Subgroups — #34059632

Order 19072.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750470	C₂	1	2	yes	maximal
2	#23749490	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#11924753	—	2	2	no	—
4	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
5	C₂×C₄×Dic₁₄₉	C₄	1	1	yes	characteristic
6	#18011818	—	2	2	no	—
7	C₂×C₄⋊C₄×C₁₄₉	C₄	1	1	yes	characteristic
8	C₂×#11924753	—	4	2	no	—
9	C₂²×Dic₁₄₉	—	2	1	no	—
10	C₂²×Dic₁₄₉	D₄	1	2	yes	—
11	C₄⋊Dic₁₄₉	—	4	1	no	—
12	C₄×Dic₁₄₉	—	2	1	no	—
13	C₄×Dic₁₄₉	C₈	1	2	yes	complemented
14	C₂²×C₄×C₁₄₉	—	2	1	no	—
15	C₂²×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
16	C₄⋊C₄×C₁₄₉	—	4	1	no	—
17	#11924753	—	8	2	no	—
18	C₂×Dic₁₄₉	—	2	2	no	—
19	C₂×Dic₁₄₉	—	2	2	no	—
20	C₂×Dic₁₄₉	—	4	1	no	—
21	C₂×Dic₁₄₉	—	4	1	no	—
22	C₂×Dic₁₄₉	—	4	2	no	—
23	C₂³×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₄₉	—	2	1	no	—
25	C₂×C₄×C₁₄₉	—	2	1	no	—
26	C₂×C₄×C₁₄₉	—	4	2	no	—
27	C₂×C₄×C₁₄₉	—	4	1	no	—
28	C₂×C₄×C₁₄₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₄₉	M₁₆	1	1	yes	characteristic
30	C₂²×C₁₄₉	—	2	1	no	—
31	C₂²×C₁₄₉	—	2	1	no	—
32	C₂²×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
33	C₂²×C₁₄₉	#99	1	1	yes	characteristic
34	C₂²×C₁₄₉	#101	1	1	yes	characteristic
35	C₄×C₁₄₉	—	2	1	no	—
36	C₄×C₁₄₉	—	2	1	no	—
37	C₄×C₁₄₉	—	8	1	no	—
38	Dic₁₄₉	—	4	2	no	—
39	Dic₁₄₉	—	4	2	no	—
40	C₂×C₁₄₉	—	2	1	no	—
41	C₂×C₁₄₉	—	2	1	no	—
42	C₂×C₁₄₉	#324	1	1	yes	characteristic
43	C₂×C₁₄₉	#354	1	1	yes	characteristic
44	C₂×C₁₄₉	#355	1	1	yes	characteristic
45	C₁₄₉	#1324	1	1	yes	characteristic, complemented, Sylow
46	#1324	—	149	1	no	maximal, Sylow
47	#382	—	149	1	no	—
48	#324	—	149	2	no	—
49	C₂×C₄⋊C₄	—	149	1	no	—
50	C₂×C₄⋊C₄	#10597010	1	1	yes	characteristic
51	C₂×C₄²	—	149	1	no	—
52	C₂²⋊C₈	—	298	2	no	—
53	#95	—	298	2	no	—
54	C₂²×C₄	—	2	1	no	—
55	C₂²×C₄	—	298	1	no	—
56	C₂²×C₄	—	149	2	no	—
57	C₂²×C₄	C₂×#10597010	1	1	yes	characteristic
58	C₂×C₈	—	596	2	no	—
59	C₄⋊C₄	—	4	1	no	—
60	C₄⋊C₄	—	596	1	no	—
61	C₄²	—	298	1	no	—
62	C₄²	—	149	2	no	—
63	C₂³	C₂²⋊#10597010	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	4	2	no	—
67	C₂×C₄	—	4	1	no	—
68	C₂×C₄	—	298	2	no	—
69	C₂×C₄	—	298	2	no	—
70	C₂×C₄	—	596	1	no	—
71	C₂×C₄	—	596	1	no	—
72	C₂×C₄	—	596	2	no	—
73	C₂×C₄	D₁₄₉⋊C₈	1	1	yes	characteristic
74	C₂×C₄	#14558746	1	1	yes	characteristic
75	C₈	—	1192	2	no	—
76	C₂²	—	2	1	no	—
77	C₂²	—	2	1	no	—
78	C₂²	#18011968	1	1	yes	characteristic
79	C₂²	#18011969	1	1	yes	characteristic
80	C₂²	#18011972	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	2	1	no	—
83	C₄	—	8	1	no	—
84	C₄	—	596	2	no	—
85	C₄	—	596	2	no	—
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	#23750471	1	1	yes	characteristic
89	C₂	#23750531	1	1	yes	characteristic
90	C₂	#23750533	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#18011969
commutator	C₂×C₄×C₁₄₉	C₂×C₈
Frattini	C₂²×C₄	C₂×#10597010
Fitting	C₂×C₄⋊C₄×C₁₄₉	C₄
socle	C₂²×C₁₄₉	#99
prime radical	C₂³×C₁₄₉	C₂²⋊C₄
cosocle	C₂×C₄⋊Dic₁₄₉	C₂²
hypercenter	C₂×C₄⋊C₄	#10597010
hypocenter	C₁₄₉	#1324
LCS	G ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
13. C₄×Dic₁₄₉	C₈	semidirect
45. C₁₄₉	#1324	semidirect

Maximal subgroups

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

subgroup	index
#23750470	2
#23749490	2
#1324	149