Subgroups — #17992900

Order 4736.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10596929	C₂	1	1	yes	maximal, characteristic
2	C₄×#10596929	C₂	1	2	yes	maximal
3	#14557255	C₂	1	2	yes	maximal, complemented
4	C₈×#64436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₇×#322	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10596929	C₄	1	2	yes	—
7	C₂×#10596929	C₄	1	4	yes	—
8	C₄²×D₃₇	C₂²	1	1	yes	characteristic
9	#11924446	C₄	1	2	yes	—
10	#11924446	C₄	1	4	yes	—
11	C₄×#64436	C₂²	1	2	yes	—
12	C₄×#64436	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₃₇	C₂²	1	2	yes	—
15	C₂×C₄×D₃₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₃₇	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
19	C₄²×C₃₇	C₂³	1	1	yes	characteristic
20	C₄×Dic₃₇	C₂×C₄	1	2	yes	—
21	C₄×Dic₃₇	C₂×C₄	1	1	yes	characteristic
22	C₂×#64436	C₂×C₄	1	2	yes	—
23	C₂×#64436	C₂×C₄	1	4	yes	—
24	#10596929	—	2	4	no	—
25	#10596929	—	2	8	no	—
26	C₂²×D₃₇	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
28	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×Dic₃₇	C₄²	1	1	yes	characteristic
30	C₂×Dic₃₇	C₄²	1	2	yes	—
31	C₄×D₃₇	—	2	4	no	—
32	C₄×D₃₇	—	2	2	no	—
33	C₈×C₃₇	—	2	4	no	—
34	C₈×C₃₇	M₁₆	1	4	yes	complemented
35	#64436	—	2	2	no	—
36	#64436	M₁₆	1	8	yes	complemented
37	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
38	C₂×D₃₇	—	2	1	no	—
39	C₂×D₃₇	—	2	2	no	—
40	C₄×C₃₇	C₂×M₁₆	1	4	yes	—
41	C₄×C₃₇	C₂×M₁₆	1	2	yes	—
42	Dic₃₇	—	2	1	no	—
43	Dic₃₇	—	2	2	no	—
44	#1455	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	C₄×M₁₆	1	1	yes	characteristic
46	C₂×C₃₇	C₄×M₁₆	1	2	yes	—
47	D₃₇	—	4	1	no	—
48	C₄×M₁₆	—	37	2	no	—
49	C₄×M₁₆	—	37	1	no	—
50	#322	—	37	2	no	—
51	#322	D₃₇	1	1	yes	characteristic, complemented
52	C₈²	—	37	1	no	—
53	C₃₇	#1455	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	37	4	no	—
55	C₂×M₁₆	—	37	2	no	—
56	C₂×C₄²	—	37	1	no	—
57	#97	—	37	4	no	—
58	#97	—	37	2	no	—
59	C₄×C₈	—	37	2	no	—
60	C₄×C₈	—	37	1	no	—
61	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
62	C₄×C₈	C₂×D₃₇	1	2	yes	—
63	C₂²×C₄	—	37	2	no	—
64	C₂²×C₄	—	37	1	no	—
65	M₁₆	—	74	8	no	—
66	M₁₆	—	74	4	no	—
67	C₂×C₈	—	37	4	no	—
68	C₂×C₈	—	37	2	no	—
69	C₂×C₈	C₄×D₃₇	1	4	yes	—
70	C₂×C₈	C₄×D₃₇	1	2	yes	—
71	C₄²	—	37	2	no	—
72	C₄²	—	37	1	no	—
73	C₄²	C₂²×D₃₇	1	1	yes	characteristic
74	C₂³	—	37	1	no	—
75	C₂×C₄	—	37	1	no	—
76	C₂×C₄	—	37	2	no	—
77	C₂×C₄	—	74	4	no	—
78	C₂×C₄	—	74	2	no	—
79	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
80	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
81	C₈	—	2	4	no	—
82	C₈	—	37	8	no	—
83	C₈	—	74	2	no	—
84	C₈	#10596929	1	4	yes	complemented
85	C₂²	—	74	1	no	—
86	C₂²	—	74	2	no	—
87	C₂²	C₄²×D₃₇	1	1	yes	characteristic
88	C₄	—	74	1	no	—
89	C₄	—	74	2	no	—
90	C₄	M₁₆×D₃₇	1	4	yes	—
91	C₄	C₂×#10596929	1	2	yes	—
92	C₂	—	148	1	no	—
93	C₂	C₄×#10596929	1	1	yes	characteristic
94	C₂	#14557485	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₃₇
commutator, socle	C₂²×C₃₇	C₂×C₄²
Fitting	C₃₇×#322	C₂
prime radical	C₂²×D₃₇	C₄²
cosocle	C₄²×C₃₇	C₂³
hypercenter	#322	D₃₇
hypocenter	C₃₇	#1455
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄² ◁ #322

Complements

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

N	H ≅ G/N	type
3. #14557255	C₂	semidirect
4. C₈×#64436	C₂	semidirect
5. C₃₇×#322	C₂	semidirect
34. C₈×C₃₇	M₁₆	semidirect
36. #64436	M₁₆	semidirect
51. #322	D₃₇	semidirect
53. C₃₇	#1455	semidirect
84. C₈	#10596929	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10596929	2
#14557255	2
C₈×#64436	2
C₃₇×#322	2
#1455	37