Subgroups — C₃×C₉×#385 #13144913

Order 1728.

1170 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₃×C₉×#95	C₂	1	2	yes	maximal, complemented
6	C₃²×#385	C₃	1	1	yes	maximal, characteristic
7	C₉×#385	C₃	1	3	yes	maximal, direct product factor
8	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄×C₉	—	2	2	no	—
10	C₂²×C₃×C₄×C₉	—	2	4	no	—
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
15	C₃×C₉×C₄⋊C₄	—	2	4	no	—
16	C₃×C₉×C₂²⋊C₄	—	2	2	no	—
17	C₃×C₉×C₂²⋊C₄	C₄	1	4	yes	complemented
18	C₂³×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	2	yes	—
20	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
22	C₂³×C₄×C₉	C₂×C₃	1	3	yes	—
23	C₃²×#95	C₂×C₃	1	2	yes	—
24	C₂×C₉×C₄⋊C₄	C₂×C₃	1	6	yes	complemented
25	C₂×C₉×C₂²⋊C₄	C₂×C₃	1	3	yes	—
26	C₂×C₉×C₂²⋊C₄	C₂×C₃	1	3	yes	—
27	C₉×#95	C₂×C₃	1	6	yes	complemented
28	C₂³×C₃×C₉	—	2	2	no	—
29	C₂³×C₃×C₉	—	2	2	no	—
30	C₂³×C₃×C₉	C₂×C₄	1	2	yes	—
31	C₂³×C₃×C₉	D₄	1	2	yes	—
32	C₂³×C₃×C₉	Q₈	1	2	yes	—
33	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₄×C₉	—	2	8	no	—
35	C₂×C₃×C₄×C₉	—	2	2	no	—
36	C₂×C₃×C₄×C₉	—	2	2	no	—
37	C₂×C₃×C₄×C₉	—	2	2	no	—
38	C₂×C₃×C₄×C₉	—	2	2	no	—
39	C₂×C₃×C₄×C₉	—	2	1	no	—
40	C₂×C₃×C₄×C₉	—	2	1	no	—
41	C₂×C₃×C₄×C₉	—	2	2	no	—
42	C₂×C₃×C₄×C₉	—	2	2	no	—
43	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
44	C₂×C₃×C₄×C₉	D₄	1	4	yes	—
45	C₃×#385	C₉	1	3	yes	direct product factor
46	C₃×#385	C₃²	1	1	yes	characteristic
47	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₃²×C₄	—	2	2	no	—
49	C₂²×C₃²×C₄	—	2	4	no	—
50	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
51	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
52	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
53	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
54	C₂⁴×C₉	C₂²×C₃	1	3	yes	—
55	C₃²×C₄⋊C₄	—	2	4	no	—
56	C₃²×C₂²⋊C₄	—	2	2	no	—
57	C₃²×C₂²⋊C₄	C₃×C₄	1	4	yes	—
58	C₂²×C₄×C₉	—	2	6	no	—
59	C₂²×C₄×C₉	—	2	12	no	—
60	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	—
61	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	—
62	C₂²×C₄×C₉	C₂²×C₃	1	6	yes	—
63	C₂²×C₄×C₉	C₂²×C₃	1	6	yes	—
64	C₉×C₄⋊C₄	—	2	12	no	—
65	C₉×C₂²⋊C₄	—	2	6	no	—
66	C₉×C₂²⋊C₄	C₃×C₄	1	12	yes	complemented
67	C₂²×C₃×C₉	—	2	4	no	—
68	C₂²×C₃×C₉	—	2	2	no	—
69	C₂²×C₃×C₉	—	2	4	no	—
70	C₂²×C₃×C₉	—	2	2	no	—
71	C₂²×C₃×C₉	C₄⋊C₄	1	4	yes	complemented
72	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
75	C₂²×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
76	C₂²×C₃×C₉	#41	1	2	yes	—
77	C₃×C₄×C₉	—	2	4	no	—
78	C₃×C₄×C₉	—	2	4	no	—
79	C₃×C₄×C₉	—	4	1	no	—
80	C₃×C₄×C₉	—	4	1	no	—
81	C₂³×C₃×C₄	C₂×C₉	1	3	yes	—
82	C₂³×C₃×C₄	C₂×C₃²	1	1	yes	characteristic
83	C₂×C₃×C₄⋊C₄	C₂×C₉	1	6	yes	complemented
84	C₂×C₃×C₄⋊C₄	C₂×C₃²	1	2	yes	—
85	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	3	yes	—
86	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	3	yes	—
87	C₂×C₃×C₂²⋊C₄	C₂×C₃²	1	1	yes	characteristic
88	C₂×C₃×C₂²⋊C₄	C₂×C₃²	1	1	yes	characteristic
89	C₃×#95	C₂×C₉	1	6	yes	complemented
90	C₃×#95	C₂×C₃²	1	2	yes	—
91	C₂³×C₃²	—	2	2	no	—
92	C₂³×C₃²	—	2	2	no	—
93	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
94	C₂³×C₃²	C₃×D₄	1	2	yes	—
95	C₂³×C₃²	C₃×Q₈	1	2	yes	—
96	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
97	C₂×C₃²×C₄	—	2	8	no	—
98	C₂×C₃²×C₄	—	2	2	no	—
99	C₂×C₃²×C₄	—	2	2	no	—
100	C₂×C₃²×C₄	—	2	2	no	—
101	C₂×C₃²×C₄	—	2	2	no	—
102	C₂×C₃²×C₄	—	2	1	no	—
103	C₂×C₃²×C₄	—	2	1	no	—
104	C₂×C₃²×C₄	—	2	2	no	—
105	C₂×C₃²×C₄	—	2	2	no	—
106	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
107	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
108	C₂³×C₉	—	2	6	no	—
109	C₂³×C₉	—	2	6	no	—
110	C₂³×C₉	C₂×C₃×C₄	1	6	yes	—
111	C₂³×C₉	C₃×D₄	1	6	yes	—
112	C₂³×C₉	C₃×Q₈	1	6	yes	—
113	C₂³×C₉	C₂³×C₃	1	3	yes	—
114	C₂×C₄×C₉	—	2	24	no	—
115	C₂×C₄×C₉	—	2	6	no	—
116	C₂×C₄×C₉	—	2	6	no	—
117	C₂×C₄×C₉	—	2	6	no	—
118	C₂×C₄×C₉	—	2	6	no	—
119	C₂×C₄×C₉	—	2	3	no	—
120	C₂×C₄×C₉	—	2	3	no	—
121	C₂×C₄×C₉	—	2	6	no	—
122	C₂×C₄×C₉	—	2	6	no	—
123	C₂×C₄×C₉	C₂×C₃×C₄	1	12	yes	complemented
124	C₂×C₄×C₉	C₃×D₄	1	12	yes	—
125	#385	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
126	C₂×C₃×C₉	—	2	4	no	—
127	C₂×C₃×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₃×C₉	C₄×D₄	1	2	yes	—
129	C₂×C₃×C₉	#120	1	1	yes	characteristic
130	C₂×C₃×C₉	C₂²⋊Q₈	1	2	yes	—
131	C₂×C₃×C₉	#123	1	1	yes	characteristic
132	C₂⁴×C₃	C₂²×C₉	1	3	yes	—
133	C₂⁴×C₃	C₂²×C₃²	1	1	yes	characteristic
134	C₂²×C₃×C₄	—	2	6	no	—
135	C₂²×C₃×C₄	—	2	2	no	—
136	C₂²×C₃×C₄	—	2	12	no	—
137	C₂²×C₃×C₄	—	2	4	no	—
138	C₂²×C₃×C₄	C₂²×C₉	1	3	yes	—
139	C₂²×C₃×C₄	C₂²×C₉	1	3	yes	—
140	C₂²×C₃×C₄	C₂²×C₉	1	6	yes	—
141	C₂²×C₃×C₄	C₂²×C₉	1	6	yes	—
142	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
143	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
145	C₂²×C₃×C₄	C₂²×C₃²	1	2	yes	—
146	C₃×C₄⋊C₄	—	2	12	no	—
147	C₃×C₄⋊C₄	—	2	4	no	—
148	C₃×C₂²⋊C₄	—	2	6	no	—
149	C₃×C₂²⋊C₄	—	2	2	no	—
150	C₃×C₂²⋊C₄	C₄×C₉	1	12	yes	complemented
151	C₃×C₂²⋊C₄	C₃²×C₄	1	4	yes	—
152	C₂²×C₃²	—	2	4	no	—
153	C₂²×C₃²	—	2	2	no	—
154	C₂²×C₃²	—	2	4	no	—
155	C₂²×C₃²	—	2	2	no	—
156	C₂²×C₃²	C₃×C₄⋊C₄	1	4	yes	—
157	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
158	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
159	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
160	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
161	C₂²×C₃²	C₃×#41	1	2	yes	—
162	C₃²×C₄	—	2	4	no	—
163	C₃²×C₄	—	2	4	no	—
164	C₃²×C₄	—	4	1	no	—
165	C₃²×C₄	—	4	1	no	—
166	C₂²×C₉	—	2	12	no	—
167	C₂²×C₉	—	2	6	no	—
168	C₂²×C₉	—	2	12	no	—
169	C₂²×C₉	—	2	6	no	—
170	C₂²×C₉	C₃×C₄⋊C₄	1	12	yes	complemented
171	C₂²×C₉	C₂²×C₃×C₄	1	3	yes	—
172	C₂²×C₉	C₂×C₃×D₄	1	3	yes	—
173	C₂²×C₉	C₂×C₃×D₄	1	6	yes	—
174	C₂²×C₉	C₂×C₃×Q₈	1	3	yes	—
175	C₂²×C₉	C₃×#41	1	6	yes	—
176	C₄×C₉	—	2	12	no	—
177	C₄×C₉	—	2	12	no	—
178	C₄×C₉	—	4	3	no	—
179	C₄×C₉	—	4	3	no	—
180	C₂³×C₄	C₂×C₃×C₉	1	1	yes	characteristic
181	C₂×C₄⋊C₄	C₂×C₃×C₉	1	2	yes	complemented
182	C₂×C₂²⋊C₄	C₂×C₃×C₉	1	1	yes	characteristic
183	C₂×C₂²⋊C₄	C₂×C₃×C₉	1	1	yes	characteristic
184	#95	C₂×C₃×C₉	1	2	yes	complemented
185	C₃×C₉	#385	1	1	yes	characteristic, direct product factor, Sylow
186	C₂³×C₃	—	2	6	no	—
187	C₂³×C₃	—	2	6	no	—
188	C₂³×C₃	—	2	2	no	—
189	C₂³×C₃	—	2	2	no	—
190	C₂³×C₃	C₂×C₄×C₉	1	6	yes	—
191	C₂³×C₃	D₄×C₉	1	6	yes	—
192	C₂³×C₃	Q₈×C₉	1	6	yes	—
193	C₂³×C₃	C₂³×C₉	1	3	yes	—
194	C₂³×C₃	C₂×C₃²×C₄	1	2	yes	—
195	C₂³×C₃	C₃²×D₄	1	2	yes	—
196	C₂³×C₃	C₃²×Q₈	1	2	yes	—
197	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
198	C₂×C₃×C₄	—	2	8	no	—
199	C₂×C₃×C₄	—	2	24	no	—
200	C₂×C₃×C₄	—	2	6	no	—
201	C₂×C₃×C₄	—	2	6	no	—
202	C₂×C₃×C₄	—	2	6	no	—
203	C₂×C₃×C₄	—	2	6	no	—
204	C₂×C₃×C₄	—	2	2	no	—
205	C₂×C₃×C₄	—	2	2	no	—
206	C₂×C₃×C₄	—	2	2	no	—
207	C₂×C₃×C₄	—	2	2	no	—
208	C₂×C₃×C₄	—	2	3	no	—
209	C₂×C₃×C₄	—	2	3	no	—
210	C₂×C₃×C₄	—	2	6	no	—
211	C₂×C₃×C₄	—	2	6	no	—
212	C₂×C₃×C₄	—	2	1	no	—
213	C₂×C₃×C₄	—	2	1	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	C₂×C₄×C₉	1	12	yes	complemented
217	C₂×C₃×C₄	D₄×C₉	1	12	yes	—
218	C₂×C₃×C₄	C₂×C₃²×C₄	1	4	yes	—
219	C₂×C₃×C₄	C₃²×D₄	1	4	yes	—
220	C₂×C₃²	—	2	4	no	—
221	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
222	C₂×C₃²	C₃×C₄×D₄	1	2	yes	—
223	C₂×C₃²	C₃×#120	1	1	yes	characteristic
224	C₂×C₃²	C₃×C₂²⋊Q₈	1	2	yes	—
225	C₂×C₃²	C₃×#123	1	1	yes	characteristic
226	C₂×C₉	—	2	12	no	—
227	C₂×C₉	C₂×C₃×C₄⋊C₄	1	3	yes	—
228	C₂×C₉	C₃×C₄×D₄	1	6	yes	—
229	C₂×C₉	C₃×#120	1	3	yes	—
230	C₂×C₉	C₃×C₂²⋊Q₈	1	6	yes	—
231	C₂×C₉	C₃×#123	1	3	yes	—
232	C₂⁴	C₂²×C₃×C₉	1	1	yes	characteristic
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	4	no	—
235	C₂²×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₃×C₉	1	2	yes	—
238	C₂²×C₄	C₂²×C₃×C₉	1	2	yes	—
239	C₄⋊C₄	—	2	4	no	—
240	C₂²⋊C₄	—	2	2	no	—
241	C₂²⋊C₄	C₃×C₄×C₉	1	4	yes	complemented
242	C₂²×C₃	—	2	12	no	—
243	C₂²×C₃	—	2	6	no	—
244	C₂²×C₃	—	2	12	no	—
245	C₂²×C₃	—	2	6	no	—
246	C₂²×C₃	—	2	4	no	—
247	C₂²×C₃	—	2	2	no	—
248	C₂²×C₃	—	2	4	no	—
249	C₂²×C₃	—	2	2	no	—
250	C₂²×C₃	C₉×C₄⋊C₄	1	12	yes	complemented
251	C₂²×C₃	C₂²×C₄×C₉	1	3	yes	—
252	C₂²×C₃	C₂×D₄×C₉	1	3	yes	—
253	C₂²×C₃	C₂×D₄×C₉	1	6	yes	—
254	C₂²×C₃	C₂×Q₈×C₉	1	3	yes	—
255	C₂²×C₃	C₉×#41	1	6	yes	—
256	C₂²×C₃	C₃²×C₄⋊C₄	1	4	yes	—
257	C₂²×C₃	C₂²×C₃²×C₄	1	1	yes	characteristic
258	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
259	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
260	C₂²×C₃	C₂×C₃²×Q₈	1	1	yes	characteristic
261	C₂²×C₃	C₃²×#41	1	2	yes	—
262	C₃×C₄	—	2	12	no	—
263	C₃×C₄	—	2	12	no	—
264	C₃×C₄	—	2	4	no	—
265	C₃×C₄	—	2	4	no	—
266	C₃×C₄	—	4	3	no	—
267	C₃×C₄	—	4	3	no	—
268	C₃×C₄	—	4	1	no	—
269	C₃×C₄	—	4	1	no	—
270	C₃²	C₃×#385	1	1	yes	characteristic
271	C₉	C₃×#385	1	3	yes	direct product factor
272	C₂³	—	2	2	no	—
273	C₂³	—	2	2	no	—
274	C₂³	C₂×C₃×C₄×C₉	1	2	yes	—
275	C₂³	C₃×D₄×C₉	1	2	yes	—
276	C₂³	C₃×Q₈×C₉	1	2	yes	—
277	C₂³	C₂³×C₃×C₉	1	1	yes	characteristic
278	C₂×C₄	—	2	8	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	C₂×C₃×C₄×C₉	1	4	yes	complemented
288	C₂×C₄	C₃×D₄×C₉	1	4	yes	—
289	C₂×C₃	—	2	12	no	—
290	C₂×C₃	—	2	4	no	—
291	C₂×C₃	C₂×C₉×C₄⋊C₄	1	3	yes	—
292	C₂×C₃	C₄×D₄×C₉	1	6	yes	—
293	C₂×C₃	C₉×#120	1	3	yes	—
294	C₂×C₃	C₉×C₂²⋊Q₈	1	6	yes	—
295	C₂×C₃	C₉×#123	1	3	yes	—
296	C₂×C₃	C₂×C₃²×C₄⋊C₄	1	1	yes	characteristic
297	C₂×C₃	C₃²×C₄×D₄	1	2	yes	—
298	C₂×C₃	C₃²×#120	1	1	yes	characteristic
299	C₂×C₃	C₃²×C₂²⋊Q₈	1	2	yes	—
300	C₂×C₃	C₃²×#123	1	1	yes	characteristic
301	C₂²	—	2	4	no	—
302	C₂²	—	2	2	no	—
303	C₂²	—	2	4	no	—
304	C₂²	—	2	2	no	—
305	C₂²	C₃×C₉×C₄⋊C₄	1	4	yes	complemented
306	C₂²	C₂²×C₃×C₄×C₉	1	1	yes	characteristic
307	C₂²	C₂×C₃×D₄×C₉	1	1	yes	characteristic
308	C₂²	C₂×C₃×D₄×C₉	1	2	yes	—
309	C₂²	C₂×C₃×Q₈×C₉	1	1	yes	characteristic
310	C₂²	C₃×C₉×#41	1	2	yes	—
311	C₄	—	2	4	no	—
312	C₄	—	2	4	no	—
313	C₄	—	4	1	no	—
314	C₄	—	4	1	no	—
315	C₃	C₉×#385	1	3	yes	direct product factor
316	C₃	C₃²×#385	1	1	yes	characteristic
317	C₂	—	2	4	no	—
318	C₂	C₂×C₃×C₉×C₄⋊C₄	1	1	yes	characteristic
319	C₂	C₃×C₄×D₄×C₉	1	2	yes	—
320	C₂	C₃×C₉×#120	1	1	yes	characteristic
321	C₂	C₃×C₉×C₂²⋊Q₈	1	2	yes	—
322	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	C₂⁴×C₃²	C₂²×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. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
5. C₃×C₉×#95	C₂	semidirect
7. C₉×#385	C₃	direct (N × H)
17. C₃×C₉×C₂²⋊C₄	C₄	semidirect
24. C₂×C₉×C₄⋊C₄	C₂×C₃	semidirect
27. C₉×#95	C₂×C₃	semidirect
43. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
45. C₃×#385	C₉	direct (N × H)
66. C₉×C₂²⋊C₄	C₃×C₄	semidirect
71. C₂²×C₃×C₉	C₄⋊C₄	semidirect
83. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
89. C₃×#95	C₂×C₉	semidirect
123. C₂×C₄×C₉	C₂×C₃×C₄	semidirect
125. #385	C₃×C₉	direct (N × H)
150. C₃×C₂²⋊C₄	C₄×C₉	semidirect
170. C₂²×C₉	C₃×C₄⋊C₄	semidirect
181. C₂×C₄⋊C₄	C₂×C₃×C₉	semidirect
184. #95	C₂×C₃×C₉	semidirect
185. C₃×C₉	#385	direct (N × H)
216. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
241. C₂²⋊C₄	C₃×C₄×C₉	semidirect
250. C₂²×C₃	C₉×C₄⋊C₄	semidirect
271. C₉	C₃×#385	direct (N × H)
287. C₂×C₄	C₂×C₃×C₄×C₉	semidirect
305. C₂²	C₃×C₉×C₄⋊C₄	semidirect
315. C₃	C₉×#385	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×C₉	2
C₂×C₃×C₉×C₄⋊C₄	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₃×C₉×#95	2
C₃²×#385	3
C₉×#385	3

Subgroups — C3×C9×#385 #13144913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#385 #13144913