Finite Group Databasebeta

← C2×#13078580 #15621607

Subgroups — C2×#13078580 #15621607

Order 2816.

2170 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623159C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic
3#13078580C2116yesmaximal, direct product factor
4C2×#10622335C211yesmaximal, characteristic, complemented
5C2×#10622422C211yesmaximal, characteristic, complemented
6C2×#10622501C211yesmaximal, characteristic, complemented
7C2×#10622609C211yesmaximal, characteristic, complemented
8C2×#10622427C211yesmaximal, characteristic, complemented
9C2×#10622475C211yesmaximal, characteristic, complemented
10C2×#10622656C211yesmaximal, characteristic, complemented
11C2×#10622474C211yesmaximal, characteristic, complemented
12C2×#10622493C211yesmaximal, characteristic, complemented
13C2×#10622415C211yesmaximal, characteristic, complemented
14C2×D11×#103C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic
16C2×C11×#485C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×#66999C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4313C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26#10623159—24no—
27#10623159C2218yes—
28#10623054—24no—
29#10623054C2218yes—
30C2×#66950C2211yescharacteristic
31C2×#66947—21no—
32C2×#66945C2211yescharacteristic
33C2×#66945C2211yescharacteristic
34C2×#66945C2211yescharacteristic
35C2×C4⋊C4×D11C2211yescharacteristic
36C2×C4⋊C4×D11C2211yescharacteristic
37C2×#66941—21no—
38C2×#66938—21no—
39C2×#66936—21no—
40C2×(C22⋊D11)⋊C4—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×C4×D44—21no—
43C2×C4×Dic22—21no—
44C11×#485C2218yescomplemented
45C2×C11×#107C2211yescharacteristic
46C2×C11×#106C2211yescharacteristic
47C2×C11×#103C2211yescharacteristic
48C2×C11×#103C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66899C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×(C2×D11)⋊C8C2211yescharacteristic
55C2×#66882C2211yescharacteristic
56C2×#66882C2211yescharacteristic
57C2×#66880C2211yescharacteristic
58C2×#66880C2211yescharacteristic
59#10622656C2218yescomplemented
60#10622609C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622501C2218yescomplemented
68#10622493C2218yescomplemented
69#10622475C2218yescomplemented
70#10622474C2218yescomplemented
71#10622427C2218yescomplemented
72#10622422C2218yescomplemented
73#10622415C2218yescomplemented
74D11×#103C2218yescomplemented
75#10622340C2218yes—
76#10622335C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C22×C22⋊D11D411yescharacteristic
80C22×C22⋊D11D411yescharacteristic
81C23×Dic11—21no—
82C2×Q8×D11—22no—
83C2×Q8×D11—24no—
84C2×Q8×D11—24no—
85C2×Q8×D11C2314yes—
86C2×#4339—24no—
87C2×#4339—24no—
88C2×#4339D414yes—
89C2×#4339C2314yes—
90C22×D44D411yescharacteristic
91C22×C4×D11—21no—
92C22×C4×D11—21no—
93C22×C4×D11—21no—
94C22×C4×D11C2311yescharacteristic
95C22×C4×D11C2311yescharacteristic
96C22×Dic22—21no—
97C22×Dic22D411yescharacteristic
98C22×Dic22C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×C22⋊Q8—22no—
102C11×C22⋊Q8C2314yes—
103C11×#117—22no—
104C11×#117C2314yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C42×C11—21no—
112C2×C22⋊Dic11—21no—
113#66999—22no—
114#66999C2314yes—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2314yes—
127#66977—22no—
128#66977C2314yes—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11—21no—
136C22×C11⋊C8C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C2×#4313—24no—
139C2×#4313C2314yes—
140C2×C8×D11—24no—
141C2×C8×D11C2314yes—
142#66950—22no—
143#66950C2314yes—
144#66947—28no—
145#66945—22no—
146#66945—22no—
147#66945—22no—
148#66945C2314yes—
149#66945C2314yes—
150#66945C2314yes—
151C4⋊C4×D11—22no—
152C4⋊C4×D11—22no—
153C4⋊C4×D11C2314yes—
154C4⋊C4×D11C2314yes—
155#66941—28no—
156#66938—28no—
157#66936—28no—
158(C22⋊D11)⋊C4—28no—
159(C22⋊D11)⋊C4—28no—
160C4×D44—28no—
161C4×Dic22—28no—
162C11×#107C2314yes—
163C11×#106C2314yes—
164C11×#103C2314yes—
165C11×#103C2314yes—
166C11×C22⋊C8C2314yes—
167#66899C2314yes—
168#66899C2314yes—
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#66872C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182C2×#3097—111nomaximal, Sylow
183C24×C11C2×D411yescharacteristic
184C23×D11C2×D411yescharacteristic
185C23×D11C2×D411yescharacteristic
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11C2412yes—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11C2×D414yes—
203C2×C22⋊D11C2×D414yes—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—24no—
209C22×Dic11—82no—
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212Q8×D11—28no—
213Q8×D11—28no—
214Q8×D11—48no—
215#4339—216no—
216#4339—28no—
217#4339—28no—
218C2×D44—24no—
219C2×D44C2×D414yes—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—24no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—44no—
226C2×C4×D11—82no—
227C2×C4×D11—82no—
228C2×C4×D11C2×D412yes—
229C2×C4×D11C2×D412yes—
230C2×C4×D11#4114yes—
231C2×C4×D11#4114yes—
232C2×C4×D11C2412yes—
233C2×C4×D11C2412yes—
234C2×Dic22—24no—
235C2×Dic22—24no—
236C2×Dic22—21no—
237C2×Dic22—22no—
238C2×Dic22—22no—
239C2×Dic22—44no—
240C2×Dic22C2×D414yes—
241C2×Dic22C2412yes—
242C2×C8×C11—22no—
243C2×C8×C11—22no—
244C2×C8×C11C2412yes—
245C2×C8×C11C2412yes—
246C11×C4⋊C4—24no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4C2412yes—
251C11×C4⋊C4C2412yes—
252C11×C4⋊C4C2412yes—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C42×C11—24no—
256C22⋊Dic11—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262C4⋊Dic11—24no—
263C4⋊Dic11—24no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11C2412yes—
268C4⋊Dic11C2412yes—
269C4⋊Dic11C2412yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274C4×Dic11—24no—
275C4×Dic11—24no—
276C4×Dic11—24no—
277C2×C11⋊C8—22no—
278C2×C11⋊C8—22no—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281#4313—28no—
282C8×D11—28no—
283C2×#536—111no—
284C2×#520—111no—
285#3097—1116no—
286C2×#484—111no—
287C2×#484—111no—
288C2×#485—111no—
289C2×#485—111no—
290C2×#485—111no—
291C2×#485D1111yescharacteristic, complemented
292C2×#483—111no—
293C2×#483—111no—
294C2×#428—111no—
295C2×#427—111no—
296C2×#419—111no—
297C22×#103—111no—
298C2×#408—111no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11C22×D412yes—
303C23×C11C22×D411yescharacteristic
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11#12314yes—
310C22×D11C22×D412yes—
311C22×D11C22×D412yes—
312Q8×C11—22no—
313Q8×C11—22no—
314Q8×C11—42no—
315C2×C4×C11—22no—
316C2×C4×C11—24no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C2×#4112yes—
330C2×C4×C11C2×#4112yes—
331C2×C4×C11C2511yescharacteristic
332C22⋊D11—28no—
333C22⋊D11—28no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—84no—
344C2×Dic11#12314yes—
345C2×Dic11C22×D412yes—
346C2×Dic11C22×D412yes—
347D44—28no—
348C4×D11—24no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—48no—
352C4×D11—84no—
353C4×D11—84no—
354C4×D11#12318yes—
355C4×D11C2×#4114yes—
356C4×D11C2×#4114yes—
357Dic22—28no—
358Dic22—22no—
359Dic22—22no—
360Dic22—42no—
361Dic22—48no—
362C8×C11—22no—
363C8×C11—22no—
364C11⋊C8—22no—
365C11⋊C8—22no—
366C22×#41—111no—
367C23×Q8—111no—
368C22×M16—111no—
369C23×C8—111no—
370#536—118no—
371#536—224no—
372C2×C4⋊Q8—221no—
373C2×#124—221no—
374C2×#123—221no—
375C2×#123—221no—
376C2×C22⋊Q8—111no—
377C2×C22⋊Q8—111no—
378C2×C22⋊Q8—111no—
379C2×C22⋊Q8C2×D1111yescharacteristic
380#520—118no—
381#520—224no—
382C2×C4×Q8—221no—
383C2×C4×D4—221no—
384C2×C4×D4—221no—
385C2×C4×D4—221no—
386C2×#117—111no—
387C2×#117—111no—
388C2×#117—111no—
389C2×#117C2×D1111yescharacteristic
390C22×C4⋊C4—111no—
391C22×C4⋊C4—111no—
392C22×C4⋊C4—111no—
393#485—118no—
394#485—118no—
395#485—118no—
396#485C2×D1118yescomplemented
397#484—118no—
398#484—118no—
399#483—118no—
400#483—118no—
401#428—118no—
402#427—118no—
403C2×#107—111no—
404C2×#107—111no—
405C2×#107—111no—
406C2×#107C2×D1111yescharacteristic
407C2×#106—111no—
408C2×#106—111no—
409C2×#106—111no—
410C2×#106C2×D1111yescharacteristic
411#419—118no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—118no—
419C2×#103C2×D1111yescharacteristic
420C2×#103C2×D1111yescharacteristic
421#408—118no—
422C2×C22⋊C8—111no—
423C2×C22⋊C8—111no—
424C2×C22⋊C8—111no—
425C2×C22⋊C8C2×D1111yescharacteristic
426C22×C11—22no—
427C22×C11—22no—
428C22×C11—22no—
429C22×C11—44no—
430C22×C11C2×#12312yes—
431C22×C11#57712yes—
432C22×C11#57812yes—
433C22×C11C23×D411yescharacteristic
434C2×D11—28no—
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—22no—
440C2×D11—44no—
441C2×D11C2×#12314yes—
442C4×C11—22no—
443C4×C11—42no—
444C4×C11—42no—
445C4×C11—42no—
446C4×C11—42no—
447C4×C11C2×#12312yes—
448C4×C11C22×#4111yescharacteristic
449C4×C11C22×#4111yescharacteristic
450Dic11—22no—
451Dic11—42no—
452Dic11—42no—
453Dic11—42no—
454Dic11—42no—
455Dic11C2×#12314yes—
456C2×#41—114no—
457C2×#41—114no—
458C2×#41—224no—
459C2×#41—224no—
460C22×Q8—111no—
461C22×Q8—114no—
462C22×Q8—111no—
463C22×Q8—221no—
464C22×Q8—222no—
465C22×Q8—224no—
466C22×Q8—224no—
467C22×Q8C22×D1111yescharacteristic
468C22×D4—111no—
469C22×D4—111no—
470C22×D4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—221no—
474C23×C4—221no—
475C23×C4—221no—
476C23×C4—221no—
477C23×C4C22×D1111yescharacteristic
478C2×M16—114no—
479C2×M16—224no—
480C22×C8—111no—
481C22×C8—111no—
482C22×C8—114no—
483C22×C8—224no—
484C22×C8C22×D1111yescharacteristic
485C22×C8C22×D1111yescharacteristic
486C4⋊Q8—228no—
487#124—228no—
488#123—228no—
489#123—228no—
490C22⋊Q8—22no—
491C22⋊Q8—114no—
492C22⋊Q8—114no—
493C22⋊Q8—114no—
494C22⋊Q8—222no—
495C22⋊Q8—222no—
496C22⋊Q8—222no—
497C22⋊Q8C22×D1114yes—
498C4×Q8—228no—
499C4×D4—228no—
500C4×D4—228no—
501C4×D4—228no—
502#117—22no—
503#117—114no—
504#117—114no—
505#117—114no—
506#117—222no—
507#117—222no—
508#117—222no—
509#117C22×D1114yes—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—111no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—222no—
518C2×C4⋊C4—222no—
519C2×C4⋊C4—221no—
520C2×C4⋊C4—221no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4—221no—
524C2×C4⋊C4—222no—
525C2×C4⋊C4—221no—
526C2×C4⋊C4C22×D1111yescharacteristic
527C2×C4⋊C4C22×D1111yescharacteristic
528C2×C4⋊C4C22×D1111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—221no—
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—221no—
539C2×C42—221no—
540C2×C42—221no—
541#107—114no—
542#107—114no—
543#107—114no—
544#107C22×D1114yes—
545#106—114no—
546#106—114no—
547#106—114no—
548#106C22×D1114yes—
549#103—114no—
550#103—114no—
551#103—114no—
552#103—114no—
553#103—114no—
554#103—114no—
555#103C22×D1114yes—
556#103C22×D1114yes—
557C22⋊C8—114no—
558C22⋊C8—114no—
559C22⋊C8—114no—
560C22⋊C8C22×D1114yes—
561C2×C11—42no—
562C2×C11#309714yescomplemented
563C2×C11C22×#12311yescharacteristic
564C2×C11C2×#57711yescharacteristic
565C2×C11C2×#57811yescharacteristic
566D11—24no—
567D11—42no—
568C24—111no—
569C24—111no—
570C24D4×D1111yescharacteristic
571#41—2216no—
572#41—228no—
573#41—228no—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—114no—
578C2×Q8—112no—
579C2×Q8—224no—
580C2×Q8—224no—
581C2×Q8—228no—
582C2×Q8—228no—
583C2×Q8—221no—
584C2×Q8—222no—
585C2×Q8—222no—
586C2×Q8—444no—
587C2×Q8—448no—
588C2×Q8C23×D1112yes—
589C2×D4—114no—
590C2×D4—114no—
591C2×D4—114no—
592C2×D4—224no—
593C2×D4—224no—
594C2×D4—224no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—111no—
602C22×C4—112no—
603C22×C4—114no—
604C22×C4—114no—
605C22×C4—112no—
606C22×C4—111no—
607C22×C4—112no—
608C22×C4—112no—
609C22×C4—224no—
610C22×C4—224no—
611C22×C4—224no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—221no—
615C22×C4—221no—
616C22×C4—221no—
617C22×C4—221no—
618C22×C4—224no—
619C22×C4—444no—
620C22×C4—882no—
621C22×C4—882no—
622C22×C4—882no—
623C22×C4D4×D1112yes—
624C22×C4D4×D1111yescharacteristic
625C22×C4C23×D1112yes—
626C22×C4C23×D1111yescharacteristic
627M16—228no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—112no—
631C2×C8—112no—
632C2×C8—228no—
633C2×C8—222no—
634C2×C8—222no—
635C2×C8C23×D1112yes—
636C2×C8C23×D1112yes—
637C4⋊C4—24no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—112no—
642C4⋊C4—112no—
643C4⋊C4—112no—
644C4⋊C4—224no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—221no—
649C4⋊C4—221no—
650C4⋊C4—224no—
651C4⋊C4—221no—
652C4⋊C4—224no—
653C4⋊C4C23×D1112yes—
654C4⋊C4C23×D1112yes—
655C4⋊C4C23×D1112yes—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—224no—
662C22⋊C4—224no—
663C22⋊C4—224no—
664C42—24no—
665C42—224no—
666C42—224no—
667C42—224no—
668C11C2×#309711yescharacteristic, complemented, Sylow
669C23—22no—
670C23—22no—
671C23—22no—
672C23—114no—
673C23—112no—
674C23—112no—
675C23—222no—
676C23—222no—
677C23—222no—
678C23—222no—
679C23—222no—
680C23C2×D4×D1112yes—
681C23C2×D4×D1111yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—228no—
686Q8—222no—
687Q8—222no—
688Q8—448no—
689Q8—442no—
690D4—228no—
691D4—228no—
692D4—228no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—114no—
706C2×C4—112no—
707C2×C4—118no—
708C2×C4—114no—
709C2×C4—114no—
710C2×C4—112no—
711C2×C4—222no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—448no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—884no—
725C2×C4—884no—
726C2×C4—884no—
727C2×C4C2×D4×D1112yes—
728C2×C4C2×D4×D1111yescharacteristic
729C2×C4#41×D1112yes—
730C2×C4#41×D1112yes—
731C2×C4C24×D1111yescharacteristic
732C8—22no—
733C8—22no—
734C8—222no—
735C8—222no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—44no—
740C22—114no—
741C22—228no—
742C22—222no—
743C22—222no—
744C22—222no—
745C22—222no—
746C22—222no—
747C22—444no—
748C22D11×#12312yes—
749C22#1062330212yes—
750C22#1062330912yes—
751C22C22×D4×D1111yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—114no—
758C4—222no—
759C4—442no—
760C4—442no—
761C4—442no—
762C4—442no—
763C4D11×#12312yes—
764C4C2×#41×D1111yescharacteristic
765C4C2×#41×D1111yescharacteristic
766C2—42no—
767C2—224no—
768C2—442no—
769C2#1307858014yesdirect product factor
770C2C2×D11×#12311yescharacteristic
771C2C2×#1062330911yescharacteristic
772C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#485D11
hypocenterC11C2×#3097
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
3. #13078580C2direct (N × H)
4. C2×#10622335C2semidirect
5. C2×#10622422C2semidirect
6. C2×#10622501C2semidirect
7. C2×#10622609C2semidirect
8. C2×#10622427C2semidirect
9. C2×#10622475C2semidirect
10. C2×#10622656C2semidirect
11. C2×#10622474C2semidirect
12. C2×#10622493C2semidirect
13. C2×#10622415C2semidirect
14. C2×D11×#103C2semidirect
16. C2×C11×#485C2semidirect
44. C11×#485C22semidirect
59. #10622656C22semidirect
60. #10622609C22semidirect
67. #10622501C22semidirect
68. #10622493C22semidirect
69. #10622475C22semidirect
70. #10622474C22semidirect
71. #10622427C22semidirect
72. #10622422C22semidirect
73. #10622415C22semidirect
74. D11×#103C22semidirect
76. #10622335C22semidirect
291. C2×#485D11semidirect
396. #485C2×D11semidirect
562. C2×C11#3097semidirect
668. C11C2×#3097semidirect
769. C2#13078580direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231592
C2×#106230542
#130785802
C2×#106223352
C2×#106224222
C2×#106225012
C2×#106226092
C2×#106224272
C2×#106224752
C2×#106226562
C2×#106224742
C2×#106224932
C2×#106224152
C2×D11×#1032
C2×#106223402
C2×C11×#4852
C2×#309711