Subgroups — C₄×C₉×#235 #13152291

Order 1728.

1038 conjugacy classes of subgroups.

The subgroup lattice has 390 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	C₄×C₉×#67	C₂	1	4	yes	maximal, complemented
4	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₉×D₁₂	C₂	1	2	yes	maximal, complemented
6	C₉×#872	C₂	1	2	yes	maximal, complemented
7	C₄²×D₃×C₉	C₂	1	2	yes	maximal, complemented
8	C₄×C₉×Dic₆	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×#235	C₃	1	1	yes	maximal, characteristic
10	C₄×C₉×#41	—	3	1	no	maximal
11	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₉×#67	C₂²	1	2	yes	—
14	C₉×#235	C₄	1	8	yes	direct product factor
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	4	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₄²×C₉	C₂²	1	2	yes	—
20	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₉×#217	C₂²	1	2	yes	—
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
24	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
25	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
26	C₄×C₉×Dic₃	C₂²	1	2	yes	—
27	C₄×C₉×Dic₃	C₂²	1	4	yes	—
28	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃²×C₄²	C₂×C₃	1	1	yes	characteristic
30	C₃×C₄×#67	C₂×C₃	1	4	yes	—
31	C₃×#926	C₂×C₃	1	1	yes	characteristic
32	C₃×C₄×D₁₂	C₂×C₃	1	2	yes	—
33	C₃×#872	C₂×C₃	1	2	yes	—
34	C₃×C₄²×D₃	C₂×C₃	1	2	yes	—
35	C₃×C₄×Dic₆	C₂×C₃	1	2	yes	—
36	C₂×C₉×#41	—	3	1	no	—
37	C₄×Q₈×C₉	—	3	2	no	—
38	C₄×D₄×C₉	—	3	4	no	—
39	C₄×D₄×C₉	—	3	2	no	—
40	C₉×#117	—	3	1	no	—
41	C₉×#117	—	3	2	no	—
42	C₂×C₄²×C₉	—	2	1	no	—
43	C₂×C₄²×C₉	—	3	2	no	—
44	C₂×C₄²×C₉	D₃	1	1	yes	characteristic, complemented
45	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
46	C₂²×D₃×C₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	—	2	4	no	—
48	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
49	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
53	C₉×#67	C₂×C₄	1	8	yes	complemented
54	C₂×C₉×Dic₃	C₂³	1	4	yes	—
55	C₂×C₉×Dic₃	C₂³	1	2	yes	—
56	C₉×D₁₂	C₂×C₄	1	4	yes	complemented
57	C₄×D₃×C₉	—	2	8	no	—
58	C₄×D₃×C₉	C₂×C₄	1	8	yes	complemented
59	C₉×Dic₆	C₂×C₄	1	4	yes	complemented
60	C₃×C₄×#41	—	3	1	no	—
61	C₄×#235	C₉	1	1	yes	characteristic, direct product factor
62	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
63	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
65	C₃×#235	C₃×C₄	1	8	yes	—
66	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
68	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
69	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
70	C₃²×C₄²	C₂²×C₃	1	2	yes	—
71	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
72	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
73	C₃×#217	C₂²×C₃	1	2	yes	—
74	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
75	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
76	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
77	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
78	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
79	C₉×#41	—	3	8	no	—
80	C₂×Q₈×C₉	—	3	1	no	—
81	C₂×D₄×C₉	—	3	2	no	—
82	C₂×D₄×C₉	—	3	1	no	—
83	C₂²×C₄×C₉	—	2	2	no	—
84	C₂²×C₄×C₉	—	2	1	no	—
85	C₂²×C₄×C₉	—	3	2	no	—
86	C₂²×C₄×C₉	—	3	4	no	—
87	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
88	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
89	C₉×C₄⋊C₄	—	3	4	no	—
90	C₉×C₄⋊C₄	—	3	2	no	—
91	C₉×C₂²⋊C₄	—	3	2	no	—
92	C₉×C₂²⋊C₄	—	3	4	no	—
93	C₄²×C₉	—	2	1	no	—
94	C₄²×C₉	—	2	2	no	—
95	C₄²×C₉	—	2	1	no	—
96	C₄²×C₉	—	3	2	no	—
97	C₄²×C₉	—	3	4	no	—
98	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
99	C₄²×C₉	C₂×D₃	1	2	yes	—
100	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
101	C₂²×C₃×C₉	—	2	2	no	—
102	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
104	C₂×D₃×C₉	—	2	4	no	—
105	C₂×D₃×C₉	C₂²×C₄	1	4	yes	—
106	C₃×C₄×C₉	—	2	2	no	—
107	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
108	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
109	C₃×C₄×C₉	#41	1	4	yes	complemented
110	C₉×Dic₃	—	2	4	no	—
111	C₉×Dic₃	C₂²×C₄	1	4	yes	—
112	C₂×C₃×#41	—	3	1	no	—
113	C₂×#235	C₂×C₉	1	1	yes	characteristic
114	C₃×C₄×Q₈	—	3	2	no	—
115	C₃×C₄×D₄	—	3	4	no	—
116	C₃×C₄×D₄	—	3	2	no	—
117	C₃×#117	—	3	1	no	—
118	C₃×#117	—	3	2	no	—
119	C₂×C₃×C₄²	—	2	1	no	—
120	C₂×C₃×C₄²	—	3	2	no	—
121	C₂×C₃×C₄²	C₂×C₉	1	1	yes	characteristic, complemented
122	C₂×C₃×C₄²	C₃×D₃	1	1	yes	characteristic
123	C₄×#67	C₂×C₉	1	4	yes	complemented
124	#926	C₂×C₉	1	1	yes	characteristic, complemented
125	C₄×D₁₂	C₂×C₉	1	2	yes	complemented
126	#872	C₂×C₉	1	2	yes	complemented
127	C₄²×D₃	C₂×C₉	1	2	yes	complemented
128	C₄×Dic₆	C₂×C₉	1	2	yes	complemented
129	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
130	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
133	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
134	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
137	C₃×#67	C₂×C₃×C₄	1	8	yes	—
138	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
139	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
140	C₃×D₁₂	C₂×C₃×C₄	1	4	yes	—
141	C₃×C₄×D₃	—	2	8	no	—
142	C₃×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
143	C₃×Dic₆	C₂×C₃×C₄	1	4	yes	—
144	C₂³×C₉	—	2	1	no	—
145	C₂³×C₉	—	3	2	no	—
146	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
147	Q₈×C₉	—	3	4	no	—
148	D₄×C₉	—	3	8	no	—
149	D₄×C₉	—	3	4	no	—
150	C₂×C₄×C₉	—	2	8	no	—
151	C₂×C₄×C₉	—	2	4	no	—
152	C₂×C₄×C₉	—	2	4	no	—
153	C₂×C₄×C₉	—	2	2	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	2	2	no	—
157	C₂×C₄×C₉	—	3	2	no	—
158	C₂×C₄×C₉	—	3	8	no	—
159	C₂×C₄×C₉	—	3	4	no	—
160	C₂×C₄×C₉	—	6	8	no	—
161	C₂×C₄×C₉	C₄×D₃	1	4	yes	complemented
162	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
163	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
164	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
165	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
166	C₄×#41	—	3	1	no	Sylow
167	C₂×C₃×C₉	—	2	2	no	—
168	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₃×C₉	C₂×#41	1	2	yes	—
170	D₃×C₉	—	2	4	no	—
171	C₃×#41	—	3	8	no	—
172	C₂×C₃×Q₈	—	3	1	no	—
173	C₂×C₃×D₄	—	3	2	no	—
174	C₂×C₃×D₄	—	3	1	no	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	3	2	no	—
178	C₂²×C₃×C₄	—	3	4	no	—
179	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
180	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
182	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
183	C₂×#67	C₂²×C₉	1	2	yes	—
184	#235	C₄×C₉	1	8	yes	direct product factor
185	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
186	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
187	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
188	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
189	C₃×C₄⋊C₄	—	3	4	no	—
190	C₃×C₄⋊C₄	—	3	2	no	—
191	C₃×C₂²⋊C₄	—	3	2	no	—
192	C₃×C₂²⋊C₄	—	3	4	no	—
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	—	2	2	no	—
196	C₃×C₄²	—	3	2	no	—
197	C₃×C₄²	—	3	4	no	—
198	C₃×C₄²	C₂²×C₉	1	2	yes	—
199	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
200	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
201	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
202	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
203	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
204	#217	C₂²×C₉	1	2	yes	—
205	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
206	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
207	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
208	C₄×Dic₃	C₂²×C₉	1	4	yes	—
209	C₄×Dic₃	C₂²×C₉	1	2	yes	—
210	C₂²×C₃²	—	2	2	no	—
211	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
212	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
213	C₂×C₃×D₃	—	2	4	no	—
214	C₂×C₃×D₃	C₂²×C₃×C₄	1	4	yes	—
215	C₃²×C₄	—	2	2	no	—
216	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
217	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
218	C₃²×C₄	C₃×#41	1	4	yes	—
219	C₃×Dic₃	—	2	4	no	—
220	C₃×Dic₃	C₂²×C₃×C₄	1	4	yes	—
221	C₂²×C₉	—	2	4	no	—
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	2	1	no	—
224	C₂²×C₉	—	2	2	no	—
225	C₂²×C₉	—	3	4	no	—
226	C₂²×C₉	—	6	4	no	—
227	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
228	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
229	C₄×C₉	—	2	4	no	—
230	C₄×C₉	—	2	2	no	—
231	C₄×C₉	—	2	2	no	—
232	C₄×C₉	—	2	2	no	—
233	C₄×C₉	—	2	4	no	—
234	C₄×C₉	—	3	4	no	—
235	C₄×C₉	—	6	4	no	—
236	C₄×C₉	C₂×C₄×D₃	1	2	yes	—
237	C₄×C₉	C₂×C₄×D₃	1	2	yes	—
238	C₄×C₉	#235	1	4	yes	direct product factor
239	C₂×#41	—	3	1	no	—
240	C₄×Q₈	—	3	2	no	—
241	C₄×D₄	—	3	4	no	—
242	C₄×D₄	—	3	2	no	—
243	#117	—	3	1	no	—
244	#117	—	3	2	no	—
245	C₂×C₄²	—	3	2	no	—
246	C₂×C₄²	D₃×C₉	1	1	yes	characteristic, complemented
247	C₃×C₉	C₄×#41	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	3	2	no	—
250	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
251	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
252	C₂²×D₃	C₂³×C₉	1	2	yes	—
253	C₃×Q₈	—	3	4	no	—
254	C₃×D₄	—	3	8	no	—
255	C₃×D₄	—	3	4	no	—
256	C₂×C₃×C₄	—	2	8	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	3	2	no	—
265	C₂×C₃×C₄	—	3	8	no	—
266	C₂×C₃×C₄	—	3	4	no	—
267	C₂×C₃×C₄	—	6	8	no	—
268	C₂×C₃×C₄	C₂×C₄×C₉	1	4	yes	complemented
269	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
270	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
273	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
274	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
275	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
278	#67	C₂×C₄×C₉	1	8	yes	complemented
279	C₂×Dic₃	C₂³×C₉	1	4	yes	—
280	C₂×Dic₃	C₂³×C₉	1	2	yes	—
281	D₁₂	C₂×C₄×C₉	1	4	yes	complemented
282	C₄×D₃	—	2	8	no	—
283	C₄×D₃	C₂×C₄×C₉	1	8	yes	complemented
284	Dic₆	C₂×C₄×C₉	1	4	yes	complemented
285	C₂×C₃²	—	2	2	no	—
286	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
287	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
288	C₃×D₃	—	2	4	no	—
289	C₂×C₉	—	2	4	no	—
290	C₂×C₉	—	2	2	no	—
291	C₂×C₉	—	2	1	no	—
292	C₂×C₉	—	2	2	no	—
293	C₂×C₉	—	6	4	no	—
294	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
295	C₂×C₉	C₂×#235	1	2	yes	—
296	#41	—	3	8	no	—
297	C₂×Q₈	—	3	1	no	—
298	C₂×D₄	—	3	2	no	—
299	C₂×D₄	—	3	1	no	—
300	C₂²×C₄	—	3	2	no	—
301	C₂²×C₄	—	3	4	no	—
302	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
303	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
304	C₄⋊C₄	—	3	4	no	—
305	C₄⋊C₄	—	3	2	no	—
306	C₂²⋊C₄	—	3	2	no	—
307	C₂²⋊C₄	—	3	4	no	—
308	C₄²	—	3	2	no	—
309	C₄²	—	3	4	no	—
310	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
311	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
312	C₄²	C₂×D₃×C₉	1	2	yes	—
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	2	no	—
318	C₂²×C₃	—	3	4	no	—
319	C₂²×C₃	—	6	4	no	—
320	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
321	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
322	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
323	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
324	C₂×D₃	—	2	4	no	—
325	C₂×D₃	C₂²×C₄×C₉	1	4	yes	—
326	C₃×C₄	—	2	4	no	—
327	C₃×C₄	—	2	2	no	—
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	3	4	no	—
333	C₃×C₄	—	6	4	no	—
334	C₃×C₄	C₂²×C₄×C₉	1	2	yes	—
335	C₃×C₄	C₂²×C₄×C₉	1	2	yes	—
336	C₃×C₄	C₉×#41	1	4	yes	complemented
337	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
338	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
339	C₃×C₄	C₃×#235	1	4	yes	—
340	Dic₃	—	2	4	no	—
341	Dic₃	C₂²×C₄×C₉	1	4	yes	—
342	C₃²	C₃×C₄×#41	1	1	yes	characteristic
343	C₉	—	2	1	no	—
344	C₉	C₄×#235	1	1	yes	characteristic, direct product factor
345	C₂³	—	3	2	no	—
346	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
347	Q₈	—	3	4	no	—
348	D₄	—	3	8	no	—
349	D₄	—	3	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	3	2	no	—
352	C₂×C₄	—	3	8	no	—
353	C₂×C₄	—	3	4	no	—
354	C₂×C₄	—	6	8	no	—
355	C₂×C₄	C₄×D₃×C₉	1	4	yes	complemented
356	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
357	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
360	C₂×C₃	—	2	4	no	—
361	C₂×C₃	—	2	2	no	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	2	no	—
365	C₂×C₃	—	6	4	no	—
366	C₂×C₃	C₂³×C₄×C₉	1	1	yes	characteristic
367	C₂×C₃	C₂×C₉×#41	1	2	yes	—
368	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
369	C₂×C₃	C₂×C₃×#235	1	2	yes	—
370	D₃	—	2	4	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	3	4	no	—
373	C₂²	—	6	4	no	—
374	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
375	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	3	4	no	—
378	C₄	—	6	4	no	—
379	C₄	C₂×C₄×D₃×C₉	1	2	yes	—
380	C₄	C₂×C₄×D₃×C₉	1	2	yes	—
381	C₄	C₉×#235	1	4	yes	direct product factor
382	C₃	—	2	1	no	—
383	C₃	C₄×C₉×#41	1	1	yes	characteristic, complemented
384	C₃	C₃×C₄×#235	1	1	yes	characteristic
385	C₂	—	2	2	no	—
386	C₂	—	6	4	no	—
387	C₂	C₂²×C₄×D₃×C₉	1	1	yes	characteristic
388	C₂	C₂×C₉×#235	1	2	yes	—

	subgroup	G/H
center	C₄²×C₉	C₂×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₄²×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×#235	C₂×C₃
hypercenter	C₂×C₄²×C₉	D₃
hypocenter	C₃	C₄×C₉×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×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. C₄×C₉×#67	C₂	semidirect
4. C₉×#926	C₂	semidirect
5. C₄×C₉×D₁₂	C₂	semidirect
6. C₉×#872	C₂	semidirect
7. C₄²×D₃×C₉	C₂	semidirect
8. C₄×C₉×Dic₆	C₂	semidirect
14. C₉×#235	C₄	direct (N × H)
44. C₂×C₄²×C₉	D₃	semidirect
48. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
53. C₉×#67	C₂×C₄	semidirect
56. C₉×D₁₂	C₂×C₄	semidirect
58. C₄×D₃×C₉	C₂×C₄	semidirect
59. C₉×Dic₆	C₂×C₄	semidirect
61. C₄×#235	C₉	direct (N × H)
109. C₃×C₄×C₉	#41	semidirect
121. C₂×C₃×C₄²	C₂×C₉	semidirect
123. C₄×#67	C₂×C₉	semidirect
124. #926	C₂×C₉	semidirect
125. C₄×D₁₂	C₂×C₉	semidirect
126. #872	C₂×C₉	semidirect
127. C₄²×D₃	C₂×C₉	semidirect
128. C₄×Dic₆	C₂×C₉	semidirect
161. C₂×C₄×C₉	C₄×D₃	semidirect
184. #235	C₄×C₉	direct (N × H)
238. C₄×C₉	#235	direct (N × H)
246. C₂×C₄²	D₃×C₉	semidirect
247. C₃×C₉	C₄×#41	semidirect
268. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
278. #67	C₂×C₄×C₉	semidirect
281. D₁₂	C₂×C₄×C₉	semidirect
283. C₄×D₃	C₂×C₄×C₉	semidirect
284. Dic₆	C₂×C₄×C₉	semidirect
336. C₃×C₄	C₉×#41	semidirect
344. C₉	C₄×#235	direct (N × H)
355. C₂×C₄	C₄×D₃×C₉	semidirect
381. C₄	C₉×#235	direct (N × H)
383. C₃	C₄×C₉×#41	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
C₂×C₃×C₄²×C₉	2
C₄×C₉×#67	2
C₉×#926	2
C₄×C₉×D₁₂	2
C₉×#872	2
C₄²×D₃×C₉	2
C₄×C₉×Dic₆	2
C₃×C₄×#235	3
C₄×C₉×#41	3

Subgroups — C4×C9×#235 #13152291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×#235 #13152291