Subgroups — C₂×C₉×#400 #11767115

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₉×#400	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₉×#95	C₂	1	1	yes	maximal, characteristic
5	C₂×C₉×#95	C₂	1	2	yes	maximal
6	C₂×C₉×#95	C₂	1	2	yes	maximal
7	C₂×C₃×#400	C₃	1	1	yes	maximal, characteristic
8	C₂³×C₄×C₉	C₂²	1	2	yes	—
9	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂³×C₄×C₉	C₂²	1	2	yes	—
11	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₉×C₄⋊C₄	—	2	4	no	—
14	C₂×C₉×C₄⋊C₄	—	2	4	no	—
15	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
16	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
17	C₉×#95	C₂²	1	8	yes	—
18	C₉×#95	C₂²	1	8	yes	—
19	C₉×#95	C₂²	1	4	yes	—
20	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
21	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
22	C₃×#400	C₂×C₃	1	8	yes	—
23	C₂×C₃×#95	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×#95	C₂×C₃	1	2	yes	—
25	C₂×C₃×#95	C₂×C₃	1	2	yes	—
26	C₂⁴×C₉	C₂³	1	1	yes	characteristic
27	C₂²×C₄×C₉	—	2	2	no	—
28	C₂²×C₄×C₉	—	2	2	no	—
29	C₂²×C₄×C₉	—	2	4	no	—
30	C₂²×C₄×C₉	—	2	2	no	—
31	C₂²×C₄×C₉	—	2	4	no	—
32	C₂²×C₄×C₉	—	2	4	no	—
33	C₂²×C₄×C₉	—	2	8	no	—
34	C₂²×C₄×C₉	—	2	4	no	—
35	C₂²×C₄×C₉	—	2	4	no	—
36	C₂²×C₄×C₉	—	2	4	no	—
37	C₂²×C₄×C₉	D₄	1	4	yes	—
38	C₂²×C₄×C₉	Q₈	1	4	yes	—
39	C₂²×C₄×C₉	C₂³	1	2	yes	—
40	C₂²×C₄×C₉	C₂³	1	4	yes	—
41	C₂²×C₄×C₉	C₂³	1	4	yes	—
42	C₂²×C₄×C₉	C₂³	1	2	yes	—
43	C₂²×C₄×C₉	C₂³	1	2	yes	—
44	C₉×C₄⋊C₄	—	2	8	no	—
45	C₉×C₄⋊C₄	—	2	8	no	—
46	C₂×#400	C₉	1	1	yes	characteristic, direct product factor, Sylow
47	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
48	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
49	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
50	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
51	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
52	C₂×C₃×C₄⋊C₄	—	2	4	no	—
53	C₂×C₃×C₄⋊C₄	—	2	4	no	—
54	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
55	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
56	C₃×#95	C₂²×C₃	1	4	yes	—
57	C₃×#95	C₂²×C₃	1	8	yes	—
58	C₃×#95	C₂²×C₃	1	8	yes	—
59	C₂³×C₉	C₂×D₄	1	2	yes	—
60	C₂³×C₉	C₂×Q₈	1	2	yes	—
61	C₂³×C₉	#41	1	2	yes	—
62	C₂³×C₉	#41	1	4	yes	—
63	C₂³×C₉	#41	1	4	yes	—
64	C₂³×C₉	C₂⁴	1	1	yes	characteristic
65	C₂×C₄×C₉	—	2	8	no	—
66	C₂×C₄×C₉	—	2	8	no	—
67	C₂×C₄×C₉	—	2	2	no	—
68	C₂×C₄×C₉	—	2	2	no	—
69	C₂×C₄×C₉	—	2	4	no	—
70	C₂×C₄×C₉	—	2	2	no	—
71	C₂×C₄×C₉	—	2	4	no	—
72	C₂×C₄×C₉	—	2	4	no	—
73	C₂×C₄×C₉	—	2	8	no	—
74	C₂×C₄×C₉	—	2	4	no	—
75	C₂×C₄×C₉	—	2	4	no	—
76	C₂×C₄×C₉	—	2	4	no	—
77	C₂×C₄×C₉	—	4	4	no	—
78	C₂×C₄×C₉	—	4	8	no	—
79	C₂×C₄×C₉	—	4	8	no	—
80	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
81	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
82	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
83	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
84	#400	C₂×C₉	1	8	yes	direct product factor
85	C₂×#95	C₂×C₉	1	2	yes	—
86	C₂×#95	C₂×C₉	1	2	yes	—
87	C₂×#95	C₂×C₉	1	1	yes	characteristic
88	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
89	C₂²×C₃×C₄	—	2	2	no	—
90	C₂²×C₃×C₄	—	2	2	no	—
91	C₂²×C₃×C₄	—	2	4	no	—
92	C₂²×C₃×C₄	—	2	2	no	—
93	C₂²×C₃×C₄	—	2	4	no	—
94	C₂²×C₃×C₄	—	2	4	no	—
95	C₂²×C₃×C₄	—	2	8	no	—
96	C₂²×C₃×C₄	—	2	4	no	—
97	C₂²×C₃×C₄	—	2	4	no	—
98	C₂²×C₃×C₄	—	2	4	no	—
99	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
100	C₂²×C₃×C₄	C₃×Q₈	1	4	yes	—
101	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
102	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
103	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
104	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
105	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
106	C₃×C₄⋊C₄	—	2	8	no	—
107	C₃×C₄⋊C₄	—	2	8	no	—
108	C₂²×C₉	C₂²⋊Q₈	1	4	yes	—
109	C₂²×C₉	#123	1	4	yes	—
110	C₂²×C₉	#124	1	4	yes	—
111	C₂²×C₉	#125	1	8	yes	—
112	C₂²×C₉	#126	1	8	yes	—
113	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
114	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
115	C₂²×C₉	C₂×#41	1	1	yes	characteristic
116	C₂²×C₉	C₂×#41	1	2	yes	—
117	C₂²×C₉	C₂×#41	1	2	yes	—
118	C₄×C₉	—	2	4	no	—
119	C₄×C₉	—	2	4	no	—
120	C₄×C₉	—	4	2	no	—
121	C₄×C₉	—	4	4	no	—
122	C₄×C₉	—	4	4	no	—
123	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
124	C₂³×C₄	C₂²×C₉	1	2	yes	—
125	C₂³×C₄	C₂²×C₉	1	2	yes	—
126	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
127	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
128	C₂×C₄⋊C₄	—	2	4	no	—
129	C₂×C₄⋊C₄	—	2	4	no	—
130	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
131	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
132	#95	C₂²×C₉	1	4	yes	—
133	#95	C₂²×C₉	1	8	yes	—
134	#95	C₂²×C₉	1	8	yes	—
135	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
136	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
137	C₂³×C₃	C₃×#41	1	2	yes	—
138	C₂³×C₃	C₃×#41	1	4	yes	—
139	C₂³×C₃	C₃×#41	1	4	yes	—
140	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
141	C₂×C₃×C₄	—	2	8	no	—
142	C₂×C₃×C₄	—	2	8	no	—
143	C₂×C₃×C₄	—	2	2	no	—
144	C₂×C₃×C₄	—	2	2	no	—
145	C₂×C₃×C₄	—	2	4	no	—
146	C₂×C₃×C₄	—	2	2	no	—
147	C₂×C₃×C₄	—	2	4	no	—
148	C₂×C₃×C₄	—	2	4	no	—
149	C₂×C₃×C₄	—	2	8	no	—
150	C₂×C₃×C₄	—	2	4	no	—
151	C₂×C₃×C₄	—	2	4	no	—
152	C₂×C₃×C₄	—	2	4	no	—
153	C₂×C₃×C₄	—	4	4	no	—
154	C₂×C₃×C₄	—	4	8	no	—
155	C₂×C₃×C₄	—	4	8	no	—
156	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
157	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
158	C₂×C₉	#400	1	8	yes	direct product factor
159	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₉	C₂×#123	1	1	yes	characteristic
161	C₂×C₉	C₂×#124	1	1	yes	characteristic
162	C₂×C₉	C₂×#125	1	2	yes	—
163	C₂×C₉	C₂×#126	1	2	yes	—
164	C₂⁴	C₂³×C₉	1	1	yes	characteristic
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	4	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	2	4	no	—
170	C₂²×C₄	—	2	4	no	—
171	C₂²×C₄	—	2	8	no	—
172	C₂²×C₄	—	2	4	no	—
173	C₂²×C₄	—	2	4	no	—
174	C₂²×C₄	—	2	4	no	—
175	C₂²×C₄	D₄×C₉	1	4	yes	—
176	C₂²×C₄	Q₈×C₉	1	4	yes	—
177	C₂²×C₄	C₂³×C₉	1	4	yes	—
178	C₂²×C₄	C₂³×C₉	1	2	yes	—
179	C₂²×C₄	C₂³×C₉	1	4	yes	—
180	C₂²×C₄	C₂³×C₉	1	2	yes	—
181	C₂²×C₄	C₂³×C₉	1	2	yes	—
182	C₄⋊C₄	—	2	8	no	—
183	C₄⋊C₄	—	2	8	no	—
184	C₂²×C₃	C₃×C₂²⋊Q₈	1	4	yes	—
185	C₂²×C₃	C₃×#123	1	4	yes	—
186	C₂²×C₃	C₃×#124	1	4	yes	—
187	C₂²×C₃	C₃×#125	1	8	yes	—
188	C₂²×C₃	C₃×#126	1	8	yes	—
189	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
190	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
191	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
192	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
193	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
194	C₃×C₄	—	2	4	no	—
195	C₃×C₄	—	2	4	no	—
196	C₃×C₄	—	4	2	no	—
197	C₃×C₄	—	4	4	no	—
198	C₃×C₄	—	4	4	no	—
199	C₉	C₂×#400	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³	C₂×D₄×C₉	1	2	yes	—
201	C₂³	C₂×Q₈×C₉	1	2	yes	—
202	C₂³	C₉×#41	1	2	yes	—
203	C₂³	C₉×#41	1	4	yes	—
204	C₂³	C₉×#41	1	4	yes	—
205	C₂³	C₂⁴×C₉	1	1	yes	characteristic
206	C₂×C₄	—	2	8	no	—
207	C₂×C₄	—	2	8	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	4	no	—
213	C₂×C₄	—	2	4	no	—
214	C₂×C₄	—	2	8	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	4	no	—
218	C₂×C₄	—	4	4	no	—
219	C₂×C₄	—	4	8	no	—
220	C₂×C₄	—	4	8	no	—
221	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
222	C₂×C₄	C₂×Q₈×C₉	1	4	yes	—
223	C₂×C₃	C₃×#400	1	8	yes	—
224	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
225	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
226	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
227	C₂×C₃	C₂×C₃×#125	1	2	yes	—
228	C₂×C₃	C₂×C₃×#126	1	2	yes	—
229	C₂²	C₉×C₂²⋊Q₈	1	4	yes	—
230	C₂²	C₉×#123	1	4	yes	—
231	C₂²	C₉×#124	1	4	yes	—
232	C₂²	C₉×#125	1	8	yes	—
233	C₂²	C₉×#126	1	8	yes	—
234	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
235	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
236	C₂²	C₂×C₉×#41	1	1	yes	characteristic
237	C₂²	C₂×C₉×#41	1	2	yes	—
238	C₂²	C₂×C₉×#41	1	2	yes	—
239	C₄	—	2	4	no	—
240	C₄	—	2	4	no	—
241	C₄	—	4	2	no	—
242	C₄	—	4	4	no	—
243	C₄	—	4	4	no	—
244	C₃	C₂×C₃×#400	1	1	yes	characteristic
245	C₂	C₉×#400	1	8	yes	direct product factor
246	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
247	C₂	C₂×C₉×#123	1	1	yes	characteristic
248	C₂	C₂×C₉×#124	1	1	yes	characteristic
249	C₂	C₂×C₉×#125	1	2	yes	—
250	C₂	C₂×C₉×#126	1	2	yes	—

	subgroup	G/H
center	C₂⁴×C₉	C₂³
commutator	C₂³	C₂⁴×C₉
Frattini, cosocle	C₂³×C₃	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×#400	C₂	direct (N × H)
46. C₂×#400	C₉	direct (N × H)
84. #400	C₂×C₉	direct (N × H)
158. C₂×C₉	#400	direct (N × H)
199. C₉	C₂×#400	direct (N × H)
245. C₂	C₉×#400	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×C₉×C₄⋊C₄	2
C₉×#400	2
C₂×C₉×#95	2
C₂×C₃×#400	3

Subgroups — C2×C9×#400 #11767115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#400 #11767115