Subgroups — #331×C₄₀₉ #39908710

Order 26176.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#127×C₄₀₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×C₄₀₉	C₂	1	2	yes	maximal, complemented
3	C₂×D₄×C₄₀₉	—	2	2	no	—
4	C₂×D₄×C₄₀₉	C₄	1	2	yes	—
5	C₂×C₈×C₄₀₉	—	2	2	no	—
6	C₄²×C₄₀₉	C₂²	1	1	yes	characteristic
7	C₂³×C₄₀₉	—	2	2	no	—
8	D₄×C₄₀₉	—	4	2	no	—
9	D₄×C₄₀₉	—	4	2	no	—
10	D₄×C₄₀₉	—	4	2	no	—
11	C₂×C₄×C₄₀₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₀₉	D₄	1	2	yes	—
13	C₈×C₄₀₉	—	4	2	no	—
14	C₂²×C₄₀₉	—	4	2	no	—
15	C₂²×C₄₀₉	—	4	4	no	—
16	C₂²×C₄₀₉	C₂²⋊C₄	1	1	yes	characteristic
17	C₄×C₄₀₉	—	2	1	no	—
18	C₄×C₄₀₉	D₈	1	2	yes	—
19	C₄×C₄₀₉	SD₁₆	1	2	yes	—
20	C₂×C₄₀₉	—	8	2	no	—
21	C₂×C₄₀₉	#100	1	1	yes	characteristic
22	C₂×C₄₀₉	#102	1	2	yes	—
23	C₄₀₉	#331	1	1	yes	characteristic, direct product factor, Sylow
24	#331	C₄₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	#127	C₂×C₄₀₉	1	1	yes	characteristic
26	C₄⋊C₈	C₂×C₄₀₉	1	2	yes	complemented
27	C₂×D₄	—	2	2	no	—
28	C₂×D₄	C₄×C₄₀₉	1	2	yes	—
29	C₂×C₈	—	2	2	no	—
30	C₄²	C₂²×C₄₀₉	1	1	yes	characteristic
31	C₂³	—	2	2	no	—
32	D₄	—	4	2	no	—
33	D₄	—	4	2	no	—
34	D₄	—	4	2	no	—
35	C₂×C₄	C₂×C₄×C₄₀₉	1	1	yes	characteristic
36	C₂×C₄	D₄×C₄₀₉	1	2	yes	—
37	C₈	—	4	2	no	—
38	C₂²	—	4	2	no	—
39	C₂²	—	4	4	no	—
40	C₂²	C₂²⋊C₄×C₄₀₉	1	1	yes	characteristic
41	C₄	—	2	1	no	—
42	C₄	D₈×C₄₀₉	1	2	yes	—
43	C₄	SD₁₆×C₄₀₉	1	2	yes	—
44	C₂	—	8	2	no	—
45	C₂	#100×C₄₀₉	1	1	yes	characteristic
46	C₂	#102×C₄₀₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₀₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄×C₄₀₉
Frattini, cosocle	C₄²	C₂²×C₄₀₉
prime radical	#127×C₄₀₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₀₉ ◁ C₄²×C₄₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄⋊C₈×C₄₀₉	C₂	semidirect
23. C₄₀₉	#331	direct (N × H)
24. #331	C₄₀₉	direct (N × H)
26. C₄⋊C₈	C₂×C₄₀₉	semidirect

Maximal subgroups

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

subgroup	index
#127×C₄₀₉	2
C₄⋊C₈×C₄₀₉	2
#331	409

Subgroups — #331×C409 #39908710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #331×C₄₀₉ #39908710