Finite Group Databasebeta

← C2×#13078864 #15622073

Subgroups — C2×#13078864 #15622073

Order 2816.

2210 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×#10623156C211yesmaximal, characteristic, complemented
2C2×#10623052C211yesmaximal, characteristic
3#13078864C2116yesmaximal, direct product factor
4C2×#10622609C211yesmaximal, characteristic, complemented
5C2×#10622504C211yesmaximal, characteristic, complemented
6C2×#10622484C211yesmaximal, characteristic, complemented
7C2×#10622431C211yesmaximal, characteristic, complemented
8C2×#10622431C211yesmaximal, characteristic, complemented
9C2×#10622344C211yesmaximal, characteristic
10C2×#10622659C211yesmaximal, characteristic
11C2×#10622430C211yesmaximal, characteristic, complemented
12C2×#10622502C211yesmaximal, characteristic, complemented
13C2×#10622465C211yesmaximal, characteristic, complemented
14C2×#10622401C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#485C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic, complemented
21C2×#66997C2211yescharacteristic, complemented
22C22×#4325C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×#4314C2211yescharacteristic
27C22×#4314C2211yescharacteristic
28#10623156—24no—
29#10623156C2218yescomplemented
30#10623052—24no—
31#10623052C2218yes—
32C2×#66946C2211yescharacteristic
33C2×#66946C2211yescharacteristic
34C2×#66946C2211yescharacteristic
35C2×#66946C2211yescharacteristic
36C2×#66943—21no—
37C2×#66943C2211yescharacteristic, complemented
38C2×#66942—21no—
39C2×#66940C2211yescharacteristic, complemented
40C2×C22⋊C4×D11—21no—
41C2×C22⋊C4×D11—21no—
42C2×#66932—21no—
43C2×#66932—21no—
44C2×C4×D44—21no—
45C2×C4×D44—21no—
46C11×#485C2218yescomplemented
47C2×C11×#107C2211yescharacteristic, complemented
48C2×C11×#106C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#103C2211yescharacteristic, complemented
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66879C2211yescharacteristic, complemented
56C2×Dic11⋊C8C2211yescharacteristic, complemented
57C2×Dic11⋊C8C2211yescharacteristic, complemented
58C2×C8×Dic11C2211yescharacteristic, complemented
59#10622659C2218yes—
60#10622609C2218yescomplemented
61C2×#66874C2211yescharacteristic, complemented
62C2×#66874C2211yescharacteristic, complemented
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic, complemented
66C2×#66871C2211yescharacteristic, complemented
67#10622504C2218yescomplemented
68#10622502C2218yescomplemented
69#10622484C2218yescomplemented
70#10622465C2218yescomplemented
71#10622431C2218yescomplemented
72#10622431C2218yescomplemented
73#10622430C2218yescomplemented
74#10622401C2218yescomplemented
75#10622344C2218yes—
76#10622333C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×D44—21no—
81C22×D44—22no—
82C22×D44—24no—
83C22×D44—24no—
84C22×D44C2314yes—
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×Dic22C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8C2314yes—
96C11×#117—22no—
97C11×#117C2314yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C42×C11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11D411yescharacteristic
107C2×C22⋊Dic11D411yescharacteristic
108Q8×Dic11—22no—
109Q8×Dic11C2314yescomplemented
110#66997—22no—
111#66997C2314yescomplemented
112C2×#4325—24no—
113C2×#4325—24no—
114C2×#4325C2314yes—
115C2×#4325C2314yes—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120#66979D414yes—
121#66979C2314yes—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11D411yescharacteristic
125C2×C4⋊Dic11D411yescharacteristic
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×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×#4314—24no—
141C2×#4314—24no—
142C2×#4314C2314yes—
143C2×#4314C2314yes—
144#66946—22no—
145#66946—22no—
146#66946—22no—
147#66946—22no—
148#66946C2314yes—
149#66946C2314yes—
150#66946C2314yes—
151#66946C2314yes—
152#66943—28no—
153#66943—22no—
154#66943C2314yescomplemented
155#66942—28no—
156#66940—22no—
157#66940C2314yescomplemented
158C22⋊C4×D11—28no—
159C22⋊C4×D11—28no—
160#66932—28no—
161#66932—28no—
162C4×D44—28no—
163C4×D44—28no—
164C11×#107C2314yescomplemented
165C11×#106C2314yescomplemented
166C11×#103C2314yescomplemented
167C11×#103C2314yescomplemented
168C11×C22⋊C8C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170#66885C2314yes—
171#66885C2314yes—
172#66879C2314yescomplemented
173Dic11⋊C8C2314yescomplemented
174Dic11⋊C8C2314yescomplemented
175C8×Dic11C2314yescomplemented
176#66874C2314yescomplemented
177#66874C2314yescomplemented
178#66873C2314yes—
179#66873C2314yes—
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182C2×#3123—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—28no—
187C23×D11—24no—
188C23×D11—82no—
189C23×D11—82no—
190C2×Q8×C11—21no—
191C2×Q8×C11—22no—
192C2×Q8×C11—22no—
193C2×Q8×C11C2412yes—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2411yescharacteristic
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11C2×D411yescharacteristic
207C22×Dic11C2×D411yescharacteristic
208C22×Dic11C2×D411yescharacteristic
209C22×Dic11C2×D411yescharacteristic
210C2×D44—28no—
211C2×D44—216no—
212C2×D44—28no—
213C2×D44—28no—
214C2×D44—24no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—22no—
218C2×D44—22no—
219C2×D44#4114yes—
220C2×D44#4114yes—
221C2×D44C2412yes—
222C2×D44C2412yes—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—82no—
228C2×C4×D11—82no—
229C2×C4×D11—82no—
230C2×C4×D11—82no—
231C2×Dic22—21no—
232C2×Dic22—22no—
233C2×Dic22—22no—
234C2×Dic22C2412yes—
235C2×C8×C11—22no—
236C2×C8×C11—22no—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4C2412yes—
244C11×C4⋊C4C2412yes—
245C11×C4⋊C4C2412yes—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C42×C11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11C2×D414yes—
251C22⋊Dic11C2×D414yes—
252#4325—28no—
253#4325—28no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11—24no—
260C4⋊Dic11—21no—
261C4⋊Dic11C2×D414yes—
262C4⋊Dic11C2×D414yes—
263C4⋊Dic11C2412yes—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269C4×Dic11—24no—
270C4×Dic11—24no—
271C4×Dic11C2×D412yes—
272C4×Dic11C2×D412yes—
273C4×Dic11C2412yes—
274C4×Dic11C2412yes—
275C2×C11⋊C8—22no—
276C2×C11⋊C8—22no—
277C2×C11⋊C8C2412yes—
278C2×C11⋊C8C2412yes—
279#4314—28no—
280#4314—28no—
281C2×#541—111no—
282C2×#518—111no—
283#3123—1116no—
284C2×#485—111no—
285C2×#485D1111yescharacteristic, complemented
286C2×#478—111no—
287C2×#478—111no—
288C2×#461—111no—
289C2×#461—111no—
290C2×#450—111no—
291C2×#450—111no—
292C2×#440—111no—
293C2×#440—111no—
294C2×C4×SD16—111no—
295C2×C4×SD16—111no—
296C2×#433—111no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11C22×D412yes—
301C23×C11C22×D411yescharacteristic
302C22×D11—24no—
303C22×D11—24no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—216no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—84no—
312C22×D11—84no—
313C22×D11—816no—
314Q8×C11—22no—
315Q8×C11—22no—
316Q8×C11—42no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11C22×D412yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2×#4112yes—
332C2×C4×C11C2×#4112yes—
333C2×C4×C11C2511yescharacteristic
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11C22×D412yes—
343C2×Dic11C22×D412yes—
344C2×Dic11C22×D412yes—
345C2×Dic11C22×D412yes—
346D44—216no—
347D44—24no—
348D44—24no—
349D44—22no—
350D44—22no—
351D44C2×#4114yes—
352D44C2×#4114yes—
353C4×D11—84no—
354C4×D11—84no—
355C4×D11—84no—
356C4×D11—84no—
357Dic22—22no—
358Dic22—22no—
359Dic22—42no—
360C8×C11—22no—
361C8×C11—22no—
362C11⋊C8—22no—
363C11⋊C8—22no—
364C23×D4—111no—
365C22×SD16—111no—
366C22×SD16—111no—
367C22×SD16—111no—
368C22×SD16—111no—
369#541—118no—
370#541—224no—
371C2×C4⋊Q8—111no—
372C2×#126—221no—
373C2×#126—221no—
374C2×#125—111no—
375C2×#125—221no—
376C2×#125—221no—
377C2×C22⋊Q8—111no—
378C2×C22⋊Q8C2×D1111yescharacteristic
379#518—118no—
380#518—224no—
381C2×C4×Q8—111no—
382C2×C4×Q8—111no—
383C2×C4×D4—111no—
384C2×C4×D4—111no—
385C2×C4×D4—111no—
386C2×C4×D4—111no—
387C2×C4×D4—221no—
388C2×C4×D4—221no—
389C2×#117—111no—
390C2×#117C2×D1111yescharacteristic
391C22×C22⋊C4—221no—
392C22×C22⋊C4—221no—
393#485—118no—
394#485C2×D1118yescomplemented
395#478—118no—
396#478—118no—
397#461—118no—
398#461—118no—
399#450—118no—
400#450—118no—
401#440—118no—
402#440—118no—
403C4×SD16—118no—
404C4×SD16—118no—
405#433—118no—
406C2×#107—111no—
407C2×#107C2×D1111yescharacteristic, complemented
408C2×#106—111no—
409C2×#106C2×D1111yescharacteristic, complemented
410C2×C4⋊C8—111no—
411C2×C4⋊C8—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103C2×D1111yescharacteristic, complemented
415C2×#103C2×D1111yescharacteristic, complemented
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×C22⋊C8—111no—
421C2×C22⋊C8C2×D1111yescharacteristic
422C2×#97—111no—
423C2×C4×C8—111no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—44no—
428C22×C11#52512yes—
429C22×C11#57712yes—
430C22×C11#57712yes—
431C22×C11C23×D411yescharacteristic
432C2×D11—24no—
433C2×D11—24no—
434C2×D11—48no—
435C2×D11—48no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—42no—
440C2×D11—816no—
441C4×C11—22no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11#52512yes—
447C4×C11C22×#4111yescharacteristic
448C4×C11C22×#4111yescharacteristic
449Dic11—22no—
450Dic11—22no—
451Dic11—22no—
452Dic11—22no—
453Dic11—42no—
454Dic11—42no—
455C25—221no—
456C22×Q8—111no—
457C22×Q8C22×D1111yescharacteristic
458C22×D4—111no—
459C22×D4—111no—
460C22×D4—114no—
461C22×D4—224no—
462C22×D4—224no—
463C22×D4—221no—
464C22×D4—222no—
465C23×C4—221no—
466C23×C4—221no—
467C23×C4—221no—
468C23×C4—221no—
469C23×C4C22×D1111yescharacteristic
470C2×SD16—114no—
471C2×SD16—114no—
472C2×SD16—114no—
473C2×SD16—114no—
474C2×SD16—224no—
475C2×SD16—224no—
476C2×SD16—224no—
477C2×SD16—224no—
478C22×C8—111no—
479C22×C8—111no—
480C22×C8C22×D1111yescharacteristic
481C22×C8C22×D1111yescharacteristic
482C4⋊Q8—114no—
483C4⋊Q8—222no—
484#126—228no—
485#126—228no—
486#125—114no—
487#125—222no—
488#125—228no—
489#125—228no—
490C22⋊Q8—22no—
491C22⋊Q8—114no—
492C22⋊Q8—222no—
493C22⋊Q8C22×D1114yes—
494C4×Q8—114no—
495C4×Q8—114no—
496C4×Q8—222no—
497C4×Q8—222no—
498C4×D4—114no—
499C4×D4—114no—
500C4×D4—114no—
501C4×D4—114no—
502C4×D4—228no—
503C4×D4—228no—
504C4×D4—222no—
505C4×D4—222no—
506C4×D4—222no—
507C4×D4—222no—
508#117—22no—
509#117—114no—
510#117—114no—
511#117C22×D1114yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—111no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—221no—
517C2×C4⋊C4—221no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4C22×D1111yescharacteristic
524C2×C4⋊C4C22×D1111yescharacteristic
525C2×C4⋊C4C22×D1111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—111no—
529C2×C22⋊C4—111no—
530C2×C22⋊C4—228no—
531C2×C22⋊C4—228no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4—221no—
534C2×C22⋊C4—221no—
535C2×C22⋊C4—221no—
536C2×C22⋊C4—221no—
537C2×C42—21no—
538C2×C42—111no—
539C2×C42—111no—
540C2×C42—221no—
541C2×C42—221no—
542#107—114no—
543#107C22×D1114yescomplemented
544#106—114no—
545#106C22×D1114yescomplemented
546C4⋊C8—114no—
547C4⋊C8—114no—
548#103—114no—
549#103—114no—
550#103C22×D1114yescomplemented
551#103C22×D1114yescomplemented
552#102—114no—
553#102—114no—
554#102—114no—
555#102—114no—
556C22⋊C8—114no—
557C22⋊C8C22×D1114yes—
558#97—114no—
559C4×C8—114no—
560C2×C11—42no—
561C2×C11#312314yescomplemented
562C2×C11C2×#52511yescharacteristic
563C2×C11C2×#57711yescharacteristic
564C2×C11C2×#57711yescharacteristic
565D11—44no—
566D11—44no—
567C24—228no—
568C24—221no—
569C24—221no—
570C24—224no—
571C24—882no—
572C24—882no—
573C24D4×D1111yescharacteristic
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—112no—
578C2×Q8—221no—
579C2×Q8—222no—
580C2×Q8—222no—
581C2×Q8C23×D1112yes—
582C2×D4—114no—
583C2×D4—114no—
584C2×D4—112no—
585C2×D4—112no—
586C2×D4—228no—
587C2×D4—228no—
588C2×D4—228no—
589C2×D4—2216no—
590C2×D4—224no—
591C2×D4—221no—
592C2×D4—221no—
593C2×D4—222no—
594C2×D4—222no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—224no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—224no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—882no—
612C22×C4—882no—
613C22×C4—882no—
614C22×C4—882no—
615C22×C4D4×D1112yes—
616C22×C4D4×D1111yescharacteristic
617C22×C4C23×D1112yes—
618C22×C4C23×D1111yescharacteristic
619SD16—228no—
620SD16—228no—
621SD16—228no—
622SD16—228no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—112no—
626C2×C8—112no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8C23×D1112yes—
630C2×C8C23×D1112yes—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—114no—
636C4⋊C4—114no—
637C4⋊C4—112no—
638C4⋊C4—224no—
639C4⋊C4—224no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—224no—
644C4⋊C4—221no—
645C4⋊C4—224no—
646C4⋊C4C23×D1112yes—
647C4⋊C4C23×D1112yes—
648C4⋊C4C23×D1112yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—114no—
652C22⋊C4—114no—
653C22⋊C4—224no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C42—24no—
659C42—112no—
660C42—112no—
661C42—112no—
662C42—112no—
663C42—224no—
664C42—224no—
665C11C2×#312311yescharacteristic, complemented, Sylow
666C23—22no—
667C23—22no—
668C23—22no—
669C23—2216no—
670C23—224no—
671C23—224no—
672C23—222no—
673C23—222no—
674C23—442no—
675C23—442no—
676C23—442no—
677C23—442no—
678C23—884no—
679C23—884no—
680C23—8816no—
681C23C2×D4×D1112yes—
682C23C2×D4×D1111yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—222no—
687Q8—222no—
688Q8—442no—
689D4—114no—
690D4—114no—
691D4—2216no—
692D4—224no—
693D4—224no—
694D4—222no—
695D4—222no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—112no—
709C2×C4—112no—
710C2×C4—112no—
711C2×C4—112no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—884no—
721C2×C4—884no—
722C2×C4—884no—
723C2×C4—884no—
724C2×C4C2×D4×D1112yes—
725C2×C4C2×D4×D1111yescharacteristic
726C2×C4#41×D1112yes—
727C2×C4#41×D1112yes—
728C2×C4C24×D1111yescharacteristic
729C8—22no—
730C8—22no—
731C8—222no—
732C8—222no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—224no—
738C22—224no—
739C22—448no—
740C22—448no—
741C22—442no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—8816no—
746C22#1062318712yes—
747C22#1062330112yes—
748C22#1062330912yes—
749C22C22×D4×D1111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—222no—
756C4—222no—
757C4—222no—
758C4—222no—
759C4—442no—
760C4—442no—
761C4#1062318712yes—
762C4C2×#41×D1111yescharacteristic
763C4C2×#41×D1111yescharacteristic
764C2—42no—
765C2—444no—
766C2—444no—
767C2#1307886414yesdirect product factor
768C2C2×#1062318711yescharacteristic
769C2C2×#1062330111yescharacteristic
770C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenterC2×#485D11
hypocenterC11C2×#3123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#10623156C2semidirect
3. #13078864C2direct (N × H)
4. C2×#10622609C2semidirect
5. C2×#10622504C2semidirect
6. C2×#10622484C2semidirect
7. C2×#10622431C2semidirect
8. C2×#10622431C2semidirect
11. C2×#10622430C2semidirect
12. C2×#10622502C2semidirect
13. C2×#10622465C2semidirect
14. C2×#10622401C2semidirect
15. C2×#10622333C2semidirect
16. C2×C11×#485C2semidirect
20. C2×Q8×Dic11C22semidirect
21. C2×#66997C22semidirect
29. #10623156C22semidirect
37. C2×#66943C22semidirect
39. C2×#66940C22semidirect
46. C11×#485C22semidirect
47. C2×C11×#107C22semidirect
48. C2×C11×#106C22semidirect
49. C2×C11×#103C22semidirect
50. C2×C11×#103C22semidirect
55. C2×#66879C22semidirect
56. C2×Dic11⋊C8C22semidirect
57. C2×Dic11⋊C8C22semidirect
58. C2×C8×Dic11C22semidirect
60. #10622609C22semidirect
61. C2×#66874C22semidirect
62. C2×#66874C22semidirect
65. C2×#66872C22semidirect
66. C2×#66871C22semidirect
67. #10622504C22semidirect
68. #10622502C22semidirect
69. #10622484C22semidirect
70. #10622465C22semidirect
71. #10622431C22semidirect
72. #10622431C22semidirect
73. #10622430C22semidirect
74. #10622401C22semidirect
76. #10622333C22semidirect
109. Q8×Dic11C23semidirect
111. #66997C23semidirect
154. #66943C23semidirect
157. #66940C23semidirect
164. C11×#107C23semidirect
165. C11×#106C23semidirect
166. C11×#103C23semidirect
167. C11×#103C23semidirect
172. #66879C23semidirect
173. Dic11⋊C8C23semidirect
174. Dic11⋊C8C23semidirect
175. C8×Dic11C23semidirect
176. #66874C23semidirect
177. #66874C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
285. C2×#485D11semidirect
394. #485C2×D11semidirect
407. C2×#107C2×D11semidirect
409. C2×#106C2×D11semidirect
414. C2×#103C2×D11semidirect
415. C2×#103C2×D11semidirect
543. #107C22×D11semidirect
545. #106C22×D11semidirect
550. #103C22×D11semidirect
551. #103C22×D11semidirect
561. C2×C11#3123semidirect
665. C11C2×#3123semidirect
767. C2#13078864direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231562
C2×#106230522
#130788642
C2×#106226092
C2×#106225042
C2×#106224842
C2×#106224312
C2×#106223442
C2×#106226592
C2×#106224302
C2×#106225022
C2×#106224652
C2×#106224012
C2×#106223332
C2×C11×#4852
C2×#312311