Finite Group Databasebeta

← C2×#13080363 #15629045

Subgroups — C2×#13080363 #15629045

Order 2816.

2742 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D11C212yesmaximal, complemented
2C2×Q8×D44C211yesmaximal, characteristic
3C2×#10623258C211yesmaximal, characteristic
4#13080363C2116yesmaximal, direct product factor
5C2×#10622705C211yesmaximal, characteristic, complemented
6C2×#10622426C212yesmaximal, complemented
7C2×#10622462C211yesmaximal, characteristic, complemented
8C2×#10622421C212yesmaximal, complemented
9C2×#10622799C212yesmaximal, complemented
10C2×C4×#4326C211yesmaximal, characteristic, complemented
11C2×#10622447C211yesmaximal, characteristic
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C22×Q8×D11C2212yes—
15C22×C11×Q16C2212yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66999C2212yes—
19C22×#4326C2212yes—
20C22×#4326C2212yes—
21C22×#4326C2211yescharacteristic
22C2×Q16×D11—216no—
23C2×Q16×D11C22116yescomplemented
24C22×Dic44C2212yes—
25C22×C8×D11C2212yes—
26#10623258—24no—
27#10623258C2218yes—
28Q8×D44—24no—
29Q8×D44C2218yes—
30C2×#66950—22no—
31C2×#66950C2212yes—
32C2×#66949—22no—
33C2×#66946—21no—
34C2×#66941—21no—
35C2×C4×D44—21no—
36C2×C4×D44C2211yescharacteristic
37C2×#66922—21no—
38C2×#66922C2211yescharacteristic
39C2×C4×Dic22C2211yescharacteristic
40C11×#462C2218yescomplemented
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66899C2211yescharacteristic
44#10622799C22116yescomplemented
45C2×(C2×D11)⋊C8C2212yes—
46C2×#66880C2212yes—
47#10622705C2218yescomplemented
48C4×#4326C2218yescomplemented
49C2×#66874C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622462C2218yescomplemented
53#10622447C2218yes—
54#10622426C22116yescomplemented
55#10622421C22116yescomplemented
56C22×Q8×C11C2312yes—
57C22×Q8×C11C2311yescharacteristic
58C2×Q8×D11—24no—
59C2×Q8×D11—24no—
60C2×Q8×D11—28no—
61C2×Q8×D11—28no—
62C2×Q8×D11—44no—
63C2×Q8×D11—44no—
64C2×Q8×D11C2318yes—
65C2×Q8×D11C2318yes—
66C22×D44D411yescharacteristic
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11C2312yes—
70C22×Dic22—22no—
71C22×Dic22—22no—
72C22×Dic22C2312yes—
73C22×Dic22C2311yescharacteristic
74C2×C11×Q16—28no—
75C2×C11×Q16C2318yes—
76C22×C8×C11C2312yes—
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8C2314yes—
79C4×Q8×C11—22no—
80C4×Q8×C11C2314yes—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87#66999—24no—
88#66999C2318yes—
89C2×#4326—28no—
90C2×#4326—44no—
91C2×#4326D418yescomplemented
92C2×#4326C2318yes—
93C2×#4326C2318yes—
94C2×#4326C2314yes—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4D412yes—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11D411yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—21no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108Q16×D11—264no—
109C2×Dic44—28no—
110C2×Dic44C2318yes—
111C2×C8×D11—28no—
112C2×C8×D11C2318yes—
113#66950—24no—
114#66950—216no—
115#66950C2318yes—
116#66949—216no—
117#66946—28no—
118#66941—28no—
119C4×D44—28no—
120C4×D44D414yes—
121C4×D44C2314yes—
122#66922—22no—
123#66922—28no—
124#66922C2314yes—
125C4×Dic22—22no—
126C4×Dic22C2314yes—
127C11×C4⋊C8C2314yes—
128C11×#103C2318yes—
129#66899C2314yes—
130(C2×D11)⋊C8C2318yes—
131#66880C2318yes—
132#66874C2314yes—
133#66871C2314yes—
134C4×C11⋊C8C2314yes—
135C2×D4×Q16—111nomaximal, Sylow
136C23×D11C2×D412yes—
137C2×Q8×C11—21no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—24no—
141C2×Q8×C11—24no—
142C2×Q8×C11C2×D414yes—
143C2×Q8×C11C2414yes—
144C2×Q8×C11C2412yes—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11C2×D412yes—
155Q8×D11—216no—
156Q8×D11—216no—
157Q8×D11—48no—
158Q8×D11—48no—
159Q8×D11—416no—
160Q8×D11—416no—
161C2×D44Q1618yescomplemented
162C2×D44C2×D414yes—
163C2×C4×D11—28no—
164C2×C4×D11—28no—
165C2×C4×D11—24no—
166C2×C4×D11—24no—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×C4×D11C2×D414yes—
170C2×C4×D11C2414yes—
171C2×Dic22—28no—
172C2×Dic22—28no—
173C2×Dic22—21no—
174C2×Dic22—24no—
175C2×Dic22—22no—
176C2×Dic22—22no—
177C2×Dic22—24no—
178C2×Dic22—48no—
179C2×Dic22—48no—
180C2×Dic22C2×D414yes—
181C2×Dic22C2414yes—
182C2×Dic22C2412yes—
183C11×Q16—216no—
184C2×C8×C11—24no—
185C2×C8×C11C2414yes—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C2412yes—
191C42×C11—24no—
192C42×C11C2×D412yes—
193C42×C11C2412yes—
194#4326—216no—
195#4326—48no—
196#4326C2×D4116yescomplemented
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4C2×D418yes—
200C4⋊Dic11—28no—
201C4⋊Dic11—21no—
202C4⋊Dic11—24no—
203C4⋊Dic11—24no—
204C4⋊Dic11C2×D414yes—
205C4⋊Dic11C2412yes—
206Dic11⋊C4—28no—
207Dic11⋊C4—24no—
208C4×Dic11—24no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8C2×D414yes—
211C2×C11⋊C8C2412yes—
212C2×C11⋊C8C2412yes—
213Dic44—216no—
214C8×D11—216no—
215C23×Q16—112no—
216C2×D4×Q8—111no—
217C2×D4×Q8—111no—
218D4×Q16—1116no—
219C2×#494—111no—
220C2×#467—112no—
221C2×#462—111no—
222C2×#462D1111yescharacteristic, complemented
223C2×#451—112no—
224C2×#451—112no—
225C2×C4×Q16—111no—
226C2×C8×D4—111no—
227C23×C11C22×D411yescharacteristic
228C22×D11—24no—
229C22×D11—24no—
230C22×D11C2×Q1618yescomplemented
231C22×D11C22×D414yes—
232Q8×C11—24no—
233Q8×C11—22no—
234Q8×C11—24no—
235Q8×C11—24no—
236Q8×C11—44no—
237Q8×C11C22×D414yes—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11C2×Q1614yescomplemented
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D412yes—
249C2×C4×C11C22×D412yes—
250C2×C4×C11H(5,𝔽2)12yes—
251C2×C4×C11C2511yescharacteristic
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—44no—
258C2×Dic11—42no—
259C2×Dic11C22×D414yes—
260D44C2×Q16116yescomplemented
261C4×D11—28no—
262C4×D11—24no—
263C4×D11—24no—
264C4×D11—416no—
265C4×D11—416no—
266Dic22—24no—
267Dic22—22no—
268Dic22—24no—
269Dic22—24no—
270Dic22—416no—
271Dic22—416no—
272Dic22—44no—
273Dic22C22×D414yes—
274C8×C11—24no—
275C11⋊C8—22no—
276C11⋊C8C22×D414yes—
277C23×Q8—112no—
278C23×Q8—112no—
279C22×Q16—111no—
280C22×Q16—112no—
281C22×Q16—112no—
282C22×Q16—1116no—
283C22×Q16—112no—
284C22×Q16—2216no—
285C22×Q16C2×D1112yes—
286C23×C8—112no—
287D4×Q8—118no—
288D4×Q8—118no—
289D4×Q8—224no—
290D4×Q8—224no—
291C2×C4⋊Q8—111no—
292C2×C4⋊Q8—221no—
293C2×C4⋊Q8—221no—
294C2×C4⋊Q8C2×D1111yescharacteristic
295C2×C22⋊Q8—112no—
296C2×C22⋊Q8—112no—
297C2×C22⋊Q8—222no—
298C2×C22⋊Q8—222no—
299C2×C4×Q8—111no—
300C2×C4×Q8C2×D1111yescharacteristic
301C2×C4×D4—111no—
302C2×C4×D4—221no—
303C2×C4×D4—221no—
304#494—118no—
305#467—1116no—
306#462—118no—
307#462C2×D1118yescomplemented
308#451—1116no—
309#451—1116no—
310C4×Q16—118no—
311C8×D4—118no—
312C2×#107—111no—
313C2×C4⋊C8C2×D1111yescharacteristic
314C2×#103—111no—
315C2×#103—112no—
316C2×#103—111no—
317C2×#103C2×D1112yes—
318C2×C22⋊C8—112no—
319C2×C4×C8—111no—
320C22×C11D4212yes—
321C22×C11C22×Q1612yes—
322C22×C11#57812yes—
323C22×C11C23×D411yescharacteristic
324C2×D11—24no—
325C2×D11—216no—
326C2×D11—24no—
327C2×D11C22×Q1618yescomplemented
328C4×C11—24no—
329C4×C11—22no—
330C4×C11—44no—
331C4×C11—42no—
332C4×C11D4212yes—
333C4×C11C22×Q1614yescomplemented
334C4×C11C23×D411yescharacteristic
335C4×C11C2×H(5,𝔽2)11yescharacteristic
336Dic11—24no—
337Dic11—24no—
338Dic11—44no—
339Dic11—42no—
340C22×Q8—118no—
341C22×Q8—118no—
342C22×Q8—111no—
343C22×Q8—112no—
344C22×Q8—222no—
345C22×Q8—222no—
346C22×Q8—224no—
347C22×Q8—224no—
348C22×Q8—228no—
349C22×Q8—228no—
350C22×Q8—444no—
351C22×Q8—444no—
352C22×Q8C22×D1112yes—
353C22×Q8C22×D1111yescharacteristic
354C22×D4—111no—
355C23×C4—112no—
356C23×C4—222no—
357C23×C4—222no—
358C2×Q16—28no—
359C2×Q16—118no—
360C2×Q16—114no—
361C2×Q16—118no—
362C2×Q16—118no—
363C2×Q16—118no—
364C2×Q16—228no—
365C2×Q16—228no—
366C2×Q16—2264no—
367C2×Q16—444no—
368C2×Q16C22×D1118yes—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—118no—
372C22×C8—228no—
373C22×C8C22×D1112yes—
374C4⋊Q8—22no—
375C4⋊Q8—114no—
376C4⋊Q8—228no—
377C4⋊Q8—228no—
378C4⋊Q8—222no—
379C4⋊Q8C22×D1114yes—
380C22⋊Q8—118no—
381C22⋊Q8—118no—
382C22⋊Q8—2216no—
383C22⋊Q8—2216no—
384C22⋊Q8—224no—
385C22⋊Q8—224no—
386C4×Q8—22no—
387C4×Q8—114no—
388C4×Q8—222no—
389C4×Q8C22×D1114yes—
390C4×D4—114no—
391C4×D4—114no—
392C4×D4—228no—
393C4×D4—228no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—112no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4—222no—
408C2×C42—21no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411#107—114no—
412C4⋊C8C22×D1114yes—
413#103—114no—
414#103—118no—
415#103—114no—
416#103C22×D1118yes—
417C22⋊C8—118no—
418C4×C8—114no—
419C2×C11D4×Q1614yescomplemented
420C2×C11C2×D4211yescharacteristic
421C2×C11C23×Q1611yescharacteristic
422C2×C11C2×#57811yescharacteristic
423D11—28no—
424C24—112no—
425C2×Q8—21no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—24no—
429C2×Q8—24no—
430C2×Q8—114no—
431C2×Q8—112no—
432C2×Q8—114no—
433C2×Q8—228no—
434C2×Q8—228no—
435C2×Q8—221no—
436C2×Q8—222no—
437C2×Q8—222no—
438C2×Q8—2216no—
439C2×Q8—2216no—
440C2×Q8—224no—
441C2×Q8—224no—
442C2×Q8—448no—
443C2×Q8—448no—
444C2×Q8—448no—
445C2×Q8—448no—
446C2×Q8—4416no—
447C2×Q8—4416no—
448C2×Q8D4×D1114yes—
449C2×Q8C23×D1114yes—
450C2×Q8C23×D1112yes—
451C2×D4—118no—
452C2×D4—114no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—228no—
460C22×C4—228no—
461C22×C4—221no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—221no—
465C22×C4—222no—
466C22×C4—448no—
467C22×C4—448no—
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471Q16—216no—
472Q16—1116no—
473Q16—2216no—
474Q16—2216no—
475Q16—448no—
476C2×C8—24no—
477C2×C8—114no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8—2216no—
481C2×C8—222no—
482C2×C8C23×D1114yes—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—114no—
488C4⋊C4—112no—
489C4⋊C4—228no—
490C4⋊C4—228no—
491C4⋊C4—221no—
492C4⋊C4—224no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4C23×D1112yes—
496C22⋊C4—118no—
497C22⋊C4—228no—
498C22⋊C4—228no—
499C42—24no—
500C42—224no—
501C42D4×D1112yes—
502C42C23×D1112yes—
503C11C2×D4×Q1611yescharacteristic, complemented, Sylow
504C23—118no—
505C23—114no—
506C23—224no—
507C23—224no—
508C23C2×D4×D1111yescharacteristic
509Q8—24no—
510Q8—22no—
511Q8—24no—
512Q8—24no—
513Q8—44no—
514Q8—114no—
515Q8—224no—
516Q8—222no—
517Q8—224no—
518Q8—224no—
519Q8—4416no—
520Q8—4416no—
521Q8—444no—
522Q8C2×D4×D1114yes—
523D4—1116no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—44no—
531C2×C4—114no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—228no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—222no—
539C2×C4—224no—
540C2×C4—4416no—
541C2×C4—4416no—
542C2×C4—442no—
543C2×C4—444no—
544C2×C4Q16×D1114yescomplemented
545C2×C4C2×D4×D1112yes—
546C2×C4C2×D4×D1112yes—
547C2×C4C2×D4×D1111yescharacteristic
548C2×C4C2×D4×D1112yes—
549C2×C4#6704212yes—
550C2×C4C24×D1111yescharacteristic
551C8—24no—
552C8—114no—
553C8—222no—
554C22—118no—
555C22—2216no—
556C22—224no—
557C22—224no—
558C22#1062314012yes—
559C22C2×Q16×D1112yes—
560C22#1062331012yes—
561C22C22×D4×D1111yescharacteristic
562C4—24no—
563C4—22no—
564C4—44no—
565C4—42no—
566C4—224no—
567C4—224no—
568C4—444no—
569C4—442no—
570C4#1062314012yes—
571C4C2×Q16×D1114yescomplemented
572C4C22×D4×D1111yescharacteristic
573C4C2×#6704211yescharacteristic
574C2—228no—
575C2#1308036314yesdirect product factor
576C2C2×#1062314011yescharacteristic
577C2C22×Q16×D1111yescharacteristic
578C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#462D11
hypocenterC11C2×D4×Q16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C22×Q16×D11C2semidirect
4. #13080363C2direct (N × H)
5. C2×#10622705C2semidirect
6. C2×#10622426C2semidirect
7. C2×#10622462C2semidirect
8. C2×#10622421C2semidirect
9. C2×#10622799C2semidirect
10. C2×C4×#4326C2semidirect
12. C2×C11×#462C2semidirect
23. C2×Q16×D11C22semidirect
40. C11×#462C22semidirect
44. #10622799C22semidirect
47. #10622705C22semidirect
48. C4×#4326C22semidirect
52. #10622462C22semidirect
54. #10622426C22semidirect
55. #10622421C22semidirect
91. C2×#4326D4semidirect
161. C2×D44Q16semidirect
196. #4326C2×D4semidirect
222. C2×#462D11semidirect
230. C22×D11C2×Q16semidirect
245. C2×C4×C11C2×Q16semidirect
260. D44C2×Q16semidirect
307. #462C2×D11semidirect
327. C2×D11C22×Q16semidirect
333. C4×C11C22×Q16semidirect
419. C2×C11D4×Q16semidirect
503. C11C2×D4×Q16semidirect
544. C2×C4Q16×D11semidirect
571. C4C2×Q16×D11semidirect
575. C2#13080363direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q16×D112
C2×Q8×D442
C2×#106232582
#130803632
C2×#106227052
C2×#106224262
C2×#106224622
C2×#106224212
C2×#106227992
C2×C4×#43262
C2×#106224472
C2×C11×#4622
C2×D4×Q1611