Subgroups — C₉×#5692 #13153167

Order 1728.

710 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#898	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#896	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#895	C₂	1	1	yes	maximal, characteristic
7	C₉×#894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#894	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#894	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
12	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#889	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#876	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5692	C₃	1	1	yes	maximal, characteristic
17	C₉×#539	—	3	1	no	maximal
18	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
19	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
20	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
26	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
41	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
42	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
44	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
45	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
46	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
51	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
53	C₃²×#125	C₂×C₃	1	1	yes	characteristic
54	C₃×#898	C₂×C₃	1	1	yes	characteristic
55	C₃×#897	C₂×C₃	1	1	yes	characteristic
56	C₃×#896	C₂×C₃	1	1	yes	characteristic
57	C₃×#896	C₂×C₃	1	1	yes	characteristic
58	C₃×#895	C₂×C₃	1	1	yes	characteristic
59	C₃×#894	C₂×C₃	1	1	yes	characteristic
60	C₃×#894	C₂×C₃	1	1	yes	characteristic
61	C₃×#894	C₂×C₃	1	1	yes	characteristic
62	C₃×#894	C₂×C₃	1	1	yes	characteristic
63	C₃×#893	C₂×C₃	1	1	yes	characteristic
64	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
65	C₃×#889	C₂×C₃	1	1	yes	characteristic
66	C₃×#876	C₂×C₃	1	1	yes	characteristic
67	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
68	C₉×#126	—	3	1	no	—
69	C₉×#126	—	3	1	no	—
70	C₉×#125	—	2	1	no	—
71	C₉×#125	—	3	1	no	—
72	C₉×#125	D₃	1	1	yes	characteristic, complemented
73	C₉×#123	—	3	1	no	—
74	C₉×#123	—	3	1	no	—
75	C₉×#123	—	3	1	no	—
76	C₉×#123	—	3	1	no	—
77	C₉×C₂²⋊Q₈	—	3	1	no	—
78	C₉×C₂²⋊Q₈	—	3	1	no	—
79	C₉×C₂²⋊Q₈	—	3	1	no	—
80	C₉×#121	—	3	1	no	—
81	C₄×D₄×C₉	—	3	1	no	—
82	C₄×D₄×C₉	—	3	1	no	—
83	C₂×C₉×C₄⋊C₄	—	3	1	no	—
84	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
85	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
86	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
95	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
96	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
97	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
99	C₉×D₁₂	—	2	2	no	—
100	C₉×D₁₂	—	2	2	no	—
101	C₉×D₁₂	—	4	1	no	—
102	C₄×D₃×C₉	—	2	2	no	—
103	C₄×D₃×C₉	—	4	1	no	—
104	C₄×D₃×C₉	—	4	1	no	—
105	C₄×D₃×C₉	—	4	1	no	—
106	C₄×D₃×C₉	—	4	1	no	—
107	C₉×Dic₆	—	4	1	no	—
108	C₃×#539	—	3	1	no	—
109	#5692	C₉	1	1	yes	characteristic, direct product factor
110	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
119	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
126	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
137	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
138	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
145	C₂×Q₈×C₉	—	3	1	no	—
146	C₂×D₄×C₉	—	3	1	no	—
147	C₂×D₄×C₉	—	3	1	no	—
148	C₂×D₄×C₉	—	3	1	no	—
149	C₂²×C₄×C₉	—	3	1	no	—
150	C₂²×C₄×C₉	—	3	1	no	—
151	C₂²×C₄×C₉	—	3	1	no	—
152	C₂²×C₄×C₉	—	3	1	no	—
153	C₂²×C₄×C₉	—	3	1	no	—
154	C₉×C₄⋊C₄	—	2	1	no	—
155	C₉×C₄⋊C₄	—	2	1	no	—
156	C₉×C₄⋊C₄	—	2	1	no	—
157	C₉×C₄⋊C₄	—	2	1	no	—
158	C₉×C₄⋊C₄	—	2	1	no	—
159	C₉×C₄⋊C₄	—	2	1	no	—
160	C₉×C₄⋊C₄	—	3	1	no	—
161	C₉×C₄⋊C₄	—	3	1	no	—
162	C₉×C₄⋊C₄	—	3	1	no	—
163	C₉×C₄⋊C₄	—	3	1	no	—
164	C₉×C₄⋊C₄	—	3	1	no	—
165	C₉×C₄⋊C₄	—	3	1	no	—
166	C₉×C₄⋊C₄	—	3	1	no	—
167	C₉×C₄⋊C₄	—	3	1	no	—
168	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
169	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
170	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
171	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
172	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
173	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
174	C₉×C₂²⋊C₄	—	3	1	no	—
175	C₉×C₂²⋊C₄	—	3	1	no	—
176	C₉×C₂²⋊C₄	—	3	1	no	—
177	C₉×C₂²⋊C₄	—	3	1	no	—
178	C₉×C₂²⋊C₄	—	3	1	no	—
179	C₉×C₂²⋊C₄	—	3	1	no	—
180	C₉×C₂²⋊C₄	—	3	1	no	—
181	C₉×C₂²⋊C₄	—	3	1	no	—
182	C₉×C₂²⋊C₄	—	3	1	no	—
183	C₉×C₂²⋊C₄	—	3	1	no	—
184	C₄²×C₉	—	2	1	no	—
185	C₄²×C₉	—	3	1	no	—
186	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
187	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
188	C₂×D₃×C₉	—	2	1	no	—
189	C₂×D₃×C₉	—	2	1	no	—
190	C₂×D₃×C₉	—	2	1	no	—
191	C₂×D₃×C₉	—	2	1	no	—
192	C₂×D₃×C₉	—	2	1	no	—
193	C₂×D₃×C₉	—	2	1	no	—
194	C₂×D₃×C₉	—	2	1	no	—
195	C₂×D₃×C₉	—	2	1	no	—
196	C₂×D₃×C₉	#41	1	2	yes	—
197	C₃×C₄×C₉	—	2	1	no	—
198	C₃×C₄×C₉	—	2	1	no	—
199	C₃×C₄×C₉	—	2	1	no	—
200	C₃×C₄×C₉	—	2	1	no	—
201	C₃×C₄×C₉	—	2	1	no	—
202	C₃×C₄×C₉	—	2	1	no	—
203	C₃×C₄×C₉	—	2	1	no	—
204	C₉×Dic₃	—	2	1	no	—
205	C₉×Dic₃	—	2	1	no	—
206	C₉×Dic₃	—	2	1	no	—
207	C₉×Dic₃	—	2	1	no	—
208	C₉×Dic₃	—	2	1	no	—
209	C₃×#126	—	3	1	no	—
210	C₃×#126	—	3	1	no	—
211	C₃×#125	—	2	1	no	—
212	C₃×#125	—	3	1	no	—
213	C₃×#125	C₂×C₉	1	1	yes	characteristic, complemented
214	C₃×#125	C₃×D₃	1	1	yes	characteristic
215	C₃×#123	—	3	1	no	—
216	C₃×#123	—	3	1	no	—
217	C₃×#123	—	3	1	no	—
218	C₃×#123	—	3	1	no	—
219	C₃×C₂²⋊Q₈	—	3	1	no	—
220	C₃×C₂²⋊Q₈	—	3	1	no	—
221	C₃×C₂²⋊Q₈	—	3	1	no	—
222	C₃×#121	—	3	1	no	—
223	C₃×C₄×D₄	—	3	1	no	—
224	C₃×C₄×D₄	—	3	1	no	—
225	C₂×C₃×C₄⋊C₄	—	3	1	no	—
226	#898	C₂×C₉	1	1	yes	characteristic, complemented
227	#897	C₂×C₉	1	1	yes	characteristic, complemented
228	#896	C₂×C₉	1	1	yes	characteristic, complemented
229	#896	C₂×C₉	1	1	yes	characteristic, complemented
230	#895	C₂×C₉	1	1	yes	characteristic
231	#894	C₂×C₉	1	1	yes	characteristic, complemented
232	#894	C₂×C₉	1	1	yes	characteristic, complemented
233	#894	C₂×C₉	1	1	yes	characteristic, complemented
234	#894	C₂×C₉	1	1	yes	characteristic, complemented
235	#893	C₂×C₉	1	1	yes	characteristic, complemented
236	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
237	#889	C₂×C₉	1	1	yes	characteristic, complemented
238	#876	C₂×C₉	1	1	yes	characteristic, complemented
239	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
240	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
241	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
242	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
245	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
246	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
247	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
251	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
252	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
253	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
254	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
255	C₃×D₁₂	—	2	2	no	—
256	C₃×D₁₂	—	2	2	no	—
257	C₃×D₁₂	—	4	1	no	—
258	C₃×C₄×D₃	—	2	2	no	—
259	C₃×C₄×D₃	—	4	1	no	—
260	C₃×C₄×D₃	—	4	1	no	—
261	C₃×C₄×D₃	—	4	1	no	—
262	C₃×C₄×D₃	—	4	1	no	—
263	C₃×Dic₆	—	4	1	no	—
264	C₂³×C₉	—	3	1	no	—
265	C₂³×C₉	—	3	1	no	—
266	C₂³×C₉	—	3	1	no	—
267	Q₈×C₉	—	12	1	no	—
268	D₄×C₉	—	6	2	no	—
269	D₄×C₉	—	6	2	no	—
270	D₄×C₉	—	12	1	no	—
271	C₂×C₄×C₉	—	2	1	no	—
272	C₂×C₄×C₉	—	2	1	no	—
273	C₂×C₄×C₉	—	2	1	no	—
274	C₂×C₄×C₉	—	2	1	no	—
275	C₂×C₄×C₉	—	2	1	no	—
276	C₂×C₄×C₉	—	2	1	no	—
277	C₂×C₄×C₉	—	2	1	no	—
278	C₂×C₄×C₉	—	3	1	no	—
279	C₂×C₄×C₉	—	3	1	no	—
280	C₂×C₄×C₉	—	3	1	no	—
281	C₂×C₄×C₉	—	3	1	no	—
282	C₂×C₄×C₉	—	3	1	no	—
283	C₂×C₄×C₉	—	6	2	no	—
284	C₂×C₄×C₉	—	12	1	no	—
285	C₂×C₄×C₉	—	12	1	no	—
286	C₂×C₄×C₉	—	12	1	no	—
287	C₂×C₄×C₉	—	12	1	no	—
288	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
289	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
290	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
291	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
292	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
293	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
294	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
295	#539	—	3	1	no	Sylow
296	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
297	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
299	D₃×C₉	—	2	2	no	—
300	D₃×C₉	—	4	1	no	—
301	D₃×C₉	—	4	1	no	—
302	C₂×C₃×Q₈	—	3	1	no	—
303	C₂×C₃×D₄	—	3	1	no	—
304	C₂×C₃×D₄	—	3	1	no	—
305	C₂×C₃×D₄	—	3	1	no	—
306	C₂²×C₃×C₄	—	3	1	no	—
307	C₂²×C₃×C₄	—	3	1	no	—
308	C₂²×C₃×C₄	—	3	1	no	—
309	C₂²×C₃×C₄	—	3	1	no	—
310	C₂²×C₃×C₄	—	3	1	no	—
311	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
312	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
313	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
314	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
315	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
316	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
317	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
318	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
319	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
320	C₃×C₄⋊C₄	—	2	1	no	—
321	C₃×C₄⋊C₄	—	2	1	no	—
322	C₃×C₄⋊C₄	—	2	1	no	—
323	C₃×C₄⋊C₄	—	2	1	no	—
324	C₃×C₄⋊C₄	—	2	1	no	—
325	C₃×C₄⋊C₄	—	2	1	no	—
326	C₃×C₄⋊C₄	—	3	1	no	—
327	C₃×C₄⋊C₄	—	3	1	no	—
328	C₃×C₄⋊C₄	—	3	1	no	—
329	C₃×C₄⋊C₄	—	3	1	no	—
330	C₃×C₄⋊C₄	—	3	1	no	—
331	C₃×C₄⋊C₄	—	3	1	no	—
332	C₃×C₄⋊C₄	—	3	1	no	—
333	C₃×C₄⋊C₄	—	3	1	no	—
334	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
335	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
336	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
337	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
338	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
339	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
340	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
341	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
342	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
343	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
344	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
345	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
346	C₃×C₂²⋊C₄	—	3	1	no	—
347	C₃×C₂²⋊C₄	—	3	1	no	—
348	C₃×C₂²⋊C₄	—	3	1	no	—
349	C₃×C₂²⋊C₄	—	3	1	no	—
350	C₃×C₂²⋊C₄	—	3	1	no	—
351	C₃×C₂²⋊C₄	—	3	1	no	—
352	C₃×C₂²⋊C₄	—	3	1	no	—
353	C₃×C₂²⋊C₄	—	3	1	no	—
354	C₃×C₂²⋊C₄	—	3	1	no	—
355	C₃×C₂²⋊C₄	—	3	1	no	—
356	C₃×C₄²	—	2	1	no	—
357	C₃×C₄²	—	3	1	no	—
358	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
359	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
360	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
361	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
362	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
363	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
364	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
365	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
366	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
367	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
368	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
369	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
370	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
371	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
372	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
373	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
374	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
375	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
376	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
377	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
378	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
379	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
380	C₂×C₃×D₃	—	2	1	no	—
381	C₂×C₃×D₃	—	2	1	no	—
382	C₂×C₃×D₃	—	2	1	no	—
383	C₂×C₃×D₃	—	2	1	no	—
384	C₂×C₃×D₃	—	2	1	no	—
385	C₂×C₃×D₃	—	2	1	no	—
386	C₂×C₃×D₃	—	2	1	no	—
387	C₂×C₃×D₃	—	2	1	no	—
388	C₂×C₃×D₃	C₃×#41	1	2	yes	—
389	C₃²×C₄	—	2	1	no	—
390	C₃²×C₄	—	2	1	no	—
391	C₃²×C₄	—	2	1	no	—
392	C₃²×C₄	—	2	1	no	—
393	C₃²×C₄	—	2	1	no	—
394	C₃²×C₄	—	2	1	no	—
395	C₃²×C₄	—	2	1	no	—
396	C₃×Dic₃	—	2	1	no	—
397	C₃×Dic₃	—	2	1	no	—
398	C₃×Dic₃	—	2	1	no	—
399	C₃×Dic₃	—	2	1	no	—
400	C₃×Dic₃	—	2	1	no	—
401	C₂²×C₉	—	2	1	no	—
402	C₂²×C₉	—	3	2	no	—
403	C₂²×C₉	—	6	1	no	—
404	C₂²×C₉	—	6	1	no	—
405	C₂²×C₉	—	6	1	no	—
406	C₂²×C₉	—	6	1	no	—
407	C₂²×C₉	—	6	1	no	—
408	C₂²×C₉	—	6	1	no	—
409	C₂²×C₉	—	6	1	no	—
410	C₂²×C₉	—	6	1	no	—
411	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
412	C₄×C₉	—	2	2	no	—
413	C₄×C₉	—	2	1	no	—
414	C₄×C₉	—	2	1	no	—
415	C₄×C₉	—	2	1	no	—
416	C₄×C₉	—	2	1	no	—
417	C₄×C₉	—	2	1	no	—
418	C₄×C₉	—	2	1	no	—
419	C₄×C₉	—	2	1	no	—
420	C₄×C₉	—	4	1	no	—
421	C₄×C₉	—	4	1	no	—
422	C₄×C₉	—	4	1	no	—
423	C₄×C₉	—	4	1	no	—
424	C₄×C₉	—	4	1	no	—
425	C₄×C₉	—	4	1	no	—
426	C₄×C₉	—	6	1	no	—
427	C₄×C₉	—	6	1	no	—
428	C₄×C₉	—	6	1	no	—
429	C₄×C₉	—	6	1	no	—
430	C₄×C₉	—	6	1	no	—
431	#126	—	3	1	no	—
432	#126	—	3	1	no	—
433	#125	—	3	1	no	—
434	#125	D₃×C₉	1	1	yes	characteristic, complemented
435	#123	—	3	1	no	—
436	#123	—	3	1	no	—
437	#123	—	3	1	no	—
438	#123	—	3	1	no	—
439	C₂²⋊Q₈	—	3	1	no	—
440	C₂²⋊Q₈	—	3	1	no	—
441	C₂²⋊Q₈	—	3	1	no	—
442	#121	—	3	1	no	—
443	C₄×D₄	—	3	1	no	—
444	C₄×D₄	—	3	1	no	—
445	C₂×C₄⋊C₄	—	3	1	no	—
446	C₃×C₉	#539	1	1	yes	characteristic, complemented, Sylow
447	C₂³×C₃	—	3	1	no	—
448	C₂³×C₃	—	3	1	no	—
449	C₂³×C₃	—	3	1	no	—
450	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
451	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
452	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
453	C₃×Q₈	—	12	1	no	—
454	C₃×D₄	—	6	2	no	—
455	C₃×D₄	—	6	2	no	—
456	C₃×D₄	—	12	1	no	—
457	C₂×C₃×C₄	—	2	1	no	—
458	C₂×C₃×C₄	—	2	1	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	1	no	—
461	C₂×C₃×C₄	—	2	1	no	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	3	1	no	—
465	C₂×C₃×C₄	—	3	1	no	—
466	C₂×C₃×C₄	—	3	1	no	—
467	C₂×C₃×C₄	—	3	1	no	—
468	C₂×C₃×C₄	—	3	1	no	—
469	C₂×C₃×C₄	—	6	2	no	—
470	C₂×C₃×C₄	—	12	1	no	—
471	C₂×C₃×C₄	—	12	1	no	—
472	C₂×C₃×C₄	—	12	1	no	—
473	C₂×C₃×C₄	—	12	1	no	—
474	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
475	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
476	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
477	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
478	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
479	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
480	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
481	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
482	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
483	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
484	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
485	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
486	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
488	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
489	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
490	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
491	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
492	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
493	D₁₂	—	2	2	no	—
494	D₁₂	—	2	2	no	—
495	D₁₂	—	4	1	no	—
496	C₄×D₃	—	2	2	no	—
497	C₄×D₃	—	4	1	no	—
498	C₄×D₃	—	4	1	no	—
499	C₄×D₃	—	4	1	no	—
500	C₄×D₃	—	4	1	no	—
501	Dic₆	—	4	1	no	—
502	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
503	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
505	C₃×D₃	—	2	2	no	—
506	C₃×D₃	—	4	1	no	—
507	C₃×D₃	—	4	1	no	—
508	C₂×C₉	—	2	1	no	—
509	C₂×C₉	—	2	1	no	—
510	C₂×C₉	—	2	1	no	—
511	C₂×C₉	—	6	2	no	—
512	C₂×C₉	—	12	1	no	—
513	C₂×C₉	—	12	1	no	—
514	C₂×C₉	#1007	1	1	yes	characteristic
515	C₂×C₉	D₃×#41	1	1	yes	characteristic
516	C₂×C₉	#1009	1	1	yes	characteristic
517	C₂×Q₈	—	3	1	no	—
518	C₂×D₄	—	3	1	no	—
519	C₂×D₄	—	3	1	no	—
520	C₂×D₄	—	3	1	no	—
521	C₂²×C₄	—	3	1	no	—
522	C₂²×C₄	—	3	1	no	—
523	C₂²×C₄	—	3	1	no	—
524	C₂²×C₄	—	3	1	no	—
525	C₂²×C₄	—	3	1	no	—
526	C₄⋊C₄	—	3	1	no	—
527	C₄⋊C₄	—	3	1	no	—
528	C₄⋊C₄	—	3	1	no	—
529	C₄⋊C₄	—	3	1	no	—
530	C₄⋊C₄	—	3	1	no	—
531	C₄⋊C₄	—	3	1	no	—
532	C₄⋊C₄	—	3	1	no	—
533	C₄⋊C₄	—	3	1	no	—
534	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
535	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
537	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
538	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
539	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
540	C₂²⋊C₄	—	3	1	no	—
541	C₂²⋊C₄	—	3	1	no	—
542	C₂²⋊C₄	—	3	1	no	—
543	C₂²⋊C₄	—	3	1	no	—
544	C₂²⋊C₄	—	3	1	no	—
545	C₂²⋊C₄	—	3	1	no	—
546	C₂²⋊C₄	—	3	1	no	—
547	C₂²⋊C₄	—	3	1	no	—
548	C₂²⋊C₄	—	3	1	no	—
549	C₂²⋊C₄	—	3	1	no	—
550	C₄²	—	3	1	no	—
551	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
552	C₂²×C₃	—	2	1	no	—
553	C₂²×C₃	—	3	2	no	—
554	C₂²×C₃	—	6	1	no	—
555	C₂²×C₃	—	6	1	no	—
556	C₂²×C₃	—	6	1	no	—
557	C₂²×C₃	—	6	1	no	—
558	C₂²×C₃	—	6	1	no	—
559	C₂²×C₃	—	6	1	no	—
560	C₂²×C₃	—	6	1	no	—
561	C₂²×C₃	—	6	1	no	—
562	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
563	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
564	C₂×D₃	—	2	1	no	—
565	C₂×D₃	—	2	1	no	—
566	C₂×D₃	—	2	1	no	—
567	C₂×D₃	—	2	1	no	—
568	C₂×D₃	—	2	1	no	—
569	C₂×D₃	—	2	1	no	—
570	C₂×D₃	—	2	1	no	—
571	C₂×D₃	—	2	1	no	—
572	C₂×D₃	C₉×#41	1	2	yes	—
573	C₃×C₄	—	2	2	no	—
574	C₃×C₄	—	2	1	no	—
575	C₃×C₄	—	2	1	no	—
576	C₃×C₄	—	2	1	no	—
577	C₃×C₄	—	2	1	no	—
578	C₃×C₄	—	2	1	no	—
579	C₃×C₄	—	2	1	no	—
580	C₃×C₄	—	2	1	no	—
581	C₃×C₄	—	2	1	no	—
582	C₃×C₄	—	2	1	no	—
583	C₃×C₄	—	2	1	no	—
584	C₃×C₄	—	2	1	no	—
585	C₃×C₄	—	2	1	no	—
586	C₃×C₄	—	2	1	no	—
587	C₃×C₄	—	2	1	no	—
588	C₃×C₄	—	4	1	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	4	1	no	—
591	C₃×C₄	—	4	1	no	—
592	C₃×C₄	—	4	1	no	—
593	C₃×C₄	—	4	1	no	—
594	C₃×C₄	—	6	1	no	—
595	C₃×C₄	—	6	1	no	—
596	C₃×C₄	—	6	1	no	—
597	C₃×C₄	—	6	1	no	—
598	C₃×C₄	—	6	1	no	—
599	Dic₃	—	2	1	no	—
600	Dic₃	—	2	1	no	—
601	Dic₃	—	2	1	no	—
602	Dic₃	—	2	1	no	—
603	Dic₃	—	2	1	no	—
604	C₃²	C₃×#539	1	1	yes	characteristic
605	C₉	—	2	1	no	—
606	C₉	#5692	1	1	yes	characteristic, direct product factor
607	C₂³	—	3	1	no	—
608	C₂³	—	3	1	no	—
609	C₂³	—	3	1	no	—
610	Q₈	—	12	1	no	—
611	D₄	—	6	2	no	—
612	D₄	—	6	2	no	—
613	D₄	—	12	1	no	—
614	C₂×C₄	—	3	1	no	—
615	C₂×C₄	—	3	1	no	—
616	C₂×C₄	—	3	1	no	—
617	C₂×C₄	—	3	1	no	—
618	C₂×C₄	—	3	1	no	—
619	C₂×C₄	—	6	2	no	—
620	C₂×C₄	—	12	1	no	—
621	C₂×C₄	—	12	1	no	—
622	C₂×C₄	—	12	1	no	—
623	C₂×C₄	—	12	1	no	—
624	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
625	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
626	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
627	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
630	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
631	C₂×C₃	—	2	1	no	—
632	C₂×C₃	—	2	1	no	—
633	C₂×C₃	—	2	1	no	—
634	C₂×C₃	—	6	2	no	—
635	C₂×C₃	—	12	1	no	—
636	C₂×C₃	—	12	1	no	—
637	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
638	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
640	C₂×C₃	C₃×#1007	1	1	yes	characteristic
641	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
642	C₂×C₃	C₃×#1009	1	1	yes	characteristic
643	D₃	—	2	2	no	—
644	D₃	—	4	1	no	—
645	D₃	—	4	1	no	—
646	C₂²	—	3	2	no	—
647	C₂²	—	6	1	no	—
648	C₂²	—	6	1	no	—
649	C₂²	—	6	1	no	—
650	C₂²	—	6	1	no	—
651	C₂²	—	6	1	no	—
652	C₂²	—	6	1	no	—
653	C₂²	—	6	1	no	—
654	C₂²	—	6	1	no	—
655	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	6	1	no	—
664	C₄	—	6	1	no	—
665	C₄	—	6	1	no	—
666	C₄	—	6	1	no	—
667	C₄	—	6	1	no	—
668	C₃	—	2	1	no	—
669	C₃	C₉×#539	1	1	yes	characteristic, complemented
670	C₃	C₃×#5692	1	1	yes	characteristic
671	C₂	—	6	2	no	—
672	C₂	—	12	1	no	—
673	C₂	—	12	1	no	—
674	C₂	C₉×#1007	1	1	yes	characteristic
675	C₂	D₃×C₉×#41	1	1	yes	characteristic
676	C₂	C₉×#1009	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×#125	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#895	C₂×C₃
hypercenter	C₉×#125	D₃
hypocenter	C₃	C₉×#539
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#125

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#125	C₂	semidirect
2. C₉×#898	C₂	semidirect
3. C₉×#897	C₂	semidirect
4. C₉×#896	C₂	semidirect
5. C₉×#896	C₂	semidirect
7. C₉×#894	C₂	semidirect
8. C₉×#894	C₂	semidirect
9. C₉×#894	C₂	semidirect
10. C₉×#894	C₂	semidirect
11. C₉×#893	C₂	semidirect
12. D₃×C₉×C₄⋊C₄	C₂	semidirect
13. C₉×#889	C₂	semidirect
14. C₉×#876	C₂	semidirect
15. C₄×C₉×D₁₂	C₂	semidirect
72. C₉×#125	D₃	semidirect
109. #5692	C₉	direct (N × H)
213. C₃×#125	C₂×C₉	semidirect
226. #898	C₂×C₉	semidirect
227. #897	C₂×C₉	semidirect
228. #896	C₂×C₉	semidirect
229. #896	C₂×C₉	semidirect
231. #894	C₂×C₉	semidirect
232. #894	C₂×C₉	semidirect
233. #894	C₂×C₉	semidirect
234. #894	C₂×C₉	semidirect
235. #893	C₂×C₉	semidirect
236. D₃×C₄⋊C₄	C₂×C₉	semidirect
237. #889	C₂×C₉	semidirect
238. #876	C₂×C₉	semidirect
239. C₄×D₁₂	C₂×C₉	semidirect
434. #125	D₃×C₉	semidirect
446. C₃×C₉	#539	semidirect
606. C₉	#5692	direct (N × H)
669. 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×#125	2
C₉×#898	2
C₉×#897	2
C₉×#896	2
C₉×#895	2
C₉×#894	2
C₉×#893	2
D₃×C₉×C₄⋊C₄	2
C₉×#889	2
C₉×#876	2
C₄×C₉×D₁₂	2
C₃×#5692	3
C₉×#539	3

Subgroups — C9×#5692 #13153167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5692 #13153167