Subgroups — C₉×#5634 #13152931

Order 1728.

800 conjugacy classes of subgroups.

The subgroup lattice has 478 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	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#897	C₂	1	2	yes	maximal, complemented
6	C₉×#896	C₂	1	2	yes	maximal, complemented
7	C₉×#896	C₂	1	2	yes	maximal, complemented
8	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal
9	C₉×#878	C₂	1	2	yes	maximal, complemented
10	C₃×#5634	C₃	1	1	yes	maximal, characteristic
11	C₉×#543	—	3	1	no	maximal
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₉×Dic₆	C₂²	1	2	yes	complemented
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₉×#217	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, complemented
29	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
32	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
33	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
34	C₃×#946	C₂×C₃	1	2	yes	—
35	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
36	C₃×#924	C₂×C₃	1	1	yes	characteristic
37	C₃×#897	C₂×C₃	1	2	yes	—
38	C₃×#896	C₂×C₃	1	2	yes	—
39	C₃×#896	C₂×C₃	1	2	yes	—
40	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
41	C₃×#878	C₂×C₃	1	2	yes	—
42	C₉×C₂²⋊Q₈	—	2	1	no	—
43	C₉×C₂²⋊Q₈	—	3	2	no	—
44	C₉×C₂²⋊Q₈	—	3	1	no	—
45	C₉×C₂²⋊Q₈	—	3	2	no	—
46	C₉×C₂²⋊Q₈	—	3	2	no	—
47	C₉×C₂²⋊Q₈	—	3	2	no	—
48	C₉×C₂²⋊Q₈	—	3	2	no	—
49	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
50	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
51	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
52	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
53	C₂²×D₃×C₉	—	4	1	no	—
54	C₂²×D₃×C₉	—	4	1	no	—
55	C₂²×D₃×C₉	Q₈	1	4	yes	complemented
56	C₂²×D₃×C₉	C₂³	1	2	yes	—
57	C₃×Q₈×C₉	—	4	1	no	—
58	C₂×C₃×C₄×C₉	—	4	1	no	—
59	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
62	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
63	C₂×C₉×Dic₃	—	4	1	no	—
64	C₂×C₉×Dic₃	C₂³	1	2	yes	—
65	C₂×C₉×Dic₃	C₂³	1	2	yes	—
66	C₂×C₉×Dic₃	C₂³	1	2	yes	—
67	C₄×D₃×C₉	—	4	2	no	—
68	C₄×D₃×C₉	—	4	2	no	—
69	C₉×Dic₆	—	4	1	no	—
70	C₉×Dic₆	—	4	2	no	—
71	C₃×#543	—	3	1	no	—
72	#5634	C₉	1	1	yes	characteristic, direct product factor
73	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
78	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
79	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
80	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
81	C₂⁴×C₉	—	3	1	no	—
82	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
85	C₃×#217	C₂²×C₃	1	2	yes	—
86	C₃×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
91	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
92	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
93	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
94	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×Q₈×C₉	—	2	1	no	—
96	C₂×Q₈×C₉	—	3	1	no	—
97	C₂×Q₈×C₉	—	3	2	no	—
98	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
99	C₂²×C₄×C₉	—	2	1	no	—
100	C₂²×C₄×C₉	—	3	1	no	—
101	C₂²×C₄×C₉	—	3	2	no	—
102	C₂²×C₄×C₉	—	3	2	no	—
103	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
104	C₉×C₄⋊C₄	—	2	1	no	—
105	C₉×C₄⋊C₄	—	2	2	no	—
106	C₉×C₄⋊C₄	—	3	2	no	—
107	C₉×C₄⋊C₄	—	3	2	no	—
108	C₉×C₄⋊C₄	—	3	2	no	—
109	C₉×C₄⋊C₄	—	3	1	no	—
110	C₉×C₄⋊C₄	—	3	2	no	—
111	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
112	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
113	C₉×C₂²⋊C₄	—	2	2	no	—
114	C₉×C₂²⋊C₄	—	3	2	no	—
115	C₉×C₂²⋊C₄	—	3	2	no	—
116	C₉×C₂²⋊C₄	—	3	2	no	—
117	C₉×C₂²⋊C₄	—	3	2	no	—
118	C₉×C₂²⋊C₄	—	3	2	no	—
119	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
120	C₂²×C₃×C₉	—	2	1	no	—
121	C₂²×C₃×C₉	—	2	1	no	—
122	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	—
123	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
124	C₂×D₃×C₉	—	2	2	no	—
125	C₂×D₃×C₉	—	2	2	no	—
126	C₂×D₃×C₉	—	4	4	no	—
127	C₂×D₃×C₉	C₂×Q₈	1	4	yes	—
128	C₃×C₄×C₉	—	2	1	no	—
129	C₃×C₄×C₉	—	2	2	no	—
130	C₃×C₄×C₉	—	2	1	no	—
131	C₃×C₄×C₉	—	2	2	no	—
132	C₉×Dic₃	—	2	2	no	—
133	C₉×Dic₃	—	2	2	no	—
134	C₉×Dic₃	—	2	2	no	—
135	C₃×C₂²⋊Q₈	—	2	1	no	—
136	C₃×C₂²⋊Q₈	—	3	2	no	—
137	C₃×C₂²⋊Q₈	—	3	1	no	—
138	C₃×C₂²⋊Q₈	—	3	2	no	—
139	C₃×C₂²⋊Q₈	—	3	2	no	—
140	C₃×C₂²⋊Q₈	—	3	2	no	—
141	C₃×C₂²⋊Q₈	—	3	2	no	—
142	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
143	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
144	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
145	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
146	#946	C₂×C₉	1	2	yes	complemented
147	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic
148	#924	C₂×C₉	1	1	yes	characteristic, complemented
149	#897	C₂×C₉	1	2	yes	complemented
150	#896	C₂×C₉	1	2	yes	complemented
151	#896	C₂×C₉	1	2	yes	complemented
152	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	—
153	#878	C₂×C₉	1	2	yes	complemented
154	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
155	C₂²×C₃×D₃	—	4	1	no	—
156	C₂²×C₃×D₃	—	4	1	no	—
157	C₂²×C₃×D₃	C₃×Q₈	1	4	yes	—
158	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
159	C₃²×Q₈	—	4	1	no	—
160	C₂×C₃²×C₄	—	4	1	no	—
161	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
162	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
163	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
164	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₃×Dic₃	—	4	1	no	—
166	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
167	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
168	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
169	C₃×C₄×D₃	—	4	2	no	—
170	C₃×C₄×D₃	—	4	2	no	—
171	C₃×Dic₆	—	4	1	no	—
172	C₃×Dic₆	—	4	2	no	—
173	C₂³×C₉	—	2	1	no	—
174	C₂³×C₉	—	3	2	no	—
175	C₂³×C₉	—	3	4	no	—
176	C₂³×C₉	—	12	1	no	—
177	C₂³×C₉	—	12	1	no	—
178	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
179	Q₈×C₉	—	4	1	no	—
180	Q₈×C₉	—	4	2	no	—
181	Q₈×C₉	—	12	1	no	—
182	Q₈×C₉	—	12	2	no	—
183	C₂×C₄×C₉	—	2	1	no	—
184	C₂×C₄×C₉	—	2	2	no	—
185	C₂×C₄×C₉	—	2	2	no	—
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	3	2	no	—
188	C₂×C₄×C₉	—	3	2	no	—
189	C₂×C₄×C₉	—	3	2	no	—
190	C₂×C₄×C₉	—	4	1	no	—
191	C₂×C₄×C₉	—	4	2	no	—
192	C₂×C₄×C₉	—	12	2	no	—
193	C₂×C₄×C₉	—	12	2	no	—
194	C₂×C₄×C₉	—	12	1	no	—
195	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
196	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
198	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
199	#543	—	3	1	no	Sylow
200	C₂×C₃×C₉	—	2	2	no	—
201	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
202	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
204	D₃×C₉	—	2	4	no	—
205	C₂⁴×C₃	—	3	1	no	—
206	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
207	C₂×C₃×Q₈	—	2	1	no	—
208	C₂×C₃×Q₈	—	3	1	no	—
209	C₂×C₃×Q₈	—	3	2	no	—
210	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
211	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
212	C₂²×C₃×C₄	—	2	1	no	—
213	C₂²×C₃×C₄	—	3	1	no	—
214	C₂²×C₃×C₄	—	3	2	no	—
215	C₂²×C₃×C₄	—	3	2	no	—
216	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
218	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
219	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
220	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
221	C₂×Dic₆	C₂²×C₉	1	2	yes	complemented
222	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
223	C₃×C₄⋊C₄	—	2	1	no	—
224	C₃×C₄⋊C₄	—	2	2	no	—
225	C₃×C₄⋊C₄	—	3	2	no	—
226	C₃×C₄⋊C₄	—	3	2	no	—
227	C₃×C₄⋊C₄	—	3	2	no	—
228	C₃×C₄⋊C₄	—	3	1	no	—
229	C₃×C₄⋊C₄	—	3	2	no	—
230	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
231	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
232	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
233	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
234	C₃×C₂²⋊C₄	—	2	2	no	—
235	C₃×C₂²⋊C₄	—	3	2	no	—
236	C₃×C₂²⋊C₄	—	3	2	no	—
237	C₃×C₂²⋊C₄	—	3	2	no	—
238	C₃×C₂²⋊C₄	—	3	2	no	—
239	C₃×C₂²⋊C₄	—	3	2	no	—
240	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
241	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
242	#217	C₂²×C₉	1	2	yes	—
243	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
244	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
245	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
246	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
247	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
248	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
249	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
250	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
251	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
252	C₂²×C₃²	—	2	1	no	—
253	C₂²×C₃²	—	2	1	no	—
254	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	—
255	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
256	C₂×C₃×D₃	—	2	2	no	—
257	C₂×C₃×D₃	—	2	2	no	—
258	C₂×C₃×D₃	—	4	4	no	—
259	C₂×C₃×D₃	C₂×C₃×Q₈	1	4	yes	—
260	C₃²×C₄	—	2	1	no	—
261	C₃²×C₄	—	2	2	no	—
262	C₃²×C₄	—	2	1	no	—
263	C₃²×C₄	—	2	2	no	—
264	C₃×Dic₃	—	2	2	no	—
265	C₃×Dic₃	—	2	2	no	—
266	C₃×Dic₃	—	2	2	no	—
267	C₂²×C₉	—	2	1	no	—
268	C₂²×C₉	—	2	1	no	—
269	C₂²×C₉	—	2	1	no	—
270	C₂²×C₉	—	2	2	no	—
271	C₂²×C₉	—	3	4	no	—
272	C₂²×C₉	—	4	1	no	—
273	C₂²×C₉	—	4	1	no	—
274	C₂²×C₉	—	6	2	no	—
275	C₂²×C₉	—	6	2	no	—
276	C₂²×C₉	—	12	4	no	—
277	C₂²×C₉	D₃×Q₈	1	2	yes	—
278	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	1	no	—
281	C₄×C₉	—	2	1	no	—
282	C₄×C₉	—	2	2	no	—
283	C₄×C₉	—	2	2	no	—
284	C₄×C₉	—	4	2	no	—
285	C₄×C₉	—	4	1	no	—
286	C₄×C₉	—	4	2	no	—
287	C₄×C₉	—	6	2	no	—
288	C₄×C₉	—	6	2	no	—
289	C₄×C₉	—	6	2	no	—
290	C₂²⋊Q₈	—	3	2	no	—
291	C₂²⋊Q₈	—	3	1	no	—
292	C₂²⋊Q₈	—	3	2	no	—
293	C₂²⋊Q₈	—	3	2	no	—
294	C₂²⋊Q₈	—	3	2	no	—
295	C₂²⋊Q₈	—	3	2	no	—
296	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
297	C₂×C₂²⋊C₄	—	3	1	no	—
298	C₂×C₂²⋊C₄	—	3	2	no	—
299	C₃×C₉	#543	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₃	—	2	1	no	—
301	C₂³×C₃	—	3	2	no	—
302	C₂³×C₃	—	3	4	no	—
303	C₂³×C₃	—	12	1	no	—
304	C₂³×C₃	—	12	1	no	—
305	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
306	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
307	C₂²×D₃	—	4	1	no	—
308	C₂²×D₃	—	4	1	no	—
309	C₂²×D₃	Q₈×C₉	1	4	yes	complemented
310	C₂²×D₃	C₂³×C₉	1	2	yes	—
311	C₃×Q₈	—	4	1	no	—
312	C₃×Q₈	—	4	1	no	—
313	C₃×Q₈	—	4	2	no	—
314	C₃×Q₈	—	12	1	no	—
315	C₃×Q₈	—	12	2	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	3	2	no	—
321	C₂×C₃×C₄	—	3	2	no	—
322	C₂×C₃×C₄	—	3	2	no	—
323	C₂×C₃×C₄	—	4	1	no	—
324	C₂×C₃×C₄	—	4	1	no	—
325	C₂×C₃×C₄	—	4	2	no	—
326	C₂×C₃×C₄	—	12	2	no	—
327	C₂×C₃×C₄	—	12	2	no	—
328	C₂×C₃×C₄	—	12	1	no	—
329	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
331	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
332	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
333	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
336	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
337	C₂×Dic₃	—	4	1	no	—
338	C₂×Dic₃	C₂³×C₉	1	2	yes	—
339	C₂×Dic₃	C₂³×C₉	1	2	yes	—
340	C₂×Dic₃	C₂³×C₉	1	2	yes	—
341	C₄×D₃	—	4	2	no	—
342	C₄×D₃	—	4	2	no	—
343	Dic₆	—	4	1	no	—
344	Dic₆	—	4	2	no	—
345	C₂×C₃²	—	2	2	no	—
346	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
347	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
349	C₃×D₃	—	2	4	no	—
350	C₂×C₉	—	2	2	no	—
351	C₂×C₉	—	2	1	no	—
352	C₂×C₉	—	2	1	no	—
353	C₂×C₉	—	2	1	no	—
354	C₂×C₉	—	4	2	no	—
355	C₂×C₉	—	6	4	no	—
356	C₂×C₉	#1004	1	1	yes	characteristic
357	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
358	C₂×C₉	#1009	1	1	yes	characteristic
359	C₂⁴	—	3	1	no	—
360	C₂×Q₈	—	3	1	no	—
361	C₂×Q₈	—	3	2	no	—
362	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	3	2	no	—
365	C₂²×C₄	—	3	2	no	—
366	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
367	C₄⋊C₄	—	3	2	no	—
368	C₄⋊C₄	—	3	2	no	—
369	C₄⋊C₄	—	3	2	no	—
370	C₄⋊C₄	—	3	1	no	—
371	C₄⋊C₄	—	3	2	no	—
372	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
373	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
374	C₂²⋊C₄	—	3	2	no	—
375	C₂²⋊C₄	—	3	2	no	—
376	C₂²⋊C₄	—	3	2	no	—
377	C₂²⋊C₄	—	3	2	no	—
378	C₂²⋊C₄	—	3	2	no	—
379	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
380	C₂²×C₃	—	2	1	no	—
381	C₂²×C₃	—	2	1	no	—
382	C₂²×C₃	—	2	1	no	—
383	C₂²×C₃	—	2	1	no	—
384	C₂²×C₃	—	2	1	no	—
385	C₂²×C₃	—	2	2	no	—
386	C₂²×C₃	—	3	4	no	—
387	C₂²×C₃	—	4	1	no	—
388	C₂²×C₃	—	4	1	no	—
389	C₂²×C₃	—	6	2	no	—
390	C₂²×C₃	—	6	2	no	—
391	C₂²×C₃	—	12	4	no	—
392	C₂²×C₃	C₂×Q₈×C₉	1	2	yes	—
393	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
394	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
395	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
396	C₂×D₃	—	2	2	no	—
397	C₂×D₃	—	2	2	no	—
398	C₂×D₃	—	4	4	no	—
399	C₂×D₃	C₂×Q₈×C₉	1	4	yes	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	1	no	—
402	C₃×C₄	—	2	1	no	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	2	no	—
408	C₃×C₄	—	2	1	no	—
409	C₃×C₄	—	4	1	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	—	6	2	no	—
413	C₃×C₄	—	6	2	no	—
414	C₃×C₄	—	6	2	no	—
415	Dic₃	—	2	2	no	—
416	Dic₃	—	2	2	no	—
417	Dic₃	—	2	2	no	—
418	C₃²	C₃×#543	1	1	yes	characteristic
419	C₉	—	2	1	no	—
420	C₉	#5634	1	1	yes	characteristic, direct product factor
421	C₂³	—	3	2	no	—
422	C₂³	—	3	4	no	—
423	C₂³	—	12	1	no	—
424	C₂³	—	12	1	no	—
425	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
426	Q₈	—	4	1	no	—
427	Q₈	—	12	1	no	—
428	Q₈	—	12	2	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	3	2	no	—
431	C₂×C₄	—	3	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	12	2	no	—
434	C₂×C₄	—	12	2	no	—
435	C₂×C₄	—	12	1	no	—
436	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
439	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
440	C₂×C₃	—	2	2	no	—
441	C₂×C₃	—	2	2	no	—
442	C₂×C₃	—	2	1	no	—
443	C₂×C₃	—	2	1	no	—
444	C₂×C₃	—	2	1	no	—
445	C₂×C₃	—	4	2	no	—
446	C₂×C₃	—	6	4	no	—
447	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
448	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂×C₃	C₃×#1004	1	1	yes	characteristic
451	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
452	C₂×C₃	C₃×#1009	1	1	yes	characteristic
453	D₃	—	2	4	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	3	4	no	—
457	C₂²	—	6	2	no	—
458	C₂²	—	6	2	no	—
459	C₂²	—	12	4	no	—
460	C₂²	D₃×Q₈×C₉	1	2	yes	—
461	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	6	2	no	—
467	C₄	—	6	2	no	—
468	C₄	—	6	2	no	—
469	C₃	—	2	1	no	—
470	C₃	C₉×#543	1	1	yes	characteristic, complemented
471	C₃	C₃×#5634	1	1	yes	characteristic
472	C₂	—	2	2	no	—
473	C₂	—	6	4	no	—
474	C₂	C₉×#1004	1	1	yes	characteristic
475	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
476	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×C₂²⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂³×C₃×D₃	C₂²×C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₉×#543
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. C₉×#924	C₂	semidirect
5. C₉×#897	C₂	semidirect
6. C₉×#896	C₂	semidirect
7. C₉×#896	C₂	semidirect
9. C₉×#878	C₂	semidirect
13. C₂×C₃×Q₈×C₉	C₂²	semidirect
18. C₂×C₉×Dic₆	C₂²	semidirect
19. C₂×C₉×Dic₆	C₂²	semidirect
20. C₃×C₉×C₄⋊C₄	C₂²	semidirect
21. C₃×C₉×C₄⋊C₄	C₂²	semidirect
28. C₉×C₄⋊Dic₃	C₂²	semidirect
29. C₉×C₄⋊Dic₃	C₂²	semidirect
30. C₉×Dic₃⋊C₄	C₂²	semidirect
31. C₉×Dic₃⋊C₄	C₂²	semidirect
32. C₉×Dic₃⋊C₄	C₂²	semidirect
49. C₉×C₂²⋊Q₈	D₃	semidirect
55. C₂²×D₃×C₉	Q₈	semidirect
72. #5634	C₉	direct (N × H)
98. C₂×Q₈×C₉	C₂×D₃	semidirect
111. C₉×C₄⋊C₄	C₂×D₃	semidirect
112. C₉×C₄⋊C₄	C₂×D₃	semidirect
142. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
146. #946	C₂×C₉	semidirect
148. #924	C₂×C₉	semidirect
149. #897	C₂×C₉	semidirect
150. #896	C₂×C₉	semidirect
151. #896	C₂×C₉	semidirect
153. #878	C₂×C₉	semidirect
210. C₂×C₃×Q₈	C₂²×C₉	semidirect
221. C₂×Dic₆	C₂²×C₉	semidirect
222. C₂×Dic₆	C₂²×C₉	semidirect
230. C₃×C₄⋊C₄	C₂²×C₉	semidirect
231. C₃×C₄⋊C₄	C₂²×C₉	semidirect
247. C₄⋊Dic₃	C₂²×C₉	semidirect
248. C₄⋊Dic₃	C₂²×C₉	semidirect
249. Dic₃⋊C₄	C₂²×C₉	semidirect
250. Dic₃⋊C₄	C₂²×C₉	semidirect
251. Dic₃⋊C₄	C₂²×C₉	semidirect
296. C₂²⋊Q₈	D₃×C₉	semidirect
299. C₃×C₉	#543	semidirect
309. C₂²×D₃	Q₈×C₉	semidirect
362. C₂×Q₈	C₂×D₃×C₉	semidirect
372. C₄⋊C₄	C₂×D₃×C₉	semidirect
373. C₄⋊C₄	C₂×D₃×C₉	semidirect
420. C₉	#5634	direct (N × H)
470. C₃	C₉×#543	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
C₂×C₉×(C₂×D₃)⋊C₄	2
C₉×#924	2
C₉×#897	2
C₉×#896	2
D₃×C₉×C₂²⋊C₄	2
C₉×#878	2
C₃×#5634	3
C₉×#543	3

Subgroups — C9×#5634 #13152931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5634 #13152931