Subgroups — #28392460

Order 14464.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20298715	C₂	1	2	yes	maximal, complemented
2	#20298428	C₂	1	1	yes	maximal, characteristic, complemented
3	#20298405	C₂	1	2	yes	maximal, complemented
4	#20298373	C₂	1	1	yes	maximal, characteristic, complemented
5	#508×C₁₁₃	C₂	1	1	yes	maximal, characteristic
6	#16813629	—	2	2	no	—
7	C₂×#14268622	C₂²	1	1	yes	characteristic
8	#16813558	C₂²	1	2	yes	—
9	#16813549	—	2	2	no	—
10	C₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
11	#135×C₁₁₃	C₂²	1	2	yes	—
12	Q₃₂×C₁₁₃	C₄	1	1	yes	characteristic, complemented
13	SD₃₂×C₁₁₃	C₄	1	2	yes	complemented
14	D₁₆×C₁₁₃	C₄	1	1	yes	characteristic, complemented
15	C₂×C₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
16	#14268631	—	2	2	no	—
17	#14268631	—	4	2	no	—
18	C₂×#11744751	—	4	2	no	—
19	C₂×#11744751	D₄	1	1	yes	characteristic
20	C₄×Dic₁₁₃	D₄	1	1	yes	characteristic
21	#14268622	—	2	1	no	—
22	#41×C₁₁₃	—	2	2	no	—
23	Q₁₆×C₁₁₃	C₂×C₄	1	2	yes	—
24	SD₁₆×C₁₁₃	—	2	2	no	—
25	D₈×C₁₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
27	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
29	Q₈×C₁₁₃	—	2	2	no	—
30	D₄×C₁₁₃	—	2	2	no	—
31	D₄×C₁₁₃	—	4	2	no	—
32	C₂×C₄×C₁₁₃	—	4	2	no	—
33	C₂×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₁₁₃	—	2	1	no	—
35	C₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₈×C₁₁₃	#41	1	1	yes	characteristic
37	#11744751	—	4	2	no	—
38	#11744751	D₈	1	2	yes	—
39	C₂²×C₁₁₃	—	4	2	no	—
40	C₂²×C₁₁₃	#135	1	1	yes	characteristic
41	C₄×C₁₁₃	—	4	2	no	—
42	C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
43	C₄×C₁₁₃	C₂×D₈	1	1	yes	characteristic
44	Dic₁₁₃	—	4	1	no	—
45	C₂×C₁₁₃	—	2	1	no	—
46	C₂×C₁₁₃	—	8	2	no	—
47	C₂×C₁₁₃	C₄×D₈	1	1	yes	characteristic
48	#2179	—	113	1	no	maximal, Sylow
49	C₁₁₃	#2179	1	1	yes	characteristic, complemented, Sylow
50	#508	D₁₁₃	1	1	yes	characteristic
51	#443	—	113	2	no	—
52	#368	—	113	1	no	—
53	#359	—	113	2	no	—
54	#346	—	113	1	no	—
55	#135	C₂×D₁₁₃	1	2	yes	—
56	#131	—	226	2	no	—
57	Q₃₂	Dic₁₁₃	1	1	yes	characteristic, complemented
58	SD₃₂	Dic₁₁₃	1	2	yes	complemented
59	D₁₆	Dic₁₁₃	1	1	yes	characteristic, complemented
60	C₂×C₁₆	—	113	1	no	—
61	C₂×C₁₆	C₂×D₁₁₃	1	1	yes	characteristic
62	#108	—	113	2	no	—
63	#104	—	226	2	no	—
64	C₄×C₈	—	113	1	no	—
65	#41	—	2	2	no	—
66	Q₁₆	C₂×Dic₁₁₃	1	2	yes	—
67	SD₁₆	—	2	2	no	—
68	D₈	C₂×Dic₁₁₃	1	2	yes	—
69	M₁₆	—	452	2	no	—
70	M₁₆	—	226	2	no	—
71	C₂×C₈	—	113	1	no	—
72	C₂×C₈	—	452	2	no	—
73	C₂×C₈	C₂²×D₁₁₃	1	1	yes	characteristic
74	C₄²	—	113	1	no	—
75	C₁₆	—	226	1	no	—
76	C₁₆	C₂×Dic₁₁₃	1	1	yes	characteristic
77	C₁₆	C₂×Dic₁₁₃	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	D₄	—	2	2	no	—
80	D₄	—	4	2	no	—
81	C₂×C₄	—	4	2	no	—
82	C₂×C₄	—	226	1	no	—
83	C₂×C₄	D₄×D₁₁₃	1	1	yes	characteristic
84	C₈	—	113	2	no	—
85	C₈	—	452	2	no	—
86	C₈	C₂²×Dic₁₁₃	1	1	yes	characteristic
87	C₈	#14268646	1	1	yes	characteristic
88	C₂²	—	4	2	no	—
89	C₂²	#16813641	1	1	yes	characteristic
90	C₄	—	4	2	no	—
91	C₄	—	452	1	no	—
92	C₄	D₄×Dic₁₁₃	1	1	yes	characteristic
93	C₄	D₈×D₁₁₃	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	8	2	no	—
96	C₂	D₈×Dic₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₁₁₃
commutator	C₈×C₁₁₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₁₃
Fitting, prime radical	#508×C₁₁₃	C₂
socle	C₂×C₁₁₃	C₄×D₈
cosocle	C₂×C₈×C₁₁₃	C₂³
hypercenter	#508	D₁₁₃
hypocenter	C₁₁₃	#2179
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #508

Complements

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

N	H ≅ G/N	type
1. #20298715	C₂	semidirect
2. #20298428	C₂	semidirect
3. #20298405	C₂	semidirect
4. #20298373	C₂	semidirect
12. Q₃₂×C₁₁₃	C₄	semidirect
13. SD₃₂×C₁₁₃	C₄	semidirect
14. D₁₆×C₁₁₃	C₄	semidirect
49. C₁₁₃	#2179	semidirect
57. Q₃₂	Dic₁₁₃	semidirect
58. SD₃₂	Dic₁₁₃	semidirect
59. D₁₆	Dic₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20298715	2
#20298428	2
#20298405	2
#20298373	2
#508×C₁₁₃	2
#2179	113