Subgroups — D₁₁₃⋊#101 #20299583

Order 7232.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁₃⋊M₁₆	C₂	1	2	yes	maximal
2	#16813683	C₂	1	4	yes	maximal, complemented
3	C₂×Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#14268657	—	2	2	no	—
5	#14268656	C₂²	1	4	yes	—
6	#14268655	—	2	2	no	—
7	C₂×Dic₂₂₆	C₄	1	1	yes	characteristic
8	C₂×Dic₂₂₆	C₂²	1	2	yes	—
9	Q₈×D₁₁₃	—	2	2	no	—
10	Q₈×D₁₁₃	—	2	2	no	—
11	C₂×C₄×D₁₁₃	C₄	1	2	yes	—
12	C₂×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₁₁₃	C₄	1	1	yes	characteristic
14	C₂²×D₁₁₃	C₂×C₄	1	1	yes	characteristic
15	Q₈×C₁₁₃	—	2	2	no	—
16	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₁₃	C₂×C₄	1	2	yes	—
19	C₂×Dic₁₁₃	C₂³	1	1	yes	characteristic
20	C₄×D₁₁₃	—	2	2	no	—
21	C₄×D₁₁₃	—	2	2	no	—
22	C₄×D₁₁₃	D₄	1	2	yes	—
23	C₄×D₁₁₃	D₄	1	2	yes	—
24	Dic₂₂₆	—	2	2	no	—
25	Dic₂₂₆	—	2	4	no	—
26	#11744753	—	2	4	no	—
27	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₁₁₃	—	2	2	no	—
29	C₂×D₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₁₁₃	—	2	2	no	—
32	C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
33	Dic₁₁₃	—	2	2	no	—
34	Dic₁₁₃	C₂×D₄	1	2	yes	—
35	C₂×C₁₁₃	—	2	1	no	—
36	C₂×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	D₁₁₃	—	2	1	no	—
38	D₁₁₃	#101	1	2	yes	complemented
39	C₁₁₃	C₂×#101	1	1	yes	characteristic, complemented, Sylow
40	C₂×#101	—	113	1	no	maximal, Sylow
41	C₂²×Q₈	—	113	1	no	—
42	C₂×M₁₆	—	113	2	no	—
43	#101	—	113	4	no	—
44	C₂×Q₈	—	113	2	no	—
45	C₂×Q₈	—	113	1	no	—
46	C₂×Q₈	—	226	2	no	—
47	C₂×Q₈	—	226	2	no	—
48	C₂×Q₈	#90673	1	1	yes	characteristic
49	C₂²×C₄	—	113	1	no	—
50	C₂²×C₄	—	113	2	no	—
51	M₁₆	—	113	4	no	—
52	M₁₆	—	226	2	no	—
53	C₂×C₈	—	226	2	no	—
54	C₂³	—	113	1	no	—
55	Q₈	—	2	2	no	—
56	Q₈	—	226	4	no	—
57	Q₈	—	226	2	no	—
58	C₂×C₄	—	113	1	no	—
59	C₂×C₄	—	113	2	no	—
60	C₂×C₄	—	113	2	no	—
61	C₂×C₄	—	113	2	no	—
62	C₂×C₄	—	226	2	no	—
63	C₂×C₄	—	226	2	no	—
64	C₂×C₄	C₂×#90673	1	2	yes	—
65	C₂×C₄	C₂×#90673	1	1	yes	characteristic
66	C₈	—	226	4	no	—
67	C₂²	—	113	1	no	—
68	C₂²	—	113	1	no	—
69	C₂²	—	226	2	no	—
70	C₂²	C₂²×#90673	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	113	2	no	—
73	C₄	—	226	2	no	—
74	C₄	C₂²⋊#90673	1	2	yes	—
75	C₂	—	2	1	no	—
76	C₂	—	113	2	no	—
77	C₂	—	226	1	no	—
78	C₂	C₂×C₂²⋊#90673	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#90673
commutator	C₂²×C₁₁₃	C₂²×C₄
Frattini	C₂²	C₂²×#90673
Fitting	C₂×Q₈×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₂×C₂²⋊C₄
hypercenter	C₂×Q₈	#90673
hypocenter	C₁₁₃	C₂×#101
LCS	G ▷ C₂²×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #16813683	C₂	semidirect
38. D₁₁₃	#101	semidirect
39. C₁₁₃	C₂×#101	semidirect

Subgroups — D113⋊#101 #20299583

Conjugacy classes of subgroups

Complements

Subgroups — D₁₁₃⋊#101 #20299583