Finite Group Databasebeta

← C2×#13078591 #15621619

Subgroups — C2×#13078591 #15621619

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623139C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3#13078591C2116yesmaximal, direct product factor
4C2×#10622497C211yesmaximal, characteristic, complemented
5C2×#10622335C211yesmaximal, characteristic, complemented
6C2×#10622480C211yesmaximal, characteristic, complemented
7C2×#10622609C211yesmaximal, characteristic, complemented
8C2×#10622397C211yesmaximal, characteristic, complemented
9C2×#10622387C211yesmaximal, characteristic, complemented
10C2×#10622646C211yesmaximal, characteristic, complemented
11C2×#10622474C211yesmaximal, characteristic, complemented
12C2×D11×#107C211yesmaximal, characteristic, complemented
13C2×#10622384C211yesmaximal, characteristic, complemented
14C2×#10622385C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×#66992—21no—
22C2×#66991—21no—
23C2×#66991C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×#4313C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28#10623139—24no—
29#10623139C2218yes—
30#10623054—24no—
31#10623054C2218yescomplemented
32C2×#66950C2211yescharacteristic
33C2×#66945C2211yescharacteristic
34C2×#66945C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×C4⋊C4×D11C2211yescharacteristic
38C2×#66937—21no—
39C2×(C22⋊D11)⋊C4—21no—
40C2×(C22⋊D11)⋊C4—21no—
41C2×#66931—21no—
42C2×C4×D44—21no—
43C2×C4×Dic22—21no—
44C11×#482C2218yescomplemented
45C2×C11×#107C2211yescharacteristic
46C2×C11×#106C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66882C2211yescharacteristic
56C2×#66882C2211yescharacteristic
57C2×#66880C2211yescharacteristic
58C2×#66880C2211yescharacteristic
59#10622646C2218yescomplemented
60#10622609C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622497C2218yescomplemented
68D11×#107C2218yescomplemented
69#10622480C2218yescomplemented
70#10622474C2218yescomplemented
71#10622397C2218yescomplemented
72#10622387C2218yescomplemented
73#10622385C2218yescomplemented
74#10622384C2218yescomplemented
75#10622340C2218yescomplemented
76#10622335C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11D411yescharacteristic
83C22×C22⋊D11D411yescharacteristic
84C23×Dic11—21no—
85C23×Dic11—21no—
86C2×#4341—22no—
87C2×#4341—24no—
88C2×#4341—24no—
89C2×#4341C2314yes—
90C2×#4339—24no—
91C2×#4339—24no—
92C2×#4339D414yes—
93C2×#4339C2314yes—
94C22×D44D411yescharacteristic
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11—21no—
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2311yescharacteristic
100C22×Dic22D411yescharacteristic
101C22×Dic22C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C11×#121—22no—
105C11×#121C2314yes—
106C11×#117—22no—
107C11×#117C2314yes—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11—21no—
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116#66992—28no—
117#66991—28no—
118#66991—22no—
119#66991C2314yes—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—22no—
125C2×C4⋊Dic11—21no—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2314yes—
130#66977—22no—
131#66977C2314yes—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C2×#4313—24no—
141C2×#4313C2314yes—
142C2×C8×D11—24no—
143C2×C8×D11C2314yes—
144#66950—22no—
145#66950C2314yes—
146#66945—22no—
147#66945—22no—
148#66945C2314yes—
149#66945C2314yes—
150C4⋊C4×D11—22no—
151C4⋊C4×D11—22no—
152C4⋊C4×D11—22no—
153C4⋊C4×D11C2314yes—
154C4⋊C4×D11C2314yes—
155C4⋊C4×D11C2314yes—
156#66937—28no—
157(C22⋊D11)⋊C4—28no—
158(C22⋊D11)⋊C4—28no—
159#66931—28no—
160C4×D44—28no—
161C4×Dic22—28no—
162C11×#107C2314yes—
163C11×#106C2314yes—
164C11×#102C2314yes—
165C11×#102C2314yes—
166C11×C22⋊C8C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169C22⋊(C11⋊C8)C2314yes—
170(C2×D11)⋊C8C2314yes—
171(C2×D11)⋊C8C2314yes—
172#66882C2314yes—
173#66882C2314yes—
174#66880C2314yes—
175#66880C2314yes—
176#66874C2314yes—
177#66874C2314yes—
178#66872C2314yes—
179#66871C2314yes—
180#66871C2314yes—
181#66871C2314yes—
182C2×#3098—111nomaximal, Sylow
183C24×C11—21no—
184C24×C11C2×D411yescharacteristic
185C23×D11C2×D411yescharacteristic
186C23×D11C2×D411yescharacteristic
187C2×D4×C11—24no—
188C2×D4×C11—21no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—82no—
192C2×D4×C11C2412yes—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2412yes—
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—82no—
208C2×C22⋊D11C2×D414yes—
209C2×C22⋊D11C2×D414yes—
210C22×Dic11—24no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—24no—
216C22×Dic11—44no—
217C22×Dic11—82no—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220#4341—28no—
221#4341—28no—
222#4341—48no—
223#4339—216no—
224#4339—28no—
225#4339—28no—
226C2×D44—24no—
227C2×D44C2×D414yes—
228C2×C4×D11—24no—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—22no—
232C2×C4×D11—22no—
233C2×C4×D11—82no—
234C2×C4×D11—82no—
235C2×C4×D11—82no—
236C2×C4×D11C2×D412yes—
237C2×C4×D11C2×D412yes—
238C2×C4×D11#4114yes—
239C2×C4×D11#4114yes—
240C2×C4×D11C2412yes—
241C2×C4×D11C2412yes—
242C2×Dic22—24no—
243C2×Dic22—21no—
244C2×Dic22—22no—
245C2×Dic22—22no—
246C2×Dic22C2×D414yes—
247C2×Dic22C2412yes—
248C2×C8×C11—22no—
249C2×C8×C11—22no—
250C2×C8×C11C2412yes—
251C2×C8×C11C2412yes—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4C2412yes—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C42×C11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266C4⋊Dic11—24no—
267C4⋊Dic11—24no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11C2412yes—
272C4⋊Dic11C2412yes—
273C4⋊Dic11C2412yes—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278C4×Dic11—24no—
279C4×Dic11—24no—
280C2×C11⋊C8—22no—
281C2×C11⋊C8—22no—
282C2×C11⋊C8C2412yes—
283C2×C11⋊C8C2412yes—
284#4313—28no—
285C8×D11—28no—
286C2×#537—111no—
287C2×#520—111no—
288#3098—1116no—
289C2×#484—111no—
290C2×#484—111no—
291C2×#485—111no—
292C2×#485—111no—
293C2×#482—111no—
294C2×#482D1111yescharacteristic, complemented
295C2×#480—111no—
296C2×#480—111no—
297C2×#428—111no—
298C22×#107—111no—
299C2×#417—111no—
300C2×#416—111no—
301C2×#408—111no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11C22×D412yes—
310C23×C11C22×D411yescharacteristic
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11#12314yes—
317C22×D11C22×D412yes—
318C22×D11C22×D412yes—
319D4×C11—22no—
320D4×C11—22no—
321D4×C11—42no—
322D4×C11—84no—
323C2×C4×C11—22no—
324C2×C4×C11—24no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11C22×D412yes—
334C2×C4×C11C22×D411yescharacteristic
335C2×C4×C11C2×#4112yes—
336C2×C4×C11C2×#4112yes—
337C2×C4×C11C2511yescharacteristic
338C22⋊D11—28no—
339C22⋊D11—28no—
340C22⋊D11—48no—
341C22⋊D11—84no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—48no—
352C2×Dic11—84no—
353C2×Dic11#12314yes—
354C2×Dic11C22×D412yes—
355C2×Dic11C22×D412yes—
356D44—28no—
357C4×D11—24no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—84no—
361C4×D11—84no—
362C4×D11—84no—
363C4×D11#12318yes—
364C4×D11C2×#4114yes—
365C4×D11C2×#4114yes—
366Dic22—28no—
367Dic22—22no—
368Dic22—22no—
369Dic22—42no—
370C8×C11—22no—
371C8×C11—22no—
372C11⋊C8—22no—
373C11⋊C8—22no—
374C22×#41—111no—
375C22×#41—111no—
376C22×M16—111no—
377C23×C8—111no—
378#537—118no—
379#537—224no—
380C2×C22⋊Q8—111no—
381C2×C22⋊Q8—111no—
382C2×C22⋊Q8—221no—
383C2×#121—111no—
384C2×#121—221no—
385C2×#121—221no—
386C2×#121—221no—
387C2×#121C2×D1111yescharacteristic
388#520—118no—
389#520—224no—
390C2×C4×Q8—221no—
391C2×C4×D4—221no—
392C2×C4×D4—221no—
393C2×C4×D4—221no—
394C2×#117—111no—
395C2×#117—111no—
396C2×#117C2×D1111yescharacteristic
397C22×C4⋊C4—111no—
398C22×C4⋊C4—111no—
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401#485—118no—
402#485—118no—
403#484—118no—
404#484—118no—
405#482—118no—
406#482C2×D1118yescomplemented
407#480—118no—
408#480—118no—
409#428—118no—
410C2×#107—111no—
411C2×#107—111no—
412C2×#107—111no—
413C2×#107—111no—
414C2×#107—111no—
415C2×#107—118no—
416C2×#107C2×D1111yescharacteristic
417C2×#106—111no—
418C2×#106C2×D1111yescharacteristic
419#417—118no—
420#416—118no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102C2×D1111yescharacteristic
428C2×#102C2×D1111yescharacteristic
429#408—118no—
430C2×C22⋊C8—111no—
431C2×C22⋊C8—111no—
432C2×C22⋊C8—111no—
433C2×C22⋊C8C2×D1111yescharacteristic
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—44no—
438C22×C11—42no—
439C22×C11—42no—
440C22×C11—42no—
441C22×C11—84no—
442C22×C11C2×#12312yes—
443C22×C11#57612yes—
444C22×C11#57812yes—
445C22×C11C23×D411yescharacteristic
446C2×D11—28no—
447C2×D11—22no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—44no—
453C2×D11C2×#12314yes—
454C4×C11—22no—
455C4×C11—42no—
456C4×C11—42no—
457C4×C11—42no—
458C4×C11C2×#12312yes—
459C4×C11C22×#4111yescharacteristic
460C4×C11C22×#4111yescharacteristic
461Dic11—22no—
462Dic11—42no—
463Dic11—42no—
464Dic11—42no—
465Dic11—42no—
466Dic11C2×#12314yes—
467C2×#41—114no—
468C2×#41—114no—
469C2×#41—114no—
470C2×#41—224no—
471C2×#41—224no—
472C2×#41—222no—
473C2×#41—224no—
474C2×#41—224no—
475C22×Q8—111no—
476C22×Q8—111no—
477C22×D4—21no—
478C22×D4—111no—
479C22×D4—111no—
480C22×D4—111no—
481C22×D4—221no—
482C22×D4—221no—
483C22×D4C22×D1111yescharacteristic
484C23×C4—111no—
485C23×C4—111no—
486C23×C4—221no—
487C23×C4—221no—
488C23×C4—221no—
489C23×C4—221no—
490C23×C4—221no—
491C23×C4C22×D1111yescharacteristic
492C2×M16—114no—
493C2×M16—224no—
494C22×C8—111no—
495C22×C8—111no—
496C22×C8—114no—
497C22×C8—224no—
498C22×C8C22×D1111yescharacteristic
499C22×C8C22×D1111yescharacteristic
500C22⋊Q8—114no—
501C22⋊Q8—114no—
502C22⋊Q8—228no—
503C22⋊Q8—222no—
504C22⋊Q8—222no—
505#121—22no—
506#121—114no—
507#121—228no—
508#121—222no—
509#121—228no—
510#121—228no—
511#121C22×D1114yes—
512C4×Q8—228no—
513C4×D4—228no—
514C4×D4—228no—
515C4×D4—228no—
516#117—22no—
517#117—114no—
518#117—114no—
519#117—222no—
520#117—222no—
521#117C22×D1114yes—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—222no—
532C2×C4⋊C4—221no—
533C2×C4⋊C4—221no—
534C2×C4⋊C4—221no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—222no—
538C2×C4⋊C4—221no—
539C2×C4⋊C4C22×D1111yescharacteristic
540C2×C4⋊C4C22×D1111yescharacteristic
541C2×C4⋊C4C22×D1111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C22⋊C4—221no—
549C2×C42—21no—
550C2×C42—221no—
551C2×C42—221no—
552#107—114no—
553#107—114no—
554#107—114no—
555#107—114no—
556#107—114no—
557#107C22×D1114yes—
558#106—114no—
559#106C22×D1114yes—
560#103—114no—
561#103—114no—
562#103—114no—
563#103—114no—
564#102—114no—
565#102—114no—
566#102C22×D1114yes—
567#102C22×D1114yes—
568C22⋊C8—114no—
569C22⋊C8—114no—
570C22⋊C8—114no—
571C22⋊C8C22×D1114yes—
572C2×C11—42no—
573C2×C11—82no—
574C2×C11#309814yescomplemented
575C2×C11C22×#12311yescharacteristic
576C2×C11C2×#57611yescharacteristic
577C2×C11C2×#57811yescharacteristic
578D11—24no—
579D11—42no—
580C24—21no—
581C24—111no—
582C24—111no—
583C24D4×D1111yescharacteristic
584#41—2216no—
585#41—228no—
586#41—228no—
587#41—228no—
588#41—228no—
589#41—448no—
590C2×Q8—114no—
591C2×Q8—112no—
592C2×Q8—224no—
593C2×Q8—221no—
594C2×Q8—222no—
595C2×Q8—222no—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—82no—
601C2×D4—114no—
602C2×D4—114no—
603C2×D4—114no—
604C2×D4—224no—
605C2×D4—224no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—444no—
610C2×D4—882no—
611C2×D4C23×D1112yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—111no—
618C22×C4—112no—
619C22×C4—114no—
620C22×C4—114no—
621C22×C4—112no—
622C22×C4—111no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—224no—
626C22×C4—224no—
627C22×C4—224no—
628C22×C4—224no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—221no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—224no—
636C22×C4—444no—
637C22×C4—882no—
638C22×C4—882no—
639C22×C4—882no—
640C22×C4—882no—
641C22×C4D4×D1112yes—
642C22×C4D4×D1111yescharacteristic
643C22×C4C23×D1112yes—
644C22×C4C23×D1111yescharacteristic
645M16—228no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—112no—
649C2×C8—112no—
650C2×C8—228no—
651C2×C8—222no—
652C2×C8—222no—
653C2×C8C23×D1112yes—
654C2×C8C23×D1112yes—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—112no—
659C4⋊C4—112no—
660C4⋊C4—112no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—221no—
666C4⋊C4—221no—
667C4⋊C4—224no—
668C4⋊C4—221no—
669C4⋊C4—224no—
670C4⋊C4C23×D1112yes—
671C4⋊C4C23×D1112yes—
672C4⋊C4C23×D1112yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C42—24no—
681C42—224no—
682C42—224no—
683C11C2×#309811yescharacteristic, complemented, Sylow
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—114no—
692C23—112no—
693C23—112no—
694C23—222no—
695C23—222no—
696C23—222no—
697C23—222no—
698C23—222no—
699C23C2×D4×D1112yes—
700C23C2×D4×D1111yescharacteristic
701Q8—228no—
702Q8—222no—
703Q8—222no—
704Q8—442no—
705D4—22no—
706D4—22no—
707D4—42no—
708D4—84no—
709D4—228no—
710D4—228no—
711D4—228no—
712D4—448no—
713D4—884no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—114no—
725C2×C4—112no—
726C2×C4—118no—
727C2×C4—114no—
728C2×C4—114no—
729C2×C4—112no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—448no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—884no—
744C2×C4—884no—
745C2×C4—884no—
746C2×C4—884no—
747C2×C4C2×D4×D1112yes—
748C2×C4C2×D4×D1111yescharacteristic
749C2×C4#41×D1112yes—
750C2×C4#41×D1112yes—
751C2×C4C24×D1111yescharacteristic
752C8—22no—
753C8—22no—
754C8—222no—
755C8—222no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—114no—
765C22—228no—
766C22—222no—
767C22—222no—
768C22—222no—
769C22—222no—
770C22—222no—
771C22—444no—
772C22D11×#12312yes—
773C22#1062330212yes—
774C22#1062330512yes—
775C22C22×D4×D1111yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—114no—
781C4—222no—
782C4—442no—
783C4—442no—
784C4—442no—
785C4—442no—
786C4D11×#12312yes—
787C4C2×#41×D1111yescharacteristic
788C4C2×#41×D1111yescharacteristic
789C2—42no—
790C2—82no—
791C2—224no—
792C2—442no—
793C2#1307859114yesdirect product factor
794C2C2×D11×#12311yescharacteristic
795C2C2×#1062330511yescharacteristic
796C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
prime radicalC2×#10623139C2
hypercenterC2×#482D11
hypocenterC11C2×#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#10623054C2semidirect
3. #13078591C2direct (N × H)
4. C2×#10622497C2semidirect
5. C2×#10622335C2semidirect
6. C2×#10622480C2semidirect
7. C2×#10622609C2semidirect
8. C2×#10622397C2semidirect
9. C2×#10622387C2semidirect
10. C2×#10622646C2semidirect
11. C2×#10622474C2semidirect
12. C2×D11×#107C2semidirect
13. C2×#10622384C2semidirect
14. C2×#10622385C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#482C2semidirect
31. #10623054C22semidirect
44. C11×#482C22semidirect
59. #10622646C22semidirect
60. #10622609C22semidirect
67. #10622497C22semidirect
68. D11×#107C22semidirect
69. #10622480C22semidirect
70. #10622474C22semidirect
71. #10622397C22semidirect
72. #10622387C22semidirect
73. #10622385C22semidirect
74. #10622384C22semidirect
75. #10622340C22semidirect
76. #10622335C22semidirect
294. C2×#482D11semidirect
406. #482C2×D11semidirect
574. C2×C11#3098semidirect
683. C11C2×#3098semidirect
793. C2#13078591direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231392
C2×#106230542
#130785912
C2×#106224972
C2×#106223352
C2×#106224802
C2×#106226092
C2×#106223972
C2×#106223872
C2×#106226462
C2×#106224742
C2×D11×#1072
C2×#106223842
C2×#106223852
C2×#106223402
C2×C11×#4822
C2×#309811