Subgroups — C₉×#2550 #11767271

Order 1152.

702 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic
3	C₉×#398	C₂	1	2	yes	maximal
4	C₉×#395	C₂	1	2	yes	maximal
5	C₉×#391	C₂	1	2	yes	maximal
6	C₉×#389	C₂	1	1	yes	maximal, characteristic
7	C₉×#389	C₂	1	1	yes	maximal, characteristic
8	C₉×#389	C₂	1	2	yes	maximal
9	C₉×#382	C₂	1	1	yes	maximal, characteristic
10	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₃×#2550	C₃	1	1	yes	maximal, characteristic
13	C₂²×Q₈×C₉	C₂²	1	2	yes	—
14	C₉×C₄⋊Q₈	—	2	4	no	—
15	C₉×#125	—	2	4	no	—
16	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
28	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
29	C₂×C₄²×C₉	C₂²	1	2	yes	—
30	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
31	C₉×#95	C₂²	1	1	yes	characteristic
32	C₉×#95	C₂²	1	1	yes	characteristic
33	C₉×#95	C₂²	1	2	yes	—
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×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
40	C₃×#398	C₂×C₃	1	2	yes	—
41	C₃×#395	C₂×C₃	1	2	yes	—
42	C₃×#391	C₂×C₃	1	2	yes	—
43	C₃×#389	C₂×C₃	1	2	yes	—
44	C₃×#389	C₂×C₃	1	1	yes	characteristic
45	C₃×#389	C₂×C₃	1	1	yes	characteristic
46	C₃×#382	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
49	C₂×Q₈×C₉	—	2	4	no	—
50	C₂×Q₈×C₉	—	2	4	no	—
51	C₂×Q₈×C₉	—	4	2	no	—
52	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
54	C₂²×C₄×C₉	C₂³	1	2	yes	—
55	C₂²×C₄×C₉	C₂³	1	2	yes	—
56	C₂²×C₄×C₉	C₂³	1	2	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	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₉×C₄⋊C₄	—	2	4	no	—
64	C₉×C₄⋊C₄	—	2	4	no	—
65	C₉×C₄⋊C₄	—	2	2	no	—
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	2	no	—
71	C₉×C₄⋊C₄	—	4	2	no	—
72	C₉×C₄⋊C₄	D₄	1	4	yes	—
73	C₉×C₄⋊C₄	Q₈	1	4	yes	complemented
74	C₄²×C₉	—	2	2	no	—
75	C₄²×C₉	—	2	2	no	—
76	C₄²×C₉	—	4	2	no	—
77	C₄²×C₉	Q₈	1	4	yes	complemented
78	#2550	C₉	1	1	yes	characteristic, direct product factor, Sylow
79	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
80	C₃×C₄⋊Q₈	—	2	4	no	—
81	C₃×#125	—	2	4	no	—
82	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
97	C₃×#95	C₂²×C₃	1	1	yes	characteristic
98	C₃×#95	C₂²×C₃	1	1	yes	characteristic
99	C₃×#95	C₂²×C₃	1	2	yes	—
100	C₃×#95	C₂²×C₃	1	2	yes	—
101	C₃×#95	C₂²×C₃	1	2	yes	—
102	C₃×#95	C₂²×C₃	1	2	yes	—
103	C₃×#95	C₂²×C₃	1	2	yes	—
104	C₂³×C₉	C₂⁴	1	1	yes	characteristic
105	Q₈×C₉	—	4	8	no	—
106	C₂×C₄×C₉	—	2	1	no	—
107	C₂×C₄×C₉	—	2	1	no	—
108	C₂×C₄×C₉	—	2	1	no	—
109	C₂×C₄×C₉	—	2	1	no	—
110	C₂×C₄×C₉	—	2	2	no	—
111	C₂×C₄×C₉	—	2	2	no	—
112	C₂×C₄×C₉	—	2	1	no	—
113	C₂×C₄×C₉	—	2	2	no	—
114	C₂×C₄×C₉	—	2	2	no	—
115	C₂×C₄×C₉	—	2	1	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	1	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	2	1	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	2	no	—
128	C₂×C₄×C₉	—	2	1	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
131	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
132	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
133	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
134	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
135	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
136	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
137	C₂×C₄×C₉	#41	1	2	yes	—
138	C₂×C₄×C₉	#41	1	2	yes	—
139	C₂×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic
140	C₂×#125	C₂×C₉	1	1	yes	characteristic
141	#398	C₂×C₉	1	2	yes	—
142	#395	C₂×C₉	1	2	yes	—
143	#391	C₂×C₉	1	2	yes	—
144	#389	C₂×C₉	1	2	yes	—
145	#389	C₂×C₉	1	1	yes	characteristic
146	#389	C₂×C₉	1	1	yes	characteristic
147	#382	C₂×C₉	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
149	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic
150	C₂×C₃×Q₈	—	2	4	no	—
151	C₂×C₃×Q₈	—	2	4	no	—
152	C₂×C₃×Q₈	—	4	2	no	—
153	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
155	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
156	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
158	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
161	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
164	C₃×C₄⋊C₄	—	2	4	no	—
165	C₃×C₄⋊C₄	—	2	4	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	—	2	4	no	—
168	C₃×C₄⋊C₄	—	2	2	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	4	2	no	—
173	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
174	C₃×C₄⋊C₄	C₃×Q₈	1	4	yes	—
175	C₃×C₄²	—	2	2	no	—
176	C₃×C₄²	—	2	2	no	—
177	C₃×C₄²	—	4	2	no	—
178	C₃×C₄²	C₃×Q₈	1	4	yes	—
179	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
180	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
181	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
182	C₂²×C₉	C₂×#41	1	1	yes	characteristic
183	C₂²×C₉	C₂×#41	1	1	yes	characteristic
184	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
186	C₄×C₉	—	2	2	no	—
187	C₄×C₉	—	2	2	no	—
188	C₄×C₉	—	2	4	no	—
189	C₄×C₉	—	2	2	no	—
190	C₄×C₉	—	2	2	no	—
191	C₄×C₉	—	2	4	no	—
192	C₄×C₉	—	4	1	no	—
193	C₄×C₉	—	4	2	no	—
194	C₄×C₉	—	4	1	no	—
195	C₄×C₉	—	4	2	no	—
196	C₄×C₉	C₄⋊Q₈	1	4	yes	—
197	C₂²×Q₈	C₂²×C₉	1	2	yes	—
198	C₄⋊Q₈	—	2	4	no	—
199	#125	—	2	4	no	—
200	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
201	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
202	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
203	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
205	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
208	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
209	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
211	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
212	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
213	C₂×C₄²	C₂²×C₉	1	2	yes	—
214	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
215	#95	C₂²×C₉	1	1	yes	characteristic
216	#95	C₂²×C₉	1	1	yes	characteristic
217	#95	C₂²×C₉	1	2	yes	—
218	#95	C₂²×C₉	1	2	yes	—
219	#95	C₂²×C₉	1	2	yes	—
220	#95	C₂²×C₉	1	2	yes	—
221	#95	C₂²×C₉	1	2	yes	—
222	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
223	C₃×Q₈	—	4	8	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
249	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
251	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
252	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
253	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
254	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
255	C₂×C₃×C₄	C₃×#41	1	2	yes	—
256	C₂×C₃×C₄	C₃×#41	1	2	yes	—
257	C₂×C₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
258	C₂×C₉	#533	1	1	yes	characteristic
259	C₂×C₉	#544	1	1	yes	characteristic
260	C₂×C₉	#546	1	1	yes	characteristic
261	C₂×C₉	#548	1	1	yes	characteristic
262	C₂×C₉	#554	1	1	yes	characteristic
263	C₂×C₉	#557	1	1	yes	characteristic
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
268	C₂²×C₄	C₂³×C₉	1	2	yes	—
269	C₂²×C₄	C₂³×C₉	1	2	yes	—
270	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
271	C₂²×C₄	C₂³×C₉	1	2	yes	—
272	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
273	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₉	1	2	yes	—
275	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
276	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
277	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	4	2	no	—
287	C₄⋊C₄	D₄×C₉	1	4	yes	—
288	C₄⋊C₄	Q₈×C₉	1	4	yes	complemented
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	4	2	no	—
292	C₄²	Q₈×C₉	1	4	yes	complemented
293	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
294	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
295	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
296	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
297	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
298	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
299	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
300	C₃×C₄	—	2	2	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	2	4	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	2	4	no	—
306	C₃×C₄	—	4	2	no	—
307	C₃×C₄	—	4	1	no	—
308	C₃×C₄	—	4	1	no	—
309	C₃×C₄	—	4	2	no	—
310	C₃×C₄	C₃×C₄⋊Q₈	1	4	yes	—
311	C₉	#2550	1	1	yes	characteristic, direct product factor, Sylow
312	C₂³	C₂⁴×C₉	1	1	yes	characteristic
313	Q₈	—	4	8	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
339	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
340	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
341	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
342	C₂×C₄	C₂×Q₈×C₉	1	4	yes	—
343	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
344	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
345	C₂×C₄	C₉×#41	1	2	yes	—
346	C₂×C₄	C₉×#41	1	2	yes	—
347	C₂×C₃	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
348	C₂×C₃	C₃×#533	1	1	yes	characteristic
349	C₂×C₃	C₃×#544	1	1	yes	characteristic
350	C₂×C₃	C₃×#546	1	1	yes	characteristic
351	C₂×C₃	C₃×#548	1	1	yes	characteristic
352	C₂×C₃	C₃×#554	1	1	yes	characteristic
353	C₂×C₃	C₃×#557	1	1	yes	characteristic
354	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
355	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
356	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
357	C₂²	C₂×C₉×#41	1	1	yes	characteristic
358	C₂²	C₂×C₉×#41	1	1	yes	characteristic
359	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	2	4	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	4	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	2	no	—
371	C₄	C₉×C₄⋊Q₈	1	4	yes	—
372	C₃	C₃×#2550	1	1	yes	characteristic
373	C₂	C₂×C₉×C₄⋊Q₈	1	1	yes	characteristic
374	C₂	C₉×#533	1	1	yes	characteristic
375	C₂	C₉×#544	1	1	yes	characteristic
376	C₂	C₉×#546	1	1	yes	characteristic
377	C₂	C₉×#548	1	1	yes	characteristic
378	C₂	C₉×#554	1	1	yes	characteristic
379	C₂	C₉×#557	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, prime radical, cosocle	C₂³×C₃	C₂⁴×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
73. C₉×C₄⋊C₄	Q₈	semidirect
77. C₄²×C₉	Q₈	semidirect
78. #2550	C₉	direct (N × H)
288. C₄⋊C₄	Q₈×C₉	semidirect
292. C₄²	Q₈×C₉	semidirect
311. C₉	#2550	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×C₄⋊Q₈	2
C₂×C₉×#125	2
C₉×#398	2
C₉×#395	2
C₉×#391	2
C₉×#389	2
C₉×#382	2
C₄×C₉×C₄⋊C₄	2
C₃×#2550	3

Subgroups — C9×#2550 #11767271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2550 #11767271