Subgroups — #101×D₃₅₉ #37526421

Order 22976.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₃₅₉	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₃₅₉	C₂	1	2	yes	maximal
3	#26039934	C₂	1	1	yes	maximal, characteristic, complemented
4	#26039933	C₂	1	2	yes	maximal, complemented
5	#101×C₃₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Dic₇₁₈	C₄	1	2	yes	—
7	C₂×Dic₇₁₈	C₂²	1	1	yes	characteristic
8	Q₈×D₃₅₉	—	2	2	no	—
9	Q₈×D₃₅₉	—	2	2	no	—
10	C₂×C₄×D₃₅₉	C₄	1	2	yes	—
11	C₂×C₄×D₃₅₉	C₂²	1	1	yes	characteristic
12	#19153325	C₂²	1	2	yes	—
13	#19153324	—	2	2	no	—
14	C₈×D₃₅₉	—	2	2	no	—
15	C₂×Q₈×C₃₅₉	C₂²	1	1	yes	characteristic
16	M₁₆×C₃₅₉	C₂²	1	2	yes	—
17	C₂²×D₃₅₉	C₂×C₄	1	1	yes	characteristic
18	Dic₇₁₈	—	2	2	no	—
19	Dic₇₁₈	—	2	4	no	—
20	C₂×Dic₃₅₉	C₂×C₄	1	2	yes	—
21	C₂×Dic₃₅₉	C₂×C₄	1	1	yes	characteristic
22	C₄×D₃₅₉	—	2	2	no	—
23	C₄×D₃₅₉	—	2	2	no	—
24	C₄×D₃₅₉	D₄	1	2	yes	—
25	C₄×D₃₅₉	D₄	1	2	yes	—
26	C₃₅₉⋊C₈	—	2	2	no	—
27	Q₈×C₃₅₉	—	2	2	no	—
28	C₂×C₄×C₃₅₉	C₂×C₄	1	2	yes	—
29	C₂×C₄×C₃₅₉	C₂³	1	1	yes	characteristic
30	C₈×C₃₅₉	—	2	2	no	—
31	C₂²×C₃₅₉	C₂²×C₄	1	1	yes	characteristic
32	C₂×D₃₅₉	—	2	2	no	—
33	C₂×D₃₅₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×D₃₅₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₃₅₉	—	2	2	no	—
36	C₄×C₃₅₉	C₂×D₄	1	2	yes	—
37	Dic₃₅₉	—	2	2	no	—
38	Dic₃₅₉	C₂²⋊C₄	1	2	yes	—
39	C₂×C₃₅₉	—	2	1	no	—
40	C₂×C₃₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
41	D₃₅₉	—	2	1	no	—
42	D₃₅₉	#101	1	2	yes	direct product factor
43	C₃₅₉	C₂×#101	1	1	yes	characteristic, complemented, Sylow
44	C₂×#101	—	359	1	no	maximal, Sylow
45	C₂²×Q₈	—	359	1	no	—
46	C₂×M₁₆	—	359	2	no	—
47	#101	—	359	1	no	—
48	#101	—	359	2	no	—
49	#101	D₃₅₉	1	1	yes	characteristic, direct product factor
50	C₂×Q₈	—	359	2	no	—
51	C₂×Q₈	—	359	1	no	—
52	C₂×Q₈	—	718	2	no	—
53	C₂×Q₈	—	718	2	no	—
54	C₂×Q₈	C₂×D₃₅₉	1	1	yes	characteristic
55	C₂²×C₄	—	359	1	no	—
56	C₂²×C₄	—	359	2	no	—
57	M₁₆	—	359	2	no	—
58	M₁₆	—	718	2	no	—
59	M₁₆	C₂×D₃₅₉	1	2	yes	—
60	C₂×C₈	—	718	2	no	—
61	C₂³	—	359	1	no	—
62	Q₈	—	2	2	no	—
63	Q₈	—	718	4	no	—
64	Q₈	—	718	2	no	—
65	C₂×C₄	—	359	1	no	—
66	C₂×C₄	—	359	2	no	—
67	C₂×C₄	—	359	2	no	—
68	C₂×C₄	—	359	2	no	—
69	C₂×C₄	—	718	2	no	—
70	C₂×C₄	—	718	2	no	—
71	C₂×C₄	C₄×D₃₅₉	1	2	yes	—
72	C₂×C₄	C₂²×D₃₅₉	1	1	yes	characteristic
73	C₈	—	2	2	no	—
74	C₈	—	718	2	no	—
75	C₂²	—	359	1	no	—
76	C₂²	—	359	1	no	—
77	C₂²	—	718	2	no	—
78	C₂²	C₂×C₄×D₃₅₉	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	359	2	no	—
81	C₄	—	718	2	no	—
82	C₄	D₄×D₃₅₉	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	359	2	no	—
85	C₂	—	718	1	no	—
86	C₂	C₂²⋊C₄×D₃₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊C₄×D₃₅₉
commutator	C₂²×C₃₅₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₅₉
Fitting	#101×C₃₅₉	C₂
socle	C₂×C₃₅₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₃₅₉	C₂×C₄
cosocle	C₂×C₄×C₃₅₉	C₂³
hypercenter	#101	D₃₅₉
hypocenter	C₃₅₉	C₂×#101
LCS	G ▷ C₂²×C₃₅₉ ▷ C₂×C₃₅₉ ▷ C₃₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
3. #26039934	C₂	semidirect
4. #26039933	C₂	semidirect
5. #101×C₃₅₉	C₂	semidirect
42. D₃₅₉	#101	direct (N × H)
43. C₃₅₉	C₂×#101	semidirect
49. #101	D₃₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₃₅₉	2
M₁₆×D₃₅₉	2
#26039934	2
#26039933	2
#101×C₃₅₉	2
C₂×#101	359

Subgroups — #101×D359 #37526421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #101×D₃₅₉ #37526421