Subgroups — #34061062

Order 19072.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750547	C₂	1	2	yes	maximal, complemented
2	#23750522	C₂	1	2	yes	maximal
3	#23750517	C₂	1	2	yes	maximal, complemented
4	#23749577	C₂	1	1	yes	maximal, characteristic
5	#18011985	C₂²	1	4	yes	—
6	C₂×#14558719	C₄	1	1	yes	characteristic
7	C₂×#14558719	C₂²	1	1	yes	characteristic
8	C₄²×D₁₄₉	C₄	1	1	yes	characteristic
9	#18011822	C₂²	1	1	yes	characteristic
10	C₈×Dic₁₄₉	C₄	1	1	yes	characteristic
11	C₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
12	#97×C₁₄₉	C₄	1	1	yes	characteristic
13	#14558739	—	2	4	no	—
14	C₂×C₄×D₁₄₉	—	2	1	no	—
15	C₂×C₄×D₁₄₉	C₂×C₄	1	1	yes	characteristic
16	#14558719	—	2	2	no	—
17	#14558719	—	2	2	no	—
18	C₂×#11924746	C₂×C₄	1	1	yes	characteristic
19	C₂×#11924746	C₂³	1	1	yes	characteristic
20	C₄×Dic₁₄₉	—	2	1	no	—
21	C₄×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×D₁₄₉	M₁₆	1	1	yes	characteristic
26	C₂×Dic₁₄₉	—	2	1	no	—
27	C₂×Dic₁₄₉	M₁₆	1	1	yes	characteristic
28	C₄×D₁₄₉	—	2	1	no	—
29	C₄×D₁₄₉	—	2	1	no	—
30	C₄×D₁₄₉	—	4	2	no	—
31	#11924746	—	2	1	no	—
32	#11924746	#41	1	2	yes	—
33	C₂×C₄×C₁₄₉	—	2	1	no	—
34	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₁₄₉	—	2	1	no	—
36	C₈×C₁₄₉	M₁₆	1	2	yes	—
37	C₂²×C₁₄₉	C₂×M₁₆	1	1	yes	characteristic
38	C₂×D₁₄₉	—	2	1	no	—
39	C₂×D₁₄₉	—	4	1	no	—
40	C₄×C₁₄₉	—	4	1	no	—
41	C₄×C₁₄₉	#117	1	1	yes	characteristic
42	C₄×C₁₄₉	C₂×M₁₆	1	1	yes	characteristic
43	Dic₁₄₉	—	2	2	no	—
44	Dic₁₄₉	—	2	1	no	—
45	C₂×C₁₄₉	—	2	1	no	—
46	C₂×C₁₄₉	#432	1	1	yes	characteristic
47	D₁₄₉	—	4	1	no	—
48	C₁₄₉	#2165	1	1	yes	characteristic, complemented, Sylow
49	#2165	—	149	1	no	maximal, Sylow
50	C₄×M₁₆	—	149	1	no	—
51	#364	—	149	2	no	—
52	#349	—	149	2	no	—
53	#347	—	149	2	no	—
54	C₂×M₁₆	—	149	1	no	—
55	C₂×M₁₆	—	149	1	no	—
56	C₂×C₄²	—	149	1	no	—
57	M₃₂	—	149	4	no	—
58	#97	—	149	1	no	—
59	#97	#10597010	1	1	yes	characteristic
60	C₄×C₈	—	149	1	no	—
61	C₄×C₈	—	149	1	no	—
62	C₂²×C₄	—	298	1	no	—
63	C₂²×C₄	—	149	1	no	—
64	M₁₆	—	298	2	no	—
65	M₁₆	—	298	2	no	—
66	C₂×C₈	—	149	1	no	—
67	C₂×C₈	—	149	1	no	—
68	C₂×C₈	C₂×#10597010	1	1	yes	characteristic
69	C₂×C₈	C₂×#10597010	1	1	yes	characteristic
70	C₄²	—	298	1	no	—
71	C₄²	—	149	1	no	—
72	C₄²	C₂×#10597010	1	1	yes	characteristic
73	C₁₆	—	298	4	no	—
74	C₂³	—	149	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	298	1	no	—
77	C₂×C₄	—	298	1	no	—
78	C₂×C₄	—	298	1	no	—
79	C₂×C₄	—	596	2	no	—
80	C₂×C₄	—	149	1	no	—
81	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	298	1	no	—
84	C₈	—	149	2	no	—
85	C₈	#14558746	1	2	yes	—
86	C₂²	—	298	1	no	—
87	C₂²	—	596	1	no	—
88	C₂²	D₁₄₉⋊M₁₆	1	1	yes	characteristic
89	C₄	—	4	1	no	—
90	C₄	—	298	2	no	—
91	C₄	—	298	1	no	—
92	C₄	#18011990	1	1	yes	characteristic
93	C₄	C₂×#14558746	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	596	1	no	—
96	C₂	#23750647	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#18011990
commutator	C₂×C₄×C₁₄₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#10597010
Fitting	#97×C₁₄₉	C₄
socle	C₂×C₁₄₉	#432
prime radical	C₂²×D₁₄₉	M₁₆
cosocle	C₂×#11924746	C₂³
hypercenter	#97	#10597010
hypocenter	C₁₄₉	#2165
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. #23750547	C₂	semidirect
3. #23750517	C₂	semidirect
48. C₁₄₉	#2165	semidirect

Maximal subgroups

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

subgroup	index
#23750547	2
#23750522	2
#23750517	2
#23749577	2
#2165	149