Subgroups — C₇×#341 #89383

Order 448.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×M₁₆	C₂	1	2	yes	maximal
2	C₂²×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
4	C₇×M₁₆	—	2	2	no	—
5	C₇×M₁₆	C₄	1	4	yes	—
6	C₂×C₇×C₈	—	2	2	no	—
7	C₂×C₇×C₈	—	2	2	no	—
8	C₂×C₇×C₈	C₄	1	2	yes	—
9	#341	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₇	Q₈	1	1	yes	characteristic
11	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₇	C₂×C₄	1	2	yes	—
13	C₂×C₄×C₇	D₄	1	2	yes	—
14	C₂×C₄×C₇	D₄	1	1	yes	characteristic
15	C₇×C₈	—	2	2	no	—
16	C₇×C₈	—	2	4	no	—
17	C₂×M₁₆	C₂×C₇	1	2	yes	—
18	C₂²×C₈	C₂×C₇	1	1	yes	characteristic
19	C₂²×C₇	—	2	2	no	—
20	C₂²×C₇	C₄⋊C₄	1	2	yes	—
21	C₂²×C₇	C₄⋊C₄	1	1	yes	characteristic
22	C₄×C₇	C₄²	1	1	yes	characteristic
23	C₄×C₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₇	C₂²⋊C₄	1	2	yes	—
25	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
26	M₁₆	—	2	2	no	—
27	M₁₆	C₄×C₇	1	4	yes	—
28	C₂×C₈	—	2	2	no	—
29	C₂×C₈	—	2	2	no	—
30	C₂×C₈	C₄×C₇	1	2	yes	—
31	C₂×C₇	—	2	2	no	—
32	C₂×C₇	#95	1	1	yes	characteristic
33	C₂×C₇	#108	1	2	yes	—
34	C₂³	C₇×Q₈	1	1	yes	characteristic
35	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
36	C₂×C₄	C₂×C₄×C₇	1	2	yes	—
37	C₂×C₄	C₇×D₄	1	1	yes	characteristic
38	C₂×C₄	C₇×D₄	1	2	yes	—
39	C₈	—	2	2	no	—
40	C₈	—	2	4	no	—
41	C₇	#341	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²	—	2	2	no	—
43	C₂²	C₇×C₄⋊C₄	1	2	yes	—
44	C₂²	C₇×C₄⋊C₄	1	1	yes	characteristic
45	C₄	C₄²×C₇	1	1	yes	characteristic
46	C₄	C₇×C₂²⋊C₄	1	1	yes	characteristic
47	C₄	C₇×C₂²⋊C₄	1	2	yes	—
48	C₂	—	2	2	no	—
49	C₂	C₇×#95	1	1	yes	characteristic
50	C₂	C₇×#108	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	D₄
commutator	C₄	C₄²×C₇
Frattini, cosocle	C₂²×C₄	C₂²×C₇
socle	C₂²×C₇	C₄⋊C₄
prime radical	C₂³×C₇	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
9. #341	C₇	direct (N × H)
41. C₇	#341	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×M₁₆	2
C₂²×C₇×C₈	2
#341	7

Subgroups — C7×#341 #89383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#341 #89383