Subgroups — C₃×#34481 #10653088

Order 768.

2132 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×#556	C₂	1	1	yes	maximal, characteristic
2	C₃×#2383	C₂	1	4	yes	maximal, complemented
3	C₃×#2367	C₂	1	2	yes	maximal
4	C₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2360	C₂	1	2	yes	maximal, complemented
6	C₃×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×Q₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₃×#2347	C₂	1	2	yes	maximal, complemented
10	C₃×#2334	C₂	1	4	yes	maximal, complemented
11	C₃×#2326	C₂	1	2	yes	maximal
12	C₃×#2323	C₂	1	2	yes	maximal, complemented
13	C₃×#2320	C₂	1	2	yes	maximal, complemented
14	C₃×#2317	C₂	1	2	yes	maximal, complemented
15	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2293	C₂	1	1	yes	maximal, characteristic
18	#34481	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×#556	C₄	1	16	yes	complemented
20	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×#126	C₂²	1	4	yes	—
22	C₂×C₃×#124	C₂²	1	2	yes	—
23	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
26	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
27	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
29	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
30	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×#117	C₂²	1	2	yes	—
32	C₂×C₃×#117	C₂²	1	2	yes	—
33	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₃×#391	C₂²	1	1	yes	characteristic
35	C₃×#391	C₂²	1	2	yes	—
36	C₃×#391	C₂²	1	1	yes	characteristic
37	C₃×#391	C₂²	1	2	yes	—
38	C₃×#390	C₂²	1	1	yes	characteristic
39	C₃×#390	C₂²	1	1	yes	characteristic
40	C₃×#389	C₂²	1	2	yes	—
41	C₃×#389	C₂²	1	4	yes	—
42	C₃×#389	C₂²	1	2	yes	—
43	C₃×#389	C₂²	1	4	yes	—
44	C₃×#389	C₂²	1	4	yes	—
45	C₃×#389	C₂²	1	1	yes	characteristic
46	C₃×#389	C₂²	1	1	yes	characteristic
47	C₃×#389	C₂²	1	1	yes	characteristic
48	C₃×#389	C₂²	1	1	yes	characteristic
49	C₃×#389	C₂²	1	2	yes	—
50	C₃×#389	C₂²	1	2	yes	—
51	C₃×#389	C₂²	1	2	yes	—
52	C₃×#388	C₂²	1	4	yes	—
53	C₃×#388	C₂²	1	4	yes	—
54	C₃×#388	C₂²	1	2	yes	—
55	C₃×#388	C₂²	1	4	yes	—
56	C₃×#388	C₂²	1	2	yes	—
57	C₃×#388	C₂²	1	4	yes	—
58	C₃×#387	C₂²	1	4	yes	—
59	C₃×#387	C₂²	1	4	yes	—
60	C₃×#387	C₂²	1	2	yes	—
61	C₃×#387	C₂²	1	2	yes	—
62	C₃×#387	C₂²	1	4	yes	—
63	C₃×#385	C₂²	1	4	yes	—
64	C₃×#385	C₂²	1	4	yes	—
65	C₃×#385	C₂²	1	4	yes	—
66	C₃×#385	C₂²	1	4	yes	—
67	C₃×#384	C₂²	1	4	yes	—
68	C₃×#384	C₂²	1	1	yes	characteristic
69	C₃×#384	C₂²	1	2	yes	—
70	C₃×#383	C₂²	1	4	yes	—
71	C₃×#382	C₂²	1	4	yes	—
72	C₃×#380	C₂²	1	2	yes	—
73	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
74	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
77	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
78	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
79	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
80	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
81	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
82	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
83	C₃×#376	C₂²	1	2	yes	—
84	C₃×C₄³	C₂²	1	1	yes	characteristic
85	C₂×#556	C₂×C₃	1	1	yes	characteristic
86	#2383	C₂×C₃	1	4	yes	complemented
87	#2367	C₂×C₃	1	2	yes	—
88	#2365	C₂×C₃	1	1	yes	characteristic, complemented
89	#2360	C₂×C₃	1	2	yes	complemented
90	Q₈×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
91	Q₈×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
92	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
93	#2347	C₂×C₃	1	2	yes	complemented
94	#2334	C₂×C₃	1	4	yes	complemented
95	#2326	C₂×C₃	1	2	yes	—
96	#2323	C₂×C₃	1	2	yes	complemented
97	#2320	C₂×C₃	1	2	yes	complemented
98	#2317	C₂×C₃	1	2	yes	complemented
99	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
100	#2295	C₂×C₃	1	1	yes	characteristic, complemented
101	#2293	C₂×C₃	1	1	yes	characteristic
102	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
103	C₂²×C₃×Q₈	C₂³	1	2	yes	—
104	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂³	1	2	yes	—
106	C₂³×C₃×C₄	C₂³	1	4	yes	—
107	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
108	C₃×#126	C₂×C₄	1	32	yes	complemented
109	C₃×#124	C₂×C₄	1	16	yes	—
110	C₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
111	C₃×C₄×Q₈	—	4	4	no	—
112	C₃×C₄×Q₈	—	4	4	no	—
113	C₃×C₄×Q₈	—	4	4	no	—
114	C₃×C₄×Q₈	C₂×C₄	1	16	yes	complemented
115	C₃×C₄×Q₈	C₂×C₄	1	8	yes	complemented
116	C₃×C₄×D₄	—	4	4	no	—
117	C₃×C₄×D₄	C₂×C₄	1	8	yes	—
118	C₃×#117	—	4	4	no	—
119	C₃×#117	C₂×C₄	1	16	yes	complemented
120	C₂×C₃×C₄⋊C₄	—	4	4	no	—
121	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
133	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
135	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
136	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
152	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
154	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
156	C₂×C₃×C₄²	C₂³	1	2	yes	—
157	C₂×C₃×C₄²	C₂³	1	2	yes	—
158	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄²	C₂³	1	4	yes	—
160	C₂×C₃×C₄²	C₂³	1	4	yes	—
161	C₂×C₃×C₄²	C₂³	1	4	yes	—
162	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
163	C₂×C₃×C₄²	C₂³	1	2	yes	—
164	C₂×C₃×C₄²	C₂³	1	4	yes	—
165	C₃×#95	C₂³	1	2	yes	—
166	C₃×#95	C₂³	1	2	yes	—
167	C₃×#95	C₂³	1	2	yes	—
168	C₃×#95	C₂³	1	2	yes	—
169	C₃×#95	C₂³	1	2	yes	—
170	C₃×#95	C₂³	1	2	yes	—
171	C₃×#95	C₂³	1	4	yes	—
172	C₃×#95	C₂³	1	2	yes	—
173	C₃×#95	C₂³	1	4	yes	—
174	C₃×#95	C₂³	1	4	yes	—
175	C₃×#95	C₂³	1	4	yes	—
176	C₃×#95	C₂³	1	4	yes	—
177	C₃×#95	C₂³	1	4	yes	—
178	C₃×#95	C₂³	1	2	yes	—
179	C₃×#95	C₂³	1	2	yes	—
180	C₃×#95	C₂³	1	2	yes	—
181	#556	C₃×C₄	1	16	yes	complemented
182	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
183	C₂×#126	C₂²×C₃	1	4	yes	—
184	C₂×#124	C₂²×C₃	1	2	yes	—
185	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
186	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
187	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
188	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
189	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
190	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
191	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
192	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
193	C₂×#117	C₂²×C₃	1	2	yes	—
194	C₂×#117	C₂²×C₃	1	2	yes	—
195	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
196	#391	C₂²×C₃	1	2	yes	—
197	#391	C₂²×C₃	1	2	yes	—
198	#391	C₂²×C₃	1	1	yes	characteristic
199	#391	C₂²×C₃	1	1	yes	characteristic
200	#390	C₂²×C₃	1	1	yes	characteristic
201	#390	C₂²×C₃	1	1	yes	characteristic
202	#389	C₂²×C₃	1	2	yes	—
203	#389	C₂²×C₃	1	2	yes	—
204	#389	C₂²×C₃	1	1	yes	characteristic
205	#389	C₂²×C₃	1	2	yes	—
206	#389	C₂²×C₃	1	2	yes	—
207	#389	C₂²×C₃	1	1	yes	characteristic
208	#389	C₂²×C₃	1	2	yes	—
209	#389	C₂²×C₃	1	4	yes	—
210	#389	C₂²×C₃	1	4	yes	—
211	#389	C₂²×C₃	1	4	yes	—
212	#389	C₂²×C₃	1	1	yes	characteristic
213	#389	C₂²×C₃	1	1	yes	characteristic
214	#388	C₂²×C₃	1	4	yes	—
215	#388	C₂²×C₃	1	4	yes	—
216	#388	C₂²×C₃	1	4	yes	—
217	#388	C₂²×C₃	1	2	yes	—
218	#388	C₂²×C₃	1	4	yes	—
219	#388	C₂²×C₃	1	2	yes	—
220	#387	C₂²×C₃	1	4	yes	—
221	#387	C₂²×C₃	1	4	yes	—
222	#387	C₂²×C₃	1	2	yes	—
223	#387	C₂²×C₃	1	4	yes	—
224	#387	C₂²×C₃	1	2	yes	—
225	#385	C₂²×C₃	1	4	yes	—
226	#385	C₂²×C₃	1	4	yes	—
227	#385	C₂²×C₃	1	4	yes	—
228	#385	C₂²×C₃	1	4	yes	—
229	#384	C₂²×C₃	1	1	yes	characteristic
230	#384	C₂²×C₃	1	4	yes	—
231	#384	C₂²×C₃	1	2	yes	—
232	#383	C₂²×C₃	1	4	yes	—
233	#382	C₂²×C₃	1	4	yes	—
234	#380	C₂²×C₃	1	2	yes	—
235	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
236	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
237	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
238	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
239	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
240	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
242	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
243	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
244	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
245	#376	C₂²×C₃	1	2	yes	—
246	C₄³	C₂²×C₃	1	1	yes	characteristic
247	C₂⁴×C₃	C₂⁴	1	2	yes	—
248	C₂×C₃×Q₈	—	2	2	no	—
249	C₂×C₃×Q₈	—	2	4	no	—
250	C₂×C₃×Q₈	—	2	2	no	—
251	C₂×C₃×Q₈	—	2	4	no	—
252	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
253	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
254	C₂×C₃×D₄	—	2	2	no	—
255	C₂×C₃×D₄	—	2	2	no	—
256	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
257	C₂²×C₃×C₄	—	2	4	no	—
258	C₂²×C₃×C₄	—	2	4	no	—
259	C₂²×C₃×C₄	—	4	4	no	—
260	C₂²×C₃×C₄	—	4	4	no	—
261	C₂²×C₃×C₄	—	4	4	no	—
262	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
263	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
264	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
265	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
266	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
268	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
269	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
270	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
271	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
273	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
274	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
275	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
276	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
279	C₃×C₄⋊C₄	—	2	2	no	—
280	C₃×C₄⋊C₄	—	2	4	no	—
281	C₃×C₄⋊C₄	—	2	4	no	—
282	C₃×C₄⋊C₄	—	2	2	no	—
283	C₃×C₄⋊C₄	—	2	4	no	—
284	C₃×C₄⋊C₄	—	2	2	no	—
285	C₃×C₄⋊C₄	—	2	2	no	—
286	C₃×C₄⋊C₄	—	4	4	no	—
287	C₃×C₄⋊C₄	—	4	2	no	—
288	C₃×C₄⋊C₄	—	4	2	no	—
289	C₃×C₄⋊C₄	—	4	4	no	—
290	C₃×C₄⋊C₄	—	4	2	no	—
291	C₃×C₄⋊C₄	—	4	2	no	—
292	C₃×C₄⋊C₄	—	4	4	no	—
293	C₃×C₄⋊C₄	—	4	4	no	—
294	C₃×C₄⋊C₄	—	4	4	no	—
295	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
296	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
297	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
298	C₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
299	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
300	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
301	C₃×C₂²⋊C₄	—	2	4	no	—
302	C₃×C₂²⋊C₄	—	4	2	no	—
303	C₃×C₂²⋊C₄	—	4	2	no	—
304	C₃×C₂²⋊C₄	—	4	2	no	—
305	C₃×C₂²⋊C₄	—	4	4	no	—
306	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
307	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
308	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
309	C₃×C₄²	—	2	2	no	—
310	C₃×C₄²	—	2	4	no	—
311	C₃×C₄²	—	2	4	no	—
312	C₃×C₄²	—	2	2	no	—
313	C₃×C₄²	—	2	2	no	—
314	C₃×C₄²	—	2	2	no	—
315	C₃×C₄²	—	2	2	no	—
316	C₃×C₄²	—	4	1	no	—
317	C₃×C₄²	—	4	4	no	—
318	C₃×C₄²	—	4	4	no	—
319	C₃×C₄²	—	4	4	no	—
320	C₃×C₄²	C₂²×C₄	1	16	yes	—
321	C₃×C₄²	C₂²×C₄	1	4	yes	—
322	C₃×C₄²	C₂²×C₄	1	8	yes	—
323	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
324	C₂²×Q₈	C₂³×C₃	1	2	yes	—
325	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₃	1	2	yes	—
327	C₂³×C₄	C₂³×C₃	1	4	yes	—
328	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
329	#126	C₂×C₃×C₄	1	32	yes	complemented
330	#124	C₂×C₃×C₄	1	16	yes	—
331	C₂²⋊Q₈	C₂×C₃×C₄	1	16	yes	complemented
332	C₄×Q₈	—	4	4	no	—
333	C₄×Q₈	—	4	4	no	—
334	C₄×Q₈	—	4	4	no	—
335	C₄×Q₈	C₂×C₃×C₄	1	16	yes	complemented
336	C₄×Q₈	C₂×C₃×C₄	1	8	yes	complemented
337	C₄×D₄	—	4	4	no	—
338	C₄×D₄	C₂×C₃×C₄	1	8	yes	—
339	#117	—	4	4	no	—
340	#117	C₂×C₃×C₄	1	16	yes	complemented
341	C₂×C₄⋊C₄	—	4	4	no	—
342	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
354	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
355	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
357	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
372	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₃	1	2	yes	—
374	C₂×C₄²	C₂³×C₃	1	2	yes	—
375	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
378	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₃	1	4	yes	—
380	C₂×C₄²	C₂³×C₃	1	4	yes	—
381	C₂×C₄²	C₂³×C₃	1	4	yes	—
382	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₃	1	4	yes	—
384	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₃	1	2	yes	—
386	#95	C₂³×C₃	1	2	yes	—
387	#95	C₂³×C₃	1	2	yes	—
388	#95	C₂³×C₃	1	2	yes	—
389	#95	C₂³×C₃	1	2	yes	—
390	#95	C₂³×C₃	1	2	yes	—
391	#95	C₂³×C₃	1	2	yes	—
392	#95	C₂³×C₃	1	4	yes	—
393	#95	C₂³×C₃	1	2	yes	—
394	#95	C₂³×C₃	1	4	yes	—
395	#95	C₂³×C₃	1	4	yes	—
396	#95	C₂³×C₃	1	4	yes	—
397	#95	C₂³×C₃	1	4	yes	—
398	#95	C₂³×C₃	1	4	yes	—
399	#95	C₂³×C₃	1	2	yes	—
400	#95	C₂³×C₃	1	2	yes	—
401	#95	C₂³×C₃	1	2	yes	—
402	C₂³×C₃	—	2	2	no	—
403	C₂³×C₃	—	2	2	no	—
404	C₂³×C₃	—	2	2	no	—
405	C₂³×C₃	—	2	2	no	—
406	C₂³×C₃	—	2	2	no	—
407	C₂³×C₃	—	2	2	no	—
408	C₂³×C₃	C₂³×C₄	1	4	yes	—
409	C₂³×C₃	C₂⁵	1	1	yes	characteristic
410	C₃×Q₈	—	2	8	no	—
411	C₃×Q₈	—	2	16	no	—
412	C₃×D₄	—	2	8	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	2	4	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	2	no	—
421	C₂×C₃×C₄	—	2	4	no	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	2	no	—
425	C₂×C₃×C₄	—	2	16	no	—
426	C₂×C₃×C₄	—	2	2	no	—
427	C₂×C₃×C₄	—	2	2	no	—
428	C₂×C₃×C₄	—	2	1	no	—
429	C₂×C₃×C₄	—	2	1	no	—
430	C₂×C₃×C₄	—	2	2	no	—
431	C₂×C₃×C₄	—	2	1	no	—
432	C₂×C₃×C₄	—	2	2	no	—
433	C₂×C₃×C₄	—	2	2	no	—
434	C₂×C₃×C₄	—	2	4	no	—
435	C₂×C₃×C₄	—	2	4	no	—
436	C₂×C₃×C₄	—	2	2	no	—
437	C₂×C₃×C₄	—	2	1	no	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	2	no	—
444	C₂×C₃×C₄	—	2	2	no	—
445	C₂×C₃×C₄	—	2	1	no	—
446	C₂×C₃×C₄	—	2	1	no	—
447	C₂×C₃×C₄	—	2	2	no	—
448	C₂×C₃×C₄	—	2	4	no	—
449	C₂×C₃×C₄	—	2	2	no	—
450	C₂×C₃×C₄	—	8	8	no	—
451	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
452	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
453	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
454	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
455	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
456	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
457	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
458	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
459	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
460	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
461	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
462	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
463	C₂⁴	C₂⁴×C₃	1	2	yes	—
464	C₂×Q₈	—	2	2	no	—
465	C₂×Q₈	—	2	4	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	4	no	—
468	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
469	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	4	4	no	—
478	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
479	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
480	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
482	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	4	4	no	—
503	C₄⋊C₄	—	4	2	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	4	no	—
506	C₄⋊C₄	—	4	4	no	—
507	C₄⋊C₄	—	4	4	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	4	no	—
511	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
512	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
513	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
514	C₄⋊C₄	C₂²×C₃×C₄	1	16	yes	—
515	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
516	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	4	2	no	—
519	C₂²⋊C₄	—	4	2	no	—
520	C₂²⋊C₄	—	4	4	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
523	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
524	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	4	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	2	no	—
531	C₄²	—	2	2	no	—
532	C₄²	—	4	4	no	—
533	C₄²	—	4	4	no	—
534	C₄²	—	4	4	no	—
535	C₄²	—	4	1	no	—
536	C₄²	C₂²×C₃×C₄	1	16	yes	—
537	C₄²	C₂²×C₃×C₄	1	4	yes	—
538	C₄²	C₂²×C₃×C₄	1	8	yes	—
539	C₂²×C₃	—	2	4	no	—
540	C₂²×C₃	—	2	4	no	—
541	C₂²×C₃	—	2	4	no	—
542	C₂²×C₃	—	4	2	no	—
543	C₂²×C₃	—	4	2	no	—
544	C₂²×C₃	—	4	2	no	—
545	C₂²×C₃	—	4	2	no	—
546	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
547	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
550	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
551	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
552	C₂²×C₃	#585	1	1	yes	characteristic
553	C₃×C₄	—	2	4	no	—
554	C₃×C₄	—	2	4	no	—
555	C₃×C₄	—	2	8	no	—
556	C₃×C₄	—	2	2	no	—
557	C₃×C₄	—	2	4	no	—
558	C₃×C₄	—	2	2	no	—
559	C₃×C₄	—	4	1	no	—
560	C₃×C₄	—	4	2	no	—
561	C₃×C₄	—	4	4	no	—
562	C₃×C₄	—	4	2	no	—
563	C₃×C₄	—	4	2	no	—
564	C₃×C₄	—	4	1	no	—
565	C₃×C₄	—	4	2	no	—
566	C₃×C₄	—	4	1	no	—
567	C₃×C₄	#520	1	4	yes	—
568	C₃×C₄	#520	1	4	yes	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	C₂³×C₃×C₄	1	4	yes	—
576	C₂³	C₂⁵×C₃	1	1	yes	characteristic
577	Q₈	—	2	8	no	—
578	Q₈	—	2	16	no	—
579	D₄	—	2	8	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	16	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	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	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	8	8	no	—
618	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
619	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
620	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
621	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
622	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
623	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
624	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
625	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
626	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
627	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
628	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
629	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
630	C₂×C₃	—	4	4	no	—
631	C₂×C₃	C₂×#520	1	1	yes	characteristic
632	C₂×C₃	C₂×#520	1	1	yes	characteristic
633	C₂×C₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
634	C₂×C₃	#3546	1	1	yes	characteristic
635	C₂×C₃	#3550	1	1	yes	characteristic
636	C₂×C₃	#3552	1	1	yes	characteristic
637	C₂×C₃	#3555	1	1	yes	characteristic
638	C₂²	—	2	4	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
646	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
647	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
649	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
650	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
651	C₂²	C₃×#585	1	1	yes	characteristic
652	C₄	—	2	4	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	8	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	2	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	4	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	C₃×#520	1	4	yes	—
667	C₄	C₃×#520	1	4	yes	—
668	C₃	#34481	1	1	yes	characteristic, direct product factor, Sylow
669	C₂	—	4	4	no	—
670	C₂	C₂×C₃×#520	1	1	yes	characteristic
671	C₂	C₂×C₃×#520	1	1	yes	characteristic
672	C₂	C₃×C₄×2₋¹⁺⁴	1	1	yes	characteristic
673	C₂	C₃×#3546	1	1	yes	characteristic
674	C₂	C₃×#3550	1	1	yes	characteristic
675	C₂	C₃×#3552	1	1	yes	characteristic
676	C₂	C₃×#3555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂²×C₃×D₄	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃×#2383	C₂	semidirect
4. C₃×#2365	C₂	semidirect
5. C₃×#2360	C₂	semidirect
6. C₃×Q₈×C₄⋊C₄	C₂	semidirect
7. C₃×Q₈×C₄⋊C₄	C₂	semidirect
9. C₃×#2347	C₂	semidirect
10. C₃×#2334	C₂	semidirect
12. C₃×#2323	C₂	semidirect
13. C₃×#2320	C₂	semidirect
14. C₃×#2317	C₂	semidirect
15. C₃×C₄×C₄⋊Q₈	C₂	semidirect
16. C₃×#2295	C₂	semidirect
18. #34481	C₃	direct (N × H)
19. C₃×#556	C₄	semidirect
86. #2383	C₂×C₃	semidirect
88. #2365	C₂×C₃	semidirect
89. #2360	C₂×C₃	semidirect
90. Q₈×C₄⋊C₄	C₂×C₃	semidirect
91. Q₈×C₄⋊C₄	C₂×C₃	semidirect
93. #2347	C₂×C₃	semidirect
94. #2334	C₂×C₃	semidirect
96. #2323	C₂×C₃	semidirect
97. #2320	C₂×C₃	semidirect
98. #2317	C₂×C₃	semidirect
99. C₄×C₄⋊Q₈	C₂×C₃	semidirect
100. #2295	C₂×C₃	semidirect
107. C₃×C₄⋊Q₈	C₂×C₄	semidirect
108. C₃×#126	C₂×C₄	semidirect
110. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
114. C₃×C₄×Q₈	C₂×C₄	semidirect
115. C₃×C₄×Q₈	C₂×C₄	semidirect
119. C₃×#117	C₂×C₄	semidirect
181. #556	C₃×C₄	semidirect
328. C₄⋊Q₈	C₂×C₃×C₄	semidirect
329. #126	C₂×C₃×C₄	semidirect
331. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
335. C₄×Q₈	C₂×C₃×C₄	semidirect
336. C₄×Q₈	C₂×C₃×C₄	semidirect
340. #117	C₂×C₃×C₄	semidirect
668. C₃	#34481	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×#556	2
C₃×#2383	2
C₃×#2367	2
C₃×#2365	2
C₃×#2360	2
C₃×Q₈×C₄⋊C₄	2
C₃×D₄×C₄⋊C₄	2
C₃×#2347	2
C₃×#2334	2
C₃×#2326	2
C₃×#2323	2
C₃×#2320	2
C₃×#2317	2
C₃×C₄×C₄⋊Q₈	2
C₃×#2295	2
C₃×#2293	2
#34481	3

Subgroups — C3×#34481 #10653088

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34481 #10653088