Subgroups — #28388539

Order 14464.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₄₅₂	C₂	1	1	yes	maximal, characteristic
2	#20298351	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₅₂	C₄	1	1	yes	characteristic
5	C₄×Dic₂₂₆	—	2	1	no	—
6	#16813556	C₄	1	1	yes	characteristic
7	C₄⋊#11744751	—	2	1	no	—
8	#16813547	—	2	1	no	—
9	C₂×C₁₆×C₁₁₃	—	2	1	no	—
10	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₂₂₆	—	2	1	no	—
12	Dic₄₅₂	—	2	1	no	—
13	Dic₄₅₂	C₈	1	2	yes	complemented
14	C₂×#11744751	—	4	1	no	—
15	C₄⋊Dic₁₁₃	—	2	1	no	—
16	#14268626	—	4	1	no	—
17	C₄×Dic₁₁₃	—	4	1	no	—
18	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₁₃	D₄	1	1	yes	characteristic
20	C₄²×C₁₁₃	D₄	1	1	yes	characteristic
21	C₁₆×C₁₁₃	—	2	2	no	—
22	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₁₃	D₈	1	1	yes	characteristic
24	C₂×C₄×C₁₁₃	SD₁₆	1	1	yes	characteristic
25	C₂×Dic₁₁₃	—	4	1	no	—
26	C₂×Dic₁₁₃	—	4	1	no	—
27	Dic₂₂₆	—	2	2	no	—
28	Dic₂₂₆	—	4	1	no	—
29	C₈×C₁₁₃	—	2	1	no	—
30	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
32	#11744751	—	8	1	no	—
33	C₂²×C₁₁₃	#102	1	1	yes	characteristic
34	C₄×C₁₁₃	—	2	1	no	—
35	C₄×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₁₁₃	#104	1	1	yes	characteristic
37	C₄×C₁₁₃	SD₃₂	1	1	yes	characteristic
38	C₄×C₁₁₃	Q₃₂	1	1	yes	characteristic
39	Dic₁₁₃	—	4	2	no	—
40	Dic₁₁₃	—	8	1	no	—
41	C₂×C₁₁₃	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₁₁₃	#358	1	1	yes	characteristic
43	C₂×C₁₁₃	#359	1	1	yes	characteristic
44	#1332	—	113	1	no	maximal, Sylow
45	C₁₁₃	#1332	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₁₆	—	113	1	no	—
47	C₄×C₁₆	D₁₁₃	1	1	yes	characteristic
48	#335	—	113	1	no	—
49	C₂×Q₁₆	—	113	1	no	—
50	C₄×Q₈	—	226	1	no	—
51	C₂×C₁₆	—	2	1	no	—
52	#107	—	113	1	no	—
53	C₄⋊C₈	—	226	1	no	—
54	#103	—	226	1	no	—
55	C₄×C₈	C₂×D₁₁₃	1	1	yes	characteristic
56	C₂×Q₈	—	226	1	no	—
57	Q₁₆	—	113	2	no	—
58	Q₁₆	—	226	1	no	—
59	C₂×C₈	—	452	1	no	—
60	C₂×C₈	C₄×D₁₁₃	1	1	yes	characteristic
61	C₂×C₈	C₂²⋊D₁₁₃	1	1	yes	characteristic
62	C₄⋊C₄	—	452	1	no	—
63	C₄⋊C₄	—	226	1	no	—
64	C₄²	—	452	1	no	—
65	C₄²	D₄₅₂	1	1	yes	characteristic
66	C₁₆	—	2	2	no	—
67	Q₈	—	452	1	no	—
68	Q₈	—	226	2	no	—
69	C₂×C₄	—	452	1	no	—
70	C₂×C₄	—	452	1	no	—
71	C₂×C₄	#14268624	1	1	yes	characteristic
72	C₂×C₄	D₉₀₄	1	1	yes	characteristic
73	C₂×C₄	#14268636	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	904	1	no	—
76	C₈	C₈×D₁₁₃	1	1	yes	characteristic
77	C₈	#14268630	1	1	yes	characteristic
78	C₂²	#16813544	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	904	1	no	—
81	C₄	—	452	2	no	—
82	C₄	#16813534	1	1	yes	characteristic
83	C₄	#16813550	1	1	yes	characteristic
84	C₄	#16813567	1	1	yes	characteristic
85	C₄	Dic₉₀₄	1	1	yes	characteristic
86	C₂	#20298327	1	1	yes	characteristic
87	C₂	#20298403	1	1	yes	characteristic
88	C₂	#20298406	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₉₀₄
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₁₃
Fitting	C₄×C₁₆×C₁₁₃	C₂
socle, prime radical	C₂²×C₁₁₃	#102
cosocle	C₄×C₈×C₁₁₃	C₂²
hypercenter	C₄×C₁₆	D₁₁₃
hypocenter	C₁₁₃	#1332
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
13. Dic₄₅₂	C₈	semidirect
45. C₁₁₃	#1332	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₄₅₂	2
#20298351	2
C₄×C₁₆×C₁₁₃	2
#1332	113