Subgroups — C₂×C₇×#97 #90049

Order 448.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₈	C₂	1	2	yes	maximal
2	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
3	C₇×#97	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	C₂×C₇×C₈	C₄	1	8	yes	complemented
7	C₂×C₇×C₈	C₂²	1	4	yes	—
8	C₄²×C₇	C₄	1	2	yes	—
9	C₄²×C₇	C₂²	1	2	yes	—
10	C₂×#97	C₇	1	1	yes	maximal, characteristic, direct product factor, 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	1	yes	characteristic
15	C₂×C₄×C₇	C₂×C₄	1	4	yes	—
16	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
17	C₇×C₈	C₂×C₄	1	8	yes	complemented
18	C₂²×C₈	C₂×C₇	1	2	yes	—
19	C₂×C₄²	C₂×C₇	1	1	yes	characteristic
20	#97	C₂×C₇	1	4	yes	direct product factor
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	C₄×C₇	1	2	yes	—
28	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
29	C₂×C₈	C₄×C₇	1	8	yes	complemented
30	C₂×C₈	C₂²×C₇	1	4	yes	—
31	C₄²	C₄×C₇	1	2	yes	—
32	C₄²	C₂²×C₇	1	2	yes	—
33	C₂×C₇	#97	1	4	yes	direct product factor
34	C₂×C₇	C₂×C₄²	1	1	yes	characteristic
35	C₂×C₇	C₂×M₁₆	1	2	yes	—
36	C₂³	C₂×C₄×C₇	1	1	yes	characteristic
37	C₂×C₄	—	2	4	no	—
38	C₂×C₄	C₂×C₄×C₇	1	4	yes	—
39	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
40	C₂×C₄	C₂×C₄×C₇	1	4	yes	—
41	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
42	C₈	C₂×C₄×C₇	1	8	yes	complemented
43	C₇	C₂×#97	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	C₄²×C₇	1	2	yes	—
45	C₂²	C₇×M₁₆	1	4	yes	—
46	C₂²	C₂²×C₄×C₇	1	1	yes	characteristic
47	C₄	—	2	4	no	—
48	C₄	C₄²×C₇	1	2	yes	—
49	C₄	C₂²×C₄×C₇	1	2	yes	—
50	C₂	C₇×#97	1	4	yes	direct product factor
51	C₂	C₂×C₄²×C₇	1	1	yes	characteristic
52	C₂	C₂×C₇×M₁₆	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₇×#97	C₂	direct (N × H)
6. C₂×C₇×C₈	C₄	semidirect
10. C₂×#97	C₇	direct (N × H)
17. C₇×C₈	C₂×C₄	semidirect
20. #97	C₂×C₇	direct (N × H)
29. C₂×C₈	C₄×C₇	semidirect
33. C₂×C₇	#97	direct (N × H)
42. C₈	C₂×C₄×C₇	semidirect
43. C₇	C₂×#97	direct (N × H)
50. C₂	C₇×#97	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×C₈	2
C₂×C₄²×C₇	2
C₇×#97	2
C₂×#97	7

Subgroups — C2×C7×#97 #90049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#97 #90049