Finite Group Databasebeta

← C2×#13079948 #15626573

Subgroups — C2×#13079948 #15626573

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623153C211yesmaximal, characteristic, complemented
2C2×#10623155C211yesmaximal, characteristic
3#13079948C2116yesmaximal, direct product factor
4C2×#10622490C211yesmaximal, characteristic, complemented
5C2×#10622412C211yesmaximal, characteristic, complemented
6C2×#10622404C211yesmaximal, characteristic, complemented
7C2×#10622503C211yesmaximal, characteristic, complemented
8C2×#10622664C211yesmaximal, characteristic, complemented
9C2×#10622661C211yesmaximal, characteristic
10C2×#10622727C211yesmaximal, characteristic
11C2×#10622411C211yesmaximal, characteristic, complemented
12C2×#10622798C211yesmaximal, characteristic, complemented
13C2×#10622795C211yesmaximal, characteristic, complemented
14C2×#10622431C211yesmaximal, characteristic, complemented
15C22×Dic11⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#467C211yesmaximal, characteristic, complemented
17C22×C11×Q16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×#67000C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×#66997C2211yescharacteristic
25C22×#4326C2211yescharacteristic
26C22×#4325C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28C2×#66977C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C23×C11⋊C8C2211yescharacteristic
31C22×#4314C2211yescharacteristic
32#10623155—24no—
33#10623155C2218yes—
34#10623153—24no—
35#10623153C2218yescomplemented
36C2×#66951—21no—
37C2×#66946C2211yescharacteristic
38C2×#66945—21no—
39C2×#66943C2211yescharacteristic
40C2×#66942—21no—
41C2×#66941C2211yescharacteristic
42C2×#66940—21no—
43C2×#66940C2211yescharacteristic
44C2×#66939—21no—
45C2×(C22⋊D11)⋊C4—21no—
46C2×#66931—21no—
47C2×#66930—21no—
48C11×#467C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#103C2211yescharacteristic
51C2×C11×#103C2211yescharacteristic
52C2×#66899C2211yescharacteristic
53C2×#66899C2211yescharacteristic
54#10622798C2218yescomplemented
55#10622795C2218yescomplemented
56#10622727C2218yes—
57C2×#66885C2211yescharacteristic
58C2×#66881C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62C2×Dic11⋊C8C2211yescharacteristic
63C2×Dic11⋊C8C2211yescharacteristic
64C2×Dic11⋊C8C2218yescomplemented
65#10622664C2218yescomplemented
66#10622661C2218yes—
67C2×#66874C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71#10622503C2218yescomplemented
72#10622490C2218yescomplemented
73#10622431C2218yescomplemented
74#10622412C2218yescomplemented
75#10622411C2218yescomplemented
76#10622404C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C23×Dic11D411yescharacteristic
82C23×Dic11D411yescharacteristic
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×Dic22—21no—
86C22×Dic22C2311yescharacteristic
87C2×C11×Q16—42no—
88C2×C11×Q16C2314yes—
89C22×C8×C11—42no—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2314yes—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8C2314yes—
96C11×C22⋊Q8C2314yes—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C22⋊Dic11—21no—
104#67000—22no—
105#67000C2314yes—
106Q8×Dic11—22no—
107Q8×Dic11—22no—
108Q8×Dic11C2314yes—
109Q8×Dic11C2314yes—
110#66997—22no—
111#66997C2314yes—
112C2×#4326—42no—
113C2×#4326C2314yes—
114C2×#4325—42no—
115C2×#4325C2314yes—
116#66983—22no—
117#66983C2314yes—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127#66977—22no—
128#66977C2314yes—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11D411yescharacteristic
139C2×C4×Dic11D411yescharacteristic
140C2×C4×Dic11D414yes—
141C2×C4×Dic11C2311yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143C2×C4×Dic11C2314yes—
144C22×C11⋊C8—42no—
145C22×C11⋊C8C2311yescharacteristic
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2314yes—
148C2×#4314—42no—
149C2×#4314C2314yes—
150#66951—28no—
151#66946—22no—
152#66946C2314yes—
153#66945—28no—
154#66943—22no—
155#66943C2314yes—
156#66942—28no—
157#66941—22no—
158#66941C2314yes—
159#66940—28no—
160#66940—22no—
161#66940C2314yes—
162#66939—28no—
163(C22⋊D11)⋊C4—28no—
164#66931—28no—
165#66930—28no—
166C11×#107C2314yes—
167C11×#103C2314yes—
168C11×#103C2314yes—
169#66899C2314yes—
170#66899C2314yes—
171#66885C2314yes—
172#66881C2314yes—
173#66880C2314yes—
174Dic11⋊C8C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177Dic11⋊C8C2314yes—
178#66874C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C2×#3248—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11C2412yes—
192C2×Q8×C11C2412yes—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—24no—
204C2×C22⋊D11—44no—
205C22×Dic11—24no—
206C22×Dic11—24no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216C2×D44—21no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44C2412yes—
220C2×C4×D11—24no—
221C2×C4×D11—44no—
222C2×Dic22—24no—
223C2×Dic22—21no—
224C2×Dic22—22no—
225C2×Dic22—22no—
226C2×Dic22—44no—
227C2×Dic22C2412yes—
228C11×Q16—44no—
229C2×C8×C11—22no—
230C2×C8×C11—22no—
231C2×C8×C11—44no—
232C2×C8×C11C2412yes—
233C2×C8×C11C2412yes—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C11×C22⋊C4—24no—
241C11×C22⋊C4—24no—
242C22⋊Dic11—24no—
243#4326—44no—
244#4325—44no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249C4⋊Dic11—24no—
250C4⋊Dic11—24no—
251C4⋊Dic11—24no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11C2412yes—
255C4⋊Dic11C2412yes—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262C4×Dic11—24no—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11C2×D414yes—
266C4×Dic11C2×D412yes—
267C4×Dic11C2×D412yes—
268C4×Dic11C2×D414yes—
269C4×Dic11C2412yes—
270C4×Dic11C2412yes—
271C2×C11⋊C8—22no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—44no—
274C2×C11⋊C8C2412yes—
275C2×C11⋊C8C2412yes—
276#4314—44no—
277C2×#533—111no—
278C2×#529—111no—
279#3248—1116no—
280C2×#479—111no—
281C2×#479—111no—
282C2×#475—111no—
283C2×#474—111no—
284C2×#467—111no—
285C2×#467D1111yescharacteristic, complemented
286C2×#465—111no—
287C2×#465—111no—
288C2×#464—111no—
289C2×#464—111no—
290C2×#462—111no—
291C2×#461—111no—
292C22×C4⋊C8—111no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11#13714yes—
296C23×C11C22×D412yes—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—42no—
300C22×D11—42no—
301C22×D11—42no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—22no—
305Q8×C11—22no—
306Q8×C11—42no—
307Q8×C11—42no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11C22×D412yes—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11H(5,𝔽2)12yes—
323C2×C4×C112−1+412yes—
324C2×C4×C11C2511yescharacteristic
325C22⋊D11—48no—
326C2×Dic11—22no—
327C2×Dic11—28no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—28no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11#13514yes—
338C2×Dic11C22×D412yes—
339C2×Dic11C22×D412yes—
340C2×Dic11C22×D412yes—
341C2×Dic11C22×D412yes—
342D44—22no—
343D44—22no—
344D44—42no—
345C4×D11—48no—
346Dic22—22no—
347Dic22—22no—
348Dic22—42no—
349Dic22—48no—
350C8×C11—22no—
351C8×C11—22no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C22×Q16—111no—
355C22×Q16C2×D1111yescharacteristic
356C22×SD16—111no—
357C22×SD16—111no—
358C23×C8—111no—
359C23×C8C2×D1111yescharacteristic
360#533—118no—
361#533—224no—
362C2×C4⋊Q8—111no—
363C2×C4⋊Q8—111no—
364#529—118no—
365#529—224no—
366C2×#126—221no—
367C2×#125—111no—
368C2×#125—221no—
369C2×#124—111no—
370C2×#123—221no—
371C2×C22⋊Q8—111no—
372C2×C22⋊Q8—221no—
373C2×C22⋊Q8C2×D1111yescharacteristic
374C2×C22⋊Q8C2×D1111yescharacteristic
375C2×#121—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8—111no—
378C2×C4×Q8—111no—
379C2×C4×Q8—221no—
380C2×C4×D4—111no—
381C2×C4×D4—221no—
382C2×#117—221no—
383C2×#117—221no—
384C22×C42—111no—
385#479—118no—
386#479—118no—
387#475—118no—
388#474—118no—
389#467—118no—
390#467C2×D1118yescomplemented
391#465—118no—
392#465—118no—
393#464—118no—
394#464—118no—
395#462—118no—
396#461—118no—
397C2×#107—111no—
398C2×#107C2×D1111yescharacteristic
399C2×#106—111no—
400C2×#106—111no—
401C2×C4⋊C8—111no—
402C2×C4⋊C8—111no—
403C2×C4⋊C8—111no—
404C2×C4⋊C8—118no—
405C2×C4⋊C8—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103C2×D1111yescharacteristic
411C2×#103C2×D1111yescharacteristic
412C2×#102—111no—
413C2×#102—111no—
414C22×C11—22no—
415C22×C11—28no—
416C22×C11—22no—
417C22×C11#53712yes—
418C22×C11C2×#13512yes—
419C22×C11C2×#13714yes—
420C22×C11C2×#13712yes—
421C22×C11C23×D411yescharacteristic
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—84no—
426C4×C11—22no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11#53712yes—
432C4×C11C2×H(5,𝔽2)11yescharacteristic
433C4×C11C2×2−1+411yescharacteristic
434Dic11—22no—
435Dic11—22no—
436Dic11—22no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11C2×#13514yes—
441C22×Q8—111no—
442C22×Q8—221no—
443C22×Q8C22×D1111yescharacteristic
444C22×Q8C22×D1111yescharacteristic
445C22×D4—111no—
446C22×D4—221no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—221no—
450C23×C4C22×D1111yescharacteristic
451C2×Q16—42no—
452C2×Q16—114no—
453C2×Q16—442no—
454C2×Q16C22×D1114yes—
455C2×SD16—114no—
456C2×SD16—114no—
457C2×SD16—442no—
458C2×SD16—442no—
459C22×C8—42no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—114no—
463C22×C8—442no—
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1114yes—
467C4⋊Q8—114no—
468C4⋊Q8—114no—
469C4⋊Q8—222no—
470C4⋊Q8—222no—
471#126—228no—
472#125—114no—
473#125—222no—
474#125—228no—
475#124—114no—
476#124—222no—
477#123—228no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—114no—
481C22⋊Q8—228no—
482C22⋊Q8—222no—
483C22⋊Q8C22×D1114yes—
484C22⋊Q8C22×D1114yes—
485#121—114no—
486#121—222no—
487C4×Q8—114no—
488C4×Q8—114no—
489C4×Q8—114no—
490C4×Q8—222no—
491C4×Q8—228no—
492C4×Q8—222no—
493C4×Q8—222no—
494C4×D4—114no—
495C4×D4—222no—
496C4×D4—228no—
497#117—228no—
498#117—228no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—111no—
522C2×C42—111no—
523C2×C42—114no—
524C2×C42—111no—
525C2×C42—111no—
526C2×C42—114no—
527C2×C42—221no—
528C2×C42—221no—
529C2×C42—221no—
530#107—114no—
531#107C22×D1114yes—
532#106—114no—
533#106—114no—
534C4⋊C8—114no—
535C4⋊C8—114no—
536C4⋊C8—114no—
537C4⋊C8—114no—
538#103—114no—
539#103—114no—
540#103—114no—
541#103—114no—
542#103C22×D1114yes—
543#103C22×D1114yes—
544#102—114no—
545#102—114no—
546C2×C11—24no—
547C2×C11#324814yescomplemented
548C2×C11C2×#53711yescharacteristic
549C2×C11C22×#13511yescharacteristic
550C2×C11C22×#13711yescharacteristic
551D11—82no—
552C24—221no—
553C24D4×D1111yescharacteristic
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—112no—
561C2×Q8—224no—
562C2×Q8—221no—
563C2×Q8—222no—
564C2×Q8—222no—
565C2×Q8—444no—
566C2×Q8C23×D1112yes—
567C2×Q8C23×D1112yes—
568C2×D4—112no—
569C2×D4—224no—
570C2×D4—221no—
571C2×D4—222no—
572C2×D4—222no—
573C2×D4—444no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—111no—
581C22×C4—114no—
582C22×C4—114no—
583C22×C4—111no—
584C22×C4—111no—
585C22×C4—111no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—224no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—444no—
593C22×C4D4×D1112yes—
594C22×C4D4×D1111yescharacteristic
595C22×C4C23×D1112yes—
596C22×C4C23×D1111yescharacteristic
597Q16—44no—
598Q16—444no—
599SD16—444no—
600SD16—444no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—44no—
604C2×C8—112no—
605C2×C8—112no—
606C2×C8—222no—
607C2×C8—222no—
608C2×C8—444no—
609C2×C8C23×D1112yes—
610C2×C8C23×D1112yes—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—112no—
616C4⋊C4—112no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—224no—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C42—114no—
638C42—112no—
639C42—112no—
640C42—114no—
641C42—112no—
642C42—112no—
643C42—224no—
644C42—224no—
645C42—224no—
646C11C2×#324811yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—222no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23#6697114yes—
654C23C2×D4×D1112yes—
655C23C2×D4×D1111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—42no—
661Q8—42no—
662Q8—222no—
663Q8—222no—
664Q8—448no—
665Q8—442no—
666D4—222no—
667D4—222no—
668D4—448no—
669D4—442no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—114no—
683C2×C4—112no—
684C2×C4—112no—
685C2×C4—112no—
686C2×C4—112no—
687C2×C4—228no—
688C2×C4—228no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—448no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4C2×D4×D1112yes—
700C2×C4C2×D4×D1111yescharacteristic
701C2×C4#6703712yes—
702C2×C4#6704312yes—
703C2×C4C24×D1111yescharacteristic
704C8—22no—
705C8—22no—
706C8—222no—
707C8—222no—
708C22—22no—
709C22—28no—
710C22—22no—
711C22—442no—
712C22—442no—
713C22—442no—
714C22—884no—
715C22#1062312812yes—
716C22C2×#6697114yes—
717C22C2×#6697112yes—
718C22D11×#13512yes—
719C22C22×D4×D1111yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—114no—
726C4—222no—
727C4—222no—
728C4—222no—
729C4—442no—
730C4—442no—
731C4—442no—
732C4#1062312812yes—
733C4C2×#6703711yescharacteristic
734C4C2×#6704311yescharacteristic
735C2—24no—
736C2—882no—
737C2#1307994814yesdirect product factor
738C2C2×#1062312811yescharacteristic
739C2C2×D11×#13511yescharacteristic
740C2C22×#6697111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#467C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#467D11
hypocenterC11C2×#3248
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
1. C2×#10623153C2semidirect
3. #13079948C2direct (N × H)
4. C2×#10622490C2semidirect
5. C2×#10622412C2semidirect
6. C2×#10622404C2semidirect
7. C2×#10622503C2semidirect
8. C2×#10622664C2semidirect
11. C2×#10622411C2semidirect
12. C2×#10622798C2semidirect
13. C2×#10622795C2semidirect
14. C2×#10622431C2semidirect
15. C22×Dic11⋊C8C2semidirect
16. C2×C11×#467C2semidirect
35. #10623153C22semidirect
48. C11×#467C22semidirect
54. #10622798C22semidirect
55. #10622795C22semidirect
64. C2×Dic11⋊C8C22semidirect
65. #10622664C22semidirect
71. #10622503C22semidirect
72. #10622490C22semidirect
73. #10622431C22semidirect
74. #10622412C22semidirect
75. #10622411C22semidirect
76. #10622404C22semidirect
285. C2×#467D11semidirect
390. #467C2×D11semidirect
547. C2×C11#3248semidirect
646. C11C2×#3248semidirect
737. C2#13079948direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231532
C2×#106231552
#130799482
C2×#106224902
C2×#106224122
C2×#106224042
C2×#106225032
C2×#106226642
C2×#106226612
C2×#106227272
C2×#106224112
C2×#106227982
C2×#106227952
C2×#106224312
C22×Dic11⋊C82
C2×C11×#4672
C2×#324811