Subgroups — #11928376

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊#261	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
3	(C₂×#261)⋊C₄	—	3	1	no	maximal, Hall
4	C₂²×C₃×D₁₃	C₂²	1	1	yes	characteristic
5	C₂×C₃⋊#261	—	2	2	no	—
6	C₂×C₃⋊#261	—	2	2	no	—
7	C₂×C₃⋊#261	C₄	1	4	yes	complemented
8	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic, complemented
9	C₂×C₃×Dic₁₃	C₄	1	1	yes	characteristic, complemented
10	C₃×C₄×D₁₃	—	2	2	no	—
11	C₂²×#261	—	3	2	no	—
12	C₂×C₄×D₁₃	D₃	1	1	yes	characteristic
13	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×D₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₃×D₁₃	D₄	1	1	yes	characteristic
16	C₂×C₃×D₁₃	D₄	1	2	yes	—
17	C₂×C₃×D₁₃	Q₈	1	1	yes	characteristic
18	C₃⋊#261	—	2	4	no	—
19	C₃×C₄×C₁₃	—	2	1	no	—
20	C₃×Dic₁₃	—	2	1	no	—
21	C₂²×D₁₃	C₂×D₃	1	1	yes	characteristic
22	C₂×#261	—	3	4	no	—
23	C₂×#261	—	6	2	no	—
24	C₂×#261	—	6	2	no	—
25	C₂×C₄×C₁₃	Dic₃	1	1	yes	characteristic, complemented
26	C₂×Dic₁₃	Dic₃	1	1	yes	characteristic, complemented
27	C₄×D₁₃	—	2	2	no	—
28	C₃⋊#95	—	13	1	no	maximal, Hall
29	C₂×C₃×C₁₃	C₄²	1	1	yes	characteristic
30	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
32	C₃×D₁₃	C₂²⋊C₄	1	2	yes	—
33	C₃×D₁₃	C₄⋊C₄	1	2	yes	—
34	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
35	C₂×D₁₃	Dic₆	1	1	yes	characteristic
36	C₂×D₁₃	C₄×D₃	1	2	yes	—
37	C₂×D₁₃	D₁₂	1	1	yes	characteristic
38	C₂×D₁₃	#67	1	2	yes	—
39	#261	—	6	4	no	—
40	C₄×C₁₃	—	2	1	no	—
41	Dic₁₃	—	2	1	no	—
42	C₂²×C₃×C₄	—	13	1	no	—
43	C₂²×Dic₃	—	13	2	no	—
44	C₃×C₁₃	#95	1	1	yes	characteristic, complemented, Hall
45	#95	—	39	1	no	Sylow
46	C₂×C₁₃	C₄×Dic₃	1	1	yes	characteristic
47	C₂×C₁₃	C₄⋊Dic₃	1	1	yes	characteristic
48	C₂×C₁₃	#217	1	1	yes	characteristic
49	D₁₃	Dic₃⋊C₄	1	2	yes	—
50	D₁₃	(C₂×D₃)⋊C₄	1	2	yes	—
51	C₂³×C₃	—	13	1	no	—
52	C₂×C₃×C₄	—	13	1	no	—
53	C₂×C₃×C₄	—	26	2	no	—
54	C₂×C₃×C₄	#261	1	1	yes	characteristic, complemented
55	C₂×Dic₃	—	13	4	no	—
56	C₂×Dic₃	—	26	2	no	—
57	C₂×Dic₃	—	26	2	no	—
58	C₂²×C₄	—	13	1	no	—
59	C₂²×C₄	—	39	2	no	—
60	C₁₃	C₃⋊#95	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₃	—	13	2	no	—
62	C₂²×C₃	—	13	1	no	—
63	C₂²×C₃	—	13	1	no	—
64	C₂²×C₃	—	13	2	no	—
65	C₂²×C₃	C₂×#261	1	1	yes	characteristic
66	C₃×C₄	—	2	1	no	—
67	C₃×C₄	—	26	1	no	—
68	Dic₃	—	26	4	no	—
69	C₂³	—	13	1	no	—
70	C₂×C₄	—	13	1	no	—
71	C₂×C₄	—	26	2	no	—
72	C₂×C₄	—	39	4	no	—
73	C₂×C₄	—	78	2	no	—
74	C₂×C₄	—	78	2	no	—
75	C₂×C₄	C₃⋊#261	1	1	yes	characteristic, complemented
76	C₂×C₃	—	13	2	no	—
77	C₂×C₃	—	13	2	no	—
78	C₂×C₃	C₄×#261	1	1	yes	characteristic
79	C₂×C₃	C₄⋊#261	1	1	yes	characteristic
80	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
81	C₂²	—	13	2	no	—
82	C₂²	—	13	1	no	—
83	C₂²	—	13	1	no	—
84	C₂²	—	13	2	no	—
85	C₂²	C₂×C₃⋊#261	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	26	1	no	—
88	C₄	—	78	4	no	—
89	C₃	(C₂×#261)⋊C₄	1	1	yes	characteristic, complemented, Sylow
90	C₂	—	13	2	no	—
91	C₂	—	13	2	no	—
92	C₂	C₄×C₃⋊#261	1	1	yes	characteristic
93	C₂	C₄⋊(C₃⋊#261)	1	1	yes	characteristic
94	C₂	#10597729	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×C₃⋊#261
commutator	C₂×C₃×C₁₃	C₄²
Fitting	C₂×C₃×C₄×C₁₃	C₄
socle	C₂²×C₃×C₁₃	C₂×C₄
prime radical, cosocle	C₂²×C₃×D₁₃	C₂²
hypercenter	C₂×C₄	C₃⋊#261
hypocenter	C₃×C₁₃	#95
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
7. C₂×C₃⋊#261	C₄	semidirect
8. C₂×C₃×C₄×C₁₃	C₄	semidirect
9. C₂×C₃×Dic₁₃	C₄	semidirect
25. C₂×C₄×C₁₃	Dic₃	semidirect
26. C₂×Dic₁₃	Dic₃	semidirect
44. C₃×C₁₃	#95	semidirect
54. C₂×C₃×C₄	#261	semidirect
60. C₁₃	C₃⋊#95	semidirect
75. C₂×C₄	C₃⋊#261	semidirect
89. C₃	(C₂×#261)⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃⋊#261	2
C₂×C₃×C₄×D₁₃	2
(C₂×#261)⋊C₄	3
C₃⋊#95	13