Subgroups — #34046576

Order 19072.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750057	C₂	1	1	yes	maximal, characteristic
2	#23749741	C₂	1	2	yes	maximal, complemented
3	#23749431	C₂	1	2	yes	maximal, complemented
4	#23749400	C₂	1	1	yes	maximal, characteristic, complemented
5	#368×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#18011933	C₂²	1	2	yes	—
7	#18011919	—	2	2	no	—
8	Dic₁₁₉₂	C₄	1	1	yes	characteristic, complemented
9	#18011856	C₄	1	2	yes	complemented
10	D₂₃₈₄	C₄	1	1	yes	characteristic, complemented
11	C₂×#14558711	C₂²	1	1	yes	characteristic
12	#18011837	—	2	2	no	—
13	C₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
15	#108×C₁₄₉	C₂²	1	2	yes	—
16	#14558736	—	2	2	no	—
17	Dic₅₉₆	C₂×C₄	1	2	yes	—
18	#14558725	—	2	2	no	—
19	D₁₁₉₂	C₂×C₄	1	2	yes	—
20	#14558719	—	4	2	no	—
21	C₂×#11924746	D₄	1	1	yes	characteristic
22	C₈×D₁₄₉	—	4	2	no	—
23	C₄×Dic₁₄₉	D₄	1	1	yes	characteristic
24	#14558711	—	2	1	no	—
25	M₁₆×C₁₄₉	—	2	2	no	—
26	C₂×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
27	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic
29	Dic₂₉₈	—	2	2	no	—
30	D₅₉₆	—	2	2	no	—
31	C₂²⋊D₁₄₉	—	4	2	no	—
32	C₂×Dic₁₄₉	—	2	1	no	—
33	C₄×D₁₄₉	—	4	2	no	—
34	#11924746	D₈	1	2	yes	—
35	C₂×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
36	C₈×C₁₄₉	—	4	2	no	—
37	C₈×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₁₄₉	#41	1	1	yes	characteristic
39	C₂²×C₁₄₉	#135	1	1	yes	characteristic
40	C₂×D₁₄₉	—	4	2	no	—
41	C₄×C₁₄₉	C₄×D₄	1	1	yes	characteristic
42	C₄×C₁₄₉	C₂×D₈	1	1	yes	characteristic
43	Dic₁₄₉	—	4	1	no	—
44	Dic₁₄₉	—	4	2	no	—
45	C₂×C₁₄₉	—	2	1	no	—
46	C₂×C₁₄₉	C₄×D₈	1	1	yes	characteristic
47	D₁₄₉	—	8	2	no	—
48	C₁₄₉	#2179	1	1	yes	characteristic, complemented, Sylow
49	#2179	—	149	1	no	maximal, Sylow
50	#508	—	149	1	no	—
51	#443	—	149	2	no	—
52	#368	D₁₄₉	1	1	yes	characteristic, complemented
53	#359	—	149	2	no	—
54	#346	—	149	1	no	—
55	#135	—	149	2	no	—
56	#131	—	298	2	no	—
57	Q₃₂	—	149	1	no	—
58	SD₃₂	—	149	2	no	—
59	D₁₆	—	149	1	no	—
60	C₂×C₁₆	—	149	1	no	—
61	C₂×C₁₆	C₂×D₁₄₉	1	1	yes	characteristic
62	#108	C₂×D₁₄₉	1	2	yes	—
63	#104	—	298	2	no	—
64	C₄×C₈	—	149	1	no	—
65	#41	—	298	2	no	—
66	Q₁₆	—	149	2	no	—
67	SD₁₆	—	298	2	no	—
68	D₈	—	149	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	596	2	no	—
71	C₂×C₈	—	596	2	no	—
72	C₂×C₈	—	149	1	no	—
73	C₂×C₈	C₂²×D₁₄₉	1	1	yes	characteristic
74	C₄²	—	149	1	no	—
75	C₁₆	—	298	1	no	—
76	C₁₆	C₄×D₁₄₉	1	1	yes	characteristic
77	C₁₆	C₄×D₁₄₉	1	1	yes	characteristic
78	Q₈	—	298	2	no	—
79	D₄	—	298	2	no	—
80	D₄	—	596	2	no	—
81	C₂×C₄	—	298	1	no	—
82	C₂×C₄	—	596	2	no	—
83	C₂×C₄	D₄×D₁₄₉	1	1	yes	characteristic
84	C₈	—	4	2	no	—
85	C₈	—	149	2	no	—
86	C₈	C₂×C₄×D₁₄₉	1	1	yes	characteristic
87	C₈	#14558737	1	1	yes	characteristic
88	C₂²	—	596	2	no	—
89	C₂²	#18011934	1	1	yes	characteristic
90	C₄	—	596	1	no	—
91	C₄	—	596	2	no	—
92	C₄	#18011873	1	1	yes	characteristic
93	C₄	D₈×D₁₄₉	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	1192	2	no	—
96	C₂	#23749707	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₁₄₉
commutator	C₈×C₁₄₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₄₉
Fitting	#368×C₁₄₉	C₂
socle	C₂×C₁₄₉	C₄×D₈
prime radical	#23750057	C₂
cosocle	C₂×C₈×C₁₄₉	C₂³
hypercenter	#368	D₁₄₉
hypocenter	C₁₄₉	#2179
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #23749741	C₂	semidirect
3. #23749431	C₂	semidirect
4. #23749400	C₂	semidirect
5. #368×C₁₄₉	C₂	semidirect
8. Dic₁₁₉₂	C₄	semidirect
9. #18011856	C₄	semidirect
10. D₂₃₈₄	C₄	semidirect
48. C₁₄₉	#2179	semidirect
52. #368	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750057	2
#23749741	2
#23749431	2
#23749400	2
#368×C₁₄₉	2
#2179	149