Subgroups — C₉×#5006 #13142684

Order 1728.

550 conjugacy classes of subgroups.

The subgroup lattice has 402 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	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#806	C₂	1	4	yes	maximal, complemented
5	C₃×#5006	C₃	1	1	yes	maximal, characteristic
6	C₉×#410	—	3	1	no	maximal
7	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₉×#67	C₂²	1	2	yes	—
9	C₉×#235	—	2	1	no	—
10	C₉×#235	—	2	1	no	—
11	C₉×#235	—	2	1	no	—
12	C₉×#235	—	2	1	no	—
13	C₂×C₉×D₁₂	C₄	1	1	yes	characteristic, complemented
14	C₂×C₄×D₃×C₉	C₄	1	2	yes	complemented
15	C₂×C₉×Dic₆	C₄	1	1	yes	characteristic, complemented
16	C₃×C₉×C₄⋊C₄	—	2	1	no	—
17	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₃×C₄²×C₉	—	2	1	no	—
19	C₉×#217	C₂²	1	2	yes	—
20	C₉×C₄⋊Dic₃	—	2	1	no	—
21	C₄×C₉×Dic₃	—	2	1	no	—
22	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
23	C₃²×#117	C₂×C₃	1	1	yes	characteristic
24	C₃×#926	C₂×C₃	1	1	yes	characteristic
25	C₂×C₉×#41	—	3	1	no	—
26	C₃×#806	C₂×C₃	1	4	yes	—
27	C₉×#117	—	2	1	no	—
28	C₉×#117	—	3	1	no	—
29	C₉×#117	D₃	1	1	yes	characteristic, complemented
30	C₉×#99	—	3	4	no	—
31	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
32	C₂²×D₃×C₉	C₂×C₄	1	2	yes	—
33	C₂×C₃×C₄×C₉	—	2	2	no	—
34	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄×C₉	D₄	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	C₉×#67	—	2	2	no	—
41	C₉×#67	—	2	2	no	—
42	C₂×C₉×Dic₃	—	2	2	no	—
43	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
44	C₉×D₁₂	—	2	1	no	—
45	C₉×D₁₂	—	2	1	no	—
46	C₄×D₃×C₉	—	2	2	no	—
47	C₄×D₃×C₉	—	2	2	no	—
48	C₉×Dic₆	—	2	1	no	—
49	C₉×Dic₆	—	2	1	no	—
50	C₃×#410	—	3	1	no	—
51	#5006	C₉	1	1	yes	characteristic, direct product factor
52	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
53	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
54	C₃×#235	—	2	1	no	—
55	C₃×#235	—	2	1	no	—
56	C₃×#235	—	2	1	no	—
57	C₃×#235	—	2	1	no	—
58	C₂×C₃×D₁₂	C₃×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₃	C₃×C₄	1	2	yes	—
60	C₂×C₃×Dic₆	C₃×C₄	1	1	yes	characteristic
61	C₃²×C₄⋊C₄	—	2	1	no	—
62	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
63	C₃²×C₄²	—	2	1	no	—
64	C₃×#217	C₂²×C₃	1	2	yes	—
65	C₃×C₄⋊Dic₃	—	2	1	no	—
66	C₃×C₄×Dic₃	—	2	1	no	—
67	C₉×#41	—	6	1	no	—
68	C₉×#41	—	6	1	no	—
69	C₉×#41	—	6	1	no	—
70	C₉×#41	—	6	1	no	—
71	C₂×Q₈×C₉	—	3	1	no	—
72	C₂×D₄×C₉	—	3	2	no	—
73	C₂×D₄×C₉	—	3	1	no	—
74	C₂²×C₄×C₉	—	2	1	no	—
75	C₂²×C₄×C₉	—	3	2	no	—
76	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
77	C₉×C₄⋊C₄	—	2	2	no	—
78	C₉×C₄⋊C₄	—	2	1	no	—
79	C₉×C₄⋊C₄	—	6	1	no	—
80	C₉×C₂²⋊C₄	—	2	2	no	—
81	C₉×C₂²⋊C₄	—	3	2	no	—
82	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
83	C₄²×C₉	—	2	2	no	—
84	C₄²×C₉	—	2	1	no	—
85	C₄²×C₉	—	6	1	no	—
86	C₂²×C₃×C₉	—	4	1	no	—
87	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₃×C₉	—	2	2	no	—
91	C₂×D₃×C₉	—	4	2	no	—
92	C₃×C₄×C₉	—	4	2	no	—
93	C₃×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
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	C₉×Dic₃	—	2	2	no	—
98	C₉×Dic₃	—	4	2	no	—
99	C₂×C₃×#41	—	3	1	no	—
100	C₂×#235	C₂×C₉	1	1	yes	characteristic
101	C₃×#117	—	2	1	no	—
102	C₃×#117	—	3	1	no	—
103	C₃×#117	C₂×C₉	1	1	yes	characteristic, complemented
104	C₃×#117	C₃×D₃	1	1	yes	characteristic
105	#926	C₂×C₉	1	1	yes	characteristic, complemented
106	C₃×#99	—	3	4	no	—
107	#806	C₂×C₉	1	4	yes	complemented
108	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
109	C₂²×C₃×D₃	C₂×C₃×C₄	1	2	yes	—
110	C₂×C₃²×C₄	—	2	2	no	—
111	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₃×D₄	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	C₃×#67	—	2	2	no	—
118	C₃×#67	—	2	2	no	—
119	C₂×C₃×Dic₃	—	2	2	no	—
120	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
121	C₃×D₁₂	—	2	1	no	—
122	C₃×D₁₂	—	2	1	no	—
123	C₃×C₄×D₃	—	2	2	no	—
124	C₃×C₄×D₃	—	2	2	no	—
125	C₃×Dic₆	—	2	1	no	—
126	C₃×Dic₆	—	2	1	no	—
127	C₂³×C₉	—	2	1	no	—
128	C₂³×C₉	—	3	2	no	—
129	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
130	Q₈×C₉	—	6	1	no	—
131	Q₈×C₉	—	6	1	no	—
132	D₄×C₉	—	6	2	no	—
133	D₄×C₉	—	6	2	no	—
134	D₄×C₉	—	6	1	no	—
135	D₄×C₉	—	6	1	no	—
136	C₂×C₄×C₉	—	2	4	no	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	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	—	3	2	no	—
145	C₂×C₄×C₉	—	6	2	no	—
146	C₂×C₄×C₉	—	6	2	no	—
147	C₂×C₄×C₉	—	6	2	no	—
148	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
149	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
150	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
151	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
152	C₂×C₄×C₉	#67	1	1	yes	characteristic
153	C₂×C₄×C₉	#67	1	1	yes	characteristic
154	#410	—	3	1	no	Sylow
155	C₂×C₃×C₉	—	2	1	no	—
156	C₂×C₃×C₉	—	2	1	no	—
157	C₂×C₃×C₉	—	2	1	no	—
158	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	D₃×C₉	—	4	2	no	—
160	C₃×#41	—	6	1	no	—
161	C₃×#41	—	6	1	no	—
162	C₃×#41	—	6	1	no	—
163	C₃×#41	—	6	1	no	—
164	C₂×C₃×Q₈	—	3	1	no	—
165	C₂×C₃×D₄	—	3	2	no	—
166	C₂×C₃×D₄	—	3	1	no	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	—	3	2	no	—
169	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
171	C₂×#67	C₂²×C₉	1	2	yes	—
172	#235	—	2	1	no	—
173	#235	—	2	1	no	—
174	#235	—	2	1	no	—
175	#235	—	2	1	no	—
176	C₂×D₁₂	C₄×C₉	1	1	yes	characteristic, complemented
177	C₂×C₄×D₃	C₄×C₉	1	2	yes	complemented
178	C₂×Dic₆	C₄×C₉	1	1	yes	characteristic, complemented
179	C₃×C₄⋊C₄	—	2	2	no	—
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	6	1	no	—
183	C₃×C₂²⋊C₄	—	2	2	no	—
184	C₃×C₂²⋊C₄	—	3	2	no	—
185	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
186	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
187	C₃×C₄²	—	2	2	no	—
188	C₃×C₄²	—	2	1	no	—
189	C₃×C₄²	—	2	1	no	—
190	C₃×C₄²	—	6	1	no	—
191	#217	C₂²×C₉	1	2	yes	—
192	C₄⋊Dic₃	—	2	1	no	—
193	C₄×Dic₃	—	2	1	no	—
194	C₂²×C₃²	—	4	1	no	—
195	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
196	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
197	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
198	C₂×C₃×D₃	—	2	2	no	—
199	C₂×C₃×D₃	—	4	2	no	—
200	C₃²×C₄	—	4	2	no	—
201	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
202	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
203	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
204	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
205	C₃×Dic₃	—	2	2	no	—
206	C₃×Dic₃	—	4	2	no	—
207	C₂²×C₉	—	2	1	no	—
208	C₂²×C₉	—	2	1	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	—	4	1	no	—
211	C₂²×C₉	—	4	2	no	—
212	C₂²×C₉	—	6	2	no	—
213	C₂²×C₉	—	12	2	no	—
214	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
215	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
216	C₂²×C₉	C₂×#67	1	1	yes	characteristic
217	C₄×C₉	—	2	1	no	—
218	C₄×C₉	—	2	1	no	—
219	C₄×C₉	—	2	1	no	—
220	C₄×C₉	—	2	1	no	—
221	C₄×C₉	—	4	4	no	—
222	C₄×C₉	—	4	2	no	—
223	C₄×C₉	—	6	2	no	—
224	C₄×C₉	—	12	2	no	—
225	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
226	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
227	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
228	C₄×C₉	(C₂×D₃)⋊C₄	1	1	yes	characteristic
229	C₂×#41	—	3	1	no	—
230	#117	—	3	1	no	—
231	#117	D₃×C₉	1	1	yes	characteristic, complemented
232	#99	—	3	4	no	—
233	C₃×C₉	#410	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₃	—	2	1	no	—
235	C₂³×C₃	—	3	2	no	—
236	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
237	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
238	C₂²×D₃	C₂×C₄×C₉	1	2	yes	—
239	C₃×Q₈	—	6	1	no	—
240	C₃×Q₈	—	6	1	no	—
241	C₃×D₄	—	6	2	no	—
242	C₃×D₄	—	6	2	no	—
243	C₃×D₄	—	6	1	no	—
244	C₃×D₄	—	6	1	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	3	2	no	—
255	C₂×C₃×C₄	—	6	2	no	—
256	C₂×C₃×C₄	—	6	2	no	—
257	C₂×C₃×C₄	—	6	2	no	—
258	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
260	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
261	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
262	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
263	C₂×C₃×C₄	D₄×C₉	1	1	yes	characteristic
264	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
265	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
266	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
267	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
268	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
269	C₂×C₃×C₄	C₃×#67	1	1	yes	characteristic
270	#67	—	2	2	no	—
271	#67	—	2	2	no	—
272	C₂×Dic₃	—	2	2	no	—
273	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
274	D₁₂	—	2	1	no	—
275	D₁₂	—	2	1	no	—
276	C₄×D₃	—	2	2	no	—
277	C₄×D₃	—	2	2	no	—
278	Dic₆	—	2	1	no	—
279	Dic₆	—	2	1	no	—
280	C₂×C₃²	—	2	1	no	—
281	C₂×C₃²	—	2	1	no	—
282	C₂×C₃²	—	2	1	no	—
283	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
284	C₃×D₃	—	4	2	no	—
285	C₂×C₉	—	2	2	no	—
286	C₂×C₉	—	2	1	no	—
287	C₂×C₉	—	2	1	no	—
288	C₂×C₉	—	2	1	no	—
289	C₂×C₉	—	2	1	no	—
290	C₂×C₉	—	4	1	no	—
291	C₂×C₉	—	4	1	no	—
292	C₂×C₉	—	12	2	no	—
293	C₂×C₉	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
294	#41	—	6	1	no	—
295	#41	—	6	1	no	—
296	#41	—	6	1	no	—
297	#41	—	6	1	no	—
298	C₂×Q₈	—	3	1	no	—
299	C₂×D₄	—	3	2	no	—
300	C₂×D₄	—	3	1	no	—
301	C₂²×C₄	—	3	2	no	—
302	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	6	1	no	—
305	C₂²⋊C₄	—	3	2	no	—
306	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
307	C₄²	—	2	1	no	—
308	C₄²	—	6	1	no	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	4	1	no	—
313	C₂²×C₃	—	4	1	no	—
314	C₂²×C₃	—	4	2	no	—
315	C₂²×C₃	—	6	2	no	—
316	C₂²×C₃	—	12	2	no	—
317	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
318	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
319	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
320	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
321	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
322	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
323	C₂×D₃	—	2	2	no	—
324	C₂×D₃	—	4	2	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	4	2	no	—
330	C₃×C₄	—	4	4	no	—
331	C₃×C₄	—	4	2	no	—
332	C₃×C₄	—	6	2	no	—
333	C₃×C₄	—	12	2	no	—
334	C₃×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
335	C₃×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
336	C₃×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
337	C₃×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
338	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
339	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
340	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
341	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
342	Dic₃	—	2	2	no	—
343	Dic₃	—	4	2	no	—
344	C₃²	C₃×#410	1	1	yes	characteristic
345	C₉	—	2	1	no	—
346	C₉	#5006	1	1	yes	characteristic, direct product factor
347	C₂³	—	3	2	no	—
348	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
349	Q₈	—	6	1	no	—
350	Q₈	—	6	1	no	—
351	D₄	—	6	2	no	—
352	D₄	—	6	2	no	—
353	D₄	—	6	1	no	—
354	D₄	—	6	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	3	2	no	—
357	C₂×C₄	—	6	2	no	—
358	C₂×C₄	—	6	2	no	—
359	C₂×C₄	—	6	2	no	—
360	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
361	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
362	C₂×C₄	C₉×D₁₂	1	1	yes	characteristic
363	C₂×C₄	C₉×D₁₂	1	1	yes	characteristic
364	C₂×C₄	C₉×#67	1	1	yes	characteristic
365	C₂×C₄	C₉×#67	1	1	yes	characteristic
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	2	1	no	—
368	C₂×C₃	—	2	1	no	—
369	C₂×C₃	—	2	1	no	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	4	1	no	—
375	C₂×C₃	—	4	1	no	—
376	C₂×C₃	—	12	2	no	—
377	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
378	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
379	D₃	—	4	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	6	2	no	—
382	C₂²	—	12	2	no	—
383	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
384	C₂²	C₂×C₉×D₁₂	1	1	yes	characteristic
385	C₂²	C₂×C₉×#67	1	1	yes	characteristic
386	C₄	—	4	2	no	—
387	C₄	—	6	2	no	—
388	C₄	—	12	2	no	—
389	C₄	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
390	C₄	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
391	C₄	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
392	C₄	C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic
393	C₃	—	2	1	no	—
394	C₃	C₉×#410	1	1	yes	characteristic, complemented
395	C₃	C₃×#5006	1	1	yes	characteristic
396	C₂	—	2	1	no	—
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	12	2	no	—
400	C₂	C₂×C₉×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₃×C₉×#117	C₂
socle	C₂×C₃²	C₂×C₃×C₂²⋊C₄
prime radical	C₂×C₃×#235	C₂×C₃
cosocle	C₂³×C₃²	C₂³×C₃
hypercenter	C₉×#117	D₃
hypocenter	C₃	C₉×#410
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ C₉×#117

Complements

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

N	H ≅ G/N	type
2. C₃×C₉×#117	C₂	semidirect
3. C₉×#926	C₂	semidirect
4. C₉×#806	C₂	semidirect
13. C₂×C₉×D₁₂	C₄	semidirect
14. C₂×C₄×D₃×C₉	C₄	semidirect
15. C₂×C₉×Dic₆	C₄	semidirect
29. C₉×#117	D₃	semidirect
51. #5006	C₉	direct (N × H)
103. C₃×#117	C₂×C₉	semidirect
105. #926	C₂×C₉	semidirect
107. #806	C₂×C₉	semidirect
176. C₂×D₁₂	C₄×C₉	semidirect
177. C₂×C₄×D₃	C₄×C₉	semidirect
178. C₂×Dic₆	C₄×C₉	semidirect
231. #117	D₃×C₉	semidirect
233. C₃×C₉	#410	semidirect
346. C₉	#5006	direct (N × H)
394. C₃	C₉×#410	semidirect

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
C₃×C₉×#117	2
C₉×#926	2
C₉×#806	2
C₃×#5006	3
C₉×#410	3

Subgroups — C9×#5006 #13142684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5006 #13142684