Subgroups — #23750475

Order 9536.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924753	C₂	1	1	yes	maximal, characteristic
2	C₄×#11924753	C₂	1	1	yes	maximal, characteristic
3	#18011876	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924753	—	2	1	no	—
5	C₂×#11924753	—	2	1	no	—
6	C₂×Dic₂₉₈	C₄	1	1	yes	characteristic
7	#14558715	—	2	1	no	—
8	C₄×Dic₁₄₉	—	2	1	no	—
9	C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₁₄₉	C₄	1	1	yes	characteristic
11	#11924753	—	2	2	no	—
12	#11924753	—	4	1	no	—
13	Dic₂₉₈	—	2	1	no	—
14	Dic₂₉₈	C₈	1	2	yes	complemented
15	C₂×Dic₁₄₉	—	2	1	no	—
16	C₂×Dic₁₄₉	D₄	1	1	yes	characteristic
17	C₂×Dic₁₄₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₄₉	—	2	1	no	—
19	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₄₉	—	4	1	no	—
22	C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
23	C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
24	Dic₁₄₉	—	2	2	no	—
25	Dic₁₄₉	—	2	1	no	—
26	Dic₁₄₉	SD₁₆	1	1	yes	characteristic
27	Dic₁₄₉	Q₁₆	1	1	yes	characteristic
28	C₂×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₁₄₉	#103	1	1	yes	characteristic
30	C₂×C₁₄₉	#104	1	1	yes	characteristic
31	C₁₄₉	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈⋊C₈	—	149	1	no	maximal, Sylow
33	C₄×Q₈	—	149	1	no	—
34	C₄⋊C₈	—	149	1	no	—
35	C₄×C₈	—	149	1	no	—
36	C₂×Q₈	—	149	1	no	—
37	C₂×C₈	—	298	1	no	—
38	C₂×C₈	—	298	1	no	—
39	C₄⋊C₄	—	298	1	no	—
40	C₄⋊C₄	#10597010	1	1	yes	characteristic
41	C₄²	—	298	1	no	—
42	C₄²	—	149	1	no	—
43	Q₈	—	298	1	no	—
44	Q₈	—	149	2	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	298	1	no	—
47	C₂×C₄	—	149	1	no	—
48	C₂×C₄	—	149	1	no	—
49	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
50	C₈	—	298	2	no	—
51	C₈	—	596	1	no	—
52	C₂²	C₂²⋊#10597010	1	1	yes	characteristic
53	C₄	—	4	1	no	—
54	C₄	—	298	2	no	—
55	C₄	—	298	1	no	—
56	C₄	—	149	1	no	—
57	C₄	—	149	1	no	—
58	C₄	D₁₄₉⋊C₈	1	1	yes	characteristic
59	C₄	#14558746	1	1	yes	characteristic
60	C₂	#18011968	1	1	yes	characteristic
61	C₂	#18011974	1	1	yes	characteristic
62	C₂	#18011975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#10597010
commutator	C₄×C₁₄₉	C₂×C₈
Frattini	C₂×C₄	C₂×#10597010
Fitting	C₄⋊C₄×C₁₄₉	C₄
socle, prime radical	C₂²×C₁₄₉	C₂²⋊C₄
cosocle	C₄×Dic₁₄₉	C₂²
hypercenter	C₄⋊C₄	#10597010
hypocenter	C₁₄₉	Q₈⋊C₈
LCS	G ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
14. Dic₂₉₈	C₈	semidirect
31. C₁₄₉	Q₈⋊C₈	semidirect