Subgroups — #34059839

Order 19072.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750534	C₂	1	1	yes	maximal, characteristic
2	#23750532	C₂	1	1	yes	maximal, characteristic
3	#23749980	C₂	1	1	yes	maximal, characteristic
4	#18011972	—	2	1	no	—
5	#18011970	—	2	1	no	—
6	#18011903	C₄	1	1	yes	characteristic, complemented
7	#18011899	C₂²	1	1	yes	characteristic
8	#18011836	—	2	1	no	—
9	#18011833	—	2	1	no	—
10	C₄×C₈×C₁₄₉	C₄	1	1	yes	characteristic, complemented
11	#14558745	—	4	1	no	—
12	C₂²⋊#10597010	—	4	1	no	—
13	C₂×Dic₂₉₈	D₄	1	1	yes	characteristic
14	C₂×D₅₉₆	D₄	1	1	yes	characteristic
15	C₄⋊Dic₁₄₉	—	2	1	no	—
16	#14558715	—	4	1	no	—
17	#14558713	—	4	1	no	—
18	C₂×C₈×C₁₄₉	—	2	1	no	—
19	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
20	C₂×#10597010	—	8	1	no	—
21	#11924753	—	8	1	no	—
22	C₂²×D₁₄₉	—	2	1	no	—
23	Dic₂₉₈	—	4	1	no	—
24	D₅₉₆	—	4	1	no	—
25	C₂×Dic₁₄₉	—	2	1	no	—
26	C₂×Dic₁₄₉	—	4	1	no	—
27	C₂×C₄×C₁₄₉	—	2	1	no	—
28	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₈×C₁₄₉	—	4	1	no	—
30	C₂²×C₁₄₉	#99	1	1	yes	characteristic
31	C₂×D₁₄₉	—	4	1	no	—
32	C₂×D₁₄₉	—	8	1	no	—
33	#10597010	—	16	1	no	—
34	C₄×C₁₄₉	—	2	1	no	—
35	C₄×C₁₄₉	—	4	1	no	—
36	Dic₁₄₉	—	4	1	no	—
37	Dic₁₄₉	—	8	1	no	—
38	C₂×C₁₄₉	—	2	1	no	—
39	C₂×C₁₄₉	#354	1	1	yes	characteristic
40	D₁₄₉	—	8	1	no	—
41	C₁₄₉	#1414	1	1	yes	characteristic, complemented, Sylow
42	#1414	—	149	1	no	maximal, Sylow
43	#488	—	149	1	no	—
44	#355	—	149	1	no	—
45	#354	—	149	1	no	—
46	#125	—	149	1	no	—
47	#124	—	149	1	no	—
48	#103	—	298	1	no	—
49	#102	—	298	1	no	—
50	#101	—	298	1	no	—
51	#99	—	298	1	no	—
52	C₄×C₈	#10597010	1	1	yes	characteristic, complemented
53	C₂×Q₈	—	149	1	no	—
54	C₂×D₄	—	149	1	no	—
55	M₁₆	—	596	1	no	—
56	C₂×C₈	—	2	1	no	—
57	C₄⋊C₄	—	298	1	no	—
58	C₄⋊C₄	—	596	1	no	—
59	C₂²⋊C₄	—	596	1	no	—
60	C₂²⋊C₄	—	596	1	no	—
61	C₄²	C₂×#10597010	1	1	yes	characteristic
62	C₂³	—	298	1	no	—
63	Q₈	—	596	1	no	—
64	D₄	—	596	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	298	1	no	—
67	C₂×C₄	—	596	1	no	—
68	C₂×C₄	—	1192	1	no	—
69	C₂×C₄	C₂²⋊#10597010	1	1	yes	characteristic
70	C₈	—	4	1	no	—
71	C₈	—	1192	1	no	—
72	C₂²	—	596	1	no	—
73	C₂²	—	1192	1	no	—
74	C₂²	#18011970	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	2384	1	no	—
78	C₄	—	596	1	no	—
79	C₄	—	1192	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	1192	1	no	—
82	C₂	#23750532	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23750532
commutator	C₄²×C₁₄₉	C₂×C₄
Frattini	C₄²	C₂×#10597010
Fitting	C₄×C₈×C₁₄₉	C₄
socle	C₂×C₁₄₉	#354
prime radical	C₂×D₅₉₆	D₄
cosocle	#18011899	C₂²
hypercenter	C₄×C₈	#10597010
hypocenter	C₁₄₉	#1414
LCS	G ▷ C₄²×C₁₄₉ ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #18011903	C₄	semidirect
10. C₄×C₈×C₁₄₉	C₄	semidirect
41. C₁₄₉	#1414	semidirect
52. C₄×C₈	#10597010	semidirect

Maximal subgroups

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

subgroup	index
#23750534	2
#23750532	2
#23749980	2
#1414	149