Subgroups — C₃×C₉×#386 #13144916

Order 1728.

1430 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₃×C₉	C₂³
commutator	C₂²	C₂²×C₃×C₄×C₉
Frattini, cosocle	C₂³×C₃	C₂³×C₃²
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂²×C₃²×D₄	C₂×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₃×C₄×C₉	C₂	semidirect
3. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
4. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
5. C₃×C₉×#95	C₂	semidirect
7. C₉×#386	C₃	direct (N × H)
12. C₂×C₃×D₄×C₉	C₄	semidirect
25. C₂³×C₄×C₉	C₂×C₃	semidirect
27. C₂×C₉×C₂²⋊C₄	C₂×C₃	semidirect
28. C₂×C₉×C₂²⋊C₄	C₂×C₃	semidirect
29. C₉×#95	C₂×C₃	semidirect
37. C₂³×C₃×C₉	C₂×C₄	semidirect
50. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
51. C₂×C₃×C₄×C₉	D₄	semidirect
52. C₃×#386	C₉	direct (N × H)
70. C₂×D₄×C₉	C₃×C₄	semidirect
87. C₂²×C₃×C₉	C₂²⋊C₄	semidirect
98. C₂³×C₃×C₄	C₂×C₉	semidirect
100. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
101. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
104. C₃×#95	C₂×C₉	semidirect
135. C₂³×C₉	C₂×C₃×C₄	semidirect
148. C₂×C₄×C₉	C₂×C₃×C₄	semidirect
149. C₂×C₄×C₉	C₃×D₄	semidirect
150. #386	C₃×C₉	direct (N × H)
166. C₂×C₃×D₄	C₄×C₉	semidirect
209. C₂²×C₉	C₃×C₂²⋊C₄	semidirect
219. C₂³×C₄	C₂×C₃×C₉	semidirect
220. C₂×C₂²⋊C₄	C₂×C₃×C₉	semidirect
221. C₂×C₂²⋊C₄	C₂×C₃×C₉	semidirect
222. #95	C₂×C₃×C₉	semidirect
223. C₃×C₉	#386	direct (N × H)
237. C₂³×C₃	C₂×C₄×C₉	semidirect
264. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
265. C₂×C₃×C₄	D₄×C₉	semidirect
286. C₂×D₄	C₃×C₄×C₉	semidirect
312. C₂²×C₃	C₉×C₂²⋊C₄	semidirect
331. C₉	C₃×#386	direct (N × H)
339. C₂³	C₂×C₃×C₄×C₉	semidirect
352. C₂×C₄	C₂×C₃×C₄×C₉	semidirect
353. C₂×C₄	C₃×D₄×C₉	semidirect
377. C₂²	C₃×C₉×C₂²⋊C₄	semidirect
386. C₃	C₉×#386	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×C₃×D₄×C₉	2
C₂³×C₃×C₄×C₉	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₃×C₉×#95	2
C₃²×#386	3
C₉×#386	3

Subgroups — C3×C9×#386 #13144916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#386 #13144916