Finite Group Databasebeta

← C2×#13079850 #15625909

Subgroups — C2×#13079850 #15625909

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#10623111C211yesmaximal, characteristic
3#13079850C2116yesmaximal, direct product factor
4C2×#10622469C212yesmaximal, complemented
5C2×#10622408C212yesmaximal, complemented
6C2×#10622422C212yesmaximal, complemented
7C2×#10622476C212yesmaximal
8C2×#10622633C211yesmaximal, characteristic, complemented
9C2×#10622459C211yesmaximal, characteristic, complemented
10C2×#10622700C211yesmaximal, characteristic, complemented
11C2×#10622448C211yesmaximal, characteristic, complemented
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#67000C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66997—21no—
19D11×C4⋊Q8—24no—
20D11×C4⋊Q8C2218yescomplemented
21#10623111—24no—
22#10623111C2218yes—
23C2×#66951—21no—
24C2×#66948C2211yescharacteristic
25C2×#66947—21no—
26C2×C4⋊C4×D11—21no—
27C2×C4⋊C4×D11C2212yes—
28C2×#66943C2211yescharacteristic
29C2×#66941—21no—
30C2×#66941C2212yes—
31C2×C4×D44—21no—
32C2×C4×D44C2211yescharacteristic
33C2×#66925—21no—
34C2×C42×D11C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C11×#475C2218yescomplemented
37C2×C11×#106C2212yes—
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2212yes—
40C2×#66899C2212yes—
41C2×#66885C2212yes—
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66882C2212yes—
44C2×#66879C2212yes—
45#10622700C2218yescomplemented
46#10622633C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622476C22116yes—
52#10622469C22116yescomplemented
53#10622459C2218yescomplemented
54#10622448C2218yescomplemented
55#10622422C22116yescomplemented
56#10622408C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C2×Q8×D11—28no—
60C2×Q8×D11—48no—
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—22no—
64C22×C4×D11—21no—
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D411yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×Dic22—21no—
69C22×Dic22—22no—
70C22×C8×C11C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C4×Q8×C11—22no—
74C4×Q8×C11C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81#67000—22no—
82#67000C2314yes—
83#66999—22no—
84#66999C2314yes—
85#66997—28no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11D411yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103#66951—28no—
104#66948—22no—
105#66948C2314yes—
106#66947—28no—
107C4⋊C4×D11—24no—
108C4⋊C4×D11—28no—
109C4⋊C4×D11C2318yes—
110#66943—22no—
111#66943C2314yes—
112#66941—24no—
113#66941—28no—
114#66941C2318yes—
115C4×D44—28no—
116C4×D44—22no—
117C4×D44C2314yes—
118#66925—28no—
119C42×D11D414yes—
120C42×D11C2314yes—
121#66922—22no—
122#66922C2314yes—
123C11×#106C2318yes—
124C11×C4⋊C8C2314yes—
125C11×#103C2318yes—
126#66899C2318yes—
127#66885C2318yes—
128(C2×D11)⋊C8C2318yes—
129#66882C2318yes—
130#66879C2318yes—
131#66873C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134C4⋊(C11⋊C8)C2314yes—
135C2×#3239—111nomaximal, Sylow
136C23×D11—21no—
137C23×D11C2×D411yescharacteristic
138C2×Q8×C11—24no—
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—44no—
143C2×Q8×C11C2412yes—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155Q8×D11—432no—
156C2×D44—24no—
157C2×D44—21no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—44no—
161C2×D44C2412yes—
162C2×C4×D11—24no—
163C2×C4×D11—28no—
164C2×C4×D11—24no—
165C2×C4×D11—24no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—48no—
169C2×C4×D11—44no—
170C2×C4×D11C2×D412yes—
171C2×C4×D11C2×D414yes—
172C2×C4×D11C2×D414yes—
173C2×C4×D11C2412yes—
174C2×Dic22—28no—
175C2×Dic22—24no—
176C2×Dic22—48no—
177C2×Dic22—44no—
178C2×C8×C11—24no—
179C2×C8×C11C2414yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4C2414yes—
185C11×C4⋊C4C2412yes—
186C42×C11—24no—
187C42×C11C2×D412yes—
188C42×C11C2412yes—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11—22no—
196C4⋊Dic11—24no—
197C4⋊Dic11—21no—
198C4⋊Dic11C2412yes—
199C4⋊Dic11C2414yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—24no—
202Dic11⋊C4—28no—
203Dic11⋊C4—28no—
204C4×Dic11C2×D412yes—
205C4×Dic11C2×D414yes—
206C4×Dic11C2×D414yes—
207C4×Dic11C2412yes—
208C2×C11⋊C8—24no—
209C2×C11⋊C8C2414yes—
210C22×C4⋊Q8—111no—
211C2×#529—111no—
212#3239—1116no—
213C2×#501—112no—
214C2×#489—112no—
215C2×#484—112no—
216C2×#481—112no—
217C2×#475—111no—
218C2×#475D1111yescharacteristic, complemented
219C2×#474—111no—
220C2×#474—111no—
221C2×#432—111no—
222C23×C11C22×D411yescharacteristic
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11#13714yes—
230C22×D11C22×D412yes—
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—42no—
234Q8×C11—48no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—42no—
240C2×C4×C11—44no—
241C2×C4×C11—42no—
242C2×C4×C11AGL(1,ℤ/8)14yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D412yes—
246C2×C4×C112−1+412yes—
247C2×C4×C112−1+412yes—
248C2×C4×C11C2511yescharacteristic
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—44no—
255C2×Dic11—42no—
256C2×Dic11C22×D412yes—
257C2×Dic11C22×D412yes—
258C2×Dic11C22×D412yes—
259D44—22no—
260D44—22no—
261D44—48no—
262D44—42no—
263C4×D11—28no—
264C4×D11—24no—
265C4×D11—28no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—416no—
269C4×D11—48no—
270Dic22—416no—
271Dic22—48no—
272C8×C11—24no—
273C11⋊C8—24no—
274C23×Q8—221no—
275C2×C4⋊Q8—118no—
276C2×C4⋊Q8—112no—
277C2×C4⋊Q8—111no—
278C2×C4⋊Q8—221no—
279C2×C4⋊Q8—224no—
280C2×C4⋊Q8—221no—
281C2×C4⋊Q8C2×D1111yescharacteristic
282#529—118no—
283#529—224no—
284C2×#126—221no—
285C2×#125—111no—
286C2×#124—111no—
287C2×#123—221no—
288C2×C22⋊Q8—111no—
289C2×#121—111no—
290C2×C4×Q8C2×D1111yescharacteristic
291C2×C4×D4—111no—
292C2×C4×D4—221no—
293C2×#117—221no—
294C22×C4⋊C4—112no—
295C22×C4⋊C4—221no—
296C22×C42—111no—
297#501—1116no—
298#489—1116no—
299#484—1116no—
300#481—1116no—
301#475—118no—
302#475C2×D1118yescomplemented
303#474—118no—
304#474—118no—
305#432—118no—
306C2×#107—112no—
307C2×#107—112no—
308C2×#106—112no—
309C2×#106C2×D1112yes—
310C2×C4⋊C8—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312C2×#103—112no—
313C2×#103C2×D1112yes—
314C2×#102—112no—
315C2×#102—112no—
316C2×C22⋊C8—112no—
317C2×#97—112no—
318C22×C11#53612yes—
319C22×C11C2×AGL(1,ℤ/8)12yes—
320C22×C11C2×#13712yes—
321C22×C11C23×D411yescharacteristic
322C2×D11—22no—
323C2×D11—28no—
324C2×D11—22no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—42no—
328C2×D11—84no—
329C2×D11C2×#13714yes—
330C4×C11—22no—
331C4×C11—42no—
332C4×C11—44no—
333C4×C11—42no—
334C4×C11#53612yes—
335C4×C11C2×AGL(1,ℤ/8)14yes—
336C4×C11C2×2−1+411yescharacteristic
337C4×C11C2×2−1+411yescharacteristic
338Dic11—22no—
339Dic11—22no—
340Dic11—22no—
341Dic11—44no—
342Dic11—42no—
343C22×Q8—21no—
344C22×Q8—222no—
345C22×Q8—228no—
346C22×Q8—221no—
347C22×Q8—448no—
348C22×Q8C22×D1111yescharacteristic
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—222no—
355C23×C4—221no—
356C22×C8—112no—
357C22×C8C22×D1112yes—
358C4⋊Q8—22no—
359C4⋊Q8—118no—
360C4⋊Q8—114no—
361C4⋊Q8—224no—
362C4⋊Q8—228no—
363C4⋊Q8—228no—
364C4⋊Q8—222no—
365C4⋊Q8C22×D1114yes—
366#126—228no—
367#125—114no—
368#125—222no—
369#124—114no—
370#124—222no—
371#123—228no—
372C22⋊Q8—114no—
373C22⋊Q8—222no—
374#121—114no—
375#121—222no—
376C4×Q8—22no—
377C4×Q8C22×D1114yes—
378C4×D4—114no—
379C4×D4—228no—
380C4×D4—222no—
381#117—228no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—118no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—228no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22×D1112yes—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C42—21no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—114no—
407C2×C42—114no—
408C2×C42C22×D1111yescharacteristic
409#107—118no—
410#107—118no—
411#106—118no—
412#106C22×D1118yes—
413C4⋊C8—114no—
414C4⋊C8C22×D1114yes—
415#103—118no—
416#103C22×D1118yes—
417#102—118no—
418#102—118no—
419C22⋊C8—118no—
420#97—118no—
421C2×C11#323914yescomplemented
422C2×C11C2×#53611yescharacteristic
423C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
424C2×C11C22×#13711yescharacteristic
425D11—24no—
426D11—82no—
427C24—111no—
428C24—221no—
429C2×Q8—21no—
430C2×Q8—24no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—44no—
434C2×Q8—228no—
435C2×Q8—224no—
436C2×Q8—448no—
437C2×Q8—4432no—
438C2×Q8—444no—
439C2×Q8C23×D1112yes—
440C2×D4—112no—
441C2×D4—224no—
442C2×D4—221no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—444no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—112no—
453C22×C4—114no—
454C22×C4—114no—
455C22×C4—112no—
456C22×C4—224no—
457C22×C4—228no—
458C22×C4—224no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—221no—
462C22×C4—222no—
463C22×C4—224no—
464C22×C4—448no—
465C22×C4—444no—
466C22×C4D4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C2×C8—24no—
470C2×C8—114no—
471C2×C8—224no—
472C2×C8C23×D1114yes—
473C4⋊C4—24no—
474C4⋊C4—24no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—114no—
478C4⋊C4—112no—
479C4⋊C4—228no—
480C4⋊C4—228no—
481C4⋊C4—224no—
482C4⋊C4—224no—
483C4⋊C4—224no—
484C4⋊C4—222no—
485C4⋊C4—221no—
486C4⋊C4—224no—
487C4⋊C4C23×D1114yes—
488C4⋊C4C23×D1112yes—
489C22⋊C4—224no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—224no—
493C22⋊C4—224no—
494C42—24no—
495C42—114no—
496C42—112no—
497C42—114no—
498C42—112no—
499C42D4×D1112yes—
500C42C23×D1112yes—
501C11C2×#323911yescharacteristic, complemented, Sylow
502C23—114no—
503C23—112no—
504C23—222no—
505C23—222no—
506C23—222no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23C2×D4×D1111yescharacteristic
511Q8—22no—
512Q8—22no—
513Q8—48no—
514Q8—42no—
515Q8—4416no—
516Q8—448no—
517D4—222no—
518D4—222no—
519D4—448no—
520D4—442no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—112no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—228no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—228no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—4416no—
542C2×C4—444no—
543C2×C4—442no—
544C2×C4—448no—
545C2×C4#6696714yes—
546C2×C4C2×D4×D1112yes—
547C2×C4C2×D4×D1112yes—
548C2×C4C2×D4×D1111yescharacteristic
549C2×C4#6704012yes—
550C2×C4#6704312yes—
551C2×C4C24×D1111yescharacteristic
552C8—24no—
553C8—224no—
554C22—114no—
555C22—228no—
556C22—222no—
557C22—222no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—884no—
562C22#1062315912yes—
563C22C2×#6696712yes—
564C22D11×#13712yes—
565C22C22×D4×D1111yescharacteristic
566C4—22no—
567C4—42no—
568C4—44no—
569C4—42no—
570C4—222no—
571C4—222no—
572C4—222no—
573C4—444no—
574C4—442no—
575C4#1062315912yes—
576C4C2×#6696714yes—
577C4C2×#6704011yescharacteristic
578C4C2×#6704311yescharacteristic
579C2—224no—
580C2—882no—
581C2#1307985014yesdirect product factor
582C2C2×#1062315911yescharacteristic
583C2C22×#6696711yescharacteristic
584C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#475D11
hypocenterC11C2×#3239
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
3. #13079850C2direct (N × H)
4. C2×#10622469C2semidirect
5. C2×#10622408C2semidirect
6. C2×#10622422C2semidirect
8. C2×#10622633C2semidirect
9. C2×#10622459C2semidirect
10. C2×#10622700C2semidirect
11. C2×#10622448C2semidirect
12. C2×C11×#475C2semidirect
20. D11×C4⋊Q8C22semidirect
36. C11×#475C22semidirect
45. #10622700C22semidirect
46. #10622633C22semidirect
52. #10622469C22semidirect
53. #10622459C22semidirect
54. #10622448C22semidirect
55. #10622422C22semidirect
56. #10622408C22semidirect
218. C2×#475D11semidirect
302. #475C2×D11semidirect
421. C2×C11#3239semidirect
501. C11C2×#3239semidirect
581. C2#13079850direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106231112
#130798502
C2×#106224692
C2×#106224082
C2×#106224222
C2×#106224762
C2×#106226332
C2×#106224592
C2×#106227002
C2×#106224482
C2×C11×#4752
C2×#323911