Subgroups — C₉×#3107 #11767828

Order 1152.

585 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic
3	C₉×#485	C₂	1	2	yes	maximal, complemented
4	C₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#474	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#452	C₂	1	2	yes	maximal
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×#3107	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
16	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₉×#125	—	2	1	no	—
19	C₉×C₂²⋊Q₈	—	2	1	no	—
20	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₄×Q₈×C₉	—	2	1	no	—
22	C₄×Q₈×C₉	C₂²	1	2	yes	—
23	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
24	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
25	C₄×D₄×C₉	—	2	1	no	—
26	C₄×D₄×C₉	—	2	1	no	—
27	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
28	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
29	C₉×#117	—	2	1	no	—
30	C₉×#117	—	2	1	no	—
31	C₉×#117	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	1	yes	characteristic
37	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₉×#103	C₂²	1	2	yes	—
39	C₉×#103	C₂²	1	2	yes	—
40	C₉×#103	C₂²	1	2	yes	—
41	C₉×#102	C₂²	1	2	yes	—
42	C₉×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₄×C₈×C₉	C₂²	1	2	yes	—
44	C₃×#533	C₂×C₃	1	1	yes	characteristic
45	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic
46	C₃×#485	C₂×C₃	1	2	yes	—
47	C₃×#475	C₂×C₃	1	1	yes	characteristic
48	C₃×#474	C₂×C₃	1	1	yes	characteristic
49	C₃×#462	C₂×C₃	1	1	yes	characteristic
50	C₃×#461	C₂×C₃	1	1	yes	characteristic
51	C₃×#452	C₂×C₃	1	2	yes	—
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	C₉×#41	—	2	2	no	—
56	C₉×#41	—	2	2	no	—
57	C₂×Q₈×C₉	—	2	1	no	—
58	C₂×Q₈×C₉	C₂³	1	2	yes	—
59	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
60	C₂×D₄×C₉	—	2	1	no	—
61	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₉	—	2	1	no	—
63	C₂²×C₄×C₉	—	2	1	no	—
64	C₂²×C₄×C₉	—	2	1	no	—
65	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
66	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
67	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₉×Q₁₆	—	2	4	no	—
69	C₉×SD₁₆	—	2	4	no	—
70	C₂×C₈×C₉	C₂³	1	2	yes	—
71	C₂×C₈×C₉	C₂³	1	2	yes	—
72	C₉×C₄⋊C₄	—	2	1	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	2	no	—
78	C₉×C₄⋊C₄	—	2	2	no	—
79	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₉×C₄⋊C₄	C₂³	1	2	yes	—
82	C₉×C₂²⋊C₄	—	2	2	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	1	no	—
87	C₄²×C₉	—	2	1	no	—
88	C₄²×C₉	—	2	1	no	—
89	C₄²×C₉	—	2	2	no	—
90	C₄²×C₉	D₄	1	1	yes	characteristic
91	C₄²×C₉	D₄	1	1	yes	characteristic
92	C₄²×C₉	C₂³	1	1	yes	characteristic
93	C₄²×C₉	C₂³	1	1	yes	characteristic
94	#3107	C₉	1	1	yes	characteristic, direct product factor, Sylow
95	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
97	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
98	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
99	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
100	C₃×#125	—	2	1	no	—
101	C₃×C₂²⋊Q₈	—	2	1	no	—
102	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
103	C₃×C₄×Q₈	—	2	1	no	—
104	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
105	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₃×C₄×D₄	—	2	1	no	—
108	C₃×C₄×D₄	—	2	1	no	—
109	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
110	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
111	C₃×#117	—	2	1	no	—
112	C₃×#117	—	2	1	no	—
113	C₃×#117	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×C₄²	—	2	1	no	—
115	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
116	C₃×#107	C₂²×C₃	1	2	yes	—
117	C₃×#106	C₂²×C₃	1	2	yes	—
118	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
119	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₃×#103	C₂²×C₃	1	2	yes	—
121	C₃×#103	C₂²×C₃	1	2	yes	—
122	C₃×#103	C₂²×C₃	1	2	yes	—
123	C₃×#102	C₂²×C₃	1	2	yes	—
124	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
125	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
126	C₂³×C₉	—	2	1	no	—
127	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
128	Q₈×C₉	—	2	1	no	—
129	Q₈×C₉	—	2	2	no	—
130	Q₈×C₉	—	2	2	no	—
131	Q₈×C₉	—	4	2	no	—
132	Q₈×C₉	#41	1	2	yes	—
133	D₄×C₉	—	2	4	no	—
134	D₄×C₉	—	2	1	no	—
135	D₄×C₉	#41	1	2	yes	—
136	C₂×C₄×C₉	—	2	4	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	2	no	—
146	C₂×C₄×C₉	—	4	2	no	—
147	C₂×C₄×C₉	—	4	2	no	—
148	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
154	C₈×C₉	—	2	2	no	—
155	C₈×C₉	—	2	2	no	—
156	#533	C₂×C₉	1	1	yes	characteristic, complemented
157	C₄×#41	C₂×C₉	1	1	yes	characteristic
158	#485	C₂×C₉	1	2	yes	complemented
159	#475	C₂×C₉	1	1	yes	characteristic, complemented
160	#474	C₂×C₉	1	1	yes	characteristic, complemented
161	#462	C₂×C₉	1	1	yes	characteristic, complemented
162	#461	C₂×C₉	1	1	yes	characteristic, complemented
163	#452	C₂×C₉	1	2	yes	—
164	C₄×Q₁₆	C₂×C₉	1	2	yes	complemented
165	C₄×SD₁₆	C₂×C₉	1	2	yes	complemented
166	#431	C₂×C₉	1	1	yes	characteristic, complemented
167	C₃×#41	—	2	2	no	—
168	C₃×#41	—	2	2	no	—
169	C₂×C₃×Q₈	—	2	1	no	—
170	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
171	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₃×D₄	—	2	1	no	—
173	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
180	C₃×Q₁₆	—	2	4	no	—
181	C₃×SD₁₆	—	2	4	no	—
182	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
183	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
184	C₃×C₄⋊C₄	—	2	1	no	—
185	C₃×C₄⋊C₄	—	2	1	no	—
186	C₃×C₄⋊C₄	—	2	1	no	—
187	C₃×C₄⋊C₄	—	2	1	no	—
188	C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×C₄⋊C₄	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
192	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
194	C₃×C₂²⋊C₄	—	2	2	no	—
195	C₃×C₂²⋊C₄	—	2	1	no	—
196	C₃×C₂²⋊C₄	—	2	1	no	—
197	C₃×C₂²⋊C₄	—	2	1	no	—
198	C₃×C₄²	—	2	1	no	—
199	C₃×C₄²	—	2	1	no	—
200	C₃×C₄²	—	2	1	no	—
201	C₃×C₄²	—	2	2	no	—
202	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
203	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
204	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
205	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
206	C₂²×C₉	—	2	1	no	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	—	2	1	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	—	4	1	no	—
211	C₂²×C₉	—	4	1	no	—
212	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	2	2	no	—
215	C₄×C₉	—	2	1	no	—
216	C₄×C₉	—	2	1	no	—
217	C₄×C₉	—	4	2	no	—
218	C₄×C₉	—	4	1	no	—
219	C₄×C₉	—	4	2	no	—
220	C₄×C₉	—	4	1	no	—
221	C₄×C₉	#135	1	2	yes	—
222	C₄×C₉	#137	1	2	yes	—
223	C₄×C₉	C₂×#41	1	1	yes	characteristic
224	C₄×C₉	C₂×#41	1	1	yes	characteristic
225	C₂×#41	C₂²×C₉	1	1	yes	characteristic
226	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
227	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
228	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
229	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
230	#125	—	2	1	no	—
231	C₂²⋊Q₈	—	2	1	no	—
232	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
233	C₄×Q₈	—	2	1	no	—
234	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
235	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
236	C₄×Q₈	C₂²×C₉	1	2	yes	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
240	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
241	#117	—	2	1	no	—
242	#117	—	2	1	no	—
243	#117	C₂²×C₉	1	1	yes	characteristic
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
246	#107	C₂²×C₉	1	2	yes	—
247	#106	C₂²×C₉	1	2	yes	—
248	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
249	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
250	#103	C₂²×C₉	1	2	yes	—
251	#103	C₂²×C₉	1	2	yes	—
252	#103	C₂²×C₉	1	2	yes	—
253	#102	C₂²×C₉	1	2	yes	—
254	C₂²⋊C₈	C₂²×C₉	1	2	yes	—
255	C₄×C₈	C₂²×C₉	1	2	yes	—
256	C₂³×C₃	—	2	1	no	—
257	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
258	C₃×Q₈	—	2	1	no	—
259	C₃×Q₈	—	2	2	no	—
260	C₃×Q₈	—	2	2	no	—
261	C₃×Q₈	—	4	2	no	—
262	C₃×Q₈	C₃×#41	1	2	yes	—
263	C₃×D₄	—	2	4	no	—
264	C₃×D₄	—	2	1	no	—
265	C₃×D₄	C₃×#41	1	2	yes	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	4	2	no	—
277	C₂×C₃×C₄	—	4	2	no	—
278	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
284	C₃×C₈	—	2	2	no	—
285	C₃×C₈	—	2	2	no	—
286	C₂×C₉	—	4	1	no	—
287	C₂×C₉	—	4	2	no	—
288	C₂×C₉	#525	1	1	yes	characteristic
289	C₂×C₉	C₂×#135	1	1	yes	characteristic
290	C₂×C₉	C₂×#137	1	1	yes	characteristic
291	#41	—	2	2	no	—
292	#41	—	2	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	C₂³×C₉	1	2	yes	—
295	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
302	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
303	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
304	Q₁₆	—	2	4	no	—
305	SD₁₆	—	2	4	no	—
306	C₂×C₈	C₂³×C₉	1	2	yes	—
307	C₂×C₈	C₂³×C₉	1	2	yes	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	C₂³×C₉	1	2	yes	—
316	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
317	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	2	no	—
326	C₄²	D₄×C₉	1	1	yes	characteristic
327	C₄²	D₄×C₉	1	1	yes	characteristic
328	C₄²	C₂³×C₉	1	1	yes	characteristic
329	C₄²	C₂³×C₉	1	1	yes	characteristic
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	2	2	no	—
334	C₂²×C₃	—	4	1	no	—
335	C₂²×C₃	—	4	1	no	—
336	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	4	1	no	—
342	C₃×C₄	—	4	2	no	—
343	C₃×C₄	—	4	1	no	—
344	C₃×C₄	—	4	2	no	—
345	C₃×C₄	C₃×#135	1	2	yes	—
346	C₃×C₄	C₃×#137	1	2	yes	—
347	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
348	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
349	C₉	#3107	1	1	yes	characteristic, direct product factor, Sylow
350	C₂³	—	2	1	no	—
351	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	2	2	no	—
354	Q₈	—	2	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	C₉×#41	1	2	yes	—
357	D₄	—	2	4	no	—
358	D₄	—	2	1	no	—
359	D₄	C₉×#41	1	2	yes	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
373	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
375	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
377	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₂×C₃	—	4	1	no	—
381	C₂×C₃	—	4	2	no	—
382	C₂×C₃	C₃×#525	1	1	yes	characteristic
383	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
384	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
385	C₂²	—	2	1	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	1	no	—
400	C₄	C₉×#135	1	2	yes	—
401	C₄	C₉×#137	1	2	yes	—
402	C₄	C₂×C₉×#41	1	1	yes	characteristic
403	C₄	C₂×C₉×#41	1	1	yes	characteristic
404	C₃	C₃×#3107	1	1	yes	characteristic
405	C₂	—	4	1	no	—
406	C₂	—	4	2	no	—
407	C₂	C₉×#525	1	1	yes	characteristic
408	C₂	C₂×C₉×#135	1	1	yes	characteristic
409	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	C₂×C₃×#41	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
1. C₉×#533	C₂	semidirect
3. C₉×#485	C₂	semidirect
4. C₉×#475	C₂	semidirect
5. C₉×#474	C₂	semidirect
6. C₉×#462	C₂	semidirect
7. C₉×#461	C₂	semidirect
9. C₄×C₉×Q₁₆	C₂	semidirect
10. C₄×C₉×SD₁₆	C₂	semidirect
11. C₉×#431	C₂	semidirect
94. #3107	C₉	direct (N × H)
156. #533	C₂×C₉	semidirect
158. #485	C₂×C₉	semidirect
159. #475	C₂×C₉	semidirect
160. #474	C₂×C₉	semidirect
161. #462	C₂×C₉	semidirect
162. #461	C₂×C₉	semidirect
164. C₄×Q₁₆	C₂×C₉	semidirect
165. C₄×SD₁₆	C₂×C₉	semidirect
166. #431	C₂×C₉	semidirect
349. C₉	#3107	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×#533	2
C₄×C₉×#41	2
C₉×#485	2
C₉×#475	2
C₉×#474	2
C₉×#462	2
C₉×#461	2
C₉×#452	2
C₄×C₉×Q₁₆	2
C₄×C₉×SD₁₆	2
C₉×#431	2
C₃×#3107	3

Subgroups — C9×#3107 #11767828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3107 #11767828