Subgroups — C₂×#95×C₄₉₁ #44536232

Order 31424.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₄₉₁	C₂	1	3	yes	maximal
2	#95×C₄₉₁	C₂	1	4	yes	maximal, direct product factor
3	C₂⁴×C₄₉₁	C₂²	1	1	yes	characteristic
4	C₂²×C₄×C₄₉₁	—	2	12	no	—
5	C₂²×C₄×C₄₉₁	C₄	1	12	yes	complemented
6	C₂²×C₄×C₄₉₁	C₂²	1	6	yes	—
7	C₂³×C₄₉₁	C₂×C₄	1	6	yes	—
8	C₂³×C₄₉₁	D₄	1	6	yes	—
9	C₂³×C₄₉₁	Q₈	1	2	yes	—
10	C₂³×C₄₉₁	C₂³	1	1	yes	characteristic
11	C₂×C₄×C₄₉₁	—	2	24	no	—
12	C₂×C₄×C₄₉₁	—	2	12	no	—
13	C₂×C₄×C₄₉₁	C₂×C₄	1	12	yes	complemented
14	C₂²×C₄₉₁	C₄²	1	4	yes	—
15	C₂²×C₄₉₁	C₂²⋊C₄	1	12	yes	—
16	C₂²×C₄₉₁	C₄⋊C₄	1	12	yes	—
17	C₂²×C₄₉₁	C₂²×C₄	1	3	yes	—
18	C₂²×C₄₉₁	C₂×D₄	1	3	yes	—
19	C₂²×C₄₉₁	C₂×Q₈	1	1	yes	characteristic
20	C₄×C₄₉₁	—	2	12	no	—
21	C₂×C₄₉₁	#95	1	8	yes	direct product factor
22	C₂×C₄₉₁	C₂×C₄²	1	1	yes	characteristic
23	C₂×C₄₉₁	C₂×C₂²⋊C₄	1	3	yes	—
24	C₂×C₄₉₁	C₂×C₄⋊C₄	1	3	yes	—
25	C₄₉₁	C₂×#95	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×#95	C₄₉₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂³×C₄	C₂×C₄₉₁	1	3	yes	—
28	#95	C₂×C₄₉₁	1	4	yes	direct product factor
29	C₂⁴	C₂²×C₄₉₁	1	1	yes	characteristic
30	C₂²×C₄	—	2	12	no	—
31	C₂²×C₄	C₄×C₄₉₁	1	12	yes	complemented
32	C₂²×C₄	C₂²×C₄₉₁	1	6	yes	—
33	C₂³	C₂×C₄×C₄₉₁	1	6	yes	—
34	C₂³	D₄×C₄₉₁	1	6	yes	—
35	C₂³	Q₈×C₄₉₁	1	2	yes	—
36	C₂³	C₂³×C₄₉₁	1	1	yes	characteristic
37	C₂×C₄	—	2	12	no	—
38	C₂×C₄	—	2	24	no	—
39	C₂×C₄	C₂×C₄×C₄₉₁	1	12	yes	complemented
40	C₂²	C₄²×C₄₉₁	1	4	yes	—
41	C₂²	C₂²⋊C₄×C₄₉₁	1	12	yes	—
42	C₂²	C₄⋊C₄×C₄₉₁	1	12	yes	—
43	C₂²	C₂²×C₄×C₄₉₁	1	3	yes	—
44	C₂²	C₂×D₄×C₄₉₁	1	3	yes	—
45	C₂²	C₂×Q₈×C₄₉₁	1	1	yes	characteristic
46	C₄	—	2	12	no	—
47	C₂	#95×C₄₉₁	1	8	yes	direct product factor
48	C₂	C₂×C₄²×C₄₉₁	1	1	yes	characteristic
49	C₂	C₂×C₂²⋊C₄×C₄₉₁	1	3	yes	—
50	C₂	C₂×C₄⋊C₄×C₄₉₁	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₉₁	C₂²
commutator	C₂	C₂×C₄²×C₄₉₁
Frattini, cosocle	C₂³	C₂³×C₄₉₁
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₉₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #95×C₄₉₁	C₂	direct (N × H)
5. C₂²×C₄×C₄₉₁	C₄	semidirect
13. C₂×C₄×C₄₉₁	C₂×C₄	semidirect
21. C₂×C₄₉₁	#95	direct (N × H)
25. C₄₉₁	C₂×#95	direct (N × H)
26. C₂×#95	C₄₉₁	direct (N × H)
28. #95	C₂×C₄₉₁	direct (N × H)
31. C₂²×C₄	C₄×C₄₉₁	semidirect
39. C₂×C₄	C₂×C₄×C₄₉₁	semidirect
47. C₂	#95×C₄₉₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₄₉₁	2
#95×C₄₉₁	2
C₂×#95	491

Subgroups — C2×#95×C491 #44536232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#95×C₄₉₁ #44536232