Subgroups — C₃×#37249 #10655856

Order 768.

2160 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2861	C₂	1	2	yes	maximal, complemented
2	C₃×#2804	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2795	C₂	1	2	yes	maximal, complemented
4	C₃×#2733	C₂	1	2	yes	maximal, complemented
5	C₃×#2711	C₂	1	4	yes	maximal, complemented
6	C₃×#2679	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2670	C₂	1	4	yes	maximal, complemented
8	C₃×#2669	C₂	1	2	yes	maximal, complemented
9	C₃×#2635	C₂	1	2	yes	maximal, complemented
10	C₃×#2459	C₂	1	4	yes	maximal, complemented
11	C₃×#2424	C₂	1	4	yes	maximal, complemented
12	C₃×#2321	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×#127	C₂	1	1	yes	maximal, characteristic, complemented
14	#37249	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₃×#127	C₂²	1	1	yes	characteristic
16	C₂×C₃×#125	C₂²	1	2	yes	complemented
17	C₂×C₃×#124	C₂²	1	2	yes	—
18	C₂×C₃×#124	C₂²	1	4	yes	complemented
19	C₂×C₃×#121	C₂²	1	2	yes	—
20	C₂×C₃×#121	C₂²	1	4	yes	—
21	C₂×C₃×#120	C₂²	1	2	yes	—
22	C₂×C₃×#120	C₂²	1	4	yes	—
23	C₂×C₃×#120	C₂²	1	4	yes	complemented
24	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
27	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
28	C₃×#400	C₂²	1	2	yes	complemented
29	C₃×#399	C₂²	1	2	yes	complemented
30	C₃×#396	C₂²	1	4	yes	complemented
31	C₃×#394	C₂²	1	2	yes	—
32	C₃×#394	C₂²	1	4	yes	—
33	C₃×#394	C₂²	1	4	yes	—
34	C₃×#394	C₂²	1	4	yes	complemented
35	C₃×#394	C₂²	1	4	yes	complemented
36	C₃×#394	C₂²	1	4	yes	complemented
37	C₃×#393	C₂²	1	4	yes	complemented
38	C₃×#392	C₂²	1	2	yes	—
39	C₃×#392	C₂²	1	4	yes	—
40	C₃×#392	C₂²	1	4	yes	—
41	C₃×#392	C₂²	1	4	yes	complemented
42	C₃×#391	C₂²	1	2	yes	complemented
43	C₃×#391	C₂²	1	2	yes	complemented
44	C₃×#390	C₂²	1	4	yes	—
45	C₃×#390	C₂²	1	2	yes	—
46	C₃×#390	C₂²	1	1	yes	characteristic
47	C₃×#390	C₂²	1	2	yes	—
48	C₃×#390	C₂²	1	4	yes	complemented
49	C₃×#390	C₂²	1	1	yes	characteristic, complemented
50	C₃×#388	C₂²	1	4	yes	complemented
51	C₃×#388	C₂²	1	4	yes	complemented
52	C₃×#388	C₂²	1	4	yes	complemented
53	C₃×#388	C₂²	1	4	yes	complemented
54	C₃×#388	C₂²	1	4	yes	complemented
55	C₃×#388	C₂²	1	4	yes	complemented
56	C₃×#388	C₂²	1	4	yes	complemented
57	C₃×#387	C₂²	1	4	yes	complemented
58	C₃×#386	C₂²	1	2	yes	—
59	C₃×#386	C₂²	1	4	yes	—
60	C₃×#386	C₂²	1	4	yes	complemented
61	C₃×#385	C₂²	1	4	yes	complemented
62	C₃×#385	C₂²	1	2	yes	complemented
63	C₃×#384	C₂²	1	1	yes	characteristic, complemented
64	C₃×#381	C₂²	1	2	yes	complemented
65	C₃×#379	C₂²	1	2	yes	complemented
66	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
67	C₃×C₄³	C₂²	1	1	yes	characteristic, complemented
68	#2861	C₂×C₃	1	2	yes	complemented
69	#2804	C₂×C₃	1	1	yes	characteristic, complemented
70	#2795	C₂×C₃	1	2	yes	complemented
71	#2733	C₂×C₃	1	2	yes	complemented
72	#2711	C₂×C₃	1	4	yes	complemented
73	#2679	C₂×C₃	1	1	yes	characteristic, complemented
74	#2670	C₂×C₃	1	4	yes	complemented
75	#2669	C₂×C₃	1	2	yes	complemented
76	#2635	C₂×C₃	1	2	yes	complemented
77	#2459	C₂×C₃	1	4	yes	complemented
78	#2424	C₂×C₃	1	4	yes	complemented
79	#2321	C₂×C₃	1	2	yes	complemented
80	C₄×#127	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂⁵×C₃	C₂³	1	2	yes	—
82	C₂²×C₃×Q₈	C₂³	1	2	yes	—
83	C₂²×C₃×D₄	C₂³	1	4	yes	—
84	C₂²×C₃×D₄	C₂³	1	4	yes	—
85	C₂²×C₃×D₄	C₂³	1	2	yes	—
86	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
87	C₂²×C₃×D₄	C₂³	1	4	yes	—
88	C₂²×C₃×D₄	C₂³	1	4	yes	—
89	C₂²×C₃×D₄	C₂³	1	2	yes	—
90	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
91	C₂³×C₃×C₄	C₂³	1	2	yes	—
92	C₂³×C₃×C₄	C₂³	1	2	yes	—
93	C₂³×C₃×C₄	C₂³	1	2	yes	—
94	C₃×#127	—	2	4	no	—
95	C₃×#125	—	4	4	no	—
96	C₃×#124	—	4	4	no	—
97	C₃×#124	—	4	8	no	—
98	C₃×#121	—	4	4	no	—
99	C₃×#121	—	4	8	no	—
100	C₃×#120	—	2	8	no	—
101	C₃×#120	—	4	8	no	—
102	C₃×#120	—	4	8	no	—
103	C₃×C₄×D₄	—	4	8	no	—
104	C₃×C₄×D₄	—	4	2	no	—
105	C₃×C₄×D₄	—	4	2	no	—
106	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
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	4	yes	—
120	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
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	4	yes	—
126	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
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	2	yes	—
133	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₄²	C₂³	1	2	yes	—
136	C₂×C₃×C₄²	C₂³	1	2	yes	—
137	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
138	C₂×C₃×C₄²	C₂³	1	4	yes	—
139	C₃×#95	C₂³	1	4	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	C₂×#127	C₂²×C₃	1	1	yes	characteristic
148	C₂×#125	C₂²×C₃	1	2	yes	complemented
149	C₂×#124	C₂²×C₃	1	2	yes	—
150	C₂×#124	C₂²×C₃	1	4	yes	complemented
151	C₂×#121	C₂²×C₃	1	2	yes	—
152	C₂×#121	C₂²×C₃	1	4	yes	—
153	C₂×#120	C₂²×C₃	1	2	yes	—
154	C₂×#120	C₂²×C₃	1	4	yes	—
155	C₂×#120	C₂²×C₃	1	4	yes	complemented
156	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
159	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
160	#400	C₂²×C₃	1	2	yes	complemented
161	#399	C₂²×C₃	1	2	yes	complemented
162	#396	C₂²×C₃	1	4	yes	complemented
163	#394	C₂²×C₃	1	2	yes	—
164	#394	C₂²×C₃	1	4	yes	—
165	#394	C₂²×C₃	1	4	yes	—
166	#394	C₂²×C₃	1	4	yes	complemented
167	#394	C₂²×C₃	1	4	yes	complemented
168	#394	C₂²×C₃	1	4	yes	complemented
169	#393	C₂²×C₃	1	4	yes	complemented
170	#392	C₂²×C₃	1	2	yes	—
171	#392	C₂²×C₃	1	4	yes	—
172	#392	C₂²×C₃	1	4	yes	—
173	#392	C₂²×C₃	1	4	yes	complemented
174	#391	C₂²×C₃	1	2	yes	complemented
175	#391	C₂²×C₃	1	2	yes	complemented
176	#390	C₂²×C₃	1	1	yes	characteristic
177	#390	C₂²×C₃	1	4	yes	—
178	#390	C₂²×C₃	1	2	yes	—
179	#390	C₂²×C₃	1	2	yes	—
180	#390	C₂²×C₃	1	4	yes	complemented
181	#390	C₂²×C₃	1	1	yes	characteristic, complemented
182	#388	C₂²×C₃	1	4	yes	complemented
183	#388	C₂²×C₃	1	4	yes	complemented
184	#388	C₂²×C₃	1	4	yes	complemented
185	#388	C₂²×C₃	1	4	yes	complemented
186	#388	C₂²×C₃	1	4	yes	complemented
187	#388	C₂²×C₃	1	4	yes	complemented
188	#388	C₂²×C₃	1	4	yes	complemented
189	#387	C₂²×C₃	1	4	yes	complemented
190	#386	C₂²×C₃	1	2	yes	—
191	#386	C₂²×C₃	1	4	yes	—
192	#386	C₂²×C₃	1	4	yes	complemented
193	#385	C₂²×C₃	1	2	yes	complemented
194	#385	C₂²×C₃	1	4	yes	complemented
195	#384	C₂²×C₃	1	1	yes	characteristic, complemented
196	#381	C₂²×C₃	1	2	yes	complemented
197	#379	C₂²×C₃	1	2	yes	complemented
198	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
199	C₄³	C₂²×C₃	1	1	yes	characteristic, complemented
200	C₂⁴×C₃	—	2	4	no	—
201	C₂⁴×C₃	—	4	2	no	—
202	C₂⁴×C₃	—	4	2	no	—
203	C₂⁴×C₃	—	4	4	no	—
204	C₂⁴×C₃	—	4	4	no	—
205	C₂⁴×C₃	C₂⁴	1	4	yes	—
206	C₂⁴×C₃	C₂⁴	1	2	yes	—
207	C₂⁴×C₃	C₂⁴	1	2	yes	—
208	C₂×C₃×Q₈	—	2	4	no	—
209	C₂×C₃×Q₈	—	4	2	no	—
210	C₂×C₃×Q₈	—	4	2	no	—
211	C₂×C₃×D₄	—	2	8	no	—
212	C₂×C₃×D₄	—	2	8	no	—
213	C₂×C₃×D₄	—	2	2	no	—
214	C₂×C₃×D₄	—	2	8	no	—
215	C₂×C₃×D₄	—	2	4	no	—
216	C₂×C₃×D₄	—	4	1	no	—
217	C₂×C₃×D₄	—	4	4	no	—
218	C₂×C₃×D₄	—	4	1	no	—
219	C₂×C₃×D₄	—	4	1	no	—
220	C₂×C₃×D₄	—	4	1	no	—
221	C₂×C₃×D₄	—	4	4	no	—
222	C₂×C₃×D₄	—	4	4	no	—
223	C₂×C₃×D₄	—	4	4	no	—
224	C₂×C₃×D₄	—	4	4	no	—
225	C₂×C₃×D₄	—	4	4	no	—
226	C₂×C₃×D₄	—	4	4	no	—
227	C₂×C₃×D₄	—	4	2	no	—
228	C₂×C₃×D₄	—	4	4	no	—
229	C₂×C₃×D₄	—	4	2	no	—
230	C₂×C₃×D₄	—	4	4	no	—
231	C₂×C₃×D₄	—	4	2	no	—
232	C₂×C₃×D₄	—	4	4	no	—
233	C₂×C₃×D₄	#41	1	4	yes	—
234	C₂²×C₃×C₄	—	2	4	no	—
235	C₂²×C₃×C₄	—	2	4	no	—
236	C₂²×C₃×C₄	—	4	2	no	—
237	C₂²×C₃×C₄	—	4	4	no	—
238	C₂²×C₃×C₄	—	4	4	no	—
239	C₂²×C₃×C₄	—	4	4	no	—
240	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
241	C₂²×C₃×C₄	C₂⁴	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	2	yes	—
245	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
248	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
249	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
250	C₃×C₄⋊C₄	—	2	8	no	—
251	C₃×C₄⋊C₄	—	4	4	no	—
252	C₃×C₄⋊C₄	—	4	1	no	—
253	C₃×C₄⋊C₄	—	4	1	no	—
254	C₃×C₄⋊C₄	—	4	2	no	—
255	C₃×C₄⋊C₄	—	4	2	no	—
256	C₃×C₄⋊C₄	—	4	2	no	—
257	C₃×C₄⋊C₄	—	4	4	no	—
258	C₃×C₂²⋊C₄	—	2	4	no	—
259	C₃×C₂²⋊C₄	—	2	8	no	—
260	C₃×C₂²⋊C₄	—	2	8	no	—
261	C₃×C₂²⋊C₄	—	2	8	no	—
262	C₃×C₂²⋊C₄	—	2	8	no	—
263	C₃×C₂²⋊C₄	—	2	8	no	—
264	C₃×C₂²⋊C₄	—	2	8	no	—
265	C₃×C₂²⋊C₄	—	2	8	no	—
266	C₃×C₂²⋊C₄	—	4	4	no	—
267	C₃×C₂²⋊C₄	—	4	2	no	—
268	C₃×C₂²⋊C₄	—	4	2	no	—
269	C₃×C₂²⋊C₄	—	4	2	no	—
270	C₃×C₂²⋊C₄	—	4	4	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×C₄²	—	2	2	no	—
277	C₃×C₄²	—	2	4	no	—
278	C₃×C₄²	—	2	2	no	—
279	C₃×C₄²	—	2	4	no	—
280	C₃×C₄²	—	4	1	no	—
281	C₃×C₄²	—	4	4	no	—
282	C₂⁵	C₂³×C₃	1	2	yes	—
283	C₂²×Q₈	C₂³×C₃	1	2	yes	—
284	C₂²×D₄	C₂³×C₃	1	4	yes	—
285	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
286	C₂²×D₄	C₂³×C₃	1	4	yes	—
287	C₂²×D₄	C₂³×C₃	1	2	yes	—
288	C₂²×D₄	C₂³×C₃	1	2	yes	—
289	C₂²×D₄	C₂³×C₃	1	4	yes	—
290	C₂²×D₄	C₂³×C₃	1	4	yes	—
291	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₃	1	2	yes	—
293	C₂³×C₄	C₂³×C₃	1	2	yes	—
294	C₂³×C₄	C₂³×C₃	1	2	yes	—
295	#127	—	2	4	no	—
296	#125	—	4	4	no	—
297	#124	—	4	4	no	—
298	#124	—	4	8	no	—
299	#121	—	4	4	no	—
300	#121	—	4	8	no	—
301	#120	—	2	8	no	—
302	#120	—	4	8	no	—
303	#120	—	4	8	no	—
304	C₄×D₄	—	4	8	no	—
305	C₄×D₄	—	4	2	no	—
306	C₄×D₄	—	4	2	no	—
307	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
310	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
315	C₂×C₂²⋊C₄	—	4	4	no	—
316	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
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×C₄²	C₂³×C₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₃	1	2	yes	—
336	C₂×C₄²	C₂³×C₃	1	2	yes	—
337	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₃	1	4	yes	—
339	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
340	#95	C₂³×C₃	1	4	yes	—
341	#95	C₂³×C₃	1	2	yes	—
342	#95	C₂³×C₃	1	2	yes	—
343	#95	C₂³×C₃	1	4	yes	—
344	#95	C₂³×C₃	1	4	yes	—
345	#95	C₂³×C₃	1	4	yes	—
346	#95	C₂³×C₃	1	4	yes	—
347	#95	C₂³×C₃	1	4	yes	—
348	C₂³×C₃	—	2	4	no	—
349	C₂³×C₃	—	2	2	no	—
350	C₂³×C₃	—	2	4	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	4	no	—
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	—	2	4	no	—
355	C₂³×C₃	—	2	4	no	—
356	C₂³×C₃	—	2	4	no	—
357	C₂³×C₃	—	2	4	no	—
358	C₂³×C₃	—	2	4	no	—
359	C₂³×C₃	—	2	2	no	—
360	C₂³×C₃	—	2	4	no	—
361	C₂³×C₃	—	2	4	no	—
362	C₂³×C₃	—	2	2	no	—
363	C₂³×C₃	—	2	4	no	—
364	C₂³×C₃	—	4	8	no	—
365	C₂³×C₃	—	8	8	no	—
366	C₂³×C₃	—	8	4	no	—
367	C₂³×C₃	—	8	4	no	—
368	C₂³×C₃	—	8	8	no	—
369	C₂³×C₃	C₂×#41	1	4	yes	—
370	C₂³×C₃	C₂⁵	1	1	yes	characteristic
371	C₃×Q₈	—	8	4	no	—
372	C₃×D₄	—	4	4	no	—
373	C₃×D₄	—	4	16	no	—
374	C₃×D₄	—	4	4	no	—
375	C₃×D₄	—	8	4	no	—
376	C₃×D₄	—	8	8	no	—
377	C₃×D₄	—	8	4	no	—
378	C₃×D₄	—	8	8	no	—
379	C₃×D₄	—	8	8	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	4	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	2	4	no	—
391	C₂×C₃×C₄	—	2	4	no	—
392	C₂×C₃×C₄	—	2	4	no	—
393	C₂×C₃×C₄	—	2	4	no	—
394	C₂×C₃×C₄	—	2	4	no	—
395	C₂×C₃×C₄	—	2	4	no	—
396	C₂×C₃×C₄	—	2	4	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	4	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	4	no	—
401	C₂×C₃×C₄	—	2	4	no	—
402	C₂×C₃×C₄	—	8	4	no	—
403	C₂×C₃×C₄	—	8	4	no	—
404	C₂×C₃×C₄	—	8	4	no	—
405	C₂×C₃×C₄	C₂×#41	1	2	yes	—
406	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
407	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
408	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	4	2	no	—
411	C₂⁴	—	4	2	no	—
412	C₂⁴	—	4	4	no	—
413	C₂⁴	—	4	4	no	—
414	C₂⁴	C₂⁴×C₃	1	4	yes	—
415	C₂⁴	C₂⁴×C₃	1	2	yes	—
416	C₂⁴	C₂⁴×C₃	1	2	yes	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	4	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	—	4	4	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	C₃×#41	1	4	yes	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
454	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	4	4	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	4	4	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	4	no	—
479	C₂²⋊C₄	—	4	4	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	2	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	4	4	no	—
490	C₄²	—	4	1	no	—
491	C₂²×C₃	—	2	4	no	—
492	C₂²×C₃	—	2	8	no	—
493	C₂²×C₃	—	4	2	no	—
494	C₂²×C₃	—	4	2	no	—
495	C₂²×C₃	—	4	4	no	—
496	C₂²×C₃	—	4	2	no	—
497	C₂²×C₃	—	4	4	no	—
498	C₂²×C₃	—	4	4	no	—
499	C₂²×C₃	—	4	4	no	—
500	C₂²×C₃	—	4	4	no	—
501	C₂²×C₃	—	4	2	no	—
502	C₂²×C₃	—	4	4	no	—
503	C₂²×C₃	—	4	2	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	2	yes	—
512	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
513	C₂²×C₃	#585	1	1	yes	characteristic
514	C₃×C₄	—	2	2	no	—
515	C₃×C₄	—	2	4	no	—
516	C₃×C₄	—	2	2	no	—
517	C₃×C₄	—	2	4	no	—
518	C₃×C₄	—	4	4	no	—
519	C₃×C₄	—	4	2	no	—
520	C₃×C₄	—	4	2	no	—
521	C₃×C₄	—	4	1	no	—
522	C₃×C₄	—	4	4	no	—
523	C₃×C₄	—	4	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	4	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	4	8	no	—
541	C₂³	—	8	8	no	—
542	C₂³	—	8	4	no	—
543	C₂³	—	8	4	no	—
544	C₂³	—	8	8	no	—
545	C₂³	C₂×C₃×#41	1	4	yes	—
546	C₂³	C₂⁵×C₃	1	1	yes	characteristic
547	Q₈	—	8	4	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	16	no	—
550	D₄	—	4	4	no	—
551	D₄	—	8	4	no	—
552	D₄	—	8	8	no	—
553	D₄	—	8	4	no	—
554	D₄	—	8	8	no	—
555	D₄	—	8	8	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	1	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	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	8	4	no	—
579	C₂×C₄	—	8	4	no	—
580	C₂×C₄	—	8	4	no	—
581	C₂×C₄	C₂×C₃×#41	1	2	yes	—
582	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
583	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
584	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
585	C₂×C₃	—	4	4	no	—
586	C₂×C₃	—	8	2	no	—
587	C₂×C₃	—	8	4	no	—
588	C₂×C₃	#3459	1	1	yes	characteristic
589	C₂×C₃	#3519	1	2	yes	—
590	C₂×C₃	#3543	1	1	yes	characteristic
591	C₂×C₃	#3549	1	1	yes	characteristic
592	C₂×C₃	#3558	1	2	yes	—
593	C₂²	—	2	4	no	—
594	C₂²	—	2	8	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	4	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	8	16	no	—
611	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
612	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
613	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
614	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
615	C₂²	C₃×#585	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	4	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	4	no	—
620	C₄	—	4	4	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	4	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	4	no	—
626	C₃	#37249	1	1	yes	characteristic, direct product factor, Sylow
627	C₂	—	4	4	no	—
628	C₂	—	8	4	no	—
629	C₂	—	8	2	no	—
630	C₂	C₃×#3459	1	1	yes	characteristic
631	C₂	C₃×#3519	1	2	yes	—
632	C₂	C₃×#3543	1	1	yes	characteristic
633	C₂	C₃×#3549	1	1	yes	characteristic
634	C₂	C₃×#3558	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
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×#2861	C₂	semidirect
2. C₃×#2804	C₂	semidirect
3. C₃×#2795	C₂	semidirect
4. C₃×#2733	C₂	semidirect
5. C₃×#2711	C₂	semidirect
6. C₃×#2679	C₂	semidirect
7. C₃×#2670	C₂	semidirect
8. C₃×#2669	C₂	semidirect
9. C₃×#2635	C₂	semidirect
10. C₃×#2459	C₂	semidirect
11. C₃×#2424	C₂	semidirect
12. C₃×#2321	C₂	semidirect
13. C₃×C₄×#127	C₂	semidirect
14. #37249	C₃	direct (N × H)
16. C₂×C₃×#125	C₂²	semidirect
18. C₂×C₃×#124	C₂²	semidirect
23. C₂×C₃×#120	C₂²	semidirect
25. C₂×C₃×C₄×D₄	C₂²	semidirect
26. C₂×C₃×C₄×D₄	C₂²	semidirect
27. C₂²×C₃×C₂²⋊C₄	C₂²	semidirect
28. C₃×#400	C₂²	semidirect
29. C₃×#399	C₂²	semidirect
30. C₃×#396	C₂²	semidirect
34. C₃×#394	C₂²	semidirect
35. C₃×#394	C₂²	semidirect
36. C₃×#394	C₂²	semidirect
37. C₃×#393	C₂²	semidirect
41. C₃×#392	C₂²	semidirect
42. C₃×#391	C₂²	semidirect
43. C₃×#391	C₂²	semidirect
48. C₃×#390	C₂²	semidirect
49. C₃×#390	C₂²	semidirect
50. C₃×#388	C₂²	semidirect
51. C₃×#388	C₂²	semidirect
52. C₃×#388	C₂²	semidirect
53. C₃×#388	C₂²	semidirect
54. C₃×#388	C₂²	semidirect
55. C₃×#388	C₂²	semidirect
56. C₃×#388	C₂²	semidirect
57. C₃×#387	C₂²	semidirect
60. C₃×#386	C₂²	semidirect
61. C₃×#385	C₂²	semidirect
62. C₃×#385	C₂²	semidirect
63. C₃×#384	C₂²	semidirect
64. C₃×#381	C₂²	semidirect
65. C₃×#379	C₂²	semidirect
66. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
67. C₃×C₄³	C₂²	semidirect
68. #2861	C₂×C₃	semidirect
69. #2804	C₂×C₃	semidirect
70. #2795	C₂×C₃	semidirect
71. #2733	C₂×C₃	semidirect
72. #2711	C₂×C₃	semidirect
73. #2679	C₂×C₃	semidirect
74. #2670	C₂×C₃	semidirect
75. #2669	C₂×C₃	semidirect
76. #2635	C₂×C₃	semidirect
77. #2459	C₂×C₃	semidirect
78. #2424	C₂×C₃	semidirect
79. #2321	C₂×C₃	semidirect
80. C₄×#127	C₂×C₃	semidirect
148. C₂×#125	C₂²×C₃	semidirect
150. C₂×#124	C₂²×C₃	semidirect
155. C₂×#120	C₂²×C₃	semidirect
157. C₂×C₄×D₄	C₂²×C₃	semidirect
158. C₂×C₄×D₄	C₂²×C₃	semidirect
159. C₂²×C₂²⋊C₄	C₂²×C₃	semidirect
160. #400	C₂²×C₃	semidirect
161. #399	C₂²×C₃	semidirect
162. #396	C₂²×C₃	semidirect
166. #394	C₂²×C₃	semidirect
167. #394	C₂²×C₃	semidirect
168. #394	C₂²×C₃	semidirect
169. #393	C₂²×C₃	semidirect
173. #392	C₂²×C₃	semidirect
174. #391	C₂²×C₃	semidirect
175. #391	C₂²×C₃	semidirect
180. #390	C₂²×C₃	semidirect
181. #390	C₂²×C₃	semidirect
182. #388	C₂²×C₃	semidirect
183. #388	C₂²×C₃	semidirect
184. #388	C₂²×C₃	semidirect
185. #388	C₂²×C₃	semidirect
186. #388	C₂²×C₃	semidirect
187. #388	C₂²×C₃	semidirect
188. #388	C₂²×C₃	semidirect
189. #387	C₂²×C₃	semidirect
192. #386	C₂²×C₃	semidirect
193. #385	C₂²×C₃	semidirect
194. #385	C₂²×C₃	semidirect
195. #384	C₂²×C₃	semidirect
196. #381	C₂²×C₃	semidirect
197. #379	C₂²×C₃	semidirect
198. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
199. C₄³	C₂²×C₃	semidirect
626. C₃	#37249	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×#2861	2
C₃×#2804	2
C₃×#2795	2
C₃×#2733	2
C₃×#2711	2
C₃×#2679	2
C₃×#2670	2
C₃×#2669	2
C₃×#2635	2
C₃×#2459	2
C₃×#2424	2
C₃×#2321	2
C₃×C₄×#127	2
#37249	3

Subgroups — C3×#37249 #10655856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37249 #10655856