Subgroups — #37526411

Order 22976.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153341	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₃₅₉)⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₃₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#19153341	—	2	2	no	—
6	#19153341	—	2	2	no	—
7	C₂×Dic₇₁₈	C₄	1	1	yes	characteristic
8	C₂×D₁₄₃₆	C₄	1	1	yes	characteristic
9	C₂×C₂²⋊D₃₅₉	C₄	1	2	yes	—
10	C₂×C₄×D₃₅₉	C₂²	1	2	yes	—
11	C₂×C₃₅₉⋊C₈	—	2	2	no	—
12	C₂×C₃₅₉⋊C₈	C₂²	1	2	yes	—
13	C₂²×C₄×C₃₅₉	C₂²	1	1	yes	characteristic
14	M₁₆×C₃₅₉	—	2	2	no	—
15	C₂×C₈×C₃₅₉	C₂²	1	2	yes	—
16	C₂²×D₃₅₉	C₂×C₄	1	2	yes	—
17	Dic₇₁₈	—	2	2	no	—
18	D₁₄₃₆	—	2	2	no	—
19	C₂²⋊D₃₅₉	—	2	4	no	—
20	C₂×Dic₃₅₉	C₂×C₄	1	2	yes	—
21	C₄×D₃₅₉	—	2	2	no	—
22	C₄×D₃₅₉	—	2	2	no	—
23	C₃₅₉⋊C₈	—	2	2	no	—
24	C₂³×C₃₅₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₅₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄×C₃₅₉	D₄	1	2	yes	—
27	C₂×C₄×C₃₅₉	D₄	1	2	yes	—
28	C₂×C₄×C₃₅₉	C₂³	1	1	yes	characteristic
29	C₈×C₃₅₉	—	2	2	no	—
30	C₂²×C₃₅₉	—	2	2	no	—
31	C₂²×C₃₅₉	C₂²⋊C₄	1	2	yes	—
32	C₂²×C₃₅₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×D₃₅₉	—	2	2	no	—
34	C₂×D₃₅₉	—	2	4	no	—
35	C₄×C₃₅₉	C₂²⋊C₄	1	2	yes	—
36	C₄×C₃₅₉	C₂×D₄	1	1	yes	characteristic
37	C₄×C₃₅₉	C₂×D₄	1	1	yes	characteristic
38	Dic₃₅₉	—	2	2	no	—
39	C₂×C₃₅₉	—	2	2	no	—
40	C₂×C₃₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₃₅₉	#131	1	2	yes	—
42	D₃₅₉	—	4	2	no	—
43	C₃₅₉	#408	1	1	yes	characteristic, complemented, Sylow
44	#408	—	359	1	no	maximal, Sylow
45	C₂×#41	—	359	1	no	—
46	C₂×M₁₆	D₃₅₉	1	1	yes	characteristic, complemented
47	C₂²×C₈	—	359	1	no	—
48	C₂²⋊C₈	—	359	4	no	—
49	#41	—	718	2	no	—
50	#41	—	718	2	no	—
51	C₂×Q₈	—	359	1	no	—
52	C₂×D₄	—	359	2	no	—
53	C₂×D₄	—	359	1	no	—
54	C₂²×C₄	—	359	2	no	—
55	C₂²×C₄	C₂×D₃₅₉	1	1	yes	characteristic
56	M₁₆	—	2	2	no	—
57	C₂×C₈	—	359	2	no	—
58	C₂×C₈	—	718	2	no	—
59	C₂×C₈	C₂×D₃₅₉	1	2	yes	—
60	C₂³	—	359	2	no	—
61	C₂³	C₄×D₃₅₉	1	1	yes	characteristic
62	Q₈	—	718	2	no	—
63	D₄	—	718	4	no	—
64	D₄	—	718	2	no	—
65	C₂×C₄	—	359	2	no	—
66	C₂×C₄	—	718	2	no	—
67	C₂×C₄	—	718	2	no	—
68	C₂×C₄	C₄×D₃₅₉	1	1	yes	characteristic
69	C₂×C₄	C₂²⋊D₃₅₉	1	2	yes	—
70	C₂×C₄	D₁₄₃₆	1	2	yes	—
71	C₂×C₄	C₂²×D₃₅₉	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₈	—	718	2	no	—
74	C₂²	—	2	2	no	—
75	C₂²	—	718	2	no	—
76	C₂²	—	718	4	no	—
77	C₂²	(C₂×D₃₅₉)⋊C₄	1	2	yes	—
78	C₂²	C₂×C₄×D₃₅₉	1	1	yes	characteristic
79	C₄	—	718	2	no	—
80	C₄	(C₂×D₃₅₉)⋊C₄	1	2	yes	—
81	C₄	C₂×C₂²⋊D₃₅₉	1	1	yes	characteristic
82	C₄	C₂×D₁₄₃₆	1	1	yes	characteristic
83	C₂	—	2	2	no	—
84	C₂	—	1436	2	no	—
85	C₂	C₂×(C₂×D₃₅₉)⋊C₄	1	1	yes	characteristic
86	C₂	#26040023	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₅₉
commutator, socle	C₂²×C₃₅₉	C₂²×C₄
Fitting	C₂×M₁₆×C₃₅₉	C₂
prime radical	C₂×#19153341	C₂
cosocle	C₂×C₄×C₃₅₉	C₂³
hypercenter	C₂×M₁₆	D₃₅₉
hypocenter	C₃₅₉	#408
LCS	G ▷ C₂²×C₃₅₉ ▷ C₃₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃₅₉⋊C₈	C₂	semidirect
3. (C₂×D₃₅₉)⋊C₈	C₂	semidirect
4. C₂×M₁₆×C₃₅₉	C₂	semidirect
43. C₃₅₉	#408	semidirect
46. C₂×M₁₆	D₃₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19153341	2
C₂²×C₃₅₉⋊C₈	2
(C₂×D₃₅₉)⋊C₈	2
C₂×M₁₆×C₃₅₉	2
#408	359