Finite Group Databasebeta

← C2×#13080712 #15630427

Subgroups — C2×#13080712 #15630427

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×#10623072C211yesmaximal, characteristic, complemented
2#13080712C2116yesmaximal, direct product factor
3C2×#10622695C211yesmaximal, characteristic, complemented
4C2×#10622657C211yesmaximal, characteristic, complemented
5C2×#10622658C211yesmaximal, characteristic, complemented
6C2×#10622622C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622664C211yesmaximal, characteristic, complemented
9C2×#10622703C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622852C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622845C211yesmaximal, characteristic, complemented
15C2×#10622846C211yesmaximal, characteristic, complemented
16C2×C11×#547C211yesmaximal, characteristic
17C22×C11×#41C2211yescharacteristic
18C22×C11×#41C2211yescharacteristic
19C11×#547—24no—
20C11×#547C2218yes—
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C4⋊C4—21no—
30C22×#4326C2211yescharacteristic
31C22×#4326C2211yescharacteristic
32C2×#66988—21no—
33C22×#4324C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C2×#66977C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4318C2211yescharacteristic
39C23×C11⋊C8C2211yescharacteristic
40#10623072—24no—
41#10623072C2218yescomplemented
42C2×#66942—21no—
43C2×#66932—21no—
44C2×#66930—21no—
45C2×#66923C2211yescharacteristic
46C2×C4×Dic22C2211yescharacteristic
47#10622852C2218yescomplemented
48#10622852C2218yescomplemented
49#10622846C2218yescomplemented
50#10622845C2218yescomplemented
51C2×#66899C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54C2×#66899C2211yescharacteristic
55C2×#66899C2211yescharacteristic
56C2×#66899C2211yescharacteristic
57C2×#66896C2211yescharacteristic
58C2×#66896C2211yescharacteristic
59C2×#66896C2211yescharacteristic
60C2×C22⋊(C11⋊C8)C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic
62#10622703C2218yescomplemented
63#10622695C2218yescomplemented
64#10622665C2218yescomplemented
65#10622664C2218yescomplemented
66#10622658C2218yescomplemented
67#10622657C2218yescomplemented
68#10622631C2218yescomplemented
69#10622624C2218yescomplemented
70#10622622C2218yescomplemented
71C2×#66874C2211yescharacteristic
72C2×#66872C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C2×C11×#41—22no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—24no—
81C2×C11×#41—42no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C2×C11×#41C2314yes—
85C22×Q8×C11C2311yescharacteristic
86C22×Q8×C11C2311yescharacteristic
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11D411yescharacteristic
90C22×D4×C11C2311yescharacteristic
91C23×C4×C11—21no—
92C23×C4×C11—21no—
93C23×C4×C11—21no—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×Dic11—21no—
97C22×Dic22C2311yescharacteristic
98C11×C4⋊Q8—22no—
99C11×C4⋊Q8C2314yes—
100C11×#123—28no—
101C11×#123—28no—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8—22no—
104C11×C22⋊Q8C2314yes—
105C11×C22⋊Q8C2314yes—
106C11×#121—28no—
107C4×D4×C11—22no—
108C4×D4×C11D414yes—
109C4×D4×C11C2314yes—
110C4×D4×C11C2314yes—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—28no—
116C2×C11×C4⋊C4D411yescharacteristic
117C2×C11×C4⋊C4C2311yescharacteristic
118C2×C11×C22⋊C4—21no—
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D411yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127C2×#4326—42no—
128C2×#4326—42no—
129C2×#4326C2314yes—
130C2×#4326C2314yes—
131#66988—28no—
132C2×#4324—24no—
133C2×#4324C2314yes—
134#66979—22no—
135#66979C2314yes—
136C2×C4⋊Dic11—21no—
137C2×C4⋊Dic11—22no—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×C4⋊Dic11C2314yes—
142#66977—22no—
143#66977—22no—
144#66977C2314yes—
145#66977C2314yes—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×#4318—42no—
154C2×#4318C2314yes—
155C22×C11⋊C8—42no—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2314yes—
161#66942—28no—
162#66932—28no—
163#66930—28no—
164#66923—22no—
165#66923C2314yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170#66899C2314yes—
171#66899C2314yes—
172#66899C2314yes—
173#66899C2314yes—
174#66896C2314yes—
175#66896C2314yes—
176#66896C2314yes—
177C22⋊(C11⋊C8)C2314yes—
178C22⋊(C11⋊C8)C2314yes—
179#66874C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182#66871C2314yes—
183C4⋊(C11⋊C8)C2314yes—
184#66867C2314yes—
185C2×#3315—111nomaximal, Sylow
186C24×C11—21no—
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C11×#41—28no—
190C11×#41—28no—
191C11×#41—44no—
192C11×#41—44no—
193C11×#41—48no—
194C11×#41—48no—
195C2×Q8×C11—21no—
196C2×Q8×C11—21no—
197C2×Q8×C11—22no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11—22no—
201C2×Q8×C11C2412yes—
202C2×Q8×C11C2412yes—
203C2×D4×C11—24no—
204C2×D4×C11—24no—
205C2×D4×C11—21no—
206C2×D4×C11—22no—
207C2×D4×C11—42no—
208C2×D4×C11—44no—
209C2×D4×C11—44no—
210C2×D4×C11C2×D414yes—
211C2×D4×C11#4114yes—
212C2×D4×C11C2412yes—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—24no—
221C22×C4×C11—24no—
222C22×C4×C11—24no—
223C22×C4×C11—44no—
224C22×C4×C11—44no—
225C22×C4×C11—44no—
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2412yes—
233C22×C4×C11C2412yes—
234C22×C4×C11C2411yescharacteristic
235C22×Dic11—24no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—44no—
241C2×Dic22—21no—
242C2×Dic22—22no—
243C2×Dic22—22no—
244C2×Dic22C2412yes—
245C11×C4⋊C4—24no—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—24no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C2×D414yes—
251C11×C4⋊C4C2412yes—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4C2×D414yes—
256C11×C22⋊C4C2×D414yes—
257C42×C11C2×D412yes—
258C42×C11C2412yes—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262#4326—44no—
263#4326—44no—
264#4324—28no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—24no—
269C4⋊Dic11C2412yes—
270C4⋊Dic11C2412yes—
271C4⋊Dic11C2412yes—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277C4×Dic11—24no—
278C4×Dic11—24no—
279#4318—44no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—44no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287C2×C11⋊C8C2412yes—
288C2×C11⋊C8C2412yes—
289C2×#552—111no—
290C2×#547D1111yescharacteristic
291#3315—1116no—
292C2×#491—111no—
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×C11—22no—
306C23×C11—22no—
307C23×C11—24no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11C22×D412yes—
316C23×C11C22×D412yes—
317C23×C11C22×D411yescharacteristic
318Q8×C11—22no—
319Q8×C11—22no—
320Q8×C11—22no—
321Q8×C11—22no—
322Q8×C11—42no—
323Q8×C11—42no—
324D4×C11—24no—
325D4×C11—22no—
326D4×C11—44no—
327D4×C11—48no—
328D4×C11—48no—
329D4×C11C2×#4114yes—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—24no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—48no—
344C2×C4×C11—48no—
345C2×C4×C11—48no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11—42no—
349C2×C4×C11C22×D412yes—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×C4×C11C22×D412yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C2×#4112yes—
355C2×C4×C11H(5,𝔽2)12yes—
356C2×C4×C11C2511yescharacteristic
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—48no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366Dic22—22no—
367Dic22—22no—
368Dic22—42no—
369C11⋊C8—22no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C11⋊C8—22no—
373C22×#41C2×D1111yescharacteristic
374C22×#41C2×D1111yescharacteristic
375C22×Q16—111no—
376C22×Q16—111no—
377C22×SD16—111no—
378C22×M16—111no—
379C23×C8—111no—
380#552—118no—
381#552—224no—
382#547—24no—
383#547C2×D1118yes—
384C2×C4⋊Q8C2×D1111yescharacteristic
385C2×#126—221no—
386C2×#125—111no—
387C2×#125—221no—
388C2×#123—21no—
389C2×#123—21no—
390C2×#123—221no—
391C2×C22⋊Q8—111no—
392C2×C22⋊Q8—111no—
393C2×C22⋊Q8C2×D1111yescharacteristic
394C2×C22⋊Q8C2×D1111yescharacteristic
395C2×#121—21no—
396C2×C4×Q8—111no—
397C2×C4×D4C2×D1111yescharacteristic
398C2×C4×D4C2×D1111yescharacteristic
399C2×#117—111no—
400C2×#117—221no—
401C22×C4⋊C4—21no—
402C22×C4⋊C4—111no—
403#491—118no—
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×#103—111no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×C22⋊C8—111no—
431C2×C22⋊C8—111no—
432C2×#97—111no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—24no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—44no—
441C22×C11—44no—
442C22×C11—48no—
443C22×C11—42no—
444C22×C11—42no—
445C22×C11#54612yes—
446C22×C11#57512yes—
447C22×C11#57812yes—
448C22×C11C23×D411yescharacteristic
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—22no—
452C4×C11—22no—
453C4×C11—42no—
454C4×C11—42no—
455C4×C11—42no—
456C4×C11#54612yes—
457C4×C11C22×#4111yescharacteristic
458C4×C11C2×H(5,𝔽2)11yescharacteristic
459Dic11—42no—
460Dic11—42no—
461Dic11—42no—
462Dic11—42no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—24no—
466C2×#41—24no—
467C2×#41—42no—
468C2×#41—42no—
469C2×#41C22×D1114yes—
470C2×#41C22×D1114yes—
471C22×Q8—111no—
472C22×Q8C22×D1111yescharacteristic
473C22×Q8C22×D1111yescharacteristic
474C22×D4—21no—
475C22×D4—21no—
476C22×D4C22⋊D1111yescharacteristic
477C22×D4C22×D1111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—221no—
482C23×C4C22×D1111yescharacteristic
483C23×C4C22×D1111yescharacteristic
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—111no—
495C22×C8—111no—
496C22×C8—114no—
497C22×C8—442no—
498C4⋊Q8—22no—
499C4⋊Q8C22×D1114yes—
500#126—228no—
501#125—114no—
502#125—228no—
503#125—222no—
504#123—28no—
505#123—28no—
506#123—228no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—114no—
510C22⋊Q8—114no—
511C22⋊Q8—222no—
512C22⋊Q8—222no—
513C22⋊Q8C22×D1114yes—
514C22⋊Q8C22×D1114yes—
515#121—28no—
516C4×Q8—114no—
517C4×Q8—222no—
518C4×D4—22no—
519C4×D4C22⋊D1114yes—
520C4×D4C22×D1114yes—
521C4×D4C22×D1114yes—
522#117—114no—
523#117—222no—
524#117—228no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—28no—
530C2×C4⋊C4—111no—
531C2×C4⋊C4—111no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—111no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—222no—
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—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4C22⋊D1111yescharacteristic
550C2×C22⋊C4C22⋊D1111yescharacteristic
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#103—114no—
562#103—114no—
563#103—114no—
564#103—114no—
565#102—114no—
566#102—114no—
567#102—114no—
568C22⋊C8—114no—
569C22⋊C8—114no—
570#97—114no—
571C2×C11—42no—
572C2×C11—42no—
573C2×C11—44no—
574C2×C11#331514yescomplemented
575C2×C11C2×#54611yescharacteristic
576C2×C11C2×#57511yescharacteristic
577C2×C11C2×#57811yescharacteristic
578C24—21no—
579C24C2×C22⋊D1111yescharacteristic
580C24C2×C22⋊D1111yescharacteristic
581#41—28no—
582#41—28no—
583#41—44no—
584#41—44no—
585#41—48no—
586#41—48no—
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—24no—
600C2×D4—24no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—42no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4#434114yes—
607C2×D4C2×C22⋊D1114yes—
608C2×D4C23×D1112yes—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—224no—
623C22×C4—221no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4—444no—
628C22×C4C2×C22⋊D1112yes—
629C22×C4C2×C22⋊D1112yes—
630C22×C4C2×C22⋊D1111yescharacteristic
631C22×C4C2×C22⋊D1111yescharacteristic
632C22×C4C2×C22⋊D1111yescharacteristic
633C22×C4C2×C22⋊D1111yescharacteristic
634C22×C4C23×D1112yes—
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637Q16—444no—
638Q16—444no—
639SD16—228no—
640M16—444no—
641C2×C8—112no—
642C2×C8—112no—
643C2×C8—112no—
644C2×C8—112no—
645C2×C8—222no—
646C2×C8—222no—
647C2×C8—222no—
648C2×C8—222no—
649C2×C8—444no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—112no—
656C4⋊C4—112no—
657C4⋊C4—112no—
658C4⋊C4—221no—
659C4⋊C4—221no—
660C4⋊C4—224no—
661C4⋊C4—221no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4C2×C22⋊D1114yes—
668C4⋊C4C23×D1112yes—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4C2×C22⋊D1114yes—
676C22⋊C4C2×C22⋊D1114yes—
677C42—224no—
678C42—224no—
679C42C2×C22⋊D1112yes—
680C42C23×D1112yes—
681C11C2×#331511yescharacteristic, complemented, Sylow
682C23—22no—
683C23—22no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23C22×C22⋊D1112yes—
693C23C22×C22⋊D1112yes—
694C23C22×C22⋊D1111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—222no—
702Q8—222no—
703Q8—442no—
704D4—24no—
705D4—22no—
706D4—44no—
707D4—48no—
708D4—48no—
709D4C2×#434114yes—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—48no—
724C2×C4—48no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—448no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4C2×#434112yes—
739C2×C4#6703712yes—
740C2×C4C22×C22⋊D1112yes—
741C2×C4C22×C22⋊D1112yes—
742C2×C4C22×C22⋊D1112yes—
743C2×C4C22×C22⋊D1112yes—
744C2×C4C22×C22⋊D1111yescharacteristic
745C2×C4C24×D1111yescharacteristic
746C8—222no—
747C8—222no—
748C8—222no—
749C8—222no—
750C22—22no—
751C22—22no—
752C22—24no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—44no—
758C22—44no—
759C22—48no—
760C22—42no—
761C22—42no—
762C22#1062333712yes—
763C22#1062335312yes—
764C22#1062336912yes—
765C22C23×C22⋊D1111yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—442no—
774C4—442no—
775C4—442no—
776C4—442no—
777C4#1062333712yes—
778C4C22×#434111yescharacteristic
779C4C2×#6703711yescharacteristic
780C2—42no—
781C2—42no—
782C2—44no—
783C2#1308071214yesdirect product factor
784C2C2×#1062333711yescharacteristic
785C2C2×#1062335311yescharacteristic
786C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3315
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623072C2semidirect
2. #13080712C2direct (N × H)
3. C2×#10622695C2semidirect
4. C2×#10622657C2semidirect
5. C2×#10622658C2semidirect
6. C2×#10622622C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622664C2semidirect
9. C2×#10622703C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622852C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622845C2semidirect
15. C2×#10622846C2semidirect
41. #10623072C22semidirect
47. #10622852C22semidirect
48. #10622852C22semidirect
49. #10622846C22semidirect
50. #10622845C22semidirect
62. #10622703C22semidirect
63. #10622695C22semidirect
64. #10622665C22semidirect
65. #10622664C22semidirect
66. #10622658C22semidirect
67. #10622657C22semidirect
68. #10622631C22semidirect
69. #10622624C22semidirect
70. #10622622C22semidirect
574. C2×C11#3315semidirect
681. C11C2×#3315semidirect
783. C2#13080712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230722
#130807122
C2×#106226952
C2×#106226572
C2×#106226582
C2×#106226222
C2×#106226652
C2×#106226642
C2×#106227032
C2×#106228522
C2×#106226312
C2×#106226242
C2×#106228452
C2×#106228462
C2×C11×#5472
C2×#331511