Subgroups — #36441407

Order 22784.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26022055	C₂	1	2	yes	maximal
2	C₈₉×#1452	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#13083549	—	2	2	no	—
4	C₂²⋊#13083549	C₄	1	4	yes	—
5	#19151374	—	2	2	no	—
6	#431×C₈₉	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
8	#322×C₈₉	—	2	2	no	—
9	C₂×#13083549	—	2	4	no	—
10	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
11	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
12	C₄⋊C₈×C₈₉	—	2	2	no	—
13	C₂²⋊C₈×C₈₉	C₈	1	4	yes	—
14	C₄×C₈×C₈₉	—	2	2	no	—
15	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₈₉	D₄	1	2	yes	—
17	C₄×C₈×C₈₉	Q₈	1	1	yes	characteristic
18	#13083549	—	4	4	no	—
19	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
20	C₂²×C₄×C₈₉	C₂×C₈	1	2	yes	—
21	C₂×C₈×C₈₉	—	2	4	no	—
22	C₂×C₈×C₈₉	—	4	2	no	—
23	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
24	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
25	C₄²×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₄²×C₈₉	C₄⋊C₄	1	1	yes	characteristic
27	C₄²×C₈₉	M₁₆	1	2	yes	—
28	C₂³×C₈₉	C₄×C₈	1	1	yes	characteristic
29	C₂×C₄×C₈₉	—	2	2	no	—
30	C₂×C₄×C₈₉	—	4	2	no	—
31	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
32	C₂×C₄×C₈₉	#97	1	1	yes	characteristic
33	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
34	C₂×C₄×C₈₉	C₄⋊C₈	1	2	yes	—
35	C₈×C₈₉	—	2	2	no	—
36	C₈×C₈₉	—	2	2	no	—
37	C₈×C₈₉	—	4	4	no	—
38	C₂²×C₈₉	—	2	1	no	—
39	C₂²×C₈₉	—	2	2	no	—
40	C₂²×C₈₉	#336	1	1	yes	characteristic
41	C₄×C₈₉	—	2	1	no	—
42	C₄×C₈₉	—	2	2	no	—
43	C₄×C₈₉	—	2	2	no	—
44	C₄×C₈₉	#344	1	2	yes	—
45	#7197	—	89	1	no	maximal, Sylow
46	C₂×C₈₉	—	4	1	no	—
47	C₂×C₈₉	#1281	1	1	yes	characteristic
48	C₂×C₈₉	#1378	1	2	yes	—
49	#2163	—	89	2	no	—
50	#1452	D₈₉	1	1	yes	characteristic
51	C₈₉	#7197	1	1	yes	characteristic, complemented, Sylow
52	#431	Dic₈₉	1	2	yes	—
53	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
54	C₄⋊C₁₆	—	178	2	no	—
55	C₂²⋊C₁₆	—	89	4	no	—
56	#346	—	178	2	no	—
57	#322	—	2	2	no	—
58	C₂²×C₈	C₄×D₈₉	1	2	yes	—
59	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
60	C₂×C₁₆	—	178	4	no	—
61	C₄⋊C₈	—	2	2	no	—
62	C₂²⋊C₈	#10623494	1	4	yes	—
63	C₄×C₈	—	2	2	no	—
64	C₄×C₈	Dic₁₇₈	1	1	yes	characteristic
65	C₄×C₈	D₃₅₆	1	1	yes	characteristic
66	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
67	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
68	C₂²×C₄	C₂×#10623494	1	2	yes	—
69	C₂×C₈	—	2	4	no	—
70	C₂×C₈	—	4	2	no	—
71	C₂×C₈	#13083551	1	2	yes	—
72	C₂×C₈	#13083553	1	2	yes	—
73	C₄²	C₂²⋊Dic₈₉	1	1	yes	characteristic
74	C₄²	C₄⋊Dic₈₉	1	1	yes	characteristic
75	C₄²	#13083558	1	2	yes	—
76	C₁₆	—	356	4	no	—
77	C₂³	C₄×#10623494	1	1	yes	characteristic
78	C₂×C₄	—	2	2	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	#15667919	1	1	yes	characteristic
81	C₂×C₄	#15667923	1	1	yes	characteristic
82	C₂×C₄	C₂²⋊#10623494	1	2	yes	—
83	C₂×C₄	C₄⋊#10623494	1	2	yes	—
84	C₈	—	2	2	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	4	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	2	1	no	—
89	C₂²	#19151353	1	1	yes	characteristic
90	C₄	—	2	2	no	—
91	C₄	—	2	2	no	—
92	C₄	—	2	1	no	—
93	C₄	#19151369	1	2	yes	—
94	C₂	—	4	1	no	—
95	C₂	#26018097	1	1	yes	characteristic
96	C₂	#26018338	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#15667919
commutator, prime radical	C₂³×C₈₉	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₈₉
Fitting	C₈₉×#1452	C₂
socle	C₂²×C₈₉	#336
cosocle	C₂×C₄×C₈×C₈₉	C₂²
hypercenter	#1452	D₈₉
hypocenter	C₈₉	#7197
LCS	G ▷ C₂³×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1452

Complements

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

N	H ≅ G/N	type
51. C₈₉	#7197	semidirect

Maximal subgroups

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

subgroup	index
#26022055	2
C₈₉×#1452	2
#7197	89