Subgroups — C₇×#3797 #11759585

Order 1008.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×Dic₆	C₂	1	2	yes	maximal, complemented
3	C₇×#627	C₂	1	2	yes	maximal, complemented
4	C₇×#624	C₂	1	2	yes	maximal
5	D₃×C₇×Q₈	—	3	2	no	maximal
6	C₂×C₇×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₃²×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₇×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
9	C₃×C₇×Dic₃	C₂²	1	4	yes	—
10	C₃×C₇×Q₈	—	3	2	no	—
11	C₄×D₃×C₇	—	3	2	no	—
12	C₄×D₃×C₇	—	3	4	no	—
13	C₄×D₃×C₇	—	6	1	no	—
14	C₇×Dic₆	—	3	4	no	—
15	C₇×Dic₆	D₃	1	2	yes	complemented
16	#3797	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃²×C₇	C₂³	1	1	yes	characteristic
18	C₇×C₃⋊D₃	Q₈	1	2	yes	complemented
19	C₂×C₇×Q₈	—	9	1	no	Hall
20	C₂×D₃×C₇	—	3	2	no	—
21	C₂×D₃×C₇	—	6	1	no	—
22	C₃×C₄×C₇	—	2	1	no	—
23	C₃×C₄×C₇	—	3	4	no	—
24	C₃×C₄×C₇	C₂×D₃	1	2	yes	—
25	C₇×Dic₃	—	3	2	no	—
26	C₇×Dic₃	—	6	1	no	—
27	C₇×Dic₃	C₂×D₃	1	4	yes	—
28	C₄×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic
29	C₃×Dic₆	C₂×C₇	1	2	yes	complemented
30	#627	C₂×C₇	1	2	yes	complemented
31	#624	C₂×C₇	1	2	yes	—
32	C₃²×C₇	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
33	C₇×Q₈	—	3	2	no	—
34	C₇×Q₈	—	9	2	no	—
35	C₂×C₄×C₇	—	9	2	no	—
36	C₂×C₄×C₇	—	9	1	no	—
37	D₃×Q₈	—	3	2	no	—
38	C₂×C₃×C₇	—	2	1	no	—
39	C₂×C₃×C₇	C₂²×D₃	1	2	yes	—
40	D₃×C₇	—	3	4	no	—
41	D₃×C₇	—	6	2	no	—
42	C₂×C₃⋊D₃	C₂²×C₇	1	1	yes	characteristic
43	C₃²×C₄	C₂²×C₇	1	1	yes	characteristic
44	C₃⋊Dic₃	C₂²×C₇	1	1	yes	characteristic
45	C₃×Dic₃	C₂²×C₇	1	4	yes	—
46	C₂²×C₇	—	9	1	no	—
47	C₄×C₇	—	3	4	no	—
48	C₄×C₇	—	9	1	no	—
49	C₄×C₇	D₃²	1	1	yes	characteristic
50	C₃×Q₈	—	3	2	no	—
51	C₄×D₃	—	3	2	no	—
52	C₄×D₃	—	3	4	no	—
53	C₄×D₃	—	6	1	no	—
54	Dic₆	—	3	4	no	—
55	Dic₆	D₃×C₇	1	2	yes	complemented
56	C₃×C₇	—	2	1	no	—
57	C₃×C₇	D₃×Q₈	1	2	yes	complemented
58	C₂×C₃²	C₂³×C₇	1	1	yes	characteristic
59	C₃⋊D₃	C₇×Q₈	1	2	yes	complemented
60	C₂×Q₈	—	9	1	no	Sylow
61	C₂×C₇	—	9	2	no	—
62	C₂×C₇	C₂×D₃²	1	1	yes	characteristic
63	C₂×D₃	—	3	2	no	—
64	C₂×D₃	—	6	1	no	—
65	C₃×C₄	—	2	1	no	—
66	C₃×C₄	—	3	4	no	—
67	C₃×C₄	C₂×D₃×C₇	1	2	yes	—
68	Dic₃	—	3	2	no	—
69	Dic₃	—	6	1	no	—
70	Dic₃	C₂×D₃×C₇	1	4	yes	—
71	C₃²	C₂×C₇×Q₈	1	1	yes	characteristic, complemented, Sylow
72	Q₈	—	3	2	no	—
73	Q₈	—	9	2	no	—
74	C₂×C₄	—	9	2	no	—
75	C₂×C₄	—	9	1	no	—
76	C₇	#3797	1	1	yes	characteristic, direct product factor, Sylow
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	C₂²×D₃×C₇	1	2	yes	—
79	D₃	—	3	4	no	—
80	D₃	—	6	2	no	—
81	C₂²	—	9	1	no	—
82	C₄	—	3	4	no	—
83	C₄	—	9	1	no	—
84	C₄	D₃²×C₇	1	1	yes	characteristic
85	C₃	—	2	1	no	—
86	C₃	D₃×C₇×Q₈	1	2	yes	complemented
87	C₂	—	9	2	no	—
88	C₂	C₂×D₃²×C₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₇	C₂×D₃²
commutator, cosocle	C₂×C₃²	C₂³×C₇
Frattini	C₂	C₂×D₃²×C₇
Fitting	C₃²×C₄×C₇	C₂²
socle	C₂×C₃²×C₇	C₂³
prime radical	C₂×C₇×C₃⋊D₃	C₂²
hypercenter	C₄×C₇	D₃²
hypocenter	C₃²	C₂×C₇×Q₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₇ ◁ C₄×C₇

Complements

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

N	H ≅ G/N	type
2. C₃×C₇×Dic₆	C₂	semidirect
3. C₇×#627	C₂	semidirect
15. C₇×Dic₆	D₃	semidirect
16. #3797	C₇	direct (N × H)
18. C₇×C₃⋊D₃	Q₈	semidirect
29. C₃×Dic₆	C₂×C₇	semidirect
30. #627	C₂×C₇	semidirect
32. C₃²×C₇	C₂×Q₈	semidirect
55. Dic₆	D₃×C₇	semidirect
57. C₃×C₇	D₃×Q₈	semidirect
59. C₃⋊D₃	C₇×Q₈	semidirect
71. C₃²	C₂×C₇×Q₈	semidirect
76. C₇	#3797	direct (N × H)
86. C₃	D₃×C₇×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₇×C₃⋊D₃	2
C₃×C₇×Dic₆	2
C₇×#627	2
C₇×#624	2
D₃×C₇×Q₈	3
#3797	7

Subgroups — C7×#3797 #11759585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#3797 #11759585