Subgroups — C₃×#36191 #10654798

Order 768.

1826 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2574	C₂	1	4	yes	maximal, complemented
5	C₃×#2570	C₂	1	2	yes	maximal, complemented
6	C₃×#2520	C₂	1	4	yes	maximal, complemented
7	C₃×#2450	C₂	1	4	yes	maximal
8	C₃×#2440	C₂	1	2	yes	maximal, complemented
9	C₃×#2439	C₂	1	2	yes	maximal, complemented
10	C₃×#2368	C₂	1	4	yes	maximal, complemented
11	C₃×#2352	C₂	1	2	yes	maximal
12	C₃×C₄×#125	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic
16	#36191	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
21	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×#117	C₂²	1	2	yes	—
23	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
26	C₃×#400	C₂²	1	4	yes	—
27	C₃×#398	C₂²	1	4	yes	—
28	C₃×#398	C₂²	1	4	yes	—
29	C₃×#396	C₂²	1	4	yes	—
30	C₃×#395	C₂²	1	4	yes	—
31	C₃×#393	C₂²	1	4	yes	—
32	C₃×#391	C₂²	1	4	yes	—
33	C₃×#391	C₂²	1	4	yes	—
34	C₃×#391	C₂²	1	4	yes	—
35	C₃×#389	C₂²	1	2	yes	—
36	C₃×#389	C₂²	1	2	yes	—
37	C₃×#389	C₂²	1	2	yes	—
38	C₃×#388	C₂²	1	4	yes	—
39	C₃×#387	C₂²	1	4	yes	—
40	C₃×#387	C₂²	1	4	yes	—
41	C₃×#387	C₂²	1	4	yes	—
42	C₃×#387	C₂²	1	4	yes	—
43	C₃×#387	C₂²	1	4	yes	—
44	C₃×#387	C₂²	1	4	yes	—
45	C₃×#387	C₂²	1	4	yes	—
46	C₃×#386	C₂²	1	4	yes	—
47	C₃×#385	C₂²	1	4	yes	—
48	C₃×#385	C₂²	1	4	yes	—
49	C₃×#385	C₂²	1	4	yes	—
50	C₃×#384	C₂²	1	2	yes	—
51	C₃×#382	C₂²	1	2	yes	—
52	C₃×#382	C₂²	1	4	yes	—
53	C₃×#382	C₂²	1	1	yes	characteristic
54	C₃×#382	C₂²	1	1	yes	characteristic
55	C₃×#382	C₂²	1	1	yes	characteristic
56	C₃×#382	C₂²	1	2	yes	—
57	C₃×#380	C₂²	1	2	yes	—
58	C₃×#380	C₂²	1	2	yes	—
59	C₃×#380	C₂²	1	4	yes	—
60	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
61	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
62	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
63	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
64	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
65	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
66	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
67	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
68	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
69	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
70	C₂×C₃×#95	C₂²	1	4	yes	—
71	C₃×C₄³	C₂²	1	1	yes	characteristic
72	#2862	C₂×C₃	1	1	yes	characteristic, complemented
73	#2851	C₂×C₃	1	1	yes	characteristic, complemented
74	#2851	C₂×C₃	1	1	yes	characteristic, complemented
75	#2574	C₂×C₃	1	4	yes	complemented
76	#2570	C₂×C₃	1	2	yes	complemented
77	#2520	C₂×C₃	1	4	yes	complemented
78	#2450	C₂×C₃	1	4	yes	—
79	#2440	C₂×C₃	1	2	yes	complemented
80	#2439	C₂×C₃	1	2	yes	complemented
81	#2368	C₂×C₃	1	4	yes	complemented
82	#2352	C₂×C₃	1	2	yes	—
83	C₄×#125	C₂×C₃	1	1	yes	characteristic, complemented
84	#2285	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂×#382	C₂×C₃	1	1	yes	characteristic, complemented
86	C₄²×D₄	C₂×C₃	1	1	yes	characteristic
87	C₂²×C₃×Q₈	C₂³	1	4	yes	—
88	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
89	C₂³×C₃×C₄	C₂³	1	2	yes	—
90	C₂³×C₃×C₄	C₂³	1	2	yes	—
91	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
92	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
93	C₂³×C₃×C₄	C₂³	1	4	yes	—
94	C₃×C₄⋊Q₈	—	4	4	no	—
95	C₃×#125	—	2	4	no	—
96	C₃×C₂²⋊Q₈	—	2	16	no	—
97	C₃×C₄×D₄	—	2	8	no	—
98	C₃×C₄×D₄	Q₈	1	8	yes	complemented
99	C₃×#117	—	4	4	no	—
100	C₂×C₃×C₄⋊C₄	—	4	4	no	—
101	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₃×C₄²	—	2	4	no	—
123	C₂×C₃×C₄²	—	2	4	no	—
124	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
125	C₂×C₃×C₄²	C₂³	1	2	yes	—
126	C₂×C₃×C₄²	C₂³	1	2	yes	—
127	C₂×C₃×C₄²	C₂³	1	2	yes	—
128	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₄²	C₂³	1	2	yes	—
131	C₂×C₃×C₄²	C₂³	1	4	yes	—
132	C₂×C₃×C₄²	C₂³	1	4	yes	—
133	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
135	C₃×#95	C₂³	1	4	yes	—
136	C₃×#95	C₂³	1	4	yes	—
137	C₃×#95	C₂³	1	4	yes	—
138	C₃×#95	C₂³	1	4	yes	—
139	C₃×#95	C₂³	1	2	yes	—
140	C₃×#95	C₂³	1	2	yes	—
141	C₃×#95	C₂³	1	2	yes	—
142	C₃×#95	C₂³	1	4	yes	—
143	C₃×#95	C₂³	1	4	yes	—
144	C₃×#95	C₂³	1	4	yes	—
145	C₃×#95	C₂³	1	4	yes	—
146	C₃×#95	C₂³	1	4	yes	—
147	C₃×#95	C₂³	1	4	yes	—
148	C₃×#95	C₂³	1	4	yes	—
149	C₃×#95	C₂³	1	4	yes	—
150	C₃×#95	C₂³	1	4	yes	—
151	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
152	C₂×#125	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
154	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
155	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×#117	C₂²×C₃	1	2	yes	—
157	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
158	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
159	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
160	#400	C₂²×C₃	1	4	yes	—
161	#398	C₂²×C₃	1	4	yes	—
162	#398	C₂²×C₃	1	4	yes	—
163	#396	C₂²×C₃	1	4	yes	—
164	#395	C₂²×C₃	1	4	yes	—
165	#393	C₂²×C₃	1	4	yes	—
166	#391	C₂²×C₃	1	4	yes	—
167	#391	C₂²×C₃	1	4	yes	—
168	#391	C₂²×C₃	1	4	yes	—
169	#389	C₂²×C₃	1	2	yes	—
170	#389	C₂²×C₃	1	2	yes	—
171	#389	C₂²×C₃	1	2	yes	—
172	#388	C₂²×C₃	1	4	yes	—
173	#387	C₂²×C₃	1	4	yes	—
174	#387	C₂²×C₃	1	4	yes	—
175	#387	C₂²×C₃	1	4	yes	—
176	#387	C₂²×C₃	1	4	yes	—
177	#387	C₂²×C₃	1	4	yes	—
178	#387	C₂²×C₃	1	4	yes	—
179	#387	C₂²×C₃	1	4	yes	—
180	#386	C₂²×C₃	1	4	yes	—
181	#385	C₂²×C₃	1	4	yes	—
182	#385	C₂²×C₃	1	4	yes	—
183	#385	C₂²×C₃	1	4	yes	—
184	#384	C₂²×C₃	1	2	yes	—
185	#382	C₂²×C₃	1	1	yes	characteristic
186	#382	C₂²×C₃	1	2	yes	—
187	#382	C₂²×C₃	1	2	yes	—
188	#382	C₂²×C₃	1	4	yes	—
189	#382	C₂²×C₃	1	1	yes	characteristic
190	#382	C₂²×C₃	1	1	yes	characteristic
191	#380	C₂²×C₃	1	4	yes	—
192	#380	C₂²×C₃	1	2	yes	—
193	#380	C₂²×C₃	1	2	yes	—
194	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
195	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
196	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
197	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
198	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
199	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
200	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
201	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
202	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
203	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
204	C₂×#95	C₂²×C₃	1	4	yes	—
205	C₄³	C₂²×C₃	1	1	yes	characteristic
206	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
207	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
208	C₂×C₃×Q₈	—	2	8	no	—
209	C₂×C₃×Q₈	—	4	4	no	—
210	C₂×C₃×Q₈	—	4	4	no	—
211	C₂×C₃×D₄	—	2	4	no	—
212	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
213	C₂²×C₃×C₄	—	2	2	no	—
214	C₂²×C₃×C₄	—	2	2	no	—
215	C₂²×C₃×C₄	—	2	2	no	—
216	C₂²×C₃×C₄	—	2	2	no	—
217	C₂²×C₃×C₄	—	2	4	no	—
218	C₂²×C₃×C₄	—	2	8	no	—
219	C₂²×C₃×C₄	—	2	4	no	—
220	C₂²×C₃×C₄	—	2	4	no	—
221	C₂²×C₃×C₄	—	2	4	no	—
222	C₂²×C₃×C₄	—	4	2	no	—
223	C₂²×C₃×C₄	—	4	2	no	—
224	C₂²×C₃×C₄	—	4	4	no	—
225	C₂²×C₃×C₄	—	4	4	no	—
226	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
227	C₂²×C₃×C₄	C₂×Q₈	1	4	yes	—
228	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
229	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
230	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
231	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
232	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
233	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
238	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
239	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
240	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
241	C₃×C₄⋊C₄	—	2	4	no	—
242	C₃×C₄⋊C₄	—	2	8	no	—
243	C₃×C₄⋊C₄	—	2	8	no	—
244	C₃×C₄⋊C₄	—	2	8	no	—
245	C₃×C₄⋊C₄	—	2	8	no	—
246	C₃×C₄⋊C₄	—	2	4	no	—
247	C₃×C₄⋊C₄	—	2	4	no	—
248	C₃×C₄⋊C₄	—	2	4	no	—
249	C₃×C₄⋊C₄	—	2	4	no	—
250	C₃×C₄⋊C₄	—	4	4	no	—
251	C₃×C₄⋊C₄	—	4	4	no	—
252	C₃×C₄⋊C₄	—	4	4	no	—
253	C₃×C₄⋊C₄	—	4	4	no	—
254	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
255	C₃×C₂²⋊C₄	—	2	8	no	—
256	C₃×C₂²⋊C₄	—	2	4	no	—
257	C₃×C₂²⋊C₄	—	4	4	no	—
258	C₃×C₂²⋊C₄	—	4	4	no	—
259	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
260	C₃×C₂²⋊C₄	C₂×Q₈	1	4	yes	—
261	C₃×C₂²⋊C₄	#41	1	8	yes	—
262	C₃×C₄²	—	2	4	no	—
263	C₃×C₄²	—	2	2	no	—
264	C₃×C₄²	—	2	4	no	—
265	C₃×C₄²	—	2	2	no	—
266	C₃×C₄²	—	2	4	no	—
267	C₃×C₄²	—	2	2	no	—
268	C₃×C₄²	—	4	2	no	—
269	C₃×C₄²	—	4	4	no	—
270	C₃×C₄²	—	4	4	no	—
271	C₃×C₄²	C₂×Q₈	1	4	yes	—
272	C₃×C₄²	#41	1	4	yes	—
273	C₂²×Q₈	C₂³×C₃	1	4	yes	—
274	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₃	1	2	yes	—
276	C₂³×C₄	C₂³×C₃	1	2	yes	—
277	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₃	1	4	yes	—
280	C₄⋊Q₈	—	4	4	no	—
281	#125	—	2	4	no	—
282	C₂²⋊Q₈	—	2	16	no	—
283	C₄×D₄	—	2	8	no	—
284	C₄×D₄	C₃×Q₈	1	8	yes	complemented
285	#117	—	4	4	no	—
286	C₂×C₄⋊C₄	—	4	4	no	—
287	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
292	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
293	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
294	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
296	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
297	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
298	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
308	C₂×C₄²	—	2	4	no	—
309	C₂×C₄²	—	2	4	no	—
310	C₂×C₄²	C₂³×C₃	1	2	yes	—
311	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₃	1	2	yes	—
313	C₂×C₄²	C₂³×C₃	1	2	yes	—
314	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₃	1	4	yes	—
317	C₂×C₄²	C₂³×C₃	1	2	yes	—
318	C₂×C₄²	C₂³×C₃	1	4	yes	—
319	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
321	#95	C₂³×C₃	1	4	yes	—
322	#95	C₂³×C₃	1	4	yes	—
323	#95	C₂³×C₃	1	4	yes	—
324	#95	C₂³×C₃	1	4	yes	—
325	#95	C₂³×C₃	1	2	yes	—
326	#95	C₂³×C₃	1	2	yes	—
327	#95	C₂³×C₃	1	2	yes	—
328	#95	C₂³×C₃	1	4	yes	—
329	#95	C₂³×C₃	1	4	yes	—
330	#95	C₂³×C₃	1	4	yes	—
331	#95	C₂³×C₃	1	4	yes	—
332	#95	C₂³×C₃	1	4	yes	—
333	#95	C₂³×C₃	1	4	yes	—
334	#95	C₂³×C₃	1	4	yes	—
335	#95	C₂³×C₃	1	4	yes	—
336	#95	C₂³×C₃	1	4	yes	—
337	C₂³×C₃	—	2	1	no	—
338	C₂³×C₃	—	2	1	no	—
339	C₂³×C₃	—	2	2	no	—
340	C₂³×C₃	—	2	2	no	—
341	C₂³×C₃	—	2	1	no	—
342	C₂³×C₃	—	2	1	no	—
343	C₂³×C₃	—	2	2	no	—
344	C₂³×C₃	C₂²×Q₈	1	2	yes	—
345	C₂³×C₃	C₂²×Q₈	1	2	yes	—
346	C₂³×C₃	C₂×#41	1	4	yes	—
347	C₂³×C₃	C₂⁵	1	1	yes	characteristic
348	C₃×Q₈	—	8	8	no	—
349	C₃×D₄	—	2	8	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	—	2	8	no	—
363	C₂×C₃×C₄	—	2	8	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	4	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	4	no	—
368	C₂×C₃×C₄	—	2	4	no	—
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	—	2	4	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	4	no	—
373	C₂×C₃×C₄	—	2	4	no	—
374	C₂×C₃×C₄	—	2	4	no	—
375	C₂×C₃×C₄	—	2	4	no	—
376	C₂×C₃×C₄	—	2	4	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	4	no	—
379	C₂×C₃×C₄	—	4	8	no	—
380	C₂×C₃×C₄	—	4	8	no	—
381	C₂×C₃×C₄	—	8	8	no	—
382	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
383	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
384	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
385	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
386	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
387	C₂×C₃×C₄	C₂×#41	1	4	yes	—
388	C₂×C₃×C₄	C₂×#41	1	4	yes	—
389	C₂×C₃×C₄	C₂×#41	1	4	yes	—
390	C₂×C₃×C₄	C₂×#41	1	2	yes	—
391	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
392	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
393	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
394	C₂×Q₈	—	2	8	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
413	C₂²×C₄	C₂×C₃×Q₈	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	4	4	no	—
437	C₄⋊C₄	—	4	4	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	4	4	no	—
445	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
446	C₂²⋊C₄	C₂×C₃×Q₈	1	4	yes	—
447	C₂²⋊C₄	C₃×#41	1	8	yes	—
448	C₄²	—	2	4	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	4	4	no	—
455	C₄²	—	4	2	no	—
456	C₄²	—	4	4	no	—
457	C₄²	C₂×C₃×Q₈	1	4	yes	—
458	C₄²	C₃×#41	1	4	yes	—
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	2	4	no	—
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	2	4	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	4	2	no	—
467	C₂²×C₃	—	4	2	no	—
468	C₂²×C₃	#533	1	4	yes	—
469	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
470	C₂²×C₃	C₂²×#41	1	2	yes	—
471	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
472	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₃	#585	1	2	yes	—
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	—	2	4	no	—
478	C₃×C₄	—	2	4	no	—
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	2	4	no	—
481	C₃×C₄	—	4	4	no	—
482	C₃×C₄	—	4	2	no	—
483	C₃×C₄	—	4	4	no	—
484	C₃×C₄	—	4	4	no	—
485	C₃×C₄	—	4	4	no	—
486	C₃×C₄	#554	1	4	yes	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	2	no	—
494	C₂³	C₂²×C₃×Q₈	1	2	yes	—
495	C₂³	C₂²×C₃×Q₈	1	2	yes	—
496	C₂³	C₂×C₃×#41	1	4	yes	—
497	C₂³	C₂⁵×C₃	1	1	yes	characteristic
498	Q₈	—	8	8	no	—
499	D₄	—	2	8	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	8	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	8	8	no	—
532	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
533	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
534	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
535	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
536	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
537	C₂×C₄	C₂×C₃×#41	1	4	yes	—
538	C₂×C₄	C₂×C₃×#41	1	4	yes	—
539	C₂×C₄	C₂×C₃×#41	1	4	yes	—
540	C₂×C₄	C₂×C₃×#41	1	2	yes	—
541	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
542	C₂×C₃	—	2	4	no	—
543	C₂×C₃	—	4	2	no	—
544	C₂×C₃	C₂×#533	1	1	yes	characteristic
545	C₂×C₃	C₂×#554	1	1	yes	characteristic
546	C₂×C₃	#3475	1	2	yes	—
547	C₂×C₃	#3504	1	1	yes	characteristic
548	C₂×C₃	#3514	1	2	yes	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	C₃×#533	1	4	yes	—
559	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
560	C₂²	C₂²×C₃×#41	1	2	yes	—
561	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
562	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂²	C₃×#585	1	2	yes	—
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	4	no	—
568	C₄	—	2	4	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	4	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	4	no	—
576	C₄	C₃×#554	1	4	yes	—
577	C₃	#36191	1	1	yes	characteristic, direct product factor, Sylow
578	C₂	—	2	4	no	—
579	C₂	—	4	2	no	—
580	C₂	C₂×C₃×#533	1	1	yes	characteristic
581	C₂	C₂×C₃×#554	1	1	yes	characteristic
582	C₂	C₃×#3475	1	2	yes	—
583	C₂	C₃×#3504	1	1	yes	characteristic
584	C₂	C₃×#3514	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2862	C₂	semidirect
2. C₃×#2851	C₂	semidirect
3. C₃×#2851	C₂	semidirect
4. C₃×#2574	C₂	semidirect
5. C₃×#2570	C₂	semidirect
6. C₃×#2520	C₂	semidirect
8. C₃×#2440	C₂	semidirect
9. C₃×#2439	C₂	semidirect
10. C₃×#2368	C₂	semidirect
12. C₃×C₄×#125	C₂	semidirect
13. C₃×#2285	C₂	semidirect
14. C₂×C₃×#382	C₂	semidirect
16. #36191	C₃	direct (N × H)
72. #2862	C₂×C₃	semidirect
73. #2851	C₂×C₃	semidirect
74. #2851	C₂×C₃	semidirect
75. #2574	C₂×C₃	semidirect
76. #2570	C₂×C₃	semidirect
77. #2520	C₂×C₃	semidirect
79. #2440	C₂×C₃	semidirect
80. #2439	C₂×C₃	semidirect
81. #2368	C₂×C₃	semidirect
83. C₄×#125	C₂×C₃	semidirect
84. #2285	C₂×C₃	semidirect
85. C₂×#382	C₂×C₃	semidirect
98. C₃×C₄×D₄	Q₈	semidirect
284. C₄×D₄	C₃×Q₈	semidirect
577. C₃	#36191	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×#2862	2
C₃×#2851	2
C₃×#2574	2
C₃×#2570	2
C₃×#2520	2
C₃×#2450	2
C₃×#2440	2
C₃×#2439	2
C₃×#2368	2
C₃×#2352	2
C₃×C₄×#125	2
C₃×#2285	2
C₂×C₃×#382	2
C₃×C₄²×D₄	2
#36191	3

Subgroups — C3×#36191 #10654798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36191 #10654798