Subgroups — C₇×#17983775 #44479233

Order 30492.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₁×C₃⋊D₃₃	C₂	1	2	yes	maximal, complemented
3	C₇×D₃₃⋊D₁₁	—	3	4	no	maximal
4	C₃²×C₇×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₁×D₃₃	—	3	8	no	—
6	C₃×C₇×C₁₁⋊D₁₁	D₃	1	4	yes	complemented
7	#17983775	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×D₁₁²	—	9	1	no	Hall
9	C₇×C₃⋊D₃×D₁₁	—	11	2	no	maximal
10	C₃×C₇×C₁₁²	C₂×D₃	1	4	yes	complemented
11	C₁₁×C₃⋊D₃₃	C₂×C₇	1	2	yes	complemented
12	C₃²×C₁₁⋊D₁₁	C₂×C₇	1	1	yes	characteristic, complemented
13	C₇×C₁₁⋊D₁₁	C₃⋊D₃	1	1	yes	characteristic, complemented
14	C₇×C₁₁×D₁₁	—	9	2	no	—
15	D₃₃⋊D₁₁	—	3	4	no	—
16	C₇×C₃⋊D₃₃	D₁₁	1	2	yes	complemented
17	C₇×C₁₁×C₃⋊D₃	—	11	2	no	—
18	C₃²×C₇×D₁₁	—	11	2	no	—
19	C₃²×C₇×D₁₁	—	22	5	no	—
20	C₃²×C₁₁²	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
21	D₃×C₇×D₁₁	—	33	8	no	—
22	C₇×C₁₁²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
23	C₁₁×D₃₃	—	3	8	no	—
24	C₃×C₁₁⋊D₁₁	D₃×C₇	1	4	yes	complemented
25	C₃²×C₇×C₁₁	—	2	5	no	—
26	C₃²×C₇×C₁₁	C₂×D₁₁	1	2	yes	complemented
27	D₁₁²	—	9	1	no	Hall
28	C₇×D₃₃	—	3	8	no	—
29	D₃×C₇×C₁₁	—	33	8	no	—
30	C₃×C₇×D₁₁	—	11	8	no	—
31	C₃×C₇×D₁₁	—	22	20	no	—
32	C₃⋊D₃×D₁₁	—	11	2	no	—
33	C₃×C₁₁²	C₂×D₃×C₇	1	4	yes	complemented
34	C₂×C₇×D₁₁	—	99	2	no	—
35	C₂×C₇×C₃⋊D₃	—	121	1	no	Hall
36	C₁₁⋊D₁₁	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
37	C₁₁×D₁₁	—	9	2	no	—
38	C₃×C₇×C₁₁	—	2	20	no	—
39	C₃×C₇×C₁₁	D₃×D₁₁	1	8	yes	complemented
40	C₃⋊D₃₃	C₇×D₁₁	1	2	yes	complemented
41	C₁₁×C₃⋊D₃	—	11	2	no	—
42	C₃²×D₁₁	—	11	2	no	—
43	C₃²×D₁₁	—	22	5	no	—
44	C₂×C₇×C₁₁	—	99	2	no	—
45	C₇×D₁₁	—	9	2	no	—
46	C₇×D₁₁	—	11	2	no	—
47	C₇×D₁₁	—	22	5	no	—
48	D₃×D₁₁	—	33	8	no	—
49	C₂×C₃²×C₇	—	121	1	no	—
50	C₇×C₃⋊D₃	—	11	2	no	—
51	C₁₁²	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
52	C₃²×C₁₁	—	2	5	no	—
53	C₃²×C₁₁	C₂×C₇×D₁₁	1	2	yes	complemented
54	C₂×D₃×C₇	—	363	4	no	—
55	C₇×C₁₁	—	2	5	no	—
56	C₇×C₁₁	C₃⋊D₃×D₁₁	1	2	yes	complemented
57	D₃₃	—	3	8	no	—
58	C₃×D₁₁	—	11	8	no	—
59	C₃×D₁₁	—	22	20	no	—
60	D₃×C₁₁	—	33	8	no	—
61	C₃²×C₇	D₁₁²	1	1	yes	characteristic, complemented, Hall
62	C₂×D₁₁	—	99	2	no	—
63	C₂×C₃×C₇	—	121	4	no	—
64	D₃×C₇	—	33	8	no	—
65	C₂×C₃⋊D₃	—	121	1	no	Hall
66	C₃×C₁₁	—	2	20	no	—
67	C₃×C₁₁	D₃×C₇×D₁₁	1	8	yes	complemented
68	C₂²×C₇	—	1089	1	no	Hall
69	C₂×C₁₁	—	99	2	no	—
70	D₁₁	—	9	2	no	—
71	D₁₁	—	11	2	no	—
72	D₁₁	—	22	5	no	—
73	C₃×C₇	D₃₃⋊D₁₁	1	4	yes	complemented
74	C₂×C₃²	—	121	1	no	—
75	C₃⋊D₃	—	11	2	no	—
76	C₂×C₇	—	99	2	no	—
77	C₂×C₇	—	121	1	no	—
78	C₂×D₃	—	363	4	no	—
79	C₁₁	—	2	5	no	—
80	C₁₁	C₇×C₃⋊D₃×D₁₁	1	2	yes	complemented
81	C₃²	C₇×D₁₁²	1	1	yes	characteristic, complemented, Sylow
82	C₇	#17983775	1	1	yes	characteristic, direct product factor, Sylow
83	C₂×C₃	—	121	4	no	—
84	D₃	—	33	8	no	—
85	C₂²	—	1089	1	no	Sylow
86	C₃	C₇×D₃₃⋊D₁₁	1	4	yes	complemented
87	C₂	—	99	2	no	—
88	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₇	#17983775
commutator, cosocle, hypocenter	C₃²×C₁₁²	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁²	C₂²
LCS	G ▷ C₃²×C₁₁²
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₁₁⋊D₁₁	C₂	semidirect
2. C₇×C₁₁×C₃⋊D₃₃	C₂	semidirect
4. C₃²×C₇×C₁₁²	C₂²	semidirect
6. C₃×C₇×C₁₁⋊D₁₁	D₃	semidirect
7. #17983775	C₇	direct (N × H)
10. C₃×C₇×C₁₁²	C₂×D₃	semidirect
11. C₁₁×C₃⋊D₃₃	C₂×C₇	semidirect
12. C₃²×C₁₁⋊D₁₁	C₂×C₇	semidirect
13. C₇×C₁₁⋊D₁₁	C₃⋊D₃	semidirect
16. C₇×C₃⋊D₃₃	D₁₁	semidirect
20. C₃²×C₁₁²	C₂²×C₇	semidirect
22. C₇×C₁₁²	C₂×C₃⋊D₃	semidirect
24. C₃×C₁₁⋊D₁₁	D₃×C₇	semidirect
26. C₃²×C₇×C₁₁	C₂×D₁₁	semidirect
33. C₃×C₁₁²	C₂×D₃×C₇	semidirect
36. C₁₁⋊D₁₁	C₇×C₃⋊D₃	semidirect
39. C₃×C₇×C₁₁	D₃×D₁₁	semidirect
40. C₃⋊D₃₃	C₇×D₁₁	semidirect
51. C₁₁²	C₂×C₇×C₃⋊D₃	semidirect
53. C₃²×C₁₁	C₂×C₇×D₁₁	semidirect
56. C₇×C₁₁	C₃⋊D₃×D₁₁	semidirect
61. C₃²×C₇	D₁₁²	semidirect
67. C₃×C₁₁	D₃×C₇×D₁₁	semidirect
73. C₃×C₇	D₃₃⋊D₁₁	semidirect
80. C₁₁	C₇×C₃⋊D₃×D₁₁	semidirect
81. C₃²	C₇×D₁₁²	semidirect
82. C₇	#17983775	direct (N × H)
86. C₃	C₇×D₃₃⋊D₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₇×C₁₁⋊D₁₁	2
C₇×C₁₁×C₃⋊D₃₃	2
C₇×D₃₃⋊D₁₁	3
#17983775	7
C₇×C₃⋊D₃×D₁₁	11

Subgroups — C7×#17983775 #44479233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17983775 #44479233