Subgroups — C₂×#10588229 #11783232

Order 1152.

768 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₉	C₂	1	2	yes	maximal
3	#10588229	C₂	1	4	yes	maximal, direct product factor
4	C₂×#4551	—	3	1	no	maximal
5	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₂³×Dic₉	—	2	2	no	—
7	C₂²×C₈×C₉	—	2	4	no	—
8	C₂²×C₈×C₉	C₄	1	4	yes	complemented
9	C₂²×C₈×C₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₉	—	2	2	no	—
11	C₂×C₄⋊Dic₉	—	2	4	no	—
12	C₂×C₄⋊Dic₉	C₄	1	8	yes	complemented
13	C₂×C₄⋊Dic₉	C₂²	1	4	yes	—
14	C₂³×C₃×C₈	D₃	1	1	yes	characteristic
15	C₂²×C₄⋊Dic₃	—	3	2	no	—
16	#4551	—	3	4	no	—
17	C₂⁴×C₉	D₄	1	1	yes	characteristic
18	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
20	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₉	D₄	1	4	yes	—
22	C₂²×C₄×C₉	Q₈	1	2	yes	—
23	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₉	—	2	8	no	—
25	C₂²×Dic₉	—	2	4	no	—
26	C₂²×Dic₉	—	4	4	no	—
27	C₂²×Dic₉	—	4	4	no	—
28	C₂×C₈×C₉	—	2	8	no	—
29	C₂×C₈×C₉	—	2	4	no	—
30	C₂×C₈×C₉	C₂×C₄	1	4	yes	complemented
31	C₄⋊Dic₉	—	2	8	no	—
32	C₄⋊Dic₉	—	2	4	no	—
33	C₄⋊Dic₉	C₂×C₄	1	8	yes	complemented
34	C₂×#340	—	9	1	no	Sylow
35	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
36	C₂³×Dic₃	—	6	2	no	—
37	C₂²×C₃×C₈	—	2	4	no	—
38	C₂²×C₃×C₈	Dic₃	1	4	yes	—
39	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
40	C₂×C₄⋊Dic₃	—	3	8	no	—
41	C₂×C₄⋊Dic₃	—	3	4	no	—
42	C₂×C₄⋊Dic₃	—	6	2	no	—
43	C₂×C₄⋊Dic₃	—	6	4	no	—
44	C₂³×C₉	C₂²⋊C₄	1	4	yes	—
45	C₂³×C₉	C₄⋊C₄	1	2	yes	—
46	C₂³×C₉	D₈	1	2	yes	—
47	C₂³×C₉	SD₁₆	1	4	yes	—
48	C₂³×C₉	Q₁₆	1	2	yes	—
49	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄×C₉	C₄²	1	4	yes	—
51	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
52	C₂×C₄×C₉	C₂²⋊C₄	1	4	yes	—
53	C₂×C₄×C₉	C₄⋊C₄	1	8	yes	—
54	C₂×C₄×C₉	C₄⋊C₄	1	2	yes	—
55	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
56	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
58	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
59	C₂×Dic₉	—	2	8	no	—
60	C₂×Dic₉	—	4	16	no	—
61	C₂×Dic₉	—	4	4	no	—
62	C₂×Dic₉	—	4	4	no	—
63	C₈×C₉	—	2	4	no	—
64	C₂³×C₈	D₉	1	1	yes	characteristic
65	C₂²×C₄⋊C₄	—	9	2	no	—
66	#340	—	9	4	no	—
67	C₂⁴×C₃	D₁₂	1	1	yes	characteristic
68	C₂²×C₃×C₄	Dic₆	1	2	yes	—
69	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
70	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
71	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
72	C₂²×C₃×C₄	#67	1	4	yes	—
73	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
74	C₂²×Dic₃	—	6	8	no	—
75	C₂²×Dic₃	—	6	4	no	—
76	C₂²×Dic₃	—	12	4	no	—
77	C₂²×Dic₃	—	12	4	no	—
78	C₂×C₃×C₈	—	2	8	no	—
79	C₂×C₃×C₈	—	2	4	no	—
80	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
81	C₄⋊Dic₃	—	3	8	no	—
82	C₄⋊Dic₃	—	6	8	no	—
83	C₄⋊Dic₃	—	6	4	no	—
84	C₂²×C₉	#95	1	4	yes	—
85	C₂²×C₉	#102	1	8	yes	—
86	C₂²×C₉	#103	1	8	yes	—
87	C₂²×C₉	#106	1	4	yes	—
88	C₂²×C₉	#107	1	4	yes	—
89	C₂²×C₉	C₂×C₂²⋊C₄	1	2	yes	—
90	C₂²×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
92	C₂²×C₉	C₂×SD₁₆	1	2	yes	—
93	C₂²×C₉	C₂×Q₁₆	1	1	yes	characteristic
94	C₄×C₉	#95	1	4	yes	—
95	C₄×C₉	C₂×C₄²	1	1	yes	characteristic
96	C₄×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₄×C₉	C₂×C₄⋊C₄	1	2	yes	—
98	Dic₉	—	4	8	no	—
99	C₂³×C₄	—	18	2	no	—
100	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
101	C₂²×C₈	—	2	4	no	—
102	C₂²×C₈	Dic₉	1	4	yes	complemented
103	C₂²×C₈	C₂×D₉	1	2	yes	—
104	C₂×C₄⋊C₄	—	9	8	no	—
105	C₂×C₄⋊C₄	—	9	4	no	—
106	C₂×C₄⋊C₄	—	18	2	no	—
107	C₂×C₄⋊C₄	—	18	4	no	—
108	C₂³×C₃	#204	1	4	yes	—
109	C₂³×C₃	D₂₄	1	2	yes	—
110	C₂³×C₃	Dic₁₂	1	2	yes	—
111	C₂³×C₃	C₄⋊Dic₃	1	2	yes	—
112	C₂³×C₃	(C₂×D₃)⋊C₄	1	4	yes	—
113	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
114	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
115	C₂×C₃×C₄	Dic₃⋊C₄	1	8	yes	—
116	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
117	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	4	yes	—
118	C₂×C₃×C₄	#217	1	4	yes	—
119	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
120	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
121	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
122	C₂×C₃×C₄	C₂×#67	1	2	yes	—
123	C₂×Dic₃	—	6	8	no	—
124	C₂×Dic₃	—	12	16	no	—
125	C₂×Dic₃	—	12	4	no	—
126	C₂×Dic₃	—	12	4	no	—
127	C₃×C₈	—	2	4	no	—
128	C₂×C₉	#340	1	8	yes	complemented
129	C₂×C₉	C₂×#95	1	1	yes	characteristic
130	C₂×C₉	C₂×#102	1	2	yes	—
131	C₂×C₉	C₂×#103	1	2	yes	—
132	C₂×C₉	C₂×#106	1	1	yes	characteristic
133	C₂×C₉	C₂×#107	1	1	yes	characteristic
134	C₂⁴	D₃₆	1	1	yes	characteristic
135	C₂²×C₄	—	18	8	no	—
136	C₂²×C₄	—	18	4	no	—
137	C₂²×C₄	—	36	4	no	—
138	C₂²×C₄	—	36	4	no	—
139	C₂²×C₄	Dic₁₈	1	2	yes	—
140	C₂²×C₄	C₄×D₉	1	4	yes	—
141	C₂²×C₄	D₃₆	1	1	yes	characteristic
142	C₂²×C₄	C₂×Dic₉	1	2	yes	—
143	C₂²×C₄	#611	1	4	yes	—
144	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
145	C₂×C₈	—	2	8	no	—
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	C₂×Dic₉	1	4	yes	complemented
148	C₄⋊C₄	—	9	8	no	—
149	C₄⋊C₄	—	18	8	no	—
150	C₄⋊C₄	—	18	4	no	—
151	C₂²×C₃	#816	1	8	yes	—
152	C₂²×C₃	#817	1	4	yes	—
153	C₂²×C₃	#818	1	4	yes	—
154	C₂²×C₃	#821	1	8	yes	—
155	C₂²×C₃	C₃⋊#95	1	4	yes	—
156	C₂²×C₃	C₂×#204	1	2	yes	—
157	C₂²×C₃	C₂×D₂₄	1	1	yes	characteristic
158	C₂²×C₃	C₂×Dic₁₂	1	1	yes	characteristic
159	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
160	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
161	C₃×C₄	C₃⋊#95	1	4	yes	—
162	C₃×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
163	C₃×C₄	C₂×Dic₃⋊C₄	1	2	yes	—
164	C₃×C₄	C₂×#217	1	1	yes	characteristic
165	Dic₃	—	12	8	no	—
166	C₉	C₂×#340	1	1	yes	characteristic, complemented, Sylow
167	C₂³	Dic₃₆	1	2	yes	—
168	C₂³	#3664	1	4	yes	—
169	C₂³	D₇₂	1	2	yes	—
170	C₂³	C₄⋊Dic₉	1	2	yes	—
171	C₂³	(C₂×D₉)⋊C₄	1	4	yes	—
172	C₂³	C₂×D₃₆	1	1	yes	characteristic
173	C₂×C₄	—	18	8	no	—
174	C₂×C₄	—	36	16	no	—
175	C₂×C₄	—	36	4	no	—
176	C₂×C₄	—	36	4	no	—
177	C₂×C₄	C₄×Dic₉	1	4	yes	—
178	C₂×C₄	Dic₉⋊C₄	1	8	yes	—
179	C₂×C₄	C₄⋊Dic₉	1	2	yes	—
180	C₂×C₄	(C₂×D₉)⋊C₄	1	4	yes	—
181	C₂×C₄	#3676	1	4	yes	—
182	C₂×C₄	C₂×Dic₁₈	1	1	yes	characteristic
183	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
184	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
185	C₂×C₄	C₂×#611	1	2	yes	—
186	C₈	—	2	4	no	—
187	C₂×C₃	#4551	1	8	yes	—
188	C₂×C₃	C₂×#816	1	2	yes	—
189	C₂×C₃	C₂×#817	1	1	yes	characteristic
190	C₂×C₃	C₂×#818	1	1	yes	characteristic
191	C₂×C₃	C₂×#821	1	2	yes	—
192	C₂×C₃	C₂×C₃⋊#95	1	1	yes	characteristic
193	C₂²	#63376	1	8	yes	—
194	C₂²	#63377	1	4	yes	—
195	C₂²	#63378	1	4	yes	—
196	C₂²	#63380	1	8	yes	—
197	C₂²	C₉⋊#95	1	4	yes	—
198	C₂²	C₂×Dic₃₆	1	1	yes	characteristic
199	C₂²	C₂×#3664	1	2	yes	—
200	C₂²	C₂×D₇₂	1	1	yes	characteristic
201	C₂²	C₂×C₄⋊Dic₉	1	1	yes	characteristic
202	C₂²	C₂×(C₂×D₉)⋊C₄	1	2	yes	—
203	C₄	—	36	8	no	—
204	C₄	C₉⋊#95	1	4	yes	—
205	C₄	C₂×C₄×Dic₉	1	1	yes	characteristic
206	C₄	C₂×Dic₉⋊C₄	1	2	yes	—
207	C₄	C₂×#3676	1	1	yes	characteristic
208	C₃	C₂×#4551	1	1	yes	characteristic
209	C₂	#10588229	1	8	yes	direct product factor
210	C₂	C₂×#63376	1	2	yes	—
211	C₂	C₂×#63377	1	1	yes	characteristic
212	C₂	C₂×#63378	1	1	yes	characteristic
213	C₂	C₂×#63380	1	2	yes	—
214	C₂	C₂×C₉⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₃₆
commutator	C₄×C₉	C₂×C₄²
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₂³×C₈×C₉	C₂
socle, prime radical	C₂⁴×C₃	D₁₂
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	C₂³×C₈	D₉
hypocenter	C₉	C₂×#340
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
3. #10588229	C₂	direct (N × H)
8. C₂²×C₈×C₉	C₄	semidirect
12. C₂×C₄⋊Dic₉	C₄	semidirect
30. C₂×C₈×C₉	C₂×C₄	semidirect
33. C₄⋊Dic₉	C₂×C₄	semidirect
102. C₂²×C₈	Dic₉	semidirect
128. C₂×C₉	#340	semidirect
147. C₂×C₈	C₂×Dic₉	semidirect
166. C₉	C₂×#340	semidirect
209. C₂	#10588229	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₈×C₉	2
C₂²×C₄⋊Dic₉	2
#10588229	2
C₂×#4551	3

Subgroups — C2×#10588229 #11783232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588229 #11783232