Subgroups — C₃²×#5642 #13179019

Order 1728.

1580 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂²⋊Q₈	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×C₄×#67	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃²×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#898	C₂	1	2	yes	maximal, complemented
7	C₃²×#892	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#890	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×#890	C₂	1	2	yes	maximal, complemented
10	C₃²×#886	C₂	1	2	yes	maximal
11	C₃²×#877	C₂	1	2	yes	maximal, complemented
12	C₃²×#552	—	3	1	no	maximal
13	C₃×#5642	C₃	1	4	yes	maximal, direct product factor
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃²×#67	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×Dic₃	C₂²	1	2	yes	—
18	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
19	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₃²×#217	C₂²	1	1	yes	characteristic
23	C₃²×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
24	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
28	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
29	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
30	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
31	C₃²×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
35	C₃²×C₄×Dic₃	C₂²	1	2	yes	—
36	C₃²×C₄×Dic₃	C₂²	1	2	yes	—
37	C₃²×#126	—	3	2	no	—
38	C₃²×#125	—	3	2	no	—
39	C₃²×#125	—	3	1	no	—
40	C₃²×#123	—	3	2	no	—
41	C₃²×C₂²⋊Q₈	—	2	4	no	—
42	C₃²×C₂²⋊Q₈	—	3	1	no	—
43	C₃²×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
44	C₃²×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
45	C₃²×C₄×Q₈	—	3	1	no	—
46	C₃²×C₄×D₄	—	3	1	no	—
47	C₃²×#117	—	3	1	no	—
48	C₃²×#117	—	3	2	no	—
49	C₂×C₃²×C₄⋊C₄	—	3	1	no	—
50	C₃×#946	C₂×C₃	1	4	yes	complemented
51	C₃×Q₈×Dic₃	C₂×C₃	1	4	yes	complemented
52	C₃×C₄×#67	C₂×C₃	1	4	yes	—
53	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	4	yes	complemented
54	C₃×#898	C₂×C₃	1	8	yes	complemented
55	C₃×#892	C₂×C₃	1	4	yes	complemented
56	C₃×#890	C₂×C₃	1	8	yes	complemented
57	C₃×#890	C₂×C₃	1	4	yes	complemented
58	C₃×#886	C₂×C₃	1	8	yes	—
59	C₃×#877	C₂×C₃	1	8	yes	complemented
60	C₂³×C₃³	C₂³	1	1	yes	characteristic
61	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
62	C₃³×Q₈	—	2	2	no	—
63	C₂×C₃³×C₄	—	2	2	no	—
64	C₂×C₃³×C₄	C₂³	1	2	yes	—
65	C₂×C₃³×C₄	C₂³	1	2	yes	—
66	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
68	C₃²×#67	—	2	2	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	C₃×#552	—	3	4	no	—
77	#5642	C₃²	1	1	yes	characteristic, direct product factor
78	C₂×C₃²×Q₈	—	2	4	no	—
79	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
81	C₂×C₃²×D₄	—	3	1	no	—
82	C₂²×C₃²×C₄	—	2	4	no	—
83	C₂²×C₃²×C₄	—	3	2	no	—
84	C₂²×C₃²×C₄	—	3	1	no	—
85	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
86	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
87	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
88	C₂²×C₃×Dic₃	C₂²×C₃	1	8	yes	—
89	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
90	C₃²×C₄⋊C₄	—	2	4	no	—
91	C₃²×C₄⋊C₄	—	2	8	no	—
92	C₃²×C₄⋊C₄	—	3	1	no	—
93	C₃²×C₄⋊C₄	—	3	1	no	—
94	C₃²×C₄⋊C₄	—	3	2	no	—
95	C₃²×C₄⋊C₄	—	3	2	no	—
96	C₃²×C₄⋊C₄	—	3	2	no	—
97	C₃²×C₄⋊C₄	—	3	1	no	—
98	C₃²×C₄⋊C₄	—	3	2	no	—
99	C₃²×C₄⋊C₄	—	3	2	no	—
100	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
101	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
102	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
103	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
104	C₃²×C₂²⋊C₄	—	2	8	no	—
105	C₃²×C₂²⋊C₄	—	3	1	no	—
106	C₃²×C₂²⋊C₄	—	3	2	no	—
107	C₃²×C₂²⋊C₄	—	3	1	no	—
108	C₃²×C₂²⋊C₄	—	3	2	no	—
109	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
110	C₃²×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
111	C₃²×C₄²	—	3	2	no	—
112	C₃²×C₄²	—	3	2	no	—
113	C₃²×C₄²	—	3	1	no	—
114	C₃×#217	C₂²×C₃	1	4	yes	—
115	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
116	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
117	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
118	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
119	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
120	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
121	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
122	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
123	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
124	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
125	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
126	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
127	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
128	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
129	C₂²×C₃³	—	2	1	no	—
130	C₂²×C₃³	—	2	1	no	—
131	C₂²×C₃³	#41	1	2	yes	—
132	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
133	C₂×C₃²×D₃	—	2	1	no	—
134	C₂×C₃²×D₃	—	2	1	no	—
135	C₂×C₃²×D₃	—	2	1	no	—
136	C₃³×C₄	—	2	1	no	—
137	C₃³×C₄	—	2	2	no	—
138	C₃³×C₄	—	2	2	no	—
139	C₃³×C₄	#41	1	2	yes	—
140	C₃²×Dic₃	—	2	1	no	—
141	C₃²×Dic₃	—	2	2	no	—
142	C₃²×Dic₃	—	2	2	no	—
143	C₃²×Dic₃	—	2	1	no	—
144	C₃²×Dic₃	—	2	1	no	—
145	C₃×#126	—	3	8	no	—
146	C₃×#125	—	3	8	no	—
147	C₃×#125	—	3	4	no	—
148	C₃×#123	—	3	8	no	—
149	C₃×C₂²⋊Q₈	—	2	4	no	—
150	C₃×C₂²⋊Q₈	—	3	4	no	—
151	C₃×C₂²⋊Q₈	C₃×D₃	1	4	yes	complemented
152	C₃×C₂²⋊Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
153	C₃×C₄×Q₈	—	3	4	no	—
154	C₃×C₄×D₄	—	3	4	no	—
155	C₃×#117	—	3	4	no	—
156	C₃×#117	—	3	8	no	—
157	C₂×C₃×C₄⋊C₄	—	3	4	no	—
158	#946	C₂×C₃²	1	1	yes	characteristic, complemented
159	Q₈×Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
160	C₄×#67	C₂×C₃²	1	1	yes	characteristic
161	C₂×C₄⋊Dic₃	C₂×C₃²	1	1	yes	characteristic, complemented
162	#898	C₂×C₃²	1	2	yes	complemented
163	#892	C₂×C₃²	1	1	yes	characteristic, complemented
164	#890	C₂×C₃²	1	2	yes	complemented
165	#890	C₂×C₃²	1	1	yes	characteristic, complemented
166	#886	C₂×C₃²	1	2	yes	—
167	#877	C₂×C₃²	1	2	yes	complemented
168	C₂³×C₃²	—	2	4	no	—
169	C₂³×C₃²	—	3	1	no	—
170	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
171	C₂³×C₃²	C₂³×C₃	1	4	yes	—
172	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
173	C₃²×Q₈	—	2	2	no	—
174	C₃²×Q₈	—	2	8	no	—
175	C₃²×Q₈	—	4	8	no	—
176	C₃²×D₄	—	6	2	no	—
177	C₂×C₃²×C₄	—	2	2	no	—
178	C₂×C₃²×C₄	—	2	4	no	—
179	C₂×C₃²×C₄	—	2	8	no	—
180	C₂×C₃²×C₄	—	2	8	no	—
181	C₂×C₃²×C₄	—	2	4	no	—
182	C₂×C₃²×C₄	—	2	8	no	—
183	C₂×C₃²×C₄	—	3	1	no	—
184	C₂×C₃²×C₄	—	3	1	no	—
185	C₂×C₃²×C₄	—	3	2	no	—
186	C₂×C₃²×C₄	—	3	1	no	—
187	C₂×C₃²×C₄	—	3	2	no	—
188	C₂×C₃²×C₄	—	4	8	no	—
189	C₂×C₃²×C₄	—	6	4	no	—
190	C₂×C₃²×C₄	—	6	2	no	—
191	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
192	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
193	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
196	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
197	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
198	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
199	C₃×#67	—	2	8	no	—
200	C₂×C₃×Dic₃	—	2	16	no	—
201	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
202	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
203	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
204	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
205	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
206	C₃×C₄×D₃	—	2	8	no	—
207	#552	—	3	1	no	Sylow
208	C₂×C₃³	—	2	2	no	—
209	C₂×C₃³	C₂×#41	1	1	yes	characteristic
210	C₂×C₃³	C₂×#41	1	1	yes	characteristic
211	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
212	C₃²×D₃	—	4	1	no	—
213	C₂×C₃×Q₈	—	2	4	no	—
214	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
215	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
216	C₂×C₃×D₄	—	3	4	no	—
217	C₂²×C₃×C₄	—	2	4	no	—
218	C₂²×C₃×C₄	—	3	8	no	—
219	C₂²×C₃×C₄	—	3	4	no	—
220	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
221	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
222	C₂×#67	C₂²×C₃²	1	1	yes	characteristic
223	C₂²×Dic₃	C₂²×C₃²	1	2	yes	—
224	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
225	C₃×C₄⋊C₄	—	2	4	no	—
226	C₃×C₄⋊C₄	—	2	8	no	—
227	C₃×C₄⋊C₄	—	3	8	no	—
228	C₃×C₄⋊C₄	—	3	8	no	—
229	C₃×C₄⋊C₄	—	3	4	no	—
230	C₃×C₄⋊C₄	—	3	4	no	—
231	C₃×C₄⋊C₄	—	3	4	no	—
232	C₃×C₄⋊C₄	—	3	8	no	—
233	C₃×C₄⋊C₄	—	3	8	no	—
234	C₃×C₄⋊C₄	—	3	8	no	—
235	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
236	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
237	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
238	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
239	C₃×C₂²⋊C₄	—	2	8	no	—
240	C₃×C₂²⋊C₄	—	3	4	no	—
241	C₃×C₂²⋊C₄	—	3	8	no	—
242	C₃×C₂²⋊C₄	—	3	4	no	—
243	C₃×C₂²⋊C₄	—	3	8	no	—
244	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
245	C₃×C₂²⋊C₄	C₂²×C₃²	1	2	yes	—
246	C₃×C₄²	—	3	8	no	—
247	C₃×C₄²	—	3	8	no	—
248	C₃×C₄²	—	3	4	no	—
249	#217	C₂²×C₃²	1	1	yes	characteristic
250	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
251	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
252	(C₂×D₃)⋊C₄	C₂²×C₃²	1	1	yes	characteristic
253	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
254	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
255	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
256	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
257	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
258	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
259	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
260	Dic₃⋊C₄	C₂²×C₃²	1	1	yes	characteristic
261	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
262	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
263	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
264	C₂²×C₃²	—	2	1	no	—
265	C₂²×C₃²	—	2	1	no	—
266	C₂²×C₃²	—	2	4	no	—
267	C₂²×C₃²	—	2	8	no	—
268	C₂²×C₃²	—	2	4	no	—
269	C₂²×C₃²	—	2	4	no	—
270	C₂²×C₃²	—	4	4	no	—
271	C₂²×C₃²	—	4	4	no	—
272	C₂²×C₃²	—	6	1	no	—
273	C₂²×C₃²	—	6	1	no	—
274	C₂²×C₃²	—	6	1	no	—
275	C₂²×C₃²	#239	1	2	yes	—
276	C₂²×C₃²	C₃×#41	1	8	yes	—
277	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
278	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
279	C₂×C₃×D₃	—	2	4	no	—
280	C₂×C₃×D₃	—	2	4	no	—
281	C₂×C₃×D₃	—	2	4	no	—
282	C₃²×C₄	—	2	1	no	—
283	C₃²×C₄	—	2	2	no	—
284	C₃²×C₄	—	2	2	no	—
285	C₃²×C₄	—	2	8	no	—
286	C₃²×C₄	—	2	4	no	—
287	C₃²×C₄	—	2	8	no	—
288	C₃²×C₄	—	2	8	no	—
289	C₃²×C₄	—	4	8	no	—
290	C₃²×C₄	—	4	4	no	—
291	C₃²×C₄	—	4	8	no	—
292	C₃²×C₄	—	6	1	no	—
293	C₃²×C₄	—	6	2	no	—
294	C₃²×C₄	—	6	2	no	—
295	C₃²×C₄	—	6	1	no	—
296	C₃²×C₄	—	6	1	no	—
297	C₃²×C₄	#237	1	2	yes	—
298	C₃²×C₄	C₃×#41	1	8	yes	—
299	C₃×Dic₃	—	2	4	no	—
300	C₃×Dic₃	—	2	8	no	—
301	C₃×Dic₃	—	2	8	no	—
302	C₃×Dic₃	—	2	4	no	—
303	C₃×Dic₃	—	2	4	no	—
304	#126	—	3	2	no	—
305	#125	—	3	2	no	—
306	#125	—	3	1	no	—
307	#123	—	3	2	no	—
308	C₂²⋊Q₈	—	3	1	no	—
309	C₂²⋊Q₈	C₃²×D₃	1	1	yes	characteristic, complemented
310	C₄×Q₈	—	3	1	no	—
311	C₄×D₄	—	3	1	no	—
312	#117	—	3	1	no	—
313	#117	—	3	2	no	—
314	C₂×C₄⋊C₄	—	3	1	no	—
315	C₃³	#552	1	1	yes	characteristic, complemented, Sylow
316	C₂³×C₃	—	2	4	no	—
317	C₂³×C₃	—	3	4	no	—
318	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
319	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
320	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
321	C₃×Q₈	—	2	8	no	—
322	C₃×Q₈	—	2	2	no	—
323	C₃×Q₈	—	4	8	no	—
324	C₃×D₄	—	6	8	no	—
325	C₂×C₃×C₄	—	2	8	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	4	no	—
328	C₂×C₃×C₄	—	2	8	no	—
329	C₂×C₃×C₄	—	2	8	no	—
330	C₂×C₃×C₄	—	2	4	no	—
331	C₂×C₃×C₄	—	3	4	no	—
332	C₂×C₃×C₄	—	3	4	no	—
333	C₂×C₃×C₄	—	3	8	no	—
334	C₂×C₃×C₄	—	3	4	no	—
335	C₂×C₃×C₄	—	3	8	no	—
336	C₂×C₃×C₄	—	4	8	no	—
337	C₂×C₃×C₄	—	6	16	no	—
338	C₂×C₃×C₄	—	6	8	no	—
339	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
340	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
341	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
342	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
343	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
344	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
345	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
347	#67	—	2	2	no	—
348	C₂×Dic₃	—	2	4	no	—
349	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
350	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
351	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
352	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
353	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
354	C₄×D₃	—	2	2	no	—
355	C₂×C₃²	—	2	2	no	—
356	C₂×C₃²	—	2	4	no	—
357	C₂×C₃²	—	2	4	no	—
358	C₂×C₃²	—	2	4	no	—
359	C₂×C₃²	—	2	8	no	—
360	C₂×C₃²	—	4	8	no	—
361	C₂×C₃²	—	12	1	no	—
362	C₂×C₃²	C₂×#237	1	1	yes	characteristic
363	C₂×C₃²	C₂×#239	1	1	yes	characteristic
364	C₂×C₃²	#1010	1	1	yes	characteristic
365	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
366	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
367	C₂×C₃²	C₃×2₋¹⁺⁴	1	4	yes	—
368	C₃×D₃	—	4	4	no	—
369	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
370	C₂×D₄	—	3	1	no	—
371	C₂²×C₄	—	3	2	no	—
372	C₂²×C₄	—	3	1	no	—
373	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
374	C₄⋊C₄	—	3	1	no	—
375	C₄⋊C₄	—	3	1	no	—
376	C₄⋊C₄	—	3	2	no	—
377	C₄⋊C₄	—	3	2	no	—
378	C₄⋊C₄	—	3	2	no	—
379	C₄⋊C₄	—	3	1	no	—
380	C₄⋊C₄	—	3	2	no	—
381	C₄⋊C₄	—	3	2	no	—
382	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
383	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	—
384	C₂²⋊C₄	—	3	1	no	—
385	C₂²⋊C₄	—	3	2	no	—
386	C₂²⋊C₄	—	3	1	no	—
387	C₂²⋊C₄	—	3	2	no	—
388	C₂²⋊C₄	C₂×C₃²×D₃	1	2	yes	—
389	C₄²	—	3	2	no	—
390	C₄²	—	3	2	no	—
391	C₄²	—	3	1	no	—
392	C₂²×C₃	—	2	4	no	—
393	C₂²×C₃	—	2	4	no	—
394	C₂²×C₃	—	2	1	no	—
395	C₂²×C₃	—	2	1	no	—
396	C₂²×C₃	—	2	4	no	—
397	C₂²×C₃	—	2	8	no	—
398	C₂²×C₃	—	4	4	no	—
399	C₂²×C₃	—	4	4	no	—
400	C₂²×C₃	—	6	4	no	—
401	C₂²×C₃	—	6	4	no	—
402	C₂²×C₃	—	6	4	no	—
403	C₂²×C₃	C₃×#239	1	8	yes	—
404	C₂²×C₃	C₃²×#41	1	2	yes	—
405	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
406	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
407	C₂×D₃	—	2	1	no	—
408	C₂×D₃	—	2	1	no	—
409	C₂×D₃	—	2	1	no	—
410	C₃×C₄	—	2	4	no	—
411	C₃×C₄	—	2	8	no	—
412	C₃×C₄	—	2	8	no	—
413	C₃×C₄	—	2	1	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	2	8	no	—
417	C₃×C₄	—	4	4	no	—
418	C₃×C₄	—	4	8	no	—
419	C₃×C₄	—	4	8	no	—
420	C₃×C₄	—	6	4	no	—
421	C₃×C₄	—	6	8	no	—
422	C₃×C₄	—	6	8	no	—
423	C₃×C₄	—	6	4	no	—
424	C₃×C₄	—	6	4	no	—
425	C₃×C₄	C₃×#237	1	8	yes	—
426	C₃×C₄	C₃²×#41	1	2	yes	—
427	Dic₃	—	2	1	no	—
428	Dic₃	—	2	2	no	—
429	Dic₃	—	2	2	no	—
430	Dic₃	—	2	1	no	—
431	Dic₃	—	2	1	no	—
432	C₃²	—	2	4	no	—
433	C₃²	#5642	1	1	yes	characteristic, direct product factor
434	C₃²	C₃×#552	1	4	yes	complemented
435	C₂³	—	3	1	no	—
436	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
437	Q₈	—	2	2	no	—
438	D₄	—	6	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	3	1	no	—
441	C₂×C₄	—	3	1	no	—
442	C₂×C₄	—	3	2	no	—
443	C₂×C₄	—	3	1	no	—
444	C₂×C₄	—	3	2	no	—
445	C₂×C₄	—	6	4	no	—
446	C₂×C₄	—	6	2	no	—
447	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
448	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
449	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
451	C₂×C₃	—	2	2	no	—
452	C₂×C₃	—	2	8	no	—
453	C₂×C₃	—	2	4	no	—
454	C₂×C₃	—	2	4	no	—
455	C₂×C₃	—	2	4	no	—
456	C₂×C₃	—	4	8	no	—
457	C₂×C₃	—	12	4	no	—
458	C₂×C₃	C₂×C₃×#237	1	4	yes	—
459	C₂×C₃	C₂×C₃×#239	1	4	yes	—
460	C₂×C₃	C₃×#1010	1	4	yes	—
461	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
462	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
463	C₂×C₃	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
464	D₃	—	4	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	6	1	no	—
468	C₂²	—	6	1	no	—
469	C₂²	—	6	1	no	—
470	C₂²	C₃²×#239	1	2	yes	—
471	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
472	C₄	—	2	1	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	6	1	no	—
476	C₄	—	6	2	no	—
477	C₄	—	6	2	no	—
478	C₄	—	6	1	no	—
479	C₄	—	6	1	no	—
480	C₄	C₃²×#237	1	2	yes	—
481	C₃	—	2	4	no	—
482	C₃	C₃×#5642	1	4	yes	direct product factor
483	C₃	C₃²×#552	1	1	yes	characteristic, complemented
484	C₂	—	2	2	no	—
485	C₂	—	12	1	no	—
486	C₂	C₂×C₃²×#237	1	1	yes	characteristic
487	C₂	C₂×C₃²×#239	1	1	yes	characteristic
488	C₂	C₃²×#1010	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×C₂²⋊Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃²×#67	C₂²
hypercenter	C₃²×C₂²⋊Q₈	D₃
hypocenter	C₃	C₃²×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₂²⋊Q₈	C₂	semidirect
2. C₃²×#946	C₂	semidirect
3. C₃²×Q₈×Dic₃	C₂	semidirect
5. C₂×C₃²×C₄⋊Dic₃	C₂	semidirect
6. C₃²×#898	C₂	semidirect
7. C₃²×#892	C₂	semidirect
8. C₃²×#890	C₂	semidirect
9. C₃²×#890	C₂	semidirect
11. C₃²×#877	C₂	semidirect
13. C₃×#5642	C₃	direct (N × H)
43. C₃²×C₂²⋊Q₈	D₃	semidirect
44. C₃²×C₂²⋊Q₈	C₂×C₃	semidirect
50. C₃×#946	C₂×C₃	semidirect
51. C₃×Q₈×Dic₃	C₂×C₃	semidirect
53. C₂×C₃×C₄⋊Dic₃	C₂×C₃	semidirect
54. C₃×#898	C₂×C₃	semidirect
55. C₃×#892	C₂×C₃	semidirect
56. C₃×#890	C₂×C₃	semidirect
57. C₃×#890	C₂×C₃	semidirect
59. C₃×#877	C₂×C₃	semidirect
77. #5642	C₃²	direct (N × H)
151. C₃×C₂²⋊Q₈	C₃×D₃	semidirect
152. C₃×C₂²⋊Q₈	C₂×C₃²	semidirect
158. #946	C₂×C₃²	semidirect
159. Q₈×Dic₃	C₂×C₃²	semidirect
161. C₂×C₄⋊Dic₃	C₂×C₃²	semidirect
162. #898	C₂×C₃²	semidirect
163. #892	C₂×C₃²	semidirect
164. #890	C₂×C₃²	semidirect
165. #890	C₂×C₃²	semidirect
167. #877	C₂×C₃²	semidirect
309. C₂²⋊Q₈	C₃²×D₃	semidirect
315. C₃³	#552	semidirect
433. C₃²	#5642	direct (N × H)
434. C₃²	C₃×#552	semidirect
482. C₃	C₃×#5642	direct (N × H)
483. C₃	C₃²×#552	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₂²⋊Q₈	2
C₃²×#946	2
C₃²×Q₈×Dic₃	2
C₃²×C₄×#67	2
C₂×C₃²×C₄⋊Dic₃	2
C₃²×#898	2
C₃²×#892	2
C₃²×#890	2
C₃²×#886	2
C₃²×#877	2
C₃²×#552	3
C₃×#5642	3

Subgroups — C32×#5642 #13179019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5642 #13179019