Subgroups — C₇×#334 #89376

Order 448.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×C₈	—	2	2	no	—
4	C₂×C₇×C₈	C₄	1	1	yes	characteristic
5	C₂×C₇×C₈	C₄	1	1	yes	characteristic
6	C₄²×C₇	C₂²	1	1	yes	characteristic
7	#334	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₇	D₄	1	1	yes	characteristic
10	C₂×C₄×C₇	Q₈	1	1	yes	characteristic
11	C₇×C₈	—	2	1	no	—
12	C₇×C₈	—	4	2	no	—
13	C₇×C₈	C₈	1	2	yes	complemented
14	C₄⋊C₈	C₂×C₇	1	2	yes	—
15	C₄×C₈	C₂×C₇	1	1	yes	characteristic
16	C₂²×C₇	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₇	—	2	1	no	—
18	C₄×C₇	C₂×C₈	1	1	yes	characteristic
19	C₄×C₇	M₁₆	1	1	yes	characteristic
20	C₄×C₇	SD₁₆	1	2	yes	—
21	C₂×C₈	—	2	2	no	—
22	C₂×C₈	C₄×C₇	1	1	yes	characteristic
23	C₂×C₈	C₄×C₇	1	1	yes	characteristic
24	C₄²	C₂²×C₇	1	1	yes	characteristic
25	C₂×C₇	C₄⋊C₈	1	1	yes	characteristic
26	C₂×C₇	#106	1	1	yes	characteristic
27	C₂×C₇	#108	1	1	yes	characteristic
28	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
29	C₂×C₄	C₇×D₄	1	1	yes	characteristic
30	C₂×C₄	C₇×Q₈	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₈	—	4	2	no	—
33	C₈	C₇×C₈	1	2	yes	complemented
34	C₇	#334	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	C₇×C₄⋊C₄	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	C₂×C₇×C₈	1	1	yes	characteristic
38	C₄	C₇×M₁₆	1	1	yes	characteristic
39	C₄	C₇×SD₁₆	1	2	yes	—
40	C₂	C₇×C₄⋊C₈	1	1	yes	characteristic
41	C₂	C₇×#106	1	1	yes	characteristic
42	C₂	C₇×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	D₄
commutator	C₄	C₂×C₇×C₈
Frattini, cosocle	C₄²	C₂²×C₇
socle, prime radical	C₂²×C₇	C₄⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
7. #334	C₇	direct (N × H)
13. C₇×C₈	C₈	semidirect
33. C₈	C₇×C₈	semidirect
34. C₇	#334	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₄⋊C₈	2
C₄×C₇×C₈	2
#334	7

Subgroups — C7×#334 #89376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#334 #89376