Subgroups — #34059818

Order 19072.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750534	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750532	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750012	C₂	1	1	yes	maximal, characteristic
4	#18011972	—	2	1	no	—
5	#18011970	—	2	1	no	—
6	C₂×#14558724	—	2	1	no	—
7	C₂×#14558721	—	2	1	no	—
8	#18011899	C₂²	1	1	yes	characteristic
9	#18011822	C₄	1	1	yes	characteristic, complemented
10	#127×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	#14558724	—	4	2	no	—
16	#14558721	—	4	2	no	—
17	C₂×#11924746	—	2	1	no	—
18	#14558713	—	4	1	no	—
19	C₂×D₄×C₁₄₉	—	2	1	no	—
20	C₂×D₄×C₁₄₉	—	4	1	no	—
21	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
22	C₂×#10597010	—	8	1	no	—
23	#11924753	—	8	1	no	—
24	C₂²×D₁₄₉	—	2	1	no	—
25	Dic₂₉₈	—	4	1	no	—
26	D₅₉₆	—	4	1	no	—
27	C₂×Dic₁₄₉	—	2	1	no	—
28	#11924746	—	2	2	no	—
29	C₂³×C₁₄₉	—	4	1	no	—
30	D₄×C₁₄₉	—	4	1	no	—
31	D₄×C₁₄₉	—	4	1	no	—
32	D₄×C₁₄₉	—	8	2	no	—
33	C₂×C₄×C₁₄₉	—	2	1	no	—
34	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₁₄₉	—	8	2	no	—
36	C₂²×C₁₄₉	—	8	1	no	—
37	C₂²×C₁₄₉	#99	1	1	yes	characteristic
38	C₂×D₁₄₉	—	4	1	no	—
39	C₂×D₁₄₉	—	8	1	no	—
40	#10597010	—	16	1	no	—
41	C₄×C₁₄₉	—	2	1	no	—
42	C₄×C₁₄₉	—	4	1	no	—
43	Dic₁₄₉	—	4	1	no	—
44	C₂×C₁₄₉	—	2	1	no	—
45	C₂×C₁₄₉	—	16	1	no	—
46	C₂×C₁₄₉	#353	1	1	yes	characteristic
47	D₁₄₉	—	8	1	no	—
48	C₁₄₉	#1406	1	1	yes	characteristic, complemented, Sylow
49	#1406	—	149	1	no	maximal, Sylow
50	#496	—	149	1	no	—
51	#355	—	149	1	no	—
52	#354	—	149	1	no	—
53	C₂×SD₁₆	—	298	1	no	—
54	C₂×D₈	—	298	1	no	—
55	#127	#10597010	1	1	yes	characteristic, complemented
56	#124	—	149	1	no	—
57	#101	—	298	1	no	—
58	#99	—	298	1	no	—
59	#97	—	149	1	no	—
60	C₂×Q₈	—	149	1	no	—
61	C₂×D₄	—	2	1	no	—
62	C₂×D₄	—	4	1	no	—
63	C₂×D₄	—	149	1	no	—
64	SD₁₆	—	596	2	no	—
65	D₈	—	596	2	no	—
66	M₁₆	—	596	1	no	—
67	C₂×C₈	—	298	1	no	—
68	C₂²⋊C₄	—	596	1	no	—
69	C₂²⋊C₄	—	596	1	no	—
70	C₄²	C₂×#10597010	1	1	yes	characteristic
71	C₂³	—	4	1	no	—
72	C₂³	—	298	1	no	—
73	Q₈	—	596	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	4	1	no	—
76	D₄	—	8	2	no	—
77	D₄	—	596	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	298	1	no	—
80	C₂×C₄	—	1192	1	no	—
81	C₂×C₄	C₂²⋊#10597010	1	1	yes	characteristic
82	C₈	—	298	2	no	—
83	C₈	—	1192	1	no	—
84	C₂²	—	8	2	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	596	1	no	—
87	C₂²	—	1192	1	no	—
88	C₂²	#18011969	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	2384	1	no	—
92	C₄	—	596	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	16	1	no	—
95	C₂	—	1192	1	no	—
96	C₂	#23750529	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23750529
commutator	C₄²×C₁₄₉	C₂×C₄
Frattini	C₄²	C₂×#10597010
Fitting	#127×C₁₄₉	C₄
socle	C₂×C₁₄₉	#353
prime radical	#23750012	C₂
cosocle	#18011899	C₂²
hypercenter	#127	#10597010
hypocenter	C₁₄₉	#1406
LCS	G ▷ C₄²×C₁₄₉ ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #23750534	C₂	semidirect
2. #23750532	C₂	semidirect
9. #18011822	C₄	semidirect
10. #127×C₁₄₉	C₄	semidirect
48. C₁₄₉	#1406	semidirect
55. #127	#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
#23750012	2
#1406	149