Subgroups — C₃×#35331 #10653938

Order 768.

2202 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#542	C₂	1	2	yes	maximal, complemented
2	C₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2850	C₂	1	2	yes	maximal, complemented
5	C₃×#2640	C₂	1	2	yes	maximal, complemented
6	C₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2619	C₂	1	1	yes	maximal, characteristic
8	C₃×#2560	C₂	1	8	yes	maximal, complemented
9	C₃×#2557	C₂	1	8	yes	maximal, complemented
10	C₃×#2328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2327	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×#124	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
14	#35331	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃×#542	—	2	16	no	—
16	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₃×#127	C₂²	1	1	yes	characteristic
19	C₂×C₃×#126	C₂²	1	4	yes	—
20	C₂×C₃×#124	C₂²	1	2	yes	—
21	C₂×C₃×#124	C₂²	1	4	yes	—
22	C₂×C₃×#124	C₂²	1	2	yes	—
23	C₂×C₃×#123	C₂²	1	4	yes	—
24	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₂×C₃×#121	C₂²	1	2	yes	—
27	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
28	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
29	C₂×C₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₃×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
32	C₃×#398	C₂²	1	4	yes	—
33	C₃×#397	C₂²	1	4	yes	—
34	C₃×#397	C₂²	1	8	yes	—
35	C₃×#394	C₂²	1	4	yes	—
36	C₃×#393	C₂²	1	8	yes	—
37	C₃×#392	C₂²	1	4	yes	—
38	C₃×#391	C₂²	1	2	yes	—
39	C₃×#391	C₂²	1	2	yes	—
40	C₃×#391	C₂²	1	8	yes	—
41	C₃×#390	C₂²	1	2	yes	—
42	C₃×#390	C₂²	1	2	yes	—
43	C₃×#390	C₂²	1	8	yes	—
44	C₃×#388	C₂²	1	8	yes	—
45	C₃×#388	C₂²	1	8	yes	—
46	C₃×#387	C₂²	1	8	yes	—
47	C₃×#386	C₂²	1	8	yes	—
48	C₃×#386	C₂²	1	8	yes	—
49	C₃×#382	C₂²	1	1	yes	characteristic
50	C₃×#382	C₂²	1	1	yes	characteristic
51	C₃×#382	C₂²	1	2	yes	—
52	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
53	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
54	C₃×C₄×C₂²⋊C₄	C₂²	1	8	yes	—
55	C₃×#376	C₂²	1	1	yes	characteristic
56	C₃×#376	C₂²	1	1	yes	characteristic
57	C₃×C₄³	C₂²	1	1	yes	characteristic
58	C₃×C₄³	C₂²	1	1	yes	characteristic
59	C₂×#542	C₂×C₃	1	2	yes	complemented
60	#2862	C₂×C₃	1	1	yes	characteristic, complemented
61	#2858	C₂×C₃	1	1	yes	characteristic, complemented
62	#2850	C₂×C₃	1	2	yes	complemented
63	#2640	C₂×C₃	1	2	yes	complemented
64	#2621	C₂×C₃	1	1	yes	characteristic, complemented
65	#2619	C₂×C₃	1	1	yes	characteristic
66	#2560	C₂×C₃	1	8	yes	complemented
67	#2557	C₂×C₃	1	8	yes	complemented
68	#2328	C₂×C₃	1	1	yes	characteristic, complemented
69	#2327	C₂×C₃	1	1	yes	characteristic, complemented
70	C₄×#124	C₂×C₃	1	2	yes	complemented
71	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂²×C₃×Q₈	C₂³	1	2	yes	—
73	C₂²×C₃×Q₈	C₂³	1	4	yes	—
74	C₂²×C₃×D₄	C₂³	1	2	yes	—
75	C₂²×C₃×D₄	C₂³	1	4	yes	—
76	C₂²×C₃×D₄	C₂³	1	4	yes	—
77	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
78	C₂³×C₃×C₄	C₂³	1	2	yes	—
79	C₂³×C₃×C₄	C₂³	1	4	yes	—
80	C₃×C₄⋊Q₈	—	2	8	no	—
81	C₃×C₄⋊Q₈	—	2	4	no	—
82	C₃×#127	—	2	4	no	—
83	C₃×#126	—	2	16	no	—
84	C₃×#124	—	2	16	no	—
85	C₃×#124	—	2	8	no	—
86	C₃×#124	—	2	8	no	—
87	C₃×#123	—	2	16	no	—
88	C₃×C₂²⋊Q₈	—	2	8	no	—
89	C₃×C₂²⋊Q₈	—	2	16	no	—
90	C₃×#121	—	2	8	no	—
91	C₃×C₄×Q₈	—	2	8	no	—
92	C₃×C₄×D₄	—	2	8	no	—
93	C₃×#117	—	2	4	no	—
94	C₃×#117	D₄	1	8	yes	complemented
95	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
113	C₂×C₃×C₄²	—	2	4	no	—
114	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
115	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
116	C₂×C₃×C₄²	C₂³	1	4	yes	—
117	C₂×C₃×C₄²	C₂³	1	2	yes	—
118	C₂×C₃×C₄²	C₂³	1	4	yes	—
119	C₂×C₃×C₄²	C₂³	1	4	yes	—
120	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
124	C₃×#95	C₂³	1	4	yes	—
125	C₃×#95	C₂³	1	4	yes	—
126	C₃×#95	C₂³	1	8	yes	—
127	C₃×#95	C₂³	1	8	yes	—
128	C₃×#95	C₂³	1	4	yes	—
129	C₃×#95	C₂³	1	4	yes	—
130	C₃×#95	C₂³	1	8	yes	—
131	#542	—	2	16	no	—
132	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
134	C₂×#127	C₂²×C₃	1	1	yes	characteristic
135	C₂×#126	C₂²×C₃	1	4	yes	—
136	C₂×#124	C₂²×C₃	1	2	yes	—
137	C₂×#124	C₂²×C₃	1	2	yes	—
138	C₂×#124	C₂²×C₃	1	4	yes	—
139	C₂×#123	C₂²×C₃	1	4	yes	—
140	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
141	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
142	C₂×#121	C₂²×C₃	1	2	yes	—
143	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
144	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
145	C₂×#117	C₂²×C₃	1	1	yes	characteristic
146	C₂×#117	C₂²×C₃	1	1	yes	characteristic
147	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
148	#398	C₂²×C₃	1	4	yes	—
149	#397	C₂²×C₃	1	8	yes	—
150	#397	C₂²×C₃	1	4	yes	—
151	#394	C₂²×C₃	1	4	yes	—
152	#393	C₂²×C₃	1	8	yes	—
153	#392	C₂²×C₃	1	4	yes	—
154	#391	C₂²×C₃	1	8	yes	—
155	#391	C₂²×C₃	1	2	yes	—
156	#391	C₂²×C₃	1	2	yes	—
157	#390	C₂²×C₃	1	8	yes	—
158	#390	C₂²×C₃	1	2	yes	—
159	#390	C₂²×C₃	1	2	yes	—
160	#388	C₂²×C₃	1	8	yes	—
161	#388	C₂²×C₃	1	8	yes	—
162	#387	C₂²×C₃	1	8	yes	—
163	#386	C₂²×C₃	1	8	yes	—
164	#386	C₂²×C₃	1	8	yes	—
165	#382	C₂²×C₃	1	1	yes	characteristic
166	#382	C₂²×C₃	1	1	yes	characteristic
167	#382	C₂²×C₃	1	2	yes	—
168	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
169	C₄×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
170	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
171	#376	C₂²×C₃	1	1	yes	characteristic
172	#376	C₂²×C₃	1	1	yes	characteristic
173	C₄³	C₂²×C₃	1	1	yes	characteristic
174	C₄³	C₂²×C₃	1	1	yes	characteristic
175	C₂⁴×C₃	C₂⁴	1	4	yes	—
176	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₃×Q₈	—	2	4	no	—
178	C₂×C₃×Q₈	—	2	8	no	—
179	C₂×C₃×Q₈	—	2	4	no	—
180	C₂×C₃×Q₈	—	2	4	no	—
181	C₂×C₃×Q₈	—	4	8	no	—
182	C₂×C₃×D₄	—	2	8	no	—
183	C₂×C₃×D₄	—	2	4	no	—
184	C₂×C₃×D₄	—	2	4	no	—
185	C₂×C₃×D₄	—	2	4	no	—
186	C₂×C₃×D₄	—	2	8	no	—
187	C₂×C₃×D₄	—	4	8	no	—
188	C₂×C₃×D₄	—	4	8	no	—
189	C₂²×C₃×C₄	—	2	2	no	—
190	C₂²×C₃×C₄	—	2	2	no	—
191	C₂²×C₃×C₄	—	2	4	no	—
192	C₂²×C₃×C₄	—	2	8	no	—
193	C₂²×C₃×C₄	—	4	4	no	—
194	C₂²×C₃×C₄	—	4	8	no	—
195	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
196	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
197	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
198	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
199	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
200	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
201	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
202	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
203	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
205	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
206	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄⋊C₄	—	2	4	no	—
209	C₃×C₄⋊C₄	—	2	8	no	—
210	C₃×C₄⋊C₄	—	2	8	no	—
211	C₃×C₄⋊C₄	—	2	8	no	—
212	C₃×C₄⋊C₄	—	2	4	no	—
213	C₃×C₄⋊C₄	—	2	8	no	—
214	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
215	C₃×C₂²⋊C₄	—	2	8	no	—
216	C₃×C₂²⋊C₄	—	2	8	no	—
217	C₃×C₂²⋊C₄	—	2	8	no	—
218	C₃×C₂²⋊C₄	—	2	8	no	—
219	C₃×C₂²⋊C₄	—	2	8	no	—
220	C₃×C₂²⋊C₄	—	2	4	no	—
221	C₃×C₂²⋊C₄	—	2	16	no	—
222	C₃×C₂²⋊C₄	—	4	8	no	—
223	C₃×C₂²⋊C₄	—	4	8	no	—
224	C₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
225	C₃×C₄²	—	2	8	no	—
226	C₃×C₄²	—	2	4	no	—
227	C₃×C₄²	—	2	2	no	—
228	C₃×C₄²	—	2	2	no	—
229	C₃×C₄²	—	4	4	no	—
230	C₃×C₄²	—	4	4	no	—
231	C₃×C₄²	C₂×D₄	1	4	yes	—
232	C₃×C₄²	C₂×D₄	1	4	yes	—
233	C₃×C₄²	#41	1	4	yes	—
234	C₃×C₄²	#41	1	4	yes	—
235	C₂²×Q₈	C₂³×C₃	1	2	yes	—
236	C₂²×Q₈	C₂³×C₃	1	4	yes	—
237	C₂²×D₄	C₂³×C₃	1	2	yes	—
238	C₂²×D₄	C₂³×C₃	1	4	yes	—
239	C₂²×D₄	C₂³×C₃	1	4	yes	—
240	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₃	1	4	yes	—
242	C₂³×C₄	C₂³×C₃	1	2	yes	—
243	C₄⋊Q₈	—	2	8	no	—
244	C₄⋊Q₈	—	2	4	no	—
245	#127	—	2	4	no	—
246	#126	—	2	16	no	—
247	#124	—	2	16	no	—
248	#124	—	2	8	no	—
249	#124	—	2	8	no	—
250	#123	—	2	16	no	—
251	C₂²⋊Q₈	—	2	8	no	—
252	C₂²⋊Q₈	—	2	16	no	—
253	#121	—	2	8	no	—
254	C₄×Q₈	—	2	8	no	—
255	C₄×D₄	—	2	8	no	—
256	#117	—	2	4	no	—
257	#117	C₃×D₄	1	8	yes	complemented
258	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
262	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
263	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
276	C₂×C₄²	—	2	4	no	—
277	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₃	1	4	yes	—
279	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₃	1	2	yes	—
281	C₂×C₄²	C₂³×C₃	1	4	yes	—
282	C₂×C₄²	C₂³×C₃	1	4	yes	—
283	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
287	#95	C₂³×C₃	1	4	yes	—
288	#95	C₂³×C₃	1	4	yes	—
289	#95	C₂³×C₃	1	8	yes	—
290	#95	C₂³×C₃	1	8	yes	—
291	#95	C₂³×C₃	1	4	yes	—
292	#95	C₂³×C₃	1	4	yes	—
293	#95	C₂³×C₃	1	8	yes	—
294	C₂³×C₃	—	2	1	no	—
295	C₂³×C₃	—	2	1	no	—
296	C₂³×C₃	—	2	4	no	—
297	C₂³×C₃	—	2	4	no	—
298	C₂³×C₃	—	2	4	no	—
299	C₂³×C₃	—	2	4	no	—
300	C₂³×C₃	—	2	8	no	—
301	C₂³×C₃	—	2	8	no	—
302	C₂³×C₃	C₂²×D₄	1	2	yes	—
303	C₂³×C₃	C₂⁵	1	1	yes	characteristic
304	C₃×Q₈	—	4	8	no	—
305	C₃×Q₈	—	8	8	no	—
306	C₃×D₄	—	4	8	no	—
307	C₃×D₄	—	8	8	no	—
308	C₃×D₄	—	8	8	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	2	4	no	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	4	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	8	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	4	no	—
322	C₂×C₃×C₄	—	2	4	no	—
323	C₂×C₃×C₄	—	2	4	no	—
324	C₂×C₃×C₄	—	2	4	no	—
325	C₂×C₃×C₄	—	2	8	no	—
326	C₂×C₃×C₄	—	2	8	no	—
327	C₂×C₃×C₄	—	4	8	no	—
328	C₂×C₃×C₄	—	8	8	no	—
329	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
330	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
331	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
332	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
333	C₂×C₃×C₄	C₂×#41	1	4	yes	—
334	C₂×C₃×C₄	C₂×#41	1	4	yes	—
335	C₂×C₃×C₄	C₂×#41	1	2	yes	—
336	C₂×C₃×C₄	C₂×#41	1	2	yes	—
337	C₂⁴	C₂⁴×C₃	1	4	yes	—
338	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	8	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	4	8	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	4	8	no	—
350	C₂×D₄	—	4	8	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	8	no	—
357	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
362	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
363	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
377	C₂²⋊C₄	—	2	8	no	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	16	no	—
384	C₂²⋊C₄	—	4	8	no	—
385	C₂²⋊C₄	—	4	8	no	—
386	C₂²⋊C₄	C₂×C₃×D₄	1	8	yes	—
387	C₄²	—	2	8	no	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	4	4	no	—
392	C₄²	—	4	4	no	—
393	C₄²	C₂×C₃×D₄	1	4	yes	—
394	C₄²	C₂×C₃×D₄	1	4	yes	—
395	C₄²	C₃×#41	1	4	yes	—
396	C₄²	C₃×#41	1	4	yes	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	2	4	no	—
399	C₂²×C₃	—	4	2	no	—
400	C₂²×C₃	—	4	2	no	—
401	C₂²×C₃	—	4	4	no	—
402	C₂²×C₃	—	4	8	no	—
403	C₂²×C₃	—	4	4	no	—
404	C₂²×C₃	—	4	4	no	—
405	C₂²×C₃	—	4	8	no	—
406	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
407	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
408	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
409	C₂²×C₃	#585	1	4	yes	—
410	C₃×C₄	—	2	2	no	—
411	C₃×C₄	—	2	4	no	—
412	C₃×C₄	—	2	4	no	—
413	C₃×C₄	—	2	4	no	—
414	C₃×C₄	—	2	4	no	—
415	C₃×C₄	—	4	4	no	—
416	C₃×C₄	—	4	2	no	—
417	C₃×C₄	—	4	4	no	—
418	C₃×C₄	—	4	4	no	—
419	C₃×C₄	—	4	2	no	—
420	C₃×C₄	#532	1	4	yes	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	8	no	—
429	C₂³	C₂²×C₃×D₄	1	2	yes	—
430	C₂³	C₂⁵×C₃	1	1	yes	characteristic
431	Q₈	—	4	8	no	—
432	Q₈	—	8	8	no	—
433	D₄	—	4	8	no	—
434	D₄	—	8	8	no	—
435	D₄	—	8	8	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	8	8	no	—
456	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
457	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
458	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
459	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
460	C₂×C₄	C₂×C₃×#41	1	4	yes	—
461	C₂×C₄	C₂×C₃×#41	1	4	yes	—
462	C₂×C₄	C₂×C₃×#41	1	2	yes	—
463	C₂×C₄	C₂×C₃×#41	1	2	yes	—
464	C₂×C₃	—	4	2	no	—
465	C₂×C₃	—	8	4	no	—
466	C₂×C₃	C₂×#532	1	1	yes	characteristic
467	C₂×C₃	#3455	1	2	yes	—
468	C₂×C₃	#3500	1	2	yes	—
469	C₂×C₃	#3510	1	2	yes	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	8	no	—
479	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
480	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
481	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
482	C₂²	C₃×#585	1	4	yes	—
483	C₄	—	2	2	no	—
484	C₄	—	2	4	no	—
485	C₄	—	2	4	no	—
486	C₄	—	2	4	no	—
487	C₄	—	2	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	2	no	—
493	C₄	C₃×#532	1	4	yes	—
494	C₃	#35331	1	1	yes	characteristic, direct product factor, Sylow
495	C₂	—	4	2	no	—
496	C₂	—	8	4	no	—
497	C₂	C₂×C₃×#532	1	1	yes	characteristic
498	C₂	C₃×#3455	1	2	yes	—
499	C₂	C₃×#3500	1	2	yes	—
500	C₂	C₃×#3510	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2619	C₂
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×#542	C₂	semidirect
2. C₃×#2862	C₂	semidirect
3. C₃×#2858	C₂	semidirect
4. C₃×#2850	C₂	semidirect
5. C₃×#2640	C₂	semidirect
6. C₃×#2621	C₂	semidirect
8. C₃×#2560	C₂	semidirect
9. C₃×#2557	C₂	semidirect
10. C₃×#2328	C₂	semidirect
11. C₃×#2327	C₂	semidirect
12. C₃×C₄×#124	C₂	semidirect
13. C₃×C₄×#117	C₂	semidirect
14. #35331	C₃	direct (N × H)
59. C₂×#542	C₂×C₃	semidirect
60. #2862	C₂×C₃	semidirect
61. #2858	C₂×C₃	semidirect
62. #2850	C₂×C₃	semidirect
63. #2640	C₂×C₃	semidirect
64. #2621	C₂×C₃	semidirect
66. #2560	C₂×C₃	semidirect
67. #2557	C₂×C₃	semidirect
68. #2328	C₂×C₃	semidirect
69. #2327	C₂×C₃	semidirect
70. C₄×#124	C₂×C₃	semidirect
71. C₄×#117	C₂×C₃	semidirect
94. C₃×#117	D₄	semidirect
257. #117	C₃×D₄	semidirect
494. C₃	#35331	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×#542	2
C₃×#2862	2
C₃×#2858	2
C₃×#2850	2
C₃×#2640	2
C₃×#2621	2
C₃×#2619	2
C₃×#2560	2
C₃×#2557	2
C₃×#2328	2
C₃×#2327	2
C₃×C₄×#124	2
C₃×C₄×#117	2
#35331	3

Subgroups — C3×#35331 #10653938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35331 #10653938