Subgroups — #17994767

Order 4736.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924471	C₂	1	4	yes	maximal
2	#14557557	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#64436	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×#10596934	C₂²	1	2	yes	—
6	C₂²×#64436	C₂²	1	2	yes	—
7	#11924471	—	2	8	no	—
8	C₄⋊#64436	—	2	2	no	—
9	C₄×#64436	C₄	1	2	yes	—
10	C₄×#64436	C₄	1	2	yes	—
11	C₂×M₁₆×C₃₇	C₂²	1	2	yes	—
12	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₃₇	—	2	2	no	—
14	C₂²×C₄×C₃₇	Q₈	1	2	yes	—
15	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
16	M₁₆×C₃₇	—	2	4	no	—
17	C₂×C₈×C₃₇	—	2	2	no	—
18	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₃₇	D₄	1	2	yes	—
21	#10596934	—	2	4	no	—
22	C₂×#64436	—	2	2	no	—
23	C₂×#64436	C₂×C₄	1	4	yes	—
24	C₂×#64436	D₄	1	4	yes	—
25	C₂×#64436	Q₈	1	4	yes	—
26	C₂³×C₃₇	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₄×C₃₇	—	2	4	no	—
28	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₃₇	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₃₇	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₃₇	C₂×Q₈	1	2	yes	—
34	C₈×C₃₇	—	4	2	no	—
35	#64436	—	4	2	no	—
36	#64436	C₄⋊C₄	1	8	yes	—
37	C₂²×C₃₇	—	2	2	no	—
38	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₃₇	C₄⋊Q₈	1	2	yes	—
40	C₄×C₃₇	—	2	2	no	—
41	C₄×C₃₇	#108	1	4	yes	complemented
42	C₄×C₃₇	C₂×C₄⋊C₄	1	2	yes	—
43	C₄×C₃₇	#127	1	1	yes	characteristic
44	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
45	#1848	—	37	1	no	maximal, Sylow
46	C₂×C₃₇	—	2	2	no	—
47	C₂×C₃₇	#384	1	1	yes	characteristic
48	C₂×C₃₇	C₂×#108	1	2	yes	—
49	C₂×#108	—	37	4	no	—
50	#423	—	37	1	no	—
51	#423	D₃₇	1	1	yes	characteristic
52	C₂×C₄×C₈	—	37	1	no	—
53	C₃₇	#1848	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	37	2	no	—
55	C₂×M₁₆	C₂×D₃₇	1	2	yes	—
56	C₂²×C₈	—	37	2	no	—
57	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
58	#108	—	74	8	no	—
59	C₄⋊C₈	—	2	2	no	—
60	C₄⋊C₈	—	74	2	no	—
61	C₄×C₈	—	37	2	no	—
62	C₄×C₈	—	37	2	no	—
63	C₂²×C₄	Dic₇₄	1	2	yes	—
64	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
65	M₁₆	—	2	4	no	—
66	M₁₆	—	74	4	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	37	4	no	—
69	C₂×C₈	—	37	4	no	—
70	C₂×C₈	—	37	4	no	—
71	C₂×C₈	—	74	2	no	—
72	C₄²	C₄×D₃₇	1	1	yes	characteristic
73	C₄²	C₄×D₃₇	1	1	yes	characteristic
74	C₄²	C₂²⋊D₃₇	1	2	yes	—
75	C₂³	C₂×Dic₇₄	1	1	yes	characteristic
76	C₂×C₄	—	2	4	no	—
77	C₂×C₄	#10596936	1	2	yes	—
78	C₂×C₄	#10596936	1	2	yes	—
79	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
80	C₂×C₄	D₄×D₃₇	1	2	yes	—
81	C₂×C₄	Q₈×D₃₇	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
83	C₈	—	4	2	no	—
84	C₈	—	37	8	no	—
85	C₈	—	148	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	C₂×#10596936	1	1	yes	characteristic
88	C₂²	#11924535	1	2	yes	—
89	C₄	—	2	2	no	—
90	C₄	#11924471	1	4	yes	complemented
91	C₄	C₄⋊C₄×D₃₇	1	2	yes	—
92	C₄	#11924532	1	1	yes	characteristic
93	C₄	#11924534	1	1	yes	characteristic
94	C₂	—	2	2	no	—
95	C₂	#14557402	1	1	yes	characteristic
96	C₂	C₂×#11924471	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₃₇
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#423	C₂
socle	C₂²×C₃₇	C₂×C₄⋊C₄
prime radical	C₂³×C₃₇	C₂×Q₈
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#423	D₃₇
hypocenter	C₃₇	#1848
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
41. C₄×C₃₇	#108	semidirect
53. C₃₇	#1848	semidirect
90. C₄	#11924471	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924471	2
#14557557	2
C₂×C₄×#64436	2
C₃₇×#423	2
#1848	37