Subgroups — #34042885

Order 19072.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₉₂	C₂	1	1	yes	maximal, characteristic
2	#23749455	C₂	1	1	yes	maximal, characteristic
3	M₆₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₅₉₆	—	2	1	no	—
5	Dic₁₁₉₂	—	2	1	no	—
6	Dic₁₁₉₂	C₄	1	2	yes	—
7	#18011847	—	2	1	no	—
8	C₂×C₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
9	C₃₂×C₁₄₉	—	2	1	no	—
10	C₂×Dic₂₉₈	—	4	1	no	—
11	Dic₅₉₆	—	2	2	no	—
12	Dic₅₉₆	—	4	1	no	—
13	#14558720	—	4	1	no	—
14	C₂×C₈×C₁₄₉	D₄	1	1	yes	characteristic
15	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₄₉	D₄	1	1	yes	characteristic
17	Dic₂₉₈	—	4	2	no	—
18	Dic₂₉₈	—	8	1	no	—
19	C₂×Dic₁₄₉	—	8	1	no	—
20	#11924746	—	8	1	no	—
21	C₂×C₄×C₁₄₉	D₈	1	1	yes	characteristic
22	C₈×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₄₉	SD₁₆	1	1	yes	characteristic
24	C₂²×C₁₄₉	SD₃₂	1	1	yes	characteristic
25	C₄×C₁₄₉	#102	1	1	yes	characteristic
26	C₄×C₁₄₉	D₁₆	1	1	yes	characteristic
27	Dic₁₄₉	—	8	2	no	—
28	C₂×C₁₄₉	—	2	1	no	—
29	C₂×C₁₄₉	#357	1	1	yes	characteristic
30	C₁₄₉	#1420	1	1	yes	characteristic, complemented, Sylow
31	#1420	—	149	1	no	maximal, Sylow
32	C₂×Q₃₂	—	149	1	no	—
33	M₆₄	D₁₄₉	1	1	yes	characteristic
34	#368	—	149	1	no	—
35	C₂×Q₁₆	—	298	1	no	—
36	Q₃₂	—	298	1	no	—
37	Q₃₂	—	149	2	no	—
38	C₂×C₁₆	C₂×D₁₄₉	1	1	yes	characteristic
39	#108	—	298	1	no	—
40	C₃₂	—	2	1	no	—
41	C₂×Q₈	—	596	1	no	—
42	Q₁₆	—	298	2	no	—
43	Q₁₆	—	596	1	no	—
44	M₁₆	—	596	1	no	—
45	C₂×C₈	D₅₉₆	1	1	yes	characteristic
46	C₁₆	C₄×D₁₄₉	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₁₄₉	1	1	yes	characteristic
48	Q₈	—	596	2	no	—
49	Q₈	—	1192	1	no	—
50	C₂×C₄	—	1192	1	no	—
51	C₂×C₄	D₁₁₉₂	1	1	yes	characteristic
52	C₈	—	1192	1	no	—
53	C₈	#14558713	1	1	yes	characteristic
54	C₈	#14558725	1	1	yes	characteristic
55	C₂²	#18011856	1	1	yes	characteristic
56	C₄	—	1192	2	no	—
57	C₄	#18011833	1	1	yes	characteristic
58	C₄	D₂₃₈₄	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#23749427	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23749427
commutator	C₁₆×C₁₄₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₄₉
Fitting	M₆₄×C₁₄₉	C₂
socle	C₂×C₁₄₉	#357
prime radical	C₂²×C₁₄₉	SD₃₂
cosocle	C₂×C₁₆×C₁₄₉	C₂²
hypercenter	M₆₄	D₁₄₉
hypocenter	C₁₄₉	#1420
LCS	G ▷ C₁₆×C₁₄₉ ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
30. C₁₄₉	#1420	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₉₂	2
#23749455	2
M₆₄×C₁₄₉	2
#1420	149