Subgroups — C₄×#14268657 #20299560

Order 7232.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268657	C₂	1	2	yes	maximal
2	#16813677	C₂	1	2	yes	maximal, complemented
3	C₄×#11744753	C₂	1	2	yes	maximal, complemented
4	C₄²×D₁₁₃	C₂	1	1	yes	maximal, characteristic
5	#14268657	C₄	1	8	yes	direct product factor
6	C₂×#11744753	C₂²	1	4	yes	—
7	C₂×C₄×D₁₁₃	C₄	1	1	yes	characteristic
8	C₂×C₄×D₁₁₃	C₄	1	1	yes	characteristic
9	C₂×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
10	C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
11	C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
12	C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
13	C₄²×C₁₁₃	C₄	1	1	yes	characteristic
14	C₂²×D₁₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₁₃	C₂³	1	1	yes	characteristic
21	C₄×D₁₁₃	—	2	2	no	—
22	C₄×D₁₁₃	—	2	2	no	—
23	C₄×D₁₁₃	C₂×C₄	1	4	yes	—
24	#11744753	C₂×C₄	1	8	yes	complemented
25	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×D₁₁₃	—	2	1	no	—
27	C₂×D₁₁₃	—	2	1	no	—
28	C₂×D₁₁₃	C₄²	1	2	yes	—
29	C₄×C₁₁₃	—	2	1	no	—
30	C₄×C₁₁₃	C₄²	1	2	yes	—
31	C₄×C₁₁₃	M₁₆	1	2	yes	complemented
32	Dic₁₁₃	—	2	1	no	—
33	Dic₁₁₃	M₁₆	1	2	yes	complemented
34	Dic₁₁₃	C₂²×C₄	1	2	yes	—
35	C₂×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₁₁₃	C₂×M₁₆	1	1	yes	characteristic
38	D₁₁₃	—	2	2	no	—
39	C₁₁₃	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
40	C₄×M₁₆	—	113	1	no	maximal, Sylow
41	C₂×M₁₆	—	113	2	no	—
42	C₂×C₄²	—	113	1	no	—
43	#97	—	113	2	no	—
44	C₄×C₈	—	113	2	no	—
45	C₂²×C₄	—	113	1	no	—
46	C₂²×C₄	—	113	1	no	—
47	C₂²×C₄	—	113	1	no	—
48	M₁₆	—	113	8	no	—
49	C₂×C₈	—	113	4	no	—
50	C₄²	—	113	1	no	—
51	C₄²	—	113	1	no	—
52	C₄²	—	113	1	no	—
53	C₄²	#90673	1	1	yes	characteristic
54	C₂³	—	113	1	no	—
55	C₂×C₄	—	113	1	no	—
56	C₂×C₄	—	113	1	no	—
57	C₂×C₄	—	113	4	no	—
58	C₂×C₄	—	113	1	no	—
59	C₂×C₄	—	226	2	no	—
60	C₂×C₄	—	226	2	no	—
61	C₂×C₄	C₂×#90673	1	1	yes	characteristic
62	C₂×C₄	C₂×#90673	1	1	yes	characteristic
63	C₂×C₄	C₂×#90673	1	1	yes	characteristic
64	C₈	—	113	8	no	—
65	C₂²	—	113	2	no	—
66	C₂²	—	226	1	no	—
67	C₂²	—	226	1	no	—
68	C₂²	C₂²×#90673	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	113	2	no	—
71	C₄	—	113	2	no	—
72	C₄	—	226	1	no	—
73	C₄	C₄×#90673	1	2	yes	—
74	C₄	#14268657	1	2	yes	direct product factor
75	C₂	—	226	2	no	—
76	C₂	C₂×C₄×#90673	1	1	yes	characteristic
77	C₂	D₁₁₃⋊M₁₆	1	1	yes	characteristic
78	C₂	C₂×#14268657	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#90673
commutator	C₂×C₁₁₃	C₂×C₄²
Frattini	C₂²	C₂²×#90673
Fitting	C₄²×C₁₁₃	C₄
socle	C₂²×C₁₁₃	C₂²×C₄
hypercenter	C₄²	#90673
hypocenter	C₁₁₃	C₄×M₁₆
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #16813677	C₂	semidirect
3. C₄×#11744753	C₂	semidirect
5. #14268657	C₄	direct (N × H)
24. #11744753	C₂×C₄	semidirect
31. C₄×C₁₁₃	M₁₆	semidirect
33. Dic₁₁₃	M₁₆	semidirect
39. C₁₁₃	C₄×M₁₆	semidirect
74. C₄	#14268657	direct (N × H)

Subgroups — C4×#14268657 #20299560

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14268657 #20299560