Subgroups — #11928380

Order 1248.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊#261)	C₂	1	1	yes	maximal, characteristic
3	D₁₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#88117	—	3	1	no	maximal, Hall
5	C₂×C₃⋊#261	—	2	1	no	—
6	C₃×Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₃×C₄×D₁₃	—	2	1	no	—
8	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
9	C₃×Dic₂₆	—	2	1	no	—
10	C₃×Dic₂₆	C₄	1	1	yes	characteristic, complemented
11	C₃⋊#1057	—	2	1	no	—
12	Q₈×D₁₃	D₃	1	1	yes	characteristic
13	C₄⋊#261	—	3	1	no	—
14	D₁₃⋊C₈	—	3	1	no	—
15	C₂×C₃×D₁₃	D₄	1	1	yes	characteristic
16	C₃⋊#261	—	4	1	no	—
17	C₃×C₄×C₁₃	—	2	1	no	—
18	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₃×Dic₁₃	—	2	1	no	—
20	C₃×Dic₁₃	D₄	1	1	yes	characteristic
21	C₂×#261	—	6	1	no	—
22	Q₈×C₁₃	Dic₃	1	1	yes	characteristic, complemented
23	C₄×D₁₃	—	2	1	no	—
24	C₄×D₁₃	C₂×D₃	1	1	yes	characteristic
25	Dic₂₆	—	2	1	no	—
26	Dic₂₆	Dic₃	1	1	yes	characteristic, complemented
27	#1057	—	6	1	no	—
28	#835	—	13	1	no	maximal, Hall
29	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₃×D₁₃	SD₁₆	1	1	yes	characteristic
31	C₃×D₁₃	Q₁₆	1	1	yes	characteristic
32	C₂×D₁₃	#67	1	1	yes	characteristic
33	#261	—	12	1	no	—
34	C₄×C₁₃	—	2	1	no	—
35	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
36	Dic₁₃	—	2	1	no	—
37	Dic₁₃	#67	1	1	yes	characteristic
38	C₂×C₃×Q₈	—	13	1	no	—
39	C₄⋊Dic₃	—	13	1	no	—
40	C₂×C₃⋊C₈	—	13	1	no	—
41	C₃×C₁₃	#103	1	1	yes	characteristic, complemented, Hall
42	#103	—	39	1	no	Sylow
43	C₂×C₁₃	#217	1	1	yes	characteristic
44	D₁₃	#215	1	1	yes	characteristic
45	D₁₃	#216	1	1	yes	characteristic
46	C₃×Q₈	—	13	1	no	—
47	C₃×Q₈	—	26	1	no	—
48	C₃×Q₈	#261	1	1	yes	characteristic, complemented
49	C₂×C₃×C₄	—	13	1	no	—
50	C₂×C₃×C₄	—	26	1	no	—
51	C₂×Dic₃	—	26	1	no	—
52	C₃⋊C₈	—	26	1	no	—
53	C₂×Q₈	—	13	1	no	—
54	C₂×C₈	—	39	1	no	—
55	C₄⋊C₄	—	39	1	no	—
56	C₁₃	#835	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	13	1	no	—
58	C₃×C₄	—	2	1	no	—
59	C₃×C₄	—	13	1	no	—
60	C₃×C₄	—	26	1	no	—
61	C₃×C₄	C₂×#261	1	1	yes	characteristic
62	Dic₃	—	52	1	no	—
63	Q₈	—	13	1	no	—
64	Q₈	—	26	1	no	—
65	Q₈	C₃⋊#261	1	1	yes	characteristic, complemented
66	C₂×C₄	—	13	1	no	—
67	C₂×C₄	—	26	1	no	—
68	C₂×C₄	—	78	1	no	—
69	C₈	—	78	1	no	—
70	C₂×C₃	—	13	1	no	—
71	C₂×C₃	—	13	1	no	—
72	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
73	C₂²	—	13	1	no	—
74	C₄	—	2	1	no	—
75	C₄	—	13	1	no	—
76	C₄	—	26	1	no	—
77	C₄	—	156	1	no	—
78	C₄	C₂×C₃⋊#261	1	1	yes	characteristic
79	C₃	#88117	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	13	1	no	—
81	C₂	—	13	1	no	—
82	C₂	#10597729	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597729
commutator	C₃×C₄×C₁₃	C₂×C₄
Frattini	C₄	C₂×C₃⋊#261
Fitting	C₃×Q₈×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₂²⋊C₄
prime radical	C₂×C₃×D₁₃	D₄
cosocle	C₃×C₄×D₁₃	C₂²
hypercenter	Q₈	C₃⋊#261
hypocenter	C₃×C₁₃	#103
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

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

N	H ≅ G/N	type
6. C₃×Q₈×C₁₃	C₄	semidirect
10. C₃×Dic₂₆	C₄	semidirect
22. Q₈×C₁₃	Dic₃	semidirect
26. Dic₂₆	Dic₃	semidirect
41. C₃×C₁₃	#103	semidirect
48. C₃×Q₈	#261	semidirect
56. C₁₃	#835	semidirect
65. Q₈	C₃⋊#261	semidirect
79. C₃	#88117	semidirect

Maximal subgroups

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

subgroup	index
C₃×Q₈×D₁₃	2
C₄⋊(C₃⋊#261)	2
D₁₃⋊(C₃⋊C₈)	2
#88117	3
#835	13