Subgroups — C₉×#2323 #11767044

Order 1152.

834 conjugacy classes of subgroups.

The subgroup lattice has 432 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	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic
4	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#389	C₂	1	2	yes	maximal, complemented
7	C₉×#388	C₂	1	2	yes	maximal
8	C₉×#388	C₂	1	2	yes	maximal
9	C₉×#387	C₂	1	2	yes	maximal, complemented
10	C₉×#380	C₂	1	1	yes	maximal, characteristic
11	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2323	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	C₄	1	8	yes	complemented
16	C₄×Q₈×C₉	—	2	4	no	—
17	C₉×#117	—	2	4	no	—
18	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₄²×C₉	C₂²	1	2	yes	—
31	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₉	C₂²	1	2	yes	—
33	C₂×C₄²×C₉	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	C₉×#95	C₂²	1	2	yes	—
39	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
42	C₃×#391	C₂×C₃	1	1	yes	characteristic
43	C₃×#389	C₂×C₃	1	2	yes	—
44	C₃×#389	C₂×C₃	1	1	yes	characteristic
45	C₃×#388	C₂×C₃	1	2	yes	—
46	C₃×#388	C₂×C₃	1	2	yes	—
47	C₃×#387	C₂×C₃	1	2	yes	—
48	C₃×#380	C₂×C₃	1	1	yes	characteristic
49	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₂⁴×C₉	C₂³	1	1	yes	characteristic
51	C₂×Q₈×C₉	—	2	2	no	—
52	C₂×Q₈×C₉	—	2	2	no	—
53	C₂×Q₈×C₉	C₂×C₄	1	4	yes	—
54	C₂²×C₄×C₉	—	2	2	no	—
55	C₂²×C₄×C₉	—	2	2	no	—
56	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
57	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂³	1	2	yes	—
59	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₉	C₂³	1	2	yes	—
61	C₂²×C₄×C₉	C₂³	1	2	yes	—
62	C₂²×C₄×C₉	C₂³	1	2	yes	—
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	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
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	2	no	—
71	C₉×C₄⋊C₄	—	2	2	no	—
72	C₉×C₄⋊C₄	—	4	2	no	—
73	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
74	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
75	C₉×C₂²⋊C₄	—	2	2	no	—
76	C₉×C₂²⋊C₄	—	2	2	no	—
77	C₉×C₂²⋊C₄	—	4	2	no	—
78	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	—
79	C₄²×C₉	—	2	2	no	—
80	C₄²×C₉	—	2	4	no	—
81	C₄²×C₉	—	4	2	no	—
82	C₄²×C₉	D₄	1	4	yes	—
83	#2323	C₉	1	1	yes	characteristic, direct product factor, Sylow
84	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
85	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
86	C₃×C₂²⋊Q₈	C₃×C₄	1	8	yes	—
87	C₃×C₄×Q₈	—	2	4	no	—
88	C₃×#117	—	2	4	no	—
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
102	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
104	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
105	C₃×#95	C₂²×C₃	1	2	yes	—
106	C₃×#95	C₂²×C₃	1	2	yes	—
107	C₃×#95	C₂²×C₃	1	2	yes	—
108	C₃×#95	C₂²×C₃	1	2	yes	—
109	C₃×#95	C₂²×C₃	1	2	yes	—
110	C₂³×C₉	—	2	1	no	—
111	C₂³×C₉	—	2	1	no	—
112	C₂³×C₉	—	2	1	no	—
113	C₂³×C₉	—	2	1	no	—
114	C₂³×C₉	—	2	1	no	—
115	C₂³×C₉	—	2	1	no	—
116	C₂³×C₉	C₂²×C₄	1	2	yes	—
117	C₂³×C₉	C₂⁴	1	1	yes	characteristic
118	Q₈×C₉	—	2	8	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	1	no	—
121	C₂×C₄×C₉	—	2	1	no	—
122	C₂×C₄×C₉	—	2	2	no	—
123	C₂×C₄×C₉	—	2	1	no	—
124	C₂×C₄×C₉	—	2	2	no	—
125	C₂×C₄×C₉	—	2	2	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	1	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	8	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	2	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	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
143	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
144	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
145	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
146	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
147	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
148	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
149	C₂×C₄×C₉	#41	1	2	yes	—
150	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic
151	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
152	C₂×#117	C₂×C₉	1	1	yes	characteristic
153	#391	C₂×C₉	1	1	yes	characteristic, complemented
154	#389	C₂×C₉	1	2	yes	complemented
155	#389	C₂×C₉	1	1	yes	characteristic, complemented
156	#388	C₂×C₉	1	2	yes	—
157	#388	C₂×C₉	1	2	yes	—
158	#387	C₂×C₉	1	2	yes	complemented
159	#380	C₂×C₉	1	1	yes	characteristic
160	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
161	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
162	C₂×C₃×Q₈	—	2	2	no	—
163	C₂×C₃×Q₈	—	2	2	no	—
164	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	—	2	2	no	—
167	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
168	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
172	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
174	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
178	C₃×C₄⋊C₄	—	2	2	no	—
179	C₃×C₄⋊C₄	—	2	2	no	—
180	C₃×C₄⋊C₄	—	2	4	no	—
181	C₃×C₄⋊C₄	—	2	2	no	—
182	C₃×C₄⋊C₄	—	2	2	no	—
183	C₃×C₄⋊C₄	—	4	2	no	—
184	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
185	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
186	C₃×C₂²⋊C₄	—	2	2	no	—
187	C₃×C₂²⋊C₄	—	2	2	no	—
188	C₃×C₂²⋊C₄	—	4	2	no	—
189	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
190	C₃×C₄²	—	2	2	no	—
191	C₃×C₄²	—	2	4	no	—
192	C₃×C₄²	—	4	2	no	—
193	C₃×C₄²	C₃×D₄	1	4	yes	—
194	C₂²×C₉	—	2	2	no	—
195	C₂²×C₉	—	2	2	no	—
196	C₂²×C₉	—	2	2	no	—
197	C₂²×C₉	—	4	1	no	—
198	C₂²×C₉	—	4	1	no	—
199	C₂²×C₉	—	4	1	no	—
200	C₂²×C₉	—	4	1	no	—
201	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
202	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
203	C₂²×C₉	C₂×#41	1	1	yes	characteristic
204	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
206	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
207	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
208	C₄×C₉	—	2	2	no	—
209	C₄×C₉	—	2	4	no	—
210	C₄×C₉	—	2	4	no	—
211	C₄×C₉	—	2	2	no	—
212	C₄×C₉	—	2	2	no	—
213	C₄×C₉	—	4	1	no	—
214	C₄×C₉	—	4	1	no	—
215	C₄×C₉	—	4	2	no	—
216	C₄×C₉	—	4	2	no	—
217	C₄×C₉	C₄×D₄	1	4	yes	—
218	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
219	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
220	C₂²⋊Q₈	C₄×C₉	1	8	yes	complemented
221	C₄×Q₈	—	2	4	no	—
222	#117	—	2	4	no	—
223	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
224	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
227	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
229	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
231	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
234	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
235	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
236	C₂×C₄²	C₂²×C₉	1	2	yes	—
237	C₂×C₄²	C₂²×C₉	1	2	yes	—
238	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
239	#95	C₂²×C₉	1	2	yes	—
240	#95	C₂²×C₉	1	2	yes	—
241	#95	C₂²×C₉	1	2	yes	—
242	#95	C₂²×C₉	1	2	yes	—
243	#95	C₂²×C₉	1	2	yes	—
244	C₂³×C₃	—	2	1	no	—
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	—	2	1	no	—
247	C₂³×C₃	—	2	1	no	—
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	—	2	1	no	—
250	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
251	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
252	C₃×Q₈	—	2	8	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	8	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	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	C₂²×C₃×C₄	1	4	yes	—
277	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
278	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
279	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
280	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
281	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
282	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
283	C₂×C₃×C₄	C₃×#41	1	2	yes	—
284	C₂×C₉	—	4	2	no	—
285	C₂×C₉	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂×C₉	#519	1	1	yes	characteristic
287	C₂×C₉	#520	1	1	yes	characteristic
288	C₂×C₉	#536	1	1	yes	characteristic
289	C₂×C₉	#537	1	1	yes	characteristic
290	C₂×C₉	#541	1	1	yes	characteristic
291	C₂×C₉	#542	1	1	yes	characteristic
292	C₂⁴	C₂³×C₉	1	1	yes	characteristic
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	C₂×C₄×C₉	1	4	yes	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	C₂×C₄×C₉	1	4	yes	—
299	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
300	C₂²×C₄	C₂³×C₉	1	2	yes	—
301	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
302	C₂²×C₄	C₂³×C₉	1	2	yes	—
303	C₂²×C₄	C₂³×C₉	1	2	yes	—
304	C₂²×C₄	C₂³×C₉	1	2	yes	—
305	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
306	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
308	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
316	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	4	2	no	—
324	C₄²	D₄×C₉	1	4	yes	—
325	C₂²×C₃	—	2	2	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	4	1	no	—
329	C₂²×C₃	—	4	1	no	—
330	C₂²×C₃	—	4	1	no	—
331	C₂²×C₃	—	4	1	no	—
332	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
333	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
334	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
335	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
336	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
337	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
338	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	2	4	no	—
341	C₃×C₄	—	2	4	no	—
342	C₃×C₄	—	2	2	no	—
343	C₃×C₄	—	2	2	no	—
344	C₃×C₄	—	4	1	no	—
345	C₃×C₄	—	4	1	no	—
346	C₃×C₄	—	4	2	no	—
347	C₃×C₄	—	4	2	no	—
348	C₃×C₄	C₃×C₄×D₄	1	4	yes	—
349	C₉	#2323	1	1	yes	characteristic, direct product factor, Sylow
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	C₂²×C₄×C₉	1	2	yes	—
357	C₂³	C₂⁴×C₉	1	1	yes	characteristic
358	Q₈	—	2	8	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
383	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
384	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
385	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
386	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
387	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
388	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
389	C₂×C₄	C₉×#41	1	2	yes	—
390	C₂×C₃	—	4	2	no	—
391	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
392	C₂×C₃	C₃×#519	1	1	yes	characteristic
393	C₂×C₃	C₃×#520	1	1	yes	characteristic
394	C₂×C₃	C₃×#536	1	1	yes	characteristic
395	C₂×C₃	C₃×#537	1	1	yes	characteristic
396	C₂×C₃	C₃×#541	1	1	yes	characteristic
397	C₂×C₃	C₃×#542	1	1	yes	characteristic
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
406	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
407	C₂²	C₂×C₉×#41	1	1	yes	characteristic
408	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
409	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
410	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
411	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	4	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	C₄×D₄×C₉	1	4	yes	—
422	C₃	C₃×#2323	1	1	yes	characteristic
423	C₂	—	4	2	no	—
424	C₂	C₂×C₄×D₄×C₉	1	1	yes	characteristic
425	C₂	C₉×#519	1	1	yes	characteristic
426	C₂	C₉×#520	1	1	yes	characteristic
427	C₂	C₉×#536	1	1	yes	characteristic
428	C₂	C₉×#537	1	1	yes	characteristic
429	C₂	C₉×#541	1	1	yes	characteristic
430	C₂	C₉×#542	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂² ▷ 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×#391	C₂	semidirect
5. C₉×#389	C₂	semidirect
6. C₉×#389	C₂	semidirect
9. C₉×#387	C₂	semidirect
11. C₄×C₉×C₄⋊C₄	C₂	semidirect
15. C₉×C₂²⋊Q₈	C₄	semidirect
83. #2323	C₉	direct (N × H)
151. C₂×C₄×Q₈	C₂×C₉	semidirect
153. #391	C₂×C₉	semidirect
154. #389	C₂×C₉	semidirect
155. #389	C₂×C₉	semidirect
158. #387	C₂×C₉	semidirect
160. C₄×C₄⋊C₄	C₂×C₉	semidirect
220. C₂²⋊Q₈	C₄×C₉	semidirect
349. C₉	#2323	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
C₂×C₉×#117	2
C₉×#391	2
C₉×#389	2
C₉×#388	2
C₉×#387	2
C₉×#380	2
C₄×C₉×C₄⋊C₄	2
C₃×#2323	3

Subgroups — C9×#2323 #11767044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2323 #11767044