Subgroups — C₂×C₉×#882 #13152347

Order 1728.

2118 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₉×D₁₂	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₉×#882	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#882	C₃	1	1	yes	maximal, characteristic
8	C₂×C₉×#120	—	3	1	no	maximal
9	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
10	C₂³×D₃×C₉	—	2	4	no	—
11	C₂³×D₃×C₉	—	2	8	no	—
12	C₂³×D₃×C₉	C₂²	1	2	yes	—
13	C₂³×D₃×C₉	C₂²	1	4	yes	complemented
14	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	complemented
16	C₂×C₉×#67	—	2	4	no	—
17	C₂×C₉×#67	C₂²	1	4	yes	complemented
18	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₉×D₁₂	—	2	8	no	—
20	C₂×C₉×D₁₂	C₂²	1	8	yes	complemented
21	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
22	C₉×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
23	C₂⁴×C₃×D₃	C₂×C₃	1	1	yes	characteristic
24	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
25	C₂²×C₃×D₁₂	C₂×C₃	1	2	yes	—
26	C₂⁵×C₉	—	3	1	no	—
27	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
28	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
29	C₃×#882	C₂×C₃	1	8	yes	—
30	C₂²×D₄×C₉	—	3	1	no	—
31	C₂²×D₄×C₉	—	3	2	no	—
32	C₉×#120	—	3	8	no	—
33	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
34	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
35	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
36	C₂³×C₃×C₉	—	2	4	no	—
37	C₂³×C₃×C₉	D₄	1	4	yes	complemented
38	C₂³×C₃×C₉	C₂³	1	2	yes	—
39	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
40	C₂²×D₃×C₉	—	2	32	no	—
41	C₂²×D₃×C₉	—	2	4	no	—
42	C₂²×D₃×C₉	—	2	4	no	—
43	C₂²×D₃×C₉	—	2	8	no	—
44	C₂²×D₃×C₉	—	2	16	no	—
45	C₂²×D₃×C₉	—	2	4	no	—
46	C₂²×D₃×C₉	—	2	2	no	—
47	C₂²×D₃×C₉	D₄	1	8	yes	complemented
48	C₂²×D₃×C₉	C₂³	1	4	yes	—
49	C₂²×D₃×C₉	C₂³	1	2	yes	complemented
50	C₂×C₃×C₄×C₉	—	2	4	no	—
51	C₂×C₃×C₄×C₉	C₂³	1	4	yes	complemented
52	C₉×#67	—	2	8	no	—
53	C₂×C₉×Dic₃	—	2	2	no	—
54	C₂×C₉×Dic₃	C₂³	1	2	yes	complemented
55	C₉×D₁₂	—	2	16	no	—
56	C₂×C₃×#120	—	3	1	no	—
57	C₂×#882	C₉	1	1	yes	characteristic, direct product factor
58	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
59	C₂³×C₃×D₃	—	2	4	no	—
60	C₂³×C₃×D₃	—	2	8	no	—
61	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	—
62	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
63	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
64	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
65	C₂×C₃×#67	—	2	4	no	—
66	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
67	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃×D₁₂	—	2	8	no	—
69	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
70	C₂⁴×C₉	—	2	1	no	—
71	C₂⁴×C₉	—	3	2	no	—
72	C₂⁴×C₉	—	3	4	no	—
73	C₂⁴×C₉	—	3	1	no	—
74	C₂⁴×C₉	—	6	8	no	—
75	C₂⁴×C₉	—	6	4	no	—
76	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
77	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
78	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
79	C₂×D₄×C₉	—	3	4	no	—
80	C₂×D₄×C₉	—	3	8	no	—
81	C₂×D₄×C₉	—	6	8	no	—
82	C₂×D₄×C₉	—	6	4	no	—
83	C₂²×C₄×C₉	—	2	2	no	—
84	C₂²×C₄×C₉	—	3	1	no	—
85	C₂²×C₄×C₉	C₂×D₃	1	2	yes	complemented
86	C₉×C₂²⋊C₄	—	2	4	no	—
87	C₉×C₂²⋊C₄	—	3	8	no	—
88	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
89	C₂²×C₃×C₉	—	2	8	no	—
90	C₂²×C₃×C₉	—	2	4	no	—
91	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
92	C₂²×C₃×C₉	C₂×D₄	1	4	yes	—
93	C₂²×C₃×C₉	C₂×D₄	1	4	yes	complemented
94	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
95	C₂×D₃×C₉	—	2	32	no	—
96	C₂×D₃×C₉	—	2	16	no	—
97	C₂×D₃×C₉	—	2	4	no	—
98	C₂×D₃×C₉	—	2	4	no	—
99	C₂×D₃×C₉	—	2	4	no	—
100	C₂×D₃×C₉	—	2	2	no	—
101	C₂×D₃×C₉	—	4	4	no	—
102	C₂×D₃×C₉	C₂×D₄	1	8	yes	complemented
103	C₃×C₄×C₉	—	2	4	no	—
104	C₉×Dic₃	—	2	2	no	—
105	C₂⁵×C₃	—	3	1	no	—
106	C₂⁴×D₃	C₂×C₉	1	1	yes	characteristic, complemented
107	C₂²×C₃×D₄	—	3	1	no	—
108	C₂²×C₃×D₄	—	3	2	no	—
109	C₂²×#67	C₂×C₉	1	1	yes	characteristic, complemented
110	C₂²×D₁₂	C₂×C₉	1	2	yes	complemented
111	C₃×#120	—	3	8	no	—
112	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
114	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
115	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
116	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	2	yes	complemented
117	#882	C₂×C₉	1	8	yes	direct product factor
118	C₂³×C₃²	—	2	4	no	—
119	C₂³×C₃²	C₃×D₄	1	4	yes	—
120	C₂³×C₃²	C₂³×C₃	1	2	yes	—
121	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
122	C₂²×C₃×D₃	—	2	32	no	—
123	C₂²×C₃×D₃	—	2	4	no	—
124	C₂²×C₃×D₃	—	2	4	no	—
125	C₂²×C₃×D₃	—	2	8	no	—
126	C₂²×C₃×D₃	—	2	16	no	—
127	C₂²×C₃×D₃	—	2	4	no	—
128	C₂²×C₃×D₃	—	2	2	no	—
129	C₂²×C₃×D₃	C₃×D₄	1	8	yes	—
130	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
131	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
132	C₂×C₃²×C₄	—	2	4	no	—
133	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
134	C₃×#67	—	2	8	no	—
135	C₂×C₃×Dic₃	—	2	2	no	—
136	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
137	C₃×D₁₂	—	2	16	no	—
138	C₂³×C₉	—	2	4	no	—
139	C₂³×C₉	—	2	4	no	—
140	C₂³×C₉	—	2	1	no	—
141	C₂³×C₉	—	2	2	no	—
142	C₂³×C₉	—	3	8	no	—
143	C₂³×C₉	—	3	4	no	—
144	C₂³×C₉	—	3	2	no	—
145	C₂³×C₉	—	4	4	no	—
146	C₂³×C₉	—	6	16	no	—
147	C₂³×C₉	—	6	32	no	—
148	C₂³×C₉	—	6	4	no	—
149	C₂³×C₉	—	6	8	no	—
150	C₂³×C₉	—	6	4	no	—
151	C₂³×C₉	—	6	2	no	—
152	C₂³×C₉	—	6	4	no	—
153	C₂³×C₉	D₁₂	1	4	yes	complemented
154	C₂³×C₉	C₂²×D₃	1	2	yes	—
155	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
156	D₄×C₉	—	6	16	no	—
157	D₄×C₉	—	6	8	no	—
158	C₂×C₄×C₉	—	2	4	no	—
159	C₂×C₄×C₉	—	2	4	no	—
160	C₂×C₄×C₉	—	3	2	no	—
161	C₂×C₄×C₉	—	4	4	no	—
162	C₂×C₄×C₉	—	6	2	no	—
163	C₂×C₄×C₉	C₂²×D₃	1	4	yes	complemented
164	C₂×#120	—	3	1	no	Sylow
165	C₂×C₃×C₉	—	2	4	no	—
166	C₂×C₃×C₉	#120	1	4	yes	complemented
167	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₃×C₉	C₂²×D₄	1	2	yes	—
169	D₃×C₉	—	2	8	no	—
170	D₃×C₉	—	4	2	no	—
171	C₂⁴×C₃	—	2	1	no	—
172	C₂⁴×C₃	—	3	2	no	—
173	C₂⁴×C₃	—	3	4	no	—
174	C₂⁴×C₃	—	3	1	no	—
175	C₂⁴×C₃	—	6	8	no	—
176	C₂⁴×C₃	—	6	4	no	—
177	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
178	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
179	C₂³×D₃	—	2	4	no	—
180	C₂³×D₃	—	2	8	no	—
181	C₂³×D₃	C₂²×C₉	1	2	yes	—
182	C₂³×D₃	C₂²×C₉	1	4	yes	complemented
183	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
184	C₂×C₃×D₄	—	3	4	no	—
185	C₂×C₃×D₄	—	3	8	no	—
186	C₂×C₃×D₄	—	6	8	no	—
187	C₂×C₃×D₄	—	6	4	no	—
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	—	3	1	no	—
190	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	complemented
191	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
192	C₂×#67	—	2	4	no	—
193	C₂×#67	C₂²×C₉	1	4	yes	complemented
194	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
195	C₂×D₁₂	—	2	8	no	—
196	C₂×D₁₂	C₂²×C₉	1	8	yes	complemented
197	C₃×C₂²⋊C₄	—	2	4	no	—
198	C₃×C₂²⋊C₄	—	3	8	no	—
199	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
200	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
201	(C₂×D₃)⋊C₄	C₂²×C₉	1	8	yes	complemented
202	C₂²×C₃²	—	2	8	no	—
203	C₂²×C₃²	—	2	4	no	—
204	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
205	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
206	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
207	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
208	C₂×C₃×D₃	—	2	32	no	—
209	C₂×C₃×D₃	—	2	16	no	—
210	C₂×C₃×D₃	—	2	4	no	—
211	C₂×C₃×D₃	—	2	4	no	—
212	C₂×C₃×D₃	—	2	4	no	—
213	C₂×C₃×D₃	—	2	2	no	—
214	C₂×C₃×D₃	—	4	4	no	—
215	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
216	C₃²×C₄	—	2	4	no	—
217	C₃×Dic₃	—	2	2	no	—
218	C₂²×C₉	—	2	8	no	—
219	C₂²×C₉	—	2	4	no	—
220	C₂²×C₉	—	2	1	no	—
221	C₂²×C₉	—	2	2	no	—
222	C₂²×C₉	—	2	4	no	—
223	C₂²×C₉	—	2	4	no	—
224	C₂²×C₉	—	3	8	no	—
225	C₂²×C₉	—	4	8	no	—
226	C₂²×C₉	—	4	4	no	—
227	C₂²×C₉	—	6	32	no	—
228	C₂²×C₉	—	6	16	no	—
229	C₂²×C₉	—	6	4	no	—
230	C₂²×C₉	—	6	4	no	—
231	C₂²×C₉	—	6	2	no	—
232	C₂²×C₉	—	6	4	no	—
233	C₂²×C₉	—	12	4	no	—
234	C₂²×C₉	C₂×D₁₂	1	2	yes	—
235	C₂²×C₉	C₂×D₁₂	1	4	yes	complemented
236	C₂²×C₉	D₃×D₄	1	4	yes	—
237	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
238	C₄×C₉	—	2	4	no	—
239	C₄×C₉	—	4	4	no	—
240	C₄×C₉	—	6	2	no	—
241	C₂⁵	—	3	1	no	—
242	C₂²×D₄	—	3	1	no	—
243	C₂²×D₄	—	3	2	no	—
244	#120	—	3	8	no	—
245	C₂×C₂²⋊C₄	—	3	2	no	—
246	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
247	C₃×C₉	C₂×#120	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₃	—	2	4	no	—
249	C₂³×C₃	—	2	4	no	—
250	C₂³×C₃	—	2	4	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	2	2	no	—
253	C₂³×C₃	—	3	4	no	—
254	C₂³×C₃	—	3	8	no	—
255	C₂³×C₃	—	3	2	no	—
256	C₂³×C₃	—	4	4	no	—
257	C₂³×C₃	—	6	16	no	—
258	C₂³×C₃	—	6	32	no	—
259	C₂³×C₃	—	6	4	no	—
260	C₂³×C₃	—	6	8	no	—
261	C₂³×C₃	—	6	4	no	—
262	C₂³×C₃	—	6	2	no	—
263	C₂³×C₃	—	6	4	no	—
264	C₂³×C₃	D₄×C₉	1	4	yes	complemented
265	C₂³×C₃	C₂³×C₉	1	2	yes	—
266	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
267	C₂³×C₃	C₃×D₁₂	1	4	yes	—
268	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
269	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
270	C₂²×D₃	—	2	32	no	—
271	C₂²×D₃	—	2	4	no	—
272	C₂²×D₃	—	2	4	no	—
273	C₂²×D₃	—	2	8	no	—
274	C₂²×D₃	—	2	16	no	—
275	C₂²×D₃	—	2	4	no	—
276	C₂²×D₃	—	2	2	no	—
277	C₂²×D₃	D₄×C₉	1	8	yes	complemented
278	C₂²×D₃	C₂³×C₉	1	4	yes	—
279	C₂²×D₃	C₂³×C₉	1	2	yes	complemented
280	C₃×D₄	—	6	16	no	—
281	C₃×D₄	—	6	8	no	—
282	C₂×C₃×C₄	—	2	4	no	—
283	C₂×C₃×C₄	—	2	4	no	—
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	3	2	no	—
286	C₂×C₃×C₄	—	4	4	no	—
287	C₂×C₃×C₄	—	6	2	no	—
288	C₂×C₃×C₄	C₂³×C₉	1	4	yes	complemented
289	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
290	#67	—	2	8	no	—
291	C₂×Dic₃	—	2	2	no	—
292	C₂×Dic₃	C₂³×C₉	1	2	yes	complemented
293	D₁₂	—	2	16	no	—
294	C₂×C₃²	—	2	4	no	—
295	C₂×C₃²	C₃×#120	1	4	yes	—
296	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
297	C₂×C₃²	C₂²×C₃×D₄	1	2	yes	—
298	C₃×D₃	—	2	8	no	—
299	C₃×D₃	—	4	2	no	—
300	C₂×C₉	—	2	4	no	—
301	C₂×C₉	—	2	4	no	—
302	C₂×C₉	—	2	1	no	—
303	C₂×C₉	—	2	2	no	—
304	C₂×C₉	—	4	4	no	—
305	C₂×C₉	—	6	8	no	—
306	C₂×C₉	—	12	2	no	—
307	C₂×C₉	#882	1	4	yes	direct product factor
308	C₂×C₉	C₂²×D₁₂	1	1	yes	characteristic
309	C₂×C₉	C₂×D₃×D₄	1	2	yes	—
310	C₂⁴	—	3	2	no	—
311	C₂⁴	—	3	4	no	—
312	C₂⁴	—	3	1	no	—
313	C₂⁴	—	6	8	no	—
314	C₂⁴	—	6	4	no	—
315	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
316	C₂×D₄	—	3	4	no	—
317	C₂×D₄	—	3	8	no	—
318	C₂×D₄	—	6	8	no	—
319	C₂×D₄	—	6	4	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂²×C₄	C₂×D₃×C₉	1	2	yes	complemented
322	C₂²⋊C₄	—	3	8	no	—
323	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
324	C₂²×C₃	—	2	8	no	—
325	C₂²×C₃	—	2	8	no	—
326	C₂²×C₃	—	2	4	no	—
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	4	no	—
331	C₂²×C₃	—	2	4	no	—
332	C₂²×C₃	—	3	8	no	—
333	C₂²×C₃	—	4	4	no	—
334	C₂²×C₃	—	4	8	no	—
335	C₂²×C₃	—	6	32	no	—
336	C₂²×C₃	—	6	16	no	—
337	C₂²×C₃	—	6	4	no	—
338	C₂²×C₃	—	6	4	no	—
339	C₂²×C₃	—	6	2	no	—
340	C₂²×C₃	—	6	4	no	—
341	C₂²×C₃	—	12	4	no	—
342	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
343	C₂²×C₃	C₂×D₄×C₉	1	4	yes	—
344	C₂²×C₃	C₂×D₄×C₉	1	4	yes	complemented
345	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
346	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
347	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
348	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
349	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
350	C₂×D₃	—	2	32	no	—
351	C₂×D₃	—	2	16	no	—
352	C₂×D₃	—	2	4	no	—
353	C₂×D₃	—	2	4	no	—
354	C₂×D₃	—	2	4	no	—
355	C₂×D₃	—	2	2	no	—
356	C₂×D₃	—	4	4	no	—
357	C₂×D₃	C₂×D₄×C₉	1	8	yes	complemented
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	4	4	no	—
361	C₃×C₄	—	6	2	no	—
362	Dic₃	—	2	2	no	—
363	C₃²	C₂×C₃×#120	1	1	yes	characteristic
364	C₉	—	2	1	no	—
365	C₉	C₂×#882	1	1	yes	characteristic, direct product factor
366	C₂³	—	2	4	no	—
367	C₂³	—	3	4	no	—
368	C₂³	—	3	8	no	—
369	C₂³	—	3	2	no	—
370	C₂³	—	6	16	no	—
371	C₂³	—	6	32	no	—
372	C₂³	—	6	4	no	—
373	C₂³	—	6	8	no	—
374	C₂³	—	6	4	no	—
375	C₂³	—	6	2	no	—
376	C₂³	—	6	4	no	—
377	C₂³	C₉×D₁₂	1	4	yes	complemented
378	C₂³	C₂²×D₃×C₉	1	2	yes	—
379	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
380	D₄	—	6	16	no	—
381	D₄	—	6	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	3	2	no	—
384	C₂×C₄	—	6	2	no	—
385	C₂×C₄	C₂²×D₃×C₉	1	4	yes	complemented
386	C₂×C₃	—	2	4	no	—
387	C₂×C₃	—	2	4	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	2	2	no	—
390	C₂×C₃	—	2	4	no	—
391	C₂×C₃	—	4	4	no	—
392	C₂×C₃	—	6	8	no	—
393	C₂×C₃	—	12	2	no	—
394	C₂×C₃	C₉×#120	1	4	yes	complemented
395	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
396	C₂×C₃	C₂²×D₄×C₉	1	2	yes	—
397	C₂×C₃	C₃×#882	1	4	yes	—
398	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
399	C₂×C₃	C₂×C₃×D₃×D₄	1	2	yes	—
400	D₃	—	2	8	no	—
401	D₃	—	4	2	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	3	8	no	—
405	C₂²	—	6	32	no	—
406	C₂²	—	6	4	no	—
407	C₂²	—	6	4	no	—
408	C₂²	—	6	16	no	—
409	C₂²	—	6	2	no	—
410	C₂²	—	6	4	no	—
411	C₂²	—	12	4	no	—
412	C₂²	C₂×C₉×D₁₂	1	2	yes	—
413	C₂²	C₂×C₉×D₁₂	1	4	yes	complemented
414	C₂²	D₃×D₄×C₉	1	4	yes	—
415	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	6	2	no	—
418	C₃	—	2	1	no	—
419	C₃	C₂×C₉×#120	1	1	yes	characteristic, complemented
420	C₃	C₂×C₃×#882	1	1	yes	characteristic
421	C₂	—	2	4	no	—
422	C₂	—	6	8	no	—
423	C₂	—	12	2	no	—
424	C₂	C₉×#882	1	4	yes	direct product factor
425	C₂	C₂²×C₉×D₁₂	1	1	yes	characteristic
426	C₂	C₂×D₃×D₄×C₉	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂×C₃×#882	C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#120
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₃×C₉	C₂	semidirect
2. C₂²×C₉×#67	C₂	semidirect
3. C₂²×C₉×D₁₂	C₂	semidirect
4. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₉×#882	C₂	direct (N × H)
13. C₂³×D₃×C₉	C₂²	semidirect
14. C₂³×D₃×C₉	C₂²	semidirect
15. C₂²×C₃×C₄×C₉	C₂²	semidirect
17. C₂×C₉×#67	C₂²	semidirect
18. C₂²×C₉×Dic₃	C₂²	semidirect
20. C₂×C₉×D₁₂	C₂²	semidirect
21. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
22. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₂×C₉×C₂²⋊C₄	D₃	semidirect
37. C₂³×C₃×C₉	D₄	semidirect
47. C₂²×D₃×C₉	D₄	semidirect
49. C₂²×D₃×C₉	C₂³	semidirect
51. C₂×C₃×C₄×C₉	C₂³	semidirect
54. C₂×C₉×Dic₃	C₂³	semidirect
57. C₂×#882	C₉	direct (N × H)
85. C₂²×C₄×C₉	C₂×D₃	semidirect
88. C₉×C₂²⋊C₄	C₂×D₃	semidirect
93. C₂²×C₃×C₉	C₂×D₄	semidirect
102. C₂×D₃×C₉	C₂×D₄	semidirect
106. C₂⁴×D₃	C₂×C₉	semidirect
109. C₂²×#67	C₂×C₉	semidirect
110. C₂²×D₁₂	C₂×C₉	semidirect
114. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
116. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
117. #882	C₂×C₉	direct (N × H)
153. C₂³×C₉	D₁₂	semidirect
163. C₂×C₄×C₉	C₂²×D₃	semidirect
166. C₂×C₃×C₉	#120	semidirect
182. C₂³×D₃	C₂²×C₉	semidirect
183. C₂³×D₃	C₂²×C₉	semidirect
190. C₂²×C₃×C₄	C₂²×C₉	semidirect
193. C₂×#67	C₂²×C₉	semidirect
194. C₂²×Dic₃	C₂²×C₉	semidirect
196. C₂×D₁₂	C₂²×C₉	semidirect
199. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
201. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
235. C₂²×C₉	C₂×D₁₂	semidirect
246. C₂×C₂²⋊C₄	D₃×C₉	semidirect
247. C₃×C₉	C₂×#120	semidirect
264. C₂³×C₃	D₄×C₉	semidirect
277. C₂²×D₃	D₄×C₉	semidirect
279. C₂²×D₃	C₂³×C₉	semidirect
288. C₂×C₃×C₄	C₂³×C₉	semidirect
292. C₂×Dic₃	C₂³×C₉	semidirect
307. C₂×C₉	#882	direct (N × H)
321. C₂²×C₄	C₂×D₃×C₉	semidirect
323. C₂²⋊C₄	C₂×D₃×C₉	semidirect
344. C₂²×C₃	C₂×D₄×C₉	semidirect
357. C₂×D₃	C₂×D₄×C₉	semidirect
365. C₉	C₂×#882	direct (N × H)
377. C₂³	C₉×D₁₂	semidirect
385. C₂×C₄	C₂²×D₃×C₉	semidirect
394. C₂×C₃	C₉×#120	semidirect
413. C₂²	C₂×C₉×D₁₂	semidirect
419. C₃	C₂×C₉×#120	semidirect
424. C₂	C₉×#882	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₃×C₉	2
C₂²×C₉×#67	2
C₂²×C₉×D₁₂	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₉×#882	2
C₂×C₃×#882	3
C₂×C₉×#120	3

Subgroups — C2×C9×#882 #13152347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#882 #13152347