Subgroups — C₃×#10589727 #13152898

Order 1728.

650 conjugacy classes of subgroups.

The subgroup lattice has 460 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
2	C₃×Q₈×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63506	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63488	C₂	1	1	yes	maximal, characteristic
5	C₃×#63486	C₂	1	1	yes	maximal, characteristic
6	C₃×#63452	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#63452	C₂	1	2	yes	maximal, complemented
8	C₃×#63451	C₂	1	2	yes	maximal, complemented
9	C₃×#63449	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63441	C₂	1	2	yes	maximal
11	C₃×#63441	C₂	1	2	yes	maximal
12	C₃×#5625	—	3	1	no	maximal
13	#10589727	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₃×#3676	C₂²	1	2	yes	—
21	C₃×#3676	C₂²	1	1	yes	characteristic
22	C₃×#3676	C₂²	1	1	yes	characteristic
23	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
24	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
27	C₃×C₄⋊Dic₉	C₂²	1	2	yes	—
28	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
29	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
30	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
31	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
32	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
33	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
34	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic
35	C₃×C₄×Dic₉	C₂²	1	2	yes	—
36	C₃×C₄×Dic₉	C₂²	1	2	yes	—
37	C₃²×C₂²⋊Q₈	D₃	1	1	yes	characteristic
38	C₃×Q₈×Dic₃	—	3	1	no	—
39	C₃×#944	—	3	1	no	—
40	C₃×#926	—	3	1	no	—
41	C₃×#924	—	3	1	no	—
42	C₃×#890	—	3	2	no	—
43	C₃×#890	—	3	1	no	—
44	C₃×#889	—	3	2	no	—
45	C₃×#887	—	3	1	no	—
46	C₃×#879	—	3	2	no	—
47	C₃×#879	—	3	2	no	—
48	C₉×C₂²⋊Q₈	—	2	1	no	—
49	C₉×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
50	Q₈×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
51	#63506	C₂×C₃	1	1	yes	characteristic, complemented
52	#63488	C₂×C₃	1	1	yes	characteristic
53	#63486	C₂×C₃	1	1	yes	characteristic
54	#63452	C₂×C₃	1	1	yes	characteristic, complemented
55	#63452	C₂×C₃	1	2	yes	complemented
56	#63451	C₂×C₃	1	2	yes	complemented
57	#63449	C₂×C₃	1	1	yes	characteristic, complemented
58	#63441	C₂×C₃	1	2	yes	—
59	#63441	C₂×C₃	1	2	yes	—
60	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
61	C₃×Q₈×C₉	—	2	2	no	—
62	C₂×C₃×C₄×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
65	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₉	C₂³	1	2	yes	—
68	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
71	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
72	C₂×C₃×Dic₉	C₂³	1	2	yes	—
73	C₃×Dic₁₈	—	2	2	no	—
74	C₃×#541	—	9	1	no	—
75	#5625	—	3	1	no	—
76	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
78	C₂×C₃×Dic₆	—	3	1	no	—
79	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
80	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
81	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
82	C₃×#217	—	3	2	no	—
83	C₃×#217	—	3	1	no	—
84	C₃×#217	—	3	1	no	—
85	C₃×C₄⋊Dic₃	—	3	2	no	—
86	C₃×C₄⋊Dic₃	—	3	2	no	—
87	C₃×C₄⋊Dic₃	—	3	1	no	—
88	C₃×C₄⋊Dic₃	—	3	1	no	—
89	C₃×C₄⋊Dic₃	—	3	1	no	—
90	C₃×Dic₃⋊C₄	—	3	2	no	—
91	C₃×Dic₃⋊C₄	—	3	2	no	—
92	C₃×Dic₃⋊C₄	—	3	2	no	—
93	C₃×Dic₃⋊C₄	—	3	2	no	—
94	C₃×Dic₃⋊C₄	—	3	2	no	—
95	C₃×C₄×Dic₃	—	3	2	no	—
96	C₃×C₄×Dic₃	—	3	2	no	—
97	C₃×C₄×Dic₃	—	3	1	no	—
98	C₃×C₄×Dic₃	—	3	1	no	—
99	C₂×Q₈×C₉	—	2	1	no	—
100	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
101	C₂²×C₄×C₉	—	2	1	no	—
102	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
103	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
104	C₉×C₄⋊C₄	—	2	1	no	—
105	C₉×C₄⋊C₄	—	2	2	no	—
106	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
108	C₉×C₂²⋊C₄	—	2	2	no	—
109	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
110	#3676	C₂²×C₃	1	1	yes	characteristic
111	#3676	C₂²×C₃	1	1	yes	characteristic
112	#3676	C₂²×C₃	1	2	yes	—
113	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
114	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
115	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
116	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
117	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
118	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
119	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
120	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
121	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
122	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
123	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
124	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
125	C₄×Dic₉	C₂²×C₃	1	2	yes	—
126	C₄×Dic₉	C₂²×C₃	1	2	yes	—
127	C₂²×C₃×C₉	—	2	1	no	—
128	C₂²×C₃×C₉	—	2	1	no	—
129	C₂²×C₃×C₉	—	2	1	no	—
130	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
131	C₃×C₄×C₉	—	2	1	no	—
132	C₃×C₄×C₉	—	2	2	no	—
133	C₃×C₄×C₉	—	2	2	no	—
134	C₃×C₄×C₉	#41	1	2	yes	—
135	C₃×Dic₉	—	2	2	no	—
136	C₃×Dic₉	—	2	1	no	—
137	C₃×Dic₉	—	2	1	no	—
138	C₃×Dic₉	—	2	2	no	—
139	C₃×Dic₉	—	2	1	no	—
140	C₃×Dic₉	—	2	1	no	—
141	C₃×C₄⋊Q₈	—	9	1	no	—
142	C₃×#126	—	9	2	no	—
143	C₃×#126	—	9	2	no	—
144	C₃×#125	—	9	2	no	—
145	C₃×#125	—	9	1	no	—
146	C₃×#125	—	9	2	no	—
147	C₃×C₂²⋊Q₈	—	2	1	no	—
148	C₃×C₂²⋊Q₈	—	9	1	no	—
149	C₃×C₂²⋊Q₈	D₉	1	1	yes	characteristic
150	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
151	C₃×C₄×Q₈	—	9	1	no	—
152	C₃×C₄×Q₈	—	9	1	no	—
153	C₃×#117	—	9	1	no	—
154	Q₈×Dic₃	—	3	1	no	—
155	#944	—	3	1	no	—
156	#926	—	3	1	no	—
157	#924	—	3	1	no	—
158	#890	—	3	2	no	—
159	#890	—	3	1	no	—
160	#889	—	3	2	no	—
161	#887	—	3	1	no	—
162	#879	—	3	2	no	—
163	#879	—	3	2	no	—
164	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
165	C₃²×Q₈	—	2	2	no	—
166	C₂×C₃²×C₄	—	2	2	no	—
167	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
168	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
169	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
171	C₂×C₃×Dic₃	—	3	1	no	—
172	C₂×C₃×Dic₃	—	3	1	no	—
173	C₂×C₃×Dic₃	—	3	1	no	—
174	C₂×C₃×Dic₃	—	3	2	no	—
175	C₂×C₃×Dic₃	—	3	2	no	—
176	C₂×C₃×Dic₃	—	3	1	no	—
177	C₃×Dic₆	—	6	2	no	—
178	C₂³×C₉	—	2	1	no	—
179	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
180	Q₈×C₉	—	2	2	no	—
181	Q₈×C₉	—	4	2	no	—
182	C₂×C₄×C₉	—	2	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	—	4	2	no	—
188	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
189	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
190	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
192	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
193	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
194	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
195	C₂×Dic₉	C₂³×C₃	1	2	yes	—
196	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
197	C₂×Dic₉	C₂³×C₃	1	2	yes	—
198	Dic₁₈	—	2	2	no	—
199	#541	—	9	1	no	Sylow
200	C₂×C₃×C₉	—	4	1	no	—
201	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×C₃×Q₈	—	2	1	no	—
205	C₂×C₃×Q₈	—	9	1	no	—
206	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
207	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
208	C₂²×C₃×C₄	—	2	1	no	—
209	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
211	C₂×Dic₆	—	3	1	no	—
212	C₃×C₄⋊C₄	—	2	1	no	—
213	C₃×C₄⋊C₄	—	2	2	no	—
214	C₃×C₄⋊C₄	—	9	2	no	—
215	C₃×C₄⋊C₄	—	9	2	no	—
216	C₃×C₄⋊C₄	—	9	2	no	—
217	C₃×C₄⋊C₄	—	9	2	no	—
218	C₃×C₄⋊C₄	—	9	2	no	—
219	C₃×C₄⋊C₄	—	9	1	no	—
220	C₃×C₄⋊C₄	—	9	1	no	—
221	C₃×C₄⋊C₄	—	9	1	no	—
222	C₃×C₄⋊C₄	—	9	2	no	—
223	C₃×C₄⋊C₄	—	9	2	no	—
224	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
225	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
226	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
227	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
228	C₃×C₂²⋊C₄	—	2	2	no	—
229	C₃×C₂²⋊C₄	—	9	1	no	—
230	C₃×C₂²⋊C₄	—	9	1	no	—
231	C₃×C₂²⋊C₄	—	9	2	no	—
232	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	—
233	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
234	C₃×C₄²	—	9	1	no	—
235	C₃×C₄²	—	9	1	no	—
236	C₃×C₄²	—	9	2	no	—
237	C₃×C₄²	—	9	2	no	—
238	#217	—	3	2	no	—
239	#217	—	3	1	no	—
240	#217	—	3	1	no	—
241	C₄⋊Dic₃	—	3	2	no	—
242	C₄⋊Dic₃	—	3	2	no	—
243	C₄⋊Dic₃	—	3	1	no	—
244	C₄⋊Dic₃	—	3	1	no	—
245	C₄⋊Dic₃	—	3	1	no	—
246	Dic₃⋊C₄	—	3	2	no	—
247	Dic₃⋊C₄	—	3	2	no	—
248	Dic₃⋊C₄	—	3	2	no	—
249	Dic₃⋊C₄	—	3	2	no	—
250	Dic₃⋊C₄	—	3	2	no	—
251	C₄×Dic₃	—	3	2	no	—
252	C₄×Dic₃	—	3	2	no	—
253	C₄×Dic₃	—	3	1	no	—
254	C₄×Dic₃	—	3	1	no	—
255	C₂²×C₃²	—	2	1	no	—
256	C₂²×C₃²	—	2	1	no	—
257	C₂²×C₃²	—	2	1	no	—
258	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
259	C₃²×C₄	—	2	1	no	—
260	C₃²×C₄	—	2	2	no	—
261	C₃²×C₄	—	2	2	no	—
262	C₃²×C₄	#237	1	2	yes	—
263	C₃×Dic₃	—	6	2	no	—
264	C₃×Dic₃	—	6	1	no	—
265	C₃×Dic₃	—	6	2	no	—
266	C₃×Dic₃	—	6	1	no	—
267	C₃×Dic₃	—	6	1	no	—
268	C₃×Dic₃	—	6	1	no	—
269	C₂²×C₉	—	2	2	no	—
270	C₂²×C₉	—	2	1	no	—
271	C₂²×C₉	—	2	1	no	—
272	C₂²×C₉	—	2	1	no	—
273	C₂²×C₉	—	2	1	no	—
274	C₂²×C₉	—	4	1	no	—
275	C₂²×C₉	—	4	1	no	—
276	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
277	C₄×C₉	—	2	1	no	—
278	C₄×C₉	—	2	2	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	2	no	—
281	C₄×C₉	—	4	2	no	—
282	C₄×C₉	—	4	1	no	—
283	C₄×C₉	—	4	2	no	—
284	C₄×C₉	C₃×#41	1	2	yes	—
285	Dic₉	—	2	2	no	—
286	Dic₉	—	2	1	no	—
287	Dic₉	—	2	1	no	—
288	Dic₉	—	2	2	no	—
289	Dic₉	—	2	1	no	—
290	Dic₉	—	2	1	no	—
291	C₄⋊Q₈	—	9	1	no	—
292	#126	—	9	2	no	—
293	#126	—	9	2	no	—
294	#125	—	9	2	no	—
295	#125	—	9	1	no	—
296	#125	—	9	2	no	—
297	C₂²⋊Q₈	—	9	1	no	—
298	C₂²⋊Q₈	C₃×D₉	1	1	yes	characteristic
299	C₄×Q₈	—	9	1	no	—
300	C₄×Q₈	—	9	1	no	—
301	#117	—	9	1	no	—
302	C₃×C₉	#541	1	1	yes	characteristic, complemented, Sylow
303	C₂³×C₃	—	2	1	no	—
304	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
305	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
306	C₃×Q₈	—	2	2	no	—
307	C₃×Q₈	—	2	2	no	—
308	C₃×Q₈	—	4	2	no	—
309	C₃×Q₈	—	18	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	1	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	4	2	no	—
317	C₂×C₃×C₄	—	9	1	no	—
318	C₂×C₃×C₄	—	9	1	no	—
319	C₂×C₃×C₄	—	9	1	no	—
320	C₂×C₃×C₄	—	9	2	no	—
321	C₂×C₃×C₄	—	9	1	no	—
322	C₂×C₃×C₄	—	9	2	no	—
323	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
324	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
325	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
328	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
330	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
331	C₂×Dic₃	—	3	1	no	—
332	C₂×Dic₃	—	3	1	no	—
333	C₂×Dic₃	—	3	1	no	—
334	C₂×Dic₃	—	3	2	no	—
335	C₂×Dic₃	—	3	2	no	—
336	C₂×Dic₃	—	3	1	no	—
337	Dic₆	—	6	2	no	—
338	C₂×C₃²	—	4	1	no	—
339	C₂×C₃²	C₂×#237	1	1	yes	characteristic
340	C₂×C₃²	#1007	1	1	yes	characteristic
341	C₂×C₃²	#1010	1	1	yes	characteristic
342	C₂×C₉	—	2	1	no	—
343	C₂×C₉	—	2	1	no	—
344	C₂×C₉	—	2	1	no	—
345	C₂×C₉	—	4	2	no	—
346	C₂×C₉	—	4	1	no	—
347	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
348	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
349	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
350	C₂×Q₈	—	9	1	no	—
351	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
353	C₄⋊C₄	—	9	1	no	—
354	C₄⋊C₄	—	9	1	no	—
355	C₄⋊C₄	—	9	1	no	—
356	C₄⋊C₄	—	9	2	no	—
357	C₄⋊C₄	—	9	2	no	—
358	C₄⋊C₄	—	9	2	no	—
359	C₄⋊C₄	—	9	2	no	—
360	C₄⋊C₄	—	9	2	no	—
361	C₄⋊C₄	—	9	2	no	—
362	C₄⋊C₄	—	9	2	no	—
363	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic
364	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
365	C₂²⋊C₄	—	9	1	no	—
366	C₂²⋊C₄	—	9	1	no	—
367	C₂²⋊C₄	—	9	2	no	—
368	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	—
369	C₄²	—	9	1	no	—
370	C₄²	—	9	1	no	—
371	C₄²	—	9	2	no	—
372	C₄²	—	9	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	2	1	no	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	2	1	no	—
380	C₂²×C₃	—	2	1	no	—
381	C₂²×C₃	—	4	1	no	—
382	C₂²×C₃	—	4	1	no	—
383	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
384	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	2	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	4	1	no	—
393	C₃×C₄	—	4	2	no	—
394	C₃×C₄	—	4	2	no	—
395	C₃×C₄	—	18	2	no	—
396	C₃×C₄	—	18	1	no	—
397	C₃×C₄	—	18	1	no	—
398	C₃×C₄	—	18	2	no	—
399	C₃×C₄	—	18	1	no	—
400	C₃×C₄	—	18	1	no	—
401	C₃×C₄	#3699	1	2	yes	—
402	C₃×C₄	C₃×#237	1	2	yes	—
403	Dic₃	—	6	2	no	—
404	Dic₃	—	6	1	no	—
405	Dic₃	—	6	2	no	—
406	Dic₃	—	6	1	no	—
407	Dic₃	—	6	1	no	—
408	Dic₃	—	6	1	no	—
409	C₃²	#5625	1	1	yes	characteristic
410	C₉	—	2	1	no	—
411	C₉	C₃×#541	1	1	yes	characteristic, complemented
412	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
413	Q₈	—	2	2	no	—
414	Q₈	—	18	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	9	1	no	—
417	C₂×C₄	—	9	1	no	—
418	C₂×C₄	—	9	1	no	—
419	C₂×C₄	—	9	2	no	—
420	C₂×C₄	—	9	1	no	—
421	C₂×C₄	—	9	2	no	—
422	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
423	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
424	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
426	C₂×C₃	—	2	1	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	4	2	no	—
430	C₂×C₃	—	4	1	no	—
431	C₂×C₃	—	4	1	no	—
432	C₂×C₃	C₂×#3699	1	1	yes	characteristic
433	C₂×C₃	#63713	1	1	yes	characteristic
434	C₂×C₃	#63716	1	1	yes	characteristic
435	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
436	C₂×C₃	C₃×#1007	1	1	yes	characteristic
437	C₂×C₃	C₃×#1010	1	1	yes	characteristic
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	18	2	no	—
446	C₄	—	18	1	no	—
447	C₄	—	18	1	no	—
448	C₄	—	18	2	no	—
449	C₄	—	18	1	no	—
450	C₄	—	18	1	no	—
451	C₄	C₃×#3699	1	2	yes	—
452	C₃	—	2	1	no	—
453	C₃	#10589727	1	1	yes	characteristic, direct product factor
454	C₃	C₃×#5625	1	1	yes	characteristic
455	C₂	—	4	1	no	—
456	C₂	C₂×C₃×#3699	1	1	yes	characteristic
457	C₂	C₃×#63713	1	1	yes	characteristic
458	C₂	C₃×#63716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₂²⋊Q₈	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂³×C₃²	C₂²×D₃
hypercenter	C₃×C₂²⋊Q₈	D₉
hypocenter	C₉	C₃×#541
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₃×Q₈×Dic₉	C₂	semidirect
3. C₃×#63506	C₂	semidirect
6. C₃×#63452	C₂	semidirect
7. C₃×#63452	C₂	semidirect
8. C₃×#63451	C₂	semidirect
9. C₃×#63449	C₂	semidirect
13. #10589727	C₃	direct (N × H)
50. Q₈×Dic₉	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
54. #63452	C₂×C₃	semidirect
55. #63452	C₂×C₃	semidirect
56. #63451	C₂×C₃	semidirect
57. #63449	C₂×C₃	semidirect
302. C₃×C₉	#541	semidirect
411. C₉	C₃×#541	semidirect
453. C₃	#10589727	direct (N × H)

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
C₃×Q₈×Dic₉	2
C₃×#63506	2
C₃×#63488	2
C₃×#63486	2
C₃×#63452	2
C₃×#63451	2
C₃×#63449	2
C₃×#63441	2
C₃×#5625	3
#10589727	3

Subgroups — C3×#10589727 #13152898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589727 #13152898