Subgroups — C₂×#16813677 #20299556

Order 7232.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11744753	C₂	1	2	yes	maximal
2	#16813677	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11744753	C₄	1	8	yes	complemented
5	C₂×#11744753	C₂²	1	4	yes	—
6	C₂²×Dic₁₁₃	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₁₃	C₂²	1	1	yes	characteristic
8	C₄×Dic₁₁₃	C₄	1	2	yes	—
9	C₄×Dic₁₁₃	C₂²	1	2	yes	—
10	C₂²×C₄×C₁₁₃	C₄	1	1	yes	characteristic
11	C₂³×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₁₃	—	2	2	no	—
13	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
14	C₂×Dic₁₁₃	—	2	2	no	—
15	C₂×Dic₁₁₃	C₂×C₄	1	2	yes	—
16	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₁₃	C₂×C₄	1	4	yes	—
18	C₂×Dic₁₁₃	C₂³	1	1	yes	characteristic
19	#11744753	C₂×C₄	1	8	yes	complemented
20	C₂²×C₁₁₃	C₄²	1	2	yes	—
21	C₂²×C₁₁₃	M₁₆	1	2	yes	—
22	C₂²×C₁₁₃	M₁₆	1	2	yes	—
23	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₁₃	—	2	2	no	—
25	Dic₁₁₃	—	2	2	no	—
26	Dic₁₁₃	C₄²	1	2	yes	—
27	Dic₁₁₃	C₂²×C₄	1	2	yes	—
28	C₂×C₁₁₃	#97	1	4	yes	complemented
29	C₂×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
30	C₂×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
31	C₂×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
32	C₁₁₃	C₂×#97	1	1	yes	characteristic, complemented, Sylow
33	C₂×#97	—	113	1	no	maximal, Sylow
34	C₂²×C₈	—	113	2	no	—
35	C₂×C₄²	—	113	1	no	—
36	#97	—	113	4	no	—
37	C₂²×C₄	—	113	1	no	—
38	C₂²×C₄	—	113	1	no	—
39	C₂²×C₄	#90673	1	1	yes	characteristic
40	C₂×C₈	—	113	4	no	—
41	C₂×C₈	—	113	8	no	—
42	C₄²	—	113	2	no	—
43	C₄²	—	113	2	no	—
44	C₂³	C₂×#90673	1	1	yes	characteristic
45	C₂×C₄	—	2	2	no	—
46	C₂×C₄	—	113	4	no	—
47	C₂×C₄	—	113	1	no	—
48	C₂×C₄	—	113	1	no	—
49	C₂×C₄	—	113	2	no	—
50	C₂×C₄	—	226	2	no	—
51	C₂×C₄	C₂×#90673	1	2	yes	—
52	C₈	—	113	8	no	—
53	C₂²	C₄×#90673	1	2	yes	—
54	C₂²	#14268656	1	2	yes	—
55	C₂²	#14268657	1	2	yes	—
56	C₂²	C₂²×#90673	1	1	yes	characteristic
57	C₄	—	2	2	no	—
58	C₄	—	113	2	no	—
59	C₄	—	113	2	no	—
60	C₄	—	226	2	no	—
61	C₂	#16813677	1	4	yes	direct product factor
62	C₂	C₂×C₄×#90673	1	1	yes	characteristic
63	C₂	C₂×#14268656	1	1	yes	characteristic
64	C₂	C₂×#14268657	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#90673
commutator	C₂×C₁₁₃	C₂×C₄²
Frattini	C₂²	C₂²×#90673
Fitting	C₂²×C₄×C₁₁₃	C₄
socle	C₂³×C₁₁₃	C₂×C₄
hypercenter	C₂²×C₄	#90673
hypocenter	C₁₁₃	C₂×#97
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #16813677	C₂	direct (N × H)
4. C₂×#11744753	C₄	semidirect
19. #11744753	C₂×C₄	semidirect
28. C₂×C₁₁₃	#97	semidirect
32. C₁₁₃	C₂×#97	semidirect
61. C₂	#16813677	direct (N × H)

Subgroups — C2×#16813677 #20299556

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16813677 #20299556