Subgroups — #399×C₁₀₁ #20264708

Order 6464.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×C₁₀₁	C₂	1	3	yes	maximal, complemented
2	C₂×C₂²⋊C₄×C₁₀₁	C₂	1	3	yes	maximal
3	#95×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×C₁₀₁	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₁₀₁	C₂²	1	3	yes	—
6	C₂²×C₄×C₁₀₁	C₂²	1	3	yes	—
7	C₄⋊C₄×C₁₀₁	—	2	6	no	—
8	C₂²⋊C₄×C₁₀₁	—	2	6	no	—
9	C₂³×C₁₀₁	—	2	3	no	—
10	C₂³×C₁₀₁	—	2	3	no	—
11	C₂³×C₁₀₁	Q₈	1	2	yes	—
12	C₂³×C₁₀₁	C₂³	1	1	yes	characteristic
13	C₂×C₄×C₁₀₁	—	2	6	no	—
14	C₂×C₄×C₁₀₁	—	2	3	no	—
15	C₂×C₄×C₁₀₁	—	2	6	no	—
16	C₂×C₄×C₁₀₁	D₄	1	6	yes	—
17	C₂²×C₁₀₁	—	2	6	no	—
18	C₂²×C₁₀₁	—	4	3	no	—
19	C₂²×C₁₀₁	—	4	1	no	—
20	C₂²×C₁₀₁	C₂×D₄	1	3	yes	—
21	C₂²×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
22	C₂²×C₁₀₁	#41	1	3	yes	—
23	C₄×C₁₀₁	—	2	6	no	—
24	C₄×C₁₀₁	—	4	3	no	—
25	C₂×C₁₀₁	—	4	2	no	—
26	C₂×C₁₀₁	C₂²⋊Q₈	1	3	yes	—
27	C₂×C₁₀₁	#123	1	3	yes	—
28	C₂×C₁₀₁	#127	1	1	yes	characteristic
29	C₁₀₁	#399	1	1	yes	characteristic, direct product factor, Sylow
30	#399	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×C₄⋊C₄	C₂×C₁₀₁	1	3	yes	complemented
32	C₂×C₂²⋊C₄	C₂×C₁₀₁	1	3	yes	—
33	#95	C₂×C₁₀₁	1	1	yes	characteristic, complemented
34	C₂⁴	C₂²×C₁₀₁	1	1	yes	characteristic
35	C₂²×C₄	C₂²×C₁₀₁	1	3	yes	—
36	C₂²×C₄	C₂²×C₁₀₁	1	3	yes	—
37	C₄⋊C₄	—	2	6	no	—
38	C₂²⋊C₄	—	2	6	no	—
39	C₂³	—	2	3	no	—
40	C₂³	—	2	3	no	—
41	C₂³	Q₈×C₁₀₁	1	2	yes	—
42	C₂³	C₂³×C₁₀₁	1	1	yes	characteristic
43	C₂×C₄	—	2	6	no	—
44	C₂×C₄	—	2	3	no	—
45	C₂×C₄	—	2	6	no	—
46	C₂×C₄	D₄×C₁₀₁	1	6	yes	—
47	C₂²	—	2	6	no	—
48	C₂²	—	4	3	no	—
49	C₂²	—	4	1	no	—
50	C₂²	C₂×D₄×C₁₀₁	1	3	yes	—
51	C₂²	C₂×Q₈×C₁₀₁	1	1	yes	characteristic
52	C₂²	#41×C₁₀₁	1	3	yes	—
53	C₄	—	2	6	no	—
54	C₄	—	4	3	no	—
55	C₂	—	4	2	no	—
56	C₂	C₂²⋊Q₈×C₁₀₁	1	3	yes	—
57	C₂	#123×C₁₀₁	1	3	yes	—
58	C₂	#127×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₀₁	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₁₀₁
prime radical	C₂⁴×C₁₀₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄⋊C₄×C₁₀₁	C₂	semidirect
3. #95×C₁₀₁	C₂	semidirect
29. C₁₀₁	#399	direct (N × H)
30. #399	C₁₀₁	direct (N × H)
31. C₂×C₄⋊C₄	C₂×C₁₀₁	semidirect
33. #95	C₂×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₄×C₁₀₁	2
C₂×C₂²⋊C₄×C₁₀₁	2
#95×C₁₀₁	2
#399	101

Subgroups — #399×C101 #20264708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #399×C₁₀₁ #20264708