Subgroups — #17994726

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	1	yes	maximal, characteristic
2	#14557399	C₂	1	1	yes	maximal, characteristic
3	#14557295	C₂	1	4	yes	maximal
4	C₃₇×#382	C₂	1	1	yes	maximal, characteristic
5	C₂²×#64436	C₂²	1	2	yes	—
6	C₂×C₄⋊Dic₃₇	C₂²	1	2	yes	—
7	C₄×#64436	C₄	1	4	yes	complemented
8	#11924443	—	2	2	no	—
9	C₂×C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
10	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
11	#95×C₃₇	—	2	2	no	—
12	C₂²×C₄×C₃₇	—	2	2	no	—
13	C₂²×C₄×C₃₇	D₄	1	2	yes	—
14	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
15	C₂²×Dic₃₇	—	2	2	no	—
16	C₄⋊C₄×C₃₇	—	2	4	no	—
17	C₄²×C₃₇	C₂×C₄	1	2	yes	—
18	C₄²×C₃₇	Q₈	1	2	yes	—
19	C₄⋊Dic₃₇	—	2	4	no	—
20	C₂×#64436	—	2	2	no	—
21	C₂×#64436	—	2	2	no	—
22	C₂×#64436	C₂×C₄	1	4	yes	—
23	C₂³×C₃₇	C₂×D₄	1	1	yes	characteristic
24	C₂×C₄×C₃₇	—	2	4	no	—
25	C₂×C₄×C₃₇	—	4	2	no	—
26	C₂×C₄×C₃₇	—	4	4	no	—
27	C₂×C₄×C₃₇	C₄⋊C₄	1	4	yes	—
28	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄×C₃₇	#41	1	2	yes	—
31	C₂×C₄×C₃₇	#41	1	2	yes	—
32	C₂×Dic₃₇	—	4	2	no	—
33	C₂×Dic₃₇	—	4	4	no	—
34	#64436	—	2	4	no	—
35	C₂²×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₃₇	#124	1	1	yes	characteristic
37	C₂²×C₃₇	#124	1	1	yes	characteristic
38	C₂²×C₃₇	#135	1	4	yes	—
39	C₄×C₃₇	—	2	4	no	—
40	C₄×C₃₇	—	8	2	no	—
41	C₄×C₃₇	#117	1	2	yes	—
42	C₄×C₃₇	#125	1	2	yes	—
43	Dic₃₇	—	8	2	no	—
44	#1835	—	37	1	no	maximal, Sylow
45	C₂×C₃₇	#382	1	1	yes	characteristic
46	C₂×C₃₇	#427	1	2	yes	—
47	C₂×C₃₇	#488	1	2	yes	—
48	C₂×C₃₇	#488	1	2	yes	—
49	C₂×C₄×C₈	—	37	1	no	—
50	#382	—	37	1	no	—
51	#382	D₃₇	1	1	yes	characteristic
52	#340	—	37	4	no	—
53	C₃₇	#1835	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	—	37	2	no	—
55	C₂×C₄⋊C₄	—	37	2	no	—
56	C₂×C₄⋊C₄	C₂×D₃₇	1	2	yes	—
57	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
58	C₄×C₈	—	37	4	no	—
59	#95	—	2	2	no	—
60	#95	—	74	2	no	—
61	C₂²×C₄	—	2	2	no	—
62	C₂²×C₄	—	74	2	no	—
63	C₂²×C₄	C₂²⋊D₃₇	1	2	yes	—
64	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
65	C₂×C₈	—	37	4	no	—
66	C₂×C₈	—	74	2	no	—
67	C₂×C₈	—	74	2	no	—
68	C₄⋊C₄	—	2	4	no	—
69	C₄⋊C₄	—	74	4	no	—
70	C₄²	Dic₇₄	1	2	yes	—
71	C₄²	C₄×D₃₇	1	2	yes	—
72	C₂³	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	4	4	no	—
76	C₂×C₄	—	148	2	no	—
77	C₂×C₄	—	148	4	no	—
78	C₂×C₄	#10596936	1	4	yes	—
79	C₂×C₄	C₂×Dic₇₄	1	1	yes	characteristic
80	C₂×C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
81	C₂×C₄	#10596964	1	2	yes	—
82	C₂×C₄	#10596966	1	2	yes	—
83	C₈	—	74	4	no	—
84	C₂²	C₂×#10596936	1	1	yes	characteristic
85	C₂²	#11924523	1	1	yes	characteristic
86	C₂²	#11924525	1	1	yes	characteristic
87	C₂²	#11924556	1	4	yes	—
88	C₄	—	2	4	no	—
89	C₄	—	8	2	no	—
90	C₄	—	296	2	no	—
91	C₄	#11924494	1	2	yes	—
92	C₄	#11924527	1	2	yes	—
93	C₂	#14557398	1	1	yes	characteristic
94	C₂	#14557569	1	2	yes	—
95	C₂	#14557887	1	2	yes	—
96	C₂	#14557890	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₃₇
commutator	C₂×C₄×C₃₇	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₃₇
Fitting	C₃₇×#382	C₂
socle, prime radical	C₂³×C₃₇	C₂×D₄
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#382	D₃₇
hypocenter	C₃₇	#1835
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #382

Complements

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

N	H ≅ G/N	type
7. C₄×#64436	C₄	semidirect
53. C₃₇	#1835	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
#14557399	2
#14557295	2
C₃₇×#382	2
#1835	37