Subgroups — #41×Dic₁₁₃ #20299069

Order 7232.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₁₁₃	C₂	1	2	yes	maximal, complemented
2	D₄×Dic₁₁₃	C₂	1	6	yes	maximal, complemented
3	#16813581	C₂	1	3	yes	maximal, complemented
4	C₂×C₄×Dic₁₁₃	C₂	1	3	yes	maximal, complemented
5	C₂×#41×C₁₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₁₃	C₂²	1	6	yes	—
7	C₄⋊Dic₁₁₃	C₂²	1	6	yes	—
8	C₂²⋊Dic₁₁₃	C₂²	1	6	yes	—
9	C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
10	C₄×Dic₁₁₃	C₂²	1	3	yes	—
11	C₄×Dic₁₁₃	C₂²	1	6	yes	—
12	#41×C₁₁₃	C₄	1	8	yes	complemented
13	C₂×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
14	C₂×D₄×C₁₁₃	C₂²	1	3	yes	—
15	C₂²×C₄×C₁₁₃	C₂²	1	3	yes	—
16	C₂³×C₁₁₃	C₂³	1	3	yes	—
17	Q₈×C₁₁₃	C₂×C₄	1	4	yes	complemented
18	D₄×C₁₁₃	C₂×C₄	1	12	yes	complemented
19	C₂×C₄×C₁₁₃	C₂×C₄	1	12	yes	complemented
20	C₂×C₄×C₁₁₃	C₂³	1	3	yes	—
21	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₁₃	—	2	12	no	—
23	C₂×Dic₁₁₃	C₂³	1	6	yes	—
24	C₂×Dic₁₁₃	C₂³	1	2	yes	—
25	C₂²×C₁₁₃	—	2	6	no	—
26	C₂²×C₁₁₃	C₂²×C₄	1	6	yes	—
27	C₂²×C₁₁₃	C₂⁴	1	1	yes	characteristic
28	C₄×C₁₁₃	C₂²×C₄	1	2	yes	—
29	C₄×C₁₁₃	C₂²×C₄	1	6	yes	—
30	Dic₁₁₃	—	2	6	no	—
31	Dic₁₁₃	#41	1	4	yes	direct product factor
32	C₂×C₁₁₃	—	2	6	no	—
33	C₂×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
34	C₂×C₁₁₃	C₂×#41	1	2	yes	—
35	C₁₁₃	C₄×#41	1	1	yes	characteristic, complemented, Sylow
36	C₄×#41	—	113	1	no	maximal, Sylow
37	C₂×#41	D₁₁₃	1	1	yes	characteristic
38	C₄×Q₈	—	113	2	no	—
39	C₄×D₄	—	113	6	no	—
40	#117	—	113	3	no	—
41	C₂×C₄²	—	113	3	no	—
42	#41	Dic₁₁₃	1	8	yes	direct product factor
43	C₂×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
44	C₂×D₄	C₂×D₁₁₃	1	3	yes	—
45	C₂²×C₄	—	113	6	no	—
46	C₂²×C₄	C₂×D₁₁₃	1	3	yes	—
47	C₄⋊C₄	—	113	6	no	—
48	C₂²⋊C₄	—	113	6	no	—
49	C₄²	—	113	6	no	—
50	C₄²	—	113	1	no	—
51	C₄²	—	113	3	no	—
52	C₂³	C₂²×D₁₁₃	1	3	yes	—
53	Q₈	C₂×Dic₁₁₃	1	4	yes	complemented
54	D₄	C₂×Dic₁₁₃	1	12	yes	complemented
55	C₂×C₄	—	113	2	no	—
56	C₂×C₄	—	113	6	no	—
57	C₂×C₄	—	226	12	no	—
58	C₂×C₄	C₂×Dic₁₁₃	1	12	yes	complemented
59	C₂×C₄	C₂²×D₁₁₃	1	3	yes	—
60	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
61	C₂²	—	2	6	no	—
62	C₂²	C₂²×Dic₁₁₃	1	6	yes	—
63	C₂²	C₂³×D₁₁₃	1	1	yes	characteristic
64	C₄	—	113	4	no	—
65	C₄	—	226	6	no	—
66	C₄	C₂²×Dic₁₁₃	1	2	yes	—
67	C₄	C₂²×Dic₁₁₃	1	6	yes	—
68	C₂	—	2	6	no	—
69	C₂	C₂³×Dic₁₁₃	1	1	yes	characteristic
70	C₂	#41×D₁₁₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₁₃
commutator	C₂×C₁₁₃	C₂³×C₄
Frattini	C₂²	C₂³×D₁₁₃
Fitting	C₂×#41×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂⁴
hypercenter	C₂×#41	D₁₁₃
hypocenter	C₁₁₃	C₄×#41
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. Q₈×Dic₁₁₃	C₂	semidirect
2. D₄×Dic₁₁₃	C₂	semidirect
3. #16813581	C₂	semidirect
4. C₂×C₄×Dic₁₁₃	C₂	semidirect
12. #41×C₁₁₃	C₄	semidirect
17. Q₈×C₁₁₃	C₂×C₄	semidirect
18. D₄×C₁₁₃	C₂×C₄	semidirect
19. C₂×C₄×C₁₁₃	C₂×C₄	semidirect
31. Dic₁₁₃	#41	direct (N × H)
35. C₁₁₃	C₄×#41	semidirect
42. #41	Dic₁₁₃	direct (N × H)
53. Q₈	C₂×Dic₁₁₃	semidirect
54. D₄	C₂×Dic₁₁₃	semidirect
58. C₂×C₄	C₂×Dic₁₁₃	semidirect

Subgroups — #41×Dic113 #20299069

Conjugacy classes of subgroups

Complements

Subgroups — #41×Dic₁₁₃ #20299069