Subgroups — C₂×#6401 #89920

Order 448.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#6401	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×D₄	—	2	1	no	—
6	C₂×Dic₁₄	—	2	1	no	—
7	C₇×D₈	—	2	1	no	—
8	C₇×D₈	C₂²	1	2	yes	—
9	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
10	Dic₂₈	—	2	1	no	—
11	Dic₂₈	C₂²	1	2	yes	complemented
12	C₇⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂×SD₃₂	—	7	1	no	maximal, Sylow
14	C₂³×C₇	—	4	1	no	—
15	C₇×D₄	—	2	2	no	—
16	C₇×D₄	—	4	1	no	—
17	C₂×C₄×C₇	D₄	1	1	yes	characteristic
18	C₂×Dic₇	—	4	1	no	—
19	Dic₁₄	—	2	2	no	—
20	Dic₁₄	—	4	1	no	—
21	C₇×C₈	D₄	1	1	yes	characteristic
22	C₇×C₈	C₂³	1	1	yes	characteristic
23	C₂×Q₁₆	—	7	1	no	—
24	C₂×D₈	D₇	1	1	yes	characteristic
25	SD₃₂	—	7	4	no	—
26	C₂×C₁₆	—	7	1	no	—
27	C₂²×C₇	—	4	2	no	—
28	C₂²×C₇	—	8	2	no	—
29	C₂²×C₇	D₈	1	1	yes	characteristic
30	C₄×C₇	D₈	1	1	yes	characteristic
31	C₄×C₇	C₂×D₄	1	1	yes	characteristic
32	Dic₇	—	4	2	no	—
33	C₂×Q₈	—	14	1	no	—
34	C₂×D₄	—	2	1	no	—
35	Q₁₆	—	7	2	no	—
36	Q₁₆	—	14	1	no	—
37	D₈	—	2	1	no	—
38	D₈	C₂×D₇	1	2	yes	—
39	C₂×C₈	C₂×D₇	1	1	yes	characteristic
40	C₁₆	—	7	2	no	—
41	C₂×C₇	—	8	2	no	—
42	C₂×C₇	SD₃₂	1	2	yes	complemented
43	C₂×C₇	C₂×D₈	1	1	yes	characteristic
44	C₂³	—	4	1	no	—
45	Q₈	—	14	2	no	—
46	Q₈	—	28	1	no	—
47	D₄	—	2	2	no	—
48	D₄	—	4	1	no	—
49	C₂×C₄	—	28	1	no	—
50	C₂×C₄	C₂²⋊D₇	1	1	yes	characteristic
51	C₈	C₂²⋊D₇	1	1	yes	characteristic
52	C₈	C₂²×D₇	1	1	yes	characteristic
53	C₇	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	4	2	no	—
55	C₂²	—	8	2	no	—
56	C₂²	#1141	1	1	yes	characteristic
57	C₄	—	28	2	no	—
58	C₄	#1141	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
60	C₂	—	8	2	no	—
61	C₂	#6401	1	2	yes	direct product factor
62	C₂	C₂×#1141	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#1141
commutator, cosocle	C₇×C₈	C₂³
Frattini	C₈	C₂²×D₇
Fitting, prime radical	C₂×C₇×D₈	C₂
socle	C₂²×C₇	D₈
hypercenter	C₂×D₈	D₇
hypocenter	C₇	C₂×SD₃₂
LCS	G ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₈	C₂	semidirect
3. #6401	C₂	direct (N × H)
4. C₂×C₇⋊C₁₆	C₂	semidirect
11. Dic₂₈	C₂²	semidirect
12. C₇⋊C₁₆	C₂²	semidirect
42. C₂×C₇	SD₃₂	semidirect
53. C₇	C₂×SD₃₂	semidirect
61. C₂	#6401	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×D₈	2
C₂×Dic₂₈	2
#6401	2
C₂×C₇⋊C₁₆	2
C₂×SD₃₂	7

Subgroups — C2×#6401 #89920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6401 #89920