Subgroups — C₉×#5726 #13153308

Order 1728.

944 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#239	C₂	1	2	yes	maximal, complemented
2	C₃×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#946	C₂	1	2	yes	maximal, complemented
4	C₉×#895	C₂	1	2	yes	maximal, complemented
5	C₉×#894	C₂	1	4	yes	maximal, complemented
6	D₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5726	C₃	1	1	yes	maximal, characteristic
10	C₉×#547	—	3	1	no	maximal
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₉×#239	—	2	8	no	—
13	C₂×C₉×D₁₂	C₂²	1	4	yes	—
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	4	yes	—
18	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
19	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
25	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
28	C₂×C₃×#239	C₂×C₃	1	2	yes	—
29	C₃²×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
30	C₃×#946	C₂×C₃	1	2	yes	—
31	C₃×#895	C₂×C₃	1	2	yes	—
32	C₃×#894	C₂×C₃	1	4	yes	—
33	C₃×D₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
34	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
35	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
36	C₂×C₉×#41	—	3	2	no	—
37	C₉×C₄⋊Q₈	—	2	1	no	—
38	C₉×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
39	C₉×#123	—	3	4	no	—
40	C₉×C₂²⋊Q₈	—	3	2	no	—
41	C₉×#121	—	3	2	no	—
42	C₄×D₄×C₉	—	3	1	no	—
43	C₄×D₄×C₉	—	3	1	no	—
44	C₂×C₉×C₄⋊C₄	—	3	2	no	—
45	C₂²×D₃×C₉	C₂³	1	2	yes	—
46	C₂²×D₃×C₉	C₂³	1	2	yes	—
47	C₃×Q₈×C₉	—	2	4	no	—
48	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₂×C₉×Dic₃	C₂³	1	2	yes	—
53	C₂×C₉×Dic₃	C₂³	1	2	yes	—
54	C₉×D₁₂	—	2	8	no	—
55	C₉×D₁₂	—	2	2	no	—
56	C₉×D₁₂	D₄	1	4	yes	complemented
57	C₄×D₃×C₉	—	2	8	no	—
58	C₄×D₃×C₉	—	2	4	no	—
59	C₄×D₃×C₉	—	2	4	no	—
60	C₃×#547	—	3	1	no	—
61	#5726	C₉	1	1	yes	characteristic, direct product factor
62	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
63	C₃×#239	—	2	8	no	—
64	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
65	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
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×C₄×D₃	C₂²×C₃	1	2	yes	—
70	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
71	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
73	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
74	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
75	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
76	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
77	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
78	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
79	C₉×#41	—	6	8	no	—
80	C₂×Q₈×C₉	—	2	2	no	—
81	C₂×Q₈×C₉	C₂×D₃	1	2	yes	—
82	C₂×D₄×C₉	—	3	1	no	—
83	C₂×D₄×C₉	—	3	1	no	—
84	C₂×D₄×C₉	—	3	4	no	—
85	C₂²×C₄×C₉	—	3	2	no	—
86	C₂²×C₄×C₉	—	3	4	no	—
87	C₂²×C₄×C₉	—	3	2	no	—
88	C₉×C₄⋊C₄	—	2	2	no	—
89	C₉×C₄⋊C₄	—	2	2	no	—
90	C₉×C₄⋊C₄	—	3	1	no	—
91	C₉×C₄⋊C₄	—	3	4	no	—
92	C₉×C₄⋊C₄	—	3	1	no	—
93	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
94	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
95	C₉×C₂²⋊C₄	—	3	2	no	—
96	C₉×C₂²⋊C₄	—	3	2	no	—
97	C₉×C₂²⋊C₄	—	3	4	no	—
98	C₄²×C₉	—	2	1	no	—
99	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
100	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
101	C₂×D₃×C₉	—	2	2	no	—
102	C₂×D₃×C₉	—	2	2	no	—
103	C₂×D₃×C₉	—	2	2	no	—
104	C₂×D₃×C₉	—	2	2	no	—
105	C₂×D₃×C₉	—	2	2	no	—
106	C₂×D₃×C₉	C₂×D₄	1	4	yes	—
107	C₃×C₄×C₉	—	2	4	no	—
108	C₃×C₄×C₉	—	2	1	no	—
109	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
110	C₃×C₄×C₉	#41	1	2	yes	complemented
111	C₉×Dic₃	—	2	2	no	—
112	C₉×Dic₃	—	2	2	no	—
113	C₂×C₃×#41	—	3	2	no	—
114	C₂×#239	C₂×C₉	1	2	yes	complemented
115	C₃×C₄⋊Q₈	—	2	1	no	—
116	C₃×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
117	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
118	C₃×#123	—	3	4	no	—
119	C₃×C₂²⋊Q₈	—	3	2	no	—
120	C₃×#121	—	3	2	no	—
121	C₃×C₄×D₄	—	3	1	no	—
122	C₃×C₄×D₄	—	3	1	no	—
123	C₂×C₃×C₄⋊C₄	—	3	2	no	—
124	#946	C₂×C₉	1	2	yes	complemented
125	#895	C₂×C₉	1	2	yes	complemented
126	#894	C₂×C₉	1	4	yes	complemented
127	D₃×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
128	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
129	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
130	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
131	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
132	C₃²×Q₈	—	2	4	no	—
133	C₂×C₃²×C₄	C₂³×C₃	1	4	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	1	yes	characteristic
137	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
138	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
139	C₃×D₁₂	—	2	8	no	—
140	C₃×D₁₂	—	2	2	no	—
141	C₃×D₁₂	C₃×D₄	1	4	yes	—
142	C₃×C₄×D₃	—	2	8	no	—
143	C₃×C₄×D₃	—	2	4	no	—
144	C₃×C₄×D₃	—	2	4	no	—
145	C₂³×C₉	—	3	2	no	—
146	C₂³×C₉	—	3	2	no	—
147	Q₈×C₉	—	2	4	no	—
148	Q₈×C₉	—	4	4	no	—
149	D₄×C₉	—	3	4	no	—
150	D₄×C₉	—	6	8	no	—
151	D₄×C₉	—	6	2	no	—
152	C₂×C₄×C₉	—	2	1	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	2	4	no	—
156	C₂×C₄×C₉	—	3	2	no	—
157	C₂×C₄×C₉	—	3	2	no	—
158	C₂×C₄×C₉	—	6	8	no	—
159	C₂×C₄×C₉	—	6	4	no	—
160	C₂×C₄×C₉	—	6	4	no	—
161	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
162	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
163	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
164	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
165	#547	—	3	1	no	Sylow
166	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
168	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
169	D₃×C₉	—	2	4	no	—
170	D₃×C₉	—	4	2	no	—
171	C₃×#41	—	6	8	no	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	C₂²×C₉	1	2	yes	—
174	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
175	C₂×C₃×D₄	—	3	1	no	—
176	C₂×C₃×D₄	—	3	1	no	—
177	C₂×C₃×D₄	—	3	4	no	—
178	C₂²×C₃×C₄	—	3	2	no	—
179	C₂²×C₃×C₄	—	3	4	no	—
180	C₂²×C₃×C₄	—	3	2	no	—
181	#239	—	2	8	no	—
182	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
183	C₂×D₁₂	C₂²×C₉	1	4	yes	—
184	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
185	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
186	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
187	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	3	4	no	—
191	C₃×C₄⋊C₄	—	3	1	no	—
192	C₃×C₄⋊C₄	—	3	1	no	—
193	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
194	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
195	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
196	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
197	C₃×C₂²⋊C₄	—	3	2	no	—
198	C₃×C₂²⋊C₄	—	3	2	no	—
199	C₃×C₂²⋊C₄	—	3	4	no	—
200	C₃×C₄²	—	2	1	no	—
201	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
202	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
203	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
204	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
205	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
206	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
207	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
208	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
209	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
210	C₂×C₃×D₃	—	2	2	no	—
211	C₂×C₃×D₃	—	2	2	no	—
212	C₂×C₃×D₃	—	2	2	no	—
213	C₂×C₃×D₃	—	2	2	no	—
214	C₂×C₃×D₃	—	2	2	no	—
215	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
216	C₃²×C₄	—	2	1	no	—
217	C₃²×C₄	—	2	4	no	—
218	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
219	C₃²×C₄	C₃×#41	1	2	yes	—
220	C₃×Dic₃	—	2	2	no	—
221	C₃×Dic₃	—	2	2	no	—
222	C₂²×C₉	—	2	1	no	—
223	C₂²×C₉	—	3	4	no	—
224	C₂²×C₉	—	6	2	no	—
225	C₂²×C₉	—	6	2	no	—
226	C₂²×C₉	—	6	2	no	—
227	C₂²×C₉	—	6	2	no	—
228	C₂²×C₉	—	6	2	no	—
229	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
230	C₄×C₉	—	2	2	no	—
231	C₄×C₉	—	2	4	no	—
232	C₄×C₉	—	2	1	no	—
233	C₄×C₉	—	2	2	no	—
234	C₄×C₉	—	2	2	no	—
235	C₄×C₉	—	4	4	no	—
236	C₄×C₉	—	6	2	no	—
237	C₄×C₉	—	6	2	no	—
238	C₄×C₉	D₃×D₄	1	2	yes	—
239	C₄×C₉	#239	1	2	yes	complemented
240	C₂×#41	—	3	2	no	—
241	C₄⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
242	#123	—	3	4	no	—
243	C₂²⋊Q₈	—	3	2	no	—
244	#121	—	3	2	no	—
245	C₄×D₄	—	3	1	no	—
246	C₄×D₄	—	3	1	no	—
247	C₂×C₄⋊C₄	—	3	2	no	—
248	C₃×C₉	#547	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₃	—	3	2	no	—
250	C₂³×C₃	—	3	2	no	—
251	C₂²×D₃	C₂³×C₉	1	2	yes	—
252	C₂²×D₃	C₂³×C₉	1	2	yes	—
253	C₃×Q₈	—	2	4	no	—
254	C₃×Q₈	—	2	4	no	—
255	C₃×Q₈	—	4	4	no	—
256	C₃×D₄	—	3	4	no	—
257	C₃×D₄	—	6	8	no	—
258	C₃×D₄	—	6	2	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	3	2	no	—
264	C₂×C₃×C₄	—	3	2	no	—
265	C₂×C₃×C₄	—	6	8	no	—
266	C₂×C₃×C₄	—	6	4	no	—
267	C₂×C₃×C₄	—	6	4	no	—
268	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
269	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
274	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
276	C₂×Dic₃	C₂³×C₉	1	2	yes	—
277	C₂×Dic₃	C₂³×C₉	1	2	yes	—
278	D₁₂	—	2	8	no	—
279	D₁₂	—	2	2	no	—
280	D₁₂	D₄×C₉	1	4	yes	complemented
281	C₄×D₃	—	2	8	no	—
282	C₄×D₃	—	2	4	no	—
283	C₄×D₃	—	2	4	no	—
284	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
285	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
286	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
287	C₃×D₃	—	2	4	no	—
288	C₃×D₃	—	4	2	no	—
289	C₂×C₉	—	2	1	no	—
290	C₂×C₉	—	2	1	no	—
291	C₂×C₉	—	2	1	no	—
292	C₂×C₉	—	6	4	no	—
293	C₂×C₉	—	12	2	no	—
294	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
295	C₂×C₉	C₂×#239	1	1	yes	characteristic
296	C₂×C₉	#1007	1	1	yes	characteristic
297	#41	—	6	8	no	—
298	C₂×Q₈	C₂×D₃×C₉	1	2	yes	—
299	C₂×D₄	—	3	1	no	—
300	C₂×D₄	—	3	1	no	—
301	C₂×D₄	—	3	4	no	—
302	C₂²×C₄	—	3	2	no	—
303	C₂²×C₄	—	3	4	no	—
304	C₂²×C₄	—	3	2	no	—
305	C₄⋊C₄	—	3	1	no	—
306	C₄⋊C₄	—	3	4	no	—
307	C₄⋊C₄	—	3	1	no	—
308	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
309	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
310	C₂²⋊C₄	—	3	2	no	—
311	C₂²⋊C₄	—	3	2	no	—
312	C₂²⋊C₄	—	3	4	no	—
313	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	3	4	no	—
316	C₂²×C₃	—	6	2	no	—
317	C₂²×C₃	—	6	2	no	—
318	C₂²×C₃	—	6	2	no	—
319	C₂²×C₃	—	6	2	no	—
320	C₂²×C₃	—	6	2	no	—
321	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
322	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
323	C₂×D₃	—	2	2	no	—
324	C₂×D₃	—	2	2	no	—
325	C₂×D₃	—	2	2	no	—
326	C₂×D₃	—	2	2	no	—
327	C₂×D₃	—	2	2	no	—
328	C₂×D₃	C₂×D₄×C₉	1	4	yes	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	4	4	no	—
337	C₃×C₄	—	6	2	no	—
338	C₃×C₄	—	6	2	no	—
339	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
340	C₃×C₄	C₉×#41	1	2	yes	complemented
341	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
342	C₃×C₄	C₃×#239	1	2	yes	—
343	Dic₃	—	2	2	no	—
344	Dic₃	—	2	2	no	—
345	C₃²	C₃×#547	1	1	yes	characteristic
346	C₉	—	2	1	no	—
347	C₉	#5726	1	1	yes	characteristic, direct product factor
348	C₂³	—	3	2	no	—
349	C₂³	—	3	2	no	—
350	Q₈	—	2	4	no	—
351	D₄	—	3	4	no	—
352	D₄	—	6	8	no	—
353	D₄	—	6	2	no	—
354	C₂×C₄	—	3	2	no	—
355	C₂×C₄	—	3	2	no	—
356	C₂×C₄	—	6	8	no	—
357	C₂×C₄	—	6	4	no	—
358	C₂×C₄	—	6	4	no	—
359	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
361	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	6	4	no	—
367	C₂×C₃	—	12	2	no	—
368	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
369	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
370	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
371	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
372	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
373	C₂×C₃	C₃×#1007	1	1	yes	characteristic
374	D₃	—	2	4	no	—
375	D₃	—	4	2	no	—
376	C₂²	—	3	4	no	—
377	C₂²	—	6	2	no	—
378	C₂²	—	6	2	no	—
379	C₂²	—	6	2	no	—
380	C₂²	—	6	2	no	—
381	C₂²	—	6	2	no	—
382	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
383	C₄	—	2	4	no	—
384	C₄	—	2	1	no	—
385	C₄	—	6	2	no	—
386	C₄	—	6	2	no	—
387	C₄	D₃×D₄×C₉	1	2	yes	—
388	C₄	C₉×#239	1	2	yes	complemented
389	C₃	—	2	1	no	—
390	C₃	C₉×#547	1	1	yes	characteristic, complemented
391	C₃	C₃×#5726	1	1	yes	characteristic
392	C₂	—	6	4	no	—
393	C₂	—	12	2	no	—
394	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
395	C₂	C₂×C₉×#239	1	1	yes	characteristic
396	C₂	C₉×#1007	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₄⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5726	C₃
hypercenter	C₉×C₄⋊Q₈	D₃
hypocenter	C₃	C₉×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#239	C₂	semidirect
2. C₃×C₉×C₄⋊Q₈	C₂	semidirect
3. C₉×#946	C₂	semidirect
4. C₉×#895	C₂	semidirect
5. C₉×#894	C₂	semidirect
6. D₃×C₉×C₄⋊C₄	C₂	semidirect
7. C₄×C₉×D₁₂	C₂	semidirect
8. C₄×C₉×D₁₂	C₂	semidirect
38. C₉×C₄⋊Q₈	D₃	semidirect
56. C₉×D₁₂	D₄	semidirect
61. #5726	C₉	direct (N × H)
110. C₃×C₄×C₉	#41	semidirect
114. C₂×#239	C₂×C₉	semidirect
116. C₃×C₄⋊Q₈	C₂×C₉	semidirect
124. #946	C₂×C₉	semidirect
125. #895	C₂×C₉	semidirect
126. #894	C₂×C₉	semidirect
127. D₃×C₄⋊C₄	C₂×C₉	semidirect
128. C₄×D₁₂	C₂×C₉	semidirect
129. C₄×D₁₂	C₂×C₉	semidirect
239. C₄×C₉	#239	semidirect
241. C₄⋊Q₈	D₃×C₉	semidirect
248. C₃×C₉	#547	semidirect
280. D₁₂	D₄×C₉	semidirect
340. C₃×C₄	C₉×#41	semidirect
347. C₉	#5726	direct (N × H)
388. C₄	C₉×#239	semidirect
390. C₃	C₉×#547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#239	2
C₃×C₉×C₄⋊Q₈	2
C₉×#946	2
C₉×#895	2
C₉×#894	2
D₃×C₉×C₄⋊C₄	2
C₄×C₉×D₁₂	2
C₃×#5726	3
C₉×#547	3

Subgroups — C9×#5726 #13153308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5726 #13153308