Subgroups — #34042657

Order 19072.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₁₉₂	C₂	1	1	yes	maximal, characteristic
2	#23749401	C₂	1	1	yes	maximal, characteristic, complemented
3	#334×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₁₉₂	C₄	1	1	yes	characteristic
5	C₄×D₅₉₆	—	2	1	no	—
6	C₂×#14558711	—	2	1	no	—
7	#18011845	C₄	1	1	yes	characteristic
8	#18011833	—	2	1	no	—
9	C₄⋊C₈×C₁₄₉	—	2	1	no	—
10	C₄×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
11	C₂×D₅₉₆	—	2	1	no	—
12	C₂×C₄×D₁₄₉	—	4	1	no	—
13	D₁₁₉₂	—	2	1	no	—
14	D₁₁₉₂	C₈	1	2	yes	complemented
15	C₄⋊Dic₁₄₉	—	2	1	no	—
16	#14558713	—	4	1	no	—
17	#14558711	—	2	2	no	—
18	C₂×C₈×C₁₄₉	—	4	1	no	—
19	C₂×C₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₄₉	D₄	1	1	yes	characteristic
21	C₄²×C₁₄₉	D₄	1	1	yes	characteristic
22	C₂²×D₁₄₉	—	4	1	no	—
23	D₅₉₆	—	2	2	no	—
24	D₅₉₆	—	4	1	no	—
25	C₂×Dic₁₄₉	—	4	1	no	—
26	C₄×D₁₄₉	—	8	2	no	—
27	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₄₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₄₉	SD₁₆	1	1	yes	characteristic
30	C₈×C₁₄₉	—	2	1	no	—
31	C₈×C₁₄₉	—	8	1	no	—
32	C₈×C₁₄₉	C₂×C₈	1	1	yes	characteristic
33	C₈×C₁₄₉	M₁₆	1	1	yes	characteristic
34	C₂²×C₁₄₉	#102	1	1	yes	characteristic
35	C₂×D₁₄₉	—	4	2	no	—
36	C₂×D₁₄₉	—	8	1	no	—
37	C₂×D₁₄₉	—	8	1	no	—
38	C₄×C₁₄₉	—	2	1	no	—
39	C₄×C₁₄₉	—	2	1	no	—
40	C₄×C₁₄₉	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₁₄₉	#104	1	1	yes	characteristic
42	Dic₁₄₉	—	8	1	no	—
43	C₂×C₁₄₉	D₄⋊C₈	1	1	yes	characteristic
44	C₂×C₁₄₉	#360	1	1	yes	characteristic
45	C₂×C₁₄₉	#361	1	1	yes	characteristic
46	D₁₄₉	—	8	2	no	—
47	C₁₄₉	#1333	1	1	yes	characteristic, complemented, Sylow
48	#1333	—	149	1	no	maximal, Sylow
49	C₄×D₈	—	149	1	no	—
50	#346	—	149	1	no	—
51	#334	D₁₄₉	1	1	yes	characteristic, complemented
52	C₂×D₈	—	149	1	no	—
53	C₄×D₄	—	298	1	no	—
54	C₂×C₁₆	—	298	1	no	—
55	#107	—	149	1	no	—
56	C₄⋊C₈	—	2	1	no	—
57	#102	—	298	1	no	—
58	C₄×C₈	C₂×D₁₄₉	1	1	yes	characteristic
59	C₂×D₄	—	298	1	no	—
60	C₂²×C₄	—	596	1	no	—
61	D₈	—	298	1	no	—
62	D₈	—	149	2	no	—
63	C₂×C₈	—	4	1	no	—
64	C₂×C₈	C₄×D₁₄₉	1	1	yes	characteristic
65	C₂×C₈	D₅₉₆	1	1	yes	characteristic
66	C₄⋊C₄	—	298	1	no	—
67	C₂²⋊C₄	—	596	1	no	—
68	C₄²	C₂²⋊D₁₄₉	1	1	yes	characteristic
69	C₁₆	—	298	2	no	—
70	C₂³	—	596	1	no	—
71	D₄	—	298	2	no	—
72	D₄	—	596	1	no	—
73	C₂×C₄	—	596	1	no	—
74	C₂×C₄	—	1192	2	no	—
75	C₂×C₄	#14558713	1	1	yes	characteristic
76	C₂×C₄	#14558721	1	1	yes	characteristic
77	C₂×C₄	#14558723	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	8	1	no	—
80	C₈	C₈×D₁₄₉	1	1	yes	characteristic
81	C₈	#14558719	1	1	yes	characteristic
82	C₂²	—	596	2	no	—
83	C₂²	—	1192	1	no	—
84	C₂²	—	1192	1	no	—
85	C₂²	#18011831	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	1	no	—
88	C₄	—	1192	1	no	—
89	C₄	#18011823	1	1	yes	characteristic
90	C₄	#18011837	1	1	yes	characteristic
91	C₂	—	1192	2	no	—
92	C₂	#23749352	1	1	yes	characteristic
93	C₂	#23749434	1	1	yes	characteristic
94	C₂	#23749437	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#18011831
commutator	C₈×C₁₄₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₄₉
Fitting	#334×C₁₄₉	C₂
socle	C₂²×C₁₄₉	#102
prime radical	C₂×D₁₁₉₂	C₄
cosocle	C₄×C₈×C₁₄₉	C₂²
hypercenter	#334	D₁₄₉
hypocenter	C₁₄₉	#1333
LCS	G ▷ C₈×C₁₄₉ ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

Complements

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

N	H ≅ G/N	type
2. #23749401	C₂	semidirect
3. #334×C₁₄₉	C₂	semidirect
14. D₁₁₉₂	C₈	semidirect
47. C₁₄₉	#1333	semidirect
51. #334	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₁₉₂	2
#23749401	2
#334×C₁₄₉	2
#1333	149