Subgroups — C₃×#42983 #10661590

Order 768.

1802 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2830	C₂	1	2	yes	maximal, complemented
2	C₃×#2736	C₂	1	2	yes	maximal, complemented
3	C₃×#2735	C₂	1	4	yes	maximal, complemented
4	C₃×#2735	C₂	1	2	yes	maximal, complemented
5	C₃×#2651	C₂	1	4	yes	maximal, complemented
6	C₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2593	C₂	1	2	yes	maximal, complemented
8	C₃×#2592	C₂	1	2	yes	maximal, complemented
9	C₃×#2545	C₂	1	2	yes	maximal, complemented
10	C₃×#2513	C₂	1	2	yes	maximal, complemented
11	C₃×#2448	C₂	1	2	yes	maximal, complemented
12	C₃×#2435	C₂	1	2	yes	maximal
13	C₃×#2396	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2362	C₂	1	2	yes	maximal, complemented
15	C₃×#2309	C₂	1	1	yes	maximal, characteristic
16	#42983	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×#124	C₂²	1	2	yes	—
20	C₂×C₃×#124	C₂²	1	2	yes	—
21	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
23	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₃×#117	C₂²	1	1	yes	characteristic
26	C₃×#400	C₂²	1	1	yes	characteristic, complemented
27	C₃×#399	C₂²	1	1	yes	characteristic
28	C₃×#399	C₂²	1	4	yes	complemented
29	C₃×#398	C₂²	1	2	yes	complemented
30	C₃×#398	C₂²	1	2	yes	complemented
31	C₃×#398	C₂²	1	2	yes	complemented
32	C₃×#397	C₂²	1	2	yes	—
33	C₃×#397	C₂²	1	2	yes	—
34	C₃×#397	C₂²	1	4	yes	complemented
35	C₃×#397	C₂²	1	4	yes	complemented
36	C₃×#397	C₂²	1	4	yes	complemented
37	C₃×#397	C₂²	1	4	yes	complemented
38	C₃×#396	C₂²	1	2	yes	—
39	C₃×#396	C₂²	1	4	yes	complemented
40	C₃×#396	C₂²	1	4	yes	complemented
41	C₃×#395	C₂²	1	1	yes	characteristic, complemented
42	C₃×#394	C₂²	1	4	yes	—
43	C₃×#394	C₂²	1	4	yes	—
44	C₃×#393	C₂²	1	1	yes	characteristic
45	C₃×#393	C₂²	1	4	yes	complemented
46	C₃×#391	C₂²	1	2	yes	complemented
47	C₃×#391	C₂²	1	2	yes	complemented
48	C₃×#390	C₂²	1	2	yes	—
49	C₃×#390	C₂²	1	2	yes	—
50	C₃×#390	C₂²	1	2	yes	—
51	C₃×#390	C₂²	1	2	yes	—
52	C₃×#390	C₂²	1	2	yes	—
53	C₃×#390	C₂²	1	2	yes	—
54	C₃×#389	C₂²	1	2	yes	complemented
55	C₃×#388	C₂²	1	4	yes	—
56	C₃×#388	C₂²	1	4	yes	—
57	C₃×#388	C₂²	1	4	yes	complemented
58	C₃×#388	C₂²	1	4	yes	complemented
59	C₃×#388	C₂²	1	4	yes	complemented
60	C₃×#388	C₂²	1	4	yes	complemented
61	C₃×#388	C₂²	1	4	yes	complemented
62	C₃×#388	C₂²	1	4	yes	complemented
63	C₃×#388	C₂²	1	4	yes	complemented
64	C₃×#388	C₂²	1	4	yes	complemented
65	C₃×#387	C₂²	1	4	yes	complemented
66	C₃×#382	C₂²	1	1	yes	characteristic, complemented
67	C₃×#379	C₂²	1	4	yes	—
68	C₃×#379	C₂²	1	4	yes	—
69	C₃×#379	C₂²	1	2	yes	—
70	C₃×#379	C₂²	1	2	yes	—
71	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	complemented
72	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
73	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
74	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
75	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
76	#2830	C₂×C₃	1	2	yes	complemented
77	#2736	C₂×C₃	1	2	yes	complemented
78	#2735	C₂×C₃	1	4	yes	complemented
79	#2735	C₂×C₃	1	2	yes	complemented
80	#2651	C₂×C₃	1	4	yes	complemented
81	#2621	C₂×C₃	1	1	yes	characteristic, complemented
82	#2593	C₂×C₃	1	2	yes	complemented
83	#2592	C₂×C₃	1	2	yes	complemented
84	#2545	C₂×C₃	1	2	yes	complemented
85	#2513	C₂×C₃	1	2	yes	complemented
86	#2448	C₂×C₃	1	2	yes	complemented
87	#2435	C₂×C₃	1	2	yes	—
88	#2396	C₂×C₃	1	1	yes	characteristic, complemented
89	#2362	C₂×C₃	1	2	yes	complemented
90	#2309	C₂×C₃	1	1	yes	characteristic
91	C₂⁵×C₃	C₂³	1	2	yes	—
92	C₂²×C₃×Q₈	C₂³	1	2	yes	—
93	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
94	C₂²×C₃×D₄	—	2	4	no	—
95	C₂²×C₃×D₄	—	4	2	no	—
96	C₂²×C₃×D₄	—	4	2	no	—
97	C₂²×C₃×D₄	C₂³	1	2	yes	—
98	C₂²×C₃×D₄	C₂³	1	2	yes	—
99	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
100	C₃×C₄⋊Q₈	—	4	2	no	—
101	C₃×#124	—	4	4	no	—
102	C₃×#124	—	4	4	no	—
103	C₃×C₂²⋊Q₈	—	2	8	no	—
104	C₃×C₄×Q₈	—	4	2	no	—
105	C₃×C₄×Q₈	—	4	4	no	—
106	C₃×#117	—	4	2	no	—
107	C₃×#117	—	4	2	no	—
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	2	yes	—
111	C₂×C₃×C₄⋊C₄	C₂³	1	4	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	4	yes	—
116	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
120	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
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	4	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₃×C₄²	C₂³	1	2	yes	—
141	C₂×C₃×C₄²	C₂³	1	2	yes	—
142	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄²	C₂³	1	2	yes	—
145	C₂×C₃×C₄²	C₂³	1	4	yes	—
146	C₂×C₃×C₄²	C₂³	1	4	yes	—
147	C₃×#95	C₂³	1	2	yes	—
148	C₃×#95	C₂³	1	2	yes	—
149	C₃×#95	C₂³	1	4	yes	—
150	C₃×#95	C₂³	1	4	yes	—
151	C₃×#95	C₂³	1	1	yes	characteristic
152	C₃×#95	C₂³	1	2	yes	—
153	C₃×#95	C₂³	1	2	yes	—
154	C₃×#95	C₂³	1	1	yes	characteristic
155	C₃×#95	C₂³	1	2	yes	—
156	C₃×#95	C₂³	1	2	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	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
162	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₂×#124	C₂²×C₃	1	2	yes	—
164	C₂×#124	C₂²×C₃	1	2	yes	—
165	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
166	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
168	C₂×#117	C₂²×C₃	1	1	yes	characteristic
169	C₂×#117	C₂²×C₃	1	1	yes	characteristic
170	#400	C₂²×C₃	1	1	yes	characteristic, complemented
171	#399	C₂²×C₃	1	1	yes	characteristic
172	#399	C₂²×C₃	1	4	yes	complemented
173	#398	C₂²×C₃	1	2	yes	complemented
174	#398	C₂²×C₃	1	2	yes	complemented
175	#398	C₂²×C₃	1	2	yes	complemented
176	#397	C₂²×C₃	1	2	yes	—
177	#397	C₂²×C₃	1	2	yes	—
178	#397	C₂²×C₃	1	4	yes	complemented
179	#397	C₂²×C₃	1	4	yes	complemented
180	#397	C₂²×C₃	1	4	yes	complemented
181	#397	C₂²×C₃	1	4	yes	complemented
182	#396	C₂²×C₃	1	2	yes	—
183	#396	C₂²×C₃	1	4	yes	complemented
184	#396	C₂²×C₃	1	4	yes	complemented
185	#395	C₂²×C₃	1	1	yes	characteristic, complemented
186	#394	C₂²×C₃	1	4	yes	—
187	#394	C₂²×C₃	1	4	yes	—
188	#393	C₂²×C₃	1	1	yes	characteristic
189	#393	C₂²×C₃	1	4	yes	complemented
190	#391	C₂²×C₃	1	2	yes	complemented
191	#391	C₂²×C₃	1	2	yes	complemented
192	#390	C₂²×C₃	1	2	yes	—
193	#390	C₂²×C₃	1	2	yes	—
194	#390	C₂²×C₃	1	2	yes	—
195	#390	C₂²×C₃	1	2	yes	—
196	#390	C₂²×C₃	1	2	yes	—
197	#390	C₂²×C₃	1	2	yes	—
198	#389	C₂²×C₃	1	2	yes	complemented
199	#388	C₂²×C₃	1	4	yes	—
200	#388	C₂²×C₃	1	4	yes	—
201	#388	C₂²×C₃	1	4	yes	complemented
202	#388	C₂²×C₃	1	4	yes	complemented
203	#388	C₂²×C₃	1	4	yes	complemented
204	#388	C₂²×C₃	1	4	yes	complemented
205	#388	C₂²×C₃	1	4	yes	complemented
206	#388	C₂²×C₃	1	4	yes	complemented
207	#388	C₂²×C₃	1	4	yes	complemented
208	#388	C₂²×C₃	1	4	yes	complemented
209	#387	C₂²×C₃	1	4	yes	complemented
210	#382	C₂²×C₃	1	1	yes	characteristic, complemented
211	#379	C₂²×C₃	1	2	yes	—
212	#379	C₂²×C₃	1	2	yes	—
213	#379	C₂²×C₃	1	4	yes	—
214	#379	C₂²×C₃	1	4	yes	—
215	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
216	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
217	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
218	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
219	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
220	C₂⁴×C₃	—	2	4	no	—
221	C₂⁴×C₃	—	4	2	no	—
222	C₂⁴×C₃	—	4	2	no	—
223	C₂⁴×C₃	—	4	4	no	—
224	C₂⁴×C₃	—	4	4	no	—
225	C₂⁴×C₃	C₂⁴	1	4	yes	—
226	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
227	C₂×C₃×Q₈	—	2	4	no	—
228	C₂×C₃×Q₈	—	2	4	no	—
229	C₂×C₃×Q₈	—	2	4	no	—
230	C₂×C₃×Q₈	—	4	1	no	—
231	C₂×C₃×Q₈	—	4	2	no	—
232	C₂×C₃×D₄	—	2	4	no	—
233	C₂×C₃×D₄	—	2	4	no	—
234	C₂×C₃×D₄	—	2	4	no	—
235	C₂×C₃×D₄	—	2	4	no	—
236	C₂×C₃×D₄	—	4	2	no	—
237	C₂×C₃×D₄	—	4	2	no	—
238	C₂×C₃×D₄	—	4	16	no	—
239	C₂²×C₃×C₄	—	2	2	no	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	#41	1	4	yes	—
242	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
243	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
244	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
246	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
247	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
248	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
249	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
253	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
254	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
255	C₃×C₄⋊C₄	—	2	4	no	—
256	C₃×C₄⋊C₄	—	2	8	no	—
257	C₃×C₄⋊C₄	—	2	4	no	—
258	C₃×C₄⋊C₄	—	4	4	no	—
259	C₃×C₄⋊C₄	—	4	2	no	—
260	C₃×C₄⋊C₄	—	4	2	no	—
261	C₃×C₄⋊C₄	—	4	2	no	—
262	C₃×C₄⋊C₄	—	4	1	no	—
263	C₃×C₄⋊C₄	—	4	1	no	—
264	C₃×C₄⋊C₄	—	4	1	no	—
265	C₃×C₄⋊C₄	—	4	2	no	—
266	C₃×C₄⋊C₄	—	4	4	no	—
267	C₃×C₄⋊C₄	—	4	2	no	—
268	C₃×C₄⋊C₄	—	4	2	no	—
269	C₃×C₂²⋊C₄	—	2	8	no	—
270	C₃×C₂²⋊C₄	—	4	2	no	—
271	C₃×C₂²⋊C₄	—	4	4	no	—
272	C₃×C₂²⋊C₄	—	4	4	no	—
273	C₃×C₂²⋊C₄	—	4	4	no	—
274	C₃×C₂²⋊C₄	—	4	4	no	—
275	C₃×C₂²⋊C₄	—	4	4	no	—
276	C₃×C₂²⋊C₄	—	4	4	no	—
277	C₃×C₂²⋊C₄	—	4	4	no	—
278	C₃×C₂²⋊C₄	—	4	4	no	—
279	C₃×C₂²⋊C₄	—	4	2	no	—
280	C₃×C₂²⋊C₄	—	4	1	no	—
281	C₃×C₂²⋊C₄	—	4	1	no	—
282	C₃×C₂²⋊C₄	—	4	2	no	—
283	C₃×C₂²⋊C₄	—	4	4	no	—
284	C₃×C₂²⋊C₄	—	4	4	no	—
285	C₃×C₂²⋊C₄	—	4	4	no	—
286	C₃×C₂²⋊C₄	—	4	4	no	—
287	C₃×C₄²	—	2	2	no	—
288	C₃×C₄²	—	2	2	no	—
289	C₃×C₄²	—	2	4	no	—
290	C₃×C₄²	—	2	4	no	—
291	C₃×C₄²	—	4	4	no	—
292	C₃×C₄²	—	4	2	no	—
293	C₃×C₄²	—	4	4	no	—
294	C₂⁵	C₂³×C₃	1	2	yes	—
295	C₂²×Q₈	C₂³×C₃	1	2	yes	—
296	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
297	C₂²×D₄	—	2	4	no	—
298	C₂²×D₄	—	4	2	no	—
299	C₂²×D₄	—	4	2	no	—
300	C₂²×D₄	C₂³×C₃	1	2	yes	—
301	C₂²×D₄	C₂³×C₃	1	2	yes	—
302	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
303	C₄⋊Q₈	—	4	2	no	—
304	#124	—	4	4	no	—
305	#124	—	4	4	no	—
306	C₂²⋊Q₈	—	2	8	no	—
307	C₄×Q₈	—	4	2	no	—
308	C₄×Q₈	—	4	4	no	—
309	#117	—	4	2	no	—
310	#117	—	4	2	no	—
311	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₃	1	2	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	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
330	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
343	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₃	1	2	yes	—
346	C₂×C₄²	C₂³×C₃	1	2	yes	—
347	C₂×C₄²	C₂³×C₃	1	2	yes	—
348	C₂×C₄²	C₂³×C₃	1	4	yes	—
349	C₂×C₄²	C₂³×C₃	1	4	yes	—
350	#95	C₂³×C₃	1	2	yes	—
351	#95	C₂³×C₃	1	2	yes	—
352	#95	C₂³×C₃	1	4	yes	—
353	#95	C₂³×C₃	1	4	yes	—
354	#95	C₂³×C₃	1	1	yes	characteristic
355	#95	C₂³×C₃	1	2	yes	—
356	#95	C₂³×C₃	1	2	yes	—
357	#95	C₂³×C₃	1	1	yes	characteristic
358	#95	C₂³×C₃	1	2	yes	—
359	#95	C₂³×C₃	1	2	yes	—
360	#95	C₂³×C₃	1	4	yes	—
361	#95	C₂³×C₃	1	4	yes	—
362	#95	C₂³×C₃	1	4	yes	—
363	#95	C₂³×C₃	1	4	yes	—
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	2	1	no	—
366	C₂³×C₃	—	2	2	no	—
367	C₂³×C₃	—	2	2	no	—
368	C₂³×C₃	—	2	4	no	—
369	C₂³×C₃	—	2	4	no	—
370	C₂³×C₃	—	2	4	no	—
371	C₂³×C₃	—	2	4	no	—
372	C₂³×C₃	—	2	4	no	—
373	C₂³×C₃	—	2	4	no	—
374	C₂³×C₃	—	2	4	no	—
375	C₂³×C₃	—	4	8	no	—
376	C₂³×C₃	—	8	8	no	—
377	C₂³×C₃	—	8	4	no	—
378	C₂³×C₃	—	8	4	no	—
379	C₂³×C₃	—	8	8	no	—
380	C₂³×C₃	C₂×#41	1	2	yes	—
381	C₂³×C₃	C₂⁵	1	1	yes	characteristic
382	C₃×Q₈	—	4	4	no	—
383	C₃×Q₈	—	4	8	no	—
384	C₃×D₄	—	4	8	no	—
385	C₃×D₄	—	4	8	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	8	no	—
389	C₂×C₃×C₄	—	2	4	no	—
390	C₂×C₃×C₄	—	2	4	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	4	no	—
400	C₂×C₃×C₄	—	2	4	no	—
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	4	no	—
404	C₂×C₃×C₄	—	2	4	no	—
405	C₂×C₃×C₄	—	2	4	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	2	2	no	—
410	C₂×C₃×C₄	—	2	4	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	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	2	no	—
418	C₂×C₃×C₄	C₂×#41	1	2	yes	—
419	C₂×C₃×C₄	C₂×#41	1	2	yes	—
420	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
421	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
422	C₂⁴	—	2	4	no	—
423	C₂⁴	—	4	2	no	—
424	C₂⁴	—	4	2	no	—
425	C₂⁴	—	4	4	no	—
426	C₂⁴	—	4	4	no	—
427	C₂⁴	C₂⁴×C₃	1	4	yes	—
428	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	4	1	no	—
433	C₂×Q₈	—	4	2	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	—	4	2	no	—
440	C₂×D₄	—	4	16	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	C₃×#41	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
452	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	4	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	—	4	4	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	4	2	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	—	4	4	no	—
477	C₂²⋊C₄	—	4	4	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	—	4	4	no	—
481	C₂²⋊C₄	—	4	4	no	—
482	C₂²⋊C₄	—	4	4	no	—
483	C₂²⋊C₄	—	4	4	no	—
484	C₂²⋊C₄	—	4	4	no	—
485	C₂²⋊C₄	—	4	4	no	—
486	C₂²⋊C₄	—	4	4	no	—
487	C₂²⋊C₄	—	4	4	no	—
488	C₂²⋊C₄	—	4	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	4	2	no	—
494	C₄²	—	4	4	no	—
495	C₄²	—	4	4	no	—
496	C₂²×C₃	—	2	2	no	—
497	C₂²×C₃	—	2	4	no	—
498	C₂²×C₃	—	4	1	no	—
499	C₂²×C₃	—	4	1	no	—
500	C₂²×C₃	—	4	2	no	—
501	C₂²×C₃	—	4	4	no	—
502	C₂²×C₃	—	4	4	no	—
503	C₂²×C₃	—	4	4	no	—
504	C₂²×C₃	—	4	4	no	—
505	C₂²×C₃	—	4	4	no	—
506	C₂²×C₃	—	4	4	no	—
507	C₂²×C₃	—	4	4	no	—
508	C₂²×C₃	—	8	16	no	—
509	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
510	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
512	C₂²×C₃	#585	1	2	yes	—
513	C₂²×C₃	#585	1	2	yes	—
514	C₃×C₄	—	2	2	no	—
515	C₃×C₄	—	4	4	no	—
516	C₃×C₄	—	4	4	no	—
517	C₃×C₄	—	4	1	no	—
518	C₃×C₄	—	4	2	no	—
519	C₃×C₄	—	4	1	no	—
520	C₃×C₄	—	4	2	no	—
521	C₃×C₄	—	4	1	no	—
522	C₃×C₄	—	4	1	no	—
523	C₃×C₄	—	4	2	no	—
524	C₃×C₄	—	4	2	no	—
525	C₃×C₄	—	4	4	no	—
526	C₃×C₄	#538	1	4	yes	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	4	8	no	—
539	C₂³	—	8	8	no	—
540	C₂³	—	8	4	no	—
541	C₂³	—	8	4	no	—
542	C₂³	—	8	8	no	—
543	C₂³	C₂×C₃×#41	1	2	yes	—
544	C₂³	C₂⁵×C₃	1	1	yes	characteristic
545	Q₈	—	4	4	no	—
546	Q₈	—	4	8	no	—
547	D₄	—	4	8	no	—
548	D₄	—	4	8	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	8	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	C₂×C₃×#41	1	2	yes	—
582	C₂×C₄	C₂×C₃×#41	1	2	yes	—
583	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
584	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
585	C₂×C₃	—	4	2	no	—
586	C₂×C₃	—	8	4	no	—
587	C₂×C₃	C₂×#538	1	1	yes	characteristic
588	C₂×C₃	#3510	1	2	yes	—
589	C₂×C₃	#3540	1	1	yes	characteristic
590	C₂×C₃	#3551	1	1	yes	characteristic
591	C₂×C₃	#3562	1	2	yes	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	8	16	no	—
605	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
606	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂²	C₃×#585	1	2	yes	—
609	C₂²	C₃×#585	1	2	yes	—
610	C₄	—	2	2	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	4	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	1	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	4	4	no	—
622	C₄	C₃×#538	1	4	yes	—
623	C₃	#42983	1	1	yes	characteristic, direct product factor, Sylow
624	C₂	—	4	2	no	—
625	C₂	—	8	4	no	—
626	C₂	C₂×C₃×#538	1	1	yes	characteristic
627	C₂	C₃×#3510	1	2	yes	—
628	C₂	C₃×#3540	1	1	yes	characteristic
629	C₂	C₃×#3551	1	1	yes	characteristic
630	C₂	C₃×#3562	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
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×#2830	C₂	semidirect
2. C₃×#2736	C₂	semidirect
3. C₃×#2735	C₂	semidirect
4. C₃×#2735	C₂	semidirect
5. C₃×#2651	C₂	semidirect
6. C₃×#2621	C₂	semidirect
7. C₃×#2593	C₂	semidirect
8. C₃×#2592	C₂	semidirect
9. C₃×#2545	C₂	semidirect
10. C₃×#2513	C₂	semidirect
11. C₃×#2448	C₂	semidirect
13. C₃×#2396	C₂	semidirect
14. C₃×#2362	C₂	semidirect
16. #42983	C₃	direct (N × H)
18. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₃×C₄×Q₈	C₂²	semidirect
23. C₂×C₃×C₄×Q₈	C₂²	semidirect
26. C₃×#400	C₂²	semidirect
28. C₃×#399	C₂²	semidirect
29. C₃×#398	C₂²	semidirect
30. C₃×#398	C₂²	semidirect
31. C₃×#398	C₂²	semidirect
34. C₃×#397	C₂²	semidirect
35. C₃×#397	C₂²	semidirect
36. C₃×#397	C₂²	semidirect
37. C₃×#397	C₂²	semidirect
39. C₃×#396	C₂²	semidirect
40. C₃×#396	C₂²	semidirect
41. C₃×#395	C₂²	semidirect
45. C₃×#393	C₂²	semidirect
46. C₃×#391	C₂²	semidirect
47. C₃×#391	C₂²	semidirect
54. C₃×#389	C₂²	semidirect
57. C₃×#388	C₂²	semidirect
58. C₃×#388	C₂²	semidirect
59. C₃×#388	C₂²	semidirect
60. C₃×#388	C₂²	semidirect
61. C₃×#388	C₂²	semidirect
62. C₃×#388	C₂²	semidirect
63. C₃×#388	C₂²	semidirect
64. C₃×#388	C₂²	semidirect
65. C₃×#387	C₂²	semidirect
66. C₃×#382	C₂²	semidirect
71. C₃×C₄×C₄⋊C₄	C₂²	semidirect
72. C₃×C₄×C₄⋊C₄	C₂²	semidirect
73. C₃×C₄×C₄⋊C₄	C₂²	semidirect
74. C₃×C₄×C₄⋊C₄	C₂²	semidirect
76. #2830	C₂×C₃	semidirect
77. #2736	C₂×C₃	semidirect
78. #2735	C₂×C₃	semidirect
79. #2735	C₂×C₃	semidirect
80. #2651	C₂×C₃	semidirect
81. #2621	C₂×C₃	semidirect
82. #2593	C₂×C₃	semidirect
83. #2592	C₂×C₃	semidirect
84. #2545	C₂×C₃	semidirect
85. #2513	C₂×C₃	semidirect
86. #2448	C₂×C₃	semidirect
88. #2396	C₂×C₃	semidirect
89. #2362	C₂×C₃	semidirect
162. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
166. C₂×C₄×Q₈	C₂²×C₃	semidirect
167. C₂×C₄×Q₈	C₂²×C₃	semidirect
170. #400	C₂²×C₃	semidirect
172. #399	C₂²×C₃	semidirect
173. #398	C₂²×C₃	semidirect
174. #398	C₂²×C₃	semidirect
175. #398	C₂²×C₃	semidirect
178. #397	C₂²×C₃	semidirect
179. #397	C₂²×C₃	semidirect
180. #397	C₂²×C₃	semidirect
181. #397	C₂²×C₃	semidirect
183. #396	C₂²×C₃	semidirect
184. #396	C₂²×C₃	semidirect
185. #395	C₂²×C₃	semidirect
189. #393	C₂²×C₃	semidirect
190. #391	C₂²×C₃	semidirect
191. #391	C₂²×C₃	semidirect
198. #389	C₂²×C₃	semidirect
201. #388	C₂²×C₃	semidirect
202. #388	C₂²×C₃	semidirect
203. #388	C₂²×C₃	semidirect
204. #388	C₂²×C₃	semidirect
205. #388	C₂²×C₃	semidirect
206. #388	C₂²×C₃	semidirect
207. #388	C₂²×C₃	semidirect
208. #388	C₂²×C₃	semidirect
209. #387	C₂²×C₃	semidirect
210. #382	C₂²×C₃	semidirect
215. C₄×C₄⋊C₄	C₂²×C₃	semidirect
216. C₄×C₄⋊C₄	C₂²×C₃	semidirect
217. C₄×C₄⋊C₄	C₂²×C₃	semidirect
218. C₄×C₄⋊C₄	C₂²×C₃	semidirect
623. C₃	#42983	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×#2830	2
C₃×#2736	2
C₃×#2735	2
C₃×#2651	2
C₃×#2621	2
C₃×#2593	2
C₃×#2592	2
C₃×#2545	2
C₃×#2513	2
C₃×#2448	2
C₃×#2435	2
C₃×#2396	2
C₃×#2362	2
C₃×#2309	2
#42983	3

Subgroups — C3×#42983 #10661590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#42983 #10661590