Subgroups — C₉×#2396 #11767117

Order 1152.

792 conjugacy classes of subgroups.

The subgroup lattice has 387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic
3	C₉×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#399	C₂	1	1	yes	maximal, characteristic
5	C₉×#398	C₂	1	2	yes	maximal, complemented
6	C₉×#396	C₂	1	2	yes	maximal
7	C₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#393	C₂	1	1	yes	maximal, characteristic
9	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₄×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal
12	C₃×#2396	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	C₄×Q₈×C₉	—	2	4	no	—
16	C₉×#117	—	2	4	no	—
17	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₂²⋊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×C₄²×C₉	C₂²	1	2	yes	—
29	C₂×C₄²×C₉	C₂²	1	2	yes	—
30	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
31	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
32	C₉×#95	C₂²	1	2	yes	—
33	C₉×#95	C₂²	1	2	yes	—
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	1	yes	characteristic
36	C₉×#95	C₂²	1	1	yes	characteristic
37	C₉×#95	C₂²	1	2	yes	—
38	C₂×C₃×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
39	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
40	C₃×#400	C₂×C₃	1	1	yes	characteristic
41	C₃×#399	C₂×C₃	1	1	yes	characteristic
42	C₃×#398	C₂×C₃	1	2	yes	—
43	C₃×#396	C₂×C₃	1	2	yes	—
44	C₃×#395	C₂×C₃	1	1	yes	characteristic
45	C₃×#393	C₂×C₃	1	1	yes	characteristic
46	C₃×C₄×C₄⋊C₄	C₂×C₃	1	2	yes	—
47	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	2	yes	—
49	C₂⁴×C₉	C₂³	1	1	yes	characteristic
50	C₂×Q₈×C₉	—	2	2	no	—
51	C₂×Q₈×C₉	—	2	4	no	—
52	C₂²×C₄×C₉	—	2	2	no	—
53	C₂²×C₄×C₉	—	2	2	no	—
54	C₂²×C₄×C₉	Q₈	1	4	yes	complemented
55	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂²×C₄×C₉	C₂³	1	2	yes	—
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	2	yes	—
63	C₂²×C₄×C₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₉×C₄⋊C₄	—	2	2	no	—
66	C₉×C₄⋊C₄	—	2	2	no	—
67	C₉×C₄⋊C₄	—	2	4	no	—
68	C₉×C₄⋊C₄	—	2	2	no	—
69	C₉×C₄⋊C₄	—	2	4	no	—
70	C₉×C₄⋊C₄	—	2	4	no	—
71	C₉×C₄⋊C₄	—	2	4	no	—
72	C₉×C₂²⋊C₄	—	2	2	no	—
73	C₉×C₂²⋊C₄	—	2	2	no	—
74	C₉×C₂²⋊C₄	—	2	4	no	—
75	C₉×C₂²⋊C₄	—	2	4	no	—
76	C₄²×C₉	—	2	2	no	—
77	C₄²×C₉	—	2	4	no	—
78	C₄²×C₉	—	2	4	no	—
79	C₄²×C₉	D₄	1	4	yes	—
80	#2396	C₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
82	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
83	C₃×C₄×Q₈	—	2	4	no	—
84	C₃×#117	—	2	4	no	—
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
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×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
97	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
98	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
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	1	yes	characteristic
104	C₃×#95	C₂²×C₃	1	1	yes	characteristic
105	C₃×#95	C₂²×C₃	1	2	yes	—
106	C₂³×C₉	—	2	1	no	—
107	C₂³×C₉	—	2	2	no	—
108	C₂³×C₉	—	2	2	no	—
109	C₂³×C₉	—	2	1	no	—
110	C₂³×C₉	C₂×Q₈	1	2	yes	—
111	C₂³×C₉	C₂⁴	1	1	yes	characteristic
112	Q₈×C₉	—	2	8	no	—
113	C₂×C₄×C₉	—	2	2	no	—
114	C₂×C₄×C₉	—	2	1	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	1	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	2	no	—
121	C₂×C₄×C₉	—	2	8	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	2	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	2	no	—
132	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
133	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
134	C₂×C₄×C₉	C₂×D₄	1	2	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	4	yes	—
138	C₂×C₄×C₉	#41	1	4	yes	—
139	C₂×C₄×C₉	#41	1	2	yes	—
140	C₂×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
141	C₂×#117	C₂×C₉	1	1	yes	characteristic
142	#400	C₂×C₉	1	1	yes	characteristic, complemented
143	#399	C₂×C₉	1	1	yes	characteristic
144	#398	C₂×C₉	1	2	yes	complemented
145	#396	C₂×C₉	1	2	yes	—
146	#395	C₂×C₉	1	1	yes	characteristic, complemented
147	#393	C₂×C₉	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
149	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊C₄	C₂×C₉	1	2	yes	—
151	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
152	C₂×C₃×Q₈	—	2	2	no	—
153	C₂×C₃×Q₈	—	2	4	no	—
154	C₂²×C₃×C₄	—	2	2	no	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	C₃×Q₈	1	4	yes	—
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	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
165	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
166	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
167	C₃×C₄⋊C₄	—	2	2	no	—
168	C₃×C₄⋊C₄	—	2	2	no	—
169	C₃×C₄⋊C₄	—	2	4	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	4	no	—
172	C₃×C₄⋊C₄	—	2	4	no	—
173	C₃×C₄⋊C₄	—	2	4	no	—
174	C₃×C₂²⋊C₄	—	2	2	no	—
175	C₃×C₂²⋊C₄	—	2	2	no	—
176	C₃×C₂²⋊C₄	—	2	4	no	—
177	C₃×C₂²⋊C₄	—	2	4	no	—
178	C₃×C₄²	—	2	2	no	—
179	C₃×C₄²	—	2	4	no	—
180	C₃×C₄²	—	2	4	no	—
181	C₃×C₄²	C₃×D₄	1	4	yes	—
182	C₂²×C₉	—	2	2	no	—
183	C₂²×C₉	—	2	4	no	—
184	C₂²×C₉	—	4	1	no	—
185	C₂²×C₉	—	4	2	no	—
186	C₂²×C₉	—	4	1	no	—
187	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
188	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
189	C₂²×C₉	C₂×#41	1	1	yes	characteristic
190	C₂²×C₉	C₂×#41	1	2	yes	—
191	C₂²×C₉	C₂×#41	1	2	yes	—
192	C₄×C₉	—	2	2	no	—
193	C₄×C₉	—	2	2	no	—
194	C₄×C₉	—	2	4	no	—
195	C₄×C₉	—	2	4	no	—
196	C₄×C₉	—	2	2	no	—
197	C₄×C₉	—	4	1	no	—
198	C₄×C₉	—	4	2	no	—
199	C₄×C₉	—	4	1	no	—
200	C₄×C₉	—	4	2	no	—
201	C₄×C₉	C₂²⋊Q₈	1	4	yes	—
202	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
203	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
204	C₄×Q₈	—	2	4	no	—
205	#117	—	2	4	no	—
206	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
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	2	yes	—
211	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
212	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
214	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
216	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
217	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₄²	C₂²×C₉	1	2	yes	—
219	C₂×C₄²	C₂²×C₉	1	2	yes	—
220	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
221	#95	C₂²×C₉	1	2	yes	—
222	#95	C₂²×C₉	1	2	yes	—
223	#95	C₂²×C₉	1	2	yes	—
224	#95	C₂²×C₉	1	1	yes	characteristic
225	#95	C₂²×C₉	1	1	yes	characteristic
226	#95	C₂²×C₉	1	2	yes	—
227	C₂³×C₃	—	2	1	no	—
228	C₂³×C₃	—	2	2	no	—
229	C₂³×C₃	—	2	2	no	—
230	C₂³×C₃	—	2	1	no	—
231	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
232	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
233	C₃×Q₈	—	2	8	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	1	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	1	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	8	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
254	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
255	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
257	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
258	C₂×C₃×C₄	C₃×#41	1	4	yes	—
259	C₂×C₃×C₄	C₃×#41	1	4	yes	—
260	C₂×C₃×C₄	C₃×#41	1	2	yes	—
261	C₂×C₉	—	4	2	no	—
262	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₉	#525	1	1	yes	characteristic
264	C₂×C₉	#529	1	2	yes	—
265	C₂×C₉	#532	1	1	yes	characteristic
266	C₂×C₉	#533	1	2	yes	—
267	C₂⁴	C₂³×C₉	1	1	yes	characteristic
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	Q₈×C₉	1	4	yes	complemented
273	C₂²×C₄	C₂³×C₉	1	2	yes	—
274	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
275	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
276	C₂²×C₄	C₂³×C₉	1	2	yes	—
277	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
278	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
279	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
280	C₂²×C₄	C₂³×C₉	1	2	yes	—
281	C₂²×C₄	C₂³×C₉	1	2	yes	—
282	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₂²⋊C₄	—	2	2	no	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₂²⋊C₄	—	2	4	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	4	no	—
296	C₄²	—	2	4	no	—
297	C₄²	D₄×C₉	1	4	yes	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	2	4	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	2	no	—
302	C₂²×C₃	—	4	1	no	—
303	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
304	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
305	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
307	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	2	4	no	—
311	C₃×C₄	—	2	4	no	—
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	4	1	no	—
314	C₃×C₄	—	4	2	no	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
318	C₉	#2396	1	1	yes	characteristic, direct product factor, Sylow
319	C₂³	—	2	1	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	1	no	—
323	C₂³	C₂×Q₈×C₉	1	2	yes	—
324	C₂³	C₂⁴×C₉	1	1	yes	characteristic
325	Q₈	—	2	8	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	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	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
346	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
347	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
348	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
349	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
350	C₂×C₄	C₉×#41	1	4	yes	—
351	C₂×C₄	C₉×#41	1	4	yes	—
352	C₂×C₄	C₉×#41	1	2	yes	—
353	C₂×C₃	—	4	2	no	—
354	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
355	C₂×C₃	C₃×#525	1	1	yes	characteristic
356	C₂×C₃	C₃×#529	1	2	yes	—
357	C₂×C₃	C₃×#532	1	1	yes	characteristic
358	C₂×C₃	C₃×#533	1	2	yes	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
365	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
366	C₂²	C₂×C₉×#41	1	1	yes	characteristic
367	C₂²	C₂×C₉×#41	1	2	yes	—
368	C₂²	C₂×C₉×#41	1	2	yes	—
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	4	no	—
372	C₄	—	2	4	no	—
373	C₄	—	2	2	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	2	no	—
378	C₄	C₉×C₂²⋊Q₈	1	4	yes	—
379	C₃	C₃×#2396	1	1	yes	characteristic
380	C₂	—	4	2	no	—
381	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
382	C₂	C₉×#525	1	1	yes	characteristic
383	C₂	C₉×#529	1	2	yes	—
384	C₂	C₉×#532	1	1	yes	characteristic
385	C₂	C₉×#533	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₄×Q₈×C₉	C₂	semidirect
3. C₉×#400	C₂	semidirect
5. C₉×#398	C₂	semidirect
7. C₉×#395	C₂	semidirect
9. C₄×C₉×C₄⋊C₄	C₂	semidirect
10. C₄×C₉×C₄⋊C₄	C₂	semidirect
54. C₂²×C₄×C₉	Q₈	semidirect
80. #2396	C₉	direct (N × H)
140. C₂×C₄×Q₈	C₂×C₉	semidirect
142. #400	C₂×C₉	semidirect
144. #398	C₂×C₉	semidirect
146. #395	C₂×C₉	semidirect
148. C₄×C₄⋊C₄	C₂×C₉	semidirect
149. C₄×C₄⋊C₄	C₂×C₉	semidirect
272. C₂²×C₄	Q₈×C₉	semidirect
318. C₉	#2396	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×C₄×Q₈×C₉	2
C₂×C₉×#117	2
C₉×#400	2
C₉×#399	2
C₉×#398	2
C₉×#396	2
C₉×#395	2
C₉×#393	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2396	3

Subgroups — C9×#2396 #11767117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2396 #11767117