Subgroups — #17994716

Order 4736.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#64436	C₂	1	2	yes	maximal
2	#14557288	C₂	1	4	yes	maximal
3	C₃₇×#376	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64436	C₂²	1	4	yes	—
5	C₄⋊#64436	—	2	4	no	—
6	C₂×C₄²×C₃₇	C₂²	1	2	yes	—
7	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
8	#95×C₃₇	C₄	1	4	yes	—
9	C₂²×C₄×C₃₇	C₂×C₄	1	4	yes	—
10	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
11	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
12	C₄²×C₃₇	—	2	4	no	—
13	C₄²×C₃₇	D₄	1	2	yes	—
14	C₄²×C₃₇	Q₈	1	2	yes	—
15	C₂×#64436	—	2	4	no	—
16	C₂×#64436	—	2	8	no	—
17	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₇	—	2	4	no	—
19	C₂×C₄×C₃₇	—	2	4	no	—
20	C₂×C₄×C₃₇	—	2	8	no	—
21	C₂×C₄×C₃₇	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₃₇	#41	1	4	yes	—
25	#64436	—	4	4	no	—
26	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₃₇	#117	1	2	yes	—
28	C₂²×C₃₇	#131	1	4	yes	—
29	C₄×C₃₇	—	2	4	no	—
30	C₄×C₃₇	—	4	4	no	—
31	C₄×C₃₇	#124	1	2	yes	—
32	C₄×C₃₇	#125	1	2	yes	—
33	#1832	—	37	1	no	maximal, Sylow
34	C₂×C₃₇	#382	1	1	yes	characteristic
35	C₂×C₃₇	#424	1	2	yes	—
36	C₂×C₃₇	#433	1	4	yes	—
37	C₂×C₄⋊C₈	—	37	2	no	—
38	#376	D₃₇	1	1	yes	characteristic
39	#336	—	37	4	no	—
40	C₃₇	#1832	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₈	—	37	4	no	—
42	C₂×C₄²	C₂×D₃₇	1	2	yes	—
43	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
44	C₄⋊C₈	—	74	4	no	—
45	#95	Dic₃₇	1	4	yes	—
46	C₂²×C₄	C₂×Dic₃₇	1	4	yes	—
47	C₂²×C₄	C₂×Dic₃₇	1	2	yes	—
48	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
49	C₂×C₈	—	74	4	no	—
50	C₂×C₈	—	74	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	Dic₇₄	1	2	yes	—
53	C₄²	D₁₄₈	1	2	yes	—
54	C₂³	C₂²×Dic₃₇	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	8	no	—
58	C₂×C₄	C₄⋊Dic₃₇	1	4	yes	—
59	C₂×C₄	C₂×Dic₇₄	1	1	yes	characteristic
60	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
61	C₂×C₄	#10596962	1	4	yes	—
62	C₈	—	148	4	no	—
63	C₂²	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
64	C₂²	#11924495	1	2	yes	—
65	C₂²	#11924543	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	4	4	no	—
68	C₄	#11924524	1	2	yes	—
69	C₄	#11924528	1	2	yes	—
70	C₂	#14557399	1	1	yes	characteristic
71	C₂	#14557560	1	2	yes	—
72	C₂	#14557594	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₇
commutator, socle, prime radical	C₂³×C₃₇	C₂²×C₄
Fitting	C₃₇×#376	C₂
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#376	D₃₇
hypocenter	C₃₇	#1832
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
40. C₃₇	#1832	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#64436	2
#14557288	2
C₃₇×#376	2
#1832	37