Subgroups — C₂×#6403 #89952

Order 448.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₈	C₂	1	1	yes	maximal, characteristic
3	#6403	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇×Q₈	—	2	1	no	—
6	C₂×Dic₁₄	—	2	1	no	—
7	C₇×Q₁₆	—	2	1	no	—
8	C₇×Q₁₆	C₂²	1	2	yes	—
9	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
10	Dic₂₈	—	2	1	no	—
11	Dic₂₈	C₂²	1	2	yes	—
12	C₇⋊C₁₆	C₂²	1	2	yes	—
13	C₂×Q₃₂	—	7	1	no	maximal, Sylow
14	C₇×Q₈	—	2	2	no	—
15	C₇×Q₈	—	4	1	no	—
16	C₂×C₄×C₇	—	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×Q₁₆	D₇	1	1	yes	characteristic
25	Q₃₂	—	7	4	no	—
26	C₂×C₁₆	—	7	1	no	—
27	C₂²×C₇	D₈	1	1	yes	characteristic
28	C₄×C₇	—	4	2	no	—
29	C₄×C₇	D₈	1	1	yes	characteristic
30	C₄×C₇	C₂×D₄	1	1	yes	characteristic
31	Dic₇	—	4	2	no	—
32	C₂×Q₈	—	2	1	no	—
33	C₂×Q₈	—	14	1	no	—
34	Q₁₆	—	2	1	no	—
35	Q₁₆	—	7	2	no	—
36	Q₁₆	—	14	1	no	—
37	Q₁₆	C₂×D₇	1	2	yes	—
38	C₂×C₈	C₂×D₇	1	1	yes	characteristic
39	C₁₆	—	7	2	no	—
40	C₂×C₇	Q₃₂	1	2	yes	complemented
41	C₂×C₇	C₂×D₈	1	1	yes	characteristic
42	Q₈	—	2	2	no	—
43	Q₈	—	4	1	no	—
44	Q₈	—	14	2	no	—
45	Q₈	—	28	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	—	28	1	no	—
48	C₂×C₄	C₂²⋊D₇	1	1	yes	characteristic
49	C₈	C₂²⋊D₇	1	1	yes	characteristic
50	C₈	C₂²×D₇	1	1	yes	characteristic
51	C₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
52	C₂²	#1141	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	28	2	no	—
55	C₄	#1141	1	1	yes	characteristic
56	C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
57	C₂	#6403	1	2	yes	direct product factor
58	C₂	C₂×#1141	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#1141
commutator, cosocle	C₇×C₈	C₂³
Frattini	C₈	C₂²×D₇
Fitting	C₂×C₇×Q₁₆	C₂
socle, prime radical	C₂²×C₇	D₈
hypercenter	C₂×Q₁₆	D₇
hypocenter	C₇	C₂×Q₃₂
LCS	G ▷ C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #6403	C₂	direct (N × H)
40. C₂×C₇	Q₃₂	semidirect
51. C₇	C₂×Q₃₂	semidirect
57. C₂	#6403	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×Q₁₆	2
C₂×Dic₂₈	2
#6403	2
C₂×C₇⋊C₁₆	2
C₂×Q₃₂	7

Subgroups — C2×#6403 #89952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6403 #89952