Subgroups — #34059653

Order 19072.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×#11924753	C₂	1	1	yes	maximal, characteristic, complemented
3	#23749742	C₂	1	1	yes	maximal, characteristic
4	#18011985	—	2	1	no	—
5	C₄×#11924753	—	2	1	no	—
6	#18011918	—	2	1	no	—
7	#18011847	C₄	1	1	yes	characteristic
8	#18011838	—	2	1	no	—
9	C₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
10	#135×C₁₄₉	C₄	1	1	yes	characteristic
11	C₂×#11924753	—	2	2	no	—
12	#14558739	—	4	1	no	—
13	#14558720	—	2	1	no	—
14	#14558720	—	4	1	no	—
15	C₂×#11924746	—	4	1	no	—
16	C₂×#11924746	D₄	1	1	yes	characteristic
17	C₄×Dic₁₄₉	D₄	1	1	yes	characteristic
18	#41×C₁₄₉	—	2	1	no	—
19	Q₁₆×C₁₄₉	C₈	1	1	yes	characteristic, complemented
20	SD₁₆×C₁₄₉	—	2	1	no	—
21	D₈×C₁₄₉	C₈	1	1	yes	characteristic, complemented
22	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
23	#11924753	—	2	4	no	—
24	C₂×Dic₁₄₉	—	2	1	no	—
25	#11924746	—	4	1	no	—
26	#11924746	D₈	1	1	yes	characteristic
27	#11924746	SD₁₆	1	1	yes	characteristic
28	Q₈×C₁₄₉	—	2	1	no	—
29	D₄×C₁₄₉	—	2	1	no	—
30	D₄×C₁₄₉	—	4	1	no	—
31	C₂×C₄×C₁₄₉	—	4	1	no	—
32	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₈×C₁₄₉	C₂×C₈	1	1	yes	characteristic
34	C₈×C₁₄₉	M₁₆	1	1	yes	characteristic
35	C₂²×C₁₄₉	—	4	1	no	—
36	C₂²×C₁₄₉	#104	1	1	yes	characteristic
37	C₄×C₁₄₉	—	4	1	no	—
38	C₄×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₁₄₉	#102	1	1	yes	characteristic
40	Dic₁₄₉	—	2	2	no	—
41	C₂×C₁₄₉	—	2	1	no	—
42	C₂×C₁₄₉	—	8	1	no	—
43	C₂×C₁₄₉	D₄⋊C₈	1	1	yes	characteristic
44	C₁₄₉	#1335	1	1	yes	characteristic, complemented, Sylow
45	#1335	—	149	1	no	maximal, Sylow
46	#443	—	149	1	no	—
47	#364	—	149	1	no	—
48	C₈²	—	149	1	no	—
49	#135	#10597010	1	1	yes	characteristic
50	#131	—	298	1	no	—
51	M₃₂	—	298	1	no	—
52	#108	—	149	1	no	—
53	#104	—	298	1	no	—
54	C₄×C₈	—	298	1	no	—
55	C₄×C₈	—	149	1	no	—
56	#41	—	2	1	no	—
57	Q₁₆	#11924753	1	1	yes	characteristic, complemented
58	SD₁₆	—	2	1	no	—
59	D₈	#11924753	1	1	yes	characteristic, complemented
60	M₁₆	—	298	1	no	—
61	M₁₆	—	596	1	no	—
62	C₂×C₈	—	298	2	no	—
63	C₂×C₈	—	596	1	no	—
64	C₂×C₈	—	149	1	no	—
65	C₂×C₈	C₂×#10597010	1	1	yes	characteristic
66	C₄²	—	149	1	no	—
67	C₁₆	—	596	1	no	—
68	Q₈	—	2	1	no	—
69	D₄	—	2	1	no	—
70	D₄	—	4	1	no	—
71	C₂×C₄	—	4	1	no	—
72	C₂×C₄	—	298	1	no	—
73	C₂×C₄	C₂²⋊#10597010	1	1	yes	characteristic
74	C₈	—	298	4	no	—
75	C₈	—	596	1	no	—
76	C₈	—	149	1	no	—
77	C₈	—	149	1	no	—
78	C₈	C₂×#11924753	1	1	yes	characteristic
79	C₈	#14558745	1	1	yes	characteristic
80	C₂²	—	4	1	no	—
81	C₂²	#18011975	1	1	yes	characteristic
82	C₄	—	4	1	no	—
83	C₄	—	298	2	no	—
84	C₄	C₂²⋊#11924753	1	1	yes	characteristic
85	C₄	#18011973	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	8	1	no	—
88	C₂	D₄⋊#11924753	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#18011973
commutator	C₈×C₁₄₉	C₂×C₈
Frattini	C₂×C₈	C₂×#10597010
Fitting, prime radical	#135×C₁₄₉	C₄
socle	C₂×C₁₄₉	D₄⋊C₈
cosocle	C₈×Dic₁₄₉	C₂²
hypercenter	#135	#10597010
hypocenter	C₁₄₉	#1335
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #23750547	C₂	semidirect
2. C₈×#11924753	C₂	semidirect
19. Q₁₆×C₁₄₉	C₈	semidirect
21. D₈×C₁₄₉	C₈	semidirect
44. C₁₄₉	#1335	semidirect
57. Q₁₆	#11924753	semidirect
59. D₈	#11924753	semidirect

Maximal subgroups

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

subgroup	index
#23750547	2
C₈×#11924753	2
#23749742	2
#1335	149