Subgroups — #34059695

Order 19072.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750517	C₂	1	2	yes	maximal, complemented
2	#23749991	C₂	1	1	yes	maximal, characteristic
3	#18011985	—	2	2	no	—
4	#18011908	C₄	1	1	yes	characteristic
5	#18011831	—	2	2	no	—
6	#18011822	C₂²	1	1	yes	characteristic
7	#125×C₁₄₉	C₄	1	1	yes	characteristic
8	#14558739	—	2	4	no	—
9	C₂×D₅₉₆	—	2	1	no	—
10	C₂×D₅₉₆	—	4	1	no	—
11	C₂×#11924746	D₄	1	2	yes	—
12	C₄⋊C₄×C₁₄₉	—	2	1	no	—
13	C₄⋊C₄×C₁₄₉	—	4	1	no	—
14	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×D₁₄₉	—	4	1	no	—
16	D₅₉₆	—	4	2	no	—
17	D₅₉₆	—	8	2	no	—
18	#11924746	—	2	2	no	—
19	C₂×C₄×C₁₄₉	—	2	1	no	—
20	C₂×C₄×C₁₄₉	—	4	1	no	—
21	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂²×C₁₄₉	#100	1	1	yes	characteristic
23	C₂×D₁₄₉	—	8	2	no	—
24	C₂×D₁₄₉	—	8	1	no	—
25	C₄×C₁₄₉	—	4	1	no	—
26	C₄×C₁₄₉	—	8	1	no	—
27	C₄×C₁₄₉	#104	1	2	yes	—
28	C₂×C₁₄₉	—	2	1	no	—
29	C₂×C₁₄₉	#329	1	1	yes	characteristic
30	D₁₄₉	—	16	1	no	—
31	C₁₄₉	#1355	1	1	yes	characteristic, complemented, Sylow
32	#1355	—	149	1	no	maximal, Sylow
33	#490	—	149	1	no	—
34	#347	—	149	2	no	—
35	#127	—	149	1	no	—
36	#125	#10597010	1	1	yes	characteristic
37	M₃₂	—	298	2	no	—
38	#102	—	298	2	no	—
39	#97	—	149	1	no	—
40	C₂×D₄	—	298	1	no	—
41	C₂×D₄	—	596	1	no	—
42	C₂×C₈	—	149	2	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	4	1	no	—
45	C₄²	C₂×#10597010	1	1	yes	characteristic
46	C₁₆	—	298	4	no	—
47	C₂³	—	596	1	no	—
48	D₄	—	596	2	no	—
49	D₄	—	1192	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	4	1	no	—
52	C₂×C₄	C₂²⋊#10597010	1	1	yes	characteristic
53	C₈	—	298	2	no	—
54	C₂²	—	1192	2	no	—
55	C₂²	—	1192	1	no	—
56	C₂²	#18011971	1	1	yes	characteristic
57	C₄	—	4	1	no	—
58	C₄	—	8	1	no	—
59	C₄	#18011976	1	2	yes	—
60	C₂	—	2	1	no	—
61	C₂	—	2384	1	no	—
62	C₂	#23750481	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23750481
commutator	C₄²×C₁₄₉	C₂×C₄
Frattini	C₄²	C₂×#10597010
Fitting	#125×C₁₄₉	C₄
socle	C₂×C₁₄₉	#329
prime radical	#18011908	C₄
cosocle	#18011822	C₂²
hypercenter	#125	#10597010
hypocenter	C₁₄₉	#1355
LCS	G ▷ C₄²×C₁₄₉ ▷ C₂×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #23750517	C₂	semidirect
31. C₁₄₉	#1355	semidirect

Maximal subgroups

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

subgroup	index
#23750517	2
#23749991	2
#1355	149