Subgroups — #11718549

Order 832.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#88151	C₂	1	1	yes	maximal, characteristic
2	#88146	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	#88060	C₂	1	1	yes	maximal, characteristic
5	#88056	C₂	1	1	yes	maximal, characteristic, complemented
6	#88050	C₂	1	1	yes	maximal, characteristic, complemented
7	#88048	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₂₆	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	#6103	—	2	1	no	—
14	#6103	—	2	1	no	—
15	C₄⋊Dic₁₃	—	2	1	no	—
16	C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
17	C₄×Dic₁₃	—	2	1	no	—
18	C₂×#1055	C₂²	1	1	yes	characteristic
19	C₂²×D₁₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₃	—	2	1	no	—
21	C₂×C₄×C₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₃	—	2	1	no	—
24	C₂×Dic₁₃	—	2	1	no	—
25	C₂×Dic₁₃	D₄	1	1	yes	characteristic
26	C₄×D₁₃	—	2	1	no	—
27	C₄×D₁₃	—	2	1	no	—
28	Dic₂₆	—	2	1	no	—
29	Dic₂₆	—	2	1	no	—
30	C₈×C₁₃	—	2	1	no	—
31	#1055	—	2	1	no	—
32	#485	—	13	1	no	maximal, Sylow
33	C₂²×C₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×D₁₃	—	2	1	no	—
35	C₂×D₁₃	—	2	1	no	—
36	C₂×D₁₃	—	2	1	no	—
37	C₄×C₁₃	—	4	1	no	—
38	C₄×C₁₃	—	4	1	no	—
39	C₄×C₁₃	#41	1	1	yes	characteristic
40	C₄×C₁₃	#41	1	1	yes	characteristic
41	Dic₁₃	—	2	1	no	—
42	Dic₁₃	—	4	1	no	—
43	Dic₁₃	—	4	1	no	—
44	C₂²⋊Q₈	—	13	1	no	—
45	#117	—	13	1	no	—
46	#107	D₁₃	1	1	yes	characteristic, complemented
47	#106	—	13	1	no	—
48	#103	—	13	1	no	—
49	#103	—	13	1	no	—
50	C₂²⋊C₈	—	13	1	no	—
51	C₂×C₁₃	#123	1	1	yes	characteristic
52	C₂×C₁₃	#135	1	1	yes	characteristic
53	C₂×C₁₃	#137	1	1	yes	characteristic
54	D₁₃	—	4	1	no	—
55	C₂×Q₈	—	13	1	no	—
56	C₂²×C₄	—	13	1	no	—
57	C₂×C₈	—	13	1	no	—
58	C₂×C₈	C₂×D₁₃	1	1	yes	characteristic
59	C₄⋊C₄	—	13	1	no	—
60	C₄⋊C₄	—	26	1	no	—
61	C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
62	C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
63	C₂²⋊C₄	—	26	1	no	—
64	C₂²⋊C₄	—	26	1	no	—
65	C₄²	—	26	1	no	—
66	C₁₃	#485	1	1	yes	characteristic, complemented, Sylow
67	C₂³	—	13	1	no	—
68	Q₈	—	26	1	no	—
69	Q₈	—	26	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	13	1	no	—
73	C₂×C₄	—	26	1	no	—
74	C₂×C₄	—	26	1	no	—
75	C₂×C₄	—	26	1	no	—
76	C₂×C₄	—	26	1	no	—
77	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	26	1	no	—
80	C₂²	—	26	1	no	—
81	C₂²	—	26	1	no	—
82	C₂²	—	26	1	no	—
83	C₂²	D₄×D₁₃	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	26	1	no	—
87	C₄	—	52	1	no	—
88	C₄	—	52	1	no	—
89	C₄	#6127	1	1	yes	characteristic
90	C₄	#6131	1	1	yes	characteristic
91	C₂	—	52	1	no	—
92	C₂	#88148	1	1	yes	characteristic
93	C₂	#88166	1	1	yes	characteristic
94	C₂	#88172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₃
commutator, cosocle	C₂×C₄×C₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₃
Fitting	C₁₃×#107	C₂
socle	C₂²×C₁₃	C₂×D₄
prime radical	C₂²×D₁₃	D₄
hypercenter	#107	D₁₃
hypocenter	C₁₃	#485
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. C₁₃×#107	C₂	semidirect
5. #88056	C₂	semidirect
6. #88050	C₂	semidirect
7. #88048	C₂	semidirect
46. #107	D₁₃	semidirect
66. C₁₃	#485	semidirect

Maximal subgroups

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

subgroup	index
#88151	2
#88146	2
C₁₃×#107	2
#88060	2
#88056	2
#88050	2
#88048	2
#485	13