Subgroups — #14558497

Order 2368.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596957	C₂	1	1	yes	maximal, characteristic
2	C₂²×#64438	C₂	1	1	yes	maximal, characteristic
3	#11924591	C₂	1	2	yes	maximal, complemented
4	C₄×#64438	C₂	1	2	yes	maximal, complemented
5	#11924492	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
7	#10596957	C₄	1	4	yes	complemented
8	C₂×#64438	C₄	1	4	yes	complemented
9	C₂×#64438	C₂²	1	1	yes	characteristic
10	C₂×#64438	C₂²	1	2	yes	—
11	C₂×#64438	C₂²	1	1	yes	characteristic
12	C₂²⋊C₄×C₃₇	C₄	1	1	yes	characteristic
13	C₂²⋊Dic₃₇	C₄	1	1	yes	characteristic
14	#10596936	C₄	1	2	yes	—
15	C₄×Dic₃₇	C₂²	1	2	yes	—
16	C₂³×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
18	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
19	C₂×Dic₃₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
21	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
22	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
23	#64438	C₂×C₄	1	2	yes	—
24	#64438	C₂×C₄	1	2	yes	—
25	#64438	C₂×C₄	1	4	yes	—
26	C₂²×C₃₇	—	2	2	no	—
27	C₂²×C₃₇	C₄²	1	2	yes	—
28	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₃₇	—	2	2	no	—
30	Dic₃₇	—	2	2	no	—
31	Dic₃₇	C₄²	1	2	yes	—
32	Dic₃₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₃₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₃₇	—	2	2	no	—
35	C₂×C₃₇	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₃₇	#131	1	2	yes	—
37	#405	—	37	1	no	maximal, Sylow
38	C₃₇	#405	1	1	yes	characteristic, complemented, Sylow
39	C₂×M₁₆	—	37	1	no	—
40	C₂²×C₈	—	37	1	no	—
41	#117	—	37	1	no	—
42	#97	—	37	2	no	—
43	C₄×C₈	—	37	2	no	—
44	C₂²×C₄	—	37	1	no	—
45	M₁₆	—	37	4	no	—
46	C₂×C₈	—	37	4	no	—
47	C₂×C₈	—	37	1	no	—
48	C₂×C₈	—	37	2	no	—
49	C₂×C₈	—	37	1	no	—
50	C₄⋊C₄	—	37	2	no	—
51	C₂²⋊C₄	—	37	1	no	—
52	C₂²⋊C₄	#3866	1	1	yes	characteristic
53	C₄²	—	37	2	no	—
54	C₂³	C₂×#3866	1	1	yes	characteristic
55	C₂×C₄	—	37	2	no	—
56	C₂×C₄	—	37	2	no	—
57	C₂×C₄	—	37	1	no	—
58	C₂×C₄	—	37	1	no	—
59	C₂×C₄	—	37	2	no	—
60	C₂×C₄	C₂×#3866	1	2	yes	—
61	C₈	—	37	2	no	—
62	C₈	—	37	2	no	—
63	C₈	—	37	4	no	—
64	C₂²	—	2	2	no	—
65	C₂²	C₄×#3866	1	2	yes	—
66	C₂²	C₂²×#3866	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	37	1	no	—
69	C₄	—	37	1	no	—
70	C₄	—	37	2	no	—
71	C₄	—	74	2	no	—
72	C₂	—	2	2	no	—
73	C₂	C₂×C₄×#3866	1	1	yes	characteristic
74	C₂	#11924623	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#3866
commutator	C₂×C₃₇	C₂×C₄²
Fitting	C₂²⋊C₄×C₃₇	C₄
socle	C₂²×C₃₇	C₂²×C₄
prime radical	C₂³×C₃₇	C₂×C₄
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₂²⋊C₄	#3866
hypocenter	C₃₇	#405
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. #11924591	C₂	semidirect
4. C₄×#64438	C₂	semidirect
7. #10596957	C₄	semidirect
8. C₂×#64438	C₄	semidirect
38. C₃₇	#405	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10596957	2
C₂²×#64438	2
#11924591	2
C₄×#64438	2
#11924492	2
#405	37