Subgroups — #28388733

Order 14464.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20298993	C₂	1	1	yes	maximal, characteristic
2	#20298395	C₂	1	1	yes	maximal, characteristic
3	#354×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268637	—	2	1	no	—
5	C₂×#14268635	—	2	1	no	—
6	#16813622	C₄	1	1	yes	characteristic, complemented
7	#16813541	—	2	1	no	—
8	#16813533	C₄	1	1	yes	characteristic, complemented
9	#124×C₁₁₃	C₂²	1	1	yes	characteristic
10	#99×C₁₁₃	—	2	1	no	—
11	C₂×Dic₂₂₆	—	2	1	no	—
12	#14268637	—	4	2	no	—
13	#14268635	—	4	2	no	—
14	#14268631	—	4	1	no	—
15	C₂×#11744751	—	2	1	no	—
16	C₄⋊Dic₁₁₃	—	4	1	no	—
17	C₂×Q₈×C₁₁₃	D₄	1	1	yes	characteristic
18	C₂×D₄×C₁₁₃	D₄	1	1	yes	characteristic
19	C₂²⋊C₄×C₁₁₃	—	4	1	no	—
20	C₂²⋊C₄×C₁₁₃	—	4	1	no	—
21	C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₁₁₃	—	2	1	no	—
23	Q₈×C₁₁₃	—	4	1	no	—
24	D₄×C₁₁₃	—	4	1	no	—
25	C₂×C₄×C₁₁₃	—	2	1	no	—
26	C₂×C₄×C₁₁₃	—	2	1	no	—
27	C₂×C₄×C₁₁₃	—	8	1	no	—
28	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₁₁₃	—	4	1	no	—
30	Dic₂₂₆	—	4	1	no	—
31	Dic₂₂₆	—	4	1	no	—
32	#11744751	—	2	2	no	—
33	#11744751	—	8	1	no	—
34	C₂²×C₁₁₃	—	4	1	no	—
35	C₂²×C₁₁₃	—	8	1	no	—
36	C₂²×C₁₁₃	#99	1	1	yes	characteristic
37	C₄×C₁₁₃	—	2	1	no	—
38	C₄×C₁₁₃	—	4	1	no	—
39	C₄×C₁₁₃	—	4	1	no	—
40	C₄×C₁₁₃	—	16	1	no	—
41	Dic₁₁₃	—	8	1	no	—
42	C₂×C₁₁₃	—	2	1	no	—
43	C₂×C₁₁₃	—	8	1	no	—
44	C₂×C₁₁₃	#353	1	1	yes	characteristic
45	#1407	—	113	1	no	maximal, Sylow
46	C₁₁₃	#1407	1	1	yes	characteristic, complemented, Sylow
47	#497	—	113	1	no	—
48	#355	—	113	1	no	—
49	#354	D₁₁₃	1	1	yes	characteristic
50	C₂×Q₁₆	—	226	1	no	—
51	C₂×SD₁₆	—	226	1	no	—
52	C₄⋊Q₈	—	113	1	no	—
53	#124	C₂×D₁₁₃	1	1	yes	characteristic
54	#101	—	226	1	no	—
55	#99	—	2	1	no	—
56	#97	—	113	1	no	—
57	C₂×Q₈	—	226	1	no	—
58	C₂×Q₈	D₄₅₂	1	1	yes	characteristic
59	C₂×D₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
60	Q₁₆	—	452	2	no	—
61	SD₁₆	—	452	2	no	—
62	M₁₆	—	452	1	no	—
63	C₂×C₈	—	226	1	no	—
64	C₄⋊C₄	—	452	1	no	—
65	C₂²⋊C₄	—	4	1	no	—
66	C₂²⋊C₄	—	4	1	no	—
67	C₄²	C₄×D₁₁₃	1	1	yes	characteristic
68	C₂³	—	2	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	452	1	no	—
71	Q₈	—	452	1	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	8	1	no	—
76	C₂×C₄	—	452	1	no	—
77	C₂×C₄	#14268624	1	1	yes	characteristic
78	C₈	—	904	1	no	—
79	C₈	—	226	2	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	8	1	no	—
82	C₂²	#16813536	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	16	1	no	—
87	C₄	—	904	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#20298390	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20298390
commutator	C₄²×C₁₁₃	C₂×C₄
Frattini	#124	C₂×D₁₁₃
Fitting	#354×C₁₁₃	C₂
socle	C₂×C₁₁₃	#353
prime radical	C₂×D₄×C₁₁₃	D₄
cosocle	#124×C₁₁₃	C₂²
hypercenter	#354	D₁₁₃
hypocenter	C₁₁₃	#1407
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
6. #16813622	C₄	semidirect
8. #16813533	C₄	semidirect
46. C₁₁₃	#1407	semidirect

Maximal subgroups

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

subgroup	index
#20298993	2
#20298395	2
#354×C₁₁₃	2
#1407	113