103C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×C22⋊(C11⋊C8)C2211yescharacteristic
54#10622799C2218yescomplemented
55#10622795C2218yescomplemented
56#10622724C2218yes—
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66880C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×#66880C2211yescharacteristic
61C2×#66880C2211yescharacteristic
62C2×#66880C2218yescomplemented
63C2×#66879C2211yescharacteristic
64C2×Dic11⋊C8C2211yescharacteristic
65#10622663C2218yescomplemented
66#10622656C2218yescomplemented
67C2×#66874C2211yescharacteristic
68C2×#66874C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71#10622501C2218yescomplemented
72#10622490C2218yescomplemented
73#10622429C2218yescomplemented
74#10622415C2218yescomplemented
75#10622410C2218yescomplemented
76#10622402C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11D411yescharacteristic
81C23×Dic11—21no—
82C23×Dic11—21no—
83C2×Q8×D11—22no—
84C2×Q8×D11—24no—
85C2×Q8×D11—42no—
86C2×Q8×D11C2314yes—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×Dic22—24no—
90C22×Dic22—21no—
91C22×Dic22—22no—
92C22×Dic22—21no—
93C22×Dic22—42no—
94C22×Dic22C2311yescharacteristic
95C22×Dic22C2314yes—
96C22×Dic22C2311yescharacteristic
97C2×C11×Q16—42no—
98C2×C11×Q16C2314yes—
99C22×C8×C11—42no—
100C22×C8×C11C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2314yes—
103C11×C22⋊Q8—22no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8C2314yes—
106C11×C22⋊Q8C2314yes—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C22⋊Dic11D411yescharacteristic
114#66999—22no—
115#66999C2314yes—
116Q8×Dic11—22no—
117Q8×Dic11C2314yes—
118#66997—22no—
119#66997C2314yes—
120C2×#4326—24no—
121C2×#4326—42no—
122C2×#4326C2314yes—
123C2×#4326C2314yes—
124C4×C22⋊D11D414yes—
125C4×C22⋊D11C2314yes—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4D411yescharacteristic
130C2×C4⋊Dic11—21no—
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11—21no—
134C2×C4⋊Dic11—21no—
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2314yes—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4D411yescharacteristic
144C2×C4×Dic11—21no—
145C2×C4×Dic11—21no—
146C2×C4×Dic11—21no—
147C2×C4×Dic11C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C2×#4313—42no—
151C2×#4313C2314yes—
152#66951—28no—
153#66950—22no—
154#66950C2314yes—
155#66949—28no—
156#66945—22no—
157#66945C2314yes—
158#66943—28no—
159#66943—22no—
160#66943C2314yes—
161#66941—28no—
162#66940—22no—
163#66940C2314yes—
164#66939—28no—
165(C22⋊D11)⋊C4—28no—
166#66931—28no—
167#66930—28no—
168C11×#107C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171#66899C2314yes—
172#66899C2314yes—
173C22⋊(C11⋊C8)C2314yes—
174(C2×D11)⋊C8C2314yes—
175#66880C2314yes—
176#66880C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179#66879C2314yes—
180Dic11⋊C8C2314yes—
181#66874C2314yes—
182#66874C2314yes—
183#66872C2314yes—
184#66872C2314yes—
185C2×#3312—111nomaximal, Sylow
186C24×C11C2×D411yescharacteristic
187C23×D11C2×D411yescharacteristic
188C2×Q8×C11—21no—
189C2×Q8×C11—21no—
190C2×Q8×C11—22no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11—22no—
194C2×Q8×C11C2412yes—
195C2×Q8×C11C2412yes—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2411yescharacteristic
206C2×C22⋊D11—24no—
207C2×C22⋊D11C2×D414yes—
208C22×Dic11—21no—
209C22×Dic11—24no—
210C22×Dic11—24no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C22×Dic11C2×D411yescharacteristic
219Q8×D11—28no—
220Q8×D11—44no—
221Q8×D11—48no—
222C2×C4×D11—24no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—44no—
226C2×C4×D11C2×D412yes—
227C2×C4×D11C2412yes—
228C2×Dic22—28no—
229C2×Dic22—24no—
230C2×Dic22—21no—
231C2×Dic22—24no—
232C2×Dic22—21no—
233C2×Dic22—22no—
234C2×Dic22—22no—
235C2×Dic22—22no—
236C2×Dic22—44no—
237C2×Dic22—48no—
238C2×Dic22—44no—
239C2×Dic22—44no—
240C2×Dic22#4114yes—
241C2×Dic22C2412yes—
242C2×Dic22C2412yes—
243C11×Q16—44no—
244C2×C8×C11—22no—
245C2×C8×C11—22no—
246C2×C8×C11—44no—
247C2×C8×C11C2412yes—
248C2×C8×C11C2412yes—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4C2412yes—
254C11×C4⋊C4C2412yes—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C22⋊Dic11C2×D414yes—
258#4326—28no—
259#4326—44no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4C2×D414yes—
264C4⋊Dic11—24no—
265C4⋊Dic11—24no—
266C4⋊Dic11—24no—
267C4⋊Dic11—24no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11C2412yes—
271C4⋊Dic11C2412yes—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4C2×D414yes—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C4×Dic11—24no—
281C4×Dic11C2×D412yes—
282C4×Dic11C2412yes—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287#4313—44no—
288C2×#552—111no—
289C2×D4×Q8—111no—
290#3312—1116no—
291C2×#491—111no—
292C2×#485—111no—
293C2×#483—111no—
294C2×#479—111no—
295C2×#470—111no—
296C2×#467D1111yescharacteristic, complemented
297C2×#462—111no—
298C2×#451—111no—
299C2×#451—111no—
300C2×#441—111no—
301C2×#435—111no—
302C2×#419—111no—
303C22×#103—111no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11#13714yes—
307C23×C11C22×D412yes—
308C23×C11C22×D411yescharacteristic
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11C22×D412yes—
313Q8×C11—22no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—22no—
317Q8×C11—42no—
318Q8×C11—42no—
319C2×C4×C11—22no—
320C2×C4×C11—24no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11C22×D412yes—
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4112yes—
334C2×C4×C11H(5,𝔽2)12yes—
335C2×C4×C11C2511yescharacteristic
336C22⋊D11—28no—
337C2×Dic11—24no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—48no—
346C2×Dic11—42no—
347C2×Dic11—48no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11C22×D412yes—
351C2×Dic11C22×D412yes—
352C2×Dic11C22×D412yes—
353C4×D11—24no—
354C4×D11—22no—
355C4×D11—22no—
356C4×D11—48no—
357Dic22—24no—
358Dic22—22no—
359Dic22—22no—
360Dic22—22no—
361Dic22—48no—
362Dic22—48no—
363Dic22—42no—
364Dic22C2×#4114yes—
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×Q16C2×D1111yescharacteristic
374C22×M16—111no—
375C23×C8C2×D1111yescharacteristic
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—111no—
384C2×#125—221no—
385C2×#123—221no—
386C2×C22⋊Q8—111no—
387C2×C22⋊Q8—111no—
388C2×C22⋊Q8—221no—
389C2×C22⋊Q8—221no—
390C2×C22⋊Q8C2×D1111yescharacteristic
391C2×C22⋊Q8C2×D1111yescharacteristic
392C2×C4×Q8—111no—
393C2×C4×Q8—111no—
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#479—118no—
403#470—118no—
404#467C2×D1118yescomplemented
405#462—118no—
406#451—118no—
407#451—118no—
408#441—118no—
409#435—118no—
410C2×#107C2×D1111yescharacteristic
411C2×#106—111no—
412C2×#106—111no—
413C2×C4⋊C8—111no—
414#419—118no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#103—111no—
421C2×#103—118no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103C2×D1111yescharacteristic
425C2×#103C2×D1111yescharacteristic
426C2×C22⋊C8—111no—
427C2×C22⋊C8—111no—
428C2×#97—111no—
429C22×C11—22no—
430C22×C11—28no—
431C22×C11—22no—
432C22×C11#54612yes—
433C22×C11C2×#13714yes—
434C22×C11C2×#13712yes—
435C22×C11#57812yes—
436C22×C11C23×D411yescharacteristic
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—44no—
441C4×C11—22no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11#54612yes—
447C4×C11C22×#4111yescharacteristic
448C4×C11C2×H(5,𝔽2)11yescharacteristic
449Dic11—24no—
450Dic11—22no—
451Dic11—22no—
452Dic11—22no—
453Dic11—42no—
454Dic11—42no—
455Dic11—42no—
456C22×Q8—114no—
457C22×Q8—111no—
458C22×Q8—111no—
459C22×Q8—114no—
460C22×Q8—221no—
461C22×Q8—224no—
462C22×Q8—222no—
463C22×Q8—221no—
464C22×Q8—222no—
465C22×Q8—224no—
466C22×Q8—442no—
467C22×Q8—442no—
468C22×Q8C22×D1111yescharacteristic
469C22×Q8C22×D1111yescharacteristic
470C22×D4—111no—
471C23×C4—111no—
472C23×C4—221no—
473C23×C4—221no—
474C23×C4—221no—
475C23×C4C22×D1111yescharacteristic
476C2×Q16—42no—
477C2×Q16—114no—
478C2×Q16—114no—
479C2×Q16—224no—
480C2×Q16—442no—
481C2×Q16C22×D1114yes—
482C2×M16—114no—
483C2×M16—442no—
484C22×C8—42no—
485C22×C8—111no—
486C22×C8—111no—
487C22×C8C22×D1111yescharacteristic
488C22×C8C22×D1111yescharacteristic
489C22×C8C22×D1114yes—
490C4⋊Q8—114no—
491C4⋊Q8—222no—
492C4⋊Q8—228no—
493#126—228no—
494#125—114no—
495#125—222no—
496#125—228no—
497#123—228no—
498C22⋊Q8—22no—
499C22⋊Q8—22no—
500C22⋊Q8—114no—
501C22⋊Q8—114no—
502C22⋊Q8—228no—
503C22⋊Q8—228no—
504C22⋊Q8—222no—
505C22⋊Q8—222no—
506C22⋊Q8C22×D1114yes—
507C22⋊Q8C22×D1114yes—
508C4×Q8—114no—
509C4×Q8—114no—
510C4×Q8—222no—
511C4×Q8—222no—
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—111no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—221no—
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⋊C4—222no—
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—111no—
539C2×C22⋊C4—111no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C42—111no—
544C2×C42—221no—
545C2×C42—221no—
546C2×C42—221no—
547#107C22×D1114yes—
548#106—114no—
549#106—114no—
550C4⋊C8—114no—
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—24no—
565C2×C11#331214yescomplemented
566C2×C11C2×#54611yescharacteristic
567C2×C11C22×#13711yescharacteristic
568C2×C11C2×#57811yescharacteristic
569D11—42no—
570C24—111no—
571C24D4×D1111yescharacteristic
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—114no—
579C2×Q8—112no—
580C2×Q8—112no—
581C2×Q8—224no—
582C2×Q8—228no—
583C2×Q8—221no—
584C2×Q8—224no—
585C2×Q8—221no—
586C2×Q8—222no—
587C2×Q8—228no—
588C2×Q8—222no—
589C2×Q8—222no—
590C2×Q8—444no—
591C2×Q8—444no—
592C2×Q8—448no—
593C2×Q8—444no—
594C2×Q8—444no—
595C2×Q8—448no—
596C2×Q8C23×D1112yes—
597C2×Q8C23×D1112yes—
598C2×D4—114no—
599C2×D4—224no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—111no—
609C22×C4—112no—
610C22×C4—112no—
611C22×C4—224no—
612C22×C4—221no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—224no—
616C22×C4—224no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—221no—
620C22×C4—444no—
621C22×C4—444no—
622C22×C4—444no—
623C22×C4D4×D1112yes—
624C22×C4D4×D1111yescharacteristic
625C22×C4C23×D1112yes—
626C22×C4C23×D1111yescharacteristic
627Q16—44no—
628Q16—228no—
629Q16—444no—
630M16—444no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—44no—
634C2×C8—112no—
635C2×C8—112no—
636C2×C8—222no—
637C2×C8—222no—
638C2×C8C23×D1112yes—
639C2×C8C23×D1112yes—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—114no—
645C4⋊C4—112no—
646C4⋊C4—112no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—224no—
652C4⋊C4—224no—
653C4⋊C4—224no—
654C4⋊C4—224no—
655C4⋊C4—221no—
656C4⋊C4—221no—
657C4⋊C4—224no—
658C4⋊C4C23×D1112yes—
659C4⋊C4C23×D1112yes—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—114no—
663C22⋊C4—114no—
664C22⋊C4—224no—
665C22⋊C4—224no—
666C22⋊C4—224no—
667C42—112no—
668C42—112no—
669C42—224no—
670C42—224no—
671C42—224no—
672C11C2×#331211yescharacteristic, complemented, Sylow
673C23—22no—
674C23—22no—
675C23—112no—
676C23—222no—
677C23—222no—
678C23—222no—
679C23#6697114yes—
680C23C2×D4×D1112yes—
681C23C2×D4×D1111yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—42no—
687Q8—42no—
688Q8—114no—
689Q8—224no—
690Q8—222no—
691Q8—222no—
692Q8—222no—
693Q8—448no—
694Q8—448no—
695Q8—442no—
696D4—228no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—112no—
710C2×C4—112no—
711C2×C4—112no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—224no—
716C2×C4—222no—
717C2×C4—224no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—222no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—448no—
724C2×C4—448no—
725C2×C4—448no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4C2×D4×D1112yes—
730C2×C4C2×D4×D1111yescharacteristic
731C2×C4#6703712yes—
732C2×C4#41×D1112yes—
733C2×C4C24×D1111yescharacteristic
734C8—22no—
735C8—22no—
736C8—222no—
737C8—222no—
738C22—28no—
739C22—22no—
740C22—22no—
741C22—222no—
742C22—222no—
743C22—222no—
744C22—444no—
745C22#1062314112yes—
746C22C2×#6697114yes—
747C22C2×#6697112yes—
748C22#1062330212yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—222no—
756C4—224no—
757C4—222no—
758C4—222no—
759C4—442no—
760C4—442no—
761C4—442no—
762C4#1062314112yes—
763C4C2×#6703711yescharacteristic
764C4C2×#41×D1111yescharacteristic
765C2—24no—
766C2—442no—
767C2#1308067314yesdirect product factor
768C2C2×#1062314111yescharacteristic
769C2C22×#6697111yescharacteristic
770C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenterC2×#467D11
hypocenterC11C2×#3312
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
3. #13080673C2direct (N × H)
4. C2×#10622410C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622656C2semidirect
7. C2×#10622490C2semidirect
8. C2×#10622429C2semidirect
9. C2×#10622795C2semidirect
10. C2×#10622663C2semidirect
11. C2×#10622799C2semidirect
12. C2×#10622402C2semidirect
14. C2×#10622415C2semidirect
15. C22×#66880C2semidirect
16. C2×C11×#467C2semidirect
47. C11×#467C22semidirect
54. #10622799C22semidirect
55. #10622795C22semidirect
62. C2×#66880C22semidirect
65. #10622663C22semidirect
66. #10622656C22semidirect
71. #10622501C22semidirect
72. #10622490C22semidirect
73. #10622429C22semidirect
74. #10622415C22semidirect
75. #10622410C22semidirect
76. #10622402C22semidirect
296. C2×#467D11semidirect
404. #467C2×D11semidirect
565. C2×C11#3312semidirect
672. C11C2×#3312semidirect
767. C2#13080673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231732
C2×#106231632
#130806732
C2×#106224102
C2×#106225012
C2×#106226562
C2×#106224902
C2×#106224292
C2×#106227952
C2×#106226632
C2×#106227992
C2×#106224022
C2×#106227242
C2×#106224152
C22×#668802
C2×C11×#4672
C2×#331211