Subgroups — C₂×#6507 #90501

Order 448.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₄	C₂	1	1	yes	maximal, characteristic
3	#6507	C₂	1	8	yes	maximal, direct product factor
4	C₂×Dic₇⋊C₄	C₂	1	4	yes	maximal
5	C₂×C₄×Dic₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×Q₈	—	2	4	no	—
7	C₂×C₇×Q₈	C₂²	1	4	yes	—
8	C₂²×C₄×C₇	C₂²	1	2	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	—
14	Dic₇⋊C₄	C₂²	1	16	yes	—
15	C₄×Dic₇	C₂²	1	4	yes	—
16	C₂×C₄⋊Q₈	—	7	1	no	maximal, Sylow
17	C₂³×C₇	C₂³	1	1	yes	characteristic
18	C₇×Q₈	—	2	8	no	—
19	C₂×C₄×C₇	—	2	4	no	—
20	C₂×C₄×C₇	D₄	1	4	yes	—
21	C₂×C₄×C₇	C₂³	1	4	yes	—
22	C₂×C₄×C₇	C₂³	1	2	yes	—
23	C₂×Dic₇	—	2	4	no	—
24	C₂×Dic₇	Q₈	1	8	yes	complemented
25	C₂×Dic₇	C₂³	1	4	yes	—
26	C₂×Dic₇	C₂³	1	4	yes	—
27	Dic₁₄	—	2	8	no	—
28	C₂²×Q₈	—	7	1	no	—
29	C₂²×Q₈	D₇	1	1	yes	characteristic
30	C₄⋊Q₈	—	7	8	no	—
31	C₂×C₄⋊C₄	—	7	4	no	—
32	C₂×C₄²	—	7	1	no	—
33	C₂²×C₇	C₂×D₄	1	2	yes	—
34	C₂²×C₇	C₂×Q₈	1	4	yes	—
35	C₂²×C₇	C₂⁴	1	1	yes	characteristic
36	C₄×C₇	—	2	4	no	—
37	C₄×C₇	C₂×D₄	1	4	yes	—
38	Dic₇	—	2	4	no	—
39	Dic₇	C₂×Q₈	1	8	yes	complemented
40	C₂×Q₈	—	2	4	no	—
41	C₂×Q₈	—	7	4	no	—
42	C₂×Q₈	—	14	4	no	—
43	C₂×Q₈	C₂×D₇	1	4	yes	—
44	C₂²×C₄	—	7	2	no	—
45	C₂²×C₄	—	7	2	no	—
46	C₂²×C₄	C₂×D₇	1	2	yes	—
47	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
48	C₄⋊C₄	—	7	16	no	—
49	C₄²	—	7	4	no	—
50	C₂×C₇	C₄⋊Q₈	1	4	yes	complemented
51	C₂×C₇	C₂²×D₄	1	1	yes	characteristic
52	C₂×C₇	C₂²×Q₈	1	2	yes	—
53	C₂³	C₂²×D₇	1	1	yes	characteristic
54	Q₈	—	2	8	no	—
55	Q₈	—	14	8	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	7	8	no	—
58	C₂×C₄	—	7	4	no	—
59	C₂×C₄	—	7	4	no	—
60	C₂×C₄	—	14	4	no	—
61	C₂×C₄	C₂²⋊D₇	1	4	yes	—
62	C₂×C₄	C₂²×D₇	1	4	yes	—
63	C₂×C₄	C₂²×D₇	1	2	yes	—
64	C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
65	C₂²	Q₈×D₇	1	4	yes	—
66	C₂²	C₂×C₂²⋊D₇	1	2	yes	—
67	C₂²	C₂³×D₇	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	—	7	8	no	—
70	C₄	—	14	4	no	—
71	C₄	C₂×C₂²⋊D₇	1	4	yes	—
72	C₂	#6507	1	4	yes	direct product factor
73	C₂	C₂×Q₈×D₇	1	2	yes	—
74	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	C₂²×C₇×Q₈	C₂
socle, prime radical	C₂³×C₇	C₂³
hypercenter	C₂²×Q₈	D₇
hypocenter	C₇	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
3. #6507	C₂	direct (N × H)
24. C₂×Dic₇	Q₈	semidirect
39. Dic₇	C₂×Q₈	semidirect
50. C₂×C₇	C₄⋊Q₈	semidirect
64. C₇	C₂×C₄⋊Q₈	semidirect
72. C₂	#6507	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×Q₈	2
C₂²×Dic₁₄	2
#6507	2
C₂×Dic₇⋊C₄	2
C₂×C₄×Dic₇	2
C₂×C₄⋊Q₈	7

Subgroups — C2×#6507 #90501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6507 #90501