Subgroups — #34060912

Order 19072.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18011985	C₂	1	2	yes	maximal
2	#23750517	C₂	1	4	yes	maximal, complemented
3	#23749581	C₂	1	1	yes	maximal, characteristic
4	#18011985	C₄	1	4	yes	complemented
5	#18011985	C₂²	1	4	yes	—
6	C₂×#14558739	C₄	1	4	yes	complemented
7	C₂×#14558720	C₄	1	1	yes	characteristic
8	C₂²×#11924746	C₂²	1	1	yes	characteristic
9	#18011822	C₂²	1	2	yes	—
10	C₄×#11924746	C₄	1	2	yes	—
11	#117×C₁₄₉	C₄	1	1	yes	characteristic
12	#14558739	C₂×C₄	1	8	yes	—
13	#14558720	—	2	2	no	—
14	C₂×#11924746	C₂×C₄	1	2	yes	—
15	C₂×#11924746	C₂×C₄	1	2	yes	—
16	C₂×#11924746	C₂×C₄	1	2	yes	—
17	C₂×#11924746	C₂×C₄	1	1	yes	characteristic
18	C₂×#11924746	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
20	C₄⋊C₄×C₁₄₉	—	2	1	no	—
21	C₂²⋊C₄×C₁₄₉	—	2	1	no	—
22	C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
23	#11924746	—	2	2	no	—
24	#11924746	C₄²	1	1	yes	characteristic
25	#11924746	C₄²	1	1	yes	characteristic
26	#11924746	C₂²×C₄	1	2	yes	—
27	C₂³×C₁₄₉	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₁₄₉	—	2	2	no	—
29	C₂×C₄×C₁₄₉	C₄²	1	2	yes	—
30	C₂×C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₁₄₉	M₁₆	1	2	yes	—
32	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₁₄₉	—	4	1	no	—
34	C₂²×C₁₄₉	#97	1	2	yes	—
35	C₂²×C₁₄₉	C₂×M₁₆	1	1	yes	characteristic
36	C₄×C₁₄₉	—	4	2	no	—
37	C₄×C₁₄₉	#97	1	2	yes	—
38	C₄×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₁₄₉	C₂×M₁₆	1	1	yes	characteristic
40	C₂×C₁₄₉	—	2	1	no	—
41	C₂×C₁₄₉	—	2	2	no	—
42	C₂×C₁₄₉	C₂×#97	1	1	yes	characteristic
43	C₁₄₉	#2110	1	1	yes	characteristic, complemented, Sylow
44	#2110	—	149	1	no	maximal, Sylow
45	C₂×M₃₂	—	149	2	no	—
46	#405	—	149	1	no	—
47	#347	—	149	4	no	—
48	C₂×M₁₆	—	149	1	no	—
49	C₂²×C₈	—	149	1	no	—
50	#117	#10597010	1	1	yes	characteristic
51	M₃₂	—	149	4	no	—
52	M₃₂	—	149	4	no	—
53	C₂×C₁₆	—	149	4	no	—
54	#97	—	149	2	no	—
55	C₄×C₈	—	149	2	no	—
56	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
57	M₁₆	—	298	2	no	—
58	C₂×C₈	—	149	2	no	—
59	C₂×C₈	—	149	2	no	—
60	C₂×C₈	—	149	2	no	—
61	C₂×C₈	—	149	1	no	—
62	C₂×C₈	—	149	1	no	—
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×#10597010	1	2	yes	—
66	C₁₆	—	149	8	no	—
67	C₂³	#14558745	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	C₄×#10597010	1	2	yes	—
70	C₂×C₄	#14558745	1	1	yes	characteristic
71	C₂×C₄	#14558746	1	2	yes	—
72	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
73	C₈	—	298	2	no	—
74	C₈	—	149	1	no	—
75	C₈	—	149	1	no	—
76	C₈	—	149	2	no	—
77	C₂²	—	4	1	no	—
78	C₂²	#18011966	1	2	yes	—
79	C₂²	C₂×#14558745	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	#18011966	1	2	yes	—
82	C₄	C₂×C₄×#10597010	1	1	yes	characteristic
83	C₄	C₂×#14558746	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×#18011966	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₄×#10597010
commutator	C₄×C₁₄₉	C₂×C₄²
Frattini	C₂×C₄	C₂²×#10597010
Fitting	#117×C₁₄₉	C₄
socle	C₂×C₁₄₉	C₂×#97
prime radical	C₂³×C₁₄₉	M₁₆
cosocle	C₂×#11924746	C₂³
hypercenter	#117	#10597010
hypocenter	C₁₄₉	#2110
LCS	G ▷ C₄×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. #23750517	C₂	semidirect
4. #18011985	C₄	semidirect
6. C₂×#14558739	C₄	semidirect
43. C₁₄₉	#2110	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18011985	2
#23750517	2
#23749581	2
#2110	149