Subgroups — C₄×#19151426 #36469831

Order 22784.

366 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151426	C₂	1	2	yes	maximal
2	C₄×#15667946	C₂	1	2	yes	maximal
3	#26018344	C₂	1	2	yes	maximal
4	C₂×C₄×C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#15667946	C₂²	1	4	yes	—
6	C₄×C₄⋊Dic₈₉	—	2	2	no	—
7	#19151426	C₄	1	8	yes	direct product factor
8	#19151361	—	2	2	no	—
9	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
12	C₄×C₁₆×C₈₉	C₄	1	4	yes	complemented
13	C₂×C₄⋊Dic₈₉	—	2	4	no	—
14	C₂×C₄×Dic₈₉	—	4	2	no	—
15	#15667946	—	2	4	no	—
16	#15667946	C₂×C₄	1	8	yes	—
17	#15667919	—	4	2	no	—
18	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
21	C₂×C₁₆×C₈₉	—	2	2	no	—
22	C₂×C₁₆×C₈₉	C₂×C₄	1	4	yes	—
23	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	—
24	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₈₉	Q₈	1	2	yes	—
27	C₂²×Dic₈₉	—	4	4	no	—
28	C₄⋊Dic₈₉	—	2	8	no	—
29	C₄⋊Dic₈₉	—	4	4	no	—
30	C₄×Dic₈₉	—	8	4	no	—
31	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
32	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
33	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₈×C₈₉	—	2	2	no	—
35	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
38	C₂×C₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₈×C₈₉	#41	1	2	yes	—
40	C₄²×C₈₉	C₄⋊C₄	1	2	yes	—
41	C₄²×C₈₉	Q₁₆	1	2	yes	—
42	C₁₆×C₈₉	—	2	2	no	—
43	C₁₆×C₈₉	C₄²	1	4	yes	complemented
44	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
45	C₂×C₄×C₈₉	—	2	2	no	—
46	C₂×C₄×C₈₉	#107	1	2	yes	—
47	C₂×C₄×C₈₉	#107	1	2	yes	—
48	C₂×C₄×C₈₉	SD₃₂	1	4	yes	—
49	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
51	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
52	C₂×C₄×C₈₉	#135	1	2	yes	—
53	C₂×Dic₈₉	—	4	8	no	—
54	C₂×Dic₈₉	—	8	4	no	—
55	C₂×Dic₈₉	—	8	4	no	—
56	C₈×C₈₉	—	2	2	no	—
57	C₈×C₈₉	C₂×C₄²	1	1	yes	characteristic
58	C₈×C₈₉	#117	1	1	yes	characteristic
59	C₈×C₈₉	C₄×Q₈	1	2	yes	—
60	C₂²×C₈₉	C₂×#107	1	1	yes	characteristic
61	C₂²×C₈₉	C₄×D₈	1	2	yes	—
62	C₂²×C₈₉	C₂×SD₃₂	1	2	yes	—
63	C₂²×C₈₉	#508	1	2	yes	—
64	C₄×C₈₉	—	2	2	no	—
65	C₄×C₈₉	#367	1	4	yes	complemented
66	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
67	C₄×C₈₉	#427	1	1	yes	characteristic
68	C₄×C₈₉	C₄×Q₁₆	1	2	yes	—
69	Dic₈₉	—	8	8	no	—
70	C₄×#367	—	89	1	no	maximal, Sylow
71	C₂×C₈₉	C₄×#107	1	1	yes	characteristic
72	C₂×C₈₉	C₂×#367	1	1	yes	characteristic
73	C₂×C₈₉	#2158	1	1	yes	characteristic
74	C₂×C₈₉	C₄×SD₃₂	1	4	yes	—
75	C₂×#367	—	89	2	no	—
76	C₂×C₄×C₁₆	D₈₉	1	1	yes	characteristic
77	C₄×#107	—	89	2	no	—
78	#1380	—	89	2	no	—
79	C₈₉	C₄×#367	1	1	yes	characteristic, complemented, Sylow
80	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
81	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
82	C₂×#107	—	89	4	no	—
83	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
84	C₄×C₄⋊C₄	—	178	2	no	—
85	#367	—	89	8	no	—
86	C₄×C₁₆	Dic₈₉	1	4	yes	complemented
87	#340	—	178	2	no	—
88	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
89	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
90	C₂×C₄⋊C₄	—	178	4	no	—
91	C₂×C₄²	—	356	2	no	—
92	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
93	C₂×C₁₆	—	2	2	no	—
94	C₂×C₁₆	C₄×D₈₉	1	4	yes	—
95	C₂×C₁₆	C₂×Dic₈₉	1	2	yes	—
96	C₂×C₁₆	C₂×Dic₈₉	1	2	yes	—
97	#107	—	89	8	no	—
98	#107	—	178	4	no	—
99	C₄×C₈	Dic₁₇₈	1	2	yes	—
100	C₄×C₈	C₂×Dic₈₉	1	2	yes	—
101	#95	—	356	2	no	—
102	C₂²×C₄	—	356	4	no	—
103	C₂²×C₄	D₇₁₂	1	1	yes	characteristic
104	C₂²×C₄	D₇₁₂	1	1	yes	characteristic
105	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
106	C₂×C₈	—	2	2	no	—
107	C₂×C₈	C₄⋊Dic₈₉	1	2	yes	—
108	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
109	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
110	C₂×C₈	C₂×Dic₁₇₈	1	1	yes	characteristic
111	C₂×C₈	#13083574	1	2	yes	—
112	C₄⋊C₄	—	356	4	no	—
113	C₄⋊C₄	—	178	8	no	—
114	C₄²	—	712	4	no	—
115	C₄²	C₄⋊Dic₈₉	1	2	yes	—
116	C₄²	Dic₃₅₆	1	2	yes	—
117	C₁₆	—	2	2	no	—
118	C₁₆	C₄×Dic₈₉	1	4	yes	complemented
119	C₂³	C₂×D₇₁₂	1	1	yes	characteristic
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	356	8	no	—
122	C₂×C₄	—	712	4	no	—
123	C₂×C₄	—	712	4	no	—
124	C₂×C₄	#15667946	1	2	yes	—
125	C₂×C₄	#15667946	1	2	yes	—
126	C₂×C₄	#15667957	1	4	yes	—
127	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
128	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
129	C₂×C₄	C₂×Dic₃₅₆	1	1	yes	characteristic
130	C₂×C₄	#15668034	1	2	yes	—
131	C₈	—	2	2	no	—
132	C₈	C₂×C₄×Dic₈₉	1	1	yes	characteristic
133	C₈	#15667971	1	1	yes	characteristic
134	C₈	C₄×Dic₁₇₈	1	2	yes	—
135	C₂²	C₂×#15667946	1	1	yes	characteristic
136	C₂²	C₄×D₇₁₂	1	2	yes	—
137	C₂²	C₂×#15667957	1	2	yes	—
138	C₂²	#19152030	1	2	yes	—
139	C₄	—	2	2	no	—
140	C₄	—	712	8	no	—
141	C₄	#19151426	1	4	yes	direct product factor
142	C₄	C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
143	C₄	#19151636	1	1	yes	characteristic
144	C₄	C₄×Dic₃₅₆	1	2	yes	—
145	C₂	C₄×#15667946	1	1	yes	characteristic
146	C₂	C₂×#19151426	1	1	yes	characteristic
147	C₂	#26022036	1	1	yes	characteristic
148	C₂	C₄×#15667957	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	D₇₁₂
commutator	C₈×C₈₉	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₂×C₄×C₁₆×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂×D₈
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×C₄×C₁₆	D₈₉
hypocenter	C₈₉	C₄×#367
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
7. #19151426	C₄	direct (N × H)
12. C₄×C₁₆×C₈₉	C₄	semidirect
43. C₁₆×C₈₉	C₄²	semidirect
65. C₄×C₈₉	#367	semidirect
79. C₈₉	C₄×#367	semidirect
86. C₄×C₁₆	Dic₈₉	semidirect
118. C₁₆	C₄×Dic₈₉	semidirect
141. C₄	#19151426	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×#19151426	2
C₄×#15667946	2
#26018344	2
C₂×C₄×C₁₆×C₈₉	2
C₄×#367	89

Subgroups — C4×#19151426 #36469831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19151426 #36469831