Subgroups — #28405589

Order 14464.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299519	C₂	1	1	yes	maximal, characteristic
2	#20299462	C₂	1	1	yes	maximal, characteristic
3	#20298976	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268650	—	2	1	no	—
5	C₄⋊#11744753	—	2	1	no	—
6	C₂×Dic₄₅₂	C₄	1	1	yes	characteristic
7	C₂×#14268637	—	2	1	no	—
8	#16813620	—	2	1	no	—
9	C₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₁₁₃	C₄	1	1	yes	characteristic
11	C₂×#11744753	—	4	1	no	—
12	#14268650	—	4	1	no	—
13	C₂×Dic₂₂₆	—	2	1	no	—
14	Dic₄₅₂	—	4	1	no	—
15	#14268637	—	4	1	no	—
16	#14268637	—	4	1	no	—
17	C₂×#11744751	D₄	1	1	yes	characteristic
18	#14268626	—	4	1	no	—
19	#14268626	—	4	1	no	—
20	C₄×Dic₁₁₃	D₄	1	1	yes	characteristic
21	C₂×Q₈×C₁₁₃	—	2	1	no	—
22	Q₁₆×C₁₁₃	—	4	1	no	—
23	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
24	Q₈×C₁₁₃	—	4	1	no	—
25	Q₈×C₁₁₃	—	4	1	no	—
26	C₂×C₄×C₁₁₃	—	4	1	no	—
27	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₁₁₃	—	4	1	no	—
29	C₂×Dic₁₁₃	D₈	1	1	yes	characteristic
30	C₂×Dic₁₁₃	SD₁₆	1	1	yes	characteristic
31	Dic₂₂₆	—	4	1	no	—
32	Dic₂₂₆	—	4	1	no	—
33	#11744753	—	8	1	no	—
34	C₈×C₁₁₃	—	2	1	no	—
35	#11744751	D₈	1	1	yes	characteristic
36	#11744751	SD₁₆	1	1	yes	characteristic
37	C₂²×C₁₁₃	#102	1	1	yes	characteristic
38	C₄×C₁₁₃	—	8	1	no	—
39	C₄×C₁₁₃	#100	1	1	yes	characteristic
40	C₄×C₁₁₃	#102	1	1	yes	characteristic
41	Dic₁₁₃	—	2	1	no	—
42	Dic₁₁₃	—	8	1	no	—
43	Dic₁₁₃	SD₃₂	1	1	yes	characteristic
44	Dic₁₁₃	Q₃₂	1	1	yes	characteristic
45	C₂×C₁₁₃	#331	1	1	yes	characteristic
46	C₂×C₁₁₃	#358	1	1	yes	characteristic
47	C₂×C₁₁₃	#362	1	1	yes	characteristic
48	#1362	—	113	1	no	maximal, Sylow
49	C₁₁₃	#1362	1	1	yes	characteristic, complemented, Sylow
50	#494	—	113	1	no	—
51	C₄⋊C₁₆	—	113	1	no	—
52	#335	—	113	1	no	—
53	C₂×Q₁₆	—	113	1	no	—
54	C₂×Q₁₆	—	226	1	no	—
55	C₂×Q₁₆	#90673	1	1	yes	characteristic
56	C₄⋊Q₈	—	226	1	no	—
57	C₂×C₁₆	—	226	1	no	—
58	C₄⋊C₈	—	226	1	no	—
59	C₄×C₈	—	113	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	226	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	452	1	no	—
64	Q₁₆	—	452	1	no	—
65	Q₁₆	—	452	1	no	—
66	C₂×C₈	—	113	1	no	—
67	C₂×C₈	—	452	1	no	—
68	C₂×C₈	C₂×#90673	1	1	yes	characteristic
69	C₄⋊C₄	—	452	1	no	—
70	C₄⋊C₄	—	452	1	no	—
71	C₄²	—	113	1	no	—
72	C₁₆	—	452	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	452	1	no	—
76	Q₈	—	452	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	113	1	no	—
79	C₂×C₄	—	113	1	no	—
80	C₂×C₄	—	452	1	no	—
81	C₂×C₄	C₂²⋊#90673	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	113	1	no	—
84	C₈	—	113	1	no	—
85	C₈	—	904	1	no	—
86	C₂²	#16813684	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	113	1	no	—
89	C₄	—	113	1	no	—
90	C₄	—	904	1	no	—
91	C₄	—	226	1	no	—
92	C₄	#16813682	1	1	yes	characteristic
93	C₄	#16813684	1	1	yes	characteristic
94	C₂	#20299456	1	1	yes	characteristic
95	C₂	#20299511	1	1	yes	characteristic
96	C₂	#20299517	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16813684
commutator	C₂×C₈×C₁₁₃	C₂×C₄
Frattini	C₂×C₈	C₂×#90673
Fitting	C₂×Q₁₆×C₁₁₃	C₄
socle, prime radical	C₂²×C₁₁₃	#102
cosocle	C₈×Dic₁₁₃	C₂²
hypercenter	C₂×Q₁₆	#90673
hypocenter	C₁₁₃	#1362
LCS	G ▷ C₂×C₈×C₁₁₃ ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
49. C₁₁₃	#1362	semidirect

Maximal subgroups

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

subgroup	index
#20299519	2
#20299462	2
#20298976	2
#1362	113