Subgroups — #11719129

Order 832.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#6122	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#88112	C₂	1	2	yes	maximal, complemented
4	C₄⋊#1057	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₃	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₃	C₂²	1	1	yes	characteristic
8	#6122	—	2	4	no	—
9	C₂×#1057	C₂²	1	4	yes	—
10	C₄×Dic₁₃	C₄	1	1	yes	characteristic
11	C₄×Dic₁₃	C₄	1	1	yes	characteristic
12	C₄×Dic₁₃	C₂²	1	1	yes	characteristic
13	C₄×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₃	—	2	2	no	—
16	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₃	—	2	2	no	—
19	C₂×Dic₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₁₃	D₄	1	2	yes	—
23	C₂×Dic₁₃	Q₈	1	2	yes	—
24	C₂×Dic₁₃	C₂³	1	1	yes	characteristic
25	#1057	—	2	4	no	—
26	#423	—	13	1	no	maximal, Sylow
27	C₂²×C₁₃	—	2	1	no	—
28	C₂²×C₁₃	—	2	1	no	—
29	C₂²×C₁₃	C₄⋊C₄	1	2	yes	—
30	C₂²×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₃	—	2	1	no	—
32	C₄×C₁₃	M₁₆	1	2	yes	complemented
33	Dic₁₃	—	2	1	no	—
34	Dic₁₃	C₄⋊C₄	1	2	yes	—
35	Dic₁₃	M₁₆	1	2	yes	complemented
36	Dic₁₃	C₂×D₄	1	1	yes	characteristic
37	Dic₁₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×M₁₆	—	13	2	no	—
39	C₂×C₄²	—	13	1	no	—
40	C₄⋊C₈	—	13	2	no	—
41	C₄⋊C₈	—	13	2	no	—
42	C₂×C₁₃	—	2	2	no	—
43	C₂×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₁₃	C₂×M₁₆	1	1	yes	characteristic
45	C₂×C₁₃	C₂×M₁₆	1	1	yes	characteristic
46	C₂²×C₄	—	13	1	no	—
47	C₂²×C₄	—	13	1	no	—
48	C₂²×C₄	#261	1	1	yes	characteristic
49	M₁₆	—	26	4	no	—
50	C₂×C₈	—	13	4	no	—
51	C₄²	—	13	1	no	—
52	C₄²	—	13	1	no	—
53	C₄²	—	13	1	no	—
54	C₄²	—	13	1	no	—
55	C₁₃	#423	1	1	yes	characteristic, complemented, Sylow
56	C₂³	C₂×#261	1	1	yes	characteristic
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	13	2	no	—
59	C₂×C₄	—	13	2	no	—
60	C₂×C₄	—	13	1	no	—
61	C₂×C₄	—	13	1	no	—
62	C₂×C₄	—	13	1	no	—
63	C₂×C₄	—	13	1	no	—
64	C₂×C₄	—	26	2	no	—
65	C₂×C₄	C₂×#261	1	1	yes	characteristic
66	C₂×C₄	C₂×#261	1	1	yes	characteristic
67	C₈	—	26	4	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	2	1	no	—
70	C₂²	C₄⋊#261	1	2	yes	—
71	C₂²	C₂²×#261	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	—	13	2	no	—
74	C₄	—	13	2	no	—
75	C₄	—	13	1	no	—
76	C₄	—	13	1	no	—
77	C₄	—	26	1	no	—
78	C₄	#6122	1	2	yes	complemented
79	C₂	—	2	2	no	—
80	C₂	D₁₃⋊M₁₆	1	1	yes	characteristic
81	C₂	C₂×C₄⋊#261	1	1	yes	characteristic
82	C₂	C₂×#6122	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄
Fitting	C₂²×C₄×C₁₃	C₄
prime radical	C₂³×C₁₃	C₂×C₄
cosocle	C₂×Dic₁₃	C₂³
hypercenter	C₂²×C₄	#261
hypocenter	C₁₃	#423
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. #88112	C₂	semidirect
4. C₄⋊#1057	C₂	semidirect
32. C₄×C₁₃	M₁₆	semidirect
35. Dic₁₃	M₁₆	semidirect
55. C₁₃	#423	semidirect
78. C₄	#6122	semidirect

Maximal subgroups

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

subgroup	index
C₂×#6122	2
C₂×C₄×Dic₁₃	2
#88112	2
C₄⋊#1057	2
#423	13