Subgroups — #34042849

Order 19072.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750015	C₂	1	1	yes	maximal, characteristic
2	#23749420	C₂	1	1	yes	maximal, characteristic, complemented
3	#355×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14558723	—	2	1	no	—
5	C₂×#14558721	—	2	1	no	—
6	#18011908	C₄	1	1	yes	characteristic, complemented
7	#18011826	—	2	1	no	—
8	#18011822	C₄	1	1	yes	characteristic, complemented
9	#124×C₁₄₉	C₂²	1	1	yes	characteristic
10	#101×C₁₄₉	—	2	1	no	—
11	C₂×D₅₉₆	—	2	1	no	—
12	C₂×D₅₉₆	—	4	1	no	—
13	#14558723	—	4	2	no	—
14	#14558721	—	4	2	no	—
15	C₂×#11924746	—	2	1	no	—
16	C₂²⋊Dic₁₄₉	—	4	1	no	—
17	C₂×Q₈×C₁₄₉	D₄	1	1	yes	characteristic
18	C₂×D₄×C₁₄₉	D₄	1	1	yes	characteristic
19	M₁₆×C₁₄₉	—	4	1	no	—
20	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
21	C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₁₄₉	—	4	1	no	—
23	D₅₉₆	—	4	1	no	—
24	D₅₉₆	—	4	1	no	—
25	D₅₉₆	—	8	2	no	—
26	C₂×Dic₁₄₉	—	8	1	no	—
27	#11924746	—	2	2	no	—
28	C₂³×C₁₄₉	—	2	1	no	—
29	Q₈×C₁₄₉	—	4	1	no	—
30	D₄×C₁₄₉	—	4	1	no	—
31	C₂×C₄×C₁₄₉	—	2	1	no	—
32	C₂×C₄×C₁₄₉	—	2	1	no	—
33	C₂×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₈×C₁₄₉	—	8	1	no	—
35	C₂²×C₁₄₉	—	4	1	no	—
36	C₂²×C₁₄₉	—	8	1	no	—
37	C₂²×C₁₄₉	#99	1	1	yes	characteristic
38	C₂×D₁₄₉	—	8	2	no	—
39	C₂×D₁₄₉	—	8	1	no	—
40	C₄×C₁₄₉	—	2	1	no	—
41	C₄×C₁₄₉	—	4	1	no	—
42	C₄×C₁₄₉	—	4	1	no	—
43	Dic₁₄₉	—	16	1	no	—
44	C₂×C₁₄₉	—	2	1	no	—
45	C₂×C₁₄₉	—	8	1	no	—
46	C₂×C₁₄₉	#353	1	1	yes	characteristic
47	D₁₄₉	—	16	1	no	—
48	C₁₄₉	#1406	1	1	yes	characteristic, complemented, Sylow
49	#1406	—	149	1	no	maximal, Sylow
50	#496	—	149	1	no	—
51	#355	D₁₄₉	1	1	yes	characteristic, complemented
52	#354	—	149	1	no	—
53	C₂×SD₁₆	—	298	1	no	—
54	C₂×D₈	—	298	1	no	—
55	#127	—	149	1	no	—
56	#124	C₂×D₁₄₉	1	1	yes	characteristic
57	#101	—	2	1	no	—
58	#99	—	298	1	no	—
59	#97	—	149	1	no	—
60	C₂×Q₈	C₂²⋊D₁₄₉	1	1	yes	characteristic
61	C₂×D₄	—	298	1	no	—
62	C₂×D₄	—	596	1	no	—
63	C₂×D₄	D₅₉₆	1	1	yes	characteristic
64	SD₁₆	—	596	2	no	—
65	D₈	—	596	2	no	—
66	M₁₆	—	4	1	no	—
67	C₂×C₈	—	298	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	596	1	no	—
70	C₄²	C₄×D₁₄₉	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	596	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	596	1	no	—
76	D₄	—	596	1	no	—
77	D₄	—	1192	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	1192	1	no	—
81	C₂×C₄	#14558713	1	1	yes	characteristic
82	C₈	—	8	1	no	—
83	C₈	—	298	2	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	1192	2	no	—
87	C₂²	—	1192	1	no	—
88	C₂²	#18011825	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	2384	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	2384	1	no	—
96	C₂	#23749417	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23749417
commutator	C₄²×C₁₄₉	C₂×C₄
Frattini	#124	C₂×D₁₄₉
Fitting	#355×C₁₄₉	C₂
socle	C₂×C₁₄₉	#353
prime radical	#23750015	C₂
cosocle	#124×C₁₄₉	C₂²
hypercenter	#355	D₁₄₉
hypocenter	C₁₄₉	#1406
LCS	G ▷ C₄²×C₁₄₉ ▷ C₂×C₄×C₁₄₉ ▷ C₂²×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
2. #23749420	C₂	semidirect
3. #355×C₁₄₉	C₂	semidirect
6. #18011908	C₄	semidirect
8. #18011822	C₄	semidirect
48. C₁₄₉	#1406	semidirect
51. #355	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750015	2
#23749420	2
#355×C₁₄₉	2
#1406	149