Finite Group Databasebeta

← C2×#13080027 #15626683

Subgroups — C2×#13080027 #15626683

Order 2816.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623066C211yesmaximal, characteristic, complemented
2#13080027C2116yesmaximal, direct product factor
3C2×#10622635C211yesmaximal, characteristic, complemented
4C2×#10622622C211yesmaximal, characteristic, complemented
5C2×#10622697C211yesmaximal, characteristic, complemented
6C2×#10622700C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622662C211yesmaximal, characteristic, complemented
9C2×#10622651C211yesmaximal, characteristic, complemented
10C2×#10622661C211yesmaximal, characteristic, complemented
11C2×#10622640C211yesmaximal, characteristic, complemented
12C2×#10622670C211yesmaximal, characteristic, complemented
13C2×#10622670C211yesmaximal, characteristic, complemented
14C2×#10622628C211yesmaximal, characteristic, complemented
15C2×#10622612C211yesmaximal, characteristic, complemented
16C2×C11×#542C211yesmaximal, characteristic, complemented
17C11×#542—24no—
18C11×#542C2218yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#126—21no—
21C2×C11×#124—21no—
22C2×C11×#124C2211yescharacteristic
23C2×C11×#123—21no—
24C2×C11×C22⋊Q8—21no—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C22×#4325C2211yescharacteristic
32C22×#4323C2211yescharacteristic
33C22×#4323C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66983C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623066—24no—
39#10623066C2218yescomplemented
40C2×#66947—21no—
41C2×#66947—21no—
42C2×#66937—21no—
43C2×#66937—21no—
44C2×#66927C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66923C2211yescharacteristic
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52#10622700C2218yescomplemented
53#10622697C2218yescomplemented
54#10622670C2218yescomplemented
55#10622670C2218yescomplemented
56#10622662C2218yescomplemented
57#10622661C2218yescomplemented
58#10622652C2218yescomplemented
59#10622651C2218yescomplemented
60#10622640C2218yescomplemented
61#10622635C2218yescomplemented
62#10622628C2218yescomplemented
63#10622622C2218yescomplemented
64#10622612C2218yescomplemented
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×C4⋊(C11⋊C8)C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×C4⋊(C11⋊C8)C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×D44—21no—
86C22×D44—21no—
87C22×D44C2311yescharacteristic
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C11×C4⋊Q8—22no—
92C11×C4⋊Q8C2314yes—
93C11×#126—28no—
94C11×#124—28no—
95C11×#124—22no—
96C11×#124C2314yes—
97C11×#123—28no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—28no—
100C11×C22⋊Q8C2314yes—
101C11×#121—22no—
102C11×#121C2314yes—
103C4×Q8×C11—22no—
104C4×Q8×C11C2314yes—
105C4×D4×C11—22no—
106C4×D4×C11C2314yes—
107C11×#117D414yes—
108C11×#117C2314yes—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
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×C11—21no—
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2311yescharacteristic
126C2×#4325—42no—
127C2×#4325—42no—
128C2×#4325C2314yes—
129C2×#4325C2314yes—
130C2×#4323—42no—
131C2×#4323—42no—
132C2×#4323C2314yes—
133C2×#4323C2314yes—
134#66983—22no—
135#66983—22no—
136#66983C2314yes—
137#66983C2314yes—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×Dic11⋊C4—21no—
145C2×Dic11⋊C4—21no—
146C2×#4318—42no—
147C2×#4318C2314yes—
148C22×C11⋊C8—42no—
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2314yes—
154#66947—28no—
155#66947—28no—
156#66937—28no—
157#66937—28no—
158#66927—22no—
159#66927C2314yes—
160C4×D44—22no—
161C4×D44—22no—
162C4×D44C2314yes—
163C4×D44C2314yes—
164#66923—22no—
165#66923C2314yes—
166#66899C2314yes—
167#66899C2314yes—
168#66896C2314yes—
169#66896C2314yes—
170#66873C2314yes—
171#66873C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177#66871C2314yes—
178C4⋊(C11⋊C8)C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180C4⋊(C11⋊C8)C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3257—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11—21no—
186C23×D11—21no—
187C2×Q8×C11—21no—
188C2×Q8×C11—24no—
189C2×Q8×C11—22no—
190C2×Q8×C11—22no—
191C2×Q8×C11—82no—
192C2×Q8×C11C2412yes—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—22no—
196C2×D4×C11—22no—
197C2×D4×C11—82no—
198C2×D4×C11C2412yes—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—24no—
205C22×C4×C11—82no—
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—24no—
215C2×C22⋊D11—24no—
216C2×C22⋊D11—82no—
217C2×C22⋊D11—82no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—24no—
223C2×D44—24no—
224C2×D44—22no—
225C2×D44—22no—
226C2×D44—22no—
227C2×D44—22no—
228C2×D44—82no—
229C2×D44—82no—
230C2×D44C2412yes—
231C2×D44C2412yes—
232C2×C4×D11—24no—
233C2×C4×D11—24no—
234C2×C4×D11—82no—
235C2×C4×D11—82no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4C2×D414yes—
242C11×C4⋊C4C2×D414yes—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4C2×D414yes—
251C11×C22⋊C4C2×D414yes—
252C42×C11—24no—
253C42×C11C2×D412yes—
254C42×C11C2×D412yes—
255C42×C11C2412yes—
256C42×C11C2412yes—
257#4325—44no—
258#4325—44no—
259#4323—44no—
260#4323—44no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11C2412yes—
268C4⋊Dic11C2412yes—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271#4318—44no—
272C2×C11⋊C8—22no—
273C2×C11⋊C8—22no—
274C2×C11⋊C8—22no—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—44no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281C2×#542D1111yescharacteristic, complemented
282C2×#540—111no—
283#3257—1116no—
284C2×#479—111no—
285C2×#478—111no—
286C2×#476—111no—
287C2×#474—111no—
288C2×#469—111no—
289C2×#468—111no—
290C2×#466—111no—
291C2×#465—111no—
292C2×#460—111no—
293C2×#463—111no—
294C2×#463—111no—
295C2×#459—111no—
296C2×#424—111no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11C22×D412yes—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—42no—
312C22×D11—42no—
313C22×D11—42no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—42no—
317Q8×C11—84no—
318D4×C11—22no—
319D4×C11—22no—
320D4×C11—42no—
321D4×C11—84no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—24no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—84no—
337C2×C4×C11C22×D412yes—
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×D412yes—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11H(5,𝔽2)12yes—
344C2×C4×C112−1+412yes—
345C2×C4×C11C2511yescharacteristic
346C22⋊D11—84no—
347C22⋊D11—84no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352D44—22no—
353D44—22no—
354D44—22no—
355D44—22no—
356D44—42no—
357D44—42no—
358D44—84no—
359D44—84no—
360C4×D11—84no—
361C4×D11—84no—
362C11⋊C8—22no—
363C11⋊C8—22no—
364C11⋊C8—22no—
365C11⋊C8—22no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×D8—111no—
369C22×D8—111no—
370C22×M16—111no—
371C23×C8—111no—
372#542—24no—
373#542C2×D1118yescomplemented
374#540—118no—
375#540—224no—
376C2×C4⋊Q8C2×D1111yescharacteristic
377C2×#127—111no—
378C2×#126—21no—
379C2×#125—111no—
380C2×#124—21no—
381C2×#124C2×D1111yescharacteristic
382C2×#123—21no—
383C2×#123—221no—
384C2×#123—221no—
385C2×C22⋊Q8—21no—
386C2×C22⋊Q8C2×D1111yescharacteristic
387C2×#121—111no—
388C2×#121—111no—
389C2×#121—221no—
390C2×#121—221no—
391C2×#121C2×D1111yescharacteristic
392C2×C4×Q8C2×D1111yescharacteristic
393C2×C4×D4—111no—
394C2×C4×D4—111no—
395C2×C4×D4C2×D1111yescharacteristic
396C2×#117C2×D1111yescharacteristic
397#479—118no—
398#478—118no—
399#476—118no—
400#474—118no—
401#469—118no—
402#468—118no—
403#466—118no—
404#465—118no—
405#463—118no—
406#463—118no—
407#460—118no—
408#459—118no—
409C2×#107—111no—
410C2×#107—111no—
411C2×#106—111no—
412C2×#106—111no—
413#424—118no—
414C2×C4⋊C8—111no—
415C2×C4⋊C8—111no—
416C2×C4⋊C8—111no—
417C2×C4⋊C8—111no—
418C2×#103—111no—
419C2×#103—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×#102—111no—
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—44no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—42no—
433C22×C11—84no—
434C22×C11#53712yes—
435C22×C11#57612yes—
436C22×C11#57712yes—
437C22×C11C23×D411yescharacteristic
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—84no—
445C2×D11—84no—
446C4×C11—22no—
447C4×C11—22no—
448C4×C11—22no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11—42no—
454C4×C11#53712yes—
455C4×C11C2×H(5,𝔽2)11yescharacteristic
456C4×C11C2×2−1+411yescharacteristic
457Dic11—42no—
458Dic11—42no—
459C22×Q8—21no—
460C22×Q8C22×D1111yescharacteristic
461C22×D4—21no—
462C22×D4—111no—
463C22×D4—111no—
464C22×D4—221no—
465C22×D4—221no—
466C22×D4—221no—
467C22×D4—221no—
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—221no—
471C23×C4—221no—
472C23×C4C22×D1111yescharacteristic
473C2×SD16—114no—
474C2×SD16—114no—
475C2×SD16—442no—
476C2×SD16—442no—
477C2×D8—114no—
478C2×D8—114no—
479C2×D8—442no—
480C2×D8—442no—
481C2×M16—114no—
482C2×M16—442no—
483C22×C8—111no—
484C22×C8—111no—
485C22×C8—111no—
486C22×C8—111no—
487C22×C8—114no—
488C22×C8—442no—
489C4⋊Q8—22no—
490C4⋊Q8C22×D1114yes—
491#127—114no—
492#127—222no—
493#126—28no—
494#125—114no—
495#125—222no—
496#124—28no—
497#124—22no—
498#124C22×D1114yes—
499#123—28no—
500#123—228no—
501#123—228no—
502C22⋊Q8—22no—
503C22⋊Q8—28no—
504C22⋊Q8C22×D1114yes—
505#121—22no—
506#121—114no—
507#121—114no—
508#121—222no—
509#121—222no—
510#121—228no—
511#121—228no—
512#121C22×D1114yes—
513C4×Q8—22no—
514C4×Q8C22×D1114yes—
515C4×D4—22no—
516C4×D4—114no—
517C4×D4—114no—
518C4×D4—222no—
519C4×D4—222no—
520C4×D4C22×D1114yes—
521#117C22⋊D1114yes—
522#117C22×D1114yes—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4C22⋊D1111yescharacteristic
531C2×C4⋊C4C22⋊D1111yescharacteristic
532C2×C4⋊C4C22×D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—221no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4C22⋊D1111yescharacteristic
544C2×C22⋊C4C22⋊D1111yescharacteristic
545C2×C42—21no—
546C2×C42C22×D1111yescharacteristic
547C2×C42C22×D1111yescharacteristic
548#107—114no—
549#107—114no—
550#106—114no—
551#106—114no—
552C4⋊C8—114no—
553C4⋊C8—114no—
554C4⋊C8—114no—
555C4⋊C8—114no—
556#103—114no—
557#103—114no—
558#102—114no—
559#102—114no—
560#102—114no—
561#102—114no—
562#102—114no—
563#102—114no—
564C2×C11—42no—
565C2×C11—82no—
566C2×C11#325714yescomplemented
567C2×C11C2×#53711yescharacteristic
568C2×C11C2×#57611yescharacteristic
569C2×C11C2×#57711yescharacteristic
570D11—82no—
571D11—82no—
572C24—21no—
573C24—221no—
574C24—221no—
575C24C2×C22⋊D1111yescharacteristic
576C2×Q8—21no—
577C2×Q8—24no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—82no—
581C2×Q8C23×D1112yes—
582C2×D4—24no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—82no—
587C2×D4—112no—
588C2×D4—112no—
589C2×D4—224no—
590C2×D4—224no—
591C2×D4—222no—
592C2×D4—222no—
593C2×D4—222no—
594C2×D4—222no—
595C2×D4—221no—
596C2×D4—221no—
597C2×D4—224no—
598C2×D4—224no—
599C2×D4—882no—
600C2×D4—882no—
601C2×D4—882no—
602C2×D4—882no—
603C2×D4C23×D1112yes—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—82no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—882no—
616C22×C4—882no—
617C22×C4C2×C22⋊D1112yes—
618C22×C4C2×C22⋊D1111yescharacteristic
619C22×C4C2×C22⋊D1111yescharacteristic
620C22×C4C2×C22⋊D1111yescharacteristic
621C22×C4C2×C22⋊D1111yescharacteristic
622C22×C4C2×C22⋊D1111yescharacteristic
623C22×C4C23×D1112yes—
624C22×C4C23×D1111yescharacteristic
625SD16—444no—
626SD16—444no—
627D8—444no—
628D8—444no—
629M16—444no—
630C2×C8—112no—
631C2×C8—112no—
632C2×C8—112no—
633C2×C8—112no—
634C2×C8—222no—
635C2×C8—222no—
636C2×C8—222no—
637C2×C8—222no—
638C2×C8—444no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—112no—
645C4⋊C4—112no—
646C4⋊C4—221no—
647C4⋊C4—221no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4C2×C22⋊D1114yes—
651C4⋊C4C2×C22⋊D1114yes—
652C4⋊C4C23×D1112yes—
653C4⋊C4C23×D1112yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4C2×C22⋊D1114yes—
664C22⋊C4C2×C22⋊D1114yes—
665C42—24no—
666C42C2×C22⋊D1112yes—
667C42C2×C22⋊D1112yes—
668C42C23×D1112yes—
669C42C23×D1112yes—
670C11C2×#325711yescharacteristic, complemented, Sylow
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—222no—
679C23—222no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23C22×C22⋊D1112yes—
687C23C22×C22⋊D1111yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—84no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—222no—
697D4—222no—
698D4—222no—
699D4—222no—
700D4—442no—
701D4—442no—
702D4—884no—
703D4—884no—
704D4—884no—
705D4—884no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—84no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—884no—
726C2×C4—884no—
727C2×C4#6704212yes—
728C2×C4#6704312yes—
729C2×C4C22×C22⋊D1112yes—
730C2×C4C22×C22⋊D1112yes—
731C2×C4C22×C22⋊D1112yes—
732C2×C4C22×C22⋊D1112yes—
733C2×C4C22×C22⋊D1112yes—
734C2×C4C22×C22⋊D1111yescharacteristic
735C2×C4C24×D1111yescharacteristic
736C8—222no—
737C8—222no—
738C8—222no—
739C8—222no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—442no—
754C22—884no—
755C22—884no—
756C22#1062336412yes—
757C22#1062336612yes—
758C22#1062336812yes—
759C22C23×C22⋊D1111yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—442no—
769C4—442no—
770C4#1062336412yes—
771C4C2×#6704211yescharacteristic
772C4C2×#6704311yescharacteristic
773C2—42no—
774C2—82no—
775C2—882no—
776C2—882no—
777C2#1308002714yesdirect product factor
778C2C2×#1062336411yescharacteristic
779C2C2×#1062336611yescharacteristic
780C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#542C2
socleC23×C11C22×D4
hypercenterC2×#542D11
hypocenterC11C2×#3257
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#10623066C2semidirect
2. #13080027C2direct (N × H)
3. C2×#10622635C2semidirect
4. C2×#10622622C2semidirect
5. C2×#10622697C2semidirect
6. C2×#10622700C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622662C2semidirect
9. C2×#10622651C2semidirect
10. C2×#10622661C2semidirect
11. C2×#10622640C2semidirect
12. C2×#10622670C2semidirect
13. C2×#10622670C2semidirect
14. C2×#10622628C2semidirect
15. C2×#10622612C2semidirect
16. C2×C11×#542C2semidirect
18. C11×#542C22semidirect
39. #10623066C22semidirect
52. #10622700C22semidirect
53. #10622697C22semidirect
54. #10622670C22semidirect
55. #10622670C22semidirect
56. #10622662C22semidirect
57. #10622661C22semidirect
58. #10622652C22semidirect
59. #10622651C22semidirect
60. #10622640C22semidirect
61. #10622635C22semidirect
62. #10622628C22semidirect
63. #10622622C22semidirect
64. #10622612C22semidirect
281. C2×#542D11semidirect
373. #542C2×D11semidirect
566. C2×C11#3257semidirect
670. C11C2×#3257semidirect
777. C2#13080027direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230662
#130800272
C2×#106226352
C2×#106226222
C2×#106226972
C2×#106227002
C2×#106226522
C2×#106226622
C2×#106226512
C2×#106226612
C2×#106226402
C2×#106226702
C2×#106226282
C2×#106226122
C2×C11×#5422
C2×#325711