Subgroups — C₉×#2329 #11767050

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 390 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	C₉×#391	C₂	1	2	yes	maximal, complemented
3	C₉×#389	C₂	1	2	yes	maximal, complemented
4	C₉×#387	C₂	1	2	yes	maximal, complemented
5	C₉×#387	C₂	1	2	yes	maximal, complemented
6	C₉×#385	C₂	1	2	yes	maximal
7	C₉×#380	C₂	1	1	yes	maximal, characteristic
8	C₄×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal
9	C₂×C₉×#95	C₂	1	1	yes	maximal, characteristic
10	C₃×#2329	C₃	1	1	yes	maximal, characteristic
11	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂³×C₄×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	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	2	yes	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₄²×C₉	C₂²	1	2	yes	—
25	C₂×C₄²×C₉	C₂²	1	2	yes	—
26	C₉×#95	C₂²	1	2	yes	—
27	C₉×#95	C₂²	1	2	yes	—
28	C₉×#95	C₂²	1	2	yes	—
29	C₉×#95	C₂²	1	2	yes	—
30	C₉×#95	C₂²	1	2	yes	—
31	C₉×#95	C₂²	1	2	yes	—
32	C₉×#95	C₂²	1	2	yes	—
33	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
34	C₃×#391	C₂×C₃	1	2	yes	—
35	C₃×#389	C₂×C₃	1	2	yes	—
36	C₃×#387	C₂×C₃	1	2	yes	—
37	C₃×#387	C₂×C₃	1	2	yes	—
38	C₃×#385	C₂×C₃	1	2	yes	—
39	C₃×#380	C₂×C₃	1	1	yes	characteristic
40	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	2	yes	—
41	C₂×C₃×#95	C₂×C₃	1	1	yes	characteristic
42	C₂⁴×C₉	C₂³	1	1	yes	characteristic
43	C₂×Q₈×C₉	—	4	1	no	—
44	C₂×Q₈×C₉	—	4	1	no	—
45	C₂×Q₈×C₉	C₂×C₄	1	4	yes	complemented
46	C₂²×C₄×C₉	—	2	2	no	—
47	C₂²×C₄×C₉	—	4	1	no	—
48	C₂²×C₄×C₉	—	4	1	no	—
49	C₂²×C₄×C₉	—	4	1	no	—
50	C₂²×C₄×C₉	—	4	1	no	—
51	C₂²×C₄×C₉	—	4	1	no	—
52	C₂²×C₄×C₉	—	4	1	no	—
53	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
54	C₂²×C₄×C₉	Q₈	1	4	yes	complemented
55	C₂²×C₄×C₉	C₂³	1	2	yes	—
56	C₂²×C₄×C₉	C₂³	1	2	yes	—
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	1	yes	characteristic
62	C₂²×C₄×C₉	C₂³	1	2	yes	—
63	C₉×C₄⋊C₄	—	4	2	no	—
64	C₉×C₄⋊C₄	—	4	1	no	—
65	C₉×C₄⋊C₄	—	4	1	no	—
66	C₉×C₄⋊C₄	—	4	2	no	—
67	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
68	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
69	C₉×C₂²⋊C₄	—	2	4	no	—
70	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	—
71	C₄²×C₉	—	4	2	no	—
72	C₄²×C₉	—	4	2	no	—
73	#2329	C₉	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
75	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
78	C₃×C₂²⋊Q₈	C₃×C₄	1	8	yes	—
79	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
88	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
89	C₃×#95	C₂²×C₃	1	2	yes	—
90	C₃×#95	C₂²×C₃	1	2	yes	—
91	C₃×#95	C₂²×C₃	1	2	yes	—
92	C₃×#95	C₂²×C₃	1	2	yes	—
93	C₃×#95	C₂²×C₃	1	2	yes	—
94	C₃×#95	C₂²×C₃	1	2	yes	—
95	C₃×#95	C₂²×C₃	1	2	yes	—
96	C₂³×C₉	—	2	1	no	—
97	C₂³×C₉	—	2	1	no	—
98	C₂³×C₉	—	2	1	no	—
99	C₂³×C₉	—	2	1	no	—
100	C₂³×C₉	C₂²×C₄	1	2	yes	—
101	C₂³×C₉	C₂×Q₈	1	2	yes	—
102	C₂³×C₉	#41	1	2	yes	—
103	C₂³×C₉	C₂⁴	1	1	yes	characteristic
104	Q₈×C₉	—	4	4	no	—
105	C₂×C₄×C₉	—	2	2	no	—
106	C₂×C₄×C₉	—	2	2	no	—
107	C₂×C₄×C₉	—	2	2	no	—
108	C₂×C₄×C₉	—	2	2	no	—
109	C₂×C₄×C₉	—	2	1	no	—
110	C₂×C₄×C₉	—	2	1	no	—
111	C₂×C₄×C₉	—	2	2	no	—
112	C₂×C₄×C₉	—	2	1	no	—
113	C₂×C₄×C₉	—	2	1	no	—
114	C₂×C₄×C₉	—	2	2	no	—
115	C₂×C₄×C₉	—	2	2	no	—
116	C₂×C₄×C₉	—	2	2	no	—
117	C₂×C₄×C₉	—	2	2	no	—
118	C₂×C₄×C₉	—	2	2	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	2	2	no	—
123	C₂×C₄×C₉	—	2	2	no	—
124	C₂×C₄×C₉	—	4	4	no	—
125	C₂×C₄×C₉	—	4	4	no	—
126	C₂×C₄×C₉	—	4	4	no	—
127	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
128	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
129	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
130	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
131	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
132	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic
133	#391	C₂×C₉	1	2	yes	complemented
134	#389	C₂×C₉	1	2	yes	complemented
135	#387	C₂×C₉	1	2	yes	complemented
136	#387	C₂×C₉	1	2	yes	complemented
137	#385	C₂×C₉	1	2	yes	—
138	#380	C₂×C₉	1	1	yes	characteristic
139	C₄×C₂²⋊C₄	C₂×C₉	1	2	yes	—
140	C₂×#95	C₂×C₉	1	1	yes	characteristic
141	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₃×Q₈	—	4	1	no	—
143	C₂×C₃×Q₈	—	4	1	no	—
144	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
145	C₂²×C₃×C₄	—	2	2	no	—
146	C₂²×C₃×C₄	—	4	1	no	—
147	C₂²×C₃×C₄	—	4	1	no	—
148	C₂²×C₃×C₄	—	4	1	no	—
149	C₂²×C₃×C₄	—	4	1	no	—
150	C₂²×C₃×C₄	—	4	1	no	—
151	C₂²×C₃×C₄	—	4	1	no	—
152	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
153	C₂²×C₃×C₄	C₃×Q₈	1	4	yes	—
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	2	yes	—
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
159	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
160	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
162	C₃×C₄⋊C₄	—	4	2	no	—
163	C₃×C₄⋊C₄	—	4	1	no	—
164	C₃×C₄⋊C₄	—	4	1	no	—
165	C₃×C₄⋊C₄	—	4	2	no	—
166	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
167	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
168	C₃×C₂²⋊C₄	—	2	4	no	—
169	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
170	C₃×C₄²	—	4	2	no	—
171	C₃×C₄²	—	4	2	no	—
172	C₂²×C₉	—	2	2	no	—
173	C₂²×C₉	—	2	2	no	—
174	C₂²×C₉	—	2	2	no	—
175	C₂²×C₉	—	2	2	no	—
176	C₂²×C₉	—	2	2	no	—
177	C₂²×C₉	—	2	2	no	—
178	C₂²×C₉	C₄×Q₈	1	4	yes	—
179	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
180	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
181	C₂²×C₉	C₂×#41	1	1	yes	characteristic
182	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂²×C₉	H(5,𝔽₂)	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	4	no	—
190	C₄×C₉	—	2	4	no	—
191	C₄×C₉	—	4	2	no	—
192	C₄×C₉	—	4	2	no	—
193	C₄×C₉	—	4	2	no	—
194	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
195	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
196	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
197	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
198	C₂²⋊Q₈	C₄×C₉	1	8	yes	complemented
199	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
206	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
207	C₂×C₄²	C₂²×C₉	1	2	yes	—
208	C₂×C₄²	C₂²×C₉	1	2	yes	—
209	#95	C₂²×C₉	1	2	yes	—
210	#95	C₂²×C₉	1	2	yes	—
211	#95	C₂²×C₉	1	2	yes	—
212	#95	C₂²×C₉	1	2	yes	—
213	#95	C₂²×C₉	1	2	yes	—
214	#95	C₂²×C₉	1	2	yes	—
215	#95	C₂²×C₉	1	2	yes	—
216	C₂³×C₃	—	2	1	no	—
217	C₂³×C₃	—	2	1	no	—
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	—	2	1	no	—
220	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
221	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
222	C₂³×C₃	C₃×#41	1	2	yes	—
223	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
224	C₃×Q₈	—	4	4	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	4	4	no	—
245	C₂×C₃×C₄	—	4	4	no	—
246	C₂×C₃×C₄	—	4	4	no	—
247	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
248	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
249	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
250	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
251	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
252	C₂×C₉	—	2	4	no	—
253	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
254	C₂×C₉	#518	1	1	yes	characteristic
255	C₂×C₉	#520	1	1	yes	characteristic
256	C₂×C₉	#538	1	1	yes	characteristic
257	C₂×C₉	#539	1	1	yes	characteristic
258	C₂×C₉	#543	1	1	yes	characteristic
259	C₂×C₉	#544	1	1	yes	characteristic
260	C₂⁴	C₂³×C₉	1	1	yes	characteristic
261	C₂×Q₈	—	4	1	no	—
262	C₂×Q₈	—	4	1	no	—
263	C₂×Q₈	C₂×C₄×C₉	1	4	yes	complemented
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	C₂×C₄×C₉	1	4	yes	—
272	C₂²×C₄	Q₈×C₉	1	4	yes	complemented
273	C₂²×C₄	C₂³×C₉	1	2	yes	—
274	C₂²×C₄	C₂³×C₉	1	2	yes	—
275	C₂²×C₄	C₂³×C₉	1	2	yes	—
276	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
277	C₂²×C₄	C₂³×C₉	1	2	yes	—
278	C₂²×C₄	C₂³×C₉	1	2	yes	—
279	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₉	1	2	yes	—
281	C₄⋊C₄	—	4	2	no	—
282	C₄⋊C₄	—	4	1	no	—
283	C₄⋊C₄	—	4	1	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	complemented
286	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	complemented
287	C₂²⋊C₄	—	2	4	no	—
288	C₂²⋊C₄	C₂×C₄×C₉	1	8	yes	—
289	C₄²	—	4	2	no	—
290	C₄²	—	4	2	no	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	C₃×C₄×Q₈	1	4	yes	—
298	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
299	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
300	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
301	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
302	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	2	4	no	—
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	4	2	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	—	4	2	no	—
313	C₉	#2329	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	C₂²×C₄×C₉	1	2	yes	—
319	C₂³	C₂×Q₈×C₉	1	2	yes	—
320	C₂³	C₉×#41	1	2	yes	—
321	C₂³	C₂⁴×C₉	1	1	yes	characteristic
322	Q₈	—	4	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	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	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
346	C₂×C₄	C₂²×C₄×C₉	1	4	yes	—
347	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
348	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
349	C₂×C₄	C₂×Q₈×C₉	1	4	yes	—
350	C₂×C₃	—	2	4	no	—
351	C₂×C₃	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
352	C₂×C₃	C₃×#518	1	1	yes	characteristic
353	C₂×C₃	C₃×#520	1	1	yes	characteristic
354	C₂×C₃	C₃×#538	1	1	yes	characteristic
355	C₂×C₃	C₃×#539	1	1	yes	characteristic
356	C₂×C₃	C₃×#543	1	1	yes	characteristic
357	C₂×C₃	C₃×#544	1	1	yes	characteristic
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	C₄×Q₈×C₉	1	4	yes	—
365	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
366	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
367	C₂²	C₂×C₉×#41	1	1	yes	characteristic
368	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
372	C₄	—	2	4	no	—
373	C₄	—	2	4	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₃	C₃×#2329	1	1	yes	characteristic
381	C₂	—	2	4	no	—
382	C₂	C₂×C₄×Q₈×C₉	1	1	yes	characteristic
383	C₂	C₉×#518	1	1	yes	characteristic
384	C₂	C₉×#520	1	1	yes	characteristic
385	C₂	C₉×#538	1	1	yes	characteristic
386	C₂	C₉×#539	1	1	yes	characteristic
387	C₂	C₉×#543	1	1	yes	characteristic
388	C₂	C₉×#544	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. C₉×#391	C₂	semidirect
3. C₉×#389	C₂	semidirect
4. C₉×#387	C₂	semidirect
5. C₉×#387	C₂	semidirect
15. C₉×C₂²⋊Q₈	C₄	semidirect
45. C₂×Q₈×C₉	C₂×C₄	semidirect
54. C₂²×C₄×C₉	Q₈	semidirect
67. C₉×C₄⋊C₄	C₂×C₄	semidirect
68. C₉×C₄⋊C₄	C₂×C₄	semidirect
73. #2329	C₉	direct (N × H)
133. #391	C₂×C₉	semidirect
134. #389	C₂×C₉	semidirect
135. #387	C₂×C₉	semidirect
136. #387	C₂×C₉	semidirect
198. C₂²⋊Q₈	C₄×C₉	semidirect
263. C₂×Q₈	C₂×C₄×C₉	semidirect
272. C₂²×C₄	Q₈×C₉	semidirect
285. C₄⋊C₄	C₂×C₄×C₉	semidirect
286. C₄⋊C₄	C₂×C₄×C₉	semidirect
313. C₉	#2329	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
C₉×#391	2
C₉×#389	2
C₉×#387	2
C₉×#385	2
C₉×#380	2
C₄×C₉×C₂²⋊C₄	2
C₂×C₉×#95	2
C₃×#2329	3

Subgroups — C9×#2329 #11767050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2329 #11767050