Subgroups — #356×C₁₄₉ #23749113

Order 9536.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#101×C₁₄₉	C₂	1	2	yes	maximal
3	C₂×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
4	C₂×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
5	M₁₆×C₁₄₉	—	2	2	no	—
6	C₄⋊C₄×C₁₄₉	—	2	2	no	—
7	C₄²×C₁₄₉	C₄	1	1	yes	characteristic
8	Q₈×C₁₄₉	—	4	1	no	—
9	Q₈×C₁₄₉	—	4	1	no	—
10	C₂×C₄×C₁₄₉	—	2	1	no	—
11	C₂×C₄×C₁₄₉	—	2	1	no	—
12	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₄₉	D₄	1	2	yes	—
14	C₈×C₁₄₉	—	4	2	no	—
15	C₂²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₁₄₉	—	2	2	no	—
17	C₄×C₁₄₉	—	2	2	no	—
18	C₄×C₁₄₉	—	2	1	no	—
19	C₄×C₁₄₉	—	4	1	no	—
20	C₂×C₁₄₉	—	2	1	no	—
21	C₂×C₁₄₉	#99	1	1	yes	characteristic
22	C₁₄₉	#356	1	1	yes	characteristic, direct product factor, Sylow
23	#356	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₄⋊Q₈	C₂×C₁₄₉	1	1	yes	characteristic
25	#101	C₂×C₁₄₉	1	2	yes	—
26	C₂×Q₈	C₄×C₁₄₉	1	1	yes	characteristic
27	C₂×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
28	M₁₆	—	2	2	no	—
29	C₄⋊C₄	—	2	2	no	—
30	C₄²	C₄×C₁₄₉	1	1	yes	characteristic
31	Q₈	—	4	1	no	—
32	Q₈	—	4	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
36	C₂×C₄	D₄×C₁₄₉	1	2	yes	—
37	C₈	—	4	2	no	—
38	C₂²	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	2	2	no	—
41	C₄	—	2	1	no	—
42	C₄	—	4	1	no	—
43	C₂	—	2	1	no	—
44	C₂	#99×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₄₉	#99
commutator	C₂×C₄	C₂×C₄×C₁₄₉
Frattini, cosocle	C₂×Q₈	C₂²×C₁₄₉
prime radical	C₂²×C₁₄₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₄₉ ◁ C₂²×C₁₄₉ ◁ C₂×Q₈×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
22. C₁₄₉	#356	direct (N × H)
23. #356	C₁₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊Q₈×C₁₄₉	2
#101×C₁₄₉	2
#356	149

Subgroups — #356×C149 #23749113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #356×C₁₄₉ #23749113