Subgroups — C₉×#2438 #11767159

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 564 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×C₉×#117	C₂	1	1	yes	maximal, characteristic
3	C₉×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#385	C₂	1	1	yes	maximal, characteristic
12	C₉×#385	C₂	1	1	yes	maximal, characteristic
13	C₉×#381	C₂	1	1	yes	maximal, characteristic
14	C₉×#380	C₂	1	1	yes	maximal, characteristic
15	C₂×C₉×#95	C₂	1	1	yes	maximal, characteristic
16	C₃×#2438	C₃	1	1	yes	maximal, characteristic
17	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
21	C₉×C₂²⋊Q₈	—	2	4	no	—
22	C₉×#117	—	2	4	no	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
39	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
40	C₉×#95	C₂²	1	1	yes	characteristic
41	C₉×#95	C₂²	1	1	yes	characteristic
42	C₉×#95	C₂²	1	1	yes	characteristic
43	C₉×#95	C₂²	1	1	yes	characteristic
44	C₉×#95	C₂²	1	1	yes	characteristic
45	C₉×#95	C₂²	1	1	yes	characteristic
46	C₉×#95	C₂²	1	1	yes	characteristic
47	C₉×#95	C₂²	1	1	yes	characteristic
48	C₉×#95	C₂²	1	1	yes	characteristic
49	C₉×#95	C₂²	1	1	yes	characteristic
50	C₉×#95	C₂²	1	1	yes	characteristic
51	C₉×#95	C₂²	1	1	yes	characteristic
52	C₉×#95	C₂²	1	1	yes	characteristic
53	C₉×#95	C₂²	1	1	yes	characteristic
54	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
56	C₃×#400	C₂×C₃	1	1	yes	characteristic
57	C₃×#398	C₂×C₃	1	1	yes	characteristic
58	C₃×#398	C₂×C₃	1	1	yes	characteristic
59	C₃×#395	C₂×C₃	1	1	yes	characteristic
60	C₃×#391	C₂×C₃	1	1	yes	characteristic
61	C₃×#389	C₂×C₃	1	1	yes	characteristic
62	C₃×#387	C₂×C₃	1	1	yes	characteristic
63	C₃×#387	C₂×C₃	1	1	yes	characteristic
64	C₃×#385	C₂×C₃	1	1	yes	characteristic
65	C₃×#385	C₂×C₃	1	1	yes	characteristic
66	C₃×#381	C₂×C₃	1	1	yes	characteristic
67	C₃×#380	C₂×C₃	1	1	yes	characteristic
68	C₂×C₃×#95	C₂×C₃	1	1	yes	characteristic
69	C₂⁴×C₉	C₂³	1	1	yes	characteristic
70	C₂×Q₈×C₉	—	2	2	no	—
71	C₂×Q₈×C₉	—	2	2	no	—
72	C₂×Q₈×C₉	—	4	1	no	—
73	C₂²×C₄×C₉	—	2	2	no	—
74	C₂²×C₄×C₉	—	2	2	no	—
75	C₂²×C₄×C₉	—	2	2	no	—
76	C₂²×C₄×C₉	—	2	2	no	—
77	C₂²×C₄×C₉	—	2	2	no	—
78	C₂²×C₄×C₉	—	2	2	no	—
79	C₂²×C₄×C₉	—	4	1	no	—
80	C₂²×C₄×C₉	—	4	1	no	—
81	C₂²×C₄×C₉	Q₈	1	4	yes	complemented
82	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₉×C₄⋊C₄	—	2	2	no	—
97	C₉×C₄⋊C₄	—	2	2	no	—
98	C₉×C₄⋊C₄	—	2	2	no	—
99	C₉×C₄⋊C₄	—	2	2	no	—
100	C₉×C₄⋊C₄	—	2	2	no	—
101	C₉×C₄⋊C₄	—	2	2	no	—
102	C₉×C₄⋊C₄	—	2	2	no	—
103	C₉×C₄⋊C₄	—	2	2	no	—
104	C₉×C₄⋊C₄	—	4	1	no	—
105	C₉×C₄⋊C₄	—	4	1	no	—
106	C₉×C₄⋊C₄	—	4	1	no	—
107	C₉×C₂²⋊C₄	—	2	2	no	—
108	C₉×C₂²⋊C₄	—	2	2	no	—
109	C₉×C₂²⋊C₄	—	2	2	no	—
110	C₉×C₂²⋊C₄	D₄	1	4	yes	—
111	C₄²×C₉	—	2	2	no	—
112	C₄²×C₉	—	2	2	no	—
113	#2438	C₉	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
118	C₃×C₂²⋊Q₈	—	2	4	no	—
119	C₃×#117	—	2	4	no	—
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
137	C₃×#95	C₂²×C₃	1	1	yes	characteristic
138	C₃×#95	C₂²×C₃	1	1	yes	characteristic
139	C₃×#95	C₂²×C₃	1	1	yes	characteristic
140	C₃×#95	C₂²×C₃	1	1	yes	characteristic
141	C₃×#95	C₂²×C₃	1	1	yes	characteristic
142	C₃×#95	C₂²×C₃	1	1	yes	characteristic
143	C₃×#95	C₂²×C₃	1	1	yes	characteristic
144	C₃×#95	C₂²×C₃	1	1	yes	characteristic
145	C₃×#95	C₂²×C₃	1	1	yes	characteristic
146	C₃×#95	C₂²×C₃	1	1	yes	characteristic
147	C₃×#95	C₂²×C₃	1	1	yes	characteristic
148	C₃×#95	C₂²×C₃	1	1	yes	characteristic
149	C₃×#95	C₂²×C₃	1	1	yes	characteristic
150	C₃×#95	C₂²×C₃	1	1	yes	characteristic
151	C₂³×C₉	—	2	1	no	—
152	C₂³×C₉	—	2	1	no	—
153	C₂³×C₉	—	2	1	no	—
154	C₂³×C₉	—	2	1	no	—
155	C₂³×C₉	C₂×D₄	1	2	yes	—
156	C₂³×C₉	C₂×Q₈	1	2	yes	—
157	C₂³×C₉	#41	1	2	yes	—
158	C₂³×C₉	C₂⁴	1	1	yes	characteristic
159	Q₈×C₉	—	4	4	no	—
160	C₂×C₄×C₉	—	2	8	no	—
161	C₂×C₄×C₉	—	2	1	no	—
162	C₂×C₄×C₉	—	2	1	no	—
163	C₂×C₄×C₉	—	2	1	no	—
164	C₂×C₄×C₉	—	2	1	no	—
165	C₂×C₄×C₉	—	2	1	no	—
166	C₂×C₄×C₉	—	2	1	no	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	2	1	no	—
169	C₂×C₄×C₉	—	2	1	no	—
170	C₂×C₄×C₉	—	2	1	no	—
171	C₂×C₄×C₉	—	2	1	no	—
172	C₂×C₄×C₉	—	2	1	no	—
173	C₂×C₄×C₉	—	2	1	no	—
174	C₂×C₄×C₉	—	2	1	no	—
175	C₂×C₄×C₉	—	2	1	no	—
176	C₂×C₄×C₉	—	2	1	no	—
177	C₂×C₄×C₉	—	2	1	no	—
178	C₂×C₄×C₉	—	2	1	no	—
179	C₂×C₄×C₉	—	2	1	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	—	2	1	no	—
184	C₂×C₄×C₉	—	2	1	no	—
185	C₂×C₄×C₉	—	2	1	no	—
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	2	1	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	—	2	1	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	4	4	no	—
198	C₂×C₄×C₉	—	4	4	no	—
199	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
200	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
201	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
202	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
203	C₂×C₄×C₉	#41	1	2	yes	—
204	C₂×C₄×C₉	#41	1	2	yes	—
205	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic
206	C₂×#117	C₂×C₉	1	1	yes	characteristic
207	#400	C₂×C₉	1	1	yes	characteristic, complemented
208	#398	C₂×C₉	1	1	yes	characteristic, complemented
209	#398	C₂×C₉	1	1	yes	characteristic, complemented
210	#395	C₂×C₉	1	1	yes	characteristic, complemented
211	#391	C₂×C₉	1	1	yes	characteristic, complemented
212	#389	C₂×C₉	1	1	yes	characteristic, complemented
213	#387	C₂×C₉	1	1	yes	characteristic, complemented
214	#387	C₂×C₉	1	1	yes	characteristic, complemented
215	#385	C₂×C₉	1	1	yes	characteristic
216	#385	C₂×C₉	1	1	yes	characteristic
217	#381	C₂×C₉	1	1	yes	characteristic
218	#380	C₂×C₉	1	1	yes	characteristic
219	C₂×#95	C₂×C₉	1	1	yes	characteristic
220	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₃×Q₈	—	2	2	no	—
222	C₂×C₃×Q₈	—	2	2	no	—
223	C₂×C₃×Q₈	—	4	1	no	—
224	C₂²×C₃×C₄	—	2	2	no	—
225	C₂²×C₃×C₄	—	2	2	no	—
226	C₂²×C₃×C₄	—	2	2	no	—
227	C₂²×C₃×C₄	—	2	2	no	—
228	C₂²×C₃×C₄	—	2	2	no	—
229	C₂²×C₃×C₄	—	2	2	no	—
230	C₂²×C₃×C₄	—	4	1	no	—
231	C₂²×C₃×C₄	—	4	1	no	—
232	C₂²×C₃×C₄	C₃×Q₈	1	4	yes	—
233	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
239	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
247	C₃×C₄⋊C₄	—	2	2	no	—
248	C₃×C₄⋊C₄	—	2	2	no	—
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	2	2	no	—
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	—	2	2	no	—
253	C₃×C₄⋊C₄	—	2	2	no	—
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	—	4	1	no	—
256	C₃×C₄⋊C₄	—	4	1	no	—
257	C₃×C₄⋊C₄	—	4	1	no	—
258	C₃×C₂²⋊C₄	—	2	2	no	—
259	C₃×C₂²⋊C₄	—	2	2	no	—
260	C₃×C₂²⋊C₄	—	2	2	no	—
261	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
262	C₃×C₄²	—	2	2	no	—
263	C₃×C₄²	—	2	2	no	—
264	C₂²×C₉	—	2	2	no	—
265	C₂²×C₉	—	2	2	no	—
266	C₂²×C₉	—	2	2	no	—
267	C₂²×C₉	—	2	2	no	—
268	C₂²×C₉	—	2	2	no	—
269	C₂²×C₉	—	2	2	no	—
270	C₂²×C₉	C₂²⋊Q₈	1	4	yes	—
271	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
272	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
273	C₂²×C₉	C₂×#41	1	1	yes	characteristic
274	C₂²×C₉	C₂×#41	1	1	yes	characteristic
275	C₂²×C₉	C₂×#41	1	1	yes	characteristic
276	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
278	C₄×C₉	—	2	2	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	2	no	—
281	C₄×C₉	—	2	2	no	—
282	C₄×C₉	—	2	2	no	—
283	C₄×C₉	—	2	2	no	—
284	C₄×C₉	—	4	1	no	—
285	C₄×C₉	—	4	1	no	—
286	C₄×C₉	—	4	1	no	—
287	C₄×C₉	—	4	1	no	—
288	C₄×C₉	—	4	1	no	—
289	C₄×C₉	—	4	1	no	—
290	C₄×C₉	—	4	1	no	—
291	C₄×C₉	—	4	1	no	—
292	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
293	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
294	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
295	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
296	C₂²⋊Q₈	—	2	4	no	—
297	#117	—	2	4	no	—
298	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
313	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
314	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
315	#95	C₂²×C₉	1	1	yes	characteristic
316	#95	C₂²×C₉	1	1	yes	characteristic
317	#95	C₂²×C₉	1	1	yes	characteristic
318	#95	C₂²×C₉	1	1	yes	characteristic
319	#95	C₂²×C₉	1	1	yes	characteristic
320	#95	C₂²×C₉	1	1	yes	characteristic
321	#95	C₂²×C₉	1	1	yes	characteristic
322	#95	C₂²×C₉	1	1	yes	characteristic
323	#95	C₂²×C₉	1	1	yes	characteristic
324	#95	C₂²×C₉	1	1	yes	characteristic
325	#95	C₂²×C₉	1	1	yes	characteristic
326	#95	C₂²×C₉	1	1	yes	characteristic
327	#95	C₂²×C₉	1	1	yes	characteristic
328	#95	C₂²×C₉	1	1	yes	characteristic
329	C₂³×C₃	—	2	1	no	—
330	C₂³×C₃	—	2	1	no	—
331	C₂³×C₃	—	2	1	no	—
332	C₂³×C₃	—	2	1	no	—
333	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
334	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
335	C₂³×C₃	C₃×#41	1	2	yes	—
336	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
337	C₃×Q₈	—	4	4	no	—
338	C₂×C₃×C₄	—	2	8	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	1	no	—
345	C₂×C₃×C₄	—	2	1	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	4	4	no	—
376	C₂×C₃×C₄	—	4	4	no	—
377	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
378	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
379	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
380	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
381	C₂×C₃×C₄	C₃×#41	1	2	yes	—
382	C₂×C₃×C₄	C₃×#41	1	2	yes	—
383	C₂×C₉	—	2	4	no	—
384	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
385	C₂×C₉	#533	1	1	yes	characteristic
386	C₂×C₉	#544	1	1	yes	characteristic
387	C₂×C₉	#546	1	1	yes	characteristic
388	C₂×C₉	#547	1	1	yes	characteristic
389	C₂×C₉	#551	1	1	yes	characteristic
390	C₂×C₉	#552	1	1	yes	characteristic
391	C₂⁴	C₂³×C₉	1	1	yes	characteristic
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	4	1	no	—
402	C₂²×C₄	—	4	1	no	—
403	C₂²×C₄	Q₈×C₉	1	4	yes	complemented
404	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
405	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
406	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
407	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
408	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
409	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
410	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
411	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
412	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
413	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
414	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
415	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
416	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
417	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	—	4	1	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	D₄×C₉	1	4	yes	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	2	2	no	—
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	2	2	no	—
439	C₂²×C₃	—	2	2	no	—
440	C₂²×C₃	—	2	2	no	—
441	C₂²×C₃	C₃×C₂²⋊Q₈	1	4	yes	—
442	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
443	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
444	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
445	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
446	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
447	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	2	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	—	4	1	no	—
457	C₃×C₄	—	4	1	no	—
458	C₃×C₄	—	4	1	no	—
459	C₃×C₄	—	4	1	no	—
460	C₃×C₄	—	4	1	no	—
461	C₃×C₄	—	4	1	no	—
462	C₃×C₄	—	4	1	no	—
463	C₉	#2438	1	1	yes	characteristic, direct product factor, Sylow
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	C₂×D₄×C₉	1	2	yes	—
469	C₂³	C₂×Q₈×C₉	1	2	yes	—
470	C₂³	C₉×#41	1	2	yes	—
471	C₂³	C₂⁴×C₉	1	1	yes	characteristic
472	Q₈	—	4	4	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
513	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
514	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
515	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
516	C₂×C₄	C₉×#41	1	2	yes	—
517	C₂×C₄	C₉×#41	1	2	yes	—
518	C₂×C₃	—	2	4	no	—
519	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
520	C₂×C₃	C₃×#533	1	1	yes	characteristic
521	C₂×C₃	C₃×#544	1	1	yes	characteristic
522	C₂×C₃	C₃×#546	1	1	yes	characteristic
523	C₂×C₃	C₃×#547	1	1	yes	characteristic
524	C₂×C₃	C₃×#551	1	1	yes	characteristic
525	C₂×C₃	C₃×#552	1	1	yes	characteristic
526	C₂²	—	2	2	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	C₉×C₂²⋊Q₈	1	4	yes	—
533	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
534	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
535	C₂²	C₂×C₉×#41	1	1	yes	characteristic
536	C₂²	C₂×C₉×#41	1	1	yes	characteristic
537	C₂²	C₂×C₉×#41	1	1	yes	characteristic
538	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	2	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₃	C₃×#2438	1	1	yes	characteristic
555	C₂	—	2	4	no	—
556	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
557	C₂	C₉×#533	1	1	yes	characteristic
558	C₂	C₉×#544	1	1	yes	characteristic
559	C₂	C₉×#546	1	1	yes	characteristic
560	C₂	C₉×#547	1	1	yes	characteristic
561	C₂	C₉×#551	1	1	yes	characteristic
562	C₂	C₉×#552	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
3. C₉×#400	C₂	semidirect
4. C₉×#398	C₂	semidirect
5. C₉×#398	C₂	semidirect
6. C₉×#395	C₂	semidirect
7. C₉×#391	C₂	semidirect
8. C₉×#389	C₂	semidirect
9. C₉×#387	C₂	semidirect
10. C₉×#387	C₂	semidirect
81. C₂²×C₄×C₉	Q₈	semidirect
113. #2438	C₉	direct (N × H)
207. #400	C₂×C₉	semidirect
208. #398	C₂×C₉	semidirect
209. #398	C₂×C₉	semidirect
210. #395	C₂×C₉	semidirect
211. #391	C₂×C₉	semidirect
212. #389	C₂×C₉	semidirect
213. #387	C₂×C₉	semidirect
214. #387	C₂×C₉	semidirect
403. C₂²×C₄	Q₈×C₉	semidirect
463. C₉	#2438	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×C₉×#117	2
C₉×#400	2
C₉×#398	2
C₉×#395	2
C₉×#391	2
C₉×#389	2
C₉×#387	2
C₉×#385	2
C₉×#381	2
C₉×#380	2
C₂×C₉×#95	2
C₃×#2438	3

Subgroups — C9×#2438 #11767159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2438 #11767159