Finite Group Databasebeta

← C2×#13079952 #15626577

Subgroups — C2×#13079952 #15626577

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×#10623109C211yesmaximal, characteristic, complemented
2C2×#10623222C211yesmaximal, characteristic
3#13079952C2116yesmaximal, direct product factor
4C2×#10622676C211yesmaximal, characteristic, complemented
5C2×#10622467C211yesmaximal, characteristic, complemented
6C2×#10622503C211yesmaximal, characteristic, complemented
7C2×#10622500C211yesmaximal, characteristic, complemented
8C2×#10622426C211yesmaximal, characteristic, complemented
9C2×#10622420C211yesmaximal, characteristic
10C2×#10622477C211yesmaximal, characteristic
11C2×#10622458C211yesmaximal, characteristic, complemented
12C2×#10622641C211yesmaximal, characteristic, complemented
13C2×#10622406C211yesmaximal, characteristic, complemented
14C2×#10622431C211yesmaximal, characteristic, complemented
15C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#479C211yesmaximal, characteristic, complemented
17C2×C11×#125C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C22×Dic44C2211yescharacteristic
24C22×#4314C2211yescharacteristic
25C22×C8×D11C2211yescharacteristic
26C22×C8×D11C2211yescharacteristic
27#10623222—24no—
28#10623222C2218yes—
29#10623109—24no—
30#10623109C2218yescomplemented
31C2×#66951—21no—
32C2×#66950C2211yescharacteristic
33C2×#66950C2211yescharacteristic
34C2×#66949—21no—
35C2×#66948C2211yescharacteristic
36C2×#66947—21no—
37C2×#66946—21no—
38C2×#66946C2211yescharacteristic
39C2×#66945—21no—
40C2×#66942—21no—
41C2×#66941C2211yescharacteristic
42C2×#66940C2211yescharacteristic
43C2×#66928C2211yescharacteristic
44C2×#66925—21no—
45C2×C42×D11C2211yescharacteristic
46C2×C4×Dic22—21no—
47C2×C4×Dic22C2211yescharacteristic
48C11×#479C2218yescomplemented
49C2×C11×#107C2211yescharacteristic
50C2×C11×#106C2211yescharacteristic
51C2×C11×C4⋊C8C2211yescharacteristic
52C2×C11×#103C2211yescharacteristic
53C2×C11×#103C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66880C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58#10622676C2218yescomplemented
59#10622641C2218yescomplemented
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622503C2218yescomplemented
68#10622500C2218yescomplemented
69#10622477C2218yes—
70#10622467C2218yescomplemented
71#10622458C2218yescomplemented
72D11×C4⋊C8C2218yescomplemented
73#10622431C2218yescomplemented
74#10622426C2218yescomplemented
75#10622420C2218yes—
76#10622406C2218yescomplemented
77C22×Q8×C11C2311yescharacteristic
78C22×D44—21no—
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C22×C4×D11D411yescharacteristic
82C22×C4×D11D411yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C22×Dic22—21no—
85C22×Dic22C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×#125—22no—
90C11×#125C2314yes—
91C4×Q8×C11—22no—
92C4×Q8×C11C2314yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101#66999—22no—
102#66999C2314yes—
103#66997—22no—
104#66997C2314yes—
105C2×#4326—42no—
106C2×#4326C2314yes—
107C2×#4325—42no—
108C2×#4325C2314yes—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×C4×Dic11—21no—
126C2×C4×Dic11—21no—
127C2×C4×Dic11D411yescharacteristic
128C2×C4×Dic11D411yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C2×Dic44—42no—
133C2×Dic44C2314yes—
134C2×#4314—42no—
135C2×#4314C2314yes—
136C2×C8×D11—42no—
137C2×C8×D11—42no—
138C2×C8×D11C2314yes—
139C2×C8×D11C2314yes—
140#66951—28no—
141#66950—22no—
142#66950—22no—
143#66950C2314yes—
144#66950C2314yes—
145#66949—28no—
146#66948—22no—
147#66948C2314yes—
148#66947—28no—
149#66946—28no—
150#66946—22no—
151#66946C2314yes—
152#66945—28no—
153#66942—28no—
154#66941—22no—
155#66941C2314yes—
156#66940—22no—
157#66940C2314yes—
158#66928—22no—
159#66928C2314yes—
160#66925—28no—
161C42×D11D414yes—
162C42×D11C2314yes—
163C4×Dic22—22no—
164C4×Dic22—28no—
165C4×Dic22C2314yes—
166C11×#107C2314yes—
167C11×#106C2314yes—
168C11×C4⋊C8C2314yes—
169C11×#103C2314yes—
170C11×#103C2314yes—
171#66885C2314yes—
172#66880C2314yes—
173Dic11⋊C8C2314yes—
174Dic11⋊C8C2314yes—
175#66874C2314yes—
176#66874C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66872C2314yes—
180#66871C2314yes—
181C4⋊(C11⋊C8)C2314yes—
182C2×#3248—111nomaximal, Sylow
183C23×D11—21no—
184C23×D11C2×D411yescharacteristic
185C2×Q8×C11—21no—
186C2×Q8×C11—22no—
187C2×Q8×C11—22no—
188C2×Q8×C11C2412yes—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201C22×Dic11C2×D411yescharacteristic
202C2×D44—24no—
203C2×D44—21no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—44no—
207C2×D44C2412yes—
208C2×C4×D11—24no—
209C2×C4×D11—24no—
210C2×C4×D11—24no—
211C2×C4×D11—22no—
212C2×C4×D11—22no—
213C2×C4×D11—44no—
214C2×C4×D11C2×D412yes—
215C2×C4×D11C2×D414yes—
216C2×C4×D11C2×D414yes—
217C2×C4×D11C2412yes—
218C2×Dic22—24no—
219C2×Dic22—21no—
220C2×Dic22—21no—
221C2×Dic22—22no—
222C2×Dic22—22no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—44no—
226C2×Dic22C2412yes—
227C2×Dic22C2412yes—
228C2×C8×C11—22no—
229C2×C8×C11—22no—
230C2×C8×C11C2412yes—
231C2×C8×C11C2412yes—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C11×C4⋊C4C2412yes—
241C42×C11—24no—
242C42×C11C2×D412yes—
243C42×C11C2412yes—
244#4326—44no—
245#4325—44no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11—21no—
256C4⋊Dic11C2412yes—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263C4×Dic11—24no—
264C4×Dic11—24no—
265C4×Dic11C2×D414yes—
266C4×Dic11C2×D412yes—
267C4×Dic11C2×D414yes—
268C4×Dic11C2412yes—
269C2×C11⋊C8—22no—
270C2×C11⋊C8—22no—
271C2×C11⋊C8C2412yes—
272C2×C11⋊C8C2412yes—
273Dic44—44no—
274#4314—44no—
275C8×D11—44no—
276C8×D11—44no—
277C2×#533—111no—
278C2×#529—111no—
279#3248—1116no—
280C2×#479—111no—
281C2×#479D1111yescharacteristic, complemented
282C2×#475—111no—
283C2×#474—111no—
284C2×#467—111no—
285C2×#467—111no—
286C2×#465—111no—
287C2×#465—111no—
288C2×#464—111no—
289C2×#464—111no—
290C2×#462—111no—
291C2×#461—111no—
292C22×C4⋊C8—111no—
293C23×C11C22×D411yescharacteristic
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11—42no—
300C22×D11#13714yes—
301C22×D11C22×D412yes—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11—42no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11H(5,𝔽2)12yes—
319C2×C4×C112−1+412yes—
320C2×C4×C11C2511yescharacteristic
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11#13514yes—
330C2×Dic11C22×D412yes—
331C2×Dic11C22×D412yes—
332C2×Dic11C22×D412yes—
333D44—22no—
334D44—22no—
335D44—48no—
336D44—42no—
337C4×D11—28no—
338C4×D11—24no—
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—28no—
342C4×D11—48no—
343Dic22—22no—
344Dic22—22no—
345Dic22—22no—
346Dic22—22no—
347Dic22—42no—
348Dic22—42no—
349Dic22—48no—
350C8×C11—22no—
351C8×C11—22no—
352C11⋊C8—22no—
353C11⋊C8—22no—
354C22×Q16—111no—
355C22×Q16—111no—
356C22×SD16—111no—
357C22×SD16—111no—
358C23×C8—111no—
359C23×C8—111no—
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—221no—
368C2×#125C2×D1111yescharacteristic
369C2×#124—111no—
370C2×#123—221no—
371C2×C22⋊Q8—111no—
372C2×C22⋊Q8—111no—
373C2×C22⋊Q8—111no—
374C2×C22⋊Q8—221no—
375C2×#121—111no—
376C2×C4×Q8—111no—
377C2×C4×Q8—111no—
378C2×C4×Q8—221no—
379C2×C4×Q8C2×D1111yescharacteristic
380C2×C4×D4—111no—
381C2×C4×D4—221no—
382C2×#117—221no—
383C2×#117—221no—
384C22×C42—111no—
385#479—118no—
386#479C2×D1118yescomplemented
387#475—118no—
388#474—118no—
389#467—118no—
390#467—118no—
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×#106C2×D1111yescharacteristic
401C2×C4⋊C8—111no—
402C2×C4⋊C8—111no—
403C2×C4⋊C8—111no—
404C2×C4⋊C8—118no—
405C2×C4⋊C8C2×D1111yescharacteristic
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#53712yes—
415C22×C11C2×#13512yes—
416C22×C11C2×#13712yes—
417C22×C11C23×D411yescharacteristic
418C2×D11—22no—
419C2×D11—28no—
420C2×D11—22no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—84no—
425C2×D11C2×#13714yes—
426C4×C11—22no—
427C4×C11—22no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11—42no—
431C4×C11—42no—
432C4×C11#53712yes—
433C4×C11C2×H(5,𝔽2)11yescharacteristic
434C4×C11C2×2−1+411yescharacteristic
435Dic11—22no—
436Dic11—22no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11C2×#13514yes—
441C22×Q8—111no—
442C22×Q8—111no—
443C22×Q8—221no—
444C22×Q8C22×D1111yescharacteristic
445C22×D4—111no—
446C22×D4—221no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—221no—
451C2×Q16—114no—
452C2×Q16—114no—
453C2×Q16—442no—
454C2×Q16—442no—
455C2×SD16—114no—
456C2×SD16—114no—
457C2×SD16—442no—
458C2×SD16—442no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8—114no—
462C22×C8—114no—
463C22×C8—442no—
464C22×C8—442no—
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1111yescharacteristic
467C4⋊Q8—114no—
468C4⋊Q8—114no—
469C4⋊Q8—222no—
470C4⋊Q8—222no—
471#126—228no—
472#125—22no—
473#125—228no—
474#125C22×D1114yes—
475#124—114no—
476#124—222no—
477#123—228no—
478C22⋊Q8—114no—
479C22⋊Q8—114no—
480C22⋊Q8—114no—
481C22⋊Q8—222no—
482C22⋊Q8—222no—
483C22⋊Q8—228no—
484C22⋊Q8—222no—
485#121—114no—
486#121—222no—
487C4×Q8—22no—
488C4×Q8—114no—
489C4×Q8—114no—
490C4×Q8—228no—
491C4×Q8—222no—
492C4×Q8—222no—
493C4×Q8C22×D1114yes—
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—21no—
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⋊C4C22×D1111yescharacteristic
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C4⋊C4C22×D1111yescharacteristic
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C42—21no—
522C2×C42—111no—
523C2×C42—111no—
524C2×C42—111no—
525C2×C42—114no—
526C2×C42—114no—
527C2×C42—221no—
528C2×C42—221no—
529C2×C42C22×D1111yescharacteristic
530#107—114no—
531#107C22×D1114yes—
532#106—114no—
533#106C22×D1114yes—
534C4⋊C8—114no—
535C4⋊C8—114no—
536C4⋊C8—114no—
537C4⋊C8C22×D1114yes—
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#324814yescomplemented
547C2×C11C2×#53711yescharacteristic
548C2×C11C22×#13511yescharacteristic
549C2×C11C22×#13711yescharacteristic
550D11—24no—
551D11—82no—
552C24—111no—
553C24—221no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—112no—
558C2×Q8—112no—
559C2×Q8—224no—
560C2×Q8—221no—
561C2×Q8—221no—
562C2×Q8—222no—
563C2×Q8—222no—
564C2×Q8—222no—
565C2×Q8—222no—
566C2×Q8—444no—
567C2×Q8C23×D1112yes—
568C2×D4—112no—
569C2×D4—224no—
570C2×D4—221no—
571C2×D4—222no—
572C2×D4—222no—
573C2×D4—444no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—114no—
582C22×C4—114no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—444no—
594C22×C4D4×D1111yescharacteristic
595C22×C4D4×D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597Q16—444no—
598Q16—444no—
599SD16—444no—
600SD16—444no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—112no—
604C2×C8—112no—
605C2×C8—222no—
606C2×C8—222no—
607C2×C8—444no—
608C2×C8—444no—
609C2×C8C23×D1112yes—
610C2×C8C23×D1112yes—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—112no—
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—224no—
627C4⋊C4C23×D1112yes—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C42—24no—
638C42—114no—
639C42—112no—
640C42—114no—
641C42—112no—
642C42—224no—
643C42—224no—
644C42D4×D1112yes—
645C42C23×D1112yes—
646C11C2×#324811yescharacteristic, complemented, Sylow
647C23—114no—
648C23—112no—
649C23—222no—
650C23—222no—
651C23—222no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23C2×D4×D1111yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—222no—
660Q8—222no—
661Q8—222no—
662Q8—222no—
663Q8—448no—
664Q8—442no—
665Q8—442no—
666D4—222no—
667D4—222no—
668D4—448no—
669D4—442no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—114no—
681C2×C4—112no—
682C2×C4—112no—
683C2×C4—112no—
684C2×C4—228no—
685C2×C4—228no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—224no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—448no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4C2×D4×D1112yes—
699C2×C4C2×D4×D1112yes—
700C2×C4C2×D4×D1111yescharacteristic
701C2×C4#6704012yes—
702C2×C4#6704212yes—
703C2×C4C24×D1111yescharacteristic
704C8—22no—
705C8—22no—
706C8—222no—
707C8—222no—
708C22—114no—
709C22—222no—
710C22—228no—
711C22—222no—
712C22—442no—
713C22—442no—
714C22—442no—
715C22—884no—
716C22#1062316012yes—
717C22D11×#13512yes—
718C22D11×#13712yes—
719C22C22×D4×D1111yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—114no—
727C4—222no—
728C4—222no—
729C4—442no—
730C4—442no—
731C4—442no—
732C4#1062316012yes—
733C4C2×#6704011yescharacteristic
734C4C2×#6704211yescharacteristic
735C2—224no—
736C2—882no—
737C2#1307995214yesdirect product factor
738C2C2×#1062316011yescharacteristic
739C2C2×D11×#13511yescharacteristic
740C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#479D11
hypocenterC11C2×#3248
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#10623109C2semidirect
3. #13079952C2direct (N × H)
4. C2×#10622676C2semidirect
5. C2×#10622467C2semidirect
6. C2×#10622503C2semidirect
7. C2×#10622500C2semidirect
8. C2×#10622426C2semidirect
11. C2×#10622458C2semidirect
12. C2×#10622641C2semidirect
13. C2×#10622406C2semidirect
14. C2×#10622431C2semidirect
15. C2×D11×C4⋊C8C2semidirect
16. C2×C11×#479C2semidirect
30. #10623109C22semidirect
48. C11×#479C22semidirect
58. #10622676C22semidirect
59. #10622641C22semidirect
67. #10622503C22semidirect
68. #10622500C22semidirect
70. #10622467C22semidirect
71. #10622458C22semidirect
72. D11×C4⋊C8C22semidirect
73. #10622431C22semidirect
74. #10622426C22semidirect
76. #10622406C22semidirect
281. C2×#479D11semidirect
386. #479C2×D11semidirect
546. C2×C11#3248semidirect
646. C11C2×#3248semidirect
737. C2#13079952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106232222
#130799522
C2×#106226762
C2×#106224672
C2×#106225032
C2×#106225002
C2×#106224262
C2×#106224202
C2×#106224772
C2×#106224582
C2×#106226412
C2×#106224062
C2×#106224312
C2×D11×C4⋊C82
C2×C11×#4792
C2×#324811