Subgroups — C₉×#2423 #11767144

Order 1152.

750 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#399	C₂	1	2	yes	maximal
4	C₉×#398	C₂	1	2	yes	maximal, complemented
5	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#388	C₂	1	2	yes	maximal
8	C₉×#387	C₂	1	2	yes	maximal, complemented
9	C₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#380	C₂	1	1	yes	maximal, characteristic
11	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₃×#2423	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₉×C₂²⋊Q₈	—	2	4	no	—
16	C₄×Q₈×C₉	—	2	4	no	—
17	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
31	C₂×C₄²×C₉	C₂²	1	2	yes	—
32	C₉×#95	C₂²	1	1	yes	characteristic
33	C₉×#95	C₂²	1	1	yes	characteristic
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	2	yes	—
36	C₉×#95	C₂²	1	2	yes	—
37	C₉×#95	C₂²	1	2	yes	—
38	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
40	C₃×#399	C₂×C₃	1	2	yes	—
41	C₃×#398	C₂×C₃	1	2	yes	—
42	C₃×#391	C₂×C₃	1	1	yes	characteristic
43	C₃×#389	C₂×C₃	1	1	yes	characteristic
44	C₃×#388	C₂×C₃	1	2	yes	—
45	C₃×#387	C₂×C₃	1	2	yes	—
46	C₃×#384	C₂×C₃	1	1	yes	characteristic
47	C₃×#380	C₂×C₃	1	1	yes	characteristic
48	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
49	C₂⁴×C₉	C₂³	1	1	yes	characteristic
50	C₂×Q₈×C₉	—	2	2	no	—
51	C₂×Q₈×C₉	—	2	2	no	—
52	C₂×Q₈×C₉	D₄	1	4	yes	—
53	C₂²×C₄×C₉	—	2	2	no	—
54	C₂²×C₄×C₉	—	2	2	no	—
55	C₂²×C₄×C₉	—	2	2	no	—
56	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₉	C₂³	1	2	yes	—
58	C₂²×C₄×C₉	C₂³	1	2	yes	—
59	C₂²×C₄×C₉	C₂³	1	2	yes	—
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	2	yes	—
62	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₉×C₄⋊C₄	—	2	4	no	—
67	C₉×C₄⋊C₄	—	2	2	no	—
68	C₉×C₄⋊C₄	—	2	2	no	—
69	C₉×C₄⋊C₄	—	2	4	no	—
70	C₉×C₄⋊C₄	—	2	4	no	—
71	C₉×C₄⋊C₄	—	2	2	no	—
72	C₉×C₄⋊C₄	—	4	2	no	—
73	C₉×C₄⋊C₄	—	4	2	no	—
74	C₉×C₂²⋊C₄	—	2	4	no	—
75	C₉×C₂²⋊C₄	—	2	2	no	—
76	C₉×C₂²⋊C₄	—	4	2	no	—
77	C₉×C₂²⋊C₄	Q₈	1	4	yes	complemented
78	C₄²×C₉	—	2	4	no	—
79	C₄²×C₉	—	2	2	no	—
80	C₄²×C₉	—	2	2	no	—
81	#2423	C₉	1	1	yes	characteristic, direct product factor, Sylow
82	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
83	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
84	C₃×C₂²⋊Q₈	—	2	4	no	—
85	C₃×C₄×Q₈	—	2	4	no	—
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
101	C₃×#95	C₂²×C₃	1	1	yes	characteristic
102	C₃×#95	C₂²×C₃	1	1	yes	characteristic
103	C₃×#95	C₂²×C₃	1	2	yes	—
104	C₃×#95	C₂²×C₃	1	2	yes	—
105	C₃×#95	C₂²×C₃	1	2	yes	—
106	C₃×#95	C₂²×C₃	1	2	yes	—
107	C₂³×C₉	—	2	1	no	—
108	C₂³×C₉	—	2	1	no	—
109	C₂³×C₉	—	2	1	no	—
110	C₂³×C₉	—	2	1	no	—
111	C₂³×C₉	—	2	1	no	—
112	C₂³×C₉	—	2	1	no	—
113	C₂³×C₉	C₂×Q₈	1	2	yes	—
114	C₂³×C₉	C₂⁴	1	1	yes	characteristic
115	Q₈×C₉	—	2	8	no	—
116	C₂×C₄×C₉	—	2	1	no	—
117	C₂×C₄×C₉	—	2	1	no	—
118	C₂×C₄×C₉	—	2	1	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	1	no	—
122	C₂×C₄×C₉	—	2	1	no	—
123	C₂×C₄×C₉	—	2	1	no	—
124	C₂×C₄×C₉	—	2	1	no	—
125	C₂×C₄×C₉	—	2	2	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	1	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	2	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	2	no	—
139	C₂×C₄×C₉	—	4	4	no	—
140	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
141	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
142	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
143	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
144	C₂×C₄×C₉	#41	1	2	yes	—
145	C₂×C₄×C₉	#41	1	2	yes	—
146	C₂×C₄×C₉	#41	1	2	yes	—
147	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic
148	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
149	#399	C₂×C₉	1	2	yes	—
150	#398	C₂×C₉	1	2	yes	complemented
151	#391	C₂×C₉	1	1	yes	characteristic, complemented
152	#389	C₂×C₉	1	1	yes	characteristic, complemented
153	#388	C₂×C₉	1	2	yes	—
154	#387	C₂×C₉	1	2	yes	complemented
155	#384	C₂×C₉	1	1	yes	characteristic, complemented
156	#380	C₂×C₉	1	1	yes	characteristic
157	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
158	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
159	C₂×C₃×Q₈	—	2	2	no	—
160	C₂×C₃×Q₈	—	2	2	no	—
161	C₂×C₃×Q₈	C₃×D₄	1	4	yes	—
162	C₂²×C₃×C₄	—	2	2	no	—
163	C₂²×C₃×C₄	—	2	2	no	—
164	C₂²×C₃×C₄	—	2	2	no	—
165	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
166	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
169	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
171	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
175	C₃×C₄⋊C₄	—	2	4	no	—
176	C₃×C₄⋊C₄	—	2	2	no	—
177	C₃×C₄⋊C₄	—	2	2	no	—
178	C₃×C₄⋊C₄	—	2	4	no	—
179	C₃×C₄⋊C₄	—	2	4	no	—
180	C₃×C₄⋊C₄	—	2	2	no	—
181	C₃×C₄⋊C₄	—	4	2	no	—
182	C₃×C₄⋊C₄	—	4	2	no	—
183	C₃×C₂²⋊C₄	—	2	4	no	—
184	C₃×C₂²⋊C₄	—	2	2	no	—
185	C₃×C₂²⋊C₄	—	4	2	no	—
186	C₃×C₂²⋊C₄	C₃×Q₈	1	4	yes	—
187	C₃×C₄²	—	2	4	no	—
188	C₃×C₄²	—	2	2	no	—
189	C₃×C₄²	—	2	2	no	—
190	C₂²×C₉	—	2	2	no	—
191	C₂²×C₉	—	2	2	no	—
192	C₂²×C₉	—	2	2	no	—
193	C₂²×C₉	—	4	1	no	—
194	C₂²×C₉	—	4	1	no	—
195	C₂²×C₉	—	4	1	no	—
196	C₂²×C₉	—	4	1	no	—
197	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
198	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
199	C₂²×C₉	C₂×#41	1	1	yes	characteristic
200	C₂²×C₉	C₂×#41	1	1	yes	characteristic
201	C₂²×C₉	C₂×#41	1	1	yes	characteristic
202	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
204	C₄×C₉	—	2	4	no	—
205	C₄×C₉	—	2	2	no	—
206	C₄×C₉	—	2	2	no	—
207	C₄×C₉	—	2	2	no	—
208	C₄×C₉	—	4	1	no	—
209	C₄×C₉	—	4	2	no	—
210	C₄×C₉	—	4	1	no	—
211	C₄×C₉	—	4	2	no	—
212	C₄×C₉	—	4	2	no	—
213	C₄×C₉	#123	1	4	yes	—
214	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
215	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
216	C₂²⋊Q₈	—	2	4	no	—
217	C₄×Q₈	—	2	4	no	—
218	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
220	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
221	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
222	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
223	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
224	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
225	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
227	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
228	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
229	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
230	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
231	C₂×C₄²	C₂²×C₉	1	2	yes	—
232	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
233	#95	C₂²×C₉	1	1	yes	characteristic
234	#95	C₂²×C₉	1	1	yes	characteristic
235	#95	C₂²×C₉	1	2	yes	—
236	#95	C₂²×C₉	1	2	yes	—
237	#95	C₂²×C₉	1	2	yes	—
238	#95	C₂²×C₉	1	2	yes	—
239	C₂³×C₃	—	2	1	no	—
240	C₂³×C₃	—	2	1	no	—
241	C₂³×C₃	—	2	1	no	—
242	C₂³×C₃	—	2	1	no	—
243	C₂³×C₃	—	2	1	no	—
244	C₂³×C₃	—	2	1	no	—
245	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
246	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
247	C₃×Q₈	—	2	8	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	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	2	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	4	4	no	—
272	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
273	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
274	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
275	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
276	C₂×C₃×C₄	C₃×#41	1	2	yes	—
277	C₂×C₃×C₄	C₃×#41	1	2	yes	—
278	C₂×C₃×C₄	C₃×#41	1	2	yes	—
279	C₂×C₉	—	4	2	no	—
280	C₂×C₉	C₂×#123	1	1	yes	characteristic
281	C₂×C₉	#533	1	1	yes	characteristic
282	C₂×C₉	#542	1	1	yes	characteristic
283	C₂×C₉	D₄×Q₈	1	1	yes	characteristic
284	C₂×C₉	#550	1	1	yes	characteristic
285	C₂×C₉	#552	1	1	yes	characteristic
286	C₂×C₉	#554	1	1	yes	characteristic
287	C₂⁴	C₂³×C₉	1	1	yes	characteristic
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	D₄×C₉	1	4	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	C₂³×C₉	1	2	yes	—
295	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
296	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
297	C₂²×C₄	C₂³×C₉	1	2	yes	—
298	C₂²×C₄	C₂³×C₉	1	2	yes	—
299	C₂²×C₄	C₂³×C₉	1	2	yes	—
300	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
301	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
303	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	Q₈×C₉	1	4	yes	complemented
316	C₄²	—	2	4	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	4	1	no	—
323	C₂²×C₃	—	4	1	no	—
324	C₂²×C₃	—	4	1	no	—
325	C₂²×C₃	—	4	1	no	—
326	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
327	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
328	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
329	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
330	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
331	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	2	2	no	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	4	1	no	—
338	C₃×C₄	—	4	2	no	—
339	C₃×C₄	—	4	1	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	2	no	—
342	C₃×C₄	C₃×#123	1	4	yes	—
343	C₉	#2423	1	1	yes	characteristic, direct product factor, Sylow
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	C₂×Q₈×C₉	1	2	yes	—
351	C₂³	C₂⁴×C₉	1	1	yes	characteristic
352	Q₈	—	2	8	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	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	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
378	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
379	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
380	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
381	C₂×C₄	C₉×#41	1	2	yes	—
382	C₂×C₄	C₉×#41	1	2	yes	—
383	C₂×C₄	C₉×#41	1	2	yes	—
384	C₂×C₃	—	4	2	no	—
385	C₂×C₃	C₂×C₃×#123	1	1	yes	characteristic
386	C₂×C₃	C₃×#533	1	1	yes	characteristic
387	C₂×C₃	C₃×#542	1	1	yes	characteristic
388	C₂×C₃	C₃×D₄×Q₈	1	1	yes	characteristic
389	C₂×C₃	C₃×#550	1	1	yes	characteristic
390	C₂×C₃	C₃×#552	1	1	yes	characteristic
391	C₂×C₃	C₃×#554	1	1	yes	characteristic
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
400	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
401	C₂²	C₂×C₉×#41	1	1	yes	characteristic
402	C₂²	C₂×C₉×#41	1	1	yes	characteristic
403	C₂²	C₂×C₉×#41	1	1	yes	characteristic
404	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
405	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
406	C₄	—	2	4	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	C₉×#123	1	4	yes	—
416	C₃	C₃×#2423	1	1	yes	characteristic
417	C₂	—	4	2	no	—
418	C₂	C₂×C₉×#123	1	1	yes	characteristic
419	C₂	C₉×#533	1	1	yes	characteristic
420	C₂	C₉×#542	1	1	yes	characteristic
421	C₂	D₄×Q₈×C₉	1	1	yes	characteristic
422	C₂	C₉×#550	1	1	yes	characteristic
423	C₂	C₉×#552	1	1	yes	characteristic
424	C₂	C₉×#554	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×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
4. C₉×#398	C₂	semidirect
5. C₉×#391	C₂	semidirect
6. C₉×#389	C₂	semidirect
8. C₉×#387	C₂	semidirect
9. C₉×#384	C₂	semidirect
77. C₉×C₂²⋊C₄	Q₈	semidirect
81. #2423	C₉	direct (N × H)
148. C₂×C₄×Q₈	C₂×C₉	semidirect
150. #398	C₂×C₉	semidirect
151. #391	C₂×C₉	semidirect
152. #389	C₂×C₉	semidirect
154. #387	C₂×C₉	semidirect
155. #384	C₂×C₉	semidirect
315. C₂²⋊C₄	Q₈×C₉	semidirect
343. C₉	#2423	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×C₂²⋊Q₈	2
C₂×C₄×Q₈×C₉	2
C₉×#399	2
C₉×#398	2
C₉×#391	2
C₉×#389	2
C₉×#388	2
C₉×#387	2
C₉×#384	2
C₉×#380	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2423	3

Subgroups — C9×#2423 #11767144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2423 #11767144