Subgroups — C₂×#6499 #90488

Order 448.

330 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	C₂²×Dic₁₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂²⋊Dic₇	C₂	1	4	yes	maximal, complemented
4	#6499	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁴×C₇	C₂²	1	2	yes	—
7	C₂×C₇×D₄	—	2	4	no	—
8	C₂×C₇×D₄	C₂²	1	4	yes	—
9	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
10	C₂²×Dic₇	C₂²	1	2	yes	—
11	C₂²×Dic₇	C₂²	1	2	yes	—
12	C₂×Dic₁₄	—	2	4	no	—
13	C₂×Dic₁₄	C₂²	1	4	yes	complemented
14	C₂²⋊Dic₇	C₂²	1	16	yes	complemented
15	C₄×Dic₇	C₂²	1	4	yes	complemented
16	C₂×#124	—	7	1	no	maximal, Sylow
17	C₂³×C₇	—	2	4	no	—
18	C₂³×C₇	—	2	8	no	—
19	C₂³×C₇	C₂³	1	4	yes	—
20	C₂³×C₇	C₂³	1	1	yes	characteristic
21	C₇×D₄	—	2	8	no	—
22	C₂×C₄×C₇	D₄	1	4	yes	—
23	C₂×C₄×C₇	C₂³	1	2	yes	—
24	C₂×Dic₇	—	2	4	no	—
25	C₂×Dic₇	—	2	4	no	—
26	C₂×Dic₇	C₂³	1	4	yes	—
27	C₂×Dic₇	C₂³	1	4	yes	—
28	Dic₁₄	—	2	8	no	—
29	C₂²×Q₈	—	7	1	no	—
30	C₂²×D₄	D₇	1	1	yes	characteristic
31	#124	—	7	8	no	—
32	C₂×C₂²⋊C₄	—	7	4	no	—
33	C₂×C₄²	—	7	1	no	—
34	C₂²×C₇	—	2	4	no	—
35	C₂²×C₇	—	2	8	no	—
36	C₂²×C₇	—	4	8	no	—
37	C₂²×C₇	C₂×D₄	1	2	yes	—
38	C₂²×C₇	#41	1	4	yes	—
39	C₂²×C₇	C₂⁴	1	1	yes	characteristic
40	C₄×C₇	C₂×D₄	1	4	yes	—
41	Dic₇	—	2	4	no	—
42	Dic₇	—	2	4	no	—
43	C₂⁴	C₂×D₇	1	2	yes	—
44	C₂×Q₈	—	7	4	no	—
45	C₂×Q₈	—	14	4	no	—
46	C₂×D₄	—	2	4	no	—
47	C₂×D₄	C₂×D₇	1	4	yes	—
48	C₂²×C₄	—	7	2	no	—
49	C₂²×C₄	—	7	2	no	—
50	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
51	C₂²⋊C₄	—	7	16	no	—
52	C₄²	—	7	4	no	—
53	C₂×C₇	—	4	4	no	—
54	C₂×C₇	#124	1	4	yes	complemented
55	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
56	C₂×C₇	C₂×#41	1	2	yes	—
57	C₂³	—	2	8	no	—
58	C₂³	—	2	4	no	—
59	C₂³	C₂²×D₇	1	4	yes	—
60	C₂³	C₂²×D₇	1	1	yes	characteristic
61	Q₈	—	14	8	no	—
62	D₄	—	2	8	no	—
63	C₂×C₄	—	7	4	no	—
64	C₂×C₄	—	7	4	no	—
65	C₂×C₄	—	14	4	no	—
66	C₂×C₄	—	14	4	no	—
67	C₂×C₄	C₂²⋊D₇	1	4	yes	—
68	C₂×C₄	C₂²×D₇	1	2	yes	—
69	C₇	C₂×#124	1	1	yes	characteristic, complemented, Sylow
70	C₂²	—	2	8	no	—
71	C₂²	—	2	4	no	—
72	C₂²	—	4	8	no	—
73	C₂²	#1159	1	4	yes	—
74	C₂²	C₂×C₂²⋊D₇	1	2	yes	—
75	C₂²	C₂³×D₇	1	1	yes	characteristic
76	C₄	—	14	4	no	—
77	C₄	—	14	4	no	—
78	C₄	C₂×C₂²⋊D₇	1	4	yes	—
79	C₂	—	4	4	no	—
80	C₂	#6499	1	4	yes	direct product factor
81	C₂	C₂×#1159	1	2	yes	—
82	C₂	C₂²×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₇
commutator, cosocle	C₂²×C₇	C₂⁴
Frattini	C₂²	C₂³×D₇
Fitting, prime radical	C₂²×C₇×D₄	C₂
socle	C₂³×C₇	C₂³
hypercenter	C₂²×D₄	D₇
hypocenter	C₇	C₂×#124
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂²×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₁₄	C₂	semidirect
3. C₂×C₂²⋊Dic₇	C₂	semidirect
4. #6499	C₂	direct (N × H)
5. C₂×C₄×Dic₇	C₂	semidirect
13. C₂×Dic₁₄	C₂²	semidirect
14. C₂²⋊Dic₇	C₂²	semidirect
15. C₄×Dic₇	C₂²	semidirect
54. C₂×C₇	#124	semidirect
69. C₇	C₂×#124	semidirect
80. C₂	#6499	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
C₂²×Dic₁₄	2
C₂×C₂²⋊Dic₇	2
#6499	2
C₂×C₄×Dic₇	2
C₂×#124	7

Subgroups — C2×#6499 #90488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6499 #90488