Subgroups — C₉×#5645 #13152940

Order 1728.

728 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#946	C₂	1	2	yes	maximal, complemented
3	C₉×#930	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#898	C₂	1	2	yes	maximal, complemented
6	C₉×#894	C₂	1	2	yes	maximal, complemented
7	C₉×#890	C₂	1	2	yes	maximal, complemented
8	C₉×#886	C₂	1	2	yes	maximal, complemented
9	C₉×#67⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃×#5645	C₃	1	1	yes	maximal, characteristic
11	C₉×#539	—	3	1	no	maximal
12	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×#67	C₂²	1	2	yes	—
15	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
19	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₉×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
28	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
29	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₄×C₉×Dic₃	C₂²	1	2	yes	—
33	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
34	C₃×#946	C₂×C₃	1	2	yes	—
35	C₃×#930	C₂×C₃	1	1	yes	characteristic
36	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
37	C₃×#898	C₂×C₃	1	2	yes	—
38	C₃×#894	C₂×C₃	1	2	yes	—
39	C₃×#890	C₂×C₃	1	2	yes	—
40	C₃×#886	C₂×C₃	1	2	yes	—
41	C₃×#67⋊C₄	C₂×C₃	1	2	yes	—
42	C₉×#126	—	3	2	no	—
43	C₉×#125	—	3	2	no	—
44	C₉×#123	—	3	2	no	—
45	C₉×#123	—	3	2	no	—
46	C₉×C₂²⋊Q₈	—	2	1	no	—
47	C₉×C₂²⋊Q₈	—	3	2	no	—
48	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
49	C₉×#121	—	3	1	no	—
50	C₄×D₄×C₉	—	3	2	no	—
51	C₂×C₉×C₄⋊C₄	—	3	1	no	—
52	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
53	C₂²×D₃×C₉	C₂³	1	2	yes	—
54	C₃×Q₈×C₉	—	4	1	no	—
55	C₂×C₃×C₄×C₉	—	4	1	no	—
56	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
57	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₉×#67	—	2	4	no	—
61	C₂×C₉×Dic₃	—	2	2	no	—
62	C₂×C₉×Dic₃	—	4	1	no	—
63	C₂×C₉×Dic₃	C₂³	1	2	yes	—
64	C₂×C₉×Dic₃	C₂³	1	2	yes	—
65	C₂×C₉×Dic₃	C₂³	1	2	yes	—
66	C₉×D₁₂	—	4	1	no	—
67	C₄×D₃×C₉	—	4	2	no	—
68	C₃×#539	—	3	1	no	—
69	#5645	C₉	1	1	yes	characteristic, direct product factor
70	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
73	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
77	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
78	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
80	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
81	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
82	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
83	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
85	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
86	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
87	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
89	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
91	C₂×Q₈×C₉	—	2	1	no	—
92	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
93	C₂×D₄×C₉	—	3	2	no	—
94	C₂×D₄×C₉	—	3	1	no	—
95	C₂²×C₄×C₉	—	2	1	no	—
96	C₂²×C₄×C₉	—	3	1	no	—
97	C₂²×C₄×C₉	—	3	1	no	—
98	C₂²×C₄×C₉	—	3	2	no	—
99	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
100	C₉×C₄⋊C₄	—	2	1	no	—
101	C₉×C₄⋊C₄	—	2	2	no	—
102	C₉×C₄⋊C₄	—	3	2	no	—
103	C₉×C₄⋊C₄	—	3	2	no	—
104	C₉×C₄⋊C₄	—	3	2	no	—
105	C₉×C₄⋊C₄	—	3	1	no	—
106	C₉×C₄⋊C₄	—	3	2	no	—
107	C₉×C₄⋊C₄	—	3	2	no	—
108	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
109	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
110	C₉×C₂²⋊C₄	—	2	2	no	—
111	C₉×C₂²⋊C₄	—	3	2	no	—
112	C₉×C₂²⋊C₄	—	3	2	no	—
113	C₉×C₂²⋊C₄	—	3	2	no	—
114	C₉×C₂²⋊C₄	—	3	2	no	—
115	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
116	C₄²×C₉	—	3	2	no	—
117	C₂²×C₃×C₉	—	2	1	no	—
118	C₂²×C₃×C₉	—	2	1	no	—
119	C₂²×C₃×C₉	#41	1	2	yes	—
120	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
121	C₂×D₃×C₉	—	2	2	no	—
122	C₂×D₃×C₉	—	2	2	no	—
123	C₂×D₃×C₉	—	2	2	no	—
124	C₃×C₄×C₉	—	2	1	no	—
125	C₃×C₄×C₉	—	2	2	no	—
126	C₃×C₄×C₉	—	2	1	no	—
127	C₃×C₄×C₉	—	2	2	no	—
128	C₉×Dic₃	—	2	2	no	—
129	C₉×Dic₃	—	2	2	no	—
130	C₉×Dic₃	—	2	2	no	—
131	C₃×#126	—	3	2	no	—
132	C₃×#125	—	3	2	no	—
133	C₃×#123	—	3	2	no	—
134	C₃×#123	—	3	2	no	—
135	C₃×C₂²⋊Q₈	—	2	1	no	—
136	C₃×C₂²⋊Q₈	—	3	2	no	—
137	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
138	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
139	C₃×#121	—	3	1	no	—
140	C₃×C₄×D₄	—	3	2	no	—
141	C₂×C₃×C₄⋊C₄	—	3	1	no	—
142	#946	C₂×C₉	1	2	yes	complemented
143	#930	C₂×C₉	1	1	yes	characteristic
144	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
145	#898	C₂×C₉	1	2	yes	complemented
146	#894	C₂×C₉	1	2	yes	complemented
147	#890	C₂×C₉	1	2	yes	complemented
148	#886	C₂×C₉	1	2	yes	complemented
149	#67⋊C₄	C₂×C₉	1	2	yes	complemented
150	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
151	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
152	C₃²×Q₈	—	4	1	no	—
153	C₂×C₃²×C₄	—	4	1	no	—
154	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
155	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
158	C₃×#67	—	2	4	no	—
159	C₂×C₃×Dic₃	—	2	2	no	—
160	C₂×C₃×Dic₃	—	4	1	no	—
161	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
162	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
163	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
164	C₃×D₁₂	—	4	1	no	—
165	C₃×C₄×D₃	—	4	2	no	—
166	C₂³×C₉	—	2	1	no	—
167	C₂³×C₉	—	3	2	no	—
168	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
169	Q₈×C₉	—	4	1	no	—
170	Q₈×C₉	—	4	2	no	—
171	D₄×C₉	—	6	4	no	—
172	D₄×C₉	—	12	1	no	—
173	C₂×C₄×C₉	—	2	1	no	—
174	C₂×C₄×C₉	—	2	2	no	—
175	C₂×C₄×C₉	—	2	2	no	—
176	C₂×C₄×C₉	—	2	1	no	—
177	C₂×C₄×C₉	—	3	2	no	—
178	C₂×C₄×C₉	—	3	2	no	—
179	C₂×C₄×C₉	—	3	2	no	—
180	C₂×C₄×C₉	—	4	1	no	—
181	C₂×C₄×C₉	—	4	2	no	—
182	C₂×C₄×C₉	—	6	2	no	—
183	C₂×C₄×C₉	—	12	2	no	—
184	C₂×C₄×C₉	—	12	1	no	—
185	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
186	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
187	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
188	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
189	#539	—	3	1	no	Sylow
190	C₂×C₃×C₉	—	2	2	no	—
191	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
192	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
193	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
194	D₃×C₉	—	4	2	no	—
195	C₂×C₃×Q₈	—	2	1	no	—
196	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
197	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
198	C₂×C₃×D₄	—	3	2	no	—
199	C₂×C₃×D₄	—	3	1	no	—
200	C₂²×C₃×C₄	—	2	1	no	—
201	C₂²×C₃×C₄	—	3	1	no	—
202	C₂²×C₃×C₄	—	3	1	no	—
203	C₂²×C₃×C₄	—	3	2	no	—
204	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
206	C₂×#67	C₂²×C₉	1	2	yes	—
207	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
208	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
209	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
210	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	2	1	no	—
213	C₃×C₄⋊C₄	—	3	2	no	—
214	C₃×C₄⋊C₄	—	3	2	no	—
215	C₃×C₄⋊C₄	—	3	2	no	—
216	C₃×C₄⋊C₄	—	3	1	no	—
217	C₃×C₄⋊C₄	—	3	2	no	—
218	C₃×C₄⋊C₄	—	3	2	no	—
219	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
220	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
221	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
222	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
223	C₃×C₂²⋊C₄	—	2	2	no	—
224	C₃×C₂²⋊C₄	—	3	2	no	—
225	C₃×C₂²⋊C₄	—	3	2	no	—
226	C₃×C₂²⋊C₄	—	3	2	no	—
227	C₃×C₂²⋊C₄	—	3	2	no	—
228	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
229	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
230	C₃×C₄²	—	3	2	no	—
231	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
232	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
233	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
234	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
235	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
236	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
237	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
238	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
239	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
240	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
241	C₄×Dic₃	C₂²×C₉	1	2	yes	—
242	C₂²×C₃²	—	2	1	no	—
243	C₂²×C₃²	—	2	1	no	—
244	C₂²×C₃²	C₃×#41	1	2	yes	—
245	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
246	C₂×C₃×D₃	—	2	2	no	—
247	C₂×C₃×D₃	—	2	2	no	—
248	C₂×C₃×D₃	—	2	2	no	—
249	C₃²×C₄	—	2	1	no	—
250	C₃²×C₄	—	2	2	no	—
251	C₃²×C₄	—	2	1	no	—
252	C₃²×C₄	—	2	2	no	—
253	C₃×Dic₃	—	2	2	no	—
254	C₃×Dic₃	—	2	2	no	—
255	C₃×Dic₃	—	2	2	no	—
256	C₂²×C₉	—	2	1	no	—
257	C₂²×C₉	—	2	1	no	—
258	C₂²×C₉	—	2	1	no	—
259	C₂²×C₉	—	2	2	no	—
260	C₂²×C₉	—	4	1	no	—
261	C₂²×C₉	—	4	1	no	—
262	C₂²×C₉	—	6	2	no	—
263	C₂²×C₉	—	6	2	no	—
264	C₂²×C₉	—	6	2	no	—
265	C₂²×C₉	#239	1	2	yes	—
266	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
267	C₄×C₉	—	2	2	no	—
268	C₄×C₉	—	2	1	no	—
269	C₄×C₉	—	2	1	no	—
270	C₄×C₉	—	2	2	no	—
271	C₄×C₉	—	2	2	no	—
272	C₄×C₉	—	4	2	no	—
273	C₄×C₉	—	4	1	no	—
274	C₄×C₉	—	4	2	no	—
275	C₄×C₉	—	6	2	no	—
276	C₄×C₉	—	6	2	no	—
277	C₄×C₉	—	6	2	no	—
278	#126	—	3	2	no	—
279	#125	—	3	2	no	—
280	#123	—	3	2	no	—
281	#123	—	3	2	no	—
282	C₂²⋊Q₈	—	3	2	no	—
283	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
284	#121	—	3	1	no	—
285	C₄×D₄	—	3	2	no	—
286	C₂×C₄⋊C₄	—	3	1	no	—
287	C₃×C₉	#539	1	1	yes	characteristic, complemented, Sylow
288	C₂³×C₃	—	2	1	no	—
289	C₂³×C₃	—	3	2	no	—
290	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
291	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
292	C₂²×D₃	C₂³×C₉	1	2	yes	—
293	C₃×Q₈	—	4	1	no	—
294	C₃×Q₈	—	4	1	no	—
295	C₃×Q₈	—	4	2	no	—
296	C₃×D₄	—	6	4	no	—
297	C₃×D₄	—	12	1	no	—
298	C₂×C₃×C₄	—	2	1	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	1	no	—
302	C₂×C₃×C₄	—	3	2	no	—
303	C₂×C₃×C₄	—	3	2	no	—
304	C₂×C₃×C₄	—	3	2	no	—
305	C₂×C₃×C₄	—	4	1	no	—
306	C₂×C₃×C₄	—	4	1	no	—
307	C₂×C₃×C₄	—	4	2	no	—
308	C₂×C₃×C₄	—	6	2	no	—
309	C₂×C₃×C₄	—	12	2	no	—
310	C₂×C₃×C₄	—	12	1	no	—
311	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
312	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
315	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
316	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
318	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
319	#67	—	2	4	no	—
320	C₂×Dic₃	—	2	2	no	—
321	C₂×Dic₃	—	4	1	no	—
322	C₂×Dic₃	C₂³×C₉	1	2	yes	—
323	C₂×Dic₃	C₂³×C₉	1	2	yes	—
324	C₂×Dic₃	C₂³×C₉	1	2	yes	—
325	D₁₂	—	4	1	no	—
326	C₄×D₃	—	4	2	no	—
327	C₂×C₃²	—	2	2	no	—
328	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
329	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
331	C₃×D₃	—	4	2	no	—
332	C₂×C₉	—	2	2	no	—
333	C₂×C₉	—	2	1	no	—
334	C₂×C₉	—	2	1	no	—
335	C₂×C₉	—	2	1	no	—
336	C₂×C₉	—	4	2	no	—
337	C₂×C₉	—	12	2	no	—
338	C₂×C₉	#1004	1	1	yes	characteristic
339	C₂×C₉	C₂×#239	1	1	yes	characteristic
340	C₂×C₉	#1010	1	1	yes	characteristic
341	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
342	C₂×D₄	—	3	2	no	—
343	C₂×D₄	—	3	1	no	—
344	C₂²×C₄	—	3	1	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	3	2	no	—
347	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
348	C₄⋊C₄	—	3	2	no	—
349	C₄⋊C₄	—	3	2	no	—
350	C₄⋊C₄	—	3	2	no	—
351	C₄⋊C₄	—	3	1	no	—
352	C₄⋊C₄	—	3	2	no	—
353	C₄⋊C₄	—	3	2	no	—
354	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
355	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
356	C₂²⋊C₄	—	3	2	no	—
357	C₂²⋊C₄	—	3	2	no	—
358	C₂²⋊C₄	—	3	2	no	—
359	C₂²⋊C₄	—	3	2	no	—
360	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
361	C₄²	—	3	2	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	—	2	1	no	—
367	C₂²×C₃	—	2	2	no	—
368	C₂²×C₃	—	4	1	no	—
369	C₂²×C₃	—	4	1	no	—
370	C₂²×C₃	—	6	2	no	—
371	C₂²×C₃	—	6	2	no	—
372	C₂²×C₃	—	6	2	no	—
373	C₂²×C₃	C₉×#41	1	2	yes	—
374	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
375	C₂²×C₃	C₃×#239	1	2	yes	—
376	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
377	C₂×D₃	—	2	2	no	—
378	C₂×D₃	—	2	2	no	—
379	C₂×D₃	—	2	2	no	—
380	C₃×C₄	—	2	2	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	4	1	no	—
390	C₃×C₄	—	4	2	no	—
391	C₃×C₄	—	4	2	no	—
392	C₃×C₄	—	6	2	no	—
393	C₃×C₄	—	6	2	no	—
394	C₃×C₄	—	6	2	no	—
395	Dic₃	—	2	2	no	—
396	Dic₃	—	2	2	no	—
397	Dic₃	—	2	2	no	—
398	C₃²	C₃×#539	1	1	yes	characteristic
399	C₉	—	2	1	no	—
400	C₉	#5645	1	1	yes	characteristic, direct product factor
401	C₂³	—	3	2	no	—
402	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
403	Q₈	—	4	1	no	—
404	D₄	—	6	4	no	—
405	D₄	—	12	1	no	—
406	C₂×C₄	—	3	2	no	—
407	C₂×C₄	—	3	2	no	—
408	C₂×C₄	—	3	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	6	2	no	—
411	C₂×C₄	—	12	2	no	—
412	C₂×C₄	—	12	1	no	—
413	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
414	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
416	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
417	C₂×C₃	—	2	2	no	—
418	C₂×C₃	—	2	2	no	—
419	C₂×C₃	—	2	1	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	4	2	no	—
423	C₂×C₃	—	12	2	no	—
424	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
425	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
427	C₂×C₃	C₃×#1004	1	1	yes	characteristic
428	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
429	C₂×C₃	C₃×#1010	1	1	yes	characteristic
430	D₃	—	4	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	6	2	no	—
434	C₂²	—	6	2	no	—
435	C₂²	—	6	2	no	—
436	C₂²	C₉×#239	1	2	yes	—
437	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	6	2	no	—
443	C₄	—	6	2	no	—
444	C₄	—	6	2	no	—
445	C₃	—	2	1	no	—
446	C₃	C₉×#539	1	1	yes	characteristic, complemented
447	C₃	C₃×#5645	1	1	yes	characteristic
448	C₂	—	2	2	no	—
449	C₂	—	12	2	no	—
450	C₂	C₉×#1004	1	1	yes	characteristic
451	C₂	C₂×C₉×#239	1	1	yes	characteristic
452	C₂	C₉×#1010	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×C₉×C₂²⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#930	C₂×C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#539
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
2. C₉×#946	C₂	semidirect
4. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
5. C₉×#898	C₂	semidirect
6. C₉×#894	C₂	semidirect
7. C₉×#890	C₂	semidirect
8. C₉×#886	C₂	semidirect
9. C₉×#67⋊C₄	C₂	semidirect
48. C₉×C₂²⋊Q₈	D₃	semidirect
69. #5645	C₉	direct (N × H)
137. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
142. #946	C₂×C₉	semidirect
144. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
145. #898	C₂×C₉	semidirect
146. #894	C₂×C₉	semidirect
147. #890	C₂×C₉	semidirect
148. #886	C₂×C₉	semidirect
149. #67⋊C₄	C₂×C₉	semidirect
283. C₂²⋊Q₈	D₃×C₉	semidirect
287. C₃×C₉	#539	semidirect
400. C₉	#5645	direct (N × H)
446. C₃	C₉×#539	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₂²⋊Q₈	2
C₉×#946	2
C₉×#930	2
C₂×C₉×Dic₃⋊C₄	2
C₉×#898	2
C₉×#894	2
C₉×#890	2
C₉×#886	2
C₉×#67⋊C₄	2
C₃×#5645	3
C₉×#539	3

Subgroups — C9×#5645 #13152940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5645 #13152940