Subgroups — C₃×#35310 #10653917

Order 768.

2346 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2848	C₂	1	2	yes	maximal
6	C₃×#2629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2625	C₂	1	2	yes	maximal, complemented
8	C₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2480	C₂	1	4	yes	maximal
10	C₃×#2478	C₂	1	4	yes	maximal, complemented
11	C₃×#2475	C₂	1	4	yes	maximal, complemented
12	C₃×#2473	C₂	1	4	yes	maximal, complemented
13	C₃×#2323	C₂	1	2	yes	maximal, complemented
14	C₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	#35310	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
18	C₃×#541	—	2	8	no	—
19	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×#126	C₂²	1	4	yes	—
21	C₂×C₃×#125	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×#125	C₂²	1	4	yes	complemented
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
27	C₂×C₃×#117	—	2	8	no	—
28	C₂×C₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₃×#117	C₂²	1	2	yes	—
31	C₂×C₃×#117	C₂²	1	2	yes	—
32	C₂×C₃×#117	C₂²	1	1	yes	characteristic
33	C₂×C₃×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
37	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
38	C₃×#400	C₂²	1	4	yes	complemented
39	C₃×#398	C₂²	1	4	yes	complemented
40	C₃×#398	C₂²	1	4	yes	complemented
41	C₃×#398	C₂²	1	4	yes	complemented
42	C₃×#397	C₂²	1	4	yes	—
43	C₃×#397	C₂²	1	4	yes	—
44	C₃×#397	C₂²	1	4	yes	—
45	C₃×#396	C₂²	1	4	yes	—
46	C₃×#391	C₂²	1	2	yes	complemented
47	C₃×#391	C₂²	1	2	yes	complemented
48	C₃×#389	C₂²	1	2	yes	complemented
49	C₃×#389	C₂²	1	2	yes	complemented
50	C₃×#389	C₂²	1	4	yes	complemented
51	C₃×#389	C₂²	1	4	yes	complemented
52	C₃×#388	C₂²	1	4	yes	—
53	C₃×#388	C₂²	1	4	yes	—
54	C₃×#388	C₂²	1	4	yes	—
55	C₃×#387	C₂²	1	4	yes	complemented
56	C₃×#387	C₂²	1	4	yes	complemented
57	C₃×#387	C₂²	1	4	yes	complemented
58	C₃×#387	C₂²	1	4	yes	complemented
59	C₃×#385	C₂²	1	4	yes	—
60	C₃×#385	C₂²	1	4	yes	—
61	C₃×#385	C₂²	1	4	yes	—
62	C₃×#385	C₂²	1	4	yes	—
63	C₃×#385	C₂²	1	4	yes	—
64	C₃×#384	C₂²	1	1	yes	characteristic, complemented
65	C₃×#382	C₂²	1	1	yes	characteristic, complemented
66	C₃×#380	C₂²	1	2	yes	—
67	C₃×#380	C₂²	1	2	yes	—
68	C₃×#380	C₂²	1	4	yes	—
69	C₃×#380	C₂²	1	2	yes	—
70	C₃×#379	C₂²	1	4	yes	—
71	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	complemented
72	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
73	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
74	C₂×#541	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂²×#117	C₂×C₃	1	1	yes	characteristic
76	#2857	C₂×C₃	1	1	yes	characteristic, complemented
77	#2851	C₂×C₃	1	1	yes	characteristic, complemented
78	#2848	C₂×C₃	1	2	yes	—
79	#2629	C₂×C₃	1	1	yes	characteristic, complemented
80	#2625	C₂×C₃	1	2	yes	complemented
81	#2621	C₂×C₃	1	1	yes	characteristic, complemented
82	#2480	C₂×C₃	1	4	yes	—
83	#2478	C₂×C₃	1	4	yes	complemented
84	#2475	C₂×C₃	1	4	yes	complemented
85	#2473	C₂×C₃	1	4	yes	complemented
86	#2323	C₂×C₃	1	2	yes	complemented
87	#2314	C₂×C₃	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
89	C₂⁵×C₃	C₂³	1	1	yes	characteristic
90	C₂²×C₃×Q₈	C₂³	1	2	yes	—
91	C₂³×C₃×C₄	—	2	4	no	—
92	C₂³×C₃×C₄	—	2	4	no	—
93	C₂³×C₃×C₄	—	2	4	no	—
94	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
95	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
96	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
97	C₂³×C₃×C₄	C₂³	1	2	yes	—
98	C₂³×C₃×C₄	C₂³	1	2	yes	—
99	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
100	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
101	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
102	C₃×C₄⋊Q₈	—	2	4	no	—
103	C₃×#126	—	2	16	no	—
104	C₃×#125	—	2	16	no	—
105	C₃×#125	—	2	4	no	—
106	C₃×C₂²⋊Q₈	—	2	8	no	—
107	C₃×C₂²⋊Q₈	—	2	8	no	—
108	C₃×C₂²⋊Q₈	—	2	8	no	—
109	C₃×C₄×Q₈	—	2	8	no	—
110	C₃×#117	—	2	4	no	—
111	C₃×#117	—	2	8	no	—
112	C₃×#117	—	2	8	no	—
113	C₃×#117	—	2	4	no	—
114	C₃×#117	—	2	4	no	—
115	C₃×#117	D₄	1	8	yes	—
116	C₂×C₃×C₄⋊C₄	—	2	8	no	—
117	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₃×C₄⋊C₄	C₂³	1	4	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	4	yes	—
126	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
130	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
132	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
134	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₂×C₃×C₂²⋊C₄	C₂³	1	2	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	—	2	4	no	—
145	C₂×C₃×C₄²	—	2	4	no	—
146	C₂×C₃×C₄²	C₂³	1	4	yes	—
147	C₂×C₃×C₄²	C₂³	1	2	yes	—
148	C₂×C₃×C₄²	C₂³	1	2	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	4	yes	—
157	C₃×#95	C₂³	1	4	yes	—
158	C₃×#95	C₂³	1	4	yes	—
159	C₃×#95	C₂³	1	4	yes	—
160	C₃×#95	C₂³	1	4	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	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
166	#541	—	2	8	no	—
167	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂×#126	C₂²×C₃	1	4	yes	—
169	C₂×#125	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₂×#125	C₂²×C₃	1	4	yes	complemented
171	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
172	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
173	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
174	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
175	C₂×#117	—	2	8	no	—
176	C₂×#117	C₂²×C₃	1	1	yes	characteristic
177	C₂×#117	C₂²×C₃	1	1	yes	characteristic
178	C₂×#117	C₂²×C₃	1	1	yes	characteristic
179	C₂×#117	C₂²×C₃	1	2	yes	—
180	C₂×#117	C₂²×C₃	1	2	yes	—
181	C₂×#117	C₂²×C₃	1	1	yes	characteristic
182	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
183	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
184	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
185	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
186	#400	C₂²×C₃	1	4	yes	complemented
187	#398	C₂²×C₃	1	4	yes	complemented
188	#398	C₂²×C₃	1	4	yes	complemented
189	#398	C₂²×C₃	1	4	yes	complemented
190	#397	C₂²×C₃	1	4	yes	—
191	#397	C₂²×C₃	1	4	yes	—
192	#397	C₂²×C₃	1	4	yes	—
193	#396	C₂²×C₃	1	4	yes	—
194	#391	C₂²×C₃	1	2	yes	complemented
195	#391	C₂²×C₃	1	2	yes	complemented
196	#389	C₂²×C₃	1	2	yes	complemented
197	#389	C₂²×C₃	1	4	yes	complemented
198	#389	C₂²×C₃	1	4	yes	complemented
199	#389	C₂²×C₃	1	2	yes	complemented
200	#388	C₂²×C₃	1	4	yes	—
201	#388	C₂²×C₃	1	4	yes	—
202	#388	C₂²×C₃	1	4	yes	—
203	#387	C₂²×C₃	1	4	yes	complemented
204	#387	C₂²×C₃	1	4	yes	complemented
205	#387	C₂²×C₃	1	4	yes	complemented
206	#387	C₂²×C₃	1	4	yes	complemented
207	#385	C₂²×C₃	1	4	yes	—
208	#385	C₂²×C₃	1	4	yes	—
209	#385	C₂²×C₃	1	4	yes	—
210	#385	C₂²×C₃	1	4	yes	—
211	#385	C₂²×C₃	1	4	yes	—
212	#384	C₂²×C₃	1	1	yes	characteristic, complemented
213	#382	C₂²×C₃	1	1	yes	characteristic, complemented
214	#380	C₂²×C₃	1	2	yes	—
215	#380	C₂²×C₃	1	2	yes	—
216	#380	C₂²×C₃	1	2	yes	—
217	#380	C₂²×C₃	1	4	yes	—
218	#379	C₂²×C₃	1	4	yes	—
219	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
220	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
221	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
222	C₂⁴×C₃	—	2	2	no	—
223	C₂⁴×C₃	—	2	2	no	—
224	C₂⁴×C₃	—	2	2	no	—
225	C₂⁴×C₃	—	2	4	no	—
226	C₂⁴×C₃	—	4	2	no	—
227	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
228	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
229	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
230	C₂×C₃×Q₈	—	2	4	no	—
231	C₂×C₃×Q₈	—	2	4	no	—
232	C₂×C₃×Q₈	—	2	4	no	—
233	C₂²×C₃×C₄	—	2	32	no	—
234	C₂²×C₃×C₄	—	2	2	no	—
235	C₂²×C₃×C₄	—	2	2	no	—
236	C₂²×C₃×C₄	—	2	2	no	—
237	C₂²×C₃×C₄	—	2	2	no	—
238	C₂²×C₃×C₄	—	2	2	no	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	—	2	2	no	—
242	C₂²×C₃×C₄	—	2	2	no	—
243	C₂²×C₃×C₄	—	2	2	no	—
244	C₂²×C₃×C₄	—	2	2	no	—
245	C₂²×C₃×C₄	—	2	2	no	—
246	C₂²×C₃×C₄	—	2	2	no	—
247	C₂²×C₃×C₄	—	2	2	no	—
248	C₂²×C₃×C₄	—	2	2	no	—
249	C₂²×C₃×C₄	—	2	4	no	—
250	C₂²×C₃×C₄	—	2	4	no	—
251	C₂²×C₃×C₄	—	2	4	no	—
252	C₂²×C₃×C₄	—	2	4	no	—
253	C₂²×C₃×C₄	—	4	2	no	—
254	C₂²×C₃×C₄	—	4	2	no	—
255	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
256	C₂²×C₃×C₄	#41	1	4	yes	—
257	C₂²×C₃×C₄	#41	1	4	yes	—
258	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
259	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
260	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
261	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
262	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
263	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
264	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
265	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
266	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
267	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
269	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
270	C₃×C₄⋊C₄	—	2	4	no	—
271	C₃×C₄⋊C₄	—	2	4	no	—
272	C₃×C₄⋊C₄	—	2	4	no	—
273	C₃×C₄⋊C₄	—	2	4	no	—
274	C₃×C₄⋊C₄	—	2	8	no	—
275	C₃×C₄⋊C₄	—	2	8	no	—
276	C₃×C₄⋊C₄	—	2	8	no	—
277	C₃×C₄⋊C₄	—	2	8	no	—
278	C₃×C₄⋊C₄	—	2	4	no	—
279	C₃×C₄⋊C₄	—	2	4	no	—
280	C₃×C₄⋊C₄	—	2	8	no	—
281	C₃×C₄⋊C₄	—	2	8	no	—
282	C₃×C₄⋊C₄	—	4	4	no	—
283	C₃×C₄⋊C₄	—	4	4	no	—
284	C₃×C₄⋊C₄	—	4	4	no	—
285	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
286	C₃×C₂²⋊C₄	—	2	4	no	—
287	C₃×C₂²⋊C₄	—	2	8	no	—
288	C₃×C₂²⋊C₄	—	2	8	no	—
289	C₃×C₂²⋊C₄	—	2	8	no	—
290	C₃×C₂²⋊C₄	—	2	8	no	—
291	C₃×C₂²⋊C₄	—	2	4	no	—
292	C₃×C₂²⋊C₄	—	2	4	no	—
293	C₃×C₂²⋊C₄	—	4	4	no	—
294	C₃×C₂²⋊C₄	—	4	4	no	—
295	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
296	C₃×C₄²	—	2	4	no	—
297	C₃×C₄²	—	2	4	no	—
298	C₃×C₄²	—	2	2	no	—
299	C₃×C₄²	—	2	2	no	—
300	C₃×C₄²	—	2	8	no	—
301	C₃×C₄²	—	4	4	no	—
302	C₃×C₄²	C₂×D₄	1	4	yes	—
303	C₃×C₄²	C₂×D₄	1	4	yes	—
304	C₂⁵	C₂³×C₃	1	1	yes	characteristic
305	C₂²×Q₈	C₂³×C₃	1	2	yes	—
306	C₂³×C₄	—	2	4	no	—
307	C₂³×C₄	—	2	4	no	—
308	C₂³×C₄	—	2	4	no	—
309	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₃	1	2	yes	—
313	C₂³×C₄	C₂³×C₃	1	2	yes	—
314	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
317	C₄⋊Q₈	—	2	4	no	—
318	#126	—	2	16	no	—
319	#125	—	2	16	no	—
320	#125	—	2	4	no	—
321	C₂²⋊Q₈	—	2	8	no	—
322	C₂²⋊Q₈	—	2	8	no	—
323	C₂²⋊Q₈	—	2	8	no	—
324	C₄×Q₈	—	2	8	no	—
325	#117	—	2	4	no	—
326	#117	—	2	8	no	—
327	#117	—	2	8	no	—
328	#117	—	2	4	no	—
329	#117	—	2	4	no	—
330	#117	C₃×D₄	1	8	yes	—
331	C₂×C₄⋊C₄	—	2	8	no	—
332	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
343	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
348	C₂×C₂²⋊C₄	—	2	8	no	—
349	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
359	C₂×C₄²	—	2	4	no	—
360	C₂×C₄²	—	2	4	no	—
361	C₂×C₄²	C₂³×C₃	1	2	yes	—
362	C₂×C₄²	C₂³×C₃	1	2	yes	—
363	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₃	1	4	yes	—
366	C₂×C₄²	C₂³×C₃	1	4	yes	—
367	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
369	#95	C₂³×C₃	1	4	yes	—
370	#95	C₂³×C₃	1	4	yes	—
371	#95	C₂³×C₃	1	4	yes	—
372	#95	C₂³×C₃	1	4	yes	—
373	#95	C₂³×C₃	1	4	yes	—
374	#95	C₂³×C₃	1	4	yes	—
375	#95	C₂³×C₃	1	4	yes	—
376	#95	C₂³×C₃	1	4	yes	—
377	#95	C₂³×C₃	1	4	yes	—
378	#95	C₂³×C₃	1	4	yes	—
379	#95	C₂³×C₃	1	4	yes	—
380	C₂³×C₃	—	2	1	no	—
381	C₂³×C₃	—	2	1	no	—
382	C₂³×C₃	—	2	2	no	—
383	C₂³×C₃	—	2	8	no	—
384	C₂³×C₃	—	2	1	no	—
385	C₂³×C₃	—	2	1	no	—
386	C₂³×C₃	—	2	1	no	—
387	C₂³×C₃	—	2	1	no	—
388	C₂³×C₃	—	2	2	no	—
389	C₂³×C₃	—	2	2	no	—
390	C₂³×C₃	—	2	2	no	—
391	C₂³×C₃	—	2	2	no	—
392	C₂³×C₃	—	4	8	no	—
393	C₂³×C₃	—	4	8	no	—
394	C₂³×C₃	—	4	4	no	—
395	C₂³×C₃	—	4	4	no	—
396	C₂³×C₃	C₂²×D₄	1	2	yes	—
397	C₂³×C₃	C₂×#41	1	2	yes	—
398	C₂³×C₃	C₂×#41	1	2	yes	—
399	C₂³×C₃	2₋¹⁺⁴	1	4	yes	—
400	C₂³×C₃	C₂⁵	1	1	yes	characteristic
401	C₃×Q₈	—	4	8	no	—
402	C₂×C₃×C₄	—	2	8	no	—
403	C₂×C₃×C₄	—	2	8	no	—
404	C₂×C₃×C₄	—	2	8	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	2	no	—
412	C₂×C₃×C₄	—	2	2	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	2	8	no	—
416	C₂×C₃×C₄	—	2	8	no	—
417	C₂×C₃×C₄	—	2	8	no	—
418	C₂×C₃×C₄	—	2	2	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	4	no	—
421	C₂×C₃×C₄	—	2	4	no	—
422	C₂×C₃×C₄	—	2	4	no	—
423	C₂×C₃×C₄	—	2	4	no	—
424	C₂×C₃×C₄	—	2	4	no	—
425	C₂×C₃×C₄	—	2	4	no	—
426	C₂×C₃×C₄	—	2	4	no	—
427	C₂×C₃×C₄	—	2	4	no	—
428	C₂×C₃×C₄	—	2	2	no	—
429	C₂×C₃×C₄	—	2	2	no	—
430	C₂×C₃×C₄	—	2	4	no	—
431	C₂×C₃×C₄	—	2	4	no	—
432	C₂×C₃×C₄	—	2	4	no	—
433	C₂×C₃×C₄	—	2	4	no	—
434	C₂×C₃×C₄	—	2	2	no	—
435	C₂×C₃×C₄	—	2	2	no	—
436	C₂×C₃×C₄	—	4	8	no	—
437	C₂×C₃×C₄	—	4	8	no	—
438	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
439	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
440	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
441	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
442	C₂×C₃×C₄	C₂×#41	1	2	yes	—
443	C₂×C₃×C₄	C₂×#41	1	2	yes	—
444	C₂×C₃×C₄	C₂×#41	1	2	yes	—
445	C₂×C₃×C₄	C₂×#41	1	2	yes	—
446	C₂⁴	—	2	2	no	—
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	2	no	—
449	C₂⁴	—	2	4	no	—
450	C₂⁴	—	4	2	no	—
451	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
452	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
453	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
454	C₂×Q₈	—	2	4	no	—
455	C₂×Q₈	—	2	4	no	—
456	C₂×Q₈	—	2	4	no	—
457	C₂²×C₄	—	2	32	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
480	C₂²×C₄	C₃×#41	1	4	yes	—
481	C₂²×C₄	C₃×#41	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
486	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	8	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	2	8	no	—
501	C₄⋊C₄	—	2	8	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	8	no	—
505	C₄⋊C₄	—	2	8	no	—
506	C₄⋊C₄	—	4	4	no	—
507	C₄⋊C₄	—	4	4	no	—
508	C₄⋊C₄	—	4	4	no	—
509	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	2	8	no	—
513	C₂²⋊C₄	—	2	8	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₂²⋊C₄	—	4	4	no	—
519	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
520	C₄²	—	2	4	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	8	no	—
525	C₄²	—	4	4	no	—
526	C₄²	C₂×C₃×D₄	1	4	yes	—
527	C₄²	C₂×C₃×D₄	1	4	yes	—
528	C₂²×C₃	—	2	2	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	4	no	—
531	C₂²×C₃	—	2	4	no	—
532	C₂²×C₃	—	2	2	no	—
533	C₂²×C₃	—	2	2	no	—
534	C₂²×C₃	—	2	4	no	—
535	C₂²×C₃	—	2	4	no	—
536	C₂²×C₃	—	4	16	no	—
537	C₂²×C₃	—	4	1	no	—
538	C₂²×C₃	—	4	1	no	—
539	C₂²×C₃	—	4	1	no	—
540	C₂²×C₃	—	4	1	no	—
541	C₂²×C₃	—	4	2	no	—
542	C₂²×C₃	—	4	2	no	—
543	C₂²×C₃	#541	1	4	yes	complemented
544	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
545	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
546	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
547	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
548	C₂²×C₃	#585	1	2	yes	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	2	2	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	4	no	—
553	C₃×C₄	—	2	4	no	—
554	C₃×C₄	—	4	4	no	—
555	C₃×C₄	—	4	4	no	—
556	C₃×C₄	—	4	4	no	—
557	C₃×C₄	—	4	2	no	—
558	C₃×C₄	—	4	2	no	—
559	C₃×C₄	—	4	4	no	—
560	C₃×C₄	#525	1	4	yes	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	8	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	4	8	no	—
574	C₂³	—	4	8	no	—
575	C₂³	—	4	4	no	—
576	C₂³	—	4	4	no	—
577	C₂³	C₂²×C₃×D₄	1	2	yes	—
578	C₂³	C₂×C₃×#41	1	2	yes	—
579	C₂³	C₂×C₃×#41	1	2	yes	—
580	C₂³	C₃×2₋¹⁺⁴	1	4	yes	—
581	C₂³	C₂⁵×C₃	1	1	yes	characteristic
582	Q₈	—	4	8	no	—
583	C₂×C₄	—	2	8	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	2	8	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	2	8	no	—
598	C₂×C₄	—	2	8	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
620	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
621	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
622	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
623	C₂×C₄	C₂×C₃×#41	1	2	yes	—
624	C₂×C₄	C₂×C₃×#41	1	2	yes	—
625	C₂×C₄	C₂×C₃×#41	1	2	yes	—
626	C₂×C₄	C₂×C₃×#41	1	2	yes	—
627	C₂×C₃	—	2	4	no	—
628	C₂×C₃	—	4	2	no	—
629	C₂×C₃	—	4	2	no	—
630	C₂×C₃	C₂×#525	1	1	yes	characteristic
631	C₂×C₃	C₂×#541	1	1	yes	characteristic
632	C₂×C₃	#3455	1	1	yes	characteristic
633	C₂×C₃	#3489	1	2	yes	—
634	C₂×C₃	#3495	1	2	yes	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	4	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	4	16	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	C₃×#541	1	4	yes	complemented
651	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
652	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
653	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
654	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
655	C₂²	C₃×#585	1	2	yes	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	4	no	—
661	C₄	—	4	4	no	—
662	C₄	—	4	4	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	4	no	—
667	C₄	C₃×#525	1	4	yes	—
668	C₃	#35310	1	1	yes	characteristic, direct product factor, Sylow
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	2	no	—
672	C₂	C₂×C₃×#525	1	1	yes	characteristic
673	C₂	C₂×C₃×#541	1	1	yes	characteristic
674	C₂	C₃×#3455	1	1	yes	characteristic
675	C₂	C₃×#3489	1	2	yes	—
676	C₂	C₃×#3495	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁵×C₃	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×#541	C₂	semidirect
3. C₃×#2857	C₂	semidirect
4. C₃×#2851	C₂	semidirect
6. C₃×#2629	C₂	semidirect
7. C₃×#2625	C₂	semidirect
8. C₃×#2621	C₂	semidirect
10. C₃×#2478	C₂	semidirect
11. C₃×#2475	C₂	semidirect
12. C₃×#2473	C₂	semidirect
13. C₃×#2323	C₂	semidirect
14. C₃×#2314	C₂	semidirect
15. C₃×C₄×C₂²⋊Q₈	C₂	semidirect
16. #35310	C₃	direct (N × H)
19. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₃×#125	C₂²	semidirect
22. C₂×C₃×#125	C₂²	semidirect
26. C₂×C₃×C₄×Q₈	C₂²	semidirect
38. C₃×#400	C₂²	semidirect
39. C₃×#398	C₂²	semidirect
40. C₃×#398	C₂²	semidirect
41. C₃×#398	C₂²	semidirect
46. C₃×#391	C₂²	semidirect
47. C₃×#391	C₂²	semidirect
48. C₃×#389	C₂²	semidirect
49. C₃×#389	C₂²	semidirect
50. C₃×#389	C₂²	semidirect
51. C₃×#389	C₂²	semidirect
55. C₃×#387	C₂²	semidirect
56. C₃×#387	C₂²	semidirect
57. C₃×#387	C₂²	semidirect
58. C₃×#387	C₂²	semidirect
64. C₃×#384	C₂²	semidirect
65. C₃×#382	C₂²	semidirect
71. C₃×C₄×C₄⋊C₄	C₂²	semidirect
72. C₃×C₄×C₄⋊C₄	C₂²	semidirect
74. C₂×#541	C₂×C₃	semidirect
76. #2857	C₂×C₃	semidirect
77. #2851	C₂×C₃	semidirect
79. #2629	C₂×C₃	semidirect
80. #2625	C₂×C₃	semidirect
81. #2621	C₂×C₃	semidirect
83. #2478	C₂×C₃	semidirect
84. #2475	C₂×C₃	semidirect
85. #2473	C₂×C₃	semidirect
86. #2323	C₂×C₃	semidirect
87. #2314	C₂×C₃	semidirect
88. C₄×C₂²⋊Q₈	C₂×C₃	semidirect
167. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
169. C₂×#125	C₂²×C₃	semidirect
170. C₂×#125	C₂²×C₃	semidirect
174. C₂×C₄×Q₈	C₂²×C₃	semidirect
186. #400	C₂²×C₃	semidirect
187. #398	C₂²×C₃	semidirect
188. #398	C₂²×C₃	semidirect
189. #398	C₂²×C₃	semidirect
194. #391	C₂²×C₃	semidirect
195. #391	C₂²×C₃	semidirect
196. #389	C₂²×C₃	semidirect
197. #389	C₂²×C₃	semidirect
198. #389	C₂²×C₃	semidirect
199. #389	C₂²×C₃	semidirect
203. #387	C₂²×C₃	semidirect
204. #387	C₂²×C₃	semidirect
205. #387	C₂²×C₃	semidirect
206. #387	C₂²×C₃	semidirect
212. #384	C₂²×C₃	semidirect
213. #382	C₂²×C₃	semidirect
219. C₄×C₄⋊C₄	C₂²×C₃	semidirect
220. C₄×C₄⋊C₄	C₂²×C₃	semidirect
543. C₂²×C₃	#541	semidirect
650. C₂²	C₃×#541	semidirect
668. C₃	#35310	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×#541	2
C₂²×C₃×#117	2
C₃×#2857	2
C₃×#2851	2
C₃×#2848	2
C₃×#2629	2
C₃×#2625	2
C₃×#2621	2
C₃×#2480	2
C₃×#2478	2
C₃×#2475	2
C₃×#2473	2
C₃×#2323	2
C₃×#2314	2
C₃×C₄×C₂²⋊Q₈	2
#35310	3

Subgroups — C3×#35310 #10653917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35310 #10653917