Subgroups — C₂×C₉×#446 #11767680

Order 1152.

600 conjugacy classes of subgroups.

The subgroup lattice has 219 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×#446	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×C₄⋊C₈	C₂	1	2	yes	maximal
5	C₂×C₉×#97	C₂	1	2	yes	maximal
6	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
7	C₂×C₃×#446	C₃	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₉	C₄	1	1	yes	characteristic
9	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₉	C₂²	1	2	yes	—
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₄×Q₈×C₉	C₄	1	4	yes	—
13	C₄×Q₈×C₉	C₂²	1	4	yes	—
14	C₂×C₉×C₄⋊C₄	C₄	1	2	yes	—
15	C₂×C₉×C₄⋊C₄	C₄	1	1	yes	characteristic
16	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₉	C₂²	1	2	yes	—
18	C₉×C₄⋊C₈	C₂²	1	4	yes	—
19	C₉×C₄⋊C₈	C₂²	1	8	yes	—
20	C₉×#97	C₂²	1	8	yes	—
21	C₄×C₈×C₉	C₂²	1	4	yes	—
22	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
23	C₃×#446	C₂×C₃	1	8	yes	—
24	C₂×C₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×C₄⋊C₈	C₂×C₃	1	2	yes	—
26	C₂×C₃×#97	C₂×C₃	1	2	yes	—
27	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
28	C₂×Q₈×C₉	—	2	4	no	—
29	C₂×Q₈×C₉	C₂×C₄	1	4	yes	—
30	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
35	C₂×C₈×C₉	—	2	2	no	—
36	C₂×C₈×C₉	—	2	4	no	—
37	C₂×C₈×C₉	Q₈	1	4	yes	complemented
38	C₂×C₈×C₉	C₂³	1	2	yes	—
39	C₂×C₈×C₉	C₂³	1	4	yes	—
40	C₂×C₈×C₉	C₂³	1	2	yes	—
41	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
42	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
43	C₄²×C₉	C₂×C₄	1	4	yes	—
44	C₄²×C₉	C₂×C₄	1	2	yes	—
45	C₄²×C₉	C₂³	1	2	yes	—
46	C₄²×C₉	C₂³	1	4	yes	—
47	C₂×#446	C₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂²×C₃×Q₈	C₃×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
50	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
51	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
52	C₃×C₄×Q₈	C₃×C₄	1	4	yes	—
53	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
54	C₂×C₃×C₄⋊C₄	C₃×C₄	1	2	yes	—
55	C₂×C₃×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
56	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
58	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
59	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	—
60	C₃×#97	C₂²×C₃	1	8	yes	—
61	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
62	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
63	Q₈×C₉	—	2	8	no	—
64	C₂×C₄×C₉	—	2	4	no	—
65	C₂×C₄×C₉	—	2	2	no	—
66	C₂×C₄×C₉	—	2	4	no	—
67	C₂×C₄×C₉	M₁₆	1	4	yes	—
68	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
69	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
70	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
71	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
73	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
74	C₂×C₄×C₉	#41	1	2	yes	—
75	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
76	C₈×C₉	—	2	2	no	—
77	C₈×C₉	—	2	4	no	—
78	C₈×C₉	C₂×Q₈	1	4	yes	complemented
79	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic
80	#446	C₂×C₉	1	8	yes	direct product factor
81	C₂×C₄⋊C₈	C₂×C₉	1	1	yes	characteristic
82	C₂×C₄⋊C₈	C₂×C₉	1	2	yes	—
83	C₂×#97	C₂×C₉	1	2	yes	—
84	C₂×C₄×C₈	C₂×C₉	1	1	yes	characteristic
85	C₂×C₃×Q₈	—	2	4	no	—
86	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
87	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
88	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
89	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
90	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
91	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
92	C₂×C₃×C₈	—	2	2	no	—
93	C₂×C₃×C₈	—	2	4	no	—
94	C₂×C₃×C₈	C₃×Q₈	1	4	yes	—
95	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
96	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
97	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
98	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
99	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
100	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
101	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
102	C₃×C₄²	C₂³×C₃	1	2	yes	—
103	C₃×C₄²	C₂³×C₃	1	4	yes	—
104	C₂²×C₉	C₄×Q₈	1	2	yes	—
105	C₂²×C₉	C₂×M₁₆	1	2	yes	—
106	C₂²×C₉	#131	1	2	yes	—
107	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
108	C₄×C₉	—	2	4	no	—
109	C₄×C₉	—	2	2	no	—
110	C₄×C₉	—	2	4	no	—
111	C₄×C₉	C₄×Q₈	1	2	yes	—
112	C₄×C₉	C₂×M₁₆	1	4	yes	—
113	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
114	C₄×C₉	C₂×#41	1	1	yes	characteristic
115	C₂²×Q₈	C₄×C₉	1	1	yes	characteristic
116	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
117	C₂²×C₈	C₂²×C₉	1	2	yes	—
118	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
119	C₄×Q₈	C₄×C₉	1	4	yes	—
120	C₄×Q₈	C₂²×C₉	1	4	yes	—
121	C₂×C₄⋊C₄	C₄×C₉	1	2	yes	—
122	C₂×C₄⋊C₄	C₄×C₉	1	1	yes	characteristic
123	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
124	C₂×C₄²	C₂²×C₉	1	2	yes	—
125	C₄⋊C₈	C₂²×C₉	1	4	yes	—
126	C₄⋊C₈	C₂²×C₉	1	8	yes	—
127	#97	C₂²×C₉	1	8	yes	—
128	C₄×C₈	C₂²×C₉	1	4	yes	—
129	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
130	C₃×Q₈	—	2	8	no	—
131	C₂×C₃×C₄	—	2	4	no	—
132	C₂×C₃×C₄	—	2	2	no	—
133	C₂×C₃×C₄	—	2	4	no	—
134	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	—
135	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
136	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
137	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
138	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
139	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
140	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
141	C₂×C₃×C₄	C₃×#41	1	2	yes	—
142	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
143	C₃×C₈	—	2	2	no	—
144	C₃×C₈	—	2	4	no	—
145	C₃×C₈	C₂×C₃×Q₈	1	4	yes	—
146	C₂×C₉	#446	1	4	yes	direct product factor
147	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
148	C₂×C₉	C₂²×M₁₆	1	1	yes	characteristic
149	C₂×C₉	C₂×#131	1	1	yes	characteristic
150	C₂×Q₈	—	2	4	no	—
151	C₂×Q₈	C₂×C₄×C₉	1	4	yes	—
152	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
153	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
154	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
155	C₂²×C₄	C₂×C₄×C₉	1	1	yes	characteristic
156	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	2	4	no	—
159	C₂×C₈	Q₈×C₉	1	4	yes	complemented
160	C₂×C₈	C₂³×C₉	1	2	yes	—
161	C₂×C₈	C₂³×C₉	1	4	yes	—
162	C₂×C₈	C₂³×C₉	1	2	yes	—
163	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
164	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
165	C₄²	C₂×C₄×C₉	1	4	yes	—
166	C₄²	C₂×C₄×C₉	1	2	yes	—
167	C₄²	C₂³×C₉	1	2	yes	—
168	C₄²	C₂³×C₉	1	4	yes	—
169	C₂²×C₃	C₃×C₄×Q₈	1	2	yes	—
170	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
171	C₂²×C₃	C₃×#131	1	2	yes	—
172	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
173	C₃×C₄	—	2	4	no	—
174	C₃×C₄	—	2	2	no	—
175	C₃×C₄	—	2	4	no	—
176	C₃×C₄	C₃×C₄×Q₈	1	2	yes	—
177	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	—
178	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
179	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
180	C₉	C₂×#446	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
182	Q₈	—	2	8	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	C₉×M₁₆	1	4	yes	—
187	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
188	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
189	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
190	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
191	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
192	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
193	C₂×C₄	C₉×#41	1	2	yes	—
194	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
195	C₈	—	2	2	no	—
196	C₈	—	2	4	no	—
197	C₈	C₂×Q₈×C₉	1	4	yes	complemented
198	C₂×C₃	C₃×#446	1	4	yes	—
199	C₂×C₃	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
200	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
201	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
202	C₂²	C₄×Q₈×C₉	1	2	yes	—
203	C₂²	C₂×C₉×M₁₆	1	2	yes	—
204	C₂²	C₉×#131	1	2	yes	—
205	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
206	C₄	—	2	4	no	—
207	C₄	—	2	2	no	—
208	C₄	—	2	4	no	—
209	C₄	C₄×Q₈×C₉	1	2	yes	—
210	C₄	C₂×C₉×M₁₆	1	4	yes	—
211	C₄	C₂²×Q₈×C₉	1	1	yes	characteristic
212	C₄	C₂×C₉×#41	1	1	yes	characteristic
213	C₃	C₂×C₃×#446	1	1	yes	characteristic
214	C₂	C₉×#446	1	4	yes	direct product factor
215	C₂	C₂×C₄×Q₈×C₉	1	1	yes	characteristic
216	C₂	C₂²×C₉×M₁₆	1	1	yes	characteristic
217	C₂	C₂×C₉×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle, prime radical	C₂³×C₃	C₂²×C₃×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#446	C₂	direct (N × H)
37. C₂×C₈×C₉	Q₈	semidirect
47. C₂×#446	C₉	direct (N × H)
78. C₈×C₉	C₂×Q₈	semidirect
80. #446	C₂×C₉	direct (N × H)
146. C₂×C₉	#446	direct (N × H)
159. C₂×C₈	Q₈×C₉	semidirect
180. C₉	C₂×#446	direct (N × H)
197. C₈	C₂×Q₈×C₉	semidirect
214. C₂	C₉×#446	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×C₄×Q₈×C₉	2
C₉×#446	2
C₂×C₉×C₄⋊C₈	2
C₂×C₉×#97	2
C₂×C₄×C₈×C₉	2
C₂×C₃×#446	3

Subgroups — C2×C9×#446 #11767680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#446 #11767680