Subgroups — C₂×#6407 #89988

Order 448.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#1136	C₂	1	2	yes	maximal, complemented
3	#6407	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₇	C₄	1	2	yes	—
5	C₂×C₇×D₄	—	2	2	no	—
6	C₂×C₇×D₄	—	2	2	no	—
7	C₂×C₇×D₄	C₄	1	2	yes	—
8	C₂×C₇×D₄	C₂²	1	2	yes	—
9	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
10	#1136	—	2	2	no	—
11	#1136	C₂²	1	4	yes	complemented
12	C₂×C₇⋊C₈	—	2	2	no	—
13	C₂×#100	—	7	1	no	maximal, Sylow
14	C₂³×C₇	—	2	2	no	—
15	C₂³×C₇	—	2	2	no	—
16	C₂³×C₇	—	4	4	no	—
17	C₂³×C₇	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₇	C₂×C₄	1	4	yes	—
19	C₇×D₄	—	2	4	no	—
20	C₇×D₄	—	2	4	no	—
21	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₇	D₄	1	2	yes	—
23	C₂×C₄×C₇	D₄	1	2	yes	—
24	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
25	C₇⋊C₈	—	2	4	no	—
26	C₂²×D₄	D₇	1	1	yes	characteristic
27	C₂×M₁₆	—	7	2	no	—
28	#100	—	7	4	no	—
29	C₂²×C₇	—	2	2	no	—
30	C₂²×C₇	—	2	4	no	—
31	C₂²×C₇	—	4	4	no	—
32	C₂²×C₇	—	4	4	no	—
33	C₂²×C₇	—	4	4	no	—
34	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₇	C₂²⋊C₄	1	2	yes	—
38	C₄×C₇	C₂×D₄	1	2	yes	—
39	C₂⁴	Dic₇	1	2	yes	—
40	C₂×D₄	—	2	2	no	—
41	C₂×D₄	—	2	2	no	—
42	C₂×D₄	Dic₇	1	2	yes	—
43	C₂×D₄	C₂×D₇	1	2	yes	—
44	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
45	M₁₆	—	7	4	no	—
46	M₁₆	—	14	2	no	—
47	C₂×C₈	—	14	2	no	—
48	C₂×C₇	—	2	1	no	—
49	C₂×C₇	—	2	1	no	—
50	C₂×C₇	—	4	4	no	—
51	C₂×C₇	#100	1	2	yes	complemented
52	C₂×C₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₂³	—	2	2	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	4	4	no	—
56	C₂³	C₂×Dic₇	1	1	yes	characteristic
57	C₂³	C₂×Dic₇	1	4	yes	—
58	D₄	—	2	4	no	—
59	D₄	—	2	4	no	—
60	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
61	C₂×C₄	C₂²⋊D₇	1	2	yes	—
62	C₂×C₄	C₂²⋊D₇	1	2	yes	—
63	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
64	C₈	—	14	4	no	—
65	C₇	C₂×#100	1	1	yes	characteristic, complemented, Sylow
66	C₂²	—	2	2	no	—
67	C₂²	—	2	4	no	—
68	C₂²	—	4	4	no	—
69	C₂²	—	4	4	no	—
70	C₂²	—	4	4	no	—
71	C₂²	C₂²⋊Dic₇	1	1	yes	characteristic
72	C₂²	C₂²⋊Dic₇	1	1	yes	characteristic
73	C₂²	C₂²×Dic₇	1	1	yes	characteristic
74	C₄	C₂²⋊Dic₇	1	2	yes	—
75	C₄	C₂×C₂²⋊D₇	1	2	yes	—
76	C₂	—	2	1	no	—
77	C₂	—	2	1	no	—
78	C₂	—	4	4	no	—
79	C₂	#6407	1	2	yes	direct product factor
80	C₂	C₂×C₂²⋊Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊Dic₇
commutator	C₂²×C₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇
Fitting, prime radical	C₂²×C₇×D₄	C₂
socle	C₂²×C₇	C₂²⋊C₄
cosocle	C₂×C₄×C₇	C₂³
hypercenter	C₂²×D₄	D₇
hypocenter	C₇	C₂×#100
LCS	G ▷ C₂²×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#1136	C₂	semidirect
3. #6407	C₂	direct (N × H)
11. #1136	C₂²	semidirect
51. C₂×C₇	#100	semidirect
65. C₇	C₂×#100	semidirect
79. C₂	#6407	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×D₄	2
C₂×#1136	2
#6407	2
C₂×#100	7

Subgroups — C2×#6407 #89988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6407 #89988