Subgroups — #13139482

Order 1728.

496 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6233	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₃⋊D₉)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63389	C₂	1	1	yes	maximal, characteristic, complemented
5	#11720282	C₂	1	1	yes	maximal, characteristic, complemented
6	#11720273	C₂	1	1	yes	maximal, characteristic, complemented
7	#11720271	C₂	1	1	yes	maximal, characteristic, complemented
8	#10591148	—	3	1	no	maximal
9	C₈×#611	—	3	1	no	maximal
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×#6233	C₄	1	1	yes	characteristic
12	C₂×C₄×C₃⋊D₉	C₂²	1	1	yes	characteristic
13	#88551	C₄	1	1	yes	characteristic
14	#88536	C₄	1	1	yes	characteristic
15	#88534	C₄	1	1	yes	characteristic
16	C₄×C₃⋊Dic₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×C₃⋊C₈	—	2	2	no	—
18	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
22	(C₃⋊D₉)⋊C₈	—	2	2	no	—
23	C₄×#638	—	3	1	no	—
24	C₂²×C₃×C₃⋊C₈	D₃	1	1	yes	characteristic
25	C₂×#3710	—	3	1	no	—
26	C₃×#830	—	3	1	no	—
27	#63572	—	3	1	no	—
28	#63557	—	3	1	no	—
29	#63553	—	3	1	no	—
30	C₂²×C₈×C₉	—	3	1	no	—
31	C₄×#611	—	3	1	no	—
32	C₄×#611	—	6	1	no	—
33	C₂×C₈×D₉	—	3	1	no	—
34	#63389	D₃	1	1	yes	characteristic, complemented
35	(C₂×D₉)⋊C₈	—	3	1	no	—
36	Dic₉⋊C₈	—	3	1	no	—
37	C₈×Dic₉	—	3	1	no	—
38	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃⋊D₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	—	2	1	no	—
41	C₂×C₃×C₄×C₉	—	2	1	no	—
42	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
44	#6233	C₈	1	4	yes	complemented
45	C₂×C₃⋊Dic₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃⋊Dic₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃⋊Dic₉	C₂×C₄	1	1	yes	characteristic
48	C₄×C₃⋊D₉	—	2	1	no	—
49	C₄×C₃⋊D₉	—	2	1	no	—
50	C₉×C₃⋊C₈	—	2	1	no	—
51	C₉×C₃⋊C₈	D₄	1	2	yes	complemented
52	C₃×C₉⋊C₈	—	2	1	no	—
53	C₃×C₉⋊C₈	—	2	1	no	—
54	C₈×#67	—	9	1	no	—
55	#67⋊C₈	—	9	1	no	—
56	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
57	C₂×#638	—	3	1	no	—
58	C₂×C₄×C₃⋊D₃	—	3	1	no	—
59	#3757	—	3	1	no	—
60	#3752	—	3	1	no	—
61	#3750	—	3	1	no	—
62	C₄×C₃⋊Dic₃	—	3	1	no	—
63	C₂×C₃×C₃⋊C₈	—	2	2	no	—
64	C₂×C₃×C₃⋊C₈	—	3	1	no	—
65	C₂×C₃×C₃⋊C₈	—	3	1	no	—
66	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
67	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
68	#3710	—	6	2	no	—
69	C₂²×C₄×C₉	—	2	1	no	—
70	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
71	C₂×#611	—	3	1	no	—
72	C₂×#611	—	6	1	no	—
73	C₂×C₄×D₉	—	3	1	no	—
74	C₂×C₄×D₉	—	6	1	no	—
75	C₂×C₈×C₉	—	3	1	no	—
76	C₂×C₈×C₉	—	3	1	no	—
77	C₂×C₈×C₉	—	6	2	no	—
78	#3676	—	3	1	no	—
79	#3676	—	6	1	no	—
80	(C₂×D₉)⋊C₄	—	3	1	no	—
81	(C₂×D₉)⋊C₄	—	6	1	no	—
82	Dic₉⋊C₄	—	3	1	no	—
83	Dic₉⋊C₄	—	6	1	no	—
84	C₄×Dic₉	—	3	1	no	—
85	C₄×Dic₉	—	6	1	no	—
86	C₂×C₉⋊C₈	C₂×D₃	1	1	yes	characteristic
87	C₂×C₉⋊C₈	C₂×D₃	1	1	yes	characteristic
88	C₈×D₉	—	6	2	no	—
89	C₂²×C₃×C₉	—	2	1	no	—
90	C₂²×C₃×C₉	—	2	1	no	—
91	C₂²×C₃×C₉	C₂×C₈	1	2	yes	complemented
92	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃⋊D₉	—	2	1	no	—
94	C₂×C₃⋊D₉	—	2	1	no	—
95	C₂×C₃⋊D₉	C₂×C₈	1	2	yes	complemented
96	C₃×C₄×C₉	—	2	1	no	—
97	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
98	C₃×C₄×C₉	#41	1	1	yes	characteristic
99	C₃⋊Dic₉	—	2	1	no	—
100	C₃⋊Dic₉	—	2	1	no	—
101	C₃⋊Dic₉	C₂×C₈	1	2	yes	complemented
102	C₂²×C₃×C₈	—	3	1	no	—
103	C₄×#67	—	9	1	no	—
104	C₄×#67	—	9	1	no	—
105	C₄×#67	—	18	1	no	—
106	C₂²×C₃⋊C₈	D₉	1	1	yes	characteristic, complemented
107	C₂×D₃×C₈	—	9	1	no	—
108	C₂×D₃×C₈	—	9	1	no	—
109	C₃×C₂²⋊C₈	—	9	1	no	—
110	#830	—	3	1	no	—
111	(C₂×D₃)⋊C₈	—	9	1	no	—
112	(C₂×D₃)⋊C₈	—	9	1	no	—
113	Dic₃⋊C₈	—	9	1	no	—
114	Dic₃⋊C₈	—	9	1	no	—
115	C₈×Dic₃	—	9	1	no	—
116	C₈×Dic₃	—	9	1	no	—
117	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
118	C₂²×C₃⋊D₃	—	3	1	no	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	—	2	1	no	—
121	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
123	#638	—	3	4	no	—
124	C₂×C₃⋊Dic₃	—	3	1	no	—
125	C₂×C₃⋊Dic₃	—	3	1	no	—
126	C₂×C₃⋊Dic₃	—	3	1	no	—
127	C₄×C₃⋊D₃	—	6	1	no	—
128	C₄×C₃⋊D₃	—	6	1	no	—
129	C₂³×C₉	—	2	1	no	—
130	C₂³×C₉	C₄×D₃	1	1	yes	characteristic
131	C₂²×D₉	—	3	1	no	—
132	C₂²×D₉	—	6	1	no	—
133	C₃×C₃⋊C₈	—	2	1	no	—
134	C₃×C₃⋊C₈	—	6	1	no	—
135	C₃×C₃⋊C₈	—	6	1	no	—
136	C₃×C₃⋊C₈	#67	1	2	yes	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	4	1	no	—
142	C₂×C₄×C₉	—	4	1	no	—
143	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
144	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
145	#611	—	3	4	no	—
146	#611	—	6	4	no	—
147	C₂×Dic₉	—	3	1	no	—
148	C₂×Dic₉	—	3	1	no	—
149	C₂×Dic₉	—	3	1	no	—
150	C₂×Dic₉	—	6	1	no	—
151	C₂×Dic₉	—	6	1	no	—
152	C₂×Dic₉	—	6	1	no	—
153	C₄×D₉	—	6	1	no	—
154	C₄×D₉	—	6	1	no	—
155	C₄×D₉	—	12	1	no	—
156	C₄×D₉	—	12	1	no	—
157	C₈×C₉	—	3	2	no	—
158	C₈×C₉	—	6	1	no	—
159	C₉⋊C₈	—	2	1	no	—
160	C₉⋊C₈	—	2	1	no	—
161	C₈×D₄	—	27	1	no	Sylow
162	C₂×C₃×C₉	—	2	2	no	—
163	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₃×C₉	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₃×C₉	#131	1	1	yes	characteristic
166	C₃⋊D₉	—	2	2	no	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
169	C₂²×C₃×C₄	D₃²	1	1	yes	characteristic
170	C₂×#67	—	9	1	no	—
171	C₂×#67	—	9	1	no	—
172	C₂×#67	—	18	1	no	—
173	C₂×C₄×D₃	—	9	1	no	—
174	C₂×C₄×D₃	—	9	1	no	—
175	C₂×C₄×D₃	—	18	1	no	—
176	C₂×C₃×C₈	—	3	1	no	—
177	C₂×C₃×C₈	—	3	1	no	—
178	C₂×C₃×C₈	—	6	2	no	—
179	C₂×C₃×C₈	—	9	1	no	—
180	C₂×C₃×C₈	—	9	1	no	—
181	#217	—	9	1	no	—
182	#217	—	9	1	no	—
183	#217	—	18	1	no	—
184	(C₂×D₃)⋊C₄	—	9	1	no	—
185	(C₂×D₃)⋊C₄	—	9	1	no	—
186	(C₂×D₃)⋊C₄	—	18	1	no	—
187	Dic₃⋊C₄	—	9	1	no	—
188	Dic₃⋊C₄	—	9	1	no	—
189	Dic₃⋊C₄	—	18	1	no	—
190	C₄×Dic₃	—	9	1	no	—
191	C₄×Dic₃	—	9	1	no	—
192	C₄×Dic₃	—	18	1	no	—
193	C₂×C₃⋊C₈	—	2	2	no	—
194	C₂×C₃⋊C₈	—	3	1	no	—
195	C₂×C₃⋊C₈	—	3	1	no	—
196	C₂×C₃⋊C₈	C₂×D₉	1	1	yes	characteristic
197	C₂×C₃⋊C₈	C₂×D₉	1	1	yes	characteristic
198	D₃×C₈	—	18	2	no	—
199	D₃×C₈	—	18	2	no	—
200	C₂²×C₃²	—	2	1	no	—
201	C₂²×C₃²	—	2	1	no	—
202	C₂²×C₃²	D₃×C₈	1	2	yes	—
203	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
204	C₂×C₃⋊D₃	—	3	2	no	—
205	C₂×C₃⋊D₃	—	6	1	no	—
206	C₂×C₃⋊D₃	—	6	1	no	—
207	C₃²×C₄	—	2	1	no	—
208	C₃²×C₄	#235	1	1	yes	characteristic
209	C₃²×C₄	C₂×#67	1	1	yes	characteristic
210	C₃⋊Dic₃	—	3	2	no	—
211	C₃⋊Dic₃	—	6	1	no	—
212	C₃⋊Dic₃	—	6	1	no	—
213	C₂²×C₉	—	2	1	no	—
214	C₂²×C₉	—	2	1	no	—
215	C₂²×C₉	—	2	2	no	—
216	C₂²×C₉	—	2	1	no	—
217	C₂²×C₉	—	4	1	no	—
218	C₂²×C₉	—	4	1	no	—
219	C₂²×C₉	D₃×C₈	1	2	yes	complemented
220	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
221	C₂×D₉	—	3	2	no	—
222	C₂×D₉	—	6	2	no	—
223	C₂×D₉	—	6	1	no	—
224	C₂×D₉	—	6	1	no	—
225	C₂×D₉	—	12	1	no	—
226	C₂×D₉	—	12	1	no	—
227	C₄×C₉	—	2	1	no	—
228	C₄×C₉	—	2	1	no	—
229	C₄×C₉	—	2	1	no	—
230	C₄×C₉	—	4	1	no	—
231	C₄×C₉	D₃×D₄	1	1	yes	characteristic
232	C₄×C₉	#237	1	1	yes	characteristic
233	Dic₉	—	3	2	no	—
234	Dic₉	—	6	2	no	—
235	Dic₉	—	6	1	no	—
236	Dic₉	—	6	1	no	—
237	Dic₉	—	12	1	no	—
238	Dic₉	—	12	1	no	—
239	C₂²×C₈	—	3	1	no	—
240	C₂²×C₈	—	27	1	no	—
241	C₄×D₄	—	27	1	no	—
242	C₄⋊C₈	—	27	1	no	—
243	C₂²⋊C₈	—	9	1	no	—
244	C₂²⋊C₈	—	27	1	no	—
245	C₄×C₈	—	27	1	no	—
246	C₃×C₉	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₃	—	2	1	no	—
248	C₂³×C₃	C₄×D₉	1	1	yes	characteristic
249	C₂³×C₃	#624	1	1	yes	characteristic
250	C₂²×D₃	—	9	1	no	—
251	C₂²×D₃	—	9	1	no	—
252	C₂²×D₃	—	18	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	4	1	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	C₄×D₉	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
263	C₂×C₃×C₄	#624	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
265	#67	—	9	4	no	—
266	#67	—	9	4	no	—
267	#67	—	18	4	no	—
268	C₂×Dic₃	—	9	1	no	—
269	C₂×Dic₃	—	9	1	no	—
270	C₂×Dic₃	—	9	1	no	—
271	C₂×Dic₃	—	9	1	no	—
272	C₂×Dic₃	—	9	1	no	—
273	C₂×Dic₃	—	9	1	no	—
274	C₂×Dic₃	—	18	1	no	—
275	C₂×Dic₃	—	18	1	no	—
276	C₂×Dic₃	—	18	1	no	—
277	C₄×D₃	—	18	1	no	—
278	C₄×D₃	—	18	1	no	—
279	C₄×D₃	—	18	1	no	—
280	C₄×D₃	—	18	1	no	—
281	C₄×D₃	—	36	1	no	—
282	C₄×D₃	—	36	1	no	—
283	C₃×C₈	—	3	2	no	—
284	C₃×C₈	—	6	1	no	—
285	C₃×C₈	—	18	1	no	—
286	C₃×C₈	—	18	1	no	—
287	C₃⋊C₈	—	2	1	no	—
288	C₃⋊C₈	—	6	1	no	—
289	C₃⋊C₈	—	6	1	no	—
290	C₃⋊C₈	#611	1	2	yes	complemented
291	C₂×C₃²	—	2	2	no	—
292	C₂×C₃²	C₂×D₃×C₈	1	1	yes	characteristic
293	C₂×C₃²	#901	1	1	yes	characteristic
294	C₂×C₃²	C₄×#67	1	1	yes	characteristic
295	C₃⋊D₃	—	6	2	no	—
296	C₂×C₉	—	2	2	no	—
297	C₂×C₉	—	2	1	no	—
298	C₂×C₉	—	2	1	no	—
299	C₂×C₉	—	2	1	no	—
300	C₂×C₉	—	4	2	no	—
301	C₂×C₉	#67⋊C₄	1	1	yes	characteristic
302	C₂×C₉	C₂×D₃×C₈	1	1	yes	characteristic
303	C₂×C₉	#907	1	1	yes	characteristic
304	D₉	—	6	2	no	—
305	D₉	—	12	2	no	—
306	C₂×D₄	—	27	1	no	—
307	C₂²×C₄	—	27	1	no	—
308	C₂²×C₄	D₃×D₉	1	1	yes	characteristic
309	C₂×C₈	—	3	1	no	—
310	C₂×C₈	—	3	1	no	—
311	C₂×C₈	—	6	2	no	—
312	C₂×C₈	—	9	1	no	—
313	C₂×C₈	—	9	1	no	—
314	C₂×C₈	—	54	2	no	—
315	C₄⋊C₄	—	27	1	no	—
316	C₂²⋊C₄	—	27	1	no	—
317	C₂²⋊C₄	—	27	1	no	—
318	C₄²	—	27	1	no	—
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	2	2	no	—
325	C₂²×C₃	—	4	1	no	—
326	C₂²×C₃	—	4	1	no	—
327	C₂²×C₃	C₈×D₉	1	2	yes	complemented
328	C₂²×C₃	C₂×C₄×D₉	1	1	yes	characteristic
329	C₂²×C₃	#3710	1	2	yes	—
330	C₂²×C₃	C₂×#624	1	1	yes	characteristic
331	C₂×D₃	—	9	2	no	—
332	C₂×D₃	—	9	2	no	—
333	C₂×D₃	—	18	2	no	—
334	C₂×D₃	—	18	1	no	—
335	C₂×D₃	—	18	1	no	—
336	C₂×D₃	—	18	1	no	—
337	C₂×D₃	—	18	1	no	—
338	C₂×D₃	—	36	1	no	—
339	C₂×D₃	—	36	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	1	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	4	1	no	—
345	C₃×C₄	#3697	1	1	yes	characteristic
346	C₃×C₄	C₂×#611	1	1	yes	characteristic
347	C₃×C₄	#3804	1	1	yes	characteristic
348	C₃×C₄	D₃×#67	1	1	yes	characteristic
349	Dic₃	—	9	2	no	—
350	Dic₃	—	9	2	no	—
351	Dic₃	—	18	2	no	—
352	Dic₃	—	18	1	no	—
353	Dic₃	—	18	1	no	—
354	Dic₃	—	18	1	no	—
355	Dic₃	—	18	1	no	—
356	Dic₃	—	36	1	no	—
357	Dic₃	—	36	1	no	—
358	C₃²	C₈×#67	1	1	yes	characteristic
359	C₉	—	2	1	no	—
360	C₉	#67⋊C₈	1	1	yes	characteristic, complemented
361	C₂³	—	27	1	no	—
362	C₂³	(C₃⋊D₉)⋊C₄	1	1	yes	characteristic
363	D₄	—	27	4	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	27	1	no	—
367	C₂×C₄	—	27	1	no	—
368	C₂×C₄	—	27	1	no	—
369	C₂×C₄	—	54	1	no	—
370	C₂×C₄	—	54	1	no	—
371	C₂×C₄	(C₃⋊D₉)⋊C₄	1	1	yes	characteristic
372	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
373	C₈	—	3	2	no	—
374	C₈	—	6	1	no	—
375	C₈	—	18	1	no	—
376	C₈	—	18	1	no	—
377	C₂×C₃	—	2	2	no	—
378	C₂×C₃	—	2	2	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	—	4	2	no	—
383	C₂×C₃	C₂×C₈×D₉	1	1	yes	characteristic
384	C₂×C₃	#63464	1	1	yes	characteristic
385	C₂×C₃	C₄×#611	1	1	yes	characteristic
386	C₂×C₃	C₂×#3710	1	1	yes	characteristic
387	C₂×C₃	#63817	1	1	yes	characteristic
388	C₂×C₃	#63952	1	1	yes	characteristic
389	D₃	—	18	2	no	—
390	D₃	—	18	2	no	—
391	D₃	—	36	2	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	27	2	no	—
395	C₂²	—	54	1	no	—
396	C₂²	—	54	1	no	—
397	C₂²	(C₃⋊D₉)⋊C₈	1	2	yes	complemented
398	C₂²	C₂×(C₃⋊D₉)⋊C₄	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	27	2	no	—
401	C₄	—	54	1	no	—
402	C₄	—	54	1	no	—
403	C₄	#88658	1	1	yes	characteristic
404	C₄	D₃×#611	1	1	yes	characteristic
405	C₃	—	2	1	no	—
406	C₃	C₈×#611	1	1	yes	characteristic, complemented
407	C₃	#10591148	1	1	yes	characteristic
408	C₂	—	2	2	no	—
409	C₂	—	54	2	no	—
410	C₂	C₂×(C₃⋊D₉)⋊C₈	1	1	yes	characteristic
411	C₂	#11720862	1	1	yes	characteristic
412	C₂	#11721240	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₃×D₉
commutator	C₂×C₃×C₉	C₂²×C₈
Frattini	C₂×C₃×C₄	C₂×D₃²
Fitting	C₂²×C₃×C₄×C₉	C₂²
socle	C₂²×C₃²	C₂×C₄×D₃
prime radical	C₂×#6233	C₄
cosocle	C₂×C₃×C₄×C₉	C₂³
hypercenter	C₂²×C₄	D₃×D₉
hypocenter	C₃×C₉	C₈×D₄
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₉×C₃⋊C₈	C₂	semidirect
3. C₂×(C₃⋊D₉)⋊C₈	C₂	semidirect
4. C₃×#63389	C₂	semidirect
5. #11720282	C₂	semidirect
6. #11720273	C₂	semidirect
7. #11720271	C₂	semidirect
34. #63389	D₃	semidirect
44. #6233	C₈	semidirect
51. C₉×C₃⋊C₈	D₄	semidirect
91. C₂²×C₃×C₉	C₂×C₈	semidirect
95. C₂×C₃⋊D₉	C₂×C₈	semidirect
101. C₃⋊Dic₉	C₂×C₈	semidirect
106. C₂²×C₃⋊C₈	D₉	semidirect
219. C₂²×C₉	D₃×C₈	semidirect
246. C₃×C₉	C₈×D₄	semidirect
290. C₃⋊C₈	#611	semidirect
327. C₂²×C₃	C₈×D₉	semidirect
360. C₉	#67⋊C₈	semidirect
397. C₂²	(C₃⋊D₉)⋊C₈	semidirect
406. C₃	C₈×#611	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6233	2
C₂²×C₉×C₃⋊C₈	2
C₂×(C₃⋊D₉)⋊C₈	2
C₃×#63389	2
#11720282	2
#11720273	2
#11720271	2
#10591148	3
C₈×#611	3