Subgroups — #28406977

Order 14464.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299642	C₂	1	2	yes	maximal, complemented
2	#20299527	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299513	C₂	1	2	yes	maximal, complemented
4	#20299485	C₂	1	1	yes	maximal, characteristic, complemented
5	#20299031	C₂	1	1	yes	maximal, characteristic
6	#16813710	—	2	2	no	—
7	#16813695	C₂²	1	1	yes	characteristic
8	#16813693	C₂²	1	2	yes	—
9	#16813687	—	2	2	no	—
10	C₈×#90673	C₂²	1	1	yes	characteristic
11	#16813645	C₂²	1	2	yes	—
12	#16813565	C₄	1	2	yes	complemented
13	D₁₈₀₈	C₄	1	1	yes	characteristic, complemented
14	C₁₆×D₁₁₃	C₂²	1	1	yes	characteristic
15	Q₃₂×C₁₁₃	C₄	1	1	yes	characteristic, complemented
16	#14268657	—	2	2	no	—
17	#14268657	—	4	2	no	—
18	#14268655	—	4	2	no	—
19	#14268655	D₄	1	1	yes	characteristic
20	C₄×#90673	D₄	1	1	yes	characteristic
21	#14268650	—	2	1	no	—
22	#14268648	—	2	2	no	—
23	#14268634	—	2	2	no	—
24	D₉₀₄	C₂×C₄	1	2	yes	—
25	C₈×D₁₁₃	C₂³	1	1	yes	characteristic
26	#14268622	C₂×C₄	1	1	yes	characteristic
27	Q₁₆×C₁₁₃	C₂×C₄	1	2	yes	—
28	C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×#90673	—	2	1	no	—
30	Q₈×C₁₁₃	—	2	2	no	—
31	D₄₅₂	—	2	2	no	—
32	D₄₅₂	—	4	2	no	—
33	C₄×D₁₁₃	—	4	2	no	—
34	C₄×D₁₁₃	C₂×D₄	1	1	yes	characteristic
35	#11744753	—	4	2	no	—
36	#11744753	D₈	1	2	yes	—
37	C₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
38	#11744751	#41	1	1	yes	characteristic
39	C₂×D₁₁₃	—	4	2	no	—
40	C₂×D₁₁₃	#135	1	1	yes	characteristic
41	#90673	—	4	1	no	—
42	C₄×C₁₁₃	—	4	2	no	—
43	C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
44	Dic₁₁₃	C₂×D₈	1	1	yes	characteristic
45	C₂×C₁₁₃	C₄×D₈	1	1	yes	characteristic
46	D₁₁₃	—	2	1	no	—
47	D₁₁₃	—	8	2	no	—
48	#2179	—	113	1	no	maximal, Sylow
49	C₁₁₃	#2179	1	1	yes	characteristic, complemented, Sylow
50	#508	—	113	1	no	—
51	#443	—	113	2	no	—
52	#368	—	113	1	no	—
53	#359	—	113	2	no	—
54	#346	—	113	1	no	—
55	#135	—	113	2	no	—
56	#131	—	226	2	no	—
57	Q₃₂	#90673	1	1	yes	characteristic, complemented
58	SD₃₂	—	113	2	no	—
59	D₁₆	—	113	1	no	—
60	C₂×C₁₆	—	113	1	no	—
61	C₂×C₁₆	—	113	1	no	—
62	#108	—	113	2	no	—
63	#104	—	226	2	no	—
64	C₄×C₈	—	113	1	no	—
65	#41	—	226	2	no	—
66	Q₁₆	C₂×#90673	1	2	yes	—
67	SD₁₆	—	226	2	no	—
68	D₈	—	113	2	no	—
69	M₁₆	—	452	2	no	—
70	M₁₆	—	226	2	no	—
71	C₂×C₈	—	113	1	no	—
72	C₂×C₈	—	113	1	no	—
73	C₂×C₈	—	452	2	no	—
74	C₄²	—	113	1	no	—
75	C₁₆	—	113	1	no	—
76	C₁₆	—	226	1	no	—
77	C₁₆	C₂×#90673	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	D₄	—	452	2	no	—
80	D₄	—	226	2	no	—
81	C₂×C₄	—	113	1	no	—
82	C₂×C₄	—	452	2	no	—
83	C₂×C₄	—	226	1	no	—
84	C₈	—	113	2	no	—
85	C₈	—	113	1	no	—
86	C₈	—	452	2	no	—
87	C₈	C₂²×#90673	1	1	yes	characteristic
88	C₂²	—	113	1	no	—
89	C₂²	—	452	2	no	—
90	C₄	—	4	2	no	—
91	C₄	—	113	1	no	—
92	C₄	—	452	1	no	—
93	C₄	D₄×#90673	1	1	yes	characteristic
94	C₂	—	904	2	no	—
95	C₂	—	226	1	no	—
96	C₂	D₈×#90673	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#90673
commutator	C₈×C₁₁₃	C₂²×C₄
Frattini	C₈	C₂²×#90673
Fitting	Q₃₂×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₄×D₈
prime radical	#20299031	C₂
cosocle	C₈×D₁₁₃	C₂³
hypercenter	Q₃₂	#90673
hypocenter	C₁₁₃	#2179
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #20299642	C₂	semidirect
2. #20299527	C₂	semidirect
3. #20299513	C₂	semidirect
4. #20299485	C₂	semidirect
12. #16813565	C₄	semidirect
13. D₁₈₀₈	C₄	semidirect
15. Q₃₂×C₁₁₃	C₄	semidirect
49. C₁₁₃	#2179	semidirect
57. Q₃₂	#90673	semidirect

Maximal subgroups

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

subgroup	index
#20299642	2
#20299527	2
#20299513	2
#20299485	2
#20299031	2
#2179	113