Subgroups — C₄⋊#14558739 #23750545

Order 9536.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14558739	C₂	1	2	yes	maximal
2	C₄×#11924746	C₂	1	1	yes	maximal, characteristic
3	#14558739	—	2	2	no	—
4	C₂×#11924746	C₄	1	1	yes	characteristic
5	C₂×#11924746	C₂²	1	1	yes	characteristic
6	C₄²×C₁₄₉	C₄	1	1	yes	characteristic
7	#11924746	—	2	1	no	—
8	#11924746	D₄	1	1	yes	characteristic
9	#11924746	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₁₄₉	C₈	1	1	yes	characteristic
11	C₂×C₄×C₁₄₉	C₈	1	1	yes	characteristic
12	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₁₄₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₁₄₉	—	2	1	no	—
15	C₄×C₁₄₉	C₁₆	1	2	yes	complemented
16	C₄×C₁₄₉	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
18	C₂×C₁₄₉	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₁₄₉	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₁₄₉	M₃₂	1	1	yes	characteristic
21	C₁₄₉	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	149	1	no	maximal, Sylow
23	C₂×C₁₆	—	149	2	no	—
24	C₄×C₈	—	149	1	no	—
25	C₂×C₈	—	149	1	no	—
26	C₂×C₈	—	149	1	no	—
27	C₄²	#10597010	1	1	yes	characteristic
28	C₁₆	—	298	2	no	—
29	C₂×C₄	#11924753	1	1	yes	characteristic
30	C₂×C₄	#11924753	1	1	yes	characteristic
31	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
32	C₈	—	298	1	no	—
33	C₈	—	149	1	no	—
34	C₈	—	149	1	no	—
35	C₂²	C₂×#11924753	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	#14558739	1	2	yes	complemented
38	C₄	C₄⋊#10597010	1	1	yes	characteristic
39	C₄	#14558746	1	1	yes	characteristic
40	C₂	C₄⋊#11924753	1	1	yes	characteristic
41	C₂	C₂×#14558739	1	1	yes	characteristic
42	C₂	#18011985	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10597010
commutator	C₂×C₁₄₉	C₂×C₁₆
Fitting	C₄²×C₁₄₉	C₄
socle, prime radical	C₂²×C₁₄₉	C₂×C₈
cosocle	C₂×#11924746	C₂²
hypercenter	C₄²	#10597010
hypocenter	C₁₄₉	C₄⋊C₁₆
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
15. C₄×C₁₄₉	C₁₆	semidirect
21. C₁₄₉	C₄⋊C₁₆	semidirect
37. C₄	#14558739	semidirect

Subgroups — C4⋊#14558739 #23750545

Conjugacy classes of subgroups

Complements

Subgroups — C₄⋊#14558739 #23750545