Subgroups — C₃×#34396 #10653003

Order 768.

2486 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₃×#2377	C₂	1	2	yes	maximal, complemented
4	C₃×#2359	C₂	1	4	yes	maximal, complemented
5	C₃×#2357	C₂	1	2	yes	maximal, complemented
6	C₃×#2353	C₂	1	2	yes	maximal, complemented
7	C₃×#2343	C₂	1	2	yes	maximal, complemented
8	C₃×#2339	C₂	1	2	yes	maximal, complemented
9	C₃×#2333	C₂	1	2	yes	maximal, complemented
10	C₃×#2332	C₂	1	2	yes	maximal, complemented
11	C₃×#2321	C₂	1	4	yes	maximal, complemented
12	C₃×#2319	C₂	1	2	yes	maximal, complemented
13	C₃×#2318	C₂	1	2	yes	maximal, complemented
14	C₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#381	C₂	1	1	yes	maximal, characteristic, complemented
16	#34396	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
18	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
19	C₃×#525	C₄	1	16	yes	complemented
20	C₂×C₃×#123	C₂²	1	2	yes	—
21	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₃×#120	C₂²	1	2	yes	—
26	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
27	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
28	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
29	C₂×C₃×#117	C₂²	1	2	yes	—
30	C₂×C₃×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃×#391	C₂²	1	4	yes	complemented
33	C₃×#390	C₂²	1	4	yes	—
34	C₃×#390	C₂²	1	4	yes	—
35	C₃×#389	C₂²	1	4	yes	complemented
36	C₃×#388	C₂²	1	4	yes	—
37	C₃×#388	C₂²	1	4	yes	—
38	C₃×#388	C₂²	1	4	yes	—
39	C₃×#388	C₂²	1	4	yes	—
40	C₃×#388	C₂²	1	4	yes	complemented
41	C₃×#388	C₂²	1	4	yes	complemented
42	C₃×#387	C₂²	1	4	yes	complemented
43	C₃×#387	C₂²	1	4	yes	complemented
44	C₃×#387	C₂²	1	4	yes	complemented
45	C₃×#387	C₂²	1	4	yes	complemented
46	C₃×#386	C₂²	1	4	yes	—
47	C₃×#386	C₂²	1	4	yes	—
48	C₃×#386	C₂²	1	4	yes	—
49	C₃×#386	C₂²	1	4	yes	complemented
50	C₃×#385	C₂²	1	4	yes	—
51	C₃×#385	C₂²	1	4	yes	complemented
52	C₃×#383	C₂²	1	2	yes	complemented
53	C₃×#382	C₂²	1	2	yes	complemented
54	C₃×#381	C₂²	1	2	yes	—
55	C₃×#381	C₂²	1	1	yes	characteristic
56	C₃×#381	C₂²	1	1	yes	characteristic
57	C₃×#381	C₂²	1	2	yes	—
58	C₃×#381	C₂²	1	2	yes	—
59	C₃×#381	C₂²	1	2	yes	—
60	C₃×#381	C₂²	1	2	yes	complemented
61	C₃×#380	C₂²	1	2	yes	—
62	C₃×#380	C₂²	1	2	yes	—
63	C₃×#380	C₂²	1	2	yes	complemented
64	C₃×#379	C₂²	1	2	yes	—
65	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
66	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	complemented
67	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
68	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
69	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
70	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
72	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
73	C₃×#376	C₂²	1	2	yes	complemented
74	C₂×C₃×#95	C₂²	1	2	yes	—
75	C₂×C₃×#95	C₂²	1	2	yes	—
76	C₂×C₃×#95	C₂²	1	2	yes	complemented
77	C₂×#525	C₂×C₃	1	1	yes	characteristic
78	#2378	C₂×C₃	1	2	yes	complemented
79	#2377	C₂×C₃	1	2	yes	complemented
80	#2359	C₂×C₃	1	4	yes	complemented
81	#2357	C₂×C₃	1	2	yes	complemented
82	#2353	C₂×C₃	1	2	yes	complemented
83	#2343	C₂×C₃	1	2	yes	complemented
84	#2339	C₂×C₃	1	2	yes	complemented
85	#2333	C₂×C₃	1	2	yes	complemented
86	#2332	C₂×C₃	1	2	yes	complemented
87	#2321	C₂×C₃	1	4	yes	complemented
88	#2319	C₂×C₃	1	2	yes	complemented
89	#2318	C₂×C₃	1	2	yes	complemented
90	#2280	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×#381	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂⁵×C₃	C₂³	1	1	yes	characteristic
93	C₂×C₃×#41	—	4	4	no	—
94	C₂×C₃×#41	C₂×C₄	1	8	yes	—
95	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
96	C₂²×C₃×D₄	C₂³	1	2	yes	—
97	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
98	C₂²×C₃×D₄	C₂³	1	2	yes	—
99	C₂²×C₃×D₄	C₂³	1	2	yes	—
100	C₂³×C₃×C₄	—	4	4	no	—
101	C₂³×C₃×C₄	C₂×C₄	1	8	yes	complemented
102	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
103	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
104	C₂³×C₃×C₄	C₂³	1	4	yes	—
105	C₂³×C₃×C₄	C₂³	1	4	yes	—
106	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
107	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
108	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
109	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
110	C₂³×C₃×C₄	C₂³	1	2	yes	—
111	C₃×#123	C₂×C₄	1	16	yes	complemented
112	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
113	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
114	C₃×#121	C₂×C₄	1	8	yes	complemented
115	C₃×#121	C₂×C₄	1	8	yes	complemented
116	C₃×#120	C₂×C₄	1	16	yes	complemented
117	C₃×C₄×D₄	—	4	8	no	—
118	C₃×C₄×D₄	C₂×C₄	1	16	yes	complemented
119	C₃×C₄×D₄	C₂×C₄	1	16	yes	complemented
120	C₃×#117	—	4	4	no	—
121	C₃×#117	C₂×C₄	1	8	yes	complemented
122	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
123	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
125	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
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	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
131	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
134	C₂×C₃×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
138	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
146	C₂×C₃×C₄²	C₂³	1	4	yes	—
147	C₂×C₃×C₄²	C₂³	1	2	yes	—
148	C₂×C₃×C₄²	C₂³	1	2	yes	—
149	C₂×C₃×C₄²	C₂³	1	4	yes	—
150	C₂×C₃×C₄²	C₂³	1	4	yes	—
151	C₂×C₃×C₄²	C₂³	1	2	yes	—
152	C₃×#95	C₂³	1	2	yes	—
153	C₃×#95	C₂³	1	2	yes	—
154	C₃×#95	C₂³	1	4	yes	—
155	C₃×#95	C₂³	1	2	yes	—
156	C₃×#95	C₂³	1	4	yes	—
157	C₃×#95	C₂³	1	2	yes	—
158	C₃×#95	C₂³	1	2	yes	—
159	C₃×#95	C₂³	1	4	yes	—
160	C₃×#95	C₂³	1	4	yes	—
161	C₃×#95	C₂³	1	2	yes	—
162	C₃×#95	C₂³	1	4	yes	—
163	C₃×#95	C₂³	1	4	yes	—
164	C₃×#95	C₂³	1	4	yes	—
165	C₃×#95	C₂³	1	4	yes	—
166	C₃×#95	C₂³	1	4	yes	—
167	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
168	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
169	#525	C₃×C₄	1	16	yes	complemented
170	C₂×#123	C₂²×C₃	1	2	yes	—
171	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
173	C₂×#121	C₂²×C₃	1	1	yes	characteristic
174	C₂×#121	C₂²×C₃	1	1	yes	characteristic
175	C₂×#120	C₂²×C₃	1	2	yes	—
176	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
177	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
178	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
179	C₂×#117	C₂²×C₃	1	2	yes	—
180	C₂×#117	C₂²×C₃	1	1	yes	characteristic
181	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
182	#391	C₂²×C₃	1	4	yes	complemented
183	#390	C₂²×C₃	1	4	yes	—
184	#390	C₂²×C₃	1	4	yes	—
185	#389	C₂²×C₃	1	4	yes	complemented
186	#388	C₂²×C₃	1	4	yes	—
187	#388	C₂²×C₃	1	4	yes	—
188	#388	C₂²×C₃	1	4	yes	—
189	#388	C₂²×C₃	1	4	yes	—
190	#388	C₂²×C₃	1	4	yes	complemented
191	#388	C₂²×C₃	1	4	yes	complemented
192	#387	C₂²×C₃	1	4	yes	complemented
193	#387	C₂²×C₃	1	4	yes	complemented
194	#387	C₂²×C₃	1	4	yes	complemented
195	#387	C₂²×C₃	1	4	yes	complemented
196	#386	C₂²×C₃	1	4	yes	—
197	#386	C₂²×C₃	1	4	yes	—
198	#386	C₂²×C₃	1	4	yes	—
199	#386	C₂²×C₃	1	4	yes	complemented
200	#385	C₂²×C₃	1	4	yes	—
201	#385	C₂²×C₃	1	4	yes	complemented
202	#383	C₂²×C₃	1	2	yes	complemented
203	#382	C₂²×C₃	1	2	yes	complemented
204	#381	C₂²×C₃	1	1	yes	characteristic
205	#381	C₂²×C₃	1	1	yes	characteristic
206	#381	C₂²×C₃	1	2	yes	—
207	#381	C₂²×C₃	1	2	yes	—
208	#381	C₂²×C₃	1	2	yes	—
209	#381	C₂²×C₃	1	2	yes	—
210	#381	C₂²×C₃	1	2	yes	complemented
211	#380	C₂²×C₃	1	2	yes	—
212	#380	C₂²×C₃	1	2	yes	—
213	#380	C₂²×C₃	1	2	yes	complemented
214	#379	C₂²×C₃	1	2	yes	—
215	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
216	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
217	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
218	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
219	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
220	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
221	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
222	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
223	#376	C₂²×C₃	1	2	yes	complemented
224	C₂×#95	C₂²×C₃	1	2	yes	—
225	C₂×#95	C₂²×C₃	1	2	yes	—
226	C₂×#95	C₂²×C₃	1	2	yes	complemented
227	C₂⁴×C₃	—	2	4	no	—
228	C₂⁴×C₃	—	4	2	no	—
229	C₂⁴×C₃	—	4	2	no	—
230	C₂⁴×C₃	C₂²×C₄	1	4	yes	—
231	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
232	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₃	C₂⁴	1	2	yes	—
234	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
235	C₃×#41	—	4	16	no	—
236	C₂×C₃×Q₈	—	4	2	no	—
237	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
238	C₂×C₃×D₄	—	2	8	no	—
239	C₂×C₃×D₄	—	4	2	no	—
240	C₂×C₃×D₄	—	4	4	no	—
241	C₂×C₃×D₄	—	4	2	no	—
242	C₂×C₃×D₄	—	4	2	no	—
243	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
244	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
245	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
246	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
247	C₂²×C₃×C₄	—	2	4	no	—
248	C₂²×C₃×C₄	—	2	4	no	—
249	C₂²×C₃×C₄	—	2	8	no	—
250	C₂²×C₃×C₄	—	4	16	no	—
251	C₂²×C₃×C₄	—	4	2	no	—
252	C₂²×C₃×C₄	—	4	2	no	—
253	C₂²×C₃×C₄	—	4	2	no	—
254	C₂²×C₃×C₄	—	4	2	no	—
255	C₂²×C₃×C₄	—	4	4	no	—
256	C₂²×C₃×C₄	—	4	4	no	—
257	C₂²×C₃×C₄	—	4	4	no	—
258	C₂²×C₃×C₄	—	4	4	no	—
259	C₂²×C₃×C₄	—	4	4	no	—
260	C₂²×C₃×C₄	—	4	4	no	—
261	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
262	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
263	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
264	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
265	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
266	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
267	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
268	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
269	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
270	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
271	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
272	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
273	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
276	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
277	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
278	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
279	C₃×C₄⋊C₄	—	4	4	no	—
280	C₃×C₄⋊C₄	—	4	4	no	—
281	C₃×C₄⋊C₄	—	4	4	no	—
282	C₃×C₄⋊C₄	—	4	4	no	—
283	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
284	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
285	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
286	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
287	C₃×C₂²⋊C₄	—	2	8	no	—
288	C₃×C₂²⋊C₄	—	4	2	no	—
289	C₃×C₂²⋊C₄	—	4	4	no	—
290	C₃×C₂²⋊C₄	—	4	2	no	—
291	C₃×C₂²⋊C₄	—	4	4	no	—
292	C₃×C₂²⋊C₄	—	4	2	no	—
293	C₃×C₂²⋊C₄	—	4	4	no	—
294	C₃×C₂²⋊C₄	—	4	2	no	—
295	C₃×C₂²⋊C₄	—	4	4	no	—
296	C₃×C₂²⋊C₄	—	4	4	no	—
297	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
298	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
299	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
300	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
301	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
302	C₃×C₄²	—	4	4	no	—
303	C₃×C₄²	—	4	4	no	—
304	C₃×C₄²	—	4	2	no	—
305	C₃×C₄²	—	4	2	no	—
306	C₃×C₄²	—	4	4	no	—
307	C₃×C₄²	C₂²×C₄	1	8	yes	—
308	C₂⁵	C₂³×C₃	1	1	yes	characteristic
309	C₂×#41	—	4	4	no	—
310	C₂×#41	C₂×C₃×C₄	1	8	yes	—
311	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
312	C₂²×D₄	C₂³×C₃	1	2	yes	—
313	C₂²×D₄	C₂³×C₃	1	2	yes	—
314	C₂²×D₄	C₂³×C₃	1	2	yes	—
315	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
316	C₂³×C₄	—	4	4	no	—
317	C₂³×C₄	C₂×C₃×C₄	1	8	yes	complemented
318	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₃	1	4	yes	—
321	C₂³×C₄	C₂³×C₃	1	4	yes	—
322	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₃	1	2	yes	—
325	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
327	#123	C₂×C₃×C₄	1	16	yes	complemented
328	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
329	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
330	#121	C₂×C₃×C₄	1	8	yes	complemented
331	#121	C₂×C₃×C₄	1	8	yes	complemented
332	#120	C₂×C₃×C₄	1	16	yes	complemented
333	C₄×D₄	—	4	8	no	—
334	C₄×D₄	C₂×C₃×C₄	1	16	yes	complemented
335	C₄×D₄	C₂×C₃×C₄	1	16	yes	complemented
336	#117	—	4	4	no	—
337	#117	C₂×C₃×C₄	1	8	yes	complemented
338	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
346	C₂×C₂²⋊C₄	—	4	4	no	—
347	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
362	C₂×C₄²	C₂³×C₃	1	2	yes	—
363	C₂×C₄²	C₂³×C₃	1	2	yes	—
364	C₂×C₄²	C₂³×C₃	1	4	yes	—
365	C₂×C₄²	C₂³×C₃	1	4	yes	—
366	C₂×C₄²	C₂³×C₃	1	4	yes	—
367	C₂×C₄²	C₂³×C₃	1	2	yes	—
368	#95	C₂³×C₃	1	2	yes	—
369	#95	C₂³×C₃	1	2	yes	—
370	#95	C₂³×C₃	1	4	yes	—
371	#95	C₂³×C₃	1	2	yes	—
372	#95	C₂³×C₃	1	4	yes	—
373	#95	C₂³×C₃	1	2	yes	—
374	#95	C₂³×C₃	1	2	yes	—
375	#95	C₂³×C₃	1	4	yes	—
376	#95	C₂³×C₃	1	4	yes	—
377	#95	C₂³×C₃	1	2	yes	—
378	#95	C₂³×C₃	1	4	yes	—
379	#95	C₂³×C₃	1	4	yes	—
380	#95	C₂³×C₃	1	4	yes	—
381	#95	C₂³×C₃	1	4	yes	—
382	#95	C₂³×C₃	1	4	yes	—
383	C₂³×C₃	—	2	2	no	—
384	C₂³×C₃	—	2	2	no	—
385	C₂³×C₃	—	2	8	no	—
386	C₂³×C₃	—	2	2	no	—
387	C₂³×C₃	—	2	2	no	—
388	C₂³×C₃	—	2	4	no	—
389	C₂³×C₃	—	2	2	no	—
390	C₂³×C₃	—	2	2	no	—
391	C₂³×C₃	—	2	2	no	—
392	C₂³×C₃	—	2	4	no	—
393	C₂³×C₃	—	2	2	no	—
394	C₂³×C₃	—	2	2	no	—
395	C₂³×C₃	—	2	2	no	—
396	C₂³×C₃	—	4	4	no	—
397	C₂³×C₃	—	4	4	no	—
398	C₂³×C₃	—	4	16	no	—
399	C₂³×C₃	C₂³×C₄	1	2	yes	—
400	C₂³×C₃	C₂³×C₄	1	2	yes	—
401	C₂³×C₃	C₂³×C₄	1	4	yes	—
402	C₂³×C₃	C₂³×C₄	1	2	yes	—
403	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
404	C₂³×C₃	C₂⁵	1	1	yes	characteristic
405	C₃×Q₈	—	4	4	no	—
406	C₃×D₄	—	2	16	no	—
407	C₃×D₄	—	4	8	no	—
408	C₃×D₄	—	4	8	no	—
409	C₃×D₄	—	4	4	no	—
410	C₂×C₃×C₄	—	2	8	no	—
411	C₂×C₃×C₄	—	2	8	no	—
412	C₂×C₃×C₄	—	2	2	no	—
413	C₂×C₃×C₄	—	2	4	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	—	2	4	no	—
419	C₂×C₃×C₄	—	2	2	no	—
420	C₂×C₃×C₄	—	2	4	no	—
421	C₂×C₃×C₄	—	2	4	no	—
422	C₂×C₃×C₄	—	2	4	no	—
423	C₂×C₃×C₄	—	2	4	no	—
424	C₂×C₃×C₄	—	2	4	no	—
425	C₂×C₃×C₄	—	2	4	no	—
426	C₂×C₃×C₄	—	2	4	no	—
427	C₂×C₃×C₄	—	2	4	no	—
428	C₂×C₃×C₄	—	2	4	no	—
429	C₂×C₃×C₄	—	2	4	no	—
430	C₂×C₃×C₄	—	2	4	no	—
431	C₂×C₃×C₄	—	2	4	no	—
432	C₂×C₃×C₄	—	4	4	no	—
433	C₂×C₃×C₄	—	4	4	no	—
434	C₂×C₃×C₄	—	4	4	no	—
435	C₂×C₃×C₄	—	4	4	no	—
436	C₂×C₃×C₄	—	4	8	no	—
437	C₂×C₃×C₄	—	8	8	no	—
438	C₂×C₃×C₄	—	8	8	no	—
439	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
440	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
441	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
442	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
443	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
444	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
445	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
446	C₂⁴	—	2	4	no	—
447	C₂⁴	—	4	2	no	—
448	C₂⁴	—	4	2	no	—
449	C₂⁴	C₂²×C₃×C₄	1	4	yes	—
450	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
451	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
452	C₂⁴	C₂⁴×C₃	1	2	yes	—
453	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
454	#41	—	4	16	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
457	C₂×D₄	—	2	8	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	2	no	—
460	C₂×D₄	—	4	4	no	—
461	C₂×D₄	—	4	2	no	—
462	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
463	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
464	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
465	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	4	16	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	4	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	4	no	—
480	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
481	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
482	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
483	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
484	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
485	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
486	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
490	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
498	C₄⋊C₄	—	4	4	no	—
499	C₄⋊C₄	—	4	4	no	—
500	C₄⋊C₄	—	4	4	no	—
501	C₄⋊C₄	—	4	4	no	—
502	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
503	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
504	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
505	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	4	2	no	—
508	C₂²⋊C₄	—	4	4	no	—
509	C₂²⋊C₄	—	4	2	no	—
510	C₂²⋊C₄	—	4	4	no	—
511	C₂²⋊C₄	—	4	4	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	4	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	4	4	no	—
516	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
517	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
518	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
519	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
520	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
521	C₄²	—	4	2	no	—
522	C₄²	—	4	2	no	—
523	C₄²	—	4	4	no	—
524	C₄²	—	4	4	no	—
525	C₄²	—	4	4	no	—
526	C₄²	C₂²×C₃×C₄	1	8	yes	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	2	no	—
529	C₂²×C₃	—	2	8	no	—
530	C₂²×C₃	—	2	2	no	—
531	C₂²×C₃	—	2	2	no	—
532	C₂²×C₃	—	2	4	no	—
533	C₂²×C₃	—	2	2	no	—
534	C₂²×C₃	—	2	2	no	—
535	C₂²×C₃	—	2	4	no	—
536	C₂²×C₃	—	2	4	no	—
537	C₂²×C₃	—	2	2	no	—
538	C₂²×C₃	—	2	2	no	—
539	C₂²×C₃	—	4	16	no	—
540	C₂²×C₃	—	4	4	no	—
541	C₂²×C₃	—	4	4	no	—
542	C₂²×C₃	—	4	4	no	—
543	C₂²×C₃	—	4	4	no	—
544	C₂²×C₃	#518	1	4	yes	—
545	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
546	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
547	C₂²×C₃	#585	1	2	yes	—
548	C₂²×C₃	#585	1	2	yes	—
549	C₃×C₄	—	2	2	no	—
550	C₃×C₄	—	2	2	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	2	no	—
553	C₃×C₄	—	2	4	no	—
554	C₃×C₄	—	2	4	no	—
555	C₃×C₄	—	2	4	no	—
556	C₃×C₄	—	4	4	no	—
557	C₃×C₄	—	4	4	no	—
558	C₃×C₄	—	4	4	no	—
559	C₃×C₄	—	4	4	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	2	2	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	4	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	2	2	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	8	no	—
573	C₂³	—	4	4	no	—
574	C₂³	—	4	4	no	—
575	C₂³	—	4	16	no	—
576	C₂³	C₂³×C₃×C₄	1	2	yes	—
577	C₂³	C₂³×C₃×C₄	1	2	yes	—
578	C₂³	C₂³×C₃×C₄	1	4	yes	—
579	C₂³	C₂³×C₃×C₄	1	2	yes	—
580	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
581	C₂³	C₂⁵×C₃	1	1	yes	characteristic
582	Q₈	—	4	4	no	—
583	D₄	—	2	16	no	—
584	D₄	—	4	4	no	—
585	D₄	—	4	8	no	—
586	D₄	—	4	8	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	4	4	no	—
610	C₂×C₄	—	4	4	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	—	8	8	no	—
615	C₂×C₄	—	8	8	no	—
616	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
617	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
618	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
619	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
620	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
621	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
622	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
623	C₂×C₃	—	2	4	no	—
624	C₂×C₃	—	4	4	no	—
625	C₂×C₃	—	4	2	no	—
626	C₂×C₃	—	4	2	no	—
627	C₂×C₃	C₂×#518	1	1	yes	characteristic
628	C₂×C₃	#3428	1	1	yes	characteristic
629	C₂×C₃	#3428	1	1	yes	characteristic
630	C₂×C₃	#3533	1	4	yes	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	8	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	4	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	4	16	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	C₃×#518	1	4	yes	—
649	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
650	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
651	C₂²	C₃×#585	1	2	yes	—
652	C₂²	C₃×#585	1	2	yes	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	4	no	—
660	C₄	—	4	4	no	—
661	C₄	—	4	4	no	—
662	C₄	—	4	4	no	—
663	C₄	—	4	4	no	—
664	C₃	#34396	1	1	yes	characteristic, direct product factor, Sylow
665	C₂	—	2	4	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	2	no	—
668	C₂	—	4	4	no	—
669	C₂	C₂×C₃×#518	1	1	yes	characteristic
670	C₂	C₃×#3428	1	1	yes	characteristic
671	C₂	C₃×#3428	1	1	yes	characteristic
672	C₂	C₃×#3533	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#525	C₂
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×#2378	C₂	semidirect
3. C₃×#2377	C₂	semidirect
4. C₃×#2359	C₂	semidirect
5. C₃×#2357	C₂	semidirect
6. C₃×#2353	C₂	semidirect
7. C₃×#2343	C₂	semidirect
8. C₃×#2339	C₂	semidirect
9. C₃×#2333	C₂	semidirect
10. C₃×#2332	C₂	semidirect
11. C₃×#2321	C₂	semidirect
12. C₃×#2319	C₂	semidirect
13. C₃×#2318	C₂	semidirect
14. C₃×#2280	C₂	semidirect
15. C₂×C₃×#381	C₂	semidirect
16. #34396	C₃	direct (N × H)
19. C₃×#525	C₄	semidirect
32. C₃×#391	C₂²	semidirect
35. C₃×#389	C₂²	semidirect
40. C₃×#388	C₂²	semidirect
41. C₃×#388	C₂²	semidirect
42. C₃×#387	C₂²	semidirect
43. C₃×#387	C₂²	semidirect
44. C₃×#387	C₂²	semidirect
45. C₃×#387	C₂²	semidirect
49. C₃×#386	C₂²	semidirect
51. C₃×#385	C₂²	semidirect
52. C₃×#383	C₂²	semidirect
53. C₃×#382	C₂²	semidirect
60. C₃×#381	C₂²	semidirect
63. C₃×#380	C₂²	semidirect
65. C₃×C₄×C₄⋊C₄	C₂²	semidirect
66. C₃×C₄×C₄⋊C₄	C₂²	semidirect
71. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
72. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
73. C₃×#376	C₂²	semidirect
76. C₂×C₃×#95	C₂²	semidirect
78. #2378	C₂×C₃	semidirect
79. #2377	C₂×C₃	semidirect
80. #2359	C₂×C₃	semidirect
81. #2357	C₂×C₃	semidirect
82. #2353	C₂×C₃	semidirect
83. #2343	C₂×C₃	semidirect
84. #2339	C₂×C₃	semidirect
85. #2333	C₂×C₃	semidirect
86. #2332	C₂×C₃	semidirect
87. #2321	C₂×C₃	semidirect
88. #2319	C₂×C₃	semidirect
89. #2318	C₂×C₃	semidirect
90. #2280	C₂×C₃	semidirect
91. C₂×#381	C₂×C₃	semidirect
101. C₂³×C₃×C₄	C₂×C₄	semidirect
111. C₃×#123	C₂×C₄	semidirect
112. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
113. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
114. C₃×#121	C₂×C₄	semidirect
115. C₃×#121	C₂×C₄	semidirect
116. C₃×#120	C₂×C₄	semidirect
118. C₃×C₄×D₄	C₂×C₄	semidirect
119. C₃×C₄×D₄	C₂×C₄	semidirect
121. C₃×#117	C₂×C₄	semidirect
169. #525	C₃×C₄	semidirect
182. #391	C₂²×C₃	semidirect
185. #389	C₂²×C₃	semidirect
190. #388	C₂²×C₃	semidirect
191. #388	C₂²×C₃	semidirect
192. #387	C₂²×C₃	semidirect
193. #387	C₂²×C₃	semidirect
194. #387	C₂²×C₃	semidirect
195. #387	C₂²×C₃	semidirect
199. #386	C₂²×C₃	semidirect
201. #385	C₂²×C₃	semidirect
202. #383	C₂²×C₃	semidirect
203. #382	C₂²×C₃	semidirect
210. #381	C₂²×C₃	semidirect
213. #380	C₂²×C₃	semidirect
215. C₄×C₄⋊C₄	C₂²×C₃	semidirect
216. C₄×C₄⋊C₄	C₂²×C₃	semidirect
221. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
222. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
223. #376	C₂²×C₃	semidirect
226. C₂×#95	C₂²×C₃	semidirect
317. C₂³×C₄	C₂×C₃×C₄	semidirect
327. #123	C₂×C₃×C₄	semidirect
328. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
329. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
330. #121	C₂×C₃×C₄	semidirect
331. #121	C₂×C₃×C₄	semidirect
332. #120	C₂×C₃×C₄	semidirect
334. C₄×D₄	C₂×C₃×C₄	semidirect
335. C₄×D₄	C₂×C₃×C₄	semidirect
337. #117	C₂×C₃×C₄	semidirect
664. C₃	#34396	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×#525	2
C₃×#2378	2
C₃×#2377	2
C₃×#2359	2
C₃×#2357	2
C₃×#2353	2
C₃×#2343	2
C₃×#2339	2
C₃×#2333	2
C₃×#2332	2
C₃×#2321	2
C₃×#2319	2
C₃×#2318	2
C₃×#2280	2
C₂×C₃×#381	2
#34396	3

Subgroups — C3×#34396 #10653003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34396 #10653003