Subgroups — C₂×#10588554 #11874942

Order 1152.

636 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63450	C₂	1	2	yes	maximal
2	C₂×C₉×#107	C₂	1	1	yes	maximal, characteristic
3	C₂×#63378	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Dic₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#63366	C₂	1	2	yes	maximal
6	#10588554	C₂	1	8	yes	maximal, direct product factor
7	C₂×#4874	—	3	1	no	maximal
8	C₂²×Dic₁₈	—	2	2	no	—
9	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
12	C₂×Dic₉⋊C₄	—	2	2	no	—
13	C₂×C₄×Dic₉	C₂²	1	1	yes	characteristic
14	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
15	#63450	—	2	4	no	—
16	#63450	C₂²	1	8	yes	—
17	C₉×#107	C₂²	1	4	yes	—
18	#63378	C₂²	1	4	yes	—
19	C₈×Dic₉	C₂²	1	4	yes	—
20	#63366	C₂²	1	8	yes	—
21	C₂×#888	—	3	2	no	—
22	C₂×C₃×#107	D₃	1	1	yes	characteristic
23	C₂×#818	—	3	1	no	—
24	C₂×C₈×Dic₃	—	3	1	no	—
25	C₂×#807	—	3	2	no	—
26	#4874	—	3	8	no	—
27	C₂²×C₄×C₉	—	2	2	no	—
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₉	—	2	2	no	—
30	C₂²×Dic₉	D₄	1	1	yes	characteristic
31	C₂²×Dic₉	D₄	1	1	yes	characteristic
32	C₂×Dic₁₈	—	2	8	no	—
33	C₂×Dic₁₈	—	4	8	no	—
34	C₂×C₈×C₉	Q₈	1	4	yes	complemented
35	C₂×C₈×C₉	C₂³	1	2	yes	—
36	C₉×C₄⋊C₄	—	2	2	no	—
37	C₉×C₄⋊C₄	C₂³	1	4	yes	—
38	C₄⋊Dic₉	—	2	2	no	—
39	C₄⋊Dic₉	C₂³	1	4	yes	—
40	Dic₉⋊C₄	—	2	8	no	—
41	C₄×Dic₉	D₄	1	2	yes	—
42	C₄×Dic₉	C₂³	1	2	yes	—
43	C₂×C₉⋊C₈	Q₈	1	4	yes	complemented
44	C₂×C₉⋊C₈	C₂³	1	2	yes	—
45	C₂×#500	—	9	1	no	Sylow
46	C₂²×Dic₆	—	6	2	no	—
47	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
48	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
49	C₂×C₄⋊Dic₃	—	3	2	no	—
50	C₂×Dic₃⋊C₄	—	6	2	no	—
51	C₂×C₄×Dic₃	—	3	1	no	—
52	C₂²×C₃⋊C₈	—	3	1	no	—
53	#888	—	3	8	no	—
54	#888	—	6	4	no	—
55	C₃×#107	C₂×D₃	1	4	yes	—
56	#818	—	3	4	no	—
57	C₈×Dic₃	—	3	4	no	—
58	#807	—	3	8	no	—
59	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₉	—	2	4	no	—
61	C₂×C₄×C₉	—	4	4	no	—
62	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
64	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
65	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
66	C₂×Dic₉	—	2	4	no	—
67	C₂×Dic₉	—	4	4	no	—
68	C₂×Dic₉	D₈	1	4	yes	—
69	C₂×Dic₉	Q₁₆	1	4	yes	—
70	C₂×Dic₉	C₂×D₄	1	2	yes	—
71	C₂×Dic₉	C₂×D₄	1	2	yes	—
72	Dic₁₈	—	4	16	no	—
73	C₈×C₉	C₂×Q₈	1	4	yes	complemented
74	C₉⋊C₈	C₂×Q₈	1	4	yes	complemented
75	C₂×C₄⋊Q₈	—	9	2	no	—
76	#500	—	9	8	no	—
77	C₂×#107	—	9	1	no	—
78	C₂×#107	—	9	2	no	—
79	C₂×#107	D₉	1	1	yes	characteristic
80	C₂×C₄×C₈	—	9	1	no	—
81	C₂²×C₃×C₄	—	2	2	no	—
82	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
83	C₂²×Dic₃	—	3	1	no	—
84	C₂²×Dic₃	—	3	1	no	—
85	C₂²×Dic₃	—	6	2	no	—
86	C₂×Dic₆	—	6	8	no	—
87	C₂×Dic₆	—	12	8	no	—
88	C₂×C₃×C₈	Dic₆	1	4	yes	—
89	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
90	C₃×C₄⋊C₄	—	2	2	no	—
91	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
92	C₄⋊Dic₃	—	3	4	no	—
93	C₄⋊Dic₃	—	6	2	no	—
94	Dic₃⋊C₄	—	6	8	no	—
95	C₄×Dic₃	—	3	2	no	—
96	C₄×Dic₃	—	3	2	no	—
97	C₂×C₃⋊C₈	—	3	4	no	—
98	C₂×C₃⋊C₈	—	3	2	no	—
99	C₂²×C₉	C₄⋊Q₈	1	2	yes	—
100	C₂²×C₉	C₂×D₈	1	2	yes	—
101	C₂²×C₉	C₂×Q₁₆	1	2	yes	—
102	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
103	C₄×C₉	—	4	4	no	—
104	C₄×C₉	C₄⋊Q₈	1	2	yes	—
105	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
106	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
107	Dic₉	—	4	4	no	—
108	Dic₉	C₂×D₈	1	4	yes	—
109	Dic₉	C₂×Q₁₆	1	4	yes	—
110	C₂²×Q₈	—	18	2	no	—
111	C₂²×C₈	—	9	1	no	—
112	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
113	C₄⋊Q₈	—	9	8	no	—
114	C₄⋊Q₈	—	18	4	no	—
115	C₂×C₄⋊C₄	—	9	2	no	—
116	C₂×C₄⋊C₄	—	18	2	no	—
117	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
118	C₂×C₄²	—	9	1	no	—
119	#107	—	9	4	no	—
120	#107	—	9	8	no	—
121	#107	C₂×D₉	1	4	yes	—
122	C₄×C₈	—	9	4	no	—
123	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
124	C₂×C₃×C₄	—	2	4	no	—
125	C₂×C₃×C₄	—	4	4	no	—
126	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
127	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
129	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
130	C₂×Dic₃	—	3	4	no	—
131	C₂×Dic₃	—	3	4	no	—
132	C₂×Dic₃	—	3	2	no	—
133	C₂×Dic₃	—	3	2	no	—
134	C₂×Dic₃	—	6	4	no	—
135	C₂×Dic₃	—	12	4	no	—
136	Dic₆	—	12	16	no	—
137	C₃×C₈	C₂×Dic₆	1	4	yes	—
138	C₃⋊C₈	—	3	4	no	—
139	C₂×C₉	#500	1	4	yes	complemented
140	C₂×C₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
141	C₂×C₉	C₂²×D₈	1	1	yes	characteristic
142	C₂×C₉	C₂²×Q₁₆	1	1	yes	characteristic
143	C₂×Q₈	—	18	8	no	—
144	C₂×Q₈	—	36	8	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	9	1	no	—
147	C₂²×C₄	—	9	1	no	—
148	C₂²×C₄	—	18	2	no	—
149	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
150	C₂×C₈	—	9	4	no	—
151	C₂×C₈	—	9	2	no	—
152	C₂×C₈	Dic₁₈	1	4	yes	complemented
153	C₂×C₈	C₂²×D₉	1	2	yes	—
154	C₄⋊C₄	—	2	2	no	—
155	C₄⋊C₄	—	9	4	no	—
156	C₄⋊C₄	—	18	8	no	—
157	C₄⋊C₄	—	18	2	no	—
158	C₄⋊C₄	C₂²×D₉	1	4	yes	—
159	C₄²	—	9	2	no	—
160	C₄²	—	9	2	no	—
161	C₂²×C₃	#888	1	2	yes	—
162	C₂²×C₃	D₃×D₈	1	2	yes	—
163	C₂²×C₃	D₃×Q₁₆	1	2	yes	—
164	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
165	C₃×C₄	—	4	4	no	—
166	C₃×C₄	#888	1	2	yes	—
167	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
168	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
169	Dic₃	—	3	4	no	—
170	Dic₃	—	3	4	no	—
171	Dic₃	—	12	4	no	—
172	C₉	C₂×#500	1	1	yes	characteristic, complemented, Sylow
173	C₂³	D₄×D₉	1	1	yes	characteristic
174	Q₈	—	36	16	no	—
175	C₂×C₄	—	2	4	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	—	9	2	no	—
178	C₂×C₄	—	9	2	no	—
179	C₂×C₄	—	9	4	no	—
180	C₂×C₄	—	9	4	no	—
181	C₂×C₄	—	18	4	no	—
182	C₂×C₄	—	36	4	no	—
183	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
184	C₂×C₄	D₄×D₉	1	1	yes	characteristic
185	C₂×C₄	Q₈×D₉	1	2	yes	—
186	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
187	C₈	—	9	4	no	—
188	C₈	C₂×Dic₁₈	1	4	yes	complemented
189	C₂×C₃	#4874	1	4	yes	—
190	C₂×C₃	C₂×#888	1	1	yes	characteristic
191	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
192	C₂×C₃	C₂×D₃×Q₁₆	1	1	yes	characteristic
193	C₂²	#63450	1	2	yes	—
194	C₂²	D₈×D₉	1	2	yes	—
195	C₂²	Q₁₆×D₉	1	2	yes	—
196	C₂²	C₂×D₄×D₉	1	1	yes	characteristic
197	C₄	—	4	4	no	—
198	C₄	—	9	4	no	—
199	C₄	—	9	4	no	—
200	C₄	—	36	4	no	—
201	C₄	#63450	1	2	yes	—
202	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
203	C₄	C₂×Q₈×D₉	1	1	yes	characteristic
204	C₃	C₂×#4874	1	1	yes	characteristic
205	C₂	#10588554	1	4	yes	direct product factor
206	C₂	C₂×#63450	1	1	yes	characteristic
207	C₂	C₂×D₈×D₉	1	1	yes	characteristic
208	C₂	C₂×Q₁₆×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×D₉
commutator, cosocle	C₂×C₄×C₉	C₂⁴
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₉×#107	C₂
socle, prime radical	C₂³×C₃	D₃×D₄
hypercenter	C₂×#107	D₉
hypocenter	C₉	C₂×#500
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

Complements

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

N	H ≅ G/N	type
6. #10588554	C₂	direct (N × H)
34. C₂×C₈×C₉	Q₈	semidirect
43. C₂×C₉⋊C₈	Q₈	semidirect
73. C₈×C₉	C₂×Q₈	semidirect
74. C₉⋊C₈	C₂×Q₈	semidirect
139. C₂×C₉	#500	semidirect
152. C₂×C₈	Dic₁₈	semidirect
172. C₉	C₂×#500	semidirect
188. C₈	C₂×Dic₁₈	semidirect
205. C₂	#10588554	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×#63450	2
C₂×C₉×#107	2
C₂×#63378	2
C₂×C₈×Dic₉	2
C₂×#63366	2
#10588554	2
C₂×#4874	3

Subgroups — C2×#10588554 #11874942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588554 #11874942