Subgroups — #28405702

Order 14464.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299507	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299505	C₂	1	1	yes	maximal, characteristic, complemented
3	#20298987	C₂	1	1	yes	maximal, characteristic
4	#16813683	—	2	1	no	—
5	#16813681	—	2	1	no	—
6	C₂×#14268636	—	2	1	no	—
7	C₂×D₉₀₄	—	2	1	no	—
8	#16813619	C₄	1	1	yes	characteristic, complemented
9	#16813610	C₂²	1	1	yes	characteristic
10	#97×C₁₁₃	C₄	1	1	yes	characteristic, complemented
11	#14268656	—	4	1	no	—
12	C₂²⋊#90673	—	4	1	no	—
13	C₂×Dic₂₂₆	D₄	1	1	yes	characteristic
14	C₂×D₄₅₂	—	2	1	no	—
15	C₂×D₄₅₂	—	4	1	no	—
16	C₂×D₄₅₂	D₄	1	1	yes	characteristic
17	#14268636	—	4	2	no	—
18	D₉₀₄	—	4	2	no	—
19	#14268624	—	4	1	no	—
20	C₂×C₈×C₁₁₃	—	2	1	no	—
21	C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₁₁₃	—	2	1	no	—
23	C₂²×D₁₁₃	—	4	1	no	—
24	C₂×#90673	—	8	1	no	—
25	C₂×C₄×C₁₁₃	—	2	1	no	—
26	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₁₃	—	2	1	no	—
28	D₄₅₂	—	4	1	no	—
29	D₄₅₂	—	4	1	no	—
30	D₄₅₂	—	4	1	no	—
31	D₄₅₂	—	8	2	no	—
32	Dic₂₂₆	—	4	1	no	—
33	#11744753	—	8	1	no	—
34	C₈×C₁₁₃	—	2	2	no	—
35	C₂²×C₁₁₃	#99	1	1	yes	characteristic
36	C₂×D₁₁₃	—	4	1	no	—
37	C₂×D₁₁₃	—	8	1	no	—
38	C₂×D₁₁₃	—	8	2	no	—
39	C₂×D₁₁₃	—	8	1	no	—
40	#90673	—	16	1	no	—
41	C₄×C₁₁₃	—	2	1	no	—
42	C₄×C₁₁₃	—	4	1	no	—
43	Dic₁₁₃	—	4	1	no	—
44	C₂×C₁₁₃	—	2	1	no	—
45	C₂×C₁₁₃	#353	1	1	yes	characteristic
46	D₁₁₃	—	8	1	no	—
47	D₁₁₃	—	16	1	no	—
48	#1406	—	113	1	no	maximal, Sylow
49	C₁₁₃	#1406	1	1	yes	characteristic, complemented, Sylow
50	#496	—	113	1	no	—
51	#355	—	113	1	no	—
52	#354	—	113	1	no	—
53	C₂×SD₁₆	—	226	1	no	—
54	C₂×D₈	—	226	1	no	—
55	#127	—	113	1	no	—
56	#124	—	113	1	no	—
57	#101	—	226	1	no	—
58	#99	—	226	1	no	—
59	#97	#90673	1	1	yes	characteristic, complemented
60	C₂×Q₈	—	113	1	no	—
61	C₂×D₄	—	113	1	no	—
62	C₂×D₄	—	452	1	no	—
63	C₂×D₄	—	226	1	no	—
64	SD₁₆	—	452	2	no	—
65	D₈	—	452	2	no	—
66	M₁₆	—	452	1	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂²⋊C₄	—	452	1	no	—
69	C₂²⋊C₄	—	452	1	no	—
70	C₄²	C₂×#90673	1	1	yes	characteristic
71	C₂³	—	452	1	no	—
72	C₂³	—	226	1	no	—
73	Q₈	—	452	1	no	—
74	D₄	—	904	2	no	—
75	D₄	—	452	1	no	—
76	D₄	—	452	1	no	—
77	D₄	—	452	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	904	1	no	—
80	C₂×C₄	—	226	1	no	—
81	C₂×C₄	C₂²⋊#90673	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	904	1	no	—
84	C₂²	—	904	2	no	—
85	C₂²	—	904	1	no	—
86	C₂²	—	904	1	no	—
87	C₂²	—	452	1	no	—
88	C₂²	#16813681	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	1808	1	no	—
92	C₄	—	452	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	1808	1	no	—
95	C₂	—	904	1	no	—
96	C₂	#20299503	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20299503
commutator	C₄²×C₁₁₃	C₂×C₄
Frattini	C₄²	C₂×#90673
Fitting	#97×C₁₁₃	C₄
socle	C₂×C₁₁₃	#353
prime radical	#20298987	C₂
cosocle	#16813610	C₂²
hypercenter	#97	#90673
hypocenter	C₁₁₃	#1406
LCS	G ▷ C₄²×C₁₁₃ ▷ C₂×C₄×C₁₁₃ ▷ C₂²×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. #20299507	C₂	semidirect
2. #20299505	C₂	semidirect
8. #16813619	C₄	semidirect
10. #97×C₁₁₃	C₄	semidirect
49. C₁₁₃	#1406	semidirect
59. #97	#90673	semidirect

Maximal subgroups

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

subgroup	index
#20299507	2
#20299505	2
#20298987	2
#1406	113