Subgroups — C₉×#5676 #13153102

Order 1728.

1078 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#239	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#938	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#884	C₂	1	2	yes	maximal, complemented
7	C₉×#883	C₂	1	2	yes	maximal, complemented
8	C₉×#882	C₂	1	2	yes	maximal, complemented
9	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5676	C₃	1	1	yes	maximal, characteristic
13	C₉×#546	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	2	yes	—
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂×C₉×#67	C₂²	1	2	yes	complemented
19	C₉×#239	—	2	4	no	—
20	D₃×D₄×C₉	—	2	4	no	—
21	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₉×D₁₂	C₂²	1	2	yes	complemented
24	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
27	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
28	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
30	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
31	C₉×#217	C₂²	1	2	yes	complemented
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
41	C₃²×#124	C₂×C₃	1	1	yes	characteristic
42	C₃×#946	C₂×C₃	1	1	yes	characteristic
43	C₃×#938	C₂×C₃	1	1	yes	characteristic
44	C₃×#884	C₂×C₃	1	2	yes	—
45	C₃×#883	C₂×C₃	1	2	yes	—
46	C₃×#882	C₂×C₃	1	2	yes	—
47	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
48	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
49	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
50	C₂×C₉×#41	—	3	1	no	—
51	C₂²×D₄×C₉	—	3	1	no	—
52	C₉×#124	—	2	1	no	—
53	C₉×#124	D₃	1	1	yes	characteristic, complemented
54	C₉×#123	—	3	2	no	—
55	C₉×C₂²⋊Q₈	—	3	1	no	—
56	C₉×#121	—	3	1	no	—
57	C₉×#121	—	3	2	no	—
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	C₂²×D₃×C₉	—	2	4	no	—
64	C₂²×D₃×C₉	—	2	4	no	—
65	C₂²×D₃×C₉	—	4	2	no	—
66	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
67	C₂²×D₃×C₉	C₂³	1	2	yes	—
68	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
69	C₃×Q₈×C₉	—	2	2	no	—
70	C₃×D₄×C₉	—	2	2	no	—
71	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
73	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₉×#67	—	2	4	no	—
76	C₉×#67	—	4	2	no	—
77	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₉×Dic₃	C₂³	1	2	yes	—
80	C₉×D₁₂	—	2	4	no	—
81	C₉×D₁₂	—	2	2	no	—
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	—	2	2	no	—
86	C₄×D₃×C₉	—	4	2	no	—
87	C₃×#546	—	3	1	no	—
88	#5676	C₉	1	1	yes	characteristic, direct product factor
89	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
90	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
93	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
94	C₃×#239	—	2	4	no	—
95	C₃×D₃×D₄	—	2	4	no	—
96	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
102	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
103	C₂⁴×C₉	—	3	2	no	—
104	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
105	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
107	C₃×#217	C₂²×C₃	1	2	yes	—
108	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
110	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
113	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
114	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
115	C₉×#41	—	6	4	no	—
116	C₂×Q₈×C₉	—	2	1	no	—
117	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
118	C₂×D₄×C₉	—	2	1	no	—
119	C₂×D₄×C₉	—	3	2	no	—
120	C₂×D₄×C₉	—	3	2	no	—
121	C₂×D₄×C₉	—	3	1	no	—
122	C₂×D₄×C₉	—	3	1	no	—
123	C₂×D₄×C₉	—	3	2	no	—
124	C₂×D₄×C₉	—	6	4	no	—
125	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
126	C₂²×C₄×C₉	—	3	2	no	—
127	C₂²×C₄×C₉	—	3	1	no	—
128	C₂²×C₄×C₉	—	3	1	no	—
129	C₂²×C₄×C₉	—	3	2	no	—
130	C₉×C₄⋊C₄	—	3	1	no	—
131	C₉×C₄⋊C₄	—	3	1	no	—
132	C₉×C₄⋊C₄	—	3	2	no	—
133	C₉×C₂²⋊C₄	—	2	2	no	—
134	C₉×C₂²⋊C₄	—	2	2	no	—
135	C₉×C₂²⋊C₄	—	3	2	no	—
136	C₉×C₂²⋊C₄	—	3	1	no	—
137	C₉×C₂²⋊C₄	—	3	2	no	—
138	C₉×C₂²⋊C₄	—	3	2	no	—
139	C₉×C₂²⋊C₄	—	3	1	no	—
140	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
141	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
142	C₄²×C₉	—	2	1	no	—
143	C₄²×C₉	C₂×D₃	1	1	yes	characteristic, complemented
144	C₂²×C₃×C₉	—	2	2	no	—
145	C₂²×C₃×C₉	—	2	2	no	—
146	C₂²×C₃×C₉	—	2	2	no	—
147	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
148	C₂×D₃×C₉	—	2	1	no	—
149	C₂×D₃×C₉	—	2	2	no	—
150	C₂×D₃×C₉	—	2	2	no	—
151	C₂×D₃×C₉	—	2	1	no	—
152	C₂×D₃×C₉	—	2	1	no	—
153	C₂×D₃×C₉	—	2	1	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	2	no	—
159	C₃×C₄×C₉	—	2	1	no	—
160	C₃×C₄×C₉	—	2	1	no	—
161	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
162	C₉×Dic₃	—	2	1	no	—
163	C₉×Dic₃	—	2	1	no	—
164	C₉×Dic₃	—	2	2	no	—
165	C₂×C₃×#41	—	3	1	no	—
166	C₂²×C₃×D₄	—	3	1	no	—
167	C₂×#239	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic, complemented
169	C₃×#124	—	2	1	no	—
170	C₃×#124	C₂×C₉	1	1	yes	characteristic, complemented
171	C₃×#124	C₃×D₃	1	1	yes	characteristic
172	C₃×#123	—	3	2	no	—
173	C₃×C₂²⋊Q₈	—	3	1	no	—
174	C₃×#121	—	3	1	no	—
175	C₃×#121	—	3	2	no	—
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	#946	C₂×C₉	1	1	yes	characteristic, complemented
181	#938	C₂×C₉	1	1	yes	characteristic, complemented
182	#884	C₂×C₉	1	2	yes	complemented
183	#883	C₂×C₉	1	2	yes	complemented
184	#882	C₂×C₉	1	2	yes	complemented
185	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	complemented
186	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
187	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
188	C₂³×C₃²	C₂³×C₃	1	2	yes	—
189	C₂²×C₃×D₃	—	2	4	no	—
190	C₂²×C₃×D₃	—	2	4	no	—
191	C₂²×C₃×D₃	—	4	2	no	—
192	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
193	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
194	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
195	C₃²×Q₈	—	2	2	no	—
196	C₃²×D₄	—	2	2	no	—
197	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
198	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₃×#67	—	2	4	no	—
202	C₃×#67	—	4	2	no	—
203	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
205	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
206	C₃×D₁₂	—	2	4	no	—
207	C₃×D₁₂	—	2	2	no	—
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	—	2	2	no	—
212	C₃×C₄×D₃	—	4	2	no	—
213	C₂³×C₉	—	2	2	no	—
214	C₂³×C₉	—	3	1	no	—
215	C₂³×C₉	—	3	2	no	—
216	C₂³×C₉	—	3	1	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	Q₈×C₉	—	2	2	no	—
222	Q₈×C₉	—	4	2	no	—
223	D₄×C₉	—	2	2	no	—
224	D₄×C₉	—	3	4	no	—
225	D₄×C₉	—	4	2	no	—
226	D₄×C₉	—	6	2	no	—
227	D₄×C₉	—	6	4	no	—
228	D₄×C₉	—	6	4	no	—
229	D₄×C₉	—	12	2	no	—
230	C₂×C₄×C₉	—	2	1	no	—
231	C₂×C₄×C₉	—	2	1	no	—
232	C₂×C₄×C₉	—	2	1	no	—
233	C₂×C₄×C₉	—	2	2	no	—
234	C₂×C₄×C₉	—	3	2	no	—
235	C₂×C₄×C₉	—	3	1	no	—
236	C₂×C₄×C₉	—	3	1	no	—
237	C₂×C₄×C₉	—	6	4	no	—
238	C₂×C₄×C₉	—	6	2	no	—
239	C₂×C₄×C₉	—	6	2	no	—
240	C₂×C₄×C₉	—	12	2	no	—
241	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
242	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
243	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
244	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
245	#546	—	3	1	no	Sylow
246	C₂×C₃×C₉	—	4	2	no	—
247	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
250	D₃×C₉	—	2	2	no	—
251	D₃×C₉	—	2	4	no	—
252	D₃×C₉	—	4	1	no	—
253	C₂⁴×C₃	—	3	2	no	—
254	C₂³×D₃	C₂²×C₉	1	2	yes	—
255	C₃×#41	—	6	4	no	—
256	C₂×C₃×Q₈	—	2	1	no	—
257	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
258	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
259	C₂×C₃×D₄	—	2	1	no	—
260	C₂×C₃×D₄	—	3	2	no	—
261	C₂×C₃×D₄	—	3	2	no	—
262	C₂×C₃×D₄	—	3	1	no	—
263	C₂×C₃×D₄	—	3	1	no	—
264	C₂×C₃×D₄	—	3	2	no	—
265	C₂×C₃×D₄	—	6	4	no	—
266	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
267	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
268	C₂²×C₃×C₄	—	3	2	no	—
269	C₂²×C₃×C₄	—	3	1	no	—
270	C₂²×C₃×C₄	—	3	1	no	—
271	C₂²×C₃×C₄	—	3	2	no	—
272	C₂×#67	C₂²×C₉	1	2	yes	—
273	C₂×#67	C₂²×C₉	1	2	yes	complemented
274	#239	—	2	4	no	—
275	D₃×D₄	—	2	4	no	—
276	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
277	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
278	C₂×D₁₂	C₂²×C₉	1	2	yes	complemented
279	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
280	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
281	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
282	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
283	C₃×C₄⋊C₄	—	3	2	no	—
284	C₃×C₄⋊C₄	—	3	1	no	—
285	C₃×C₄⋊C₄	—	3	1	no	—
286	C₃×C₂²⋊C₄	—	2	2	no	—
287	C₃×C₂²⋊C₄	—	2	2	no	—
288	C₃×C₂²⋊C₄	—	3	2	no	—
289	C₃×C₂²⋊C₄	—	3	1	no	—
290	C₃×C₂²⋊C₄	—	3	2	no	—
291	C₃×C₂²⋊C₄	—	3	2	no	—
292	C₃×C₂²⋊C₄	—	3	1	no	—
293	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
294	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
295	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
296	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
297	C₃×C₄²	—	2	1	no	—
298	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
299	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
300	#217	C₂²×C₉	1	2	yes	complemented
301	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
302	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
303	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
304	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
305	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
306	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
307	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
308	C₂²×C₃²	—	2	2	no	—
309	C₂²×C₃²	—	2	2	no	—
310	C₂²×C₃²	—	2	2	no	—
311	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
312	C₂×C₃×D₃	—	2	1	no	—
313	C₂×C₃×D₃	—	2	2	no	—
314	C₂×C₃×D₃	—	2	2	no	—
315	C₂×C₃×D₃	—	2	1	no	—
316	C₂×C₃×D₃	—	2	1	no	—
317	C₂×C₃×D₃	—	2	1	no	—
318	C₂×C₃×D₃	—	2	1	no	—
319	C₂×C₃×D₃	—	4	8	no	—
320	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
321	C₂×C₃×D₃	C₃×#41	1	2	yes	—
322	C₃²×C₄	—	2	2	no	—
323	C₃²×C₄	—	2	1	no	—
324	C₃²×C₄	—	2	1	no	—
325	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
326	C₃×Dic₃	—	2	1	no	—
327	C₃×Dic₃	—	2	1	no	—
328	C₃×Dic₃	—	2	2	no	—
329	C₂²×C₉	—	2	2	no	—
330	C₂²×C₉	—	2	2	no	—
331	C₂²×C₉	—	2	2	no	—
332	C₂²×C₉	—	2	1	no	—
333	C₂²×C₉	—	3	4	no	—
334	C₂²×C₉	—	3	2	no	—
335	C₂²×C₉	—	4	2	no	—
336	C₂²×C₉	—	4	2	no	—
337	C₂²×C₉	—	4	2	no	—
338	C₂²×C₉	—	6	1	no	—
339	C₂²×C₉	—	6	2	no	—
340	C₂²×C₉	—	6	2	no	—
341	C₂²×C₉	—	6	1	no	—
342	C₂²×C₉	—	6	1	no	—
343	C₂²×C₉	—	6	1	no	—
344	C₂²×C₉	—	6	1	no	—
345	C₂²×C₉	—	12	8	no	—
346	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
347	C₄×C₉	—	2	2	no	—
348	C₄×C₉	—	2	1	no	—
349	C₄×C₉	—	2	1	no	—
350	C₄×C₉	—	2	2	no	—
351	C₄×C₉	—	4	1	no	—
352	C₄×C₉	—	4	1	no	—
353	C₄×C₉	—	4	2	no	—
354	C₄×C₉	—	6	1	no	—
355	C₄×C₉	—	6	1	no	—
356	C₄×C₉	—	6	2	no	—
357	C₄×C₉	D₃×D₄	1	2	yes	—
358	C₂×#41	—	3	1	no	—
359	C₂²×D₄	—	3	1	no	—
360	#124	D₃×C₉	1	1	yes	characteristic, complemented
361	#123	—	3	2	no	—
362	C₂²⋊Q₈	—	3	1	no	—
363	#121	—	3	1	no	—
364	#121	—	3	2	no	—
365	#120	—	3	2	no	—
366	C₄×D₄	—	3	1	no	—
367	C₄×D₄	—	3	1	no	—
368	C₂×C₂²⋊C₄	—	3	2	no	—
369	C₃×C₉	#546	1	1	yes	characteristic, complemented, Sylow
370	C₂³×C₃	—	2	2	no	—
371	C₂³×C₃	—	3	1	no	—
372	C₂³×C₃	—	3	2	no	—
373	C₂³×C₃	—	3	1	no	—
374	C₂³×C₃	—	6	4	no	—
375	C₂³×C₃	—	6	4	no	—
376	C₂³×C₃	—	12	2	no	—
377	C₂³×C₃	C₂³×C₉	1	2	yes	—
378	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
379	C₂²×D₃	—	2	4	no	—
380	C₂²×D₃	—	2	4	no	—
381	C₂²×D₃	—	4	2	no	—
382	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
383	C₂²×D₃	C₂³×C₉	1	2	yes	—
384	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
385	C₃×Q₈	—	2	2	no	—
386	C₃×Q₈	—	2	2	no	—
387	C₃×Q₈	—	4	2	no	—
388	C₃×D₄	—	2	2	no	—
389	C₃×D₄	—	2	2	no	—
390	C₃×D₄	—	3	4	no	—
391	C₃×D₄	—	4	2	no	—
392	C₃×D₄	—	6	2	no	—
393	C₃×D₄	—	6	4	no	—
394	C₃×D₄	—	6	4	no	—
395	C₃×D₄	—	12	2	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	3	2	no	—
401	C₂×C₃×C₄	—	3	1	no	—
402	C₂×C₃×C₄	—	3	1	no	—
403	C₂×C₃×C₄	—	6	4	no	—
404	C₂×C₃×C₄	—	6	2	no	—
405	C₂×C₃×C₄	—	6	2	no	—
406	C₂×C₃×C₄	—	12	2	no	—
407	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
408	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
414	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
415	#67	—	2	4	no	—
416	#67	—	4	2	no	—
417	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
418	C₂×Dic₃	C₂³×C₉	1	2	yes	—
419	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
420	D₁₂	—	2	4	no	—
421	D₁₂	—	2	2	no	—
422	D₁₂	D₄×C₉	1	4	yes	complemented
423	C₄×D₃	—	2	4	no	—
424	C₄×D₃	—	2	2	no	—
425	C₄×D₃	—	2	2	no	—
426	C₄×D₃	—	4	2	no	—
427	C₂×C₃²	—	4	2	no	—
428	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
429	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
430	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
431	C₃×D₃	—	2	2	no	—
432	C₃×D₃	—	2	4	no	—
433	C₃×D₃	—	4	1	no	—
434	C₂×C₉	—	2	1	no	—
435	C₂×C₉	—	2	1	no	—
436	C₂×C₉	—	2	1	no	—
437	C₂×C₉	—	4	2	no	—
438	C₂×C₉	—	6	4	no	—
439	C₂×C₉	—	6	2	no	—
440	C₂×C₉	—	8	2	no	—
441	C₂×C₉	—	12	1	no	—
442	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
443	C₂×C₉	D₃×#41	1	1	yes	characteristic
444	C₂×C₉	#1009	1	1	yes	characteristic
445	C₂⁴	—	3	2	no	—
446	#41	—	6	4	no	—
447	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
448	C₂×D₄	—	3	2	no	—
449	C₂×D₄	—	3	2	no	—
450	C₂×D₄	—	3	1	no	—
451	C₂×D₄	—	3	1	no	—
452	C₂×D₄	—	3	2	no	—
453	C₂×D₄	—	6	4	no	—
454	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
455	C₂²×C₄	—	3	2	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	—	3	2	no	—
459	C₄⋊C₄	—	3	1	no	—
460	C₄⋊C₄	—	3	1	no	—
461	C₄⋊C₄	—	3	2	no	—
462	C₂²⋊C₄	—	3	2	no	—
463	C₂²⋊C₄	—	3	1	no	—
464	C₂²⋊C₄	—	3	2	no	—
465	C₂²⋊C₄	—	3	2	no	—
466	C₂²⋊C₄	—	3	1	no	—
467	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
468	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
469	C₄²	C₂×D₃×C₉	1	1	yes	characteristic, complemented
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	3	4	no	—
478	C₂²×C₃	—	3	2	no	—
479	C₂²×C₃	—	4	2	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	4	2	no	—
482	C₂²×C₃	—	6	1	no	—
483	C₂²×C₃	—	6	2	no	—
484	C₂²×C₃	—	6	2	no	—
485	C₂²×C₃	—	6	1	no	—
486	C₂²×C₃	—	6	1	no	—
487	C₂²×C₃	—	6	1	no	—
488	C₂²×C₃	—	6	1	no	—
489	C₂²×C₃	—	12	8	no	—
490	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
491	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
492	C₂×D₃	—	2	1	no	—
493	C₂×D₃	—	2	2	no	—
494	C₂×D₃	—	2	2	no	—
495	C₂×D₃	—	2	1	no	—
496	C₂×D₃	—	2	1	no	—
497	C₂×D₃	—	2	1	no	—
498	C₂×D₃	—	2	1	no	—
499	C₂×D₃	—	4	8	no	—
500	C₂×D₃	C₂×D₄×C₉	1	4	yes	—
501	C₂×D₃	C₉×#41	1	2	yes	complemented
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	2	1	no	—
505	C₃×C₄	—	2	2	no	—
506	C₃×C₄	—	2	1	no	—
507	C₃×C₄	—	2	1	no	—
508	C₃×C₄	—	2	2	no	—
509	C₃×C₄	—	4	2	no	—
510	C₃×C₄	—	4	1	no	—
511	C₃×C₄	—	4	1	no	—
512	C₃×C₄	—	6	1	no	—
513	C₃×C₄	—	6	1	no	—
514	C₃×C₄	—	6	2	no	—
515	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
516	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
517	Dic₃	—	2	1	no	—
518	Dic₃	—	2	1	no	—
519	Dic₃	—	2	2	no	—
520	C₃²	C₃×#546	1	1	yes	characteristic
521	C₉	—	2	1	no	—
522	C₉	#5676	1	1	yes	characteristic, direct product factor
523	C₂³	—	3	1	no	—
524	C₂³	—	3	2	no	—
525	C₂³	—	3	1	no	—
526	C₂³	—	6	4	no	—
527	C₂³	—	6	4	no	—
528	C₂³	—	12	2	no	—
529	C₂³	C₂²×D₃×C₉	1	2	yes	—
530	Q₈	—	2	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	3	4	no	—
533	D₄	—	6	4	no	—
534	D₄	—	6	2	no	—
535	D₄	—	6	4	no	—
536	D₄	—	12	2	no	—
537	C₂×C₄	—	3	2	no	—
538	C₂×C₄	—	3	1	no	—
539	C₂×C₄	—	3	1	no	—
540	C₂×C₄	—	6	4	no	—
541	C₂×C₄	—	6	2	no	—
542	C₂×C₄	—	6	2	no	—
543	C₂×C₄	—	12	2	no	—
544	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
547	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
548	C₂×C₃	—	2	1	no	—
549	C₂×C₃	—	2	1	no	—
550	C₂×C₃	—	2	1	no	—
551	C₂×C₃	—	4	2	no	—
552	C₂×C₃	—	4	2	no	—
553	C₂×C₃	—	6	2	no	—
554	C₂×C₃	—	6	4	no	—
555	C₂×C₃	—	8	2	no	—
556	C₂×C₃	—	12	1	no	—
557	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
558	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
559	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
560	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
561	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
562	C₂×C₃	C₃×#1009	1	1	yes	characteristic
563	D₃	—	2	2	no	—
564	D₃	—	2	4	no	—
565	D₃	—	4	1	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	3	4	no	—
570	C₂²	—	3	2	no	—
571	C₂²	—	6	1	no	—
572	C₂²	—	6	2	no	—
573	C₂²	—	6	2	no	—
574	C₂²	—	6	1	no	—
575	C₂²	—	6	1	no	—
576	C₂²	—	6	1	no	—
577	C₂²	—	6	1	no	—
578	C₂²	—	12	8	no	—
579	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	6	1	no	—
584	C₄	—	6	1	no	—
585	C₄	—	6	2	no	—
586	C₄	D₃×D₄×C₉	1	2	yes	—
587	C₃	—	2	1	no	—
588	C₃	C₉×#546	1	1	yes	characteristic, complemented
589	C₃	C₃×#5676	1	1	yes	characteristic
590	C₂	—	4	2	no	—
591	C₂	—	6	2	no	—
592	C₂	—	6	4	no	—
593	C₂	—	12	1	no	—
594	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
595	C₂	D₃×C₉×#41	1	1	yes	characteristic
596	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×#124	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5676	C₃
hypercenter	C₉×#124	D₃
hypocenter	C₃	C₉×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#239	C₂	semidirect
2. C₂×D₃×D₄×C₉	C₂	semidirect
3. C₃×C₉×#124	C₂	semidirect
4. C₉×#946	C₂	semidirect
5. C₉×#938	C₂	semidirect
6. C₉×#884	C₂	semidirect
7. C₉×#883	C₂	semidirect
8. C₉×#882	C₂	semidirect
9. D₃×C₉×C₂²⋊C₄	C₂	semidirect
10. C₄×C₉×D₁₂	C₂	semidirect
11. C₄×C₉×D₁₂	C₂	semidirect
15. C₂×C₃×Q₈×C₉	C₂²	semidirect
18. C₂×C₉×#67	C₂²	semidirect
23. C₂×C₉×D₁₂	C₂²	semidirect
25. C₂×C₄×D₃×C₉	C₂²	semidirect
26. C₂×C₄×D₃×C₉	C₂²	semidirect
27. C₂×C₄×D₃×C₉	C₂²	semidirect
28. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
29. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
30. C₃×C₄²×C₉	C₂²	semidirect
31. C₉×#217	C₂²	semidirect
34. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×C₄⋊Dic₃	C₂²	semidirect
37. C₉×C₄⋊Dic₃	C₂²	semidirect
38. C₉×Dic₃⋊C₄	C₂²	semidirect
53. C₉×#124	D₃	semidirect
82. C₉×D₁₂	D₄	semidirect
88. #5676	C₉	direct (N × H)
117. C₂×Q₈×C₉	C₂×D₃	semidirect
140. C₉×C₂²⋊C₄	C₂×D₃	semidirect
141. C₉×C₂²⋊C₄	C₂×D₃	semidirect
143. C₄²×C₉	C₂×D₃	semidirect
157. C₂×D₃×C₉	#41	semidirect
167. C₂×#239	C₂×C₉	semidirect
168. C₂×D₃×D₄	C₂×C₉	semidirect
170. C₃×#124	C₂×C₉	semidirect
180. #946	C₂×C₉	semidirect
181. #938	C₂×C₉	semidirect
182. #884	C₂×C₉	semidirect
183. #883	C₂×C₉	semidirect
184. #882	C₂×C₉	semidirect
185. D₃×C₂²⋊C₄	C₂×C₉	semidirect
186. C₄×D₁₂	C₂×C₉	semidirect
187. C₄×D₁₂	C₂×C₉	semidirect
257. C₂×C₃×Q₈	C₂²×C₉	semidirect
273. C₂×#67	C₂²×C₉	semidirect
278. C₂×D₁₂	C₂²×C₉	semidirect
280. C₂×C₄×D₃	C₂²×C₉	semidirect
281. C₂×C₄×D₃	C₂²×C₉	semidirect
282. C₂×C₄×D₃	C₂²×C₉	semidirect
293. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
294. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
298. C₃×C₄²	C₂²×C₉	semidirect
300. #217	C₂²×C₉	semidirect
303. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
304. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
305. C₄⋊Dic₃	C₂²×C₉	semidirect
306. C₄⋊Dic₃	C₂²×C₉	semidirect
307. Dic₃⋊C₄	C₂²×C₉	semidirect
360. #124	D₃×C₉	semidirect
369. C₃×C₉	#546	semidirect
422. D₁₂	D₄×C₉	semidirect
447. C₂×Q₈	C₂×D₃×C₉	semidirect
467. C₂²⋊C₄	C₂×D₃×C₉	semidirect
468. C₂²⋊C₄	C₂×D₃×C₉	semidirect
469. C₄²	C₂×D₃×C₉	semidirect
501. C₂×D₃	C₉×#41	semidirect
522. C₉	#5676	direct (N × H)
588. 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×C₉×#239	2
C₂×D₃×D₄×C₉	2
C₃×C₉×#124	2
C₉×#946	2
C₉×#938	2
C₉×#884	2
C₉×#883	2
C₉×#882	2
D₃×C₉×C₂²⋊C₄	2
C₄×C₉×D₁₂	2
C₃×#5676	3
C₉×#546	3

Subgroups — C9×#5676 #13153102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5676 #13153102