Subgroups — C₂×#26020000 #36551893

Order 22784.

1310 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15667923	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×Dic₈₉	C₂	1	1	yes	maximal, characteristic
3	#26020000	C₂	1	8	yes	maximal, direct product factor
4	C₂×#19151352	C₂	1	4	yes	maximal
5	C₂²×#97×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂³×#10623494	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₈₉	C₄	1	4	yes	—
8	C₂²×C₄×Dic₈₉	C₂²	1	2	yes	—
9	C₂×#15667923	C₄	1	8	yes	complemented
10	C₂×#15667923	C₂²	1	4	yes	—
11	C₄²×Dic₈₉	C₄	1	4	yes	—
12	C₄²×Dic₈₉	C₂²	1	4	yes	—
13	#19151352	C₂²	1	16	yes	—
14	C₂³×C₈×C₈₉	C₂²	1	2	yes	—
15	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#97×C₈₉	C₄	1	8	yes	complemented
17	C₂×#97×C₈₉	C₂²	1	4	yes	—
18	C₂³×Dic₈₉	C₂×C₄	1	4	yes	—
19	C₂²×#10623494	—	2	8	no	—
20	C₂²×#10623494	C₂×C₄	1	8	yes	—
21	C₂²×#10623494	C₂³	1	4	yes	—
22	C₂×C₄×Dic₈₉	—	2	16	no	—
23	C₂×C₄×Dic₈₉	—	2	8	no	—
24	C₂×C₄×Dic₈₉	C₂×C₄	1	4	yes	—
25	C₂×C₄×Dic₈₉	C₂×C₄	1	16	yes	—
26	C₂×C₄×Dic₈₉	C₂³	1	4	yes	—
27	#15667923	C₂×C₄	1	16	yes	complemented
28	C₂³×C₄×C₈₉	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₈₉	—	2	8	no	—
31	C₂²×C₈×C₈₉	C₂×C₄	1	8	yes	—
32	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
33	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
36	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
37	#97×C₈₉	C₂×C₄	1	16	yes	complemented
38	C₂²×Dic₈₉	—	2	8	no	—
39	C₂²×Dic₈₉	—	2	8	no	—
40	C₂²×Dic₈₉	M₁₆	1	16	yes	—
41	C₂²×Dic₈₉	C₂²×C₄	1	8	yes	—
42	C₂×#10623494	—	2	16	no	—
43	C₂×#10623494	—	2	8	no	—
44	C₂×#10623494	C₂²×C₄	1	8	yes	—
45	C₄×Dic₈₉	—	2	8	no	—
46	C₄×Dic₈₉	—	2	8	no	—
47	C₄×Dic₈₉	—	2	32	no	—
48	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₈₉	—	2	8	no	—
50	C₂²×C₄×C₈₉	C₄²	1	8	yes	—
51	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
52	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
54	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
55	C₂²×C₄×C₈₉	#41	1	8	yes	—
56	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
57	C₂×C₈×C₈₉	—	2	16	no	—
58	C₂×C₈×C₈₉	—	2	8	no	—
59	C₂×C₈×C₈₉	C₂²×C₄	1	8	yes	—
60	C₄²×C₈₉	C₄²	1	8	yes	—
61	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
62	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
63	C₂³×C₈₉	C₂×C₄²	1	2	yes	—
64	C₂³×C₈₉	#117	1	4	yes	—
65	C₂³×C₈₉	C₂×M₁₆	1	8	yes	—
66	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
67	C₂×C₄×C₈₉	—	2	8	no	—
68	C₂×C₄×C₈₉	—	2	16	no	—
69	C₂×C₄×C₈₉	C₂×C₄²	1	8	yes	—
70	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
71	C₂×C₄×C₈₉	#117	1	8	yes	—
72	C₂×C₄×C₈₉	#117	1	4	yes	—
73	C₂×C₄×C₈₉	#117	1	8	yes	—
74	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
75	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
76	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
77	C₂×Dic₈₉	—	2	8	no	—
78	C₂×Dic₈₉	—	2	8	no	—
79	C₂×Dic₈₉	—	2	32	no	—
80	C₂×Dic₈₉	C₂×M₁₆	1	16	yes	—
81	C₈×C₈₉	—	2	8	no	—
82	#10623494	—	2	8	no	—
83	C₂²×C₈₉	#376	1	4	yes	—
84	C₂²×C₈₉	C₄×M₁₆	1	8	yes	—
85	C₂²×C₈₉	#432	1	16	yes	—
86	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
87	C₂²×C₈₉	C₂×#117	1	2	yes	—
88	C₂²×C₈₉	C₂²×M₁₆	1	4	yes	—
89	C₄×C₈₉	—	2	8	no	—
90	C₄×C₈₉	#376	1	4	yes	—
91	C₄×C₈₉	C₂×#117	1	2	yes	—
92	C₄×C₈₉	C₂×#117	1	2	yes	—
93	Dic₈₉	—	2	16	no	—
94	C₂×#1745	—	89	1	no	maximal, Sylow
95	C₂×C₈₉	#1745	1	8	yes	complemented
96	C₂×C₈₉	C₂×#376	1	1	yes	characteristic
97	C₂×C₈₉	C₂×C₄×M₁₆	1	2	yes	—
98	C₂×C₈₉	C₂×#432	1	4	yes	—
99	C₂²×#97	—	89	1	no	—
100	C₂²×#97	D₈₉	1	1	yes	characteristic
101	C₂×C₄³	—	89	1	no	—
102	#1745	—	89	8	no	—
103	C₂×#336	—	89	4	no	—
104	C₈₉	C₂×#1745	1	1	yes	characteristic, complemented, Sylow
105	C₂³×C₈	—	89	2	no	—
106	C₂³×C₈	C₂×D₈₉	1	2	yes	—
107	C₂²×C₄²	—	89	4	no	—
108	C₂²×C₄²	—	89	2	no	—
109	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
110	C₂×#97	—	89	8	no	—
111	C₂×#97	—	89	4	no	—
112	C₂×#97	Dic₈₉	1	8	yes	complemented
113	C₂×#97	C₂×D₈₉	1	4	yes	—
114	C₄³	—	89	4	no	—
115	C₄³	—	89	4	no	—
116	#336	—	89	16	no	—
117	C₂³×C₄	—	89	4	no	—
118	C₂³×C₄	C₄×D₈₉	1	2	yes	—
119	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
120	C₂²×C₈	—	2	8	no	—
121	C₂²×C₈	—	89	8	no	—
122	C₂²×C₈	—	89	4	no	—
123	C₂²×C₈	—	178	8	no	—
124	C₂²×C₈	C₂×Dic₈₉	1	8	yes	—
125	C₂²×C₈	C₂²×D₈₉	1	4	yes	—
126	C₂×C₄²	—	89	16	no	—
127	C₂×C₄²	—	89	4	no	—
128	C₂×C₄²	—	89	4	no	—
129	C₂×C₄²	—	178	16	no	—
130	C₂×C₄²	—	178	8	no	—
131	C₂×C₄²	C₄×D₈₉	1	2	yes	—
132	C₂×C₄²	C₄×D₈₉	1	4	yes	—
133	C₂×C₄²	C₂×Dic₈₉	1	4	yes	—
134	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
135	#97	—	89	16	no	—
136	#97	C₂×Dic₈₉	1	16	yes	complemented
137	C₂⁴	C₂×C₄×D₈₉	1	1	yes	characteristic
138	C₂²×C₄	—	2	8	no	—
139	C₂²×C₄	—	89	16	no	—
140	C₂²×C₄	—	89	8	no	—
141	C₂²×C₄	—	178	8	no	—
142	C₂²×C₄	—	178	8	no	—
143	C₂²×C₄	C₄×Dic₈₉	1	8	yes	—
144	C₂²×C₄	C₂×C₄×D₈₉	1	4	yes	—
145	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
146	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
147	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
148	C₂²×C₄	#13083574	1	8	yes	—
149	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
150	C₂×C₈	—	2	16	no	—
151	C₂×C₈	—	2	8	no	—
152	C₂×C₈	—	89	8	no	—
153	C₂×C₈	—	178	16	no	—
154	C₂×C₈	—	178	8	no	—
155	C₂×C₈	C₂²×Dic₈₉	1	8	yes	—
156	C₄²	—	178	32	no	—
157	C₄²	—	178	8	no	—
158	C₄²	—	178	8	no	—
159	C₄²	C₄×Dic₈₉	1	8	yes	—
160	C₄²	C₂×C₄×D₈₉	1	4	yes	—
161	C₄²	C₂²×Dic₈₉	1	4	yes	—
162	C₂³	C₂×C₄×Dic₈₉	1	2	yes	—
163	C₂³	#15667969	1	4	yes	—
164	C₂³	M₁₆×D₈₉	1	8	yes	—
165	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
166	C₂×C₄	—	2	16	no	—
167	C₂×C₄	—	2	8	no	—
168	C₂×C₄	—	89	16	no	—
169	C₂×C₄	—	178	32	no	—
170	C₂×C₄	—	178	8	no	—
171	C₂×C₄	—	178	8	no	—
172	C₂×C₄	C₂×C₄×Dic₈₉	1	8	yes	—
173	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
174	C₂×C₄	#15667969	1	4	yes	—
175	C₂×C₄	#15667969	1	8	yes	—
176	C₂×C₄	#15667971	1	8	yes	—
177	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
178	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
179	C₂×C₄	C₂×#13083574	1	4	yes	—
180	C₈	—	2	8	no	—
181	C₈	—	178	8	no	—
182	C₂²	#19151444	1	4	yes	—
183	C₂²	M₁₆×Dic₈₉	1	8	yes	—
184	C₂²	#19151653	1	16	yes	—
185	C₂²	C₂²×C₄×Dic₈₉	1	1	yes	characteristic
186	C₂²	C₂×#15667969	1	2	yes	—
187	C₂²	C₂×M₁₆×D₈₉	1	4	yes	—
188	C₄	—	2	8	no	—
189	C₄	—	178	16	no	—
190	C₄	#19151444	1	4	yes	—
191	C₄	C₂×#15667969	1	2	yes	—
192	C₄	C₂×#15667971	1	2	yes	—
193	C₂	#26020000	1	8	yes	direct product factor
194	C₂	C₂×#19151444	1	1	yes	characteristic
195	C₂	C₂×M₁₆×Dic₈₉	1	2	yes	—
196	C₂	C₂×#19151653	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₈₉
commutator	C₂²×C₈₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₂²×#97×C₈₉	C₂
socle, prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂²×#97	D₈₉
hypocenter	C₈₉	C₂×#1745
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
3. #26020000	C₂	direct (N × H)
9. C₂×#15667923	C₄	semidirect
16. C₂×#97×C₈₉	C₄	semidirect
27. #15667923	C₂×C₄	semidirect
37. #97×C₈₉	C₂×C₄	semidirect
95. C₂×C₈₉	#1745	semidirect
104. C₈₉	C₂×#1745	semidirect
112. C₂×#97	Dic₈₉	semidirect
136. #97	C₂×Dic₈₉	semidirect
193. C₂	#26020000	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#15667923	2
C₂×C₄²×Dic₈₉	2
#26020000	2
C₂×#19151352	2
C₂²×#97×C₈₉	2
C₂×#1745	89

Subgroups — C2×#26020000 #36551893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26020000 #36551893