Subgroups — C₂×C₇×#2104 #13201062

Order 1792.

822 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2104	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₇×#342	C₂	1	7	yes	maximal
3	C₂²×C₇×C₂²⋊C₄	C₂²	1	7	yes	—
4	C₇×#342	C₂²	1	28	yes	—
5	C₂×#2104	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂⁵×C₇	C₂³	1	1	yes	characteristic
7	C₂³×C₄×C₇	—	2	7	no	—
8	C₂×C₇×C₂²⋊C₄	—	2	14	no	—
9	C₂×C₇×C₂²⋊C₄	—	2	14	no	—
10	C₂×C₇×C₂²⋊C₄	—	2	7	no	—
11	C₂×C₇×C₂²⋊C₄	C₂³	1	14	yes	—
12	#2104	C₂×C₇	1	8	yes	direct product factor
13	C₂×#342	C₂×C₇	1	7	yes	—
14	C₂⁴×C₇	—	8	2	no	—
15	C₂⁴×C₇	#41	1	7	yes	—
16	C₂⁴×C₇	#41	1	7	yes	—
17	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
18	C₂²×C₄×C₇	—	2	14	no	—
19	C₂²×C₄×C₇	—	4	7	no	—
20	C₂²×C₄×C₇	—	4	7	no	—
21	C₂²×C₄×C₇	—	8	14	no	—
22	C₇×C₂²⋊C₄	—	2	28	no	—
23	C₇×C₂²⋊C₄	—	4	14	no	—
24	C₂²×C₂²⋊C₄	C₂²×C₇	1	7	yes	—
25	#342	C₂²×C₇	1	28	yes	—
26	C₂³×C₇	—	4	14	no	—
27	C₂³×C₇	—	8	7	no	—
28	C₂³×C₇	—	8	1	no	—
29	C₂³×C₇	#126	1	7	yes	—
30	C₂³×C₇	#126	1	14	yes	—
31	C₂³×C₇	#126	1	7	yes	—
32	C₂³×C₇	C₂×#41	1	7	yes	—
33	C₂×C₄×C₇	—	4	14	no	—
34	C₂×C₄×C₇	—	8	14	no	—
35	C₂×C₄×C₇	—	8	14	no	—
36	C₂×C₄×C₇	—	8	14	no	—
37	C₂⁵	C₂³×C₇	1	1	yes	characteristic
38	C₂³×C₄	—	2	7	no	—
39	C₂×C₂²⋊C₄	—	2	14	no	—
40	C₂×C₂²⋊C₄	—	2	14	no	—
41	C₂×C₂²⋊C₄	—	2	7	no	—
42	C₂×C₂²⋊C₄	C₂³×C₇	1	14	yes	—
43	C₂²×C₇	—	2	14	no	—
44	C₂²×C₇	—	4	7	no	—
45	C₂²×C₇	—	4	7	no	—
46	C₂²×C₇	—	4	14	no	—
47	C₂²×C₇	#401	1	7	yes	—
48	C₂²×C₇	#401	1	1	yes	characteristic
49	C₂²×C₇	C₂×#126	1	7	yes	—
50	C₄×C₇	—	8	14	no	—
51	C₂⁴	—	8	2	no	—
52	C₂⁴	C₇×#41	1	7	yes	—
53	C₂⁴	C₇×#41	1	7	yes	—
54	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
55	C₂²×C₄	—	2	14	no	—
56	C₂²×C₄	—	4	7	no	—
57	C₂²×C₄	—	4	7	no	—
58	C₂²×C₄	—	8	14	no	—
59	C₂²⋊C₄	—	2	28	no	—
60	C₂²⋊C₄	—	4	14	no	—
61	C₂×C₇	—	2	7	no	—
62	C₂×C₇	—	2	7	no	—
63	C₂×C₇	#2104	1	2	yes	direct product factor
64	C₂×C₇	C₂×#401	1	1	yes	characteristic
65	C₂³	—	4	14	no	—
66	C₂³	—	8	7	no	—
67	C₂³	—	8	1	no	—
68	C₂³	C₇×#126	1	7	yes	—
69	C₂³	C₇×#126	1	14	yes	—
70	C₂³	C₇×#126	1	7	yes	—
71	C₂³	C₂×C₇×#41	1	7	yes	—
72	C₂×C₄	—	4	14	no	—
73	C₂×C₄	—	8	14	no	—
74	C₂×C₄	—	8	14	no	—
75	C₂×C₄	—	8	14	no	—
76	C₇	C₂×#2104	1	1	yes	characteristic, direct product factor, Sylow
77	C₂²	—	2	14	no	—
78	C₂²	—	4	7	no	—
79	C₂²	—	4	7	no	—
80	C₂²	—	4	14	no	—
81	C₂²	C₇×#401	1	7	yes	—
82	C₂²	C₇×#401	1	1	yes	characteristic
83	C₂²	C₂×C₇×#126	1	7	yes	—
84	C₄	—	8	14	no	—
85	C₂	—	2	7	no	—
86	C₂	—	2	7	no	—
87	C₂	C₇×#2104	1	2	yes	direct product factor
88	C₂	C₂×C₇×#401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	#401
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₇
prime radical	C₂⁵×C₇	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂⁵×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2104	C₂	direct (N × H)
5. C₂×#2104	C₇	direct (N × H)
12. #2104	C₂×C₇	direct (N × H)
63. C₂×C₇	#2104	direct (N × H)
76. C₇	C₂×#2104	direct (N × H)
87. C₂	C₇×#2104	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×#2104	2
C₂×C₇×#342	2
C₂×#2104	7

Subgroups — C2×C7×#2104 #13201062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2104 #13201062