Subgroups — #17992899

Order 4736.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10596934	C₂	1	2	yes	maximal
2	#14557255	C₂	1	2	yes	maximal, complemented
3	#14557254	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#64436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×M₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10596934	C₄	1	4	yes	—
7	#11924447	C₄	1	4	yes	—
8	C₄×#64436	C₂²	1	2	yes	—
9	C₄×#64436	C₂²	1	2	yes	—
10	C₂×M₁₆×C₃₇	C₄	1	2	yes	—
11	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
12	#97×C₃₇	C₄	1	2	yes	—
13	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
17	M₁₆×C₃₇	—	2	4	no	—
18	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
20	C₄²×C₃₇	C₂×C₄	1	2	yes	—
21	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₃₇	C₂³	1	1	yes	characteristic
23	#10596934	—	2	8	no	—
24	C₂×#64436	C₂×C₄	1	4	yes	—
25	C₂×#64436	C₂×C₄	1	4	yes	—
26	C₂³×C₃₇	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₃₇	—	2	4	no	—
28	C₂×C₄×C₃₇	—	2	2	no	—
29	C₂×C₄×C₃₇	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₃₇	C₄²	1	2	yes	—
31	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
32	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₃₇	—	2	2	no	—
34	C₈×C₃₇	M₁₆	1	4	yes	complemented
35	#64436	—	2	4	no	—
36	#64436	M₁₆	1	8	yes	complemented
37	C₂²×C₃₇	—	2	2	no	—
38	C₂²×C₃₇	—	2	1	no	—
39	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
40	C₄×C₃₇	—	2	2	no	—
41	C₄×C₃₇	—	2	1	no	—
42	C₄×C₃₇	C₂×M₁₆	1	4	yes	—
43	C₄×C₃₇	C₂×M₁₆	1	2	yes	—
44	#1455	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	—	4	1	no	—
46	C₂×C₃₇	C₄×M₁₆	1	2	yes	—
47	C₂×C₃₇	C₄×M₁₆	1	1	yes	characteristic
48	C₄×M₁₆	—	37	2	no	—
49	C₄×M₁₆	D₃₇	1	1	yes	characteristic
50	#322	—	37	1	no	—
51	#322	—	37	2	no	—
52	C₈²	—	37	1	no	—
53	C₃₇	#1455	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	37	4	no	—
55	C₂×M₁₆	Dic₃₇	1	2	yes	—
56	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
57	#97	—	37	4	no	—
58	#97	Dic₃₇	1	2	yes	—
59	C₄×C₈	—	37	2	no	—
60	C₄×C₈	—	37	2	no	—
61	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
62	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
63	C₂²×C₄	C₄×D₃₇	1	2	yes	—
64	C₂²×C₄	C₂×Dic₃₇	1	1	yes	characteristic
65	M₁₆	—	2	4	no	—
66	M₁₆	—	74	8	no	—
67	C₂×C₈	—	37	4	no	—
68	C₂×C₈	—	37	4	no	—
69	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
70	C₂×C₈	C₂×Dic₃₇	1	2	yes	—
71	C₄²	C₄×D₃₇	1	2	yes	—
72	C₄²	C₂×Dic₃₇	1	1	yes	characteristic
73	C₄²	C₂²×D₃₇	1	1	yes	characteristic
74	C₂³	C₄×Dic₃₇	1	1	yes	characteristic
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	C₄×Dic₃₇	1	1	yes	characteristic
78	C₂×C₄	C₄×Dic₃₇	1	2	yes	—
79	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
80	C₂×C₄	C₂²×Dic₃₇	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	37	8	no	—
83	C₈	—	74	4	no	—
84	C₈	#10596934	1	4	yes	complemented
85	C₂²	—	2	2	no	—
86	C₂²	—	2	1	no	—
87	C₂²	C₂×C₄×Dic₃₇	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	2	1	no	—
90	C₄	M₁₆×D₃₇	1	4	yes	—
91	C₄	C₂×#10596934	1	2	yes	—
92	C₂	—	4	1	no	—
93	C₂	M₁₆×Dic₃₇	1	2	yes	—
94	C₂	C₄×#10596934	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₃₇
commutator, socle	C₂²×C₃₇	C₂×C₄²
Fitting	C₄×M₁₆×C₃₇	C₂
prime radical	C₂³×C₃₇	C₄²
cosocle	C₄²×C₃₇	C₂³
hypercenter	C₄×M₁₆	D₃₇
hypocenter	C₃₇	#1455
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #14557255	C₂	semidirect
3. #14557254	C₂	semidirect
4. C₈×#64436	C₂	semidirect
34. C₈×C₃₇	M₁₆	semidirect
36. #64436	M₁₆	semidirect
53. C₃₇	#1455	semidirect
84. C₈	#10596934	semidirect

Maximal subgroups

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

subgroup	index
C₄×#10596934	2
#14557255	2
#14557254	2
C₈×#64436	2
C₄×M₁₆×C₃₇	2
#1455	37