Subgroups — C₂×#6489 #90477

Order 448.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊Dic₇	C₂	1	2	yes	maximal
3	#6489	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄⋊Dic₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×Dic₇	C₂	1	2	yes	maximal, complemented
6	C₂⁴×C₇	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₇	C₄	1	8	yes	complemented
8	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₇	C₂²	1	4	yes	—
11	C₂²×Dic₇	C₂²	1	4	yes	—
12	C₂²⋊Dic₇	C₂²	1	8	yes	—
13	C₄⋊Dic₇	C₂²	1	8	yes	complemented
14	C₄×Dic₇	C₂²	1	8	yes	complemented
15	C₂×#117	—	7	1	no	maximal, Sylow
16	C₂³×C₇	—	2	4	no	—
17	C₂³×C₇	C₂×C₄	1	4	yes	—
18	C₂³×C₇	C₂³	1	2	yes	—
19	C₂³×C₇	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
21	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
22	C₂×C₄×C₇	C₂×C₄	1	16	yes	complemented
23	C₂×C₄×C₇	C₂³	1	2	yes	—
24	C₂×C₄×C₇	C₂³	1	2	yes	—
25	C₂×Dic₇	—	2	8	no	—
26	C₂×Dic₇	C₂³	1	8	yes	—
27	C₂³×C₄	D₇	1	1	yes	characteristic
28	#117	—	7	8	no	—
29	C₂×C₄⋊C₄	—	7	2	no	—
30	C₂×C₂²⋊C₄	—	7	2	no	—
31	C₂×C₄²	—	7	2	no	—
32	C₂²×C₇	—	2	8	no	—
33	C₂²×C₇	—	2	4	no	—
34	C₂²×C₇	C₂²×C₄	1	4	yes	—
35	C₂²×C₇	C₂²×C₄	1	2	yes	—
36	C₂²×C₇	#41	1	4	yes	—
37	C₂²×C₇	C₂⁴	1	1	yes	characteristic
38	C₄×C₇	C₂²×C₄	1	4	yes	—
39	C₄×C₇	C₂²×C₄	1	4	yes	—
40	Dic₇	—	2	8	no	—
41	C₂⁴	C₂×D₇	1	1	yes	characteristic
42	C₂²×C₄	—	7	4	no	—
43	C₂²×C₄	Dic₇	1	8	yes	complemented
44	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
45	C₂²×C₄	C₂×D₇	1	4	yes	—
46	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
47	C₄⋊C₄	—	7	8	no	—
48	C₂²⋊C₄	—	7	8	no	—
49	C₄²	—	7	8	no	—
50	C₂×C₇	—	2	4	no	—
51	C₂×C₇	#117	1	4	yes	complemented
52	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
53	C₂×C₇	C₂×#41	1	2	yes	—
54	C₂³	—	2	4	no	—
55	C₂³	C₂×Dic₇	1	4	yes	—
56	C₂³	C₂²×D₇	1	2	yes	—
57	C₂³	C₂²×D₇	1	1	yes	characteristic
58	C₂×C₄	—	7	8	no	—
59	C₂×C₄	—	14	8	no	—
60	C₂×C₄	C₂×Dic₇	1	4	yes	—
61	C₂×C₄	C₂×Dic₇	1	4	yes	—
62	C₂×C₄	C₂×Dic₇	1	16	yes	complemented
63	C₂×C₄	C₂²×D₇	1	2	yes	—
64	C₂×C₄	C₂²×D₇	1	2	yes	—
65	C₇	C₂×#117	1	1	yes	characteristic, complemented, Sylow
66	C₂²	—	2	8	no	—
67	C₂²	—	2	4	no	—
68	C₂²	#1157	1	4	yes	—
69	C₂²	C₂²×Dic₇	1	4	yes	—
70	C₂²	C₂²×Dic₇	1	2	yes	—
71	C₂²	C₂³×D₇	1	1	yes	characteristic
72	C₄	—	14	8	no	—
73	C₄	C₂²×Dic₇	1	4	yes	—
74	C₄	C₂²×Dic₇	1	4	yes	—
75	C₂	—	2	4	no	—
76	C₂	#6489	1	4	yes	direct product factor
77	C₂	C₂×#1157	1	2	yes	—
78	C₂	C₂³×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇
commutator	C₂×C₇	C₂³×C₄
Frattini	C₂²	C₂³×D₇
Fitting	C₂³×C₄×C₇	C₂
socle	C₂³×C₇	C₂³
prime radical	C₂⁴×C₇	C₂²
cosocle	C₂²×C₇	C₂⁴
hypercenter	C₂³×C₄	D₇
hypocenter	C₇	C₂×#117
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. #6489	C₂	direct (N × H)
4. C₂×C₄⋊Dic₇	C₂	semidirect
5. C₂×C₄×Dic₇	C₂	semidirect
7. C₂²×C₄×C₇	C₄	semidirect
13. C₄⋊Dic₇	C₂²	semidirect
14. C₄×Dic₇	C₂²	semidirect
22. C₂×C₄×C₇	C₂×C₄	semidirect
43. C₂²×C₄	Dic₇	semidirect
51. C₂×C₇	#117	semidirect
62. C₂×C₄	C₂×Dic₇	semidirect
65. C₇	C₂×#117	semidirect
76. C₂	#6489	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₇	2
C₂×C₂²⋊Dic₇	2
#6489	2
C₂×C₄⋊Dic₇	2
C₂×C₄×Dic₇	2
C₂×#117	7

Subgroups — C2×#6489 #90477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6489 #90477