Subgroups — #34061115

Order 19072.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750558	C₂	1	2	yes	maximal, complemented
2	#23750557	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₄₉⋊C₃₂	C₂	1	2	yes	maximal, complemented
4	C₂×#18011961	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750043	C₂	1	1	yes	maximal, characteristic
6	#18011961	C₂²	1	1	yes	characteristic
7	#18011961	C₂²	1	1	yes	characteristic
8	#18011961	C₂²	1	2	yes	—
9	#18011917	C₄	1	1	yes	characteristic
10	#18011850	C₄	1	2	yes	—
11	C₂×#14558711	C₂²	1	1	yes	characteristic
12	C₁₆×D₁₄₉	C₂²	1	2	yes	—
13	M₃₂×C₁₄₉	C₄	1	1	yes	characteristic
14	#14558736	C₈	1	1	yes	characteristic
15	#14558720	C₈	1	1	yes	characteristic
16	#14558719	C₈	1	2	yes	—
17	C₈×D₁₄₉	C₂×C₄	1	2	yes	—
18	#14558711	C₂×C₄	1	1	yes	characteristic
19	#14558711	C₂³	1	1	yes	characteristic
20	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
21	C₁₆×C₁₄₉	C₂×C₄	1	2	yes	—
22	Dic₂₉₈	C₁₆	1	1	yes	characteristic
23	D₅₉₆	C₁₆	1	1	yes	characteristic
24	C₂²⋊D₁₄₉	C₁₆	1	2	yes	—
25	C₄×D₁₄₉	C₂×C₈	1	2	yes	—
26	#11924746	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
28	C₈×C₁₄₉	C₂×C₈	1	1	yes	characteristic
29	C₈×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₁₄₉	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₁₄₉	C₂×C₁₆	1	2	yes	—
32	C₄×C₁₄₉	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
34	Dic₁₄₉	C₂×C₁₆	1	2	yes	—
35	C₂×C₁₄₉	—	2	1	no	—
36	C₂×C₁₄₉	C₂²×C₁₆	1	1	yes	characteristic
37	D₁₄₉	—	2	2	no	—
38	C₁₄₉	#2258	1	1	yes	characteristic, complemented, Sylow
39	#2258	—	149	1	no	maximal, Sylow
40	#504	—	149	1	no	—
41	M₆₄	—	149	1	no	—
42	M₆₄	—	149	2	no	—
43	C₂×C₃₂	—	149	1	no	—
44	C₂×C₃₂	—	149	2	no	—
45	#131	—	149	1	no	—
46	M₃₂	—	149	2	no	—
47	M₃₂	#10597010	1	1	yes	characteristic
48	C₂×C₁₆	—	149	1	no	—
49	C₂×C₁₆	—	149	2	no	—
50	C₃₂	—	149	1	no	—
51	C₃₂	—	149	1	no	—
52	C₃₂	—	149	2	no	—
53	#41	—	149	1	no	—
54	M₁₆	—	149	1	no	—
55	M₁₆	—	149	2	no	—
56	C₂×C₈	—	149	2	no	—
57	C₂×C₈	C₂×#10597010	1	1	yes	characteristic
58	C₁₆	—	149	1	no	—
59	C₁₆	—	149	1	no	—
60	C₁₆	C₂×#10597010	1	2	yes	—
61	Q₈	—	149	1	no	—
62	D₄	—	149	2	no	—
63	D₄	—	149	1	no	—
64	C₂×C₄	—	149	2	no	—
65	C₂×C₄	D₁₄₉⋊C₈	1	1	yes	characteristic
66	C₈	—	149	2	no	—
67	C₈	D₁₄₉⋊C₈	1	1	yes	characteristic
68	C₈	C₂²×#10597010	1	1	yes	characteristic
69	C₂²	—	149	2	no	—
70	C₂²	D₁₄₉⋊C₁₆	1	1	yes	characteristic
71	C₄	—	149	2	no	—
72	C₄	D₁₄₉⋊C₁₆	1	1	yes	characteristic
73	C₄	C₂×D₁₄₉⋊C₈	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	298	2	no	—
76	C₂	C₂×D₁₄₉⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#10597010
commutator, socle	C₂×C₁₄₉	C₂²×C₁₆
Fitting	M₃₂×C₁₄₉	C₄
prime radical	#14558736	C₈
cosocle	#14558711	C₂³
hypercenter	M₃₂	#10597010
hypocenter	C₁₄₉	#2258
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
1. #23750558	C₂	semidirect
2. #23750557	C₂	semidirect
3. D₁₄₉⋊C₃₂	C₂	semidirect
4. C₂×#18011961	C₂	semidirect
38. C₁₄₉	#2258	semidirect

Maximal subgroups

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

subgroup	index
#23750558	2
#23750557	2
D₁₄₉⋊C₃₂	2
C₂×#18011961	2
#23750043	2
#2258	149