Subgroups — #11719055

Order 832.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic
2	#88112	C₂	1	2	yes	maximal, complemented
3	#88111	C₂	1	2	yes	maximal
4	#88110	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄×D₁₃	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×#1057	C₂²	1	4	yes	—
9	C₄²×C₁₃	C₄	1	1	yes	characteristic
10	C₄×Dic₁₃	C₄	1	1	yes	characteristic
11	C₄×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₄×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₂²×D₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₁₃	C₂³	1	1	yes	characteristic
20	C₄×D₁₃	—	2	2	no	—
21	C₄×D₁₃	—	2	2	no	—
22	C₄×D₁₃	—	2	2	no	—
23	#1057	—	2	4	no	—
24	#432	—	13	1	no	maximal, Sylow
25	C₂²×C₁₃	C₂²×C₄	1	1	yes	characteristic
26	C₂×D₁₃	—	2	1	no	—
27	C₂×D₁₃	—	2	1	no	—
28	C₂×D₁₃	M₁₆	1	2	yes	—
29	C₄×C₁₃	—	2	1	no	—
30	C₄×C₁₃	—	2	1	no	—
31	C₄×C₁₃	—	2	1	no	—
32	Dic₁₃	—	2	1	no	—
33	Dic₁₃	M₁₆	1	2	yes	—
34	Dic₁₃	#41	1	2	yes	—
35	C₂×C₄²	—	13	1	no	—
36	C₄⋊C₈	—	13	2	no	—
37	C₂²⋊C₈	—	13	2	no	—
38	#97	—	13	2	no	—
39	C₂×C₁₃	#117	1	1	yes	characteristic
40	C₂×C₁₃	C₂×M₁₆	1	1	yes	characteristic
41	C₂×C₁₃	C₂×M₁₆	1	1	yes	characteristic
42	D₁₃	—	2	2	no	—
43	C₂²×C₄	—	13	1	no	—
44	C₂²×C₄	—	13	1	no	—
45	C₂²×C₄	—	13	1	no	—
46	C₂×C₈	—	13	4	no	—
47	C₄²	—	13	1	no	—
48	C₄²	—	13	1	no	—
49	C₄²	—	13	1	no	—
50	C₄²	#261	1	1	yes	characteristic
51	C₁₃	#432	1	1	yes	characteristic, complemented, Sylow
52	C₂³	—	13	1	no	—
53	C₂×C₄	—	13	1	no	—
54	C₂×C₄	—	13	1	no	—
55	C₂×C₄	—	13	1	no	—
56	C₂×C₄	—	26	2	no	—
57	C₂×C₄	—	26	2	no	—
58	C₂×C₄	—	26	2	no	—
59	C₂×C₄	C₂×#261	1	1	yes	characteristic
60	C₂×C₄	C₂×#261	1	1	yes	characteristic
61	C₂×C₄	C₂×#261	1	1	yes	characteristic
62	C₈	—	26	4	no	—
63	C₂²	—	13	2	no	—
64	C₂²	—	26	1	no	—
65	C₂²	—	26	1	no	—
66	C₂²	C₂²×#261	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	2	1	no	—
69	C₄	—	2	1	no	—
70	C₄	—	13	2	no	—
71	C₄	—	13	2	no	—
72	C₄	—	26	1	no	—
73	C₂	—	26	2	no	—
74	C₂	D₁₃⋊M₁₆	1	1	yes	characteristic
75	C₂	D₁₃⋊M₁₆	1	1	yes	characteristic
76	C₂	#88237	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄
Fitting	C₄²×C₁₃	C₄
prime radical	C₂²×D₁₃	C₂×C₄
cosocle	C₂×Dic₁₃	C₂³
hypercenter	C₄²	#261
hypocenter	C₁₃	#432
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #88112	C₂	semidirect
4. #88110	C₂	semidirect
51. C₁₃	#432	semidirect

Maximal subgroups

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

subgroup	index
C₄²×D₁₃	2
#88112	2
#88111	2
#88110	2
#432	13