Subgroups — #37525642

Order 22932.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₃⋊D₂₇₃	C₂	1	2	yes	maximal, complemented
3	#21439774	—	3	4	no	maximal
4	C₃²×C₇²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₂₇₃	—	3	8	no	—
6	C₃×C₁₃×C₇⋊D₇	D₃	1	4	yes	complemented
7	D₇×C₃⋊D₃₉	—	7	2	no	maximal
8	(C₇⋊D₇)⋊D₁₃	—	9	1	no	Hall
9	C₃×C₇²×C₁₃	C₂×D₃	1	4	yes	complemented
10	#13183685	—	13	1	no	maximal, Hall
11	C₃⋊D₂₇₃	D₇	1	2	yes	complemented
12	C₇×C₃⋊D₃₉	—	7	2	no	—
13	C₃²×C₁₃×D₇	—	7	2	no	—
14	C₃²×C₁₃×D₇	—	14	3	no	—
15	C₁₃×C₇⋊D₇	C₃⋊D₃	1	1	yes	characteristic, complemented
16	C₇×D₉₁	—	9	2	no	—
17	D₇×D₃₉	—	21	8	no	—
18	C₇×C₃⋊D₂₁	—	13	2	no	—
19	C₃²×C₇⋊D₇	D₁₃	1	1	yes	characteristic, complemented
20	C₃²×C₇×C₁₃	—	2	3	no	—
21	C₃²×C₇×C₁₃	C₂×D₇	1	2	yes	complemented
22	C₇²×C₁₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
23	D₂₁⋊D₇	—	39	4	no	—
24	D₂₇₃	—	3	8	no	—
25	C₇×D₃₉	—	21	8	no	—
26	C₃×C₁₃×D₇	—	7	8	no	—
27	C₃×C₁₃×D₇	—	14	12	no	—
28	C₂×C₃⋊D₃₉	—	49	1	no	Hall
29	C₃²×C₇²	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	D₇×D₁₃	—	63	2	no	—
31	C₇×D₂₁	—	39	8	no	—
32	C₃×C₇⋊D₇	D₃₉	1	4	yes	complemented
33	C₃×C₇×C₁₃	—	2	12	no	—
34	C₃×C₇×C₁₃	D₃×D₇	1	8	yes	complemented
35	D₇×C₃⋊D₃	—	91	2	no	—
36	C₂×C₃²×C₁₃	—	49	1	no	—
37	C₃⋊D₃₉	—	7	2	no	—
38	D₇²	—	117	1	no	Hall
39	D₉₁	—	9	2	no	—
40	C₇×D₁₃	—	63	2	no	—
41	C₁₃×D₇	—	7	2	no	—
42	C₁₃×D₇	—	14	3	no	—
43	C₂×D₃₉	—	147	4	no	—
44	C₃×C₇²	C₂×D₃₉	1	4	yes	complemented
45	C₃⋊D₂₁	—	13	2	no	—
46	C₇×C₃⋊D₃	—	91	2	no	—
47	C₃²×D₇	—	7	2	no	—
48	C₃²×D₇	—	14	3	no	—
49	C₃²×C₁₃	D₇²	1	1	yes	characteristic, complemented, Hall
50	C₇⋊D₇	C₃⋊D₃₉	1	1	yes	characteristic, complemented
51	C₇×D₇	—	117	2	no	—
52	C₇×C₁₃	—	2	3	no	—
53	C₇×C₁₃	D₇×C₃⋊D₃	1	2	yes	complemented
54	D₃×D₇	—	273	8	no	—
55	C₂×C₃×C₁₃	—	49	4	no	—
56	D₃₉	—	21	8	no	—
57	C₃²×C₇	—	2	3	no	—
58	C₃²×C₇	D₇×D₁₃	1	2	yes	complemented
59	C₂×D₁₃	—	441	1	no	Hall
60	C₇²	C₂×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Sylow
61	D₂₁	—	39	8	no	—
62	C₃×D₇	—	7	8	no	—
63	C₃×D₇	—	14	12	no	—
64	D₃×C₇	—	273	8	no	—
65	C₃×C₁₃	D₂₁⋊D₇	1	4	yes	complemented
66	C₂×C₃⋊D₃	—	637	1	no	Hall
67	C₂×D₇	—	819	2	no	—
68	C₂×C₁₃	—	49	1	no	—
69	D₁₃	—	63	2	no	—
70	C₃×C₇	—	2	12	no	—
71	C₃×C₇	D₇×D₃₉	1	8	yes	complemented
72	C₂×C₃²	—	49	1	no	—
73	C₃⋊D₃	—	91	2	no	—
74	C₂×C₇	—	819	2	no	—
75	D₇	—	7	2	no	—
76	D₇	—	14	3	no	—
77	D₇	—	117	2	no	—
78	C₁₃	#13183685	1	1	yes	characteristic, complemented, Sylow
79	C₂×D₃	—	1911	4	no	—
80	C₃²	(C₇⋊D₇)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
81	C₇	—	2	3	no	—
82	C₇	D₇×C₃⋊D₃₉	1	2	yes	complemented
83	C₂×C₃	—	49	4	no	—
84	D₃	—	273	8	no	—
85	C₂²	—	5733	1	no	Sylow
86	C₃	#21439774	1	4	yes	complemented
87	C₂	—	49	1	no	—
88	C₂	—	819	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇²×C₁₃	C₂²
LCS	G ▷ C₃²×C₇²×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₃×C₇⋊D₇	C₂	semidirect
2. C₇×C₃⋊D₂₇₃	C₂	semidirect
4. C₃²×C₇²×C₁₃	C₂²	semidirect
6. C₃×C₁₃×C₇⋊D₇	D₃	semidirect
9. C₃×C₇²×C₁₃	C₂×D₃	semidirect
11. C₃⋊D₂₇₃	D₇	semidirect
15. C₁₃×C₇⋊D₇	C₃⋊D₃	semidirect
19. C₃²×C₇⋊D₇	D₁₃	semidirect
21. C₃²×C₇×C₁₃	C₂×D₇	semidirect
22. C₇²×C₁₃	C₂×C₃⋊D₃	semidirect
29. C₃²×C₇²	C₂×D₁₃	semidirect
32. C₃×C₇⋊D₇	D₃₉	semidirect
34. C₃×C₇×C₁₃	D₃×D₇	semidirect
44. C₃×C₇²	C₂×D₃₉	semidirect
49. C₃²×C₁₃	D₇²	semidirect
50. C₇⋊D₇	C₃⋊D₃₉	semidirect
53. C₇×C₁₃	D₇×C₃⋊D₃	semidirect
58. C₃²×C₇	D₇×D₁₃	semidirect
60. C₇²	C₂×C₃⋊D₃₉	semidirect
65. C₃×C₁₃	D₂₁⋊D₇	semidirect
71. C₃×C₇	D₇×D₃₉	semidirect
78. C₁₃	#13183685	semidirect
80. C₃²	(C₇⋊D₇)⋊D₁₃	semidirect
82. C₇	D₇×C₃⋊D₃₉	semidirect
86. C₃	#21439774	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₃×C₇⋊D₇	2
C₇×C₃⋊D₂₇₃	2
#21439774	3
D₇×C₃⋊D₃₉	7
#13183685	13