Subgroups — Dic₁₃⋊#89205 #37524367

Order 22932.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊#89205	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇²×Dic₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₃⋊#89205	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
5	#15692566	—	7	1	no	maximal
6	#15692565	—	7	1	no	maximal
7	C₇²×Dic₁₃	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
9	C₄×#89205	—	13	1	no	maximal, Hall
10	C₂×#11717942	—	7	1	no	—
11	C₂×#11717941	—	7	1	no	—
12	C₂×C₇²×C₁₃	C₂×C₉	1	1	yes	characteristic
13	C₃×C₇×Dic₁₃	—	3	2	no	—
14	C₃×C₇×Dic₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₃×C₇×Dic₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
16	C₂×#89205	—	13	1	no	—
17	#11717942	—	7	1	no	—
18	#11717941	—	7	1	no	—
19	C₇²×C₁₃	C₄×C₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₄×C₇²	—	39	1	no	—
21	C₂×C₃×C₇×C₁₃	—	3	2	no	—
22	C₂×C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
23	C₂×C₃×C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
24	Dic₁₃⋊C₉	—	49	1	no	Hall
25	#89205	—	13	1	no	Hall
26	C₇×Dic₁₃	—	3	2	no	—
27	C₇×Dic₁₃	C₇⋊C₉	1	1	yes	characteristic, complemented
28	C₇×Dic₁₃	C₇⋊C₉	1	1	yes	characteristic, complemented
29	C₂×C₃×C₇²	D₁₃⋊C₃	1	1	yes	characteristic
30	C₃×C₇×C₁₃	—	3	2	no	—
31	C₃×C₇×C₁₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
32	C₃×C₇×C₁₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₄×C₇⋊C₉	—	91	1	no	—
34	C₄×C₇⋊C₉	—	91	1	no	—
35	C₂×C₁₃⋊C₉	—	49	1	no	—
36	C₄×C₇²	—	39	1	no	Hall
37	C₂×C₇×C₁₃	—	3	2	no	—
38	C₂×C₇×C₁₃	C₂×C₇⋊C₉	1	1	yes	characteristic
39	C₂×C₇×C₁₃	C₂×C₇⋊C₉	1	1	yes	characteristic
40	C₃×Dic₁₃	#3862	1	1	yes	characteristic
41	C₃×C₇²	Dic₁₃⋊C₃	1	1	yes	characteristic
42	C₂×C₇⋊C₉	—	91	1	no	—
43	C₂×C₇⋊C₉	—	91	1	no	—
44	C₁₃⋊C₉	—	49	1	no	Hall
45	C₂×C₇²	D₁₃⋊C₉	1	1	yes	characteristic
46	C₇×C₁₃	—	3	2	no	—
47	C₇×C₁₃	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented
48	C₇×C₁₃	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented
49	C₃×C₄×C₇	—	39	2	no	—
50	C₃×C₄×C₇	—	39	1	no	—
51	C₃×C₄×C₇	—	39	1	no	—
52	C₂×C₃×C₁₃	C₂×#3862	1	1	yes	characteristic
53	C₇⋊C₉	—	91	1	no	—
54	C₇⋊C₉	—	91	1	no	—
55	Dic₁₃	#89205	1	1	yes	characteristic, complemented, Hall
56	C₇²	Dic₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃×C₇	—	3	2	no	—
58	C₂×C₃×C₇	#10587716	1	1	yes	characteristic
59	C₂×C₃×C₇	#10587717	1	1	yes	characteristic
60	C₃×C₁₃	C₄×#3862	1	1	yes	characteristic
61	C₄×C₉	—	637	1	no	Hall
62	C₄×C₇	—	39	2	no	—
63	C₄×C₇	—	39	1	no	—
64	C₄×C₇	—	39	1	no	—
65	C₂×C₁₃	C₂×#89205	1	1	yes	characteristic
66	C₃×C₇	—	3	2	no	—
67	C₃×C₇	#11763957	1	1	yes	characteristic
68	C₃×C₇	#11763958	1	1	yes	characteristic
69	C₂×C₉	—	637	1	no	—
70	C₂×C₇	—	3	2	no	—
71	C₂×C₇	#13109896	1	1	yes	characteristic
72	C₂×C₇	#13109897	1	1	yes	characteristic
73	C₁₃	C₄×#89205	1	1	yes	characteristic, complemented, Sylow
74	C₃×C₄	—	39	1	no	—
75	C₉	—	637	1	no	Sylow
76	C₇	—	3	2	no	—
77	C₇	#15692565	1	1	yes	characteristic, complemented
78	C₇	#15692566	1	1	yes	characteristic, complemented
79	C₂×C₃	D₁₃⋊#3862	1	1	yes	characteristic
80	C₄	—	39	1	no	Sylow
81	C₃	Dic₁₃⋊#3862	1	1	yes	characteristic
82	C₂	D₁₃⋊#89205	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₁₃⋊#3862
commutator, hypocenter	C₇²×C₁₃	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₁₃⋊#89205	C₄	semidirect
7. C₇²×Dic₁₃	C₉	semidirect
19. C₇²×C₁₃	C₄×C₉	semidirect
27. C₇×Dic₁₃	C₇⋊C₉	semidirect
28. C₇×Dic₁₃	C₇⋊C₉	semidirect
47. C₇×C₁₃	C₄×C₇⋊C₉	semidirect
48. C₇×C₁₃	C₄×C₇⋊C₉	semidirect
55. Dic₁₃	#89205	semidirect
56. C₇²	Dic₁₃⋊C₉	semidirect
73. C₁₃	C₄×#89205	semidirect
77. C₇	#15692565	semidirect
78. C₇	#15692566	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃⋊#89205	2
C₃×C₇²×Dic₁₃	3
#15692566	7
#15692565	7
C₄×#89205	13

Subgroups — Dic13⋊#89205 #37524367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₃⋊#89205 #37524367