Subgroups — C₉×#2427 #11767148

Order 1152.

990 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#397	C₂	1	2	yes	maximal, complemented
6	C₉×#394	C₂	1	2	yes	maximal, complemented
7	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#386	C₂	1	2	yes	maximal, complemented
10	C₉×#380	C₂	1	2	yes	maximal, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2427	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₉	C₂²	1	2	yes	—
15	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₉	C₂²	1	2	yes	—
18	C₉×#124	—	2	4	no	—
19	C₉×C₂²⋊Q₈	—	2	4	no	—
20	C₉×#121	—	2	4	no	—
21	C₄×D₄×C₉	—	2	4	no	—
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	2	yes	—
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
35	C₉×#95	C₂²	1	1	yes	characteristic
36	C₉×#95	C₂²	1	1	yes	characteristic
37	C₉×#95	C₂²	1	2	yes	—
38	C₉×#95	C₂²	1	2	yes	—
39	C₉×#95	C₂²	1	2	yes	—
40	C₂×C₃×#124	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
42	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
43	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
44	C₃×#397	C₂×C₃	1	2	yes	—
45	C₃×#394	C₂×C₃	1	2	yes	—
46	C₃×#391	C₂×C₃	1	1	yes	characteristic
47	C₃×#389	C₂×C₃	1	1	yes	characteristic
48	C₃×#386	C₂×C₃	1	2	yes	—
49	C₃×#380	C₂×C₃	1	2	yes	—
50	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
51	C₂⁴×C₉	C₂³	1	2	yes	—
52	C₂⁴×C₉	C₂³	1	1	yes	characteristic
53	C₂×Q₈×C₉	—	2	2	no	—
54	C₂×Q₈×C₉	—	2	2	no	—
55	C₂×Q₈×C₉	—	2	2	no	—
56	C₂×D₄×C₉	—	2	4	no	—
57	C₂×D₄×C₉	—	2	4	no	—
58	C₂×D₄×C₉	—	2	2	no	—
59	C₂×D₄×C₉	—	2	2	no	—
60	C₂×D₄×C₉	—	4	2	no	—
61	C₂×D₄×C₉	D₄	1	4	yes	—
62	C₂²×C₄×C₉	—	2	4	no	—
63	C₂²×C₄×C₉	—	2	2	no	—
64	C₂²×C₄×C₉	—	2	2	no	—
65	C₂²×C₄×C₉	—	2	4	no	—
66	C₂²×C₄×C₉	—	2	2	no	—
67	C₂²×C₄×C₉	—	4	2	no	—
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₉	C₂³	1	2	yes	—
72	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₉	C₂³	1	2	yes	—
74	C₂²×C₄×C₉	C₂³	1	2	yes	—
75	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
77	C₉×C₄⋊C₄	—	2	2	no	—
78	C₉×C₄⋊C₄	—	2	4	no	—
79	C₉×C₄⋊C₄	—	4	2	no	—
80	C₉×C₄⋊C₄	D₄	1	4	yes	complemented
81	C₉×C₂²⋊C₄	—	2	4	no	—
82	C₉×C₂²⋊C₄	—	2	4	no	—
83	C₉×C₂²⋊C₄	—	2	4	no	—
84	C₉×C₂²⋊C₄	—	2	2	no	—
85	C₉×C₂²⋊C₄	—	2	4	no	—
86	C₉×C₂²⋊C₄	—	2	4	no	—
87	C₉×C₂²⋊C₄	—	2	2	no	—
88	C₄²×C₉	—	2	2	no	—
89	C₄²×C₉	—	2	2	no	—
90	#2427	C₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
93	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
94	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
96	C₃×#124	—	2	4	no	—
97	C₃×C₂²⋊Q₈	—	2	4	no	—
98	C₃×#121	—	2	4	no	—
99	C₃×C₄×D₄	—	2	4	no	—
100	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
113	C₃×#95	C₂²×C₃	1	1	yes	characteristic
114	C₃×#95	C₂²×C₃	1	1	yes	characteristic
115	C₃×#95	C₂²×C₃	1	2	yes	—
116	C₃×#95	C₂²×C₃	1	2	yes	—
117	C₃×#95	C₂²×C₃	1	2	yes	—
118	C₂³×C₉	—	2	1	no	—
119	C₂³×C₉	—	2	2	no	—
120	C₂³×C₉	—	2	1	no	—
121	C₂³×C₉	—	2	1	no	—
122	C₂³×C₉	—	2	1	no	—
123	C₂³×C₉	—	2	2	no	—
124	C₂³×C₉	—	2	2	no	—
125	C₂³×C₉	—	2	2	no	—
126	C₂³×C₉	—	2	2	no	—
127	C₂³×C₉	—	2	1	no	—
128	C₂³×C₉	—	2	2	no	—
129	C₂³×C₉	—	2	1	no	—
130	C₂³×C₉	C₂×D₄	1	4	yes	—
131	C₂³×C₉	#41	1	2	yes	—
132	C₂³×C₉	C₂⁴	1	1	yes	characteristic
133	Q₈×C₉	—	4	4	no	—
134	D₄×C₉	—	2	8	no	—
135	D₄×C₉	—	4	8	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	—	2	1	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	—	2	2	no	—
147	C₂×C₄×C₉	—	2	1	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	2	no	—
153	C₂×C₄×C₉	—	2	2	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	2	2	no	—
156	C₂×C₄×C₉	—	2	1	no	—
157	C₂×C₄×C₉	—	2	1	no	—
158	C₂×C₄×C₉	—	4	8	no	—
159	C₂×C₄×C₉	—	4	4	no	—
160	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
161	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
162	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₉	#41	1	2	yes	—
164	C₂×C₄×C₉	#41	1	2	yes	—
165	C₂×#124	C₂×C₉	1	1	yes	characteristic, complemented
166	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
167	C₂×#121	C₂×C₉	1	1	yes	characteristic
168	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
169	#397	C₂×C₉	1	2	yes	complemented
170	#394	C₂×C₉	1	2	yes	complemented
171	#391	C₂×C₉	1	1	yes	characteristic, complemented
172	#389	C₂×C₉	1	1	yes	characteristic, complemented
173	#386	C₂×C₉	1	2	yes	complemented
174	#380	C₂×C₉	1	2	yes	complemented
175	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
176	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
177	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
178	C₂×C₃×Q₈	—	2	2	no	—
179	C₂×C₃×Q₈	—	2	2	no	—
180	C₂×C₃×Q₈	—	2	2	no	—
181	C₂×C₃×D₄	—	2	4	no	—
182	C₂×C₃×D₄	—	2	4	no	—
183	C₂×C₃×D₄	—	2	2	no	—
184	C₂×C₃×D₄	—	2	2	no	—
185	C₂×C₃×D₄	—	4	2	no	—
186	C₂×C₃×D₄	C₃×D₄	1	4	yes	—
187	C₂²×C₃×C₄	—	2	4	no	—
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	—	2	2	no	—
190	C₂²×C₃×C₄	—	2	4	no	—
191	C₂²×C₃×C₄	—	2	2	no	—
192	C₂²×C₃×C₄	—	4	2	no	—
193	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
196	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
197	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
200	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
202	C₃×C₄⋊C₄	—	2	2	no	—
203	C₃×C₄⋊C₄	—	2	4	no	—
204	C₃×C₄⋊C₄	—	4	2	no	—
205	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
206	C₃×C₂²⋊C₄	—	2	4	no	—
207	C₃×C₂²⋊C₄	—	2	4	no	—
208	C₃×C₂²⋊C₄	—	2	4	no	—
209	C₃×C₂²⋊C₄	—	2	2	no	—
210	C₃×C₂²⋊C₄	—	2	4	no	—
211	C₃×C₂²⋊C₄	—	2	4	no	—
212	C₃×C₂²⋊C₄	—	2	2	no	—
213	C₃×C₄²	—	2	2	no	—
214	C₃×C₄²	—	2	2	no	—
215	C₂²×C₉	—	2	4	no	—
216	C₂²×C₉	—	2	2	no	—
217	C₂²×C₉	—	2	2	no	—
218	C₂²×C₉	—	2	4	no	—
219	C₂²×C₉	—	2	4	no	—
220	C₂²×C₉	—	2	2	no	—
221	C₂²×C₉	—	4	1	no	—
222	C₂²×C₉	—	4	2	no	—
223	C₂²×C₉	—	4	1	no	—
224	C₂²×C₉	—	4	2	no	—
225	C₂²×C₉	—	4	2	no	—
226	C₂²×C₉	—	4	1	no	—
227	C₂²×C₉	—	4	1	no	—
228	C₂²×C₉	—	4	2	no	—
229	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
230	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
231	C₂²×C₉	C₂×#41	1	1	yes	characteristic
232	C₂²×C₉	C₂×#41	1	1	yes	characteristic
233	C₂²×C₉	C₂×#41	1	1	yes	characteristic
234	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
236	C₄×C₉	—	2	2	no	—
237	C₄×C₉	—	2	4	no	—
238	C₄×C₉	—	4	1	no	—
239	C₄×C₉	—	4	2	no	—
240	C₄×C₉	—	4	1	no	—
241	C₄×C₉	—	4	2	no	—
242	C₄×C₉	—	4	1	no	—
243	C₄×C₉	—	4	1	no	—
244	C₄×C₉	#121	1	4	yes	—
245	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
246	C₂²×D₄	C₂²×C₉	1	2	yes	—
247	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
248	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
249	C₂³×C₄	C₂²×C₉	1	2	yes	—
250	#124	—	2	4	no	—
251	C₂²⋊Q₈	—	2	4	no	—
252	#121	—	2	4	no	—
253	C₄×D₄	—	2	4	no	—
254	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
257	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
259	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
265	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
266	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
267	#95	C₂²×C₉	1	1	yes	characteristic
268	#95	C₂²×C₉	1	1	yes	characteristic
269	#95	C₂²×C₉	1	2	yes	—
270	#95	C₂²×C₉	1	2	yes	—
271	#95	C₂²×C₉	1	2	yes	—
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	1	no	—
275	C₂³×C₃	—	2	1	no	—
276	C₂³×C₃	—	2	1	no	—
277	C₂³×C₃	—	2	2	no	—
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	—	2	1	no	—
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	—	2	1	no	—
284	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
285	C₂³×C₃	C₃×#41	1	2	yes	—
286	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
287	C₃×Q₈	—	4	4	no	—
288	C₃×D₄	—	2	8	no	—
289	C₃×D₄	—	4	8	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	1	no	—
302	C₂×C₃×C₄	—	2	1	no	—
303	C₂×C₃×C₄	—	2	1	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	1	no	—
312	C₂×C₃×C₄	—	4	8	no	—
313	C₂×C₃×C₄	—	4	4	no	—
314	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
315	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
316	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
317	C₂×C₃×C₄	C₃×#41	1	2	yes	—
318	C₂×C₃×C₄	C₃×#41	1	2	yes	—
319	C₂×C₉	—	4	4	no	—
320	C₂×C₉	—	4	2	no	—
321	C₂×C₉	C₂×#121	1	1	yes	characteristic
322	C₂×C₉	#529	1	1	yes	characteristic
323	C₂×C₉	#542	1	1	yes	characteristic
324	C₂×C₉	#546	1	1	yes	characteristic
325	C₂×C₉	#546	1	1	yes	characteristic
326	C₂×C₉	#547	1	1	yes	characteristic
327	C₂×C₉	#548	1	1	yes	characteristic
328	C₂⁴	C₂³×C₉	1	2	yes	—
329	C₂⁴	C₂³×C₉	1	1	yes	characteristic
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	D₄×C₉	1	4	yes	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
346	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
347	C₂²×C₄	C₂³×C₉	1	2	yes	—
348	C₂²×C₄	C₂³×C₉	1	2	yes	—
349	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
350	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
351	C₂²×C₄	C₂³×C₉	1	2	yes	—
352	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
353	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	D₄×C₉	1	4	yes	complemented
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	2	2	no	—
369	C₂²×C₃	—	2	2	no	—
370	C₂²×C₃	—	2	4	no	—
371	C₂²×C₃	—	2	4	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	4	1	no	—
374	C₂²×C₃	—	4	2	no	—
375	C₂²×C₃	—	4	1	no	—
376	C₂²×C₃	—	4	2	no	—
377	C₂²×C₃	—	4	2	no	—
378	C₂²×C₃	—	4	1	no	—
379	C₂²×C₃	—	4	1	no	—
380	C₂²×C₃	—	4	2	no	—
381	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
382	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
383	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
384	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
385	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
386	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	2	4	no	—
390	C₃×C₄	—	4	1	no	—
391	C₃×C₄	—	4	2	no	—
392	C₃×C₄	—	4	2	no	—
393	C₃×C₄	—	4	1	no	—
394	C₃×C₄	—	4	1	no	—
395	C₃×C₄	—	4	1	no	—
396	C₃×C₄	C₃×#121	1	4	yes	—
397	C₉	#2427	1	1	yes	characteristic, direct product factor, Sylow
398	C₂³	—	2	1	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	1	no	—
410	C₂³	C₂×D₄×C₉	1	4	yes	—
411	C₂³	C₉×#41	1	2	yes	—
412	C₂³	C₂⁴×C₉	1	1	yes	characteristic
413	Q₈	—	4	4	no	—
414	D₄	—	2	8	no	—
415	D₄	—	4	8	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
441	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
442	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
443	C₂×C₄	C₉×#41	1	2	yes	—
444	C₂×C₄	C₉×#41	1	2	yes	—
445	C₂×C₃	—	4	4	no	—
446	C₂×C₃	—	4	2	no	—
447	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
448	C₂×C₃	C₃×#529	1	1	yes	characteristic
449	C₂×C₃	C₃×#542	1	1	yes	characteristic
450	C₂×C₃	C₃×#546	1	1	yes	characteristic
451	C₂×C₃	C₃×#546	1	1	yes	characteristic
452	C₂×C₃	C₃×#547	1	1	yes	characteristic
453	C₂×C₃	C₃×#548	1	1	yes	characteristic
454	C₂²	—	2	4	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
469	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
470	C₂²	C₂×C₉×#41	1	1	yes	characteristic
471	C₂²	C₂×C₉×#41	1	1	yes	characteristic
472	C₂²	C₂×C₉×#41	1	1	yes	characteristic
473	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	4	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	1	no	—
483	C₄	C₉×#121	1	4	yes	—
484	C₃	C₃×#2427	1	1	yes	characteristic
485	C₂	—	4	4	no	—
486	C₂	—	4	2	no	—
487	C₂	C₂×C₉×#121	1	1	yes	characteristic
488	C₂	C₉×#529	1	1	yes	characteristic
489	C₂	C₉×#542	1	1	yes	characteristic
490	C₂	C₉×#546	1	1	yes	characteristic
491	C₂	C₉×#546	1	1	yes	characteristic
492	C₂	C₉×#547	1	1	yes	characteristic
493	C₂	C₉×#548	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#121	C₂×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
1. C₂×C₉×#124	C₂	semidirect
2. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₂×C₄×D₄×C₉	C₂	semidirect
5. C₉×#397	C₂	semidirect
6. C₉×#394	C₂	semidirect
7. C₉×#391	C₂	semidirect
8. C₉×#389	C₂	semidirect
9. C₉×#386	C₂	semidirect
10. C₉×#380	C₂	semidirect
11. C₄×C₉×C₂²⋊C₄	C₂	semidirect
80. C₉×C₄⋊C₄	D₄	semidirect
90. #2427	C₉	direct (N × H)
165. C₂×#124	C₂×C₉	semidirect
166. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
168. C₂×C₄×D₄	C₂×C₉	semidirect
169. #397	C₂×C₉	semidirect
170. #394	C₂×C₉	semidirect
171. #391	C₂×C₉	semidirect
172. #389	C₂×C₉	semidirect
173. #386	C₂×C₉	semidirect
174. #380	C₂×C₉	semidirect
175. C₄×C₂²⋊C₄	C₂×C₉	semidirect
357. C₄⋊C₄	D₄×C₉	semidirect
397. C₉	#2427	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×#124	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₉×#121	2
C₂×C₄×D₄×C₉	2
C₉×#397	2
C₉×#394	2
C₉×#391	2
C₉×#389	2
C₉×#386	2
C₉×#380	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2427	3

Subgroups — C9×#2427 #11767148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2427 #11767148