Subgroups — C₂×#6511 #90509

Order 448.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#41	C₂	1	1	yes	maximal, characteristic
2	#6511	C₂	1	8	yes	maximal, direct product factor
3	C₂×#1136	C₂	1	3	yes	maximal, complemented
4	C₂²×C₇⋊C₈	C₂	1	3	yes	maximal, complemented
5	C₇×#41	C₄	1	4	yes	—
6	C₇×#41	C₂²	1	4	yes	—
7	C₂×C₇×Q₈	C₄	1	1	yes	characteristic
8	C₂×C₇×D₄	C₄	1	3	yes	—
9	C₂²×C₄×C₇	C₂²	1	3	yes	—
10	#1136	C₂²	1	12	yes	complemented
11	C₂×C₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₇⋊C₈	C₂²	1	3	yes	—
13	C₂×C₇⋊C₈	C₂²	1	12	yes	complemented
14	C₂×#131	—	7	1	no	maximal, Sylow
15	C₂³×C₇	C₂×C₄	1	3	yes	—
16	C₇×Q₈	C₂×C₄	1	4	yes	—
17	C₇×D₄	C₂×C₄	1	12	yes	—
18	C₂×C₄×C₇	C₂×C₄	1	3	yes	—
19	C₂×C₄×C₇	C₂×C₄	1	6	yes	—
20	C₂×C₄×C₇	C₂³	1	6	yes	—
21	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
22	C₇⋊C₈	C₂³	1	2	yes	—
23	C₇⋊C₈	C₂³	1	6	yes	—
24	C₂×#41	D₇	1	1	yes	characteristic
25	#131	—	7	8	no	—
26	C₂×M₁₆	—	7	3	no	—
27	C₂²×C₈	—	7	3	no	—
28	C₂²×C₇	—	2	6	no	—
29	C₂²×C₇	C₂²×C₄	1	6	yes	—
30	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₇	C₂²×C₄	1	6	yes	—
33	C₄×C₇	C₂⁴	1	1	yes	characteristic
34	#41	Dic₇	1	4	yes	—
35	#41	C₂×D₇	1	4	yes	—
36	C₂×Q₈	Dic₇	1	1	yes	characteristic
37	C₂×D₄	Dic₇	1	3	yes	—
38	C₂²×C₄	C₂×D₇	1	3	yes	—
39	M₁₆	—	7	12	no	—
40	C₂×C₈	—	7	12	no	—
41	C₂×C₈	—	7	1	no	—
42	C₂×C₈	—	7	3	no	—
43	C₂×C₇	—	2	6	no	—
44	C₂×C₇	#131	1	2	yes	complemented
45	C₂×C₇	C₂³×C₄	1	1	yes	characteristic
46	C₂³	C₂×Dic₇	1	3	yes	—
47	Q₈	C₂×Dic₇	1	4	yes	—
48	D₄	C₂×Dic₇	1	12	yes	—
49	C₂×C₄	C₂×Dic₇	1	3	yes	—
50	C₂×C₄	C₂×Dic₇	1	6	yes	—
51	C₂×C₄	C₂²×D₇	1	6	yes	—
52	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
53	C₈	—	7	2	no	—
54	C₈	—	7	6	no	—
55	C₇	C₂×#131	1	1	yes	characteristic, complemented, Sylow
56	C₂²	—	2	6	no	—
57	C₂²	C₂²×Dic₇	1	6	yes	—
58	C₂²	C₂²×Dic₇	1	1	yes	characteristic
59	C₄	C₂²×Dic₇	1	1	yes	characteristic
60	C₄	C₂²×Dic₇	1	6	yes	—
61	C₄	C₂³×D₇	1	1	yes	characteristic
62	C₂	—	2	6	no	—
63	C₂	#6511	1	2	yes	direct product factor
64	C₂	C₂³×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₇
commutator	C₂×C₇	C₂³×C₄
Frattini	C₄	C₂³×D₇
Fitting, prime radical	C₂×C₇×#41	C₂
socle	C₂²×C₇	C₂²×C₄
cosocle	C₄×C₇	C₂⁴
hypercenter	C₂×#41	D₇
hypocenter	C₇	C₂×#131
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. #6511	C₂	direct (N × H)
3. C₂×#1136	C₂	semidirect
4. C₂²×C₇⋊C₈	C₂	semidirect
10. #1136	C₂²	semidirect
13. C₂×C₇⋊C₈	C₂²	semidirect
44. C₂×C₇	#131	semidirect
55. C₇	C₂×#131	semidirect
63. C₂	#6511	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#41	2
#6511	2
C₂×#1136	2
C₂²×C₇⋊C₈	2
C₂×#131	7

Subgroups — C2×#6511 #90509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6511 #90509