Subgroups — C₉×#5612 #13152831

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#938	C₂	1	2	yes	maximal, complemented
5	C₉×#937	C₂	1	2	yes	maximal, complemented
6	C₉×#936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#883	C₂	1	2	yes	maximal, complemented
11	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#5612	C₃	1	1	yes	maximal, characteristic
13	C₉×#546	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	2	yes	—
15	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
17	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₉×#67	C₂²	1	2	yes	—
19	C₂×C₉×#67	C₂²	1	1	yes	characteristic
20	C₂×C₉×#67	C₂²	1	2	yes	complemented
21	D₃×D₄×C₉	—	2	4	no	—
22	C₉×#235	—	2	4	no	—
23	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
26	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
27	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
30	C₉×#217	C₂²	1	1	yes	characteristic, complemented
31	C₉×#217	C₂²	1	2	yes	complemented
32	C₉×#217	C₂²	1	2	yes	complemented
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
37	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
41	C₃²×#121	C₂×C₃	1	1	yes	characteristic
42	C₃×#938	C₂×C₃	1	2	yes	—
43	C₃×#937	C₂×C₃	1	2	yes	—
44	C₃×#936	C₂×C₃	1	1	yes	characteristic
45	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
46	C₃×#897	C₂×C₃	1	1	yes	characteristic
47	C₃×#893	C₂×C₃	1	1	yes	characteristic
48	C₃×#883	C₂×C₃	1	2	yes	—
49	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
50	C₂×C₉×#41	—	3	1	no	—
51	C₂²×D₄×C₉	—	3	1	no	—
52	C₉×#124	—	3	1	no	—
53	C₉×#123	—	3	2	no	—
54	C₉×C₂²⋊Q₈	—	3	1	no	—
55	C₉×#121	—	2	1	no	—
56	C₉×#121	—	3	2	no	—
57	C₉×#121	D₃	1	1	yes	characteristic, complemented
58	C₉×#120	—	3	2	no	—
59	C₄×D₄×C₉	—	3	1	no	—
60	C₄×D₄×C₉	—	3	1	no	—
61	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
62	C₂³×C₃×C₉	C₂³	1	2	yes	—
63	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
64	C₂²×D₃×C₉	—	2	4	no	—
65	C₂²×D₃×C₉	—	2	4	no	—
66	C₂²×D₃×C₉	—	4	2	no	—
67	C₂²×D₃×C₉	C₂³	1	2	yes	—
68	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
69	C₃×D₄×C₉	—	2	2	no	—
70	C₃×D₄×C₉	—	4	2	no	—
71	C₂×C₃×C₄×C₉	—	2	2	no	—
72	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
74	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₉×#67	—	2	4	no	—
76	C₉×#67	—	2	4	no	—
77	C₉×#67	—	2	2	no	—
78	C₂×C₉×Dic₃	C₂³	1	2	yes	—
79	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
82	C₉×D₁₂	D₄	1	4	yes	complemented
83	C₄×D₃×C₉	—	2	4	no	—
84	C₄×D₃×C₉	—	2	2	no	—
85	C₄×D₃×C₉	—	4	2	no	—
86	C₉×Dic₆	—	2	2	no	—
87	C₃×#546	—	3	1	no	—
88	#5612	C₉	1	1	yes	characteristic, direct product factor
89	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
90	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
92	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
94	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
96	C₃×D₃×D₄	—	2	4	no	—
97	C₃×#235	—	2	4	no	—
98	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
101	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
102	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
103	C₂⁴×C₉	—	3	2	no	—
104	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃×#217	C₂²×C₃	1	2	yes	—
107	C₃×#217	C₂²×C₃	1	2	yes	—
108	C₃×#217	C₂²×C₃	1	1	yes	characteristic
109	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
112	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
113	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
115	C₉×#41	—	6	4	no	—
116	C₂×Q₈×C₉	—	3	1	no	—
117	C₂×D₄×C₉	—	2	1	no	—
118	C₂×D₄×C₉	—	2	2	no	—
119	C₂×D₄×C₉	—	3	1	no	—
120	C₂×D₄×C₉	—	3	2	no	—
121	C₂×D₄×C₉	—	3	2	no	—
122	C₂×D₄×C₉	—	3	1	no	—
123	C₂×D₄×C₉	—	6	4	no	—
124	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
125	C₂×D₄×C₉	C₂×D₃	1	2	yes	complemented
126	C₂²×C₄×C₉	—	2	1	no	—
127	C₂²×C₄×C₉	—	3	2	no	—
128	C₂²×C₄×C₉	—	3	1	no	—
129	C₂²×C₄×C₉	—	3	2	no	—
130	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
131	C₉×C₄⋊C₄	—	2	1	no	—
132	C₉×C₄⋊C₄	—	3	1	no	—
133	C₉×C₄⋊C₄	—	3	2	no	—
134	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
135	C₉×C₂²⋊C₄	—	2	2	no	—
136	C₉×C₂²⋊C₄	—	3	2	no	—
137	C₉×C₂²⋊C₄	—	3	1	no	—
138	C₉×C₂²⋊C₄	—	3	2	no	—
139	C₉×C₂²⋊C₄	—	3	1	no	—
140	C₉×C₂²⋊C₄	—	3	2	no	—
141	C₉×C₂²⋊C₄	—	3	2	no	—
142	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
143	C₄²×C₉	—	3	1	no	—
144	C₂²×C₃×C₉	—	2	1	no	—
145	C₂²×C₃×C₉	—	2	2	no	—
146	C₂²×C₃×C₉	—	2	1	no	—
147	C₂²×C₃×C₉	—	2	2	no	—
148	C₂²×C₃×C₉	—	2	1	no	—
149	C₂²×C₃×C₉	—	2	2	no	—
150	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
151	C₂×D₃×C₉	—	2	1	no	—
152	C₂×D₃×C₉	—	2	2	no	—
153	C₂×D₃×C₉	—	2	2	no	—
154	C₂×D₃×C₉	—	2	1	no	—
155	C₂×D₃×C₉	—	4	8	no	—
156	C₂×D₃×C₉	C₂×D₄	1	4	yes	—
157	C₂×D₃×C₉	#41	1	2	yes	complemented
158	C₃×C₄×C₉	—	2	1	no	—
159	C₃×C₄×C₉	—	2	2	no	—
160	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
161	C₉×Dic₃	—	2	2	no	—
162	C₉×Dic₃	—	2	1	no	—
163	C₉×Dic₃	—	2	1	no	—
164	C₉×Dic₃	—	2	1	no	—
165	C₂×C₃×#41	—	3	1	no	—
166	C₂²×C₃×D₄	—	3	1	no	—
167	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
169	C₃×#124	—	3	1	no	—
170	C₃×#123	—	3	2	no	—
171	C₃×C₂²⋊Q₈	—	3	1	no	—
172	C₃×#121	—	2	1	no	—
173	C₃×#121	—	3	2	no	—
174	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
175	C₃×#121	C₃×D₃	1	1	yes	characteristic
176	C₃×#120	—	3	2	no	—
177	C₃×C₄×D₄	—	3	1	no	—
178	C₃×C₄×D₄	—	3	1	no	—
179	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
180	#938	C₂×C₉	1	2	yes	complemented
181	#937	C₂×C₉	1	2	yes	complemented
182	#936	C₂×C₉	1	1	yes	characteristic, complemented
183	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
184	#897	C₂×C₉	1	1	yes	characteristic, complemented
185	#893	C₂×C₉	1	1	yes	characteristic, complemented
186	#883	C₂×C₉	1	2	yes	complemented
187	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
188	C₂³×C₃²	C₂³×C₃	1	2	yes	—
189	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₃×D₃	—	2	4	no	—
191	C₂²×C₃×D₃	—	2	4	no	—
192	C₂²×C₃×D₃	—	4	2	no	—
193	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
194	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
195	C₃²×D₄	—	2	2	no	—
196	C₃²×D₄	—	4	2	no	—
197	C₂×C₃²×C₄	—	2	2	no	—
198	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
200	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₃×#67	—	2	4	no	—
202	C₃×#67	—	2	4	no	—
203	C₃×#67	—	2	2	no	—
204	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
208	C₃×D₁₂	C₃×D₄	1	4	yes	—
209	C₃×C₄×D₃	—	2	4	no	—
210	C₃×C₄×D₃	—	2	2	no	—
211	C₃×C₄×D₃	—	4	2	no	—
212	C₃×Dic₆	—	2	2	no	—
213	C₂³×C₉	—	2	1	no	—
214	C₂³×C₉	—	2	2	no	—
215	C₂³×C₉	—	3	1	no	—
216	C₂³×C₉	—	3	2	no	—
217	C₂³×C₉	—	6	4	no	—
218	C₂³×C₉	—	6	4	no	—
219	C₂³×C₉	—	12	2	no	—
220	C₂³×C₉	C₂²×D₃	1	2	yes	—
221	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
222	Q₈×C₉	—	6	2	no	—
223	D₄×C₉	—	2	2	no	—
224	D₄×C₉	—	3	4	no	—
225	D₄×C₉	—	4	2	no	—
226	D₄×C₉	—	4	2	no	—
227	D₄×C₉	—	4	4	no	—
228	D₄×C₉	—	6	2	no	—
229	D₄×C₉	—	6	4	no	—
230	D₄×C₉	—	6	4	no	—
231	C₂×C₄×C₉	—	2	2	no	—
232	C₂×C₄×C₉	—	2	1	no	—
233	C₂×C₄×C₉	—	2	1	no	—
234	C₂×C₄×C₉	—	2	2	no	—
235	C₂×C₄×C₉	—	3	1	no	—
236	C₂×C₄×C₉	—	3	1	no	—
237	C₂×C₄×C₉	—	3	2	no	—
238	C₂×C₄×C₉	—	3	1	no	—
239	C₂×C₄×C₉	—	4	2	no	—
240	C₂×C₄×C₉	—	6	4	no	—
241	C₂×C₄×C₉	—	6	2	no	—
242	C₂×C₄×C₉	—	12	2	no	—
243	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
244	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
245	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
246	#546	—	3	1	no	Sylow
247	C₂×C₃×C₉	—	4	1	no	—
248	C₂×C₃×C₉	—	4	2	no	—
249	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
251	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
252	D₃×C₉	—	2	2	no	—
253	D₃×C₉	—	2	4	no	—
254	C₂⁴×C₃	—	3	2	no	—
255	C₂³×D₃	C₂²×C₉	1	2	yes	—
256	C₃×#41	—	6	4	no	—
257	C₂×C₃×Q₈	—	3	1	no	—
258	C₂×C₃×D₄	—	2	1	no	—
259	C₂×C₃×D₄	—	2	2	no	—
260	C₂×C₃×D₄	—	3	1	no	—
261	C₂×C₃×D₄	—	3	2	no	—
262	C₂×C₃×D₄	—	3	2	no	—
263	C₂×C₃×D₄	—	3	1	no	—
264	C₂×C₃×D₄	—	6	4	no	—
265	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
266	C₂×C₃×D₄	C₂²×C₉	1	2	yes	complemented
267	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
268	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	—	3	2	no	—
271	C₂²×C₃×C₄	—	3	1	no	—
272	C₂²×C₃×C₄	—	3	2	no	—
273	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
274	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
275	C₂×#67	C₂²×C₉	1	2	yes	—
276	C₂×#67	C₂²×C₉	1	1	yes	characteristic
277	C₂×#67	C₂²×C₉	1	2	yes	complemented
278	D₃×D₄	—	2	4	no	—
279	#235	—	2	4	no	—
280	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
281	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
282	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
283	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
284	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
285	C₃×C₄⋊C₄	—	2	1	no	—
286	C₃×C₄⋊C₄	—	3	1	no	—
287	C₃×C₄⋊C₄	—	3	2	no	—
288	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
289	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
290	C₃×C₂²⋊C₄	—	2	2	no	—
291	C₃×C₂²⋊C₄	—	3	2	no	—
292	C₃×C₂²⋊C₄	—	3	1	no	—
293	C₃×C₂²⋊C₄	—	3	2	no	—
294	C₃×C₂²⋊C₄	—	3	1	no	—
295	C₃×C₂²⋊C₄	—	3	2	no	—
296	C₃×C₂²⋊C₄	—	3	2	no	—
297	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
298	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
299	C₃×C₄²	—	3	1	no	—
300	#217	C₂²×C₉	1	2	yes	complemented
301	#217	C₂²×C₉	1	2	yes	complemented
302	#217	C₂²×C₉	1	1	yes	characteristic, complemented
303	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
304	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
305	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
306	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
307	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
308	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
309	C₂²×C₃²	—	2	1	no	—
310	C₂²×C₃²	—	2	1	no	—
311	C₂²×C₃²	—	2	2	no	—
312	C₂²×C₃²	—	2	1	no	—
313	C₂²×C₃²	—	2	2	no	—
314	C₂²×C₃²	—	2	2	no	—
315	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
316	C₂×C₃×D₃	—	2	1	no	—
317	C₂×C₃×D₃	—	2	2	no	—
318	C₂×C₃×D₃	—	2	2	no	—
319	C₂×C₃×D₃	—	2	1	no	—
320	C₂×C₃×D₃	—	4	8	no	—
321	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
322	C₂×C₃×D₃	C₃×#41	1	2	yes	—
323	C₃²×C₄	—	2	1	no	—
324	C₃²×C₄	—	2	2	no	—
325	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
326	C₃×Dic₃	—	2	2	no	—
327	C₃×Dic₃	—	2	1	no	—
328	C₃×Dic₃	—	2	1	no	—
329	C₃×Dic₃	—	2	1	no	—
330	C₂²×C₉	—	2	2	no	—
331	C₂²×C₉	—	2	1	no	—
332	C₂²×C₉	—	2	2	no	—
333	C₂²×C₉	—	2	1	no	—
334	C₂²×C₉	—	2	2	no	—
335	C₂²×C₉	—	2	1	no	—
336	C₂²×C₉	—	2	2	no	—
337	C₂²×C₉	—	2	1	no	—
338	C₂²×C₉	—	3	4	no	—
339	C₂²×C₉	—	3	2	no	—
340	C₂²×C₉	—	4	1	no	—
341	C₂²×C₉	—	4	1	no	—
342	C₂²×C₉	—	4	2	no	—
343	C₂²×C₉	—	4	2	no	—
344	C₂²×C₉	—	4	2	no	—
345	C₂²×C₉	—	6	1	no	—
346	C₂²×C₉	—	6	2	no	—
347	C₂²×C₉	—	6	1	no	—
348	C₂²×C₉	—	6	2	no	—
349	C₂²×C₉	—	12	8	no	—
350	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
351	C₄×C₉	—	2	1	no	—
352	C₄×C₉	—	2	2	no	—
353	C₄×C₉	—	2	2	no	—
354	C₄×C₉	—	4	1	no	—
355	C₄×C₉	—	4	2	no	—
356	C₄×C₉	—	6	1	no	—
357	C₄×C₉	—	6	2	no	—
358	C₄×C₉	—	6	1	no	—
359	C₄×C₉	—	6	1	no	—
360	C₄×C₉	D₃×D₄	1	2	yes	—
361	C₂×#41	—	3	1	no	—
362	C₂²×D₄	—	3	1	no	—
363	#124	—	3	1	no	—
364	#123	—	3	2	no	—
365	C₂²⋊Q₈	—	3	1	no	—
366	#121	—	3	2	no	—
367	#121	D₃×C₉	1	1	yes	characteristic, complemented
368	#120	—	3	2	no	—
369	C₄×D₄	—	3	1	no	—
370	C₄×D₄	—	3	1	no	—
371	C₂×C₂²⋊C₄	—	3	2	no	—
372	C₃×C₉	#546	1	1	yes	characteristic, complemented, Sylow
373	C₂³×C₃	—	2	1	no	—
374	C₂³×C₃	—	2	2	no	—
375	C₂³×C₃	—	3	1	no	—
376	C₂³×C₃	—	3	2	no	—
377	C₂³×C₃	—	6	4	no	—
378	C₂³×C₃	—	6	4	no	—
379	C₂³×C₃	—	12	2	no	—
380	C₂³×C₃	C₂³×C₉	1	2	yes	—
381	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
382	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
383	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
384	C₂²×D₃	—	2	4	no	—
385	C₂²×D₃	—	2	4	no	—
386	C₂²×D₃	—	4	2	no	—
387	C₂²×D₃	C₂³×C₉	1	2	yes	—
388	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
389	C₃×Q₈	—	6	2	no	—
390	C₃×D₄	—	2	2	no	—
391	C₃×D₄	—	2	2	no	—
392	C₃×D₄	—	3	4	no	—
393	C₃×D₄	—	4	2	no	—
394	C₃×D₄	—	4	2	no	—
395	C₃×D₄	—	4	2	no	—
396	C₃×D₄	—	4	4	no	—
397	C₃×D₄	—	6	2	no	—
398	C₃×D₄	—	6	4	no	—
399	C₃×D₄	—	6	4	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	3	1	no	—
406	C₂×C₃×C₄	—	3	1	no	—
407	C₂×C₃×C₄	—	3	2	no	—
408	C₂×C₃×C₄	—	3	1	no	—
409	C₂×C₃×C₄	—	4	2	no	—
410	C₂×C₃×C₄	—	6	4	no	—
411	C₂×C₃×C₄	—	6	2	no	—
412	C₂×C₃×C₄	—	12	2	no	—
413	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
415	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
417	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
419	#67	—	2	4	no	—
420	#67	—	2	4	no	—
421	#67	—	2	2	no	—
422	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
423	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
424	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
425	C₂×Dic₃	C₂³×C₉	1	2	yes	—
426	D₁₂	D₄×C₉	1	4	yes	complemented
427	C₄×D₃	—	2	4	no	—
428	C₄×D₃	—	2	2	no	—
429	C₄×D₃	—	4	2	no	—
430	Dic₆	—	2	2	no	—
431	C₂×C₃²	—	4	1	no	—
432	C₂×C₃²	—	4	2	no	—
433	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
434	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
435	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
436	C₃×D₃	—	2	2	no	—
437	C₃×D₃	—	2	4	no	—
438	C₂×C₉	—	2	1	no	—
439	C₂×C₉	—	2	1	no	—
440	C₂×C₉	—	2	1	no	—
441	C₂×C₉	—	4	2	no	—
442	C₂×C₉	—	4	1	no	—
443	C₂×C₉	—	4	2	no	—
444	C₂×C₉	—	6	4	no	—
445	C₂×C₉	—	6	2	no	—
446	C₂×C₉	—	8	2	no	—
447	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
448	C₂×C₉	#1004	1	1	yes	characteristic
449	C₂×C₉	D₃×#41	1	1	yes	characteristic
450	C₂⁴	—	3	2	no	—
451	#41	—	6	4	no	—
452	C₂×Q₈	—	3	1	no	—
453	C₂×D₄	—	3	1	no	—
454	C₂×D₄	—	3	2	no	—
455	C₂×D₄	—	3	2	no	—
456	C₂×D₄	—	3	1	no	—
457	C₂×D₄	—	6	4	no	—
458	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
459	C₂×D₄	C₂×D₃×C₉	1	2	yes	complemented
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	3	1	no	—
462	C₂²×C₄	—	3	2	no	—
463	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	3	2	no	—
466	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
467	C₂²⋊C₄	—	3	2	no	—
468	C₂²⋊C₄	—	3	1	no	—
469	C₂²⋊C₄	—	3	2	no	—
470	C₂²⋊C₄	—	3	1	no	—
471	C₂²⋊C₄	—	3	2	no	—
472	C₂²⋊C₄	—	3	2	no	—
473	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
474	C₄²	—	3	1	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	2	no	—
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	2	2	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	2	2	no	—
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	2	2	no	—
486	C₂²×C₃	—	2	1	no	—
487	C₂²×C₃	—	2	2	no	—
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	3	4	no	—
490	C₂²×C₃	—	3	2	no	—
491	C₂²×C₃	—	4	1	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	4	2	no	—
494	C₂²×C₃	—	4	2	no	—
495	C₂²×C₃	—	4	2	no	—
496	C₂²×C₃	—	6	1	no	—
497	C₂²×C₃	—	6	2	no	—
498	C₂²×C₃	—	6	1	no	—
499	C₂²×C₃	—	6	2	no	—
500	C₂²×C₃	—	12	8	no	—
501	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
502	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
503	C₂×D₃	—	2	1	no	—
504	C₂×D₃	—	2	2	no	—
505	C₂×D₃	—	2	2	no	—
506	C₂×D₃	—	2	1	no	—
507	C₂×D₃	—	4	8	no	—
508	C₂×D₃	C₂×D₄×C₉	1	4	yes	—
509	C₂×D₃	C₉×#41	1	2	yes	complemented
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	2	2	no	—
514	C₃×C₄	—	2	2	no	—
515	C₃×C₄	—	4	1	no	—
516	C₃×C₄	—	4	2	no	—
517	C₃×C₄	—	6	1	no	—
518	C₃×C₄	—	6	2	no	—
519	C₃×C₄	—	6	1	no	—
520	C₃×C₄	—	6	1	no	—
521	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
522	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
523	Dic₃	—	2	2	no	—
524	Dic₃	—	2	1	no	—
525	Dic₃	—	2	1	no	—
526	Dic₃	—	2	1	no	—
527	C₃²	C₃×#546	1	1	yes	characteristic
528	C₉	—	2	1	no	—
529	C₉	#5612	1	1	yes	characteristic, direct product factor
530	C₂³	—	3	1	no	—
531	C₂³	—	3	2	no	—
532	C₂³	—	6	4	no	—
533	C₂³	—	6	4	no	—
534	C₂³	—	12	2	no	—
535	C₂³	C₂²×D₃×C₉	1	2	yes	—
536	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
537	Q₈	—	6	2	no	—
538	D₄	—	2	2	no	—
539	D₄	—	3	4	no	—
540	D₄	—	4	2	no	—
541	D₄	—	6	4	no	—
542	D₄	—	6	4	no	—
543	D₄	—	6	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	3	1	no	—
546	C₂×C₄	—	3	1	no	—
547	C₂×C₄	—	3	2	no	—
548	C₂×C₄	—	3	1	no	—
549	C₂×C₄	—	6	4	no	—
550	C₂×C₄	—	6	2	no	—
551	C₂×C₄	—	12	2	no	—
552	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
553	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
555	C₂×C₃	—	2	1	no	—
556	C₂×C₃	—	2	1	no	—
557	C₂×C₃	—	2	1	no	—
558	C₂×C₃	—	4	2	no	—
559	C₂×C₃	—	4	2	no	—
560	C₂×C₃	—	4	1	no	—
561	C₂×C₃	—	4	2	no	—
562	C₂×C₃	—	4	1	no	—
563	C₂×C₃	—	6	2	no	—
564	C₂×C₃	—	6	4	no	—
565	C₂×C₃	—	8	2	no	—
566	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
567	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
568	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
570	C₂×C₃	C₃×#1004	1	1	yes	characteristic
571	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
572	D₃	—	2	2	no	—
573	D₃	—	2	4	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	3	4	no	—
581	C₂²	—	3	2	no	—
582	C₂²	—	6	1	no	—
583	C₂²	—	6	2	no	—
584	C₂²	—	6	1	no	—
585	C₂²	—	6	2	no	—
586	C₂²	—	12	8	no	—
587	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
588	C₄	—	2	1	no	—
589	C₄	—	2	2	no	—
590	C₄	—	6	1	no	—
591	C₄	—	6	2	no	—
592	C₄	—	6	1	no	—
593	C₄	—	6	1	no	—
594	C₄	D₃×D₄×C₉	1	2	yes	—
595	C₃	—	2	1	no	—
596	C₃	C₉×#546	1	1	yes	characteristic, complemented
597	C₃	C₃×#5612	1	1	yes	characteristic
598	C₂	—	4	2	no	—
599	C₂	—	4	1	no	—
600	C₂	—	6	2	no	—
601	C₂	—	6	4	no	—
602	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
603	C₂	C₉×#1004	1	1	yes	characteristic
604	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×C₉×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5612	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×D₄×C₉	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₃×C₉×#121	C₂	semidirect
4. C₉×#938	C₂	semidirect
5. C₉×#937	C₂	semidirect
6. C₉×#936	C₂	semidirect
7. C₄×C₉×#67	C₂	semidirect
8. C₉×#897	C₂	semidirect
9. C₉×#893	C₂	semidirect
10. C₉×#883	C₂	semidirect
11. D₃×C₉×C₂²⋊C₄	C₂	semidirect
16. C₂×C₃×D₄×C₉	C₂²	semidirect
17. C₂²×C₃×C₄×C₉	C₂²	semidirect
20. C₂×C₉×#67	C₂²	semidirect
25. C₂×C₄×D₃×C₉	C₂²	semidirect
26. C₂×C₄×D₃×C₉	C₂²	semidirect
27. C₂×C₉×Dic₆	C₂²	semidirect
28. C₃×C₉×C₄⋊C₄	C₂²	semidirect
29. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
30. C₉×#217	C₂²	semidirect
31. C₉×#217	C₂²	semidirect
32. C₉×#217	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×C₄⋊Dic₃	C₂²	semidirect
37. C₉×Dic₃⋊C₄	C₂²	semidirect
38. C₄×C₉×Dic₃	C₂²	semidirect
57. C₉×#121	D₃	semidirect
82. C₉×D₁₂	D₄	semidirect
88. #5612	C₉	direct (N × H)
125. C₂×D₄×C₉	C₂×D₃	semidirect
130. C₂²×C₄×C₉	C₂×D₃	semidirect
134. C₉×C₄⋊C₄	C₂×D₃	semidirect
142. C₉×C₂²⋊C₄	C₂×D₃	semidirect
157. C₂×D₃×C₉	#41	semidirect
167. C₂×D₃×D₄	C₂×C₉	semidirect
168. C₂×#235	C₂×C₉	semidirect
174. C₃×#121	C₂×C₉	semidirect
180. #938	C₂×C₉	semidirect
181. #937	C₂×C₉	semidirect
182. #936	C₂×C₉	semidirect
183. C₄×#67	C₂×C₉	semidirect
184. #897	C₂×C₉	semidirect
185. #893	C₂×C₉	semidirect
186. #883	C₂×C₉	semidirect
187. D₃×C₂²⋊C₄	C₂×C₉	semidirect
266. C₂×C₃×D₄	C₂²×C₉	semidirect
273. C₂²×C₃×C₄	C₂²×C₉	semidirect
277. C₂×#67	C₂²×C₉	semidirect
282. C₂×C₄×D₃	C₂²×C₉	semidirect
283. C₂×C₄×D₃	C₂²×C₉	semidirect
284. C₂×Dic₆	C₂²×C₉	semidirect
288. C₃×C₄⋊C₄	C₂²×C₉	semidirect
297. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
300. #217	C₂²×C₉	semidirect
301. #217	C₂²×C₉	semidirect
302. #217	C₂²×C₉	semidirect
305. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
306. C₄⋊Dic₃	C₂²×C₉	semidirect
307. Dic₃⋊C₄	C₂²×C₉	semidirect
308. C₄×Dic₃	C₂²×C₉	semidirect
367. #121	D₃×C₉	semidirect
372. C₃×C₉	#546	semidirect
426. D₁₂	D₄×C₉	semidirect
459. C₂×D₄	C₂×D₃×C₉	semidirect
463. C₂²×C₄	C₂×D₃×C₉	semidirect
466. C₄⋊C₄	C₂×D₃×C₉	semidirect
473. C₂²⋊C₄	C₂×D₃×C₉	semidirect
509. C₂×D₃	C₉×#41	semidirect
529. C₉	#5612	direct (N × H)
596. C₃	C₉×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄×C₉	2
C₂×C₉×#235	2
C₃×C₉×#121	2
C₉×#938	2
C₉×#937	2
C₉×#936	2
C₄×C₉×#67	2
C₉×#897	2
C₉×#893	2
C₉×#883	2
D₃×C₉×C₂²⋊C₄	2
C₃×#5612	3
C₉×#546	3

Subgroups — C9×#5612 #13152831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5612 #13152831