Subgroups — D₃×C₉×#117 #13152494

Order 1728.

1066 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₃×C₉	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×#892	C₂	1	2	yes	maximal, complemented
5	D₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
6	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal
7	C₉×#877	C₂	1	2	yes	maximal, complemented
8	C₉×#872	C₂	1	2	yes	maximal, complemented
9	C₄²×D₃×C₉	C₂	1	2	yes	maximal, complemented
10	C₃×D₃×#117	C₃	1	1	yes	maximal, characteristic
11	C₂×C₉×#117	—	3	1	no	maximal
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	C₄	1	8	yes	complemented
16	C₂×C₄×D₃×C₉	C₂²	1	4	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃×C₄²×C₉	C₂²	1	2	yes	complemented
24	C₉×#217	C₂²	1	2	yes	—
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
26	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
27	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
28	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
29	C₄×C₉×Dic₃	C₂²	1	4	yes	complemented
30	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
31	C₃²×#117	C₂×C₃	1	1	yes	characteristic
32	C₃×#926	C₂×C₃	1	1	yes	characteristic
33	C₃×#892	C₂×C₃	1	2	yes	—
34	C₃×D₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
35	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
36	C₃×#877	C₂×C₃	1	2	yes	—
37	C₃×#872	C₂×C₃	1	2	yes	—
38	C₃×C₄²×D₃	C₂×C₃	1	2	yes	—
39	C₂³×C₄×C₉	—	3	1	no	—
40	C₉×#117	—	2	1	no	—
41	C₉×#117	—	3	1	no	—
42	C₉×#117	—	3	2	no	—
43	C₉×#117	—	3	2	no	—
44	C₉×#117	—	3	2	no	—
45	C₉×#117	D₃	1	1	yes	characteristic, direct product factor
46	C₂×C₉×C₄⋊C₄	—	3	2	no	—
47	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
48	C₂×C₄²×C₉	—	3	2	no	—
49	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
50	C₂²×D₃×C₉	—	2	4	no	—
51	C₂²×D₃×C₉	C₂×C₄	1	4	yes	—
52	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
53	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
55	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
56	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂×C₉×Dic₃	C₂×C₄	1	4	yes	complemented
59	C₂×C₉×Dic₃	C₂³	1	4	yes	—
60	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
61	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
62	C₄×D₃×C₉	—	2	8	no	—
63	C₄×D₃×C₉	C₂×C₄	1	4	yes	—
64	C₄×D₃×C₉	C₂×C₄	1	4	yes	—
65	C₄×D₃×C₉	C₂×C₄	1	4	yes	complemented
66	C₄×D₃×C₉	C₂×C₄	1	4	yes	complemented
67	C₂×C₃×#117	—	3	1	no	—
68	D₃×#117	C₉	1	1	yes	characteristic, direct product factor
69	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₃×C₄×D₃	C₃×C₄	1	8	yes	—
73	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
74	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
78	C₂⁴×C₉	—	3	1	no	—
79	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₃²×C₄²	C₂²×C₃	1	2	yes	—
82	C₃×#217	C₂²×C₃	1	2	yes	—
83	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
84	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
85	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
86	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
87	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
88	C₂²×C₄×C₉	—	2	1	no	—
89	C₂²×C₄×C₉	—	3	1	no	—
90	C₂²×C₄×C₉	—	3	8	no	—
91	C₂²×C₄×C₉	—	3	1	no	—
92	C₂²×C₄×C₉	—	3	1	no	—
93	C₂²×C₄×C₉	—	3	1	no	—
94	C₂²×C₄×C₉	—	3	1	no	—
95	C₂²×C₄×C₉	—	3	4	no	—
96	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
97	C₉×C₄⋊C₄	—	2	2	no	—
98	C₉×C₄⋊C₄	—	3	4	no	—
99	C₉×C₄⋊C₄	—	3	2	no	—
100	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
101	C₉×C₂²⋊C₄	—	2	2	no	—
102	C₉×C₂²⋊C₄	—	3	2	no	—
103	C₉×C₂²⋊C₄	—	3	4	no	—
104	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
105	C₄²×C₉	—	2	2	no	—
106	C₄²×C₉	—	3	4	no	—
107	C₄²×C₉	—	3	2	no	—
108	C₄²×C₉	C₂×D₃	1	2	yes	complemented
109	C₂²×C₃×C₉	—	2	2	no	—
110	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
112	C₂×D₃×C₉	—	2	2	no	—
113	C₂×D₃×C₉	—	2	8	no	—
114	C₂×D₃×C₉	C₂²×C₄	1	2	yes	—
115	C₂×D₃×C₉	C₂²×C₄	1	2	yes	—
116	C₂×D₃×C₉	#41	1	4	yes	—
117	C₃×C₄×C₉	—	2	4	no	—
118	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
119	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
120	C₉×Dic₃	—	2	4	no	—
121	C₉×Dic₃	C₂²×C₄	1	2	yes	—
122	C₉×Dic₃	C₂²×C₄	1	2	yes	—
123	C₂³×C₃×C₄	—	3	1	no	—
124	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic
125	C₃×#117	—	2	1	no	—
126	C₃×#117	—	3	1	no	—
127	C₃×#117	—	3	2	no	—
128	C₃×#117	—	3	2	no	—
129	C₃×#117	—	3	2	no	—
130	C₃×#117	C₂×C₉	1	1	yes	characteristic, complemented
131	C₃×#117	C₃×D₃	1	1	yes	characteristic
132	C₂×C₃×C₄⋊C₄	—	3	2	no	—
133	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
134	C₂×C₃×C₄²	—	3	2	no	—
135	#926	C₂×C₉	1	1	yes	characteristic, complemented
136	#892	C₂×C₉	1	2	yes	complemented
137	D₃×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
138	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	—
139	#877	C₂×C₉	1	2	yes	complemented
140	#872	C₂×C₉	1	2	yes	complemented
141	C₄²×D₃	C₂×C₉	1	2	yes	complemented
142	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
143	C₂²×C₃×D₃	—	2	4	no	—
144	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
145	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
146	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
148	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
149	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
150	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
151	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
152	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
153	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
154	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
155	C₃×C₄×D₃	—	2	8	no	—
156	C₃×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
157	C₃×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
158	C₃×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
159	C₃×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
160	C₂³×C₉	—	2	1	no	—
161	C₂³×C₉	—	3	1	no	—
162	C₂³×C₉	—	3	4	no	—
163	C₂³×C₉	—	3	1	no	—
164	C₂³×C₉	—	6	4	no	—
165	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
166	C₂×C₄×C₉	—	2	4	no	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	2	1	no	—
169	C₂×C₄×C₉	—	2	4	no	—
170	C₂×C₄×C₉	—	3	4	no	—
171	C₂×C₄×C₉	—	3	1	no	—
172	C₂×C₄×C₉	—	3	1	no	—
173	C₂×C₄×C₉	—	3	4	no	—
174	C₂×C₄×C₉	—	3	4	no	—
175	C₂×C₄×C₉	—	3	4	no	—
176	C₂×C₄×C₉	—	3	4	no	—
177	C₂×C₄×C₉	—	3	4	no	—
178	C₂×C₄×C₉	—	6	8	no	—
179	C₂×C₄×C₉	C₄×D₃	1	4	yes	complemented
180	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
181	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
182	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
183	C₂×#117	—	3	1	no	Sylow
184	C₂×C₃×C₉	—	2	2	no	—
185	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₃×C₉	C₂×#41	1	2	yes	—
187	D₃×C₉	—	2	2	no	—
188	D₃×C₉	#117	1	4	yes	direct product factor
189	C₂⁴×C₃	—	3	1	no	—
190	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂²×C₃×C₄	—	3	1	no	—
193	C₂²×C₃×C₄	—	3	8	no	—
194	C₂²×C₃×C₄	—	3	1	no	—
195	C₂²×C₃×C₄	—	3	1	no	—
196	C₂²×C₃×C₄	—	3	1	no	—
197	C₂²×C₃×C₄	—	3	1	no	—
198	C₂²×C₃×C₄	—	3	4	no	—
199	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
201	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
202	C₂×C₄×D₃	C₄×C₉	1	8	yes	complemented
203	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
204	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
205	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
206	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
208	C₃×C₄⋊C₄	—	2	2	no	—
209	C₃×C₄⋊C₄	—	3	4	no	—
210	C₃×C₄⋊C₄	—	3	2	no	—
211	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
212	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
213	C₃×C₂²⋊C₄	—	2	2	no	—
214	C₃×C₂²⋊C₄	—	3	2	no	—
215	C₃×C₂²⋊C₄	—	3	4	no	—
216	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
217	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
218	C₃×C₄²	—	2	2	no	—
219	C₃×C₄²	—	3	4	no	—
220	C₃×C₄²	—	3	2	no	—
221	C₃×C₄²	C₂²×C₉	1	2	yes	complemented
222	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
223	#217	C₂²×C₉	1	2	yes	—
224	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
225	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
226	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
227	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
228	C₄×Dic₃	C₂²×C₉	1	4	yes	complemented
229	C₂²×C₃²	—	2	2	no	—
230	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
231	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
232	C₂×C₃×D₃	—	2	2	no	—
233	C₂×C₃×D₃	—	2	8	no	—
234	C₂×C₃×D₃	C₂²×C₃×C₄	1	2	yes	—
235	C₂×C₃×D₃	C₂²×C₃×C₄	1	2	yes	—
236	C₂×C₃×D₃	C₃×#41	1	4	yes	—
237	C₃²×C₄	—	2	4	no	—
238	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
239	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
240	C₃×Dic₃	—	2	4	no	—
241	C₃×Dic₃	C₂²×C₃×C₄	1	2	yes	—
242	C₃×Dic₃	C₂²×C₃×C₄	1	2	yes	—
243	C₂²×C₉	—	2	2	no	—
244	C₂²×C₉	—	2	1	no	—
245	C₂²×C₉	—	2	2	no	—
246	C₂²×C₉	—	3	2	no	—
247	C₂²×C₉	—	3	4	no	—
248	C₂²×C₉	—	3	2	no	—
249	C₂²×C₉	—	4	2	no	—
250	C₂²×C₉	—	6	8	no	—
251	C₂²×C₉	—	6	2	no	—
252	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
253	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
254	C₄×C₉	—	2	4	no	—
255	C₄×C₉	—	2	2	no	—
256	C₄×C₉	—	2	2	no	—
257	C₄×C₉	—	3	2	no	—
258	C₄×C₉	—	3	2	no	—
259	C₄×C₉	—	4	4	no	—
260	C₄×C₉	—	6	4	no	—
261	C₄×C₉	C₂×C₄×D₃	1	2	yes	—
262	C₄×C₉	C₂×C₄×D₃	1	2	yes	—
263	C₂³×C₄	—	3	1	no	—
264	#117	—	3	1	no	—
265	#117	—	3	2	no	—
266	#117	—	3	2	no	—
267	#117	—	3	2	no	—
268	#117	D₃×C₉	1	1	yes	characteristic, direct product factor
269	C₂×C₄⋊C₄	—	3	2	no	—
270	C₂×C₂²⋊C₄	—	3	2	no	—
271	C₂×C₄²	—	3	2	no	—
272	C₃×C₉	C₂×#117	1	1	yes	characteristic, complemented, Sylow
273	C₂³×C₃	—	2	1	no	—
274	C₂³×C₃	—	3	1	no	—
275	C₂³×C₃	—	3	1	no	—
276	C₂³×C₃	—	3	4	no	—
277	C₂³×C₃	—	6	4	no	—
278	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
279	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
280	C₂²×D₃	—	2	4	no	—
281	C₂²×D₃	C₂×C₄×C₉	1	4	yes	—
282	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
283	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	3	1	no	—
289	C₂×C₃×C₄	—	3	1	no	—
290	C₂×C₃×C₄	—	3	4	no	—
291	C₂×C₃×C₄	—	3	4	no	—
292	C₂×C₃×C₄	—	3	4	no	—
293	C₂×C₃×C₄	—	3	4	no	—
294	C₂×C₃×C₄	—	3	4	no	—
295	C₂×C₃×C₄	—	3	4	no	—
296	C₂×C₃×C₄	—	6	8	no	—
297	C₂×C₃×C₄	C₂×C₄×C₉	1	4	yes	complemented
298	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
299	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
301	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
302	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
303	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
305	C₂×Dic₃	C₂×C₄×C₉	1	4	yes	complemented
306	C₂×Dic₃	C₂³×C₉	1	4	yes	—
307	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
308	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
309	C₄×D₃	—	2	8	no	—
310	C₄×D₃	C₂×C₄×C₉	1	4	yes	—
311	C₄×D₃	C₂×C₄×C₉	1	4	yes	—
312	C₄×D₃	C₂×C₄×C₉	1	4	yes	complemented
313	C₄×D₃	C₂×C₄×C₉	1	4	yes	complemented
314	C₂×C₃²	—	2	2	no	—
315	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
316	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
317	C₃×D₃	—	2	2	no	—
318	C₃×D₃	C₃×#117	1	4	yes	—
319	C₂×C₉	—	2	2	no	—
320	C₂×C₉	—	2	1	no	—
321	C₂×C₉	—	2	2	no	—
322	C₂×C₉	—	3	4	no	—
323	C₂×C₉	—	4	2	no	—
324	C₂×C₉	—	6	2	no	—
325	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
326	C₂×C₉	D₃×#41	1	2	yes	—
327	C₂⁴	—	3	1	no	—
328	C₂²×C₄	—	3	1	no	—
329	C₂²×C₄	—	3	8	no	—
330	C₂²×C₄	—	3	1	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	3	4	no	—
335	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
336	C₄⋊C₄	—	3	4	no	—
337	C₄⋊C₄	—	3	2	no	—
338	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
339	C₂²⋊C₄	—	3	2	no	—
340	C₂²⋊C₄	—	3	4	no	—
341	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
342	C₄²	—	3	4	no	—
343	C₄²	—	3	2	no	—
344	C₄²	C₂×D₃×C₉	1	2	yes	complemented
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	3	2	no	—
350	C₂²×C₃	—	3	4	no	—
351	C₂²×C₃	—	3	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	6	8	no	—
354	C₂²×C₃	—	6	2	no	—
355	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
356	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
358	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
359	C₂×D₃	—	2	2	no	—
360	C₂×D₃	—	2	8	no	—
361	C₂×D₃	C₂²×C₄×C₉	1	2	yes	—
362	C₂×D₃	C₂²×C₄×C₉	1	2	yes	—
363	C₂×D₃	C₉×#41	1	4	yes	—
364	C₃×C₄	—	2	4	no	—
365	C₃×C₄	—	2	4	no	—
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	3	2	no	—
369	C₃×C₄	—	3	2	no	—
370	C₃×C₄	—	4	4	no	—
371	C₃×C₄	—	6	4	no	—
372	C₃×C₄	C₂²×C₄×C₉	1	2	yes	—
373	C₃×C₄	C₂²×C₄×C₉	1	2	yes	—
374	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
375	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
376	Dic₃	—	2	4	no	—
377	Dic₃	C₂²×C₄×C₉	1	2	yes	—
378	Dic₃	C₂²×C₄×C₉	1	2	yes	—
379	C₃²	C₂×C₃×#117	1	1	yes	characteristic
380	C₉	—	2	1	no	—
381	C₉	D₃×#117	1	1	yes	characteristic, direct product factor
382	C₂³	—	3	1	no	—
383	C₂³	—	3	1	no	—
384	C₂³	—	3	4	no	—
385	C₂³	—	6	4	no	—
386	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
387	C₂×C₄	—	3	1	no	—
388	C₂×C₄	—	3	1	no	—
389	C₂×C₄	—	3	4	no	—
390	C₂×C₄	—	3	4	no	—
391	C₂×C₄	—	3	4	no	—
392	C₂×C₄	—	3	4	no	—
393	C₂×C₄	—	3	4	no	—
394	C₂×C₄	—	3	4	no	—
395	C₂×C₄	—	6	8	no	—
396	C₂×C₄	C₄×D₃×C₉	1	4	yes	complemented
397	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
398	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
400	C₂×C₃	—	2	2	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	2	no	—
404	C₂×C₃	—	3	4	no	—
405	C₂×C₃	—	4	2	no	—
406	C₂×C₃	—	6	2	no	—
407	C₂×C₃	C₂³×C₄×C₉	1	1	yes	characteristic
408	C₂×C₃	C₂×C₉×#41	1	2	yes	—
409	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
410	C₂×C₃	C₃×D₃×#41	1	2	yes	—
411	D₃	—	2	2	no	—
412	D₃	C₉×#117	1	4	yes	direct product factor
413	C₂²	—	2	2	no	—
414	C₂²	—	3	2	no	—
415	C₂²	—	3	4	no	—
416	C₂²	—	3	2	no	—
417	C₂²	—	6	8	no	—
418	C₂²	—	6	2	no	—
419	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
420	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
421	C₄	—	2	4	no	—
422	C₄	—	3	2	no	—
423	C₄	—	3	2	no	—
424	C₄	—	6	4	no	—
425	C₄	C₂×C₄×D₃×C₉	1	2	yes	—
426	C₄	C₂×C₄×D₃×C₉	1	2	yes	—
427	C₃	—	2	1	no	—
428	C₃	C₂×C₉×#117	1	1	yes	characteristic, complemented
429	C₃	C₃×D₃×#117	1	1	yes	characteristic
430	C₂	—	2	2	no	—
431	C₂	—	3	4	no	—
432	C₂	—	6	2	no	—
433	C₂	C₂²×C₄×D₃×C₉	1	1	yes	characteristic
434	C₂	D₃×C₉×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#117	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂³×C₃×D₃	C₂²×C₃
hypercenter	C₉×#117	D₃
hypocenter	C₃	C₂×C₉×#117
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×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×#892	C₂	semidirect
5. D₃×C₉×C₄⋊C₄	C₂	semidirect
7. C₉×#877	C₂	semidirect
8. C₉×#872	C₂	semidirect
9. C₄²×D₃×C₉	C₂	semidirect
15. C₂×C₄×D₃×C₉	C₄	semidirect
21. C₃×C₉×C₄⋊C₄	C₂²	semidirect
23. C₃×C₄²×C₉	C₂²	semidirect
26. C₉×C₄⋊Dic₃	C₂²	semidirect
27. C₉×Dic₃⋊C₄	C₂²	semidirect
28. C₄×C₉×Dic₃	C₂²	semidirect
29. C₄×C₉×Dic₃	C₂²	semidirect
45. C₉×#117	D₃	direct (N × H)
54. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
58. C₂×C₉×Dic₃	C₂×C₄	semidirect
65. C₄×D₃×C₉	C₂×C₄	semidirect
66. C₄×D₃×C₉	C₂×C₄	semidirect
68. D₃×#117	C₉	direct (N × H)
100. C₉×C₄⋊C₄	C₂×D₃	semidirect
108. C₄²×C₉	C₂×D₃	semidirect
130. C₃×#117	C₂×C₉	semidirect
135. #926	C₂×C₉	semidirect
136. #892	C₂×C₉	semidirect
137. D₃×C₄⋊C₄	C₂×C₉	semidirect
139. #877	C₂×C₉	semidirect
140. #872	C₂×C₉	semidirect
141. C₄²×D₃	C₂×C₉	semidirect
179. C₂×C₄×C₉	C₄×D₃	semidirect
188. D₃×C₉	#117	direct (N × H)
202. C₂×C₄×D₃	C₄×C₉	semidirect
211. C₃×C₄⋊C₄	C₂²×C₉	semidirect
221. C₃×C₄²	C₂²×C₉	semidirect
225. C₄⋊Dic₃	C₂²×C₉	semidirect
226. Dic₃⋊C₄	C₂²×C₉	semidirect
227. C₄×Dic₃	C₂²×C₉	semidirect
228. C₄×Dic₃	C₂²×C₉	semidirect
268. #117	D₃×C₉	direct (N × H)
272. C₃×C₉	C₂×#117	semidirect
297. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
305. C₂×Dic₃	C₂×C₄×C₉	semidirect
312. C₄×D₃	C₂×C₄×C₉	semidirect
313. C₄×D₃	C₂×C₄×C₉	semidirect
338. C₄⋊C₄	C₂×D₃×C₉	semidirect
344. C₄²	C₂×D₃×C₉	semidirect
381. C₉	D₃×#117	direct (N × H)
396. C₂×C₄	C₄×D₃×C₉	semidirect
412. D₃	C₉×#117	direct (N × H)
428. C₃	C₂×C₉×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₃×C₉	2
C₃×C₉×#117	2
C₉×#926	2
C₉×#892	2
D₃×C₉×C₄⋊C₄	2
D₃×C₉×C₂²⋊C₄	2
C₉×#877	2
C₉×#872	2
C₄²×D₃×C₉	2
C₃×D₃×#117	3
C₂×C₉×#117	3

Subgroups — D3×C9×#117 #13152494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×#117 #13152494