Subgroups — C₉×#2409 #11767130

Order 1152.

1260 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	C₂³×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
4	C₉×#395	C₂	1	2	yes	maximal, complemented
5	C₉×#393	C₂	1	2	yes	maximal, complemented
6	C₉×#391	C₂	1	2	yes	maximal, complemented
7	C₉×#386	C₂	1	2	yes	maximal
8	C₉×#385	C₂	1	2	yes	maximal, complemented
9	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2409	C₃	1	1	yes	maximal, characteristic
11	C₂²×Q₈×C₉	—	2	8	no	—
12	C₂²×Q₈×C₉	—	2	4	no	—
13	C₂²×Q₈×C₉	C₂²	1	2	yes	—
14	C₂²×Q₈×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	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₉×C₂²⋊Q₈	—	2	8	no	—
20	C₄×D₄×C₉	—	2	4	no	—
21	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₂²⋊C₄	C₂²	1	4	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	1	yes	characteristic
29	C₉×#95	C₂²	1	2	yes	—
30	C₉×#95	C₂²	1	4	yes	—
31	C₉×#95	C₂²	1	4	yes	—
32	C₂³×C₃×Q₈	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
34	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
35	C₃×#395	C₂×C₃	1	2	yes	—
36	C₃×#393	C₂×C₃	1	2	yes	—
37	C₃×#391	C₂×C₃	1	2	yes	—
38	C₃×#386	C₂×C₃	1	2	yes	—
39	C₃×#385	C₂×C₃	1	2	yes	—
40	C₃×#380	C₂×C₃	1	1	yes	characteristic
41	C₂⁴×C₉	C₂³	1	1	yes	characteristic
42	C₂⁴×C₉	C₂³	1	1	yes	characteristic
43	C₂×Q₈×C₉	—	2	32	no	—
44	C₂×Q₈×C₉	—	2	8	no	—
45	C₂×Q₈×C₉	—	2	4	no	—
46	C₂×Q₈×C₉	—	2	4	no	—
47	C₂×Q₈×C₉	—	2	4	no	—
48	C₂×Q₈×C₉	D₄	1	8	yes	complemented
49	C₂×D₄×C₉	—	2	2	no	—
50	C₂×D₄×C₉	—	2	2	no	—
51	C₂×D₄×C₉	Q₈	1	4	yes	complemented
52	C₂²×C₄×C₉	—	2	4	no	—
53	C₂²×C₄×C₉	—	2	8	no	—
54	C₂²×C₄×C₉	—	2	4	no	—
55	C₂²×C₄×C₉	—	2	2	no	—
56	C₂²×C₄×C₉	—	2	4	no	—
57	C₂²×C₄×C₉	D₄	1	4	yes	—
58	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	4	yes	—
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	4	yes	—
62	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₉×C₄⋊C₄	—	2	2	no	—
66	C₉×C₄⋊C₄	—	2	4	no	—
67	C₉×C₄⋊C₄	—	2	8	no	—
68	C₉×C₂²⋊C₄	—	2	2	no	—
69	C₉×C₂²⋊C₄	—	2	4	no	—
70	C₉×C₂²⋊C₄	—	2	2	no	—
71	C₉×C₂²⋊C₄	—	2	8	no	—
72	C₄²×C₉	—	2	2	no	—
73	#2409	C₉	1	1	yes	characteristic, direct product factor, Sylow
74	C₂²×C₃×Q₈	—	2	8	no	—
75	C₂²×C₃×Q₈	—	2	4	no	—
76	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
77	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
78	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
79	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
80	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
82	C₃×C₂²⋊Q₈	—	2	8	no	—
83	C₃×C₄×D₄	—	2	4	no	—
84	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
90	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
92	C₃×#95	C₂²×C₃	1	2	yes	—
93	C₃×#95	C₂²×C₃	1	4	yes	—
94	C₃×#95	C₂²×C₃	1	4	yes	—
95	C₂³×C₉	—	2	2	no	—
96	C₂³×C₉	—	2	2	no	—
97	C₂³×C₉	—	2	2	no	—
98	C₂³×C₉	—	2	1	no	—
99	C₂³×C₉	—	2	1	no	—
100	C₂³×C₉	—	2	2	no	—
101	C₂³×C₉	C₂×D₄	1	2	yes	—
102	C₂³×C₉	C₂×Q₈	1	2	yes	—
103	C₂³×C₉	C₂×Q₈	1	2	yes	complemented
104	C₂³×C₉	#41	1	2	yes	—
105	C₂³×C₉	C₂⁴	1	1	yes	characteristic
106	Q₈×C₉	—	2	16	no	—
107	Q₈×C₉	—	2	16	no	—
108	D₄×C₉	—	2	8	no	—
109	C₂×C₄×C₉	—	2	16	no	—
110	C₂×C₄×C₉	—	2	1	no	—
111	C₂×C₄×C₉	—	2	4	no	—
112	C₂×C₄×C₉	—	2	4	no	—
113	C₂×C₄×C₉	—	2	2	no	—
114	C₂×C₄×C₉	—	2	1	no	—
115	C₂×C₄×C₉	—	2	8	no	—
116	C₂×C₄×C₉	—	2	1	no	—
117	C₂×C₄×C₉	—	2	4	no	—
118	C₂×C₄×C₉	—	2	1	no	—
119	C₂×C₄×C₉	—	2	2	no	—
120	C₂×C₄×C₉	—	2	4	no	—
121	C₂×C₄×C₉	—	2	2	no	—
122	C₂×C₄×C₉	—	2	4	no	—
123	C₂×C₄×C₉	—	4	4	no	—
124	C₂×C₄×C₉	C₂×D₄	1	8	yes	—
125	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
126	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
127	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
128	C₂×C₄×C₉	C₂×Q₈	1	2	yes	complemented
129	C₂³×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
130	C₂×C₂²⋊Q₈	C₂×C₉	1	2	yes	complemented
131	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
132	#395	C₂×C₉	1	2	yes	complemented
133	#393	C₂×C₉	1	2	yes	complemented
134	#391	C₂×C₉	1	2	yes	complemented
135	#386	C₂×C₉	1	2	yes	—
136	#385	C₂×C₉	1	2	yes	complemented
137	#380	C₂×C₉	1	1	yes	characteristic, complemented
138	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
139	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
140	C₂×C₃×Q₈	—	2	32	no	—
141	C₂×C₃×Q₈	—	2	8	no	—
142	C₂×C₃×Q₈	—	2	4	no	—
143	C₂×C₃×Q₈	—	2	4	no	—
144	C₂×C₃×Q₈	—	2	4	no	—
145	C₂×C₃×Q₈	C₃×D₄	1	8	yes	—
146	C₂×C₃×D₄	—	2	2	no	—
147	C₂×C₃×D₄	—	2	2	no	—
148	C₂×C₃×D₄	C₃×Q₈	1	4	yes	—
149	C₂²×C₃×C₄	—	2	4	no	—
150	C₂²×C₃×C₄	—	2	8	no	—
151	C₂²×C₃×C₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	2	2	no	—
153	C₂²×C₃×C₄	—	2	4	no	—
154	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
155	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
159	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₃×C₄⋊C₄	—	2	2	no	—
163	C₃×C₄⋊C₄	—	2	4	no	—
164	C₃×C₄⋊C₄	—	2	8	no	—
165	C₃×C₂²⋊C₄	—	2	2	no	—
166	C₃×C₂²⋊C₄	—	2	4	no	—
167	C₃×C₂²⋊C₄	—	2	2	no	—
168	C₃×C₂²⋊C₄	—	2	8	no	—
169	C₃×C₄²	—	2	2	no	—
170	C₂²×C₉	—	2	2	no	—
171	C₂²×C₉	—	2	2	no	—
172	C₂²×C₉	—	2	4	no	—
173	C₂²×C₉	—	2	4	no	—
174	C₂²×C₉	—	2	2	no	—
175	C₂²×C₉	—	2	4	no	—
176	C₂²×C₉	—	4	1	no	—
177	C₂²×C₉	—	4	1	no	—
178	C₂²×C₉	—	4	2	no	—
179	C₂²×C₉	C₂²⋊Q₈	1	4	yes	complemented
180	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
181	C₂²×C₉	C₂²×D₄	1	2	yes	—
182	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
183	C₂²×C₉	C₂×#41	1	1	yes	characteristic
184	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
185	C₄×C₉	—	2	8	no	—
186	C₄×C₉	—	2	2	no	—
187	C₄×C₉	—	2	2	no	—
188	C₄×C₉	—	4	1	no	—
189	C₄×C₉	—	4	1	no	—
190	C₄×C₉	—	4	4	no	—
191	C₄×C₉	#120	1	4	yes	—
192	C₂²×Q₈	—	2	8	no	—
193	C₂²×Q₈	—	2	4	no	—
194	C₂²×Q₈	C₂²×C₉	1	2	yes	—
195	C₂²×Q₈	C₂²×C₉	1	2	yes	—
196	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
197	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
198	C₂³×C₄	C₂²×C₉	1	2	yes	—
199	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
200	C₂²⋊Q₈	—	2	8	no	—
201	C₄×D₄	—	2	4	no	—
202	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
203	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
204	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
205	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
206	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
208	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
209	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
210	#95	C₂²×C₉	1	2	yes	—
211	#95	C₂²×C₉	1	4	yes	—
212	#95	C₂²×C₉	1	4	yes	—
213	C₂³×C₃	—	2	2	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	2	1	no	—
217	C₂³×C₃	—	2	1	no	—
218	C₂³×C₃	—	2	2	no	—
219	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
220	C₂³×C₃	C₂×C₃×Q₈	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	—	2	16	no	—
225	C₃×Q₈	—	2	16	no	—
226	C₃×D₄	—	2	8	no	—
227	C₂×C₃×C₄	—	2	16	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	8	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	4	4	no	—
242	C₂×C₃×C₄	C₂×C₃×D₄	1	8	yes	—
243	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
244	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
245	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
246	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
247	C₂×C₉	—	2	4	no	—
248	C₂×C₉	—	4	2	no	—
249	C₂×C₉	C₂×#120	1	1	yes	characteristic
250	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₉	#536	1	1	yes	characteristic
252	C₂×C₉	#548	1	2	yes	—
253	C₂×C₉	D₄×Q₈	1	2	yes	—
254	C₂⁴	C₂³×C₉	1	1	yes	characteristic
255	C₂⁴	C₂³×C₉	1	1	yes	characteristic
256	C₂×Q₈	—	2	32	no	—
257	C₂×Q₈	—	2	8	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	D₄×C₉	1	8	yes	complemented
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	Q₈×C₉	1	4	yes	complemented
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	D₄×C₉	1	4	yes	—
271	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
272	C₂²×C₄	C₂³×C₉	1	4	yes	—
273	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
274	C₂²×C₄	C₂³×C₉	1	4	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	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	8	no	—
281	C₂²⋊C₄	—	2	2	no	—
282	C₂²⋊C₄	—	2	4	no	—
283	C₂²⋊C₄	—	2	2	no	—
284	C₂²⋊C₄	—	2	8	no	—
285	C₄²	—	2	2	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	4	no	—
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	2	2	no	—
291	C₂²×C₃	—	2	4	no	—
292	C₂²×C₃	—	4	1	no	—
293	C₂²×C₃	—	4	1	no	—
294	C₂²×C₃	—	4	2	no	—
295	C₂²×C₃	C₃×C₂²⋊Q₈	1	4	yes	—
296	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
297	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
298	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
299	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
300	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
301	C₃×C₄	—	2	8	no	—
302	C₃×C₄	—	2	2	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	4	1	no	—
305	C₃×C₄	—	4	1	no	—
306	C₃×C₄	—	4	4	no	—
307	C₃×C₄	C₃×#120	1	4	yes	—
308	C₉	#2409	1	1	yes	characteristic, direct product factor, Sylow
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	2	no	—
315	C₂³	C₂×D₄×C₉	1	2	yes	—
316	C₂³	C₂×Q₈×C₉	1	2	yes	—
317	C₂³	C₂×Q₈×C₉	1	2	yes	complemented
318	C₂³	C₉×#41	1	2	yes	—
319	C₂³	C₂⁴×C₉	1	1	yes	characteristic
320	Q₈	—	2	16	no	—
321	Q₈	—	2	16	no	—
322	D₄	—	2	8	no	—
323	C₂×C₄	—	2	16	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	C₂×D₄×C₉	1	8	yes	—
339	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
340	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
341	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
342	C₂×C₄	C₂×Q₈×C₉	1	2	yes	complemented
343	C₂×C₃	—	2	4	no	—
344	C₂×C₃	—	4	2	no	—
345	C₂×C₃	C₂×C₃×#120	1	1	yes	characteristic
346	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
347	C₂×C₃	C₃×#536	1	1	yes	characteristic
348	C₂×C₃	C₃×#548	1	2	yes	—
349	C₂×C₃	C₃×D₄×Q₈	1	2	yes	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	2	no	—
359	C₂²	C₉×C₂²⋊Q₈	1	4	yes	complemented
360	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
361	C₂²	C₂²×D₄×C₉	1	2	yes	—
362	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
363	C₂²	C₂×C₉×#41	1	1	yes	characteristic
364	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
365	C₄	—	2	8	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	4	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	4	no	—
371	C₄	C₉×#120	1	4	yes	—
372	C₃	C₃×#2409	1	1	yes	characteristic
373	C₂	—	2	4	no	—
374	C₂	—	4	2	no	—
375	C₂	C₂×C₉×#120	1	1	yes	characteristic
376	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
377	C₂	C₉×#536	1	1	yes	characteristic
378	C₂	C₉×#548	1	2	yes	—
379	C₂	D₄×Q₈×C₉	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²×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. C₂³×Q₈×C₉	C₂	semidirect
2. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₉×#395	C₂	semidirect
5. C₉×#393	C₂	semidirect
6. C₉×#391	C₂	semidirect
8. C₉×#385	C₂	semidirect
9. C₉×#380	C₂	semidirect
48. C₂×Q₈×C₉	D₄	semidirect
51. C₂×D₄×C₉	Q₈	semidirect
73. #2409	C₉	direct (N × H)
103. C₂³×C₉	C₂×Q₈	semidirect
128. C₂×C₄×C₉	C₂×Q₈	semidirect
129. C₂³×Q₈	C₂×C₉	semidirect
130. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
132. #395	C₂×C₉	semidirect
133. #393	C₂×C₉	semidirect
134. #391	C₂×C₉	semidirect
136. #385	C₂×C₉	semidirect
137. #380	C₂×C₉	semidirect
179. C₂²×C₉	C₂²⋊Q₈	semidirect
261. C₂×Q₈	D₄×C₉	semidirect
264. C₂×D₄	Q₈×C₉	semidirect
308. C₉	#2409	direct (N × H)
317. C₂³	C₂×Q₈×C₉	semidirect
342. C₂×C₄	C₂×Q₈×C₉	semidirect
359. C₂²	C₉×C₂²⋊Q₈	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×Q₈×C₉	2
C₂×C₉×C₂²⋊Q₈	2
C₂×C₄×D₄×C₉	2
C₉×#395	2
C₉×#393	2
C₉×#391	2
C₉×#386	2
C₉×#385	2
C₉×#380	2
C₃×#2409	3

Subgroups — C9×#2409 #11767130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2409 #11767130