Subgroups — C₃×#34965 #10653572

Order 768.

3114 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2603	C₂	1	4	yes	maximal, complemented
4	C₃×#2566	C₂	1	2	yes	maximal, complemented
5	C₃×#2544	C₂	1	2	yes	maximal, complemented
6	C₃×#2504	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2502	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2433	C₂	1	1	yes	maximal, characteristic
10	C₃×#2411	C₂	1	4	yes	maximal, complemented
11	C₃×#2392	C₂	1	4	yes	maximal, complemented
12	C₃×C₄×#127	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×#124	C₂	1	2	yes	maximal, complemented
14	C₃×C₄×#120	C₂	1	4	yes	maximal, complemented
15	C₃×C₄×#117	C₂	1	1	yes	maximal, characteristic, complemented
16	#34965	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
18	C₂⁴×C₃×C₄	C₂²	1	2	yes	—
19	C₂×C₃×#127	C₂²	1	2	yes	—
20	C₃×#529	—	2	8	no	—
21	C₂×C₃×#126	C₂²	1	2	yes	complemented
22	C₂×C₃×#125	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×#124	C₂²	1	2	yes	—
24	C₂×C₃×#124	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#123	C₂²	1	2	yes	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₃×#120	C₂²	1	4	yes	—
29	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄×D₄	—	2	8	no	—
31	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
32	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
34	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₄×D₄	C₂²	1	8	yes	complemented
38	C₂×C₃×#117	C₂²	1	2	yes	—
39	C₂×C₃×#117	C₂²	1	2	yes	complemented
40	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
42	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
43	C₃×#398	C₂²	1	4	yes	complemented
44	C₃×#397	C₂²	1	4	yes	complemented
45	C₃×#396	C₂²	1	8	yes	complemented
46	C₃×#394	C₂²	1	4	yes	—
47	C₃×#394	C₂²	1	8	yes	complemented
48	C₃×#392	C₂²	1	4	yes	—
49	C₃×#391	C₂²	1	2	yes	complemented
50	C₃×#390	C₂²	1	2	yes	—
51	C₃×#390	C₂²	1	2	yes	—
52	C₃×#390	C₂²	1	8	yes	complemented
53	C₃×#390	C₂²	1	2	yes	complemented
54	C₃×#388	C₂²	1	8	yes	complemented
55	C₃×#386	C₂²	1	4	yes	—
56	C₃×#386	C₂²	1	8	yes	complemented
57	C₃×#385	C₂²	1	4	yes	—
58	C₃×#385	C₂²	1	8	yes	complemented
59	C₃×#384	C₂²	1	2	yes	complemented
60	C₃×#382	C₂²	1	2	yes	complemented
61	C₃×#379	C₂²	1	4	yes	—
62	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
63	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
64	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
65	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
66	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
67	C₃×C₄×C₂²⋊C₄	C₂²	1	8	yes	complemented
68	C₃×#376	C₂²	1	2	yes	complemented
69	C₃×C₄³	C₂²	1	2	yes	complemented
70	C₂×#529	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂²×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
72	#2603	C₂×C₃	1	4	yes	complemented
73	#2566	C₂×C₃	1	2	yes	complemented
74	#2544	C₂×C₃	1	2	yes	complemented
75	#2504	C₂×C₃	1	1	yes	characteristic, complemented
76	#2502	C₂×C₃	1	1	yes	characteristic, complemented
77	#2435	C₂×C₃	1	1	yes	characteristic, complemented
78	#2433	C₂×C₃	1	1	yes	characteristic
79	#2411	C₂×C₃	1	4	yes	complemented
80	#2392	C₂×C₃	1	4	yes	complemented
81	C₄×#127	C₂×C₃	1	2	yes	complemented
82	C₄×#124	C₂×C₃	1	2	yes	complemented
83	C₄×#120	C₂×C₃	1	4	yes	complemented
84	C₄×#117	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂⁵×C₃	C₂³	1	2	yes	—
86	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₃×D₄	—	2	8	no	—
88	C₂²×C₃×D₄	—	2	4	no	—
89	C₂²×C₃×D₄	C₂³	1	2	yes	—
90	C₂²×C₃×D₄	C₂³	1	2	yes	—
91	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
92	C₂²×C₃×D₄	C₂³	1	8	yes	—
93	C₂²×C₃×D₄	C₂³	1	2	yes	—
94	C₂³×C₃×C₄	—	2	8	no	—
95	C₂³×C₃×C₄	—	4	8	no	—
96	C₂³×C₃×C₄	C₂³	1	4	yes	—
97	C₂³×C₃×C₄	C₂³	1	2	yes	—
98	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
99	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
100	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
101	C₂³×C₃×C₄	C₂³	1	2	yes	—
102	C₂³×C₃×C₄	C₂³	1	4	yes	—
103	C₃×#127	—	2	8	no	—
104	C₃×#126	—	2	8	no	—
105	C₃×#125	—	2	4	no	—
106	C₃×#124	—	2	8	no	—
107	C₃×#124	—	2	4	no	—
108	C₃×#123	—	2	8	no	—
109	C₃×C₂²⋊Q₈	—	2	4	no	—
110	C₃×#121	—	2	4	no	—
111	C₃×#120	—	2	16	no	—
112	C₃×C₄×Q₈	—	2	4	no	—
113	C₃×C₄×D₄	—	2	8	no	—
114	C₃×C₄×D₄	—	2	8	no	—
115	C₃×C₄×D₄	—	2	8	no	—
116	C₃×C₄×D₄	—	2	8	no	—
117	C₃×C₄×D₄	—	2	8	no	—
118	C₃×C₄×D₄	—	2	4	no	—
119	C₃×C₄×D₄	—	4	16	no	—
120	C₃×#117	—	2	8	no	—
121	C₃×#117	—	2	8	no	—
122	C₂×C₃×C₄⋊C₄	—	2	4	no	—
123	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
124	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₃×C₄⋊C₄	C₂³	1	2	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	8	yes	—
133	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
134	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
136	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
137	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
146	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄²	D₄	1	8	yes	complemented
148	C₂×C₃×C₄²	C₂³	1	4	yes	—
149	C₂×C₃×C₄²	C₂³	1	2	yes	—
150	C₂×C₃×C₄²	C₂³	1	2	yes	—
151	C₂×C₃×C₄²	C₂³	1	4	yes	—
152	C₂×C₃×C₄²	C₂³	1	2	yes	—
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	1	yes	characteristic
157	C₃×#95	C₂³	1	4	yes	—
158	C₃×#95	C₂³	1	2	yes	—
159	C₃×#95	C₂³	1	2	yes	—
160	C₃×#95	C₂³	1	8	yes	—
161	C₃×#95	C₂³	1	8	yes	—
162	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
163	C₂⁴×C₄	C₂²×C₃	1	2	yes	—
164	C₂×#127	C₂²×C₃	1	2	yes	—
165	#529	—	2	8	no	—
166	C₂×#126	C₂²×C₃	1	2	yes	complemented
167	C₂×#125	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂×#124	C₂²×C₃	1	2	yes	—
169	C₂×#124	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₂×#123	C₂²×C₃	1	2	yes	—
171	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
172	C₂×#121	C₂²×C₃	1	1	yes	characteristic
173	C₂×#120	C₂²×C₃	1	4	yes	—
174	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₂×C₄×D₄	—	2	8	no	—
176	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
177	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
178	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
179	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
180	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
181	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₂×C₄×D₄	C₂²×C₃	1	8	yes	complemented
183	C₂×#117	C₂²×C₃	1	2	yes	—
184	C₂×#117	C₂²×C₃	1	2	yes	complemented
185	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
186	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
187	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
188	#398	C₂²×C₃	1	4	yes	complemented
189	#397	C₂²×C₃	1	4	yes	complemented
190	#396	C₂²×C₃	1	8	yes	complemented
191	#394	C₂²×C₃	1	4	yes	—
192	#394	C₂²×C₃	1	8	yes	complemented
193	#392	C₂²×C₃	1	4	yes	—
194	#391	C₂²×C₃	1	2	yes	complemented
195	#390	C₂²×C₃	1	2	yes	—
196	#390	C₂²×C₃	1	2	yes	—
197	#390	C₂²×C₃	1	8	yes	complemented
198	#390	C₂²×C₃	1	2	yes	complemented
199	#388	C₂²×C₃	1	8	yes	complemented
200	#386	C₂²×C₃	1	4	yes	—
201	#386	C₂²×C₃	1	8	yes	complemented
202	#385	C₂²×C₃	1	4	yes	—
203	#385	C₂²×C₃	1	8	yes	complemented
204	#384	C₂²×C₃	1	2	yes	complemented
205	#382	C₂²×C₃	1	2	yes	complemented
206	#379	C₂²×C₃	1	4	yes	—
207	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
208	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
209	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
210	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
211	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
212	C₄×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
213	#376	C₂²×C₃	1	2	yes	complemented
214	C₄³	C₂²×C₃	1	2	yes	complemented
215	C₂⁴×C₃	—	2	4	no	—
216	C₂⁴×C₃	—	2	8	no	—
217	C₂⁴×C₃	—	2	8	no	—
218	C₂⁴×C₃	—	4	4	no	—
219	C₂⁴×C₃	C₂⁴	1	2	yes	—
220	C₂⁴×C₃	C₂⁴	1	4	yes	—
221	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
222	C₂×C₃×Q₈	—	2	2	no	—
223	C₂×C₃×Q₈	—	2	4	no	—
224	C₂×C₃×D₄	—	2	32	no	—
225	C₂×C₃×D₄	—	2	8	no	—
226	C₂×C₃×D₄	—	2	4	no	—
227	C₂×C₃×D₄	—	2	8	no	—
228	C₂×C₃×D₄	—	2	16	no	—
229	C₂×C₃×D₄	—	2	4	no	—
230	C₂×C₃×D₄	—	2	4	no	—
231	C₂×C₃×D₄	—	2	2	no	—
232	C₂×C₃×D₄	—	2	4	no	—
233	C₂×C₃×D₄	—	2	16	no	—
234	C₂×C₃×D₄	—	2	4	no	—
235	C₂×C₃×D₄	—	4	8	no	—
236	C₂×C₃×D₄	#41	1	8	yes	—
237	C₂²×C₃×C₄	—	2	4	no	—
238	C₂²×C₃×C₄	—	2	4	no	—
239	C₂²×C₃×C₄	—	2	4	no	—
240	C₂²×C₃×C₄	—	2	4	no	—
241	C₂²×C₃×C₄	—	2	4	no	—
242	C₂²×C₃×C₄	—	2	8	no	—
243	C₂²×C₃×C₄	—	2	8	no	—
244	C₂²×C₃×C₄	—	2	8	no	—
245	C₂²×C₃×C₄	—	2	16	no	—
246	C₂²×C₃×C₄	—	4	8	no	—
247	C₂²×C₃×C₄	—	4	4	no	—
248	C₂²×C₃×C₄	—	4	32	no	—
249	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
250	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
251	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
252	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
253	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
254	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
255	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
256	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
257	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
262	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
263	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
264	C₃×C₄⋊C₄	—	2	4	no	—
265	C₃×C₄⋊C₄	—	2	4	no	—
266	C₃×C₄⋊C₄	—	2	4	no	—
267	C₃×C₄⋊C₄	—	2	4	no	—
268	C₃×C₄⋊C₄	—	2	2	no	—
269	C₃×C₄⋊C₄	—	2	4	no	—
270	C₃×C₄⋊C₄	—	2	2	no	—
271	C₃×C₄⋊C₄	—	2	4	no	—
272	C₃×C₄⋊C₄	—	2	8	no	—
273	C₃×C₄⋊C₄	—	4	8	no	—
274	C₃×C₂²⋊C₄	—	2	4	no	—
275	C₃×C₂²⋊C₄	—	2	4	no	—
276	C₃×C₂²⋊C₄	—	2	16	no	—
277	C₃×C₂²⋊C₄	—	2	8	no	—
278	C₃×C₂²⋊C₄	—	2	8	no	—
279	C₃×C₂²⋊C₄	—	2	4	no	—
280	C₃×C₂²⋊C₄	—	2	4	no	—
281	C₃×C₂²⋊C₄	—	2	4	no	—
282	C₃×C₂²⋊C₄	—	2	4	no	—
283	C₃×C₂²⋊C₄	—	2	16	no	—
284	C₃×C₂²⋊C₄	—	4	8	no	—
285	C₃×C₂²⋊C₄	—	4	8	no	—
286	C₃×C₂²⋊C₄	#41	1	8	yes	—
287	C₃×C₄²	—	2	4	no	—
288	C₃×C₄²	—	2	8	no	—
289	C₃×C₄²	—	2	4	no	—
290	C₃×C₄²	—	2	4	no	—
291	C₃×C₄²	—	2	8	no	—
292	C₃×C₄²	C₂×D₄	1	4	yes	—
293	C₃×C₄²	C₂×D₄	1	4	yes	—
294	C₃×C₄²	C₂×D₄	1	4	yes	—
295	C₃×C₄²	C₂×D₄	1	4	yes	—
296	C₂⁵	C₂³×C₃	1	2	yes	—
297	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
298	C₂²×D₄	—	2	8	no	—
299	C₂²×D₄	—	2	4	no	—
300	C₂²×D₄	C₂³×C₃	1	2	yes	—
301	C₂²×D₄	C₂³×C₃	1	2	yes	—
302	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₃	1	8	yes	—
304	C₂²×D₄	C₂³×C₃	1	2	yes	—
305	C₂³×C₄	—	2	8	no	—
306	C₂³×C₄	—	4	8	no	—
307	C₂³×C₄	C₂³×C₃	1	2	yes	—
308	C₂³×C₄	C₂³×C₃	1	4	yes	—
309	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₃	1	2	yes	—
313	C₂³×C₄	C₂³×C₃	1	4	yes	—
314	#127	—	2	8	no	—
315	#126	—	2	8	no	—
316	#125	—	2	4	no	—
317	#124	—	2	8	no	—
318	#124	—	2	4	no	—
319	#123	—	2	8	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	#121	—	2	4	no	—
322	#120	—	2	16	no	—
323	C₄×Q₈	—	2	4	no	—
324	C₄×D₄	—	2	8	no	—
325	C₄×D₄	—	2	8	no	—
326	C₄×D₄	—	2	8	no	—
327	C₄×D₄	—	2	8	no	—
328	C₄×D₄	—	2	8	no	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	—	4	16	no	—
331	#117	—	2	8	no	—
332	#117	—	2	8	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
344	C₂×C₂²⋊C₄	—	2	8	no	—
345	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
358	C₂×C₄²	C₃×D₄	1	8	yes	complemented
359	C₂×C₄²	C₂³×C₃	1	4	yes	—
360	C₂×C₄²	C₂³×C₃	1	2	yes	—
361	C₂×C₄²	C₂³×C₃	1	4	yes	—
362	C₂×C₄²	C₂³×C₃	1	2	yes	—
363	C₂×C₄²	C₂³×C₃	1	2	yes	—
364	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
368	#95	C₂³×C₃	1	4	yes	—
369	#95	C₂³×C₃	1	2	yes	—
370	#95	C₂³×C₃	1	2	yes	—
371	#95	C₂³×C₃	1	8	yes	—
372	#95	C₂³×C₃	1	8	yes	—
373	C₂³×C₃	—	2	2	no	—
374	C₂³×C₃	—	2	2	no	—
375	C₂³×C₃	—	2	16	no	—
376	C₂³×C₃	—	2	4	no	—
377	C₂³×C₃	—	2	8	no	—
378	C₂³×C₃	—	2	4	no	—
379	C₂³×C₃	—	2	8	no	—
380	C₂³×C₃	—	2	2	no	—
381	C₂³×C₃	—	2	4	no	—
382	C₂³×C₃	—	2	4	no	—
383	C₂³×C₃	—	2	4	no	—
384	C₂³×C₃	—	4	32	no	—
385	C₂³×C₃	—	4	8	no	—
386	C₂³×C₃	—	4	8	no	—
387	C₂³×C₃	C₂²×D₄	1	2	yes	—
388	C₂³×C₃	C₂×#41	1	8	yes	—
389	C₂³×C₃	C₂×#41	1	4	yes	—
390	C₂³×C₃	C₂⁵	1	1	yes	characteristic
391	C₃×Q₈	—	4	4	no	—
392	C₃×D₄	—	2	16	no	—
393	C₃×D₄	—	2	16	no	—
394	C₃×D₄	—	4	32	no	—
395	C₃×D₄	—	4	8	no	—
396	C₃×D₄	—	4	4	no	—
397	C₂×C₃×C₄	—	2	8	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	4	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	4	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	8	no	—
405	C₂×C₃×C₄	—	2	8	no	—
406	C₂×C₃×C₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	2	4	no	—
410	C₂×C₃×C₄	—	2	4	no	—
411	C₂×C₃×C₄	—	2	4	no	—
412	C₂×C₃×C₄	—	2	4	no	—
413	C₂×C₃×C₄	—	2	4	no	—
414	C₂×C₃×C₄	—	2	4	no	—
415	C₂×C₃×C₄	—	2	4	no	—
416	C₂×C₃×C₄	—	2	8	no	—
417	C₂×C₃×C₄	—	4	16	no	—
418	C₂×C₃×C₄	—	4	8	no	—
419	C₂×C₃×C₄	—	4	8	no	—
420	C₂×C₃×C₄	—	4	16	no	—
421	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
422	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
423	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
424	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
425	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
426	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
427	C₂×C₃×C₄	C₂×#41	1	8	yes	—
428	C₂×C₃×C₄	C₂×#41	1	4	yes	—
429	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
430	C₂⁴	—	2	4	no	—
431	C₂⁴	—	2	8	no	—
432	C₂⁴	—	2	8	no	—
433	C₂⁴	—	4	4	no	—
434	C₂⁴	C₂⁴×C₃	1	2	yes	—
435	C₂⁴	C₂⁴×C₃	1	4	yes	—
436	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×D₄	—	2	32	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	2	16	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	16	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	4	8	no	—
451	C₂×D₄	C₃×#41	1	8	yes	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	8	no	—
458	C₂²×C₄	—	2	8	no	—
459	C₂²×C₄	—	2	8	no	—
460	C₂²×C₄	—	2	16	no	—
461	C₂²×C₄	—	4	8	no	—
462	C₂²×C₄	—	4	4	no	—
463	C₂²×C₄	—	4	32	no	—
464	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
465	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
466	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
468	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
471	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
474	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	8	no	—
488	C₄⋊C₄	—	4	8	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	16	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	8	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	16	no	—
499	C₂²⋊C₄	—	4	8	no	—
500	C₂²⋊C₄	—	4	8	no	—
501	C₂²⋊C₄	C₃×#41	1	8	yes	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	8	no	—
504	C₄²	—	2	4	no	—
505	C₄²	—	2	4	no	—
506	C₄²	—	2	8	no	—
507	C₄²	C₂×C₃×D₄	1	4	yes	—
508	C₄²	C₂×C₃×D₄	1	4	yes	—
509	C₄²	C₂×C₃×D₄	1	4	yes	—
510	C₄²	C₂×C₃×D₄	1	4	yes	—
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	2	2	no	—
513	C₂²×C₃	—	2	8	no	—
514	C₂²×C₃	—	2	8	no	—
515	C₂²×C₃	—	2	16	no	—
516	C₂²×C₃	—	4	32	no	—
517	C₂²×C₃	—	4	4	no	—
518	C₂²×C₃	—	4	4	no	—
519	C₂²×C₃	—	4	8	no	—
520	C₂²×C₃	—	4	2	no	—
521	C₂²×C₃	—	4	2	no	—
522	C₂²×C₃	—	4	2	no	—
523	C₂²×C₃	—	4	8	no	—
524	C₂²×C₃	#532	1	4	yes	—
525	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
526	C₂²×C₃	C₂²×#41	1	2	yes	—
527	C₂²×C₃	C₂²×#41	1	2	yes	—
528	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
529	C₃×C₄	—	2	2	no	—
530	C₃×C₄	—	2	2	no	—
531	C₃×C₄	—	2	2	no	—
532	C₃×C₄	—	2	2	no	—
533	C₃×C₄	—	2	8	no	—
534	C₃×C₄	—	4	2	no	—
535	C₃×C₄	—	4	2	no	—
536	C₃×C₄	—	4	2	no	—
537	C₃×C₄	—	4	4	no	—
538	C₃×C₄	—	4	4	no	—
539	C₃×C₄	#525	1	4	yes	—
540	C₃×C₄	#535	1	4	yes	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	16	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	8	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	4	no	—
552	C₂³	—	4	32	no	—
553	C₂³	—	4	8	no	—
554	C₂³	—	4	8	no	—
555	C₂³	C₂²×C₃×D₄	1	2	yes	—
556	C₂³	C₂×C₃×#41	1	8	yes	—
557	C₂³	C₂×C₃×#41	1	4	yes	—
558	C₂³	C₂⁵×C₃	1	1	yes	characteristic
559	Q₈	—	4	4	no	—
560	D₄	—	2	16	no	—
561	D₄	—	2	16	no	—
562	D₄	—	4	32	no	—
563	D₄	—	4	8	no	—
564	D₄	—	4	4	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	8	no	—
585	C₂×C₄	—	4	16	no	—
586	C₂×C₄	—	4	8	no	—
587	C₂×C₄	—	4	16	no	—
588	C₂×C₄	—	4	8	no	—
589	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
590	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
591	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
592	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
593	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
594	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
595	C₂×C₄	C₂×C₃×#41	1	8	yes	—
596	C₂×C₄	C₂×C₃×#41	1	4	yes	—
597	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
598	C₂×C₃	—	2	4	no	—
599	C₂×C₃	—	4	8	no	—
600	C₂×C₃	—	8	2	no	—
601	C₂×C₃	C₂×#525	1	1	yes	characteristic
602	C₂×C₃	C₂×#532	1	1	yes	characteristic
603	C₂×C₃	C₂×#535	1	1	yes	characteristic
604	C₂×C₃	#3481	1	4	yes	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	8	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	2	16	no	—
610	C₂²	—	4	32	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	8	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	8	no	—
618	C₂²	C₃×#532	1	4	yes	—
619	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
620	C₂²	C₂²×C₃×#41	1	2	yes	—
621	C₂²	C₂²×C₃×#41	1	2	yes	—
622	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
623	C₄	—	2	2	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	2	no	—
627	C₄	—	2	8	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	4	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	4	no	—
633	C₄	C₃×#525	1	4	yes	—
634	C₄	C₃×#535	1	4	yes	—
635	C₃	#34965	1	1	yes	characteristic, direct product factor, Sylow
636	C₂	—	2	4	no	—
637	C₂	—	4	8	no	—
638	C₂	—	8	2	no	—
639	C₂	C₂×C₃×#525	1	1	yes	characteristic
640	C₂	C₂×C₃×#532	1	1	yes	characteristic
641	C₂	C₂×C₃×#535	1	1	yes	characteristic
642	C₂	C₃×#3481	1	4	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
socle	C₂³×C₃	C₂⁵
prime radical	C₃×#2433	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#529	C₂	semidirect
2. C₂²×C₃×C₄×D₄	C₂	semidirect
3. C₃×#2603	C₂	semidirect
4. C₃×#2566	C₂	semidirect
5. C₃×#2544	C₂	semidirect
6. C₃×#2504	C₂	semidirect
7. C₃×#2502	C₂	semidirect
8. C₃×#2435	C₂	semidirect
10. C₃×#2411	C₂	semidirect
11. C₃×#2392	C₂	semidirect
12. C₃×C₄×#127	C₂	semidirect
13. C₃×C₄×#124	C₂	semidirect
14. C₃×C₄×#120	C₂	semidirect
15. C₃×C₄×#117	C₂	semidirect
16. #34965	C₃	direct (N × H)
21. C₂×C₃×#126	C₂²	semidirect
22. C₂×C₃×#125	C₂²	semidirect
24. C₂×C₃×#124	C₂²	semidirect
29. C₂×C₃×C₄×Q₈	C₂²	semidirect
36. C₂×C₃×C₄×D₄	C₂²	semidirect
37. C₂×C₃×C₄×D₄	C₂²	semidirect
39. C₂×C₃×#117	C₂²	semidirect
43. C₃×#398	C₂²	semidirect
44. C₃×#397	C₂²	semidirect
45. C₃×#396	C₂²	semidirect
47. C₃×#394	C₂²	semidirect
49. C₃×#391	C₂²	semidirect
52. C₃×#390	C₂²	semidirect
53. C₃×#390	C₂²	semidirect
54. C₃×#388	C₂²	semidirect
56. C₃×#386	C₂²	semidirect
58. C₃×#385	C₂²	semidirect
59. C₃×#384	C₂²	semidirect
60. C₃×#382	C₂²	semidirect
62. C₃×C₄×C₄⋊C₄	C₂²	semidirect
63. C₃×C₄×C₄⋊C₄	C₂²	semidirect
67. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
68. C₃×#376	C₂²	semidirect
69. C₃×C₄³	C₂²	semidirect
70. C₂×#529	C₂×C₃	semidirect
71. C₂²×C₄×D₄	C₂×C₃	semidirect
72. #2603	C₂×C₃	semidirect
73. #2566	C₂×C₃	semidirect
74. #2544	C₂×C₃	semidirect
75. #2504	C₂×C₃	semidirect
76. #2502	C₂×C₃	semidirect
77. #2435	C₂×C₃	semidirect
79. #2411	C₂×C₃	semidirect
80. #2392	C₂×C₃	semidirect
81. C₄×#127	C₂×C₃	semidirect
82. C₄×#124	C₂×C₃	semidirect
83. C₄×#120	C₂×C₃	semidirect
84. C₄×#117	C₂×C₃	semidirect
147. C₂×C₃×C₄²	D₄	semidirect
166. C₂×#126	C₂²×C₃	semidirect
167. C₂×#125	C₂²×C₃	semidirect
169. C₂×#124	C₂²×C₃	semidirect
174. C₂×C₄×Q₈	C₂²×C₃	semidirect
181. C₂×C₄×D₄	C₂²×C₃	semidirect
182. C₂×C₄×D₄	C₂²×C₃	semidirect
184. C₂×#117	C₂²×C₃	semidirect
188. #398	C₂²×C₃	semidirect
189. #397	C₂²×C₃	semidirect
190. #396	C₂²×C₃	semidirect
192. #394	C₂²×C₃	semidirect
194. #391	C₂²×C₃	semidirect
197. #390	C₂²×C₃	semidirect
198. #390	C₂²×C₃	semidirect
199. #388	C₂²×C₃	semidirect
201. #386	C₂²×C₃	semidirect
203. #385	C₂²×C₃	semidirect
204. #384	C₂²×C₃	semidirect
205. #382	C₂²×C₃	semidirect
207. C₄×C₄⋊C₄	C₂²×C₃	semidirect
208. C₄×C₄⋊C₄	C₂²×C₃	semidirect
212. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
213. #376	C₂²×C₃	semidirect
214. C₄³	C₂²×C₃	semidirect
358. C₂×C₄²	C₃×D₄	semidirect
635. C₃	#34965	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×#529	2
C₂²×C₃×C₄×D₄	2
C₃×#2603	2
C₃×#2566	2
C₃×#2544	2
C₃×#2504	2
C₃×#2502	2
C₃×#2435	2
C₃×#2433	2
C₃×#2411	2
C₃×#2392	2
C₃×C₄×#127	2
C₃×C₄×#124	2
C₃×C₄×#120	2
C₃×C₄×#117	2
#34965	3

Subgroups — C3×#34965 #10653572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34965 #10653572