Subgroups — C₉×#3108 #11767829

Order 1152.

585 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	C₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#480	C₂	1	1	yes	maximal, characteristic
5	C₉×#479	C₂	1	2	yes	maximal, complemented
6	C₉×#464	C₂	1	2	yes	maximal, complemented
7	C₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#448	C₂	1	1	yes	maximal, characteristic
9	C₄×C₉×Q₁₆	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×SD₁₆	C₂	1	2	yes	maximal, complemented
11	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3108	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
16	C₉×#126	—	2	1	no	—
17	C₉×#125	C₂²	1	1	yes	characteristic
18	C₉×#124	C₂²	1	1	yes	characteristic
19	C₉×#123	—	2	1	no	—
20	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₉×#121	C₂²	1	1	yes	characteristic
22	C₄×Q₈×C₉	—	2	1	no	—
23	C₄×Q₈×C₉	—	2	1	no	—
24	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
25	C₄×Q₈×C₉	C₂²	1	2	yes	—
26	C₄×Q₈×C₉	C₂²	1	2	yes	—
27	C₄×D₄×C₉	—	2	1	no	—
28	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
29	C₉×#117	—	2	1	no	—
30	C₂×C₉×C₄⋊C₄	—	2	1	no	—
31	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₉	—	2	1	no	—
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₉×#107	C₂²	1	2	yes	—
35	C₉×#106	C₂²	1	2	yes	—
36	C₉×C₄⋊C₈	C₂²	1	2	yes	—
37	C₉×#103	C₂²	1	2	yes	—
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#103	C₂²	1	2	yes	—
40	C₉×#102	C₂²	1	2	yes	—
41	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₄×C₈×C₉	C₂²	1	2	yes	—
44	C₃×#529	C₂×C₃	1	1	yes	characteristic
45	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
46	C₃×#483	C₂×C₃	1	1	yes	characteristic
47	C₃×#480	C₂×C₃	1	1	yes	characteristic
48	C₃×#479	C₂×C₃	1	2	yes	—
49	C₃×#464	C₂×C₃	1	2	yes	—
50	C₃×#451	C₂×C₃	1	1	yes	characteristic
51	C₃×#448	C₂×C₃	1	1	yes	characteristic
52	C₃×C₄×Q₁₆	C₂×C₃	1	2	yes	—
53	C₃×C₄×SD₁₆	C₂×C₃	1	2	yes	—
54	C₃×#431	C₂×C₃	1	1	yes	characteristic
55	C₂×Q₈×C₉	—	2	4	no	—
56	C₂×Q₈×C₉	—	2	1	no	—
57	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
58	C₂×Q₈×C₉	C₂³	1	2	yes	—
59	C₂×D₄×C₉	—	2	1	no	—
60	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	—	2	1	no	—
62	C₂²×C₄×C₉	—	2	1	no	—
63	C₂²×C₄×C₉	—	2	1	no	—
64	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
65	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₉×Q₁₆	—	2	4	no	—
68	C₉×SD₁₆	—	2	4	no	—
69	C₂×C₈×C₉	C₂³	1	2	yes	—
70	C₂×C₈×C₉	C₂³	1	2	yes	—
71	C₉×C₄⋊C₄	—	2	2	no	—
72	C₉×C₄⋊C₄	—	2	2	no	—
73	C₉×C₄⋊C₄	—	2	1	no	—
74	C₉×C₄⋊C₄	—	2	1	no	—
75	C₉×C₄⋊C₄	—	2	1	no	—
76	C₉×C₄⋊C₄	—	2	1	no	—
77	C₉×C₄⋊C₄	—	2	1	no	—
78	C₉×C₄⋊C₄	C₂³	1	2	yes	—
79	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₉×C₂²⋊C₄	—	2	1	no	—
82	C₉×C₂²⋊C₄	—	2	1	no	—
83	C₉×C₂²⋊C₄	—	2	1	no	—
84	C₉×C₂²⋊C₄	—	2	1	no	—
85	C₉×C₂²⋊C₄	—	2	1	no	—
86	C₄²×C₉	—	2	2	no	—
87	C₄²×C₉	—	2	2	no	—
88	C₄²×C₉	—	2	1	no	—
89	C₄²×C₉	D₄	1	1	yes	characteristic
90	C₄²×C₉	D₄	1	1	yes	characteristic
91	C₄²×C₉	C₂³	1	1	yes	characteristic
92	C₄²×C₉	C₂³	1	1	yes	characteristic
93	#3108	C₉	1	1	yes	characteristic, direct product factor, Sylow
94	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
96	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
97	C₃×#126	—	2	1	no	—
98	C₃×#125	C₂²×C₃	1	1	yes	characteristic
99	C₃×#124	C₂²×C₃	1	1	yes	characteristic
100	C₃×#123	—	2	1	no	—
101	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₃×#121	C₂²×C₃	1	1	yes	characteristic
103	C₃×C₄×Q₈	—	2	1	no	—
104	C₃×C₄×Q₈	—	2	1	no	—
105	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
106	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
108	C₃×C₄×D₄	—	2	1	no	—
109	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
110	C₃×#117	—	2	1	no	—
111	C₂×C₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×C₄²	—	2	1	no	—
114	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
115	C₃×#107	C₂²×C₃	1	2	yes	—
116	C₃×#106	C₂²×C₃	1	2	yes	—
117	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
118	C₃×#103	C₂²×C₃	1	2	yes	—
119	C₃×#103	C₂²×C₃	1	2	yes	—
120	C₃×#103	C₂²×C₃	1	2	yes	—
121	C₃×#102	C₂²×C₃	1	2	yes	—
122	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
123	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
124	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
127	Q₈×C₉	—	2	4	no	—
128	Q₈×C₉	—	2	2	no	—
129	Q₈×C₉	—	2	2	no	—
130	Q₈×C₉	#41	1	4	yes	—
131	D₄×C₉	—	2	2	no	—
132	D₄×C₉	—	4	2	no	—
133	C₂×C₄×C₉	—	2	4	no	—
134	C₂×C₄×C₉	—	2	2	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	2	no	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	4	2	no	—
143	C₂×C₄×C₉	—	4	2	no	—
144	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
150	C₈×C₉	—	2	2	no	—
151	C₈×C₉	—	2	2	no	—
152	#529	C₂×C₉	1	1	yes	characteristic
153	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
154	#483	C₂×C₉	1	1	yes	characteristic, complemented
155	#480	C₂×C₉	1	1	yes	characteristic
156	#479	C₂×C₉	1	2	yes	complemented
157	#464	C₂×C₉	1	2	yes	complemented
158	#451	C₂×C₉	1	1	yes	characteristic, complemented
159	#448	C₂×C₉	1	1	yes	characteristic
160	C₄×Q₁₆	C₂×C₉	1	2	yes	complemented
161	C₄×SD₁₆	C₂×C₉	1	2	yes	complemented
162	#431	C₂×C₉	1	1	yes	characteristic, complemented
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	—	2	1	no	—
165	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
167	C₂×C₃×D₄	—	2	1	no	—
168	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	—	2	1	no	—
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
175	C₃×Q₁₆	—	2	4	no	—
176	C₃×SD₁₆	—	2	4	no	—
177	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
178	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
179	C₃×C₄⋊C₄	—	2	2	no	—
180	C₃×C₄⋊C₄	—	2	2	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	1	no	—
185	C₃×C₄⋊C₄	—	2	1	no	—
186	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
187	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
189	C₃×C₂²⋊C₄	—	2	1	no	—
190	C₃×C₂²⋊C₄	—	2	1	no	—
191	C₃×C₂²⋊C₄	—	2	1	no	—
192	C₃×C₂²⋊C₄	—	2	1	no	—
193	C₃×C₂²⋊C₄	—	2	1	no	—
194	C₃×C₄²	—	2	2	no	—
195	C₃×C₄²	—	2	2	no	—
196	C₃×C₄²	—	2	1	no	—
197	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
198	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
199	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
200	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₉	—	2	1	no	—
202	C₂²×C₉	—	2	1	no	—
203	C₂²×C₉	—	4	1	no	—
204	C₂²×C₉	—	4	1	no	—
205	C₂²×C₉	—	4	1	no	—
206	C₂²×C₉	#135	1	2	yes	—
207	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
208	C₄×C₉	—	2	4	no	—
209	C₄×C₉	—	2	1	no	—
210	C₄×C₉	—	2	1	no	—
211	C₄×C₉	—	2	1	no	—
212	C₄×C₉	—	2	1	no	—
213	C₄×C₉	—	4	1	no	—
214	C₄×C₉	—	4	2	no	—
215	C₄×C₉	—	4	1	no	—
216	C₄×C₉	—	4	1	no	—
217	C₄×C₉	#137	1	2	yes	—
218	C₄×C₉	C₂×#41	1	2	yes	—
219	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
220	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
221	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
222	#126	—	2	1	no	—
223	#125	C₂²×C₉	1	1	yes	characteristic
224	#124	C₂²×C₉	1	1	yes	characteristic
225	#123	—	2	1	no	—
226	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
227	#121	C₂²×C₉	1	1	yes	characteristic
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	—	2	1	no	—
230	C₄×Q₈	C₂²×C₉	1	2	yes	—
231	C₄×Q₈	C₂²×C₉	1	2	yes	—
232	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
233	C₄×D₄	—	2	1	no	—
234	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
235	#117	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
240	#107	C₂²×C₉	1	2	yes	—
241	#106	C₂²×C₉	1	2	yes	—
242	C₄⋊C₈	C₂²×C₉	1	2	yes	—
243	#103	C₂²×C₉	1	2	yes	—
244	#103	C₂²×C₉	1	2	yes	—
245	#103	C₂²×C₉	1	2	yes	—
246	#102	C₂²×C₉	1	2	yes	—
247	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
248	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
249	C₄×C₈	C₂²×C₉	1	2	yes	—
250	C₂³×C₃	—	2	1	no	—
251	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
252	C₃×Q₈	—	2	4	no	—
253	C₃×Q₈	—	2	2	no	—
254	C₃×Q₈	—	2	2	no	—
255	C₃×Q₈	C₃×#41	1	4	yes	—
256	C₃×D₄	—	2	2	no	—
257	C₃×D₄	—	4	2	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	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	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	4	2	no	—
268	C₂×C₃×C₄	—	4	2	no	—
269	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
275	C₃×C₈	—	2	2	no	—
276	C₃×C₈	—	2	2	no	—
277	C₂×C₉	—	2	2	no	—
278	C₂×C₉	—	8	1	no	—
279	C₂×C₉	#525	1	1	yes	characteristic
280	C₂×C₉	C₂×#135	1	1	yes	characteristic
281	C₂×C₉	C₂×#137	1	1	yes	characteristic
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
285	C₂×Q₈	C₂³×C₉	1	2	yes	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
292	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
294	Q₁₆	—	2	4	no	—
295	SD₁₆	—	2	4	no	—
296	C₂×C₈	C₂³×C₉	1	2	yes	—
297	C₂×C₈	C₂³×C₉	1	2	yes	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	C₂³×C₉	1	2	yes	—
306	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
307	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	—	2	1	no	—
310	C₂²⋊C₄	—	2	1	no	—
311	C₂²⋊C₄	—	2	1	no	—
312	C₂²⋊C₄	—	2	1	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	1	no	—
316	C₄²	D₄×C₉	1	1	yes	characteristic
317	C₄²	D₄×C₉	1	1	yes	characteristic
318	C₄²	C₂³×C₉	1	1	yes	characteristic
319	C₄²	C₂³×C₉	1	1	yes	characteristic
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	4	1	no	—
323	C₂²×C₃	—	4	1	no	—
324	C₂²×C₃	—	4	1	no	—
325	C₂²×C₃	C₃×#135	1	2	yes	—
326	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	2	1	no	—
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	4	2	no	—
333	C₃×C₄	—	4	1	no	—
334	C₃×C₄	—	4	1	no	—
335	C₃×C₄	—	4	1	no	—
336	C₃×C₄	C₃×#137	1	2	yes	—
337	C₃×C₄	C₂×C₃×#41	1	2	yes	—
338	C₉	#3108	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	2	1	no	—
340	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
341	Q₈	—	2	4	no	—
342	Q₈	—	2	2	no	—
343	Q₈	—	2	2	no	—
344	Q₈	C₉×#41	1	4	yes	—
345	D₄	—	2	2	no	—
346	D₄	—	4	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
360	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
361	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
362	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
363	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	8	1	no	—
368	C₂×C₃	C₃×#525	1	1	yes	characteristic
369	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
370	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	C₉×#135	1	2	yes	—
377	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
378	C₄	—	2	4	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	1	no	—
387	C₄	C₉×#137	1	2	yes	—
388	C₄	C₂×C₉×#41	1	2	yes	—
389	C₃	C₃×#3108	1	1	yes	characteristic
390	C₂	—	2	2	no	—
391	C₂	—	8	1	no	—
392	C₂	C₉×#525	1	1	yes	characteristic
393	C₂	C₂×C₉×#135	1	1	yes	characteristic
394	C₂	C₂×C₉×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#121	C₂²×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₈×C₉	C₂	semidirect
3. C₉×#483	C₂	semidirect
5. C₉×#479	C₂	semidirect
6. C₉×#464	C₂	semidirect
7. C₉×#451	C₂	semidirect
9. C₄×C₉×Q₁₆	C₂	semidirect
10. C₄×C₉×SD₁₆	C₂	semidirect
11. C₉×#431	C₂	semidirect
93. #3108	C₉	direct (N × H)
153. C₂×C₄×Q₈	C₂×C₉	semidirect
154. #483	C₂×C₉	semidirect
156. #479	C₂×C₉	semidirect
157. #464	C₂×C₉	semidirect
158. #451	C₂×C₉	semidirect
160. C₄×Q₁₆	C₂×C₉	semidirect
161. C₄×SD₁₆	C₂×C₉	semidirect
162. #431	C₂×C₉	semidirect
338. C₉	#3108	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#529	2
C₂×C₄×Q₈×C₉	2
C₉×#483	2
C₉×#480	2
C₉×#479	2
C₉×#464	2
C₉×#451	2
C₉×#448	2
C₄×C₉×Q₁₆	2
C₄×C₉×SD₁₆	2
C₉×#431	2
C₃×#3108	3

Subgroups — C9×#3108 #11767829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3108 #11767829