Subgroups — #17995701

Order 4736.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558333	C₂	1	3	yes	maximal, complemented
2	#14557501	C₂	1	3	yes	maximal, complemented
3	C₃₇×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10596962	C₂²	1	3	yes	—
5	#11924569	—	2	6	no	—
6	#11924564	—	2	6	no	—
7	#11924558	—	2	6	no	—
8	C₂²×#64436	C₂²	1	1	yes	characteristic
9	#11924448	—	2	6	no	—
10	C₂×M₁₆×C₃₇	C₂²	1	3	yes	—
11	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
12	C₂×C₂²⋊D₃₇	—	2	3	no	—
13	#10596962	—	2	6	no	—
14	#10596962	—	2	6	no	—
15	C₂×D₁₄₈	D₄	1	3	yes	—
16	C₂×C₄×D₃₇	—	2	3	no	—
17	C₂×Dic₇₄	D₄	1	3	yes	—
18	M₁₆×C₃₇	—	2	6	no	—
19	C₂×C₈×C₃₇	D₄	1	6	yes	—
20	C₂×#64436	—	2	3	no	—
21	Dic₁₄₈	—	2	6	no	—
22	D₂₉₆	—	2	6	no	—
23	#10596930	—	2	12	no	—
24	C₂³×C₃₇	#41	1	1	yes	characteristic
25	C₂²×D₃₇	—	2	3	no	—
26	C₂×C₄×C₃₇	C₂×D₄	1	3	yes	—
27	C₂×C₄×C₃₇	C₂×D₄	1	3	yes	—
28	C₂²⋊D₃₇	—	4	6	no	—
29	C₂×Dic₃₇	—	2	3	no	—
30	D₁₄₈	—	2	6	no	—
31	C₄×D₃₇	—	4	3	no	—
32	C₄×D₃₇	—	4	3	no	—
33	Dic₇₄	—	2	6	no	—
34	C₈×C₃₇	—	2	6	no	—
35	#64436	—	4	1	no	—
36	C₂²×C₃₇	—	4	1	no	—
37	C₂²×C₃₇	#121	1	3	yes	—
38	C₂×D₃₇	—	4	6	no	—
39	C₂×D₃₇	—	4	3	no	—
40	C₄×C₃₇	#120	1	3	yes	—
41	C₄×C₃₇	#127	1	1	yes	characteristic
42	Dic₃₇	—	4	3	no	—
43	#2017	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	2	3	no	—
45	C₂×C₃₇	#392	1	1	yes	characteristic
46	D₃₇	—	8	3	no	—
47	#575	—	37	3	no	—
48	#408	—	37	3	no	—
49	#338	D₃₇	1	1	yes	characteristic, complemented
50	C₃₇	#2017	1	1	yes	characteristic, complemented, Sylow
51	C₂×#41	—	37	3	no	—
52	#137	—	74	6	no	—
53	AGL(1,ℤ/8)	—	74	6	no	—
54	#135	—	74	6	no	—
55	C₂×M₁₆	C₂×D₃₇	1	3	yes	—
56	C₂²×C₈	—	37	1	no	—
57	C₂²⋊C₈	—	74	6	no	—
58	#41	—	74	6	no	—
59	#41	—	74	6	no	—
60	C₂×Q₈	—	37	3	no	—
61	C₂×D₄	—	37	3	no	—
62	C₂×D₄	—	74	3	no	—
63	C₂²×C₄	—	74	3	no	—
64	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
65	Q₁₆	—	74	6	no	—
66	SD₁₆	—	74	12	no	—
67	D₈	—	74	6	no	—
68	M₁₆	—	2	6	no	—
69	C₂×C₈	—	74	3	no	—
70	C₂×C₈	D₁₄₈	1	6	yes	—
71	C₂³	—	74	3	no	—
72	C₂³	#10596966	1	1	yes	characteristic
73	Q₈	—	74	6	no	—
74	D₄	—	74	6	no	—
75	D₄	—	148	6	no	—
76	C₂×C₄	—	74	3	no	—
77	C₂×C₄	—	148	3	no	—
78	C₂×C₄	—	148	3	no	—
79	C₂×C₄	C₂×D₁₄₈	1	3	yes	—
80	C₂×C₄	D₄×D₃₇	1	3	yes	—
81	C₈	—	2	6	no	—
82	C₈	—	148	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	148	6	no	—
85	C₂²	—	148	3	no	—
86	C₂²	#11924511	1	3	yes	—
87	C₄	—	148	3	no	—
88	C₄	#11924506	1	3	yes	—
89	C₄	#11924533	1	1	yes	characteristic
90	C₂	—	2	3	no	—
91	C₂	—	296	3	no	—
92	C₂	#14557443	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924533
commutator, cosocle	C₂²×C₄×C₃₇	C₂³
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#338	C₂
socle	C₂×C₃₇	#392
hypercenter	#338	D₃₇
hypocenter	C₃₇	#2017
LCS	G ▷ C₂²×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #14558333	C₂	semidirect
2. #14557501	C₂	semidirect
3. C₃₇×#338	C₂	semidirect
49. #338	D₃₇	semidirect
50. C₃₇	#2017	semidirect

Maximal subgroups

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

subgroup	index
#14558333	2
#14557501	2
C₃₇×#338	2
#2017	37