Subgroups — C₂×C₉×#805 #13142399

Order 1728.

618 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#805	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×#805	C₃	1	1	yes	maximal, characteristic
6	C₂×C₉×#104	—	3	1	no	maximal
7	C₂²×C₃×C₄×C₉	—	2	1	no	—
8	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₉×#67	—	2	1	no	—
10	C₉×#235	—	2	1	no	—
11	C₉×#235	—	2	1	no	—
12	C₉×#235	C₄	1	2	yes	complemented
13	C₉×#235	C₂²	1	2	yes	—
14	C₂×C₉×D₁₂	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×D₃×C₉	—	2	1	no	—
16	C₂×C₉×Dic₆	C₄	1	1	yes	characteristic, complemented
17	C₃×C₄²×C₉	—	2	1	no	—
18	C₃×C₄²×C₉	C₂²	1	2	yes	complemented
19	C₉×#208	—	2	1	no	—
20	C₉×#208	C₂²	1	2	yes	complemented
21	C₂×C₉×C₃⋊C₈	—	2	1	no	—
22	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃²×C₄²	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×#208	C₂×C₃	1	1	yes	characteristic
25	C₂×C₉×#41	—	3	1	no	—
26	C₃×#805	C₂×C₃	1	4	yes	—
27	C₂×C₉×M₁₆	—	3	1	no	—
28	C₂×C₄²×C₉	—	2	1	no	—
29	C₂×C₄²×C₉	D₃	1	1	yes	characteristic, complemented
30	C₉×#104	—	3	4	no	—
31	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
32	C₂²×D₃×C₉	—	2	1	no	—
33	C₂×C₃×C₄×C₉	—	2	4	no	—
34	C₂×C₃×C₄×C₉	—	2	2	no	—
35	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
38	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
39	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
41	C₉×#67	—	2	2	no	—
42	C₉×#67	—	2	2	no	—
43	C₂×C₉×Dic₃	—	2	1	no	—
44	C₉×D₁₂	—	2	1	no	—
45	C₉×D₁₂	C₂×C₄	1	2	yes	complemented
46	C₄×D₃×C₉	—	2	2	no	—
47	C₄×D₃×C₉	—	2	2	no	—
48	C₉×Dic₆	—	2	1	no	—
49	C₉×Dic₆	C₂×C₄	1	2	yes	complemented
50	C₉×C₃⋊C₈	—	2	2	no	—
51	C₂×C₃×#104	—	3	1	no	—
52	C₂×#805	C₉	1	1	yes	characteristic, direct product factor
53	C₂²×C₃²×C₄	—	2	1	no	—
54	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₃×#67	—	2	1	no	—
56	C₃×#235	—	2	1	no	—
57	C₃×#235	—	2	1	no	—
58	C₃×#235	C₃×C₄	1	2	yes	—
59	C₃×#235	C₂²×C₃	1	2	yes	—
60	C₂×C₃×D₁₂	C₃×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄×D₃	—	2	1	no	—
62	C₂×C₃×Dic₆	C₃×C₄	1	1	yes	characteristic
63	C₃²×C₄²	—	2	1	no	—
64	C₃²×C₄²	C₂²×C₃	1	2	yes	—
65	C₃×#208	—	2	1	no	—
66	C₃×#208	C₂²×C₃	1	2	yes	—
67	C₂×C₃×C₃⋊C₈	—	2	1	no	—
68	C₉×#41	—	3	2	no	—
69	C₉×#41	—	3	2	no	—
70	C₉×#41	—	6	1	no	—
71	C₉×#41	—	6	1	no	—
72	C₂×Q₈×C₉	—	3	1	no	—
73	C₂×D₄×C₉	—	3	1	no	—
74	C₂×D₄×C₉	—	6	1	no	—
75	C₂²×C₄×C₉	—	2	2	no	—
76	C₂²×C₄×C₉	—	2	1	no	—
77	C₂²×C₄×C₉	—	2	1	no	—
78	C₂²×C₄×C₉	—	6	1	no	—
79	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
80	C₉×M₁₆	—	3	2	no	—
81	C₉×M₁₆	—	6	1	no	—
82	C₂×C₈×C₉	—	6	1	no	—
83	C₄²×C₉	—	2	2	no	—
84	C₄²×C₉	—	2	2	no	—
85	C₄²×C₉	—	2	1	no	—
86	C₄²×C₉	C₂×D₃	1	2	yes	complemented
87	C₂²×C₃×C₉	—	2	2	no	—
88	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
91	C₂×D₃×C₉	—	2	2	no	—
92	C₂×D₃×C₉	—	4	2	no	—
93	C₃×C₄×C₉	—	2	4	no	—
94	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
97	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
98	C₉×Dic₃	—	2	2	no	—
99	C₂×C₃×#41	—	3	1	no	—
100	C₂×#235	C₂×C₉	1	1	yes	characteristic
101	C₂×C₃×M₁₆	—	3	1	no	—
102	C₂×C₃×C₄²	—	2	1	no	—
103	C₂×C₃×C₄²	C₂×C₉	1	1	yes	characteristic, complemented
104	C₂×C₃×C₄²	C₃×D₃	1	1	yes	characteristic
105	C₂×#208	C₂×C₉	1	1	yes	characteristic, complemented
106	C₃×#104	—	3	4	no	—
107	#805	C₂×C₉	1	4	yes	direct product factor
108	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
109	C₂²×C₃×D₃	—	2	1	no	—
110	C₂×C₃²×C₄	—	2	4	no	—
111	C₂×C₃²×C₄	—	2	2	no	—
112	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
114	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
117	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
118	C₃×#67	—	2	2	no	—
119	C₃×#67	—	2	2	no	—
120	C₂×C₃×Dic₃	—	2	1	no	—
121	C₃×D₁₂	—	2	1	no	—
122	C₃×D₁₂	C₂×C₃×C₄	1	2	yes	—
123	C₃×C₄×D₃	—	2	2	no	—
124	C₃×C₄×D₃	—	2	2	no	—
125	C₃×Dic₆	—	2	1	no	—
126	C₃×Dic₆	C₂×C₃×C₄	1	2	yes	—
127	C₂³×C₉	—	2	1	no	—
128	C₂³×C₉	—	6	1	no	—
129	C₂³×C₉	#67	1	1	yes	characteristic
130	C₃×C₃⋊C₈	—	2	2	no	—
131	Q₈×C₉	—	3	2	no	—
132	Q₈×C₉	—	6	1	no	—
133	D₄×C₉	—	3	2	no	—
134	D₄×C₉	—	6	2	no	—
135	D₄×C₉	—	6	2	no	—
136	D₄×C₉	—	6	1	no	—
137	C₂×C₄×C₉	—	2	4	no	—
138	C₂×C₄×C₉	—	2	8	no	—
139	C₂×C₄×C₉	—	2	4	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	1	no	—
147	C₂×C₄×C₉	—	6	1	no	—
148	C₂×C₄×C₉	—	6	2	no	—
149	C₂×C₄×C₉	—	6	2	no	—
150	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
151	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
152	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
153	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
154	C₂×C₄×C₉	#67	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
156	C₈×C₉	—	6	2	no	—
157	C₂×#104	—	3	1	no	Sylow
158	C₂×C₃×C₉	—	2	1	no	—
159	C₂×C₃×C₉	—	2	1	no	—
160	C₂×C₃×C₉	#104	1	2	yes	complemented
161	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	D₃×C₉	—	4	2	no	—
163	C₃×#41	—	3	2	no	—
164	C₃×#41	—	3	2	no	—
165	C₃×#41	—	6	1	no	—
166	C₃×#41	—	6	1	no	—
167	C₂×C₃×Q₈	—	3	1	no	—
168	C₂×C₃×D₄	—	3	1	no	—
169	C₂×C₃×D₄	—	6	1	no	—
170	C₂²×C₃×C₄	—	2	2	no	—
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	2	1	no	—
174	C₂²×C₃×C₄	—	6	1	no	—
175	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂×#67	—	2	1	no	—
178	#235	—	2	1	no	—
179	#235	—	2	1	no	—
180	#235	C₄×C₉	1	2	yes	complemented
181	#235	C₂²×C₉	1	2	yes	—
182	C₂×D₁₂	C₄×C₉	1	1	yes	characteristic, complemented
183	C₂×C₄×D₃	—	2	1	no	—
184	C₂×Dic₆	C₄×C₉	1	1	yes	characteristic, complemented
185	C₃×M₁₆	—	3	2	no	—
186	C₃×M₁₆	—	6	1	no	—
187	C₂×C₃×C₈	—	6	1	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₃×C₄²	—	2	1	no	—
190	C₃×C₄²	—	2	1	no	—
191	C₃×C₄²	—	2	2	no	—
192	C₃×C₄²	C₂²×C₉	1	2	yes	complemented
193	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
194	#208	—	2	1	no	—
195	#208	C₂²×C₉	1	2	yes	complemented
196	C₂×C₃⋊C₈	—	2	1	no	—
197	C₂²×C₃²	—	2	2	no	—
198	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
201	C₂×C₃×D₃	—	2	2	no	—
202	C₂×C₃×D₃	—	4	2	no	—
203	C₃²×C₄	—	2	4	no	—
204	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
205	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
206	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
207	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
208	C₃×Dic₃	—	2	2	no	—
209	C₂²×C₉	—	2	4	no	—
210	C₂²×C₉	—	2	2	no	—
211	C₂²×C₉	—	2	1	no	—
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	2	1	no	—
214	C₂²×C₉	—	6	2	no	—
215	C₂²×C₉	—	12	2	no	—
216	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
217	C₂²×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
218	C₂²×C₉	C₂×#67	1	1	yes	characteristic
219	C₄×C₉	—	2	8	no	—
220	C₄×C₉	—	2	4	no	—
221	C₄×C₉	—	2	1	no	—
222	C₄×C₉	—	2	1	no	—
223	C₄×C₉	—	2	1	no	—
224	C₄×C₉	—	2	1	no	—
225	C₄×C₉	—	6	2	no	—
226	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
227	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
228	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
229	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
230	C₂×#41	—	3	1	no	—
231	C₂×M₁₆	—	3	1	no	—
232	C₂×C₄²	D₃×C₉	1	1	yes	characteristic, complemented
233	#104	—	3	4	no	—
234	C₃×C₉	C₂×#104	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₃	—	2	1	no	—
236	C₂³×C₃	—	6	1	no	—
237	C₂³×C₃	D₄×C₉	1	1	yes	characteristic
238	C₂³×C₃	C₃×#67	1	1	yes	characteristic
239	C₂²×D₃	—	2	1	no	—
240	C₃×Q₈	—	3	2	no	—
241	C₃×Q₈	—	6	1	no	—
242	C₃×D₄	—	3	2	no	—
243	C₃×D₄	—	6	2	no	—
244	C₃×D₄	—	6	2	no	—
245	C₃×D₄	—	6	1	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	8	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	6	1	no	—
259	C₂×C₃×C₄	—	6	2	no	—
260	C₂×C₃×C₄	—	6	2	no	—
261	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
263	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
264	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
265	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
267	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
268	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
269	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
270	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
271	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
273	#67	—	2	2	no	—
274	#67	—	2	2	no	—
275	C₂×Dic₃	—	2	1	no	—
276	D₁₂	—	2	1	no	—
277	D₁₂	C₂×C₄×C₉	1	2	yes	complemented
278	C₄×D₃	—	2	2	no	—
279	C₄×D₃	—	2	2	no	—
280	Dic₆	—	2	1	no	—
281	Dic₆	C₂×C₄×C₉	1	2	yes	complemented
282	C₃×C₈	—	6	2	no	—
283	C₃⋊C₈	—	2	2	no	—
284	C₂×C₃²	—	2	1	no	—
285	C₂×C₃²	—	2	1	no	—
286	C₂×C₃²	C₃×#104	1	2	yes	—
287	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
288	C₃×D₃	—	4	2	no	—
289	C₂×C₉	—	2	2	no	—
290	C₂×C₉	—	2	2	no	—
291	C₂×C₉	—	2	1	no	—
292	C₂×C₉	—	2	1	no	—
293	C₂×C₉	—	2	1	no	—
294	C₂×C₉	—	2	2	no	—
295	C₂×C₉	—	12	2	no	—
296	C₂×C₉	#805	1	2	yes	direct product factor
297	C₂×C₉	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
298	#41	—	3	2	no	—
299	#41	—	3	2	no	—
300	#41	—	6	1	no	—
301	#41	—	6	1	no	—
302	C₂×Q₈	—	3	1	no	—
303	C₂×D₄	—	3	1	no	—
304	C₂×D₄	—	6	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	6	1	no	—
307	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
308	M₁₆	—	3	2	no	—
309	M₁₆	—	6	1	no	—
310	C₂×C₈	—	6	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	C₂×D₃×C₉	1	2	yes	complemented
313	C₂²×C₃	—	2	4	no	—
314	C₂²×C₃	—	2	2	no	—
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	6	2	no	—
320	C₂²×C₃	—	12	2	no	—
321	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₃	C₉×C₂²⋊C₄	1	1	yes	characteristic
323	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
324	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
325	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
326	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
327	C₂×D₃	—	2	2	no	—
328	C₂×D₃	—	4	2	no	—
329	C₃×C₄	—	2	4	no	—
330	C₃×C₄	—	2	8	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	6	2	no	—
337	C₃×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
338	C₃×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
339	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
340	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
341	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
342	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
344	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
345	Dic₃	—	2	2	no	—
346	C₃²	C₂×C₃×#104	1	1	yes	characteristic
347	C₉	—	2	1	no	—
348	C₉	C₂×#805	1	1	yes	characteristic, direct product factor
349	C₂³	—	6	1	no	—
350	C₂³	C₉×#67	1	1	yes	characteristic
351	Q₈	—	3	2	no	—
352	Q₈	—	6	1	no	—
353	D₄	—	3	2	no	—
354	D₄	—	6	2	no	—
355	D₄	—	6	2	no	—
356	D₄	—	6	1	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	6	1	no	—
360	C₂×C₄	—	6	2	no	—
361	C₂×C₄	—	6	2	no	—
362	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
363	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
364	C₂×C₄	C₉×D₁₂	1	1	yes	characteristic
365	C₂×C₄	C₉×D₁₂	1	1	yes	characteristic
366	C₂×C₄	C₉×#67	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
368	C₈	—	6	2	no	—
369	C₂×C₃	—	2	2	no	—
370	C₂×C₃	—	2	2	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	1	no	—
376	C₂×C₃	—	2	2	no	—
377	C₂×C₃	—	12	2	no	—
378	C₂×C₃	C₉×#104	1	2	yes	complemented
379	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
380	C₂×C₃	C₃×#805	1	2	yes	—
381	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
382	D₃	—	4	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	6	2	no	—
385	C₂²	—	12	2	no	—
386	C₂²	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
387	C₂²	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
388	C₂²	C₂×C₉×#67	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	6	2	no	—
391	C₄	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
392	C₄	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
393	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
394	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
395	C₃	—	2	1	no	—
396	C₃	C₂×C₉×#104	1	1	yes	characteristic, complemented
397	C₃	C₂×C₃×#805	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	12	2	no	—
401	C₂	C₉×#805	1	2	yes	direct product factor
402	C₂	C₂×C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	D₁₂
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃×C₄²×C₉	C₂
socle	C₂²×C₃²	C₃×C₂²⋊C₄
prime radical	C₂×C₃×#235	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₄²×C₉	D₃
hypocenter	C₃	C₂×C₉×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂²×C₄×C₉ ◁ C₂×C₄²×C₉

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄²×C₉	C₂	semidirect
3. C₂×C₉×#208	C₂	semidirect
4. C₉×#805	C₂	direct (N × H)
12. C₉×#235	C₄	semidirect
14. C₂×C₉×D₁₂	C₄	semidirect
16. C₂×C₉×Dic₆	C₄	semidirect
18. C₃×C₄²×C₉	C₂²	semidirect
20. C₉×#208	C₂²	semidirect
29. C₂×C₄²×C₉	D₃	semidirect
45. C₉×D₁₂	C₂×C₄	semidirect
49. C₉×Dic₆	C₂×C₄	semidirect
52. C₂×#805	C₉	direct (N × H)
86. C₄²×C₉	C₂×D₃	semidirect
103. C₂×C₃×C₄²	C₂×C₉	semidirect
105. C₂×#208	C₂×C₉	semidirect
107. #805	C₂×C₉	direct (N × H)
160. C₂×C₃×C₉	#104	semidirect
180. #235	C₄×C₉	semidirect
182. C₂×D₁₂	C₄×C₉	semidirect
184. C₂×Dic₆	C₄×C₉	semidirect
192. C₃×C₄²	C₂²×C₉	semidirect
195. #208	C₂²×C₉	semidirect
232. C₂×C₄²	D₃×C₉	semidirect
234. C₃×C₉	C₂×#104	semidirect
277. D₁₂	C₂×C₄×C₉	semidirect
281. Dic₆	C₂×C₄×C₉	semidirect
296. C₂×C₉	#805	direct (N × H)
312. C₄²	C₂×D₃×C₉	semidirect
348. C₉	C₂×#805	direct (N × H)
378. C₂×C₃	C₉×#104	semidirect
396. C₃	C₂×C₉×#104	semidirect
401. C₂	C₉×#805	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×C₉×#235	2
C₂×C₃×C₄²×C₉	2
C₂×C₉×#208	2
C₉×#805	2
C₂×C₃×#805	3
C₂×C₉×#104	3

Subgroups — C2×C9×#805 #13142399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#805 #13142399