Subgroups — #28388748

Order 14464.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20298952	C₂	1	1	yes	maximal, characteristic
2	#20298395	C₂	1	1	yes	maximal, characteristic
3	#354×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	#16813614	C₄	1	1	yes	characteristic, complemented
5	#16813546	—	2	1	no	—
6	#16813543	—	2	1	no	—
7	#16813541	—	2	1	no	—
8	C₄×#11744751	C₄	1	1	yes	characteristic, complemented
9	#124×C₁₁₃	C₂²	1	1	yes	characteristic
10	#99×C₁₁₃	—	2	1	no	—
11	#14268631	—	4	1	no	—
12	C₂×#11744751	—	2	1	no	—
13	C₄⋊Dic₁₁₃	—	2	1	no	—
14	#14268626	—	4	1	no	—
15	C₂×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
16	C₂×D₄×C₁₁₃	D₄	1	1	yes	characteristic
17	C₂²⋊C₄×C₁₁₃	—	4	1	no	—
18	C₂²⋊C₄×C₁₁₃	—	4	1	no	—
19	C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₁₁₃	—	2	1	no	—
21	Q₈×C₁₁₃	—	4	1	no	—
22	D₄×C₁₁₃	—	4	1	no	—
23	C₂×C₄×C₁₁₃	—	2	1	no	—
24	C₂×C₄×C₁₁₃	—	2	1	no	—
25	C₂×C₄×C₁₁₃	—	8	1	no	—
26	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₁₃	—	4	1	no	—
28	#11744751	—	4	1	no	—
29	#11744751	—	8	1	no	—
30	C₂²×C₁₁₃	—	4	1	no	—
31	C₂²×C₁₁₃	—	8	1	no	—
32	C₂²×C₁₁₃	#99	1	1	yes	characteristic
33	C₄×C₁₁₃	—	2	1	no	—
34	C₄×C₁₁₃	—	4	1	no	—
35	C₄×C₁₁₃	—	4	1	no	—
36	C₄×C₁₁₃	—	16	1	no	—
37	Dic₁₁₃	—	8	1	no	—
38	C₂×C₁₁₃	—	2	1	no	—
39	C₂×C₁₁₃	—	8	1	no	—
40	C₂×C₁₁₃	#354	1	1	yes	characteristic
41	#1414	—	113	1	no	maximal, Sylow
42	C₁₁₃	#1414	1	1	yes	characteristic, complemented, Sylow
43	#488	—	113	1	no	—
44	#355	—	113	1	no	—
45	#354	D₁₁₃	1	1	yes	characteristic
46	#125	—	113	1	no	—
47	#124	C₂×D₁₁₃	1	1	yes	characteristic
48	#103	—	226	1	no	—
49	#102	—	226	1	no	—
50	#101	—	226	1	no	—
51	#99	—	2	1	no	—
52	C₄×C₈	—	113	1	no	—
53	C₂×Q₈	D₄₅₂	1	1	yes	characteristic
54	C₂×D₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
55	M₁₆	—	452	1	no	—
56	C₂×C₈	—	226	1	no	—
57	C₄⋊C₄	—	452	1	no	—
58	C₄⋊C₄	—	226	1	no	—
59	C₂²⋊C₄	—	4	1	no	—
60	C₂²⋊C₄	—	4	1	no	—
61	C₄²	C₄×D₁₁₃	1	1	yes	characteristic
62	C₂³	—	2	1	no	—
63	Q₈	—	4	1	no	—
64	D₄	—	4	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	8	1	no	—
68	C₂×C₄	—	452	1	no	—
69	C₂×C₄	#14268624	1	1	yes	characteristic
70	C₈	—	904	1	no	—
71	C₈	—	452	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	8	1	no	—
74	C₂²	#16813536	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	16	1	no	—
79	C₄	—	904	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	8	1	no	—
82	C₂	#20298392	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20298392
commutator	C₄²×C₁₁₃	C₂×C₄
Frattini	#124	C₂×D₁₁₃
Fitting	#354×C₁₁₃	C₂
socle	C₂×C₁₁₃	#354
prime radical	C₂×D₄×C₁₁₃	D₄
cosocle	#124×C₁₁₃	C₂²
hypercenter	#354	D₁₁₃
hypocenter	C₁₁₃	#1414
LCS	G ▷ C₄²×C₁₁₃ ▷ C₂×C₄×C₁₁₃ ▷ C₂²×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
4. #16813614	C₄	semidirect
8. C₄×#11744751	C₄	semidirect
42. C₁₁₃	#1414	semidirect

Maximal subgroups

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

subgroup	index
#20298952	2
#20298395	2
#354×C₁₁₃	2
#1414	113