Subgroups — C₇×#7451 #13184667

Order 1792.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2252	C₂	1	1	yes	maximal, characteristic
2	C₇×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₇×#1371	C₂	1	1	yes	maximal, characteristic
4	C₇×#500	—	2	1	no	—
5	C₂×C₇×C₃₂	—	2	1	no	—
6	C₇×#366	—	2	1	no	—
7	C₇×#366	C₄	1	2	yes	—
8	C₄×C₇×C₁₆	C₂²	1	1	yes	characteristic
9	C₇×#335	—	2	1	no	—
10	#7451	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₇×C₄⋊Q₈	—	4	1	no	—
12	C₂×C₇×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₇×C₁₆	D₄	1	1	yes	characteristic
14	C₇×#107	—	2	2	no	—
15	C₇×#107	—	4	1	no	—
16	C₇×C₄⋊C₈	—	4	1	no	—
17	C₄×C₇×C₈	D₄	1	1	yes	characteristic
18	C₇×C₃₂	—	4	1	no	—
19	#2252	C₂×C₇	1	1	yes	characteristic
20	C₄⋊C₃₂	C₂×C₇	1	1	yes	characteristic
21	#1371	C₂×C₇	1	1	yes	characteristic
22	C₂×C₇×Q₈	—	8	1	no	—
23	C₂×C₇×C₈	—	8	1	no	—
24	C₂×C₇×C₈	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₇×C₈	SD₁₆	1	1	yes	characteristic
26	C₇×C₄⋊C₄	—	4	2	no	—
27	C₇×C₄⋊C₄	—	8	1	no	—
28	C₄²×C₇	D₈	1	1	yes	characteristic
29	C₇×C₁₆	—	2	1	no	—
30	C₇×C₁₆	SD₁₆	1	1	yes	characteristic
31	C₇×C₁₆	Q₁₆	1	1	yes	characteristic
32	#500	—	2	1	no	—
33	C₂×C₃₂	—	2	1	no	—
34	#366	—	2	1	no	—
35	#366	C₄×C₇	1	2	yes	—
36	C₄×C₁₆	C₂²×C₇	1	1	yes	characteristic
37	#335	—	2	1	no	—
38	C₇×Q₈	—	16	2	no	—
39	C₂×C₄×C₇	—	8	2	no	—
40	C₂×C₄×C₇	#102	1	1	yes	characteristic
41	C₂×C₄×C₇	D₁₆	1	1	yes	characteristic
42	C₂×C₄×C₇	SD₃₂	1	1	yes	characteristic
43	C₇×C₈	—	2	1	no	—
44	C₇×C₈	—	16	1	no	—
45	C₇×C₈	#101	1	1	yes	characteristic
46	C₇×C₈	#103	1	1	yes	characteristic
47	C₄⋊Q₈	—	4	1	no	—
48	C₂×C₁₆	C₂×C₄×C₇	1	1	yes	characteristic
49	C₂×C₁₆	C₇×D₄	1	1	yes	characteristic
50	#107	—	2	2	no	—
51	#107	—	4	1	no	—
52	C₄⋊C₈	—	4	1	no	—
53	C₄×C₈	C₇×D₄	1	1	yes	characteristic
54	C₃₂	—	4	1	no	—
55	C₂²×C₇	#357	1	1	yes	characteristic
56	C₄×C₇	—	2	1	no	—
57	C₄×C₇	—	16	2	no	—
58	C₄×C₇	#332	1	1	yes	characteristic
59	C₄×C₇	#362	1	1	yes	characteristic
60	C₄×C₇	SD₆₄	1	1	yes	characteristic
61	C₄×C₇	Q₆₄	1	1	yes	characteristic
62	C₂×Q₈	—	8	1	no	—
63	C₂×C₈	—	8	1	no	—
64	C₂×C₈	C₇×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₈	C₇×SD₁₆	1	1	yes	characteristic
66	C₄⋊C₄	—	4	2	no	—
67	C₄⋊C₄	—	8	1	no	—
68	C₄²	C₇×D₈	1	1	yes	characteristic
69	C₁₆	—	2	1	no	—
70	C₁₆	C₇×SD₁₆	1	1	yes	characteristic
71	C₁₆	C₇×Q₁₆	1	1	yes	characteristic
72	C₂×C₇	#1364	1	1	yes	characteristic
73	C₂×C₇	#1416	1	1	yes	characteristic
74	C₂×C₇	#1419	1	1	yes	characteristic
75	Q₈	—	16	2	no	—
76	C₂×C₄	—	8	2	no	—
77	C₂×C₄	C₇×#102	1	1	yes	characteristic
78	C₂×C₄	C₇×D₁₆	1	1	yes	characteristic
79	C₂×C₄	C₇×SD₃₂	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	16	1	no	—
82	C₈	C₇×#101	1	1	yes	characteristic
83	C₈	C₇×#103	1	1	yes	characteristic
84	C₇	#7451	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²	C₇×#357	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	16	2	no	—
88	C₄	C₇×#332	1	1	yes	characteristic
89	C₄	C₇×#362	1	1	yes	characteristic
90	C₄	C₇×SD₆₄	1	1	yes	characteristic
91	C₄	C₇×Q₆₄	1	1	yes	characteristic
92	C₂	C₇×#1364	1	1	yes	characteristic
93	C₂	C₇×#1416	1	1	yes	characteristic
94	C₂	C₇×#1419	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₇	#357
commutator	C₂×C₁₆	C₂×C₄×C₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₇
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇ ◁ C₄×C₇×C₈ ◁ C₄×C₇×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
10. #7451	C₇	direct (N × H)
84. C₇	#7451	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#2252	2
C₇×C₄⋊C₃₂	2
C₇×#1371	2
#7451	7

Subgroups — C7×#7451 #13184667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#7451 #13184667