Subgroups — C₂×#6377 #89693

Order 448.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇⋊C₈	C₂	1	2	yes	maximal
3	#6377	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₇	C₄	1	2	yes	—
5	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
6	C₄²×C₇	C₄	1	2	yes	—
7	C₄²×C₇	C₂²	1	2	yes	—
8	C₂×C₇⋊C₈	C₄	1	8	yes	complemented
9	C₂×C₇⋊C₈	C₂²	1	4	yes	—
10	C₂×#97	—	7	1	no	maximal, Sylow
11	C₂³×C₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₇	—	2	4	no	—
13	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
17	C₇⋊C₈	C₂×C₄	1	8	yes	complemented
18	C₂²×C₈	—	7	2	no	—
19	C₂×C₄²	D₇	1	1	yes	characteristic
20	#97	—	7	4	no	—
21	C₂²×C₇	C₄²	1	2	yes	—
22	C₂²×C₇	M₁₆	1	4	yes	—
23	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₇	—	2	4	no	—
25	C₄×C₇	C₄²	1	2	yes	—
26	C₄×C₇	C₂²×C₄	1	2	yes	—
27	C₂²×C₄	Dic₇	1	2	yes	—
28	C₂²×C₄	C₂×D₇	1	1	yes	characteristic
29	C₂×C₈	—	7	8	no	—
30	C₂×C₈	—	7	4	no	—
31	C₄²	Dic₇	1	2	yes	—
32	C₄²	C₂×D₇	1	2	yes	—
33	C₂×C₇	#97	1	4	yes	complemented
34	C₂×C₇	C₂×C₄²	1	1	yes	characteristic
35	C₂×C₇	C₂×M₁₆	1	2	yes	—
36	C₂³	C₂×Dic₇	1	1	yes	characteristic
37	C₂×C₄	—	2	4	no	—
38	C₂×C₄	C₄×D₇	1	4	yes	—
39	C₂×C₄	C₂×Dic₇	1	4	yes	—
40	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
41	C₂×C₄	C₂²×D₇	1	1	yes	characteristic
42	C₈	—	7	8	no	—
43	C₇	C₂×#97	1	1	yes	characteristic, complemented, Sylow
44	C₂²	#1136	1	4	yes	—
45	C₂²	C₄×Dic₇	1	2	yes	—
46	C₂²	C₂²×Dic₇	1	1	yes	characteristic
47	C₄	—	2	4	no	—
48	C₄	C₄×Dic₇	1	2	yes	—
49	C₄	C₂×C₄×D₇	1	2	yes	—
50	C₂	#6377	1	4	yes	direct product factor
51	C₂	C₂×#1136	1	2	yes	—
52	C₂	C₂×C₄×Dic₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₇
commutator	C₂×C₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₂×C₄²×C₇	C₂
socle, prime radical	C₂³×C₇	C₂×C₄
cosocle	C₂×C₄×C₇	C₂³
hypercenter	C₂×C₄²	D₇
hypocenter	C₇	C₂×#97
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. #6377	C₂	direct (N × H)
8. C₂×C₇⋊C₈	C₄	semidirect
17. C₇⋊C₈	C₂×C₄	semidirect
33. C₂×C₇	#97	semidirect
43. C₇	C₂×#97	semidirect
50. C₂	#6377	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×C₄²×C₇	2
C₂²×C₇⋊C₈	2
#6377	2
C₂×#97	7

Subgroups — C2×#6377 #89693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6377 #89693