Subgroups — #28388403

Order 14464.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20298651	C₂	1	2	yes	maximal
2	#376×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11744751	—	2	2	no	—
4	C₂²⋊#11744751	—	2	2	no	—
5	C₄×#11744751	C₄	1	4	yes	complemented
6	C₂×C₄²×C₁₁₃	C₄	1	2	yes	—
7	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
8	#95×C₁₁₃	—	2	2	no	—
9	C₂×#11744751	—	2	4	no	—
10	C₂²×C₄×C₁₁₃	—	2	2	no	—
11	C₂²×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₁₃	D₄	1	2	yes	—
13	C₄²×C₁₁₃	—	2	2	no	—
14	C₄²×C₁₁₃	C₈	1	4	yes	complemented
15	C₄²×C₁₁₃	C₂×C₄	1	2	yes	—
16	C₄²×C₁₁₃	D₄	1	1	yes	characteristic
17	C₄²×C₁₁₃	Q₈	1	1	yes	characteristic
18	C₂³×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₁₃	—	2	4	no	—
20	C₂×C₄×C₁₁₃	—	4	2	no	—
21	C₂×C₄×C₁₁₃	—	4	4	no	—
22	C₂×C₄×C₁₁₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₁₁₃	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₁₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₁₃	M₁₆	1	2	yes	—
28	#11744751	—	4	4	no	—
29	C₂²×C₁₁₃	—	2	2	no	—
30	C₂²×C₁₁₃	#95	1	1	yes	characteristic
31	C₂²×C₁₁₃	C₂²⋊C₈	1	2	yes	—
32	C₄×C₁₁₃	—	2	2	no	—
33	C₄×C₁₁₃	—	2	2	no	—
34	C₄×C₁₁₃	—	4	4	no	—
35	C₄×C₁₁₃	C₄×C₈	1	1	yes	characteristic
36	C₄×C₁₁₃	#97	1	1	yes	characteristic
37	C₄×C₁₁₃	C₄⋊C₈	1	2	yes	—
38	C₂×C₁₁₃	—	2	2	no	—
39	C₂×C₁₁₃	#336	1	1	yes	characteristic
40	C₂×C₁₁₃	H(3,ℤ/4)	1	2	yes	—
41	#1274	—	113	1	no	maximal, Sylow
42	C₁₁₃	#1274	1	1	yes	characteristic, complemented, Sylow
43	#431	—	113	2	no	—
44	#376	D₁₁₃	1	1	yes	characteristic
45	C₂×C₄²	Dic₁₁₃	1	2	yes	—
46	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
47	C₄⋊C₈	—	226	2	no	—
48	C₂²⋊C₈	—	226	2	no	—
49	C₄×C₈	—	113	4	no	—
50	#95	—	2	2	no	—
51	C₂²×C₄	—	2	2	no	—
52	C₂²×C₄	C₂×Dic₁₁₃	1	1	yes	characteristic
53	C₂²×C₄	C₂²⋊D₁₁₃	1	2	yes	—
54	C₂×C₈	—	226	4	no	—
55	C₄²	—	2	2	no	—
56	C₄²	#11744751	1	4	yes	complemented
57	C₄²	Dic₂₂₆	1	1	yes	characteristic
58	C₄²	C₄×D₁₁₃	1	2	yes	—
59	C₄²	D₄₅₂	1	1	yes	characteristic
60	C₂³	C₂²⋊Dic₁₁₃	1	1	yes	characteristic
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	—	4	2	no	—
63	C₂×C₄	—	4	4	no	—
64	C₂×C₄	C₄×Dic₁₁₃	1	1	yes	characteristic
65	C₂×C₄	#14268624	1	2	yes	—
66	C₂×C₄	#14268626	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₁₁₃	1	1	yes	characteristic
68	C₂×C₄	C₂×#11744751	1	2	yes	—
69	C₂×C₄	#14268631	1	2	yes	—
70	C₈	—	452	4	no	—
71	C₂²	—	2	2	no	—
72	C₂²	#16813529	1	1	yes	characteristic
73	C₂²	C₂²⋊#11744751	1	2	yes	—
74	C₄	—	2	2	no	—
75	C₄	—	2	2	no	—
76	C₄	—	4	4	no	—
77	C₄	C₄×#11744751	1	1	yes	characteristic
78	C₄	#16813533	1	1	yes	characteristic
79	C₄	C₄⋊#11744751	1	2	yes	—
80	C₂	—	2	2	no	—
81	C₂	#20298353	1	1	yes	characteristic
82	C₂	#20298354	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×Dic₁₁₃
commutator	C₄×C₁₁₃	C₄×C₈
Frattini	C₂×C₄²	C₂×D₁₁₃
Fitting	#376×C₁₁₃	C₂
socle	C₂²×C₁₁₃	#95
prime radical	C₂³×C₁₁₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁₃	C₂²
hypercenter	#376	D₁₁₃
hypocenter	C₁₁₃	#1274
LCS	G ▷ C₄×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
5. C₄×#11744751	C₄	semidirect
14. C₄²×C₁₁₃	C₈	semidirect
42. C₁₁₃	#1274	semidirect
56. C₄²	#11744751	semidirect

Maximal subgroups

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

subgroup	index
#20298651	2
#376×C₁₁₃	2
#1274	113