Subgroups — C₃²×#5680 #13179058

Order 1728.

1708 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#946	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×Q₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#938	C₂	1	1	yes	maximal, characteristic
5	C₃²×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#883	C₂	1	2	yes	maximal, complemented
7	C₃²×#67⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₃²×#879	C₂	1	2	yes	maximal, complemented
9	C₃²×#877	C₂	1	2	yes	maximal, complemented
10	C₃²×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#870	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#529	—	3	1	no	maximal
13	C₃×#5680	C₃	1	4	yes	maximal, direct product factor
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃²×#67	C₂²	1	2	yes	—
17	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
18	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
21	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃³×C₄²	C₂²	1	1	yes	characteristic
24	C₃²×#217	C₂²	1	2	yes	—
25	C₃²×#217	C₂²	1	2	yes	—
26	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
28	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
30	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
34	C₃²×C₄×Dic₃	C₂²	1	2	yes	—
35	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
36	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
37	C₃²×#126	—	3	2	no	—
38	C₃²×#125	—	3	1	no	—
39	C₃²×#124	—	2	4	no	—
40	C₃²×#124	D₃	1	1	yes	characteristic, complemented
41	C₃²×#124	C₂×C₃	1	4	yes	complemented
42	C₃²×#123	—	3	2	no	—
43	C₃²×C₂²⋊Q₈	—	3	1	no	—
44	C₃²×#121	—	3	1	no	—
45	C₃²×C₄×Q₈	—	3	1	no	—
46	C₃²×C₄×D₄	—	3	1	no	—
47	C₃²×C₄×D₄	—	3	2	no	—
48	C₃²×#117	—	3	2	no	—
49	C₂×C₃²×C₄²	—	3	1	no	—
50	C₃×#946	C₂×C₃	1	4	yes	complemented
51	C₃×Q₈×Dic₃	C₂×C₃	1	4	yes	complemented
52	C₃×#938	C₂×C₃	1	4	yes	—
53	C₃×D₄×Dic₃	C₂×C₃	1	4	yes	complemented
54	C₃×#883	C₂×C₃	1	8	yes	complemented
55	C₃×#67⋊C₄	C₂×C₃	1	8	yes	complemented
56	C₃×#879	C₂×C₃	1	8	yes	complemented
57	C₃×#877	C₂×C₃	1	8	yes	complemented
58	C₃×C₄²×D₃	C₂×C₃	1	4	yes	complemented
59	C₃×#870	C₂×C₃	1	4	yes	complemented
60	C₂³×C₃³	C₂³	1	2	yes	—
61	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
62	C₃³×Q₈	—	2	2	no	—
63	C₃³×D₄	—	2	2	no	—
64	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
65	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
66	C₂×C₃³×C₄	C₂³	1	2	yes	—
67	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
68	C₃²×#67	—	2	4	no	—
69	C₂×C₃²×Dic₃	—	2	4	no	—
70	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
73	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
74	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
75	C₃²×C₄×D₃	—	2	2	no	—
76	C₃²×C₄×D₃	—	2	2	no	—
77	C₃²×C₄×D₃	—	2	2	no	—
78	C₃×#529	—	3	4	no	—
79	#5680	C₃²	1	1	yes	characteristic, direct product factor
80	C₂×C₃²×Q₈	—	2	4	no	—
81	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
82	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
83	C₂×C₃²×D₄	—	2	4	no	—
84	C₂×C₃²×D₄	—	3	2	no	—
85	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
86	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
87	C₂²×C₃²×C₄	—	3	2	no	—
88	C₂²×C₃²×C₄	—	3	1	no	—
89	C₂²×C₃²×C₄	—	3	1	no	—
90	C₂²×C₃²×C₄	—	3	1	no	—
91	C₂×C₃×#67	C₂²×C₃	1	8	yes	—
92	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
93	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
94	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
95	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
96	C₃²×C₄⋊C₄	—	3	2	no	—
97	C₃²×C₄⋊C₄	—	3	2	no	—
98	C₃²×C₄⋊C₄	—	3	1	no	—
99	C₃²×C₄⋊C₄	—	3	2	no	—
100	C₃²×C₄⋊C₄	—	3	1	no	—
101	C₃²×C₄⋊C₄	—	3	2	no	—
102	C₃²×C₂²⋊C₄	—	2	8	no	—
103	C₃²×C₂²⋊C₄	—	2	8	no	—
104	C₃²×C₂²⋊C₄	—	3	2	no	—
105	C₃²×C₂²⋊C₄	—	3	2	no	—
106	C₃²×C₂²⋊C₄	—	3	2	no	—
107	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
108	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
109	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
110	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
111	C₃²×C₄²	—	2	4	no	—
112	C₃²×C₄²	—	3	1	no	—
113	C₃²×C₄²	—	3	1	no	—
114	C₃²×C₄²	—	3	1	no	—
115	C₃²×C₄²	—	3	2	no	—
116	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
117	C₃²×C₄²	C₂²×C₃	1	4	yes	—
118	C₃×#217	C₂²×C₃	1	8	yes	—
119	C₃×#217	C₂²×C₃	1	8	yes	—
120	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
121	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
122	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
123	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
124	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
125	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
126	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
127	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
128	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
129	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
130	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
131	C₂²×C₃³	—	2	2	no	—
132	C₂²×C₃³	—	2	2	no	—
133	C₂²×C₃³	—	2	2	no	—
134	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
135	C₂×C₃²×D₃	—	2	1	no	—
136	C₂×C₃²×D₃	—	2	1	no	—
137	C₂×C₃²×D₃	#41	1	2	yes	—
138	C₃³×C₄	—	2	1	no	—
139	C₃³×C₄	—	2	1	no	—
140	C₃³×C₄	—	2	2	no	—
141	C₃³×C₄	#41	1	2	yes	—
142	C₃²×Dic₃	—	2	1	no	—
143	C₃²×Dic₃	—	2	1	no	—
144	C₃²×Dic₃	—	2	2	no	—
145	C₃²×Dic₃	—	2	2	no	—
146	C₃²×Dic₃	#41	1	2	yes	—
147	C₃×#126	—	3	8	no	—
148	C₃×#125	—	3	4	no	—
149	C₃×#124	—	2	4	no	—
150	C₃×#124	C₃×D₃	1	4	yes	complemented
151	C₃×#124	C₂×C₃²	1	1	yes	characteristic, complemented
152	C₃×#123	—	3	8	no	—
153	C₃×C₂²⋊Q₈	—	3	4	no	—
154	C₃×#121	—	3	4	no	—
155	C₃×C₄×Q₈	—	3	4	no	—
156	C₃×C₄×D₄	—	3	4	no	—
157	C₃×C₄×D₄	—	3	8	no	—
158	C₃×#117	—	3	8	no	—
159	C₂×C₃×C₄²	—	3	4	no	—
160	#946	C₂×C₃²	1	1	yes	characteristic, complemented
161	Q₈×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
162	#938	C₂×C₃²	1	1	yes	characteristic
163	D₄×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
164	#883	C₂×C₃²	1	2	yes	complemented
165	#67⋊C₄	C₂×C₃²	1	2	yes	complemented
166	#879	C₂×C₃²	1	2	yes	complemented
167	#877	C₂×C₃²	1	2	yes	complemented
168	C₄²×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
169	#870	C₂×C₃²	1	1	yes	characteristic, complemented
170	C₂³×C₃²	—	2	8	no	—
171	C₂³×C₃²	—	3	1	no	—
172	C₂³×C₃²	C₂²×D₃	1	2	yes	—
173	C₂³×C₃²	C₂³×C₃	1	8	yes	—
174	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
175	C₃²×Q₈	—	2	2	no	—
176	C₃²×Q₈	—	2	8	no	—
177	C₃²×Q₈	—	4	8	no	—
178	C₃²×D₄	—	2	2	no	—
179	C₃²×D₄	—	2	8	no	—
180	C₃²×D₄	—	4	8	no	—
181	C₃²×D₄	—	6	4	no	—
182	C₂×C₃²×C₄	—	2	4	no	—
183	C₂×C₃²×C₄	—	2	4	no	—
184	C₂×C₃²×C₄	—	2	4	no	—
185	C₂×C₃²×C₄	—	2	8	no	—
186	C₂×C₃²×C₄	—	3	1	no	—
187	C₂×C₃²×C₄	—	3	1	no	—
188	C₂×C₃²×C₄	—	3	1	no	—
189	C₂×C₃²×C₄	—	3	2	no	—
190	C₂×C₃²×C₄	—	3	2	no	—
191	C₂×C₃²×C₄	—	6	2	no	—
192	C₂×C₃²×C₄	—	6	2	no	—
193	C₂×C₃²×C₄	—	6	4	no	—
194	C₂×C₃²×C₄	—	6	2	no	—
195	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
196	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
198	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
199	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
200	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
201	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
202	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
203	C₃×#67	—	2	16	no	—
204	C₂×C₃×Dic₃	—	2	16	no	—
205	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
206	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
207	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
208	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
209	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
210	C₃×C₄×D₃	—	2	8	no	—
211	C₃×C₄×D₃	—	2	8	no	—
212	C₃×C₄×D₃	—	2	8	no	—
213	#529	—	3	1	no	Sylow
214	C₂×C₃³	—	4	2	no	—
215	C₂×C₃³	C₂×#41	1	1	yes	characteristic
216	C₂×C₃³	C₂×#41	1	1	yes	characteristic
217	C₂×C₃³	C₂×#41	1	1	yes	characteristic
218	C₃²×D₃	—	2	2	no	—
219	C₂×C₃×Q₈	—	2	4	no	—
220	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
221	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
222	C₂×C₃×D₄	—	2	4	no	—
223	C₂×C₃×D₄	—	3	8	no	—
224	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
225	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
226	C₂²×C₃×C₄	—	3	8	no	—
227	C₂²×C₃×C₄	—	3	4	no	—
228	C₂²×C₃×C₄	—	3	4	no	—
229	C₂²×C₃×C₄	—	3	4	no	—
230	C₂×#67	C₂²×C₃²	1	2	yes	—
231	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
232	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
233	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
234	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
235	C₃×C₄⋊C₄	—	3	8	no	—
236	C₃×C₄⋊C₄	—	3	8	no	—
237	C₃×C₄⋊C₄	—	3	8	no	—
238	C₃×C₄⋊C₄	—	3	4	no	—
239	C₃×C₄⋊C₄	—	3	4	no	—
240	C₃×C₄⋊C₄	—	3	8	no	—
241	C₃×C₂²⋊C₄	—	2	8	no	—
242	C₃×C₂²⋊C₄	—	2	8	no	—
243	C₃×C₂²⋊C₄	—	3	8	no	—
244	C₃×C₂²⋊C₄	—	3	8	no	—
245	C₃×C₂²⋊C₄	—	3	8	no	—
246	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
247	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
248	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
249	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
250	C₃×C₄²	—	2	4	no	—
251	C₃×C₄²	—	3	4	no	—
252	C₃×C₄²	—	3	4	no	—
253	C₃×C₄²	—	3	4	no	—
254	C₃×C₄²	—	3	8	no	—
255	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
256	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
257	#217	C₂²×C₃²	1	2	yes	—
258	#217	C₂²×C₃²	1	2	yes	—
259	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
260	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
261	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
262	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
263	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
264	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
265	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
266	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
267	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
268	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
269	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
270	C₂²×C₃²	—	2	2	no	—
271	C₂²×C₃²	—	2	2	no	—
272	C₂²×C₃²	—	2	2	no	—
273	C₂²×C₃²	—	2	4	no	—
274	C₂²×C₃²	—	2	8	no	—
275	C₂²×C₃²	—	2	8	no	—
276	C₂²×C₃²	—	2	8	no	—
277	C₂²×C₃²	—	3	2	no	—
278	C₂²×C₃²	—	4	8	no	—
279	C₂²×C₃²	—	4	8	no	—
280	C₂²×C₃²	—	4	8	no	—
281	C₂²×C₃²	—	6	1	no	—
282	C₂²×C₃²	—	6	1	no	—
283	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
284	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
285	C₂×C₃×D₃	—	2	4	no	—
286	C₂×C₃×D₃	—	2	4	no	—
287	C₂×C₃×D₃	C₃×#41	1	8	yes	—
288	C₃²×C₄	—	2	2	no	—
289	C₃²×C₄	—	2	1	no	—
290	C₃²×C₄	—	2	1	no	—
291	C₃²×C₄	—	2	8	no	—
292	C₃²×C₄	—	2	4	no	—
293	C₃²×C₄	—	2	4	no	—
294	C₃²×C₄	—	2	8	no	—
295	C₃²×C₄	—	3	2	no	—
296	C₃²×C₄	—	4	4	no	—
297	C₃²×C₄	—	4	4	no	—
298	C₃²×C₄	—	4	8	no	—
299	C₃²×C₄	—	6	1	no	—
300	C₃²×C₄	—	6	2	no	—
301	C₃²×C₄	—	6	1	no	—
302	C₃²×C₄	—	6	2	no	—
303	C₃²×C₄	#237	1	2	yes	—
304	C₃²×C₄	C₃×#41	1	8	yes	—
305	C₃×Dic₃	—	2	4	no	—
306	C₃×Dic₃	—	2	4	no	—
307	C₃×Dic₃	—	2	8	no	—
308	C₃×Dic₃	—	2	8	no	—
309	C₃×Dic₃	C₃×#41	1	8	yes	—
310	#126	—	3	2	no	—
311	#125	—	3	1	no	—
312	#124	C₃²×D₃	1	1	yes	characteristic, complemented
313	#123	—	3	2	no	—
314	C₂²⋊Q₈	—	3	1	no	—
315	#121	—	3	1	no	—
316	C₄×Q₈	—	3	1	no	—
317	C₄×D₄	—	3	1	no	—
318	C₄×D₄	—	3	2	no	—
319	#117	—	3	2	no	—
320	C₂×C₄²	—	3	1	no	—
321	C₃³	#529	1	1	yes	characteristic, complemented, Sylow
322	C₂³×C₃	—	2	8	no	—
323	C₂³×C₃	—	3	4	no	—
324	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
325	C₂³×C₃	C₂³×C₃²	1	2	yes	—
326	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
327	C₃×Q₈	—	2	8	no	—
328	C₃×Q₈	—	2	2	no	—
329	C₃×Q₈	—	4	8	no	—
330	C₃×D₄	—	2	8	no	—
331	C₃×D₄	—	2	2	no	—
332	C₃×D₄	—	4	8	no	—
333	C₃×D₄	—	6	16	no	—
334	C₂×C₃×C₄	—	2	4	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	4	no	—
337	C₂×C₃×C₄	—	2	8	no	—
338	C₂×C₃×C₄	—	3	4	no	—
339	C₂×C₃×C₄	—	3	4	no	—
340	C₂×C₃×C₄	—	3	4	no	—
341	C₂×C₃×C₄	—	3	8	no	—
342	C₂×C₃×C₄	—	3	8	no	—
343	C₂×C₃×C₄	—	6	8	no	—
344	C₂×C₃×C₄	—	6	8	no	—
345	C₂×C₃×C₄	—	6	16	no	—
346	C₂×C₃×C₄	—	6	8	no	—
347	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
348	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
349	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
350	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
351	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
354	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
355	#67	—	2	4	no	—
356	C₂×Dic₃	—	2	4	no	—
357	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
358	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
359	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
360	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
361	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
362	C₄×D₃	—	2	2	no	—
363	C₄×D₃	—	2	2	no	—
364	C₄×D₃	—	2	2	no	—
365	C₂×C₃²	—	2	4	no	—
366	C₂×C₃²	—	2	4	no	—
367	C₂×C₃²	—	2	4	no	—
368	C₂×C₃²	—	4	2	no	—
369	C₂×C₃²	—	4	8	no	—
370	C₂×C₃²	—	6	2	no	—
371	C₂×C₃²	—	8	8	no	—
372	C₂×C₃²	C₂×#237	1	1	yes	characteristic
373	C₂×C₃²	D₃×#41	1	1	yes	characteristic
374	C₂×C₃²	D₃×#41	1	1	yes	characteristic
375	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
376	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
377	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
378	C₃×D₃	—	2	8	no	—
379	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
380	C₂×D₄	—	3	2	no	—
381	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
382	C₂²×C₄	—	3	2	no	—
383	C₂²×C₄	—	3	1	no	—
384	C₂²×C₄	—	3	1	no	—
385	C₂²×C₄	—	3	1	no	—
386	C₄⋊C₄	—	3	2	no	—
387	C₄⋊C₄	—	3	2	no	—
388	C₄⋊C₄	—	3	1	no	—
389	C₄⋊C₄	—	3	2	no	—
390	C₄⋊C₄	—	3	1	no	—
391	C₄⋊C₄	—	3	2	no	—
392	C₂²⋊C₄	—	3	2	no	—
393	C₂²⋊C₄	—	3	2	no	—
394	C₂²⋊C₄	—	3	2	no	—
395	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	—
396	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	—
397	C₄²	—	3	1	no	—
398	C₄²	—	3	1	no	—
399	C₄²	—	3	1	no	—
400	C₄²	—	3	2	no	—
401	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
402	C₂²×C₃	—	2	8	no	—
403	C₂²×C₃	—	2	8	no	—
404	C₂²×C₃	—	2	8	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	4	no	—
409	C₂²×C₃	—	3	8	no	—
410	C₂²×C₃	—	4	8	no	—
411	C₂²×C₃	—	4	8	no	—
412	C₂²×C₃	—	4	8	no	—
413	C₂²×C₃	—	6	4	no	—
414	C₂²×C₃	—	6	4	no	—
415	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
416	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
417	C₂×D₃	—	2	1	no	—
418	C₂×D₃	—	2	1	no	—
419	C₂×D₃	C₃²×#41	1	2	yes	—
420	C₃×C₄	—	2	8	no	—
421	C₃×C₄	—	2	4	no	—
422	C₃×C₄	—	2	4	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	8	no	—
427	C₃×C₄	—	3	8	no	—
428	C₃×C₄	—	4	8	no	—
429	C₃×C₄	—	4	4	no	—
430	C₃×C₄	—	4	4	no	—
431	C₃×C₄	—	6	4	no	—
432	C₃×C₄	—	6	8	no	—
433	C₃×C₄	—	6	4	no	—
434	C₃×C₄	—	6	8	no	—
435	C₃×C₄	C₃×#237	1	8	yes	—
436	C₃×C₄	C₃²×#41	1	2	yes	—
437	Dic₃	—	2	1	no	—
438	Dic₃	—	2	1	no	—
439	Dic₃	—	2	2	no	—
440	Dic₃	—	2	2	no	—
441	Dic₃	C₃²×#41	1	2	yes	—
442	C₃²	—	2	4	no	—
443	C₃²	#5680	1	1	yes	characteristic, direct product factor
444	C₃²	C₃×#529	1	4	yes	complemented
445	C₂³	—	3	1	no	—
446	C₂³	C₂²×C₃²×D₃	1	2	yes	—
447	Q₈	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	6	4	no	—
450	C₂×C₄	—	3	1	no	—
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	3	2	no	—
455	C₂×C₄	—	6	2	no	—
456	C₂×C₄	—	6	2	no	—
457	C₂×C₄	—	6	4	no	—
458	C₂×C₄	—	6	2	no	—
459	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
461	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
462	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
463	C₂×C₃	—	2	4	no	—
464	C₂×C₃	—	2	4	no	—
465	C₂×C₃	—	2	4	no	—
466	C₂×C₃	—	4	8	no	—
467	C₂×C₃	—	4	2	no	—
468	C₂×C₃	—	6	8	no	—
469	C₂×C₃	—	8	8	no	—
470	C₂×C₃	C₂×C₃×#237	1	4	yes	—
471	C₂×C₃	C₃×D₃×#41	1	4	yes	—
472	C₂×C₃	C₃×D₃×#41	1	4	yes	—
473	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
474	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
475	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
476	D₃	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	3	2	no	—
481	C₂²	—	6	1	no	—
482	C₂²	—	6	1	no	—
483	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	3	2	no	—
488	C₄	—	6	1	no	—
489	C₄	—	6	2	no	—
490	C₄	—	6	1	no	—
491	C₄	—	6	2	no	—
492	C₄	C₃²×#237	1	2	yes	—
493	C₃	—	2	4	no	—
494	C₃	C₃×#5680	1	4	yes	direct product factor
495	C₃	C₃²×#529	1	1	yes	characteristic, complemented
496	C₂	—	4	2	no	—
497	C₂	—	6	2	no	—
498	C₂	C₂×C₃²×#237	1	1	yes	characteristic
499	C₂	C₃²×D₃×#41	1	1	yes	characteristic
500	C₂	C₃²×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×#124	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₃²×#938	C₂
hypercenter	C₃²×#124	D₃
hypocenter	C₃	C₃²×#529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×#124

Complements

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

N	H ≅ G/N	type
1. C₃³×#124	C₂	semidirect
2. C₃²×#946	C₂	semidirect
3. C₃²×Q₈×Dic₃	C₂	semidirect
5. C₃²×D₄×Dic₃	C₂	semidirect
6. C₃²×#883	C₂	semidirect
7. C₃²×#67⋊C₄	C₂	semidirect
8. C₃²×#879	C₂	semidirect
9. C₃²×#877	C₂	semidirect
10. C₃²×C₄²×D₃	C₂	semidirect
11. C₃²×#870	C₂	semidirect
13. C₃×#5680	C₃	direct (N × H)
40. C₃²×#124	D₃	semidirect
41. C₃²×#124	C₂×C₃	semidirect
50. C₃×#946	C₂×C₃	semidirect
51. C₃×Q₈×Dic₃	C₂×C₃	semidirect
53. C₃×D₄×Dic₃	C₂×C₃	semidirect
54. C₃×#883	C₂×C₃	semidirect
55. C₃×#67⋊C₄	C₂×C₃	semidirect
56. C₃×#879	C₂×C₃	semidirect
57. C₃×#877	C₂×C₃	semidirect
58. C₃×C₄²×D₃	C₂×C₃	semidirect
59. C₃×#870	C₂×C₃	semidirect
79. #5680	C₃²	direct (N × H)
150. C₃×#124	C₃×D₃	semidirect
151. C₃×#124	C₂×C₃²	semidirect
160. #946	C₂×C₃²	semidirect
161. Q₈×Dic₃	C₂×C₃²	semidirect
163. D₄×Dic₃	C₂×C₃²	semidirect
164. #883	C₂×C₃²	semidirect
165. #67⋊C₄	C₂×C₃²	semidirect
166. #879	C₂×C₃²	semidirect
167. #877	C₂×C₃²	semidirect
168. C₄²×D₃	C₂×C₃²	semidirect
169. #870	C₂×C₃²	semidirect
312. #124	C₃²×D₃	semidirect
321. C₃³	#529	semidirect
443. C₃²	#5680	direct (N × H)
444. C₃²	C₃×#529	semidirect
494. C₃	C₃×#5680	direct (N × H)
495. C₃	C₃²×#529	semidirect

Maximal subgroups

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

subgroup	index
C₃³×#124	2
C₃²×#946	2
C₃²×Q₈×Dic₃	2
C₃²×#938	2
C₃²×D₄×Dic₃	2
C₃²×#883	2
C₃²×#67⋊C₄	2
C₃²×#879	2
C₃²×#877	2
C₃²×C₄²×D₃	2
C₃²×#870	2
C₃²×#529	3
C₃×#5680	3

Subgroups — C32×#5680 #13179058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5680 #13179058