Subgroups — C₃×#39365 #10657972

Order 768.

2070 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#544	C₂	1	2	yes	maximal, complemented
2	C₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2734	C₂	1	2	yes	maximal, complemented
4	C₃×#2732	C₂	1	2	yes	maximal
5	C₃×#2726	C₂	1	2	yes	maximal, complemented
6	C₃×#2683	C₂	1	2	yes	maximal
7	C₃×#2629	C₂	1	2	yes	maximal, complemented
8	C₃×#2556	C₂	1	4	yes	maximal, complemented
9	C₃×#2550	C₂	1	2	yes	maximal, complemented
10	C₃×#2441	C₂	1	2	yes	maximal, complemented
11	C₃×#2440	C₂	1	2	yes	maximal, complemented
12	C₃×#2429	C₂	1	4	yes	maximal, complemented
13	C₃×#2352	C₂	1	2	yes	maximal
14	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2293	C₂	1	1	yes	maximal, characteristic
16	#39365	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×#544	—	2	16	no	—
18	C₂×C₃×C₄⋊Q₈	C₂²	1	4	yes	—
19	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×#125	C₂²	1	2	yes	—
22	C₂×C₃×#125	C₂²	1	2	yes	—
23	C₂×C₃×#125	C₂²	1	4	yes	—
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
28	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×#117	C₂²	1	2	yes	—
30	C₂×C₃×#117	C₂²	1	2	yes	—
31	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₃×#399	C₂²	1	4	yes	—
33	C₃×#398	C₂²	1	4	yes	—
34	C₃×#398	C₂²	1	4	yes	—
35	C₃×#398	C₂²	1	4	yes	—
36	C₃×#398	C₂²	1	4	yes	—
37	C₃×#396	C₂²	1	4	yes	—
38	C₃×#396	C₂²	1	4	yes	—
39	C₃×#396	C₂²	1	4	yes	—
40	C₃×#395	C₂²	1	4	yes	—
41	C₃×#395	C₂²	1	4	yes	—
42	C₃×#391	C₂²	1	4	yes	—
43	C₃×#391	C₂²	1	2	yes	—
44	C₃×#390	C₂²	1	1	yes	characteristic
45	C₃×#390	C₂²	1	1	yes	characteristic
46	C₃×#389	C₂²	1	2	yes	—
47	C₃×#389	C₂²	1	2	yes	—
48	C₃×#389	C₂²	1	2	yes	—
49	C₃×#389	C₂²	1	2	yes	—
50	C₃×#389	C₂²	1	2	yes	—
51	C₃×#389	C₂²	1	4	yes	—
52	C₃×#389	C₂²	1	4	yes	—
53	C₃×#389	C₂²	1	2	yes	—
54	C₃×#389	C₂²	1	1	yes	characteristic
55	C₃×#389	C₂²	1	2	yes	—
56	C₃×#389	C₂²	1	1	yes	characteristic
57	C₃×#389	C₂²	1	2	yes	—
58	C₃×#388	C₂²	1	2	yes	—
59	C₃×#388	C₂²	1	4	yes	—
60	C₃×#388	C₂²	1	2	yes	—
61	C₃×#387	C₂²	1	4	yes	—
62	C₃×#387	C₂²	1	4	yes	—
63	C₃×#386	C₂²	1	4	yes	—
64	C₃×#385	C₂²	1	4	yes	—
65	C₃×#384	C₂²	1	1	yes	characteristic
66	C₃×#384	C₂²	1	1	yes	characteristic
67	C₃×#384	C₂²	1	1	yes	characteristic
68	C₃×#382	C₂²	1	2	yes	—
69	C₃×#380	C₂²	1	2	yes	—
70	C₃×#380	C₂²	1	2	yes	—
71	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
72	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
73	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
74	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
75	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₃×C₄³	C₂²	1	1	yes	characteristic
77	C₂×#544	C₂×C₃	1	2	yes	complemented
78	#2859	C₂×C₃	1	1	yes	characteristic, complemented
79	#2734	C₂×C₃	1	2	yes	complemented
80	#2732	C₂×C₃	1	2	yes	—
81	#2726	C₂×C₃	1	2	yes	complemented
82	#2683	C₂×C₃	1	2	yes	—
83	#2629	C₂×C₃	1	2	yes	complemented
84	#2556	C₂×C₃	1	4	yes	complemented
85	#2550	C₂×C₃	1	2	yes	complemented
86	#2441	C₂×C₃	1	2	yes	complemented
87	#2440	C₂×C₃	1	2	yes	complemented
88	#2429	C₂×C₃	1	4	yes	complemented
89	#2352	C₂×C₃	1	2	yes	—
90	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
91	#2293	C₂×C₃	1	1	yes	characteristic
92	C₂²×C₃×Q₈	C₂³	1	4	yes	—
93	C₂²×C₃×Q₈	C₂³	1	2	yes	—
94	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
95	C₂³×C₃×C₄	C₂³	1	2	yes	—
96	C₂³×C₃×C₄	C₂³	1	4	yes	—
97	C₃×C₄⋊Q₈	—	2	16	no	—
98	C₃×C₄⋊Q₈	—	2	8	no	—
99	C₃×C₄⋊Q₈	D₄	1	8	yes	complemented
100	C₃×#125	—	2	16	no	—
101	C₃×#125	—	2	8	no	—
102	C₃×#125	—	2	8	no	—
103	C₃×C₂²⋊Q₈	—	2	16	no	—
104	C₃×C₂²⋊Q₈	—	2	16	no	—
105	C₃×C₂²⋊Q₈	—	4	8	no	—
106	C₃×C₄×Q₈	—	4	4	no	—
107	C₃×C₄×D₄	Q₈	1	8	yes	complemented
108	C₃×#117	—	2	8	no	—
109	C₃×#117	—	2	8	no	—
110	C₂×C₃×C₄⋊C₄	—	2	8	no	—
111	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
146	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
147	C₂×C₃×C₄²	C₂³	1	2	yes	—
148	C₂×C₃×C₄²	C₂³	1	4	yes	—
149	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
150	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₄²	C₂³	1	4	yes	—
152	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
154	C₃×#95	C₂³	1	4	yes	—
155	C₃×#95	C₂³	1	4	yes	—
156	C₃×#95	C₂³	1	2	yes	—
157	C₃×#95	C₂³	1	2	yes	—
158	C₃×#95	C₂³	1	4	yes	—
159	C₃×#95	C₂³	1	4	yes	—
160	C₃×#95	C₂³	1	2	yes	—
161	C₃×#95	C₂³	1	4	yes	—
162	C₃×#95	C₂³	1	4	yes	—
163	C₃×#95	C₂³	1	4	yes	—
164	C₃×#95	C₂³	1	4	yes	—
165	#544	—	2	16	no	—
166	C₂×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
167	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
168	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
169	C₂×#125	C₂²×C₃	1	2	yes	—
170	C₂×#125	C₂²×C₃	1	2	yes	—
171	C₂×#125	C₂²×C₃	1	4	yes	—
172	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
173	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
174	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
175	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
176	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
177	C₂×#117	C₂²×C₃	1	2	yes	—
178	C₂×#117	C₂²×C₃	1	2	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
180	#399	C₂²×C₃	1	4	yes	—
181	#398	C₂²×C₃	1	4	yes	—
182	#398	C₂²×C₃	1	4	yes	—
183	#398	C₂²×C₃	1	4	yes	—
184	#398	C₂²×C₃	1	4	yes	—
185	#396	C₂²×C₃	1	4	yes	—
186	#396	C₂²×C₃	1	4	yes	—
187	#396	C₂²×C₃	1	4	yes	—
188	#395	C₂²×C₃	1	4	yes	—
189	#395	C₂²×C₃	1	4	yes	—
190	#391	C₂²×C₃	1	2	yes	—
191	#391	C₂²×C₃	1	4	yes	—
192	#390	C₂²×C₃	1	1	yes	characteristic
193	#390	C₂²×C₃	1	1	yes	characteristic
194	#389	C₂²×C₃	1	2	yes	—
195	#389	C₂²×C₃	1	2	yes	—
196	#389	C₂²×C₃	1	2	yes	—
197	#389	C₂²×C₃	1	2	yes	—
198	#389	C₂²×C₃	1	2	yes	—
199	#389	C₂²×C₃	1	2	yes	—
200	#389	C₂²×C₃	1	2	yes	—
201	#389	C₂²×C₃	1	2	yes	—
202	#389	C₂²×C₃	1	4	yes	—
203	#389	C₂²×C₃	1	4	yes	—
204	#389	C₂²×C₃	1	1	yes	characteristic
205	#389	C₂²×C₃	1	1	yes	characteristic
206	#388	C₂²×C₃	1	4	yes	—
207	#388	C₂²×C₃	1	2	yes	—
208	#388	C₂²×C₃	1	2	yes	—
209	#387	C₂²×C₃	1	4	yes	—
210	#387	C₂²×C₃	1	4	yes	—
211	#386	C₂²×C₃	1	4	yes	—
212	#385	C₂²×C₃	1	4	yes	—
213	#384	C₂²×C₃	1	1	yes	characteristic
214	#384	C₂²×C₃	1	1	yes	characteristic
215	#384	C₂²×C₃	1	1	yes	characteristic
216	#382	C₂²×C₃	1	2	yes	—
217	#380	C₂²×C₃	1	2	yes	—
218	#380	C₂²×C₃	1	2	yes	—
219	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
220	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
221	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
222	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
223	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
224	C₄³	C₂²×C₃	1	1	yes	characteristic
225	C₂⁴×C₃	C₂⁴	1	2	yes	—
226	C₂×C₃×Q₈	—	2	8	no	—
227	C₂×C₃×Q₈	—	4	2	no	—
228	C₂×C₃×Q₈	—	4	2	no	—
229	C₂×C₃×Q₈	—	4	4	no	—
230	C₂×C₃×Q₈	—	4	4	no	—
231	C₂×C₃×Q₈	C₂×D₄	1	8	yes	—
232	C₂×C₃×D₄	—	4	1	no	—
233	C₂×C₃×D₄	—	4	1	no	—
234	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
235	C₂²×C₃×C₄	—	2	4	no	—
236	C₂²×C₃×C₄	—	2	4	no	—
237	C₂²×C₃×C₄	—	2	8	no	—
238	C₂²×C₃×C₄	—	4	4	no	—
239	C₂²×C₃×C₄	—	4	4	no	—
240	C₂²×C₃×C₄	C₂×Q₈	1	8	yes	—
241	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
242	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
243	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
244	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
245	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
246	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
247	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
252	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
254	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
255	C₃×C₄⋊C₄	—	2	8	no	—
256	C₃×C₄⋊C₄	—	2	4	no	—
257	C₃×C₄⋊C₄	—	2	4	no	—
258	C₃×C₄⋊C₄	—	2	4	no	—
259	C₃×C₄⋊C₄	—	2	4	no	—
260	C₃×C₄⋊C₄	—	2	8	no	—
261	C₃×C₄⋊C₄	—	2	8	no	—
262	C₃×C₄⋊C₄	—	2	8	no	—
263	C₃×C₄⋊C₄	—	2	8	no	—
264	C₃×C₄⋊C₄	—	2	8	no	—
265	C₃×C₄⋊C₄	—	2	8	no	—
266	C₃×C₄⋊C₄	—	2	4	no	—
267	C₃×C₄⋊C₄	—	2	4	no	—
268	C₃×C₄⋊C₄	—	2	4	no	—
269	C₃×C₄⋊C₄	—	4	2	no	—
270	C₃×C₄⋊C₄	—	4	2	no	—
271	C₃×C₄⋊C₄	—	4	2	no	—
272	C₃×C₄⋊C₄	—	4	1	no	—
273	C₃×C₄⋊C₄	—	4	1	no	—
274	C₃×C₄⋊C₄	—	4	4	no	—
275	C₃×C₄⋊C₄	—	4	2	no	—
276	C₃×C₄⋊C₄	—	4	4	no	—
277	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
278	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
279	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
280	C₃×C₂²⋊C₄	—	2	8	no	—
281	C₃×C₂²⋊C₄	—	2	4	no	—
282	C₃×C₂²⋊C₄	—	2	4	no	—
283	C₃×C₂²⋊C₄	—	2	4	no	—
284	C₃×C₂²⋊C₄	—	2	4	no	—
285	C₃×C₂²⋊C₄	—	4	4	no	—
286	C₃×C₂²⋊C₄	—	4	4	no	—
287	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
288	C₃×C₄²	—	2	8	no	—
289	C₃×C₄²	—	2	4	no	—
290	C₃×C₄²	—	2	2	no	—
291	C₃×C₄²	—	2	2	no	—
292	C₃×C₄²	—	2	2	no	—
293	C₃×C₄²	—	4	1	no	—
294	C₃×C₄²	—	4	1	no	—
295	C₃×C₄²	—	4	4	no	—
296	C₃×C₄²	C₂×D₄	1	4	yes	—
297	C₃×C₄²	C₂×Q₈	1	4	yes	—
298	C₂²×Q₈	C₂³×C₃	1	4	yes	—
299	C₂²×Q₈	C₂³×C₃	1	2	yes	—
300	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₃	1	2	yes	—
302	C₂³×C₄	C₂³×C₃	1	4	yes	—
303	C₄⋊Q₈	—	2	16	no	—
304	C₄⋊Q₈	—	2	8	no	—
305	C₄⋊Q₈	C₃×D₄	1	8	yes	complemented
306	#125	—	2	16	no	—
307	#125	—	2	8	no	—
308	#125	—	2	8	no	—
309	C₂²⋊Q₈	—	2	16	no	—
310	C₂²⋊Q₈	—	2	16	no	—
311	C₂²⋊Q₈	—	4	8	no	—
312	C₄×Q₈	—	4	4	no	—
313	C₄×D₄	C₃×Q₈	1	8	yes	complemented
314	#117	—	2	8	no	—
315	#117	—	2	8	no	—
316	C₂×C₄⋊C₄	—	2	8	no	—
317	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
319	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
329	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
333	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
350	C₂×C₄²	C₂³×C₃	1	2	yes	—
351	C₂×C₄²	C₂³×C₃	1	4	yes	—
352	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₃	1	4	yes	—
356	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
360	#95	C₂³×C₃	1	4	yes	—
361	#95	C₂³×C₃	1	4	yes	—
362	#95	C₂³×C₃	1	2	yes	—
363	#95	C₂³×C₃	1	2	yes	—
364	#95	C₂³×C₃	1	4	yes	—
365	#95	C₂³×C₃	1	4	yes	—
366	#95	C₂³×C₃	1	2	yes	—
367	#95	C₂³×C₃	1	4	yes	—
368	#95	C₂³×C₃	1	4	yes	—
369	#95	C₂³×C₃	1	4	yes	—
370	#95	C₂³×C₃	1	4	yes	—
371	C₂³×C₃	—	2	2	no	—
372	C₂³×C₃	—	2	2	no	—
373	C₂³×C₃	—	2	2	no	—
374	C₂³×C₃	—	2	2	no	—
375	C₂³×C₃	—	2	2	no	—
376	C₂³×C₃	—	2	2	no	—
377	C₂³×C₃	C₂²×Q₈	1	4	yes	—
378	C₂³×C₃	C₂⁵	1	1	yes	characteristic
379	C₃×Q₈	—	4	8	no	—
380	C₃×Q₈	—	8	8	no	—
381	C₃×D₄	—	4	4	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	4	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	4	no	—
398	C₂×C₃×C₄	—	2	16	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	4	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	4	no	—
403	C₂×C₃×C₄	—	2	4	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	4	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	4	no	—
408	C₂×C₃×C₄	—	2	4	no	—
409	C₂×C₃×C₄	—	2	4	no	—
410	C₂×C₃×C₄	—	2	4	no	—
411	C₂×C₃×C₄	—	2	2	no	—
412	C₂×C₃×C₄	—	2	4	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	8	8	no	—
415	C₂×C₃×C₄	C₂²×D₄	1	8	yes	—
416	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
417	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
418	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
419	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
420	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
421	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
422	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
423	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
424	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
425	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
426	C₂⁴	C₂⁴×C₃	1	2	yes	—
427	C₂×Q₈	—	2	8	no	—
428	C₂×Q₈	—	4	2	no	—
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	4	4	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	C₂×C₃×D₄	1	8	yes	—
433	C₂×D₄	—	4	1	no	—
434	C₂×D₄	—	4	1	no	—
435	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	—	4	4	no	—
441	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	—
442	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
447	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
451	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
452	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	—	4	4	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	4	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	4	4	no	—
478	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
479	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
480	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₂²⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
489	C₄²	—	2	8	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	4	4	no	—
495	C₄²	—	4	1	no	—
496	C₄²	—	4	1	no	—
497	C₄²	C₂×C₃×D₄	1	4	yes	—
498	C₄²	C₂×C₃×Q₈	1	4	yes	—
499	C₂²×C₃	—	2	4	no	—
500	C₂²×C₃	—	2	4	no	—
501	C₂²×C₃	—	2	4	no	—
502	C₂²×C₃	—	4	2	no	—
503	C₂²×C₃	—	4	2	no	—
504	C₂²×C₃	—	4	2	no	—
505	C₂²×C₃	—	4	2	no	—
506	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
507	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
508	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
510	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
511	C₂²×C₃	#585	1	1	yes	characteristic
512	C₂²×C₃	#585	1	1	yes	characteristic
513	C₃×C₄	—	2	2	no	—
514	C₃×C₄	—	2	4	no	—
515	C₃×C₄	—	2	8	no	—
516	C₃×C₄	—	2	2	no	—
517	C₃×C₄	—	2	2	no	—
518	C₃×C₄	—	2	2	no	—
519	C₃×C₄	—	2	2	no	—
520	C₃×C₄	—	2	2	no	—
521	C₃×C₄	—	4	4	no	—
522	C₃×C₄	—	4	2	no	—
523	C₃×C₄	—	4	2	no	—
524	C₃×C₄	—	4	4	no	—
525	C₃×C₄	—	4	4	no	—
526	C₃×C₄	D₄×Q₈	1	4	yes	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	C₂²×C₃×Q₈	1	4	yes	—
534	C₂³	C₂⁵×C₃	1	1	yes	characteristic
535	Q₈	—	4	8	no	—
536	Q₈	—	8	8	no	—
537	D₄	—	4	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	16	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	8	8	no	—
571	C₂×C₄	C₂²×C₃×D₄	1	8	yes	—
572	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
573	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
574	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
575	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
576	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
577	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
578	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
579	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
580	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
581	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
582	C₂×C₃	—	4	4	no	—
583	C₂×C₃	#3458	1	1	yes	characteristic
584	C₂×C₃	C₂×D₄×Q₈	1	1	yes	characteristic
585	C₂×C₃	#3496	1	1	yes	characteristic
586	C₂×C₃	#3497	1	1	yes	characteristic
587	C₂×C₃	#3503	1	1	yes	characteristic
588	C₂×C₃	#3559	1	1	yes	characteristic
589	C₂×C₃	#3563	1	1	yes	characteristic
590	C₂²	—	2	4	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
598	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
599	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
600	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
601	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
602	C₂²	C₃×#585	1	1	yes	characteristic
603	C₂²	C₃×#585	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	4	no	—
606	C₄	—	2	8	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	4	4	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	2	no	—
615	C₄	—	4	4	no	—
616	C₄	—	4	4	no	—
617	C₄	C₃×D₄×Q₈	1	4	yes	—
618	C₃	#39365	1	1	yes	characteristic, direct product factor, Sylow
619	C₂	—	4	4	no	—
620	C₂	C₃×#3458	1	1	yes	characteristic
621	C₂	C₂×C₃×D₄×Q₈	1	1	yes	characteristic
622	C₂	C₃×#3496	1	1	yes	characteristic
623	C₂	C₃×#3497	1	1	yes	characteristic
624	C₂	C₃×#3503	1	1	yes	characteristic
625	C₂	C₃×#3559	1	1	yes	characteristic
626	C₂	C₃×#3563	1	1	yes	characteristic

	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. C₂×C₃×#544	C₂	semidirect
2. C₃×#2859	C₂	semidirect
3. C₃×#2734	C₂	semidirect
5. C₃×#2726	C₂	semidirect
7. C₃×#2629	C₂	semidirect
8. C₃×#2556	C₂	semidirect
9. C₃×#2550	C₂	semidirect
10. C₃×#2441	C₂	semidirect
11. C₃×#2440	C₂	semidirect
12. C₃×#2429	C₂	semidirect
14. C₃×C₄×C₄⋊Q₈	C₂	semidirect
16. #39365	C₃	direct (N × H)
77. C₂×#544	C₂×C₃	semidirect
78. #2859	C₂×C₃	semidirect
79. #2734	C₂×C₃	semidirect
81. #2726	C₂×C₃	semidirect
83. #2629	C₂×C₃	semidirect
84. #2556	C₂×C₃	semidirect
85. #2550	C₂×C₃	semidirect
86. #2441	C₂×C₃	semidirect
87. #2440	C₂×C₃	semidirect
88. #2429	C₂×C₃	semidirect
90. C₄×C₄⋊Q₈	C₂×C₃	semidirect
99. C₃×C₄⋊Q₈	D₄	semidirect
107. C₃×C₄×D₄	Q₈	semidirect
305. C₄⋊Q₈	C₃×D₄	semidirect
313. C₄×D₄	C₃×Q₈	semidirect
618. C₃	#39365	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#544	2
C₃×#2859	2
C₃×#2734	2
C₃×#2732	2
C₃×#2726	2
C₃×#2683	2
C₃×#2629	2
C₃×#2556	2
C₃×#2550	2
C₃×#2441	2
C₃×#2440	2
C₃×#2429	2
C₃×#2352	2
C₃×C₄×C₄⋊Q₈	2
C₃×#2293	2
#39365	3

Subgroups — C3×#39365 #10657972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#39365 #10657972