Subgroups — C₃×#35277 #10653884

Order 768.

2370 conjugacy classes of subgroups.

The subgroup lattice has 586 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×#2868	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2856	C₂	1	1	yes	maximal, characteristic
6	C₃×#2640	C₂	1	2	yes	maximal, complemented
7	C₃×#2620	C₂	1	2	yes	maximal, complemented
8	C₃×#2512	C₂	1	4	yes	maximal, complemented
9	C₃×#2491	C₂	1	4	yes	maximal, complemented
10	C₃×#2452	C₂	1	4	yes	maximal, complemented
11	C₃×#2422	C₂	1	4	yes	maximal, complemented
12	C₃×#2326	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×#127	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	#35277	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×#542	—	2	16	no	—
18	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₃×#126	C₂²	1	4	yes	—
23	C₂×C₃×#124	C₂²	1	2	yes	—
24	C₂×C₃×#124	C₂²	1	2	yes	—
25	C₂×C₃×#124	C₂²	1	4	yes	—
26	C₂×C₃×#123	C₂²	1	4	yes	—
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
29	C₂×C₃×#121	C₂²	1	2	yes	—
30	C₂×C₃×#121	C₂²	1	4	yes	—
31	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
32	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
34	C₂×C₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₃×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
37	C₃×#397	C₂²	1	8	yes	—
38	C₃×#396	C₂²	1	8	yes	—
39	C₃×#394	C₂²	1	8	yes	—
40	C₃×#393	C₂²	1	8	yes	—
41	C₃×#391	C₂²	1	2	yes	—
42	C₃×#391	C₂²	1	2	yes	—
43	C₃×#390	C₂²	1	2	yes	—
44	C₃×#390	C₂²	1	2	yes	—
45	C₃×#390	C₂²	1	4	yes	—
46	C₃×#390	C₂²	1	4	yes	—
47	C₃×#390	C₂²	1	4	yes	—
48	C₃×#390	C₂²	1	4	yes	—
49	C₃×#389	C₂²	1	4	yes	—
50	C₃×#389	C₂²	1	4	yes	—
51	C₃×#388	C₂²	1	8	yes	—
52	C₃×#385	C₂²	1	8	yes	—
53	C₃×#384	C₂²	1	2	yes	—
54	C₃×#384	C₂²	1	4	yes	—
55	C₃×#384	C₂²	1	1	yes	characteristic
56	C₃×#384	C₂²	1	1	yes	characteristic
57	C₃×#380	C₂²	1	4	yes	—
58	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
59	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
60	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
61	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
62	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₃×#376	C₂²	1	1	yes	characteristic
64	C₃×#376	C₂²	1	1	yes	characteristic
65	C₃×C₄³	C₂²	1	1	yes	characteristic
66	C₃×C₄³	C₂²	1	1	yes	characteristic
67	C₂×#542	C₂×C₃	1	2	yes	complemented
68	#2868	C₂×C₃	1	1	yes	characteristic, complemented
69	#2858	C₂×C₃	1	1	yes	characteristic, complemented
70	#2857	C₂×C₃	1	1	yes	characteristic, complemented
71	#2856	C₂×C₃	1	1	yes	characteristic
72	#2640	C₂×C₃	1	2	yes	complemented
73	#2620	C₂×C₃	1	2	yes	complemented
74	#2512	C₂×C₃	1	4	yes	complemented
75	#2491	C₂×C₃	1	4	yes	complemented
76	#2452	C₂×C₃	1	4	yes	complemented
77	#2422	C₂×C₃	1	4	yes	complemented
78	#2326	C₂×C₃	1	2	yes	complemented
79	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
80	C₄×#127	C₂×C₃	1	1	yes	characteristic, complemented
81	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂²×C₃×Q₈	C₂³	1	2	yes	—
83	C₂²×C₃×Q₈	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	4	yes	—
87	C₂³×C₃×C₄	C₂³	1	2	yes	—
88	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
89	C₂³×C₃×C₄	C₂³	1	4	yes	—
90	C₃×C₄⋊Q₈	—	2	8	no	—
91	C₃×C₄⋊Q₈	—	2	4	no	—
92	C₃×C₄⋊Q₈	—	4	8	no	—
93	C₃×#127	—	2	4	no	—
94	C₃×#126	—	2	16	no	—
95	C₃×#124	—	2	16	no	—
96	C₃×#124	—	2	8	no	—
97	C₃×#124	—	2	8	no	—
98	C₃×#123	—	2	16	no	—
99	C₃×C₂²⋊Q₈	—	2	8	no	—
100	C₃×C₂²⋊Q₈	—	2	16	no	—
101	C₃×#121	—	2	8	no	—
102	C₃×#121	—	4	8	no	—
103	C₃×C₄×Q₈	—	2	8	no	—
104	C₃×C₄×D₄	—	2	8	no	—
105	C₃×C₄×D₄	—	4	8	no	—
106	C₃×#117	—	2	4	no	—
107	C₃×#117	D₄	1	8	yes	complemented
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	4	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	4	yes	—
115	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
118	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
123	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₃×C₂²⋊C₄	C₂³	1	4	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	8	yes	—
128	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
129	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
131	C₂×C₃×C₄²	—	2	4	no	—
132	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₄²	C₂³	1	2	yes	—
134	C₂×C₃×C₄²	C₂³	1	2	yes	—
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	C₂×C₃×C₄²	C₂³	1	2	yes	—
140	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
141	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
142	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
144	C₃×#95	C₂³	1	2	yes	—
145	C₃×#95	C₂³	1	2	yes	—
146	C₃×#95	C₂³	1	2	yes	—
147	C₃×#95	C₂³	1	2	yes	—
148	C₃×#95	C₂³	1	8	yes	—
149	C₃×#95	C₂³	1	8	yes	—
150	#542	—	2	16	no	—
151	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
153	C₂×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
154	C₂×#127	C₂²×C₃	1	1	yes	characteristic
155	C₂×#126	C₂²×C₃	1	4	yes	—
156	C₂×#124	C₂²×C₃	1	2	yes	—
157	C₂×#124	C₂²×C₃	1	2	yes	—
158	C₂×#124	C₂²×C₃	1	4	yes	—
159	C₂×#123	C₂²×C₃	1	4	yes	—
160	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
161	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
162	C₂×#121	C₂²×C₃	1	2	yes	—
163	C₂×#121	C₂²×C₃	1	4	yes	—
164	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
165	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
166	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
167	C₂×#117	C₂²×C₃	1	1	yes	characteristic
168	C₂×#117	C₂²×C₃	1	1	yes	characteristic
169	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
170	#397	C₂²×C₃	1	8	yes	—
171	#396	C₂²×C₃	1	8	yes	—
172	#394	C₂²×C₃	1	8	yes	—
173	#393	C₂²×C₃	1	8	yes	—
174	#391	C₂²×C₃	1	2	yes	—
175	#391	C₂²×C₃	1	2	yes	—
176	#390	C₂²×C₃	1	2	yes	—
177	#390	C₂²×C₃	1	4	yes	—
178	#390	C₂²×C₃	1	2	yes	—
179	#390	C₂²×C₃	1	4	yes	—
180	#390	C₂²×C₃	1	4	yes	—
181	#390	C₂²×C₃	1	4	yes	—
182	#389	C₂²×C₃	1	4	yes	—
183	#389	C₂²×C₃	1	4	yes	—
184	#388	C₂²×C₃	1	8	yes	—
185	#385	C₂²×C₃	1	8	yes	—
186	#384	C₂²×C₃	1	1	yes	characteristic
187	#384	C₂²×C₃	1	1	yes	characteristic
188	#384	C₂²×C₃	1	2	yes	—
189	#384	C₂²×C₃	1	4	yes	—
190	#380	C₂²×C₃	1	4	yes	—
191	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
192	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
193	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
194	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
195	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
196	#376	C₂²×C₃	1	1	yes	characteristic
197	#376	C₂²×C₃	1	1	yes	characteristic
198	C₄³	C₂²×C₃	1	1	yes	characteristic
199	C₄³	C₂²×C₃	1	1	yes	characteristic
200	C₂⁴×C₃	C₂⁴	1	4	yes	—
201	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
202	C₂×C₃×Q₈	—	2	4	no	—
203	C₂×C₃×Q₈	—	2	8	no	—
204	C₂×C₃×Q₈	—	2	4	no	—
205	C₂×C₃×Q₈	—	2	4	no	—
206	C₂×C₃×Q₈	—	4	8	no	—
207	C₂×C₃×D₄	—	2	8	no	—
208	C₂×C₃×D₄	—	2	4	no	—
209	C₂×C₃×D₄	—	2	4	no	—
210	C₂×C₃×D₄	—	2	4	no	—
211	C₂×C₃×D₄	—	2	8	no	—
212	C₂×C₃×D₄	—	2	8	no	—
213	C₂×C₃×D₄	—	2	8	no	—
214	C₂×C₃×D₄	—	4	8	no	—
215	C₂²×C₃×C₄	—	2	2	no	—
216	C₂²×C₃×C₄	—	2	2	no	—
217	C₂²×C₃×C₄	—	2	4	no	—
218	C₂²×C₃×C₄	—	2	4	no	—
219	C₂²×C₃×C₄	—	2	4	no	—
220	C₂²×C₃×C₄	—	2	8	no	—
221	C₂²×C₃×C₄	—	4	8	no	—
222	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
223	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
224	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
225	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
226	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
227	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
228	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
234	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
236	C₃×C₄⋊C₄	—	2	4	no	—
237	C₃×C₄⋊C₄	—	2	4	no	—
238	C₃×C₄⋊C₄	—	2	8	no	—
239	C₃×C₄⋊C₄	—	2	8	no	—
240	C₃×C₄⋊C₄	—	2	8	no	—
241	C₃×C₄⋊C₄	—	2	4	no	—
242	C₃×C₄⋊C₄	—	2	8	no	—
243	C₃×C₄⋊C₄	—	2	8	no	—
244	C₃×C₄⋊C₄	—	2	8	no	—
245	C₃×C₄⋊C₄	—	4	8	no	—
246	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
247	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
248	C₃×C₂²⋊C₄	—	2	8	no	—
249	C₃×C₂²⋊C₄	—	2	8	no	—
250	C₃×C₂²⋊C₄	—	2	8	no	—
251	C₃×C₂²⋊C₄	—	2	8	no	—
252	C₃×C₂²⋊C₄	—	2	8	no	—
253	C₃×C₂²⋊C₄	—	2	4	no	—
254	C₃×C₂²⋊C₄	—	2	16	no	—
255	C₃×C₂²⋊C₄	—	4	8	no	—
256	C₃×C₂²⋊C₄	—	4	8	no	—
257	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
258	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
259	C₃×C₄²	—	2	8	no	—
260	C₃×C₄²	—	2	4	no	—
261	C₃×C₄²	—	2	2	no	—
262	C₃×C₄²	—	2	2	no	—
263	C₃×C₄²	—	2	4	no	—
264	C₃×C₄²	—	2	4	no	—
265	C₃×C₄²	—	2	4	no	—
266	C₃×C₄²	—	2	4	no	—
267	C₃×C₄²	C₂×D₄	1	4	yes	—
268	C₃×C₄²	C₂×D₄	1	4	yes	—
269	C₃×C₄²	#41	1	4	yes	—
270	C₃×C₄²	#41	1	4	yes	—
271	C₂²×Q₈	C₂³×C₃	1	2	yes	—
272	C₂²×Q₈	C₂³×C₃	1	4	yes	—
273	C₂²×D₄	C₂³×C₃	1	2	yes	—
274	C₂²×D₄	C₂³×C₃	1	4	yes	—
275	C₂²×D₄	C₂³×C₃	1	4	yes	—
276	C₂³×C₄	C₂³×C₃	1	2	yes	—
277	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₃	1	4	yes	—
279	C₄⋊Q₈	—	2	8	no	—
280	C₄⋊Q₈	—	2	4	no	—
281	C₄⋊Q₈	—	4	8	no	—
282	#127	—	2	4	no	—
283	#126	—	2	16	no	—
284	#124	—	2	16	no	—
285	#124	—	2	8	no	—
286	#124	—	2	8	no	—
287	#123	—	2	16	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	C₂²⋊Q₈	—	2	16	no	—
290	#121	—	2	8	no	—
291	#121	—	4	8	no	—
292	C₄×Q₈	—	2	8	no	—
293	C₄×D₄	—	2	8	no	—
294	C₄×D₄	—	4	8	no	—
295	#117	—	2	4	no	—
296	#117	C₃×D₄	1	8	yes	complemented
297	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
300	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
302	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
303	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
304	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
305	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
306	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
307	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
320	C₂×C₄²	—	2	4	no	—
321	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₃	1	2	yes	—
323	C₂×C₄²	C₂³×C₃	1	4	yes	—
324	C₂×C₄²	C₂³×C₃	1	2	yes	—
325	C₂×C₄²	C₂³×C₃	1	2	yes	—
326	C₂×C₄²	C₂³×C₃	1	2	yes	—
327	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₃	1	2	yes	—
329	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
333	#95	C₂³×C₃	1	2	yes	—
334	#95	C₂³×C₃	1	2	yes	—
335	#95	C₂³×C₃	1	2	yes	—
336	#95	C₂³×C₃	1	2	yes	—
337	#95	C₂³×C₃	1	8	yes	—
338	#95	C₂³×C₃	1	8	yes	—
339	C₂³×C₃	—	2	1	no	—
340	C₂³×C₃	—	2	1	no	—
341	C₂³×C₃	—	2	2	no	—
342	C₂³×C₃	—	2	2	no	—
343	C₂³×C₃	—	2	4	no	—
344	C₂³×C₃	—	2	4	no	—
345	C₂³×C₃	—	2	4	no	—
346	C₂³×C₃	—	2	8	no	—
347	C₂³×C₃	—	2	8	no	—
348	C₂³×C₃	C₂²×D₄	1	2	yes	—
349	C₂³×C₃	C₂⁵	1	1	yes	characteristic
350	C₃×Q₈	—	4	8	no	—
351	C₃×Q₈	—	8	8	no	—
352	C₃×D₄	—	4	8	no	—
353	C₃×D₄	—	4	16	no	—
354	C₃×D₄	—	8	8	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	8	no	—
364	C₂×C₃×C₄	—	2	4	no	—
365	C₂×C₃×C₄	—	2	4	no	—
366	C₂×C₃×C₄	—	2	4	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	4	no	—
370	C₂×C₃×C₄	—	2	4	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	8	no	—
374	C₂×C₃×C₄	—	2	8	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	4	8	no	—
378	C₂×C₃×C₄	—	8	8	no	—
379	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
380	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
381	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
382	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
383	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
384	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
385	C₂×C₃×C₄	C₂×#41	1	4	yes	—
386	C₂×C₃×C₄	C₂×#41	1	2	yes	—
387	C₂×C₃×C₄	C₂×#41	1	2	yes	—
388	C₂×C₃×C₄	C₂×#41	1	4	yes	—
389	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
390	C₂×C₃×C₄	2₋¹⁺⁴	1	4	yes	—
391	C₂⁴	C₂⁴×C₃	1	4	yes	—
392	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	2	8	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	4	8	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	8	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	4	8	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	—	4	8	no	—
413	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
421	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	4	8	no	—
437	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
438	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	16	no	—
446	C₂²⋊C₄	—	4	8	no	—
447	C₂²⋊C₄	—	4	8	no	—
448	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
449	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
450	C₄²	—	2	8	no	—
451	C₄²	—	2	4	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	4	no	—
455	C₄²	—	2	4	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	2	4	no	—
458	C₄²	C₂×C₃×D₄	1	4	yes	—
459	C₄²	C₂×C₃×D₄	1	4	yes	—
460	C₄²	C₃×#41	1	4	yes	—
461	C₄²	C₃×#41	1	4	yes	—
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	4	2	no	—
466	C₂²×C₃	—	4	2	no	—
467	C₂²×C₃	—	4	4	no	—
468	C₂²×C₃	—	4	8	no	—
469	C₂²×C₃	—	4	4	no	—
470	C₂²×C₃	—	4	4	no	—
471	C₂²×C₃	—	4	8	no	—
472	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
473	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
474	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
475	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
476	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
477	C₃×C₄	—	2	2	no	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	2	2	no	—
481	C₃×C₄	—	2	2	no	—
482	C₃×C₄	—	2	4	no	—
483	C₃×C₄	—	4	4	no	—
484	C₃×C₄	—	4	2	no	—
485	C₃×C₄	—	4	4	no	—
486	C₃×C₄	—	4	4	no	—
487	C₃×C₄	—	4	2	no	—
488	C₃×C₄	#532	1	4	yes	—
489	C₃×C₄	#542	1	8	yes	complemented
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	4	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	8	no	—
498	C₂³	—	2	8	no	—
499	C₂³	C₂²×C₃×D₄	1	2	yes	—
500	C₂³	C₂⁵×C₃	1	1	yes	characteristic
501	Q₈	—	4	8	no	—
502	Q₈	—	8	8	no	—
503	D₄	—	4	8	no	—
504	D₄	—	4	16	no	—
505	D₄	—	8	8	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	8	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	8	no	—
529	C₂×C₄	—	8	8	no	—
530	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
531	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
532	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
533	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
534	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
535	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
536	C₂×C₄	C₂×C₃×#41	1	4	yes	—
537	C₂×C₄	C₂×C₃×#41	1	2	yes	—
538	C₂×C₄	C₂×C₃×#41	1	2	yes	—
539	C₂×C₄	C₂×C₃×#41	1	4	yes	—
540	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
541	C₂×C₄	C₃×2₋¹⁺⁴	1	4	yes	—
542	C₂×C₃	—	4	2	no	—
543	C₂×C₃	—	8	4	no	—
544	C₂×C₃	C₂×#532	1	1	yes	characteristic
545	C₂×C₃	C₂×#542	1	2	yes	—
546	C₂×C₃	#3498	1	1	yes	characteristic
547	C₂×C₃	#3499	1	1	yes	characteristic
548	C₂×C₃	#3511	1	2	yes	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	8	no	—
556	C₂²	—	4	4	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	8	no	—
559	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
560	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
561	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
562	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
563	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	4	no	—
570	C₄	—	4	4	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	4	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	2	no	—
575	C₄	C₃×#532	1	4	yes	—
576	C₄	C₃×#542	1	8	yes	complemented
577	C₃	#35277	1	1	yes	characteristic, direct product factor, Sylow
578	C₂	—	4	2	no	—
579	C₂	—	8	4	no	—
580	C₂	C₂×C₃×#532	1	1	yes	characteristic
581	C₂	C₂×C₃×#542	1	2	yes	—
582	C₂	C₃×#3498	1	1	yes	characteristic
583	C₂	C₃×#3499	1	1	yes	characteristic
584	C₂	C₃×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2856	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×#2868	C₂	semidirect
3. C₃×#2858	C₂	semidirect
4. C₃×#2857	C₂	semidirect
6. C₃×#2640	C₂	semidirect
7. C₃×#2620	C₂	semidirect
8. C₃×#2512	C₂	semidirect
9. C₃×#2491	C₂	semidirect
10. C₃×#2452	C₂	semidirect
11. C₃×#2422	C₂	semidirect
12. C₃×#2326	C₂	semidirect
13. C₃×C₄×C₄⋊Q₈	C₂	semidirect
14. C₃×C₄×#127	C₂	semidirect
15. C₃×C₄×#117	C₂	semidirect
16. #35277	C₃	direct (N × H)
67. C₂×#542	C₂×C₃	semidirect
68. #2868	C₂×C₃	semidirect
69. #2858	C₂×C₃	semidirect
70. #2857	C₂×C₃	semidirect
72. #2640	C₂×C₃	semidirect
73. #2620	C₂×C₃	semidirect
74. #2512	C₂×C₃	semidirect
75. #2491	C₂×C₃	semidirect
76. #2452	C₂×C₃	semidirect
77. #2422	C₂×C₃	semidirect
78. #2326	C₂×C₃	semidirect
79. C₄×C₄⋊Q₈	C₂×C₃	semidirect
80. C₄×#127	C₂×C₃	semidirect
81. C₄×#117	C₂×C₃	semidirect
107. C₃×#117	D₄	semidirect
296. #117	C₃×D₄	semidirect
489. C₃×C₄	#542	semidirect
576. C₄	C₃×#542	semidirect
577. C₃	#35277	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×#2868	2
C₃×#2858	2
C₃×#2857	2
C₃×#2856	2
C₃×#2640	2
C₃×#2620	2
C₃×#2512	2
C₃×#2491	2
C₃×#2452	2
C₃×#2422	2
C₃×#2326	2
C₃×C₄×C₄⋊Q₈	2
C₃×C₄×#127	2
C₃×C₄×#117	2
#35277	3

Subgroups — C3×#35277 #10653884

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35277 #10653884