Subgroups — C₉×#5568 #13152674

Order 1728.

706 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#947	C₂	1	1	yes	maximal, characteristic
3	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#898	C₂	1	2	yes	maximal, complemented
5	C₉×#896	C₂	1	2	yes	maximal, complemented
6	C₉×#893	C₂	1	1	yes	maximal, characteristic
7	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#876	C₂	1	2	yes	maximal, complemented
9	C₉×#875	C₂	1	1	yes	maximal, characteristic
10	C₉×#872	C₂	1	2	yes	maximal, complemented
11	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5568	C₃	1	1	yes	maximal, characteristic
13	C₉×#556	—	3	1	no	maximal
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
17	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₃×C₄²×C₉	C₂²	1	2	yes	—
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
30	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
35	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
38	C₃×#947	C₂×C₃	1	1	yes	characteristic
39	C₃×#944	C₂×C₃	1	1	yes	characteristic
40	C₃×#898	C₂×C₃	1	2	yes	—
41	C₃×#896	C₂×C₃	1	2	yes	—
42	C₃×#893	C₂×C₃	1	1	yes	characteristic
43	C₃×#887	C₂×C₃	1	1	yes	characteristic
44	C₃×#876	C₂×C₃	1	2	yes	—
45	C₃×#875	C₂×C₃	1	1	yes	characteristic
46	C₃×#872	C₂×C₃	1	2	yes	—
47	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
48	C₉×C₄⋊Q₈	—	3	1	no	—
49	C₉×#126	—	3	2	no	—
50	C₉×#126	—	3	2	no	—
51	C₉×#124	—	3	1	no	—
52	C₉×#124	—	3	1	no	—
53	C₉×C₂²⋊Q₈	—	3	2	no	—
54	C₄×Q₈×C₉	—	2	1	no	—
55	C₄×Q₈×C₉	—	3	1	no	—
56	C₄×Q₈×C₉	—	3	1	no	—
57	C₄×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
58	C₄×D₄×C₉	—	3	1	no	—
59	C₉×#117	—	3	2	no	—
60	C₂²×D₃×C₉	C₂³	1	2	yes	—
61	C₃×Q₈×C₉	—	2	2	no	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
68	C₂×C₉×Dic₃	C₂³	1	2	yes	—
69	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
72	C₉×D₁₂	—	2	2	no	—
73	C₄×D₃×C₉	—	2	4	no	—
74	C₉×Dic₆	—	2	2	no	—
75	C₉×Dic₆	—	2	2	no	—
76	C₃×#556	—	3	1	no	—
77	#5568	C₉	1	1	yes	characteristic, direct product factor
78	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
81	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
83	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₄²	C₂²×C₃	1	2	yes	—
87	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
89	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
92	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
93	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
94	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
99	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
100	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₂×Q₈×C₉	—	2	1	no	—
102	C₂×Q₈×C₉	—	3	1	no	—
103	C₂×Q₈×C₉	—	3	1	no	—
104	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
105	C₂×D₄×C₉	—	3	1	no	—
106	C₂²×C₄×C₉	—	3	2	no	—
107	C₉×C₄⋊C₄	—	2	1	no	—
108	C₉×C₄⋊C₄	—	2	2	no	—
109	C₉×C₄⋊C₄	—	3	1	no	—
110	C₉×C₄⋊C₄	—	3	2	no	—
111	C₉×C₄⋊C₄	—	3	2	no	—
112	C₉×C₄⋊C₄	—	3	1	no	—
113	C₉×C₄⋊C₄	—	3	1	no	—
114	C₉×C₄⋊C₄	—	3	2	no	—
115	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
116	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
117	C₉×C₂²⋊C₄	—	3	2	no	—
118	C₉×C₂²⋊C₄	—	3	2	no	—
119	C₉×C₂²⋊C₄	—	3	2	no	—
120	C₉×C₂²⋊C₄	—	3	2	no	—
121	C₉×C₂²⋊C₄	—	3	2	no	—
122	C₄²×C₉	—	2	2	no	—
123	C₄²×C₉	—	2	1	no	—
124	C₄²×C₉	—	3	2	no	—
125	C₄²×C₉	—	3	1	no	—
126	C₄²×C₉	—	3	1	no	—
127	C₄²×C₉	C₂×D₃	1	2	yes	—
128	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
129	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
130	C₂×D₃×C₉	—	2	2	no	—
131	C₂×D₃×C₉	—	2	2	no	—
132	C₂×D₃×C₉	—	2	2	no	—
133	C₃×C₄×C₉	—	2	2	no	—
134	C₃×C₄×C₉	—	2	1	no	—
135	C₃×C₄×C₉	—	2	2	no	—
136	C₃×C₄×C₉	—	2	1	no	—
137	C₃×C₄×C₉	#41	1	2	yes	—
138	C₉×Dic₃	—	2	2	no	—
139	C₉×Dic₃	—	2	1	no	—
140	C₉×Dic₃	—	2	1	no	—
141	C₉×Dic₃	—	2	1	no	—
142	C₉×Dic₃	#41	1	2	yes	—
143	C₃×C₄⋊Q₈	—	3	1	no	—
144	C₃×#126	—	3	2	no	—
145	C₃×#126	—	3	2	no	—
146	C₃×#124	—	3	1	no	—
147	C₃×#124	—	3	1	no	—
148	C₃×C₂²⋊Q₈	—	3	2	no	—
149	C₃×C₄×Q₈	—	2	1	no	—
150	C₃×C₄×Q₈	—	3	1	no	—
151	C₃×C₄×Q₈	—	3	1	no	—
152	C₃×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
153	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
154	C₃×C₄×D₄	—	3	1	no	—
155	C₃×#117	—	3	2	no	—
156	#947	C₂×C₉	1	1	yes	characteristic
157	#944	C₂×C₉	1	1	yes	characteristic, complemented
158	#898	C₂×C₉	1	2	yes	complemented
159	#896	C₂×C₉	1	2	yes	complemented
160	#893	C₂×C₉	1	1	yes	characteristic
161	#887	C₂×C₉	1	1	yes	characteristic, complemented
162	#876	C₂×C₉	1	2	yes	complemented
163	#875	C₂×C₉	1	1	yes	characteristic
164	#872	C₂×C₉	1	2	yes	complemented
165	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
166	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
167	C₃²×Q₈	—	2	2	no	—
168	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
169	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
171	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
176	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
178	C₃×D₁₂	—	2	2	no	—
179	C₃×C₄×D₃	—	2	4	no	—
180	C₃×Dic₆	—	2	2	no	—
181	C₃×Dic₆	—	2	2	no	—
182	C₂³×C₉	—	3	2	no	—
183	Q₈×C₉	—	2	4	no	—
184	Q₈×C₉	—	2	2	no	—
185	Q₈×C₉	—	6	2	no	—
186	Q₈×C₉	—	6	2	no	—
187	D₄×C₉	—	6	2	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	2	2	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	2	2	no	—
192	C₂×C₄×C₉	—	2	1	no	—
193	C₂×C₄×C₉	—	3	1	no	—
194	C₂×C₄×C₉	—	3	1	no	—
195	C₂×C₄×C₉	—	3	1	no	—
196	C₂×C₄×C₉	—	3	2	no	—
197	C₂×C₄×C₉	—	3	1	no	—
198	C₂×C₄×C₉	—	6	4	no	—
199	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
200	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
202	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
203	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
204	#556	—	3	1	no	Sylow
205	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
208	D₃×C₉	—	4	2	no	—
209	C₂×C₃×Q₈	—	2	1	no	—
210	C₂×C₃×Q₈	—	3	1	no	—
211	C₂×C₃×Q₈	—	3	1	no	—
212	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
213	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
214	C₂×C₃×D₄	—	3	1	no	—
215	C₂²×C₃×C₄	—	3	2	no	—
216	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
217	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
218	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
219	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
220	C₃×C₄⋊C₄	—	2	1	no	—
221	C₃×C₄⋊C₄	—	2	2	no	—
222	C₃×C₄⋊C₄	—	3	1	no	—
223	C₃×C₄⋊C₄	—	3	2	no	—
224	C₃×C₄⋊C₄	—	3	2	no	—
225	C₃×C₄⋊C₄	—	3	1	no	—
226	C₃×C₄⋊C₄	—	3	2	no	—
227	C₃×C₄⋊C₄	—	3	1	no	—
228	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
229	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
230	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
231	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
232	C₃×C₂²⋊C₄	—	3	2	no	—
233	C₃×C₂²⋊C₄	—	3	2	no	—
234	C₃×C₂²⋊C₄	—	3	2	no	—
235	C₃×C₂²⋊C₄	—	3	2	no	—
236	C₃×C₂²⋊C₄	—	3	2	no	—
237	C₃×C₄²	—	2	2	no	—
238	C₃×C₄²	—	2	1	no	—
239	C₃×C₄²	—	3	2	no	—
240	C₃×C₄²	—	3	1	no	—
241	C₃×C₄²	—	3	1	no	—
242	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
243	C₃×C₄²	C₂²×C₉	1	2	yes	—
244	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
245	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
246	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
247	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
248	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
249	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
250	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
251	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
252	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
253	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
254	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
255	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
256	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
257	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
258	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
259	C₄×Dic₃	C₂²×C₉	1	2	yes	—
260	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
261	C₂×C₃×D₃	—	2	2	no	—
262	C₂×C₃×D₃	—	2	2	no	—
263	C₂×C₃×D₃	—	2	2	no	—
264	C₃²×C₄	—	2	2	no	—
265	C₃²×C₄	—	2	1	no	—
266	C₃²×C₄	—	2	1	no	—
267	C₃²×C₄	—	2	2	no	—
268	C₃²×C₄	C₃×#41	1	2	yes	—
269	C₃×Dic₃	—	2	2	no	—
270	C₃×Dic₃	—	2	1	no	—
271	C₃×Dic₃	—	2	1	no	—
272	C₃×Dic₃	—	2	1	no	—
273	C₃×Dic₃	C₃×#41	1	2	yes	—
274	C₂²×C₉	—	2	1	no	—
275	C₂²×C₉	—	6	2	no	—
276	C₂²×C₉	—	6	2	no	—
277	C₂²×C₉	—	6	2	no	—
278	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	4	no	—
281	C₄×C₉	—	2	2	no	—
282	C₄×C₉	—	2	1	no	—
283	C₄×C₉	—	2	2	no	—
284	C₄×C₉	—	2	1	no	—
285	C₄×C₉	—	2	2	no	—
286	C₄×C₉	—	3	2	no	—
287	C₄×C₉	—	4	2	no	—
288	C₄×C₉	—	4	1	no	—
289	C₄×C₉	—	6	2	no	—
290	C₄×C₉	—	6	1	no	—
291	C₄×C₉	—	6	1	no	—
292	C₄×C₉	—	6	1	no	—
293	C₄×C₉	#235	1	2	yes	—
294	C₄⋊Q₈	—	3	1	no	—
295	#126	—	3	2	no	—
296	#126	—	3	2	no	—
297	#124	—	3	1	no	—
298	#124	—	3	1	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₄×Q₈	—	3	1	no	—
301	C₄×Q₈	—	3	1	no	—
302	C₄×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
303	C₄×D₄	—	3	1	no	—
304	#117	—	3	2	no	—
305	C₃×C₉	#556	1	1	yes	characteristic, complemented, Sylow
306	C₂³×C₃	—	3	2	no	—
307	C₂²×D₃	C₂³×C₉	1	2	yes	—
308	C₃×Q₈	—	2	4	no	—
309	C₃×Q₈	—	2	2	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	6	2	no	—
312	C₃×Q₈	—	6	2	no	—
313	C₃×D₄	—	6	2	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	3	1	no	—
320	C₂×C₃×C₄	—	3	1	no	—
321	C₂×C₃×C₄	—	3	1	no	—
322	C₂×C₃×C₄	—	3	2	no	—
323	C₂×C₃×C₄	—	3	1	no	—
324	C₂×C₃×C₄	—	6	4	no	—
325	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
326	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
328	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
331	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
333	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
335	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
336	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
337	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
338	C₂×Dic₃	C₂³×C₉	1	2	yes	—
339	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
340	D₁₂	—	2	2	no	—
341	C₄×D₃	—	2	4	no	—
342	Dic₆	—	2	2	no	—
343	Dic₆	—	2	2	no	—
344	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
345	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
346	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
347	C₃×D₃	—	4	2	no	—
348	C₂×C₉	—	2	1	no	—
349	C₂×C₉	—	2	1	no	—
350	C₂×C₉	—	2	1	no	—
351	C₂×C₉	—	12	2	no	—
352	C₂×C₉	C₂×#235	1	1	yes	characteristic
353	C₂×C₉	#1007	1	1	yes	characteristic
354	C₂×C₉	D₃×#41	1	1	yes	characteristic
355	C₂×Q₈	—	3	1	no	—
356	C₂×Q₈	—	3	1	no	—
357	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
358	C₂×D₄	—	3	1	no	—
359	C₂²×C₄	—	3	2	no	—
360	C₄⋊C₄	—	3	1	no	—
361	C₄⋊C₄	—	3	2	no	—
362	C₄⋊C₄	—	3	2	no	—
363	C₄⋊C₄	—	3	1	no	—
364	C₄⋊C₄	—	3	1	no	—
365	C₄⋊C₄	—	3	2	no	—
366	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
367	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
368	C₂²⋊C₄	—	3	2	no	—
369	C₂²⋊C₄	—	3	2	no	—
370	C₂²⋊C₄	—	3	2	no	—
371	C₂²⋊C₄	—	3	2	no	—
372	C₂²⋊C₄	—	3	2	no	—
373	C₄²	—	3	2	no	—
374	C₄²	—	3	1	no	—
375	C₄²	—	3	1	no	—
376	C₄²	C₂×D₃×C₉	1	2	yes	—
377	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	6	2	no	—
380	C₂²×C₃	—	6	2	no	—
381	C₂²×C₃	—	6	2	no	—
382	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
383	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
384	C₂×D₃	—	2	2	no	—
385	C₂×D₃	—	2	2	no	—
386	C₂×D₃	—	2	2	no	—
387	C₃×C₄	—	2	4	no	—
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	3	2	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	—	4	1	no	—
401	C₃×C₄	—	6	2	no	—
402	C₃×C₄	—	6	1	no	—
403	C₃×C₄	—	6	1	no	—
404	C₃×C₄	—	6	1	no	—
405	C₃×C₄	C₉×#41	1	2	yes	—
406	C₃×C₄	C₃×#235	1	2	yes	—
407	Dic₃	—	2	2	no	—
408	Dic₃	—	2	1	no	—
409	Dic₃	—	2	1	no	—
410	Dic₃	—	2	1	no	—
411	Dic₃	C₉×#41	1	2	yes	—
412	C₃²	C₃×#556	1	1	yes	characteristic
413	C₉	—	2	1	no	—
414	C₉	#5568	1	1	yes	characteristic, direct product factor
415	C₂³	—	3	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	6	2	no	—
418	Q₈	—	6	2	no	—
419	D₄	—	6	2	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	2	no	—
424	C₂×C₄	—	3	1	no	—
425	C₂×C₄	—	6	4	no	—
426	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
427	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
429	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	2	1	no	—
433	C₂×C₃	—	2	1	no	—
434	C₂×C₃	—	12	2	no	—
435	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
436	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
437	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
438	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
439	C₂×C₃	C₃×#1007	1	1	yes	characteristic
440	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
441	D₃	—	4	2	no	—
442	C₂²	—	6	2	no	—
443	C₂²	—	6	2	no	—
444	C₂²	—	6	2	no	—
445	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	3	2	no	—
451	C₄	—	6	2	no	—
452	C₄	—	6	1	no	—
453	C₄	—	6	1	no	—
454	C₄	—	6	1	no	—
455	C₄	C₉×#235	1	2	yes	—
456	C₃	—	2	1	no	—
457	C₃	C₉×#556	1	1	yes	characteristic, complemented
458	C₃	C₃×#5568	1	1	yes	characteristic
459	C₂	—	12	2	no	—
460	C₂	C₂×C₉×#235	1	1	yes	characteristic
461	C₂	C₉×#1007	1	1	yes	characteristic
462	C₂	D₃×C₉×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₄×Q₈×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₄×Q₈×C₉	D₃
hypocenter	C₃	C₉×#556
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₄×Q₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×Q₈×C₉	C₂	semidirect
3. C₉×#944	C₂	semidirect
4. C₉×#898	C₂	semidirect
5. C₉×#896	C₂	semidirect
7. C₉×#887	C₂	semidirect
8. C₉×#876	C₂	semidirect
10. C₉×#872	C₂	semidirect
11. C₄×C₉×Dic₆	C₂	semidirect
57. C₄×Q₈×C₉	D₃	semidirect
77. #5568	C₉	direct (N × H)
152. C₃×C₄×Q₈	C₂×C₉	semidirect
157. #944	C₂×C₉	semidirect
158. #898	C₂×C₉	semidirect
159. #896	C₂×C₉	semidirect
161. #887	C₂×C₉	semidirect
162. #876	C₂×C₉	semidirect
164. #872	C₂×C₉	semidirect
165. C₄×Dic₆	C₂×C₉	semidirect
302. C₄×Q₈	D₃×C₉	semidirect
305. C₃×C₉	#556	semidirect
414. C₉	#5568	direct (N × H)
457. C₃	C₉×#556	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×Q₈×C₉	2
C₉×#947	2
C₉×#944	2
C₉×#898	2
C₉×#896	2
C₉×#893	2
C₉×#887	2
C₉×#876	2
C₉×#875	2
C₉×#872	2
C₄×C₉×Dic₆	2
C₃×#5568	3
C₉×#556	3

Subgroups — C9×#5568 #13152674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5568 #13152674