Subgroups — C₃×C₄×#908 #11860277

Order 1152.

1167 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#908	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5133	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5131	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4711	C₂	1	2	yes	maximal, complemented
9	C₃×#4710	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₂₄	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#204	C₂	1	2	yes	maximal, complemented
12	C₃×C₄×AGL(1,ℤ/8)	—	3	1	no	maximal
13	C₄×#908	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#235	C₂²	1	1	yes	characteristic
15	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×D₃	—	2	1	no	—
17	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
20	C₃×C₄×#67	—	2	1	no	—
21	C₃×C₄×#67	—	2	1	no	—
22	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
23	C₃×#926	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₃×#908	C₄	1	8	yes	direct product factor
26	C₂×C₃×D₂₄	C₂²	1	2	yes	—
27	C₂×C₃×#204	C₂²	1	2	yes	—
28	C₃×C₄×D₁₂	—	2	1	no	—
29	C₃×C₄×D₁₂	—	2	1	no	—
30	C₃×C₄×D₁₂	C₂²	1	2	yes	—
31	C₃×C₄×D₁₂	C₂²	1	2	yes	—
32	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic, complemented
34	C₃×#872	—	2	1	no	—
35	C₃×C₄²×D₃	—	2	1	no	—
36	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
38	C₃²×#97	C₂²	1	2	yes	complemented
39	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
40	C₃×#821	C₂²	1	2	yes	—
41	C₃×#821	C₂²	1	2	yes	—
42	C₃×#821	C₂²	1	2	yes	complemented
43	C₃×#818	C₂²	1	2	yes	complemented
44	C₃×#817	C₂²	1	2	yes	complemented
45	C₃×#816	C₂²	1	2	yes	complemented
46	C₂×C₃×AGL(1,ℤ/8)	—	3	1	no	—
47	C₃×C₄×#41	—	3	1	no	—
48	C₂×C₃×C₄×D₄	—	3	1	no	—
49	C₂×#908	C₂×C₃	1	1	yes	characteristic
50	C₄×#235	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×#442	—	3	2	no	—
53	C₃×#440	—	3	2	no	—
54	C₃×C₄×SD₁₆	—	3	2	no	—
55	C₃×C₄×D₈	—	3	2	no	—
56	C₃×#428	—	3	1	no	—
57	C₃×#418	—	3	1	no	—
58	C₃×#417	—	3	1	no	—
59	C₃×C₄×M₁₆	—	2	1	no	—
60	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic, complemented
61	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
62	#5133	C₂×C₃	1	1	yes	characteristic, complemented
63	#5131	C₂×C₃	1	1	yes	characteristic, complemented
64	#5121	C₂×C₃	1	1	yes	characteristic, complemented
65	#4711	C₂×C₃	1	2	yes	complemented
66	#4710	C₂×C₃	1	2	yes	complemented
67	C₄×D₂₄	C₂×C₃	1	2	yes	complemented
68	C₄×#204	C₂×C₃	1	2	yes	complemented
69	C₂³×C₃×D₃	—	2	1	no	—
70	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
71	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
72	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
73	C₂×C₃×#67	—	2	1	no	—
74	C₂²×C₃×Dic₃	—	2	1	no	—
75	C₃×#235	—	2	2	no	—
76	C₃×#235	C₂×C₄	1	4	yes	complemented
77	C₂×C₃×D₁₂	—	2	1	no	—
78	C₂×C₃×D₁₂	—	2	2	no	—
79	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	complemented
80	C₂×C₃×D₁₂	C₂³	1	2	yes	—
81	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄×D₃	—	2	1	no	—
83	C₂×C₃×C₄×D₃	—	2	1	no	—
84	C₂×C₃×C₄×D₃	—	2	1	no	—
85	C₂×C₃×C₄×D₃	—	2	2	no	—
86	C₂×C₃×C₄×D₃	—	2	2	no	—
87	C₂×C₃×C₄×D₃	—	4	4	no	—
88	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
89	C₃²×M₁₆	—	2	2	no	—
90	C₃²×M₁₆	C₂×C₄	1	4	yes	complemented
91	C₂×C₃²×C₈	C₂³	1	2	yes	—
92	C₂×C₃²×C₈	C₂³	1	2	yes	—
93	C₃²×C₄²	D₄	1	1	yes	characteristic
94	C₃²×C₄²	D₄	1	1	yes	characteristic
95	C₃²×C₄²	C₂³	1	1	yes	characteristic
96	C₃²×C₄²	C₂³	1	1	yes	characteristic
97	C₃×#217	—	2	1	no	—
98	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
99	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
100	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
101	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
102	C₃×C₄⋊Dic₃	—	2	1	no	—
103	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
104	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
105	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
106	C₃×Dic₃⋊C₄	—	2	1	no	—
107	C₃×Dic₃⋊C₄	—	2	1	no	—
108	C₃×C₄×Dic₃	—	2	1	no	—
109	C₃×C₄×Dic₃	—	2	1	no	—
110	C₃×C₄×Dic₃	—	2	1	no	—
111	C₃×D₂₄	C₂×C₄	1	8	yes	complemented
112	C₃×#204	C₂×C₄	1	8	yes	complemented
113	C₄×AGL(1,ℤ/8)	—	3	1	no	Sylow
114	C₂×C₃×#41	—	3	1	no	—
115	C₂²×C₃×D₄	—	3	1	no	—
116	C₂³×C₃×C₄	—	6	1	no	—
117	C₂×#235	C₂²×C₃	1	1	yes	characteristic
118	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₄×D₃	—	2	1	no	—
120	C₃×AGL(1,ℤ/8)	—	3	8	no	—
121	C₂×C₃×SD₁₆	—	3	2	no	—
122	C₂×C₃×D₈	—	3	2	no	—
123	C₂×C₃×M₁₆	—	2	1	no	—
124	C₂×C₃×M₁₆	—	2	1	no	—
125	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
126	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
127	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
129	C₃×C₄×Q₈	—	3	1	no	—
130	C₃×C₄×Q₈	—	3	1	no	—
131	C₃×C₄×D₄	—	3	1	no	—
132	C₃×C₄×D₄	—	3	2	no	—
133	C₃×C₄×D₄	—	3	2	no	—
134	C₃×C₄×D₄	—	3	1	no	—
135	C₃×C₄×D₄	—	6	1	no	—
136	C₃×C₄×D₄	—	6	1	no	—
137	C₃×C₄×D₄	—	6	1	no	—
138	C₃×C₄×D₄	—	6	1	no	—
139	C₃×#117	—	3	1	no	—
140	C₃×#117	—	6	1	no	—
141	C₂×C₃×C₄⋊C₄	—	3	1	no	—
142	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
143	C₂×C₃×C₄²	—	2	1	no	—
144	C₂×C₃×C₄²	—	6	1	no	—
145	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
146	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
147	C₄×#67	—	2	1	no	—
148	C₄×#67	—	2	1	no	—
149	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
150	#926	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
152	#908	C₃×C₄	1	8	yes	direct product factor
153	C₂×D₂₄	C₂²×C₃	1	2	yes	—
154	C₂×#204	C₂²×C₃	1	2	yes	—
155	C₄×D₁₂	—	2	1	no	—
156	C₄×D₁₂	—	2	1	no	—
157	C₄×D₁₂	C₂²×C₃	1	2	yes	—
158	C₄×D₁₂	C₂²×C₃	1	2	yes	—
159	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
160	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
161	#872	—	2	1	no	—
162	C₄²×D₃	—	2	1	no	—
163	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₃×#107	—	3	2	no	—
166	C₃×#106	—	3	2	no	—
167	C₃×#103	—	3	2	no	—
168	C₃×#102	—	3	2	no	—
169	C₃×#102	—	3	2	no	—
170	C₃×#102	—	3	2	no	—
171	C₃×#97	—	2	2	no	—
172	C₃×#97	C₂×D₃	1	2	yes	complemented
173	C₃×#97	C₂²×C₃	1	2	yes	complemented
174	C₃×C₄×C₈	—	2	2	no	—
175	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
176	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
177	#821	C₂²×C₃	1	2	yes	—
178	#821	C₂²×C₃	1	2	yes	—
179	#821	C₂²×C₃	1	2	yes	complemented
180	#818	C₂²×C₃	1	2	yes	complemented
181	#817	C₂²×C₃	1	2	yes	complemented
182	#816	C₂²×C₃	1	2	yes	complemented
183	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₃×D₃	—	2	4	no	—
185	C₂²×C₃×D₃	—	2	2	no	—
186	C₂²×C₃×D₃	—	2	1	no	—
187	C₂²×C₃×D₃	—	4	2	no	—
188	C₂²×C₃×D₃	—	4	2	no	—
189	C₂×C₃²×C₄	—	2	2	no	—
190	C₂×C₃²×C₄	—	4	1	no	—
191	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
192	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
193	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
194	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
195	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
196	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
197	C₂×C₃²×C₄	#41	1	2	yes	—
198	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
199	C₃×#67	—	2	4	no	—
200	C₂×C₃×Dic₃	—	2	1	no	—
201	C₂×C₃×Dic₃	—	2	1	no	—
202	C₂×C₃×Dic₃	—	2	1	no	—
203	C₂×C₃×Dic₃	—	2	2	no	—
204	C₂×C₃×Dic₃	—	4	2	no	—
205	C₃×D₁₂	—	2	4	no	—
206	C₃×D₁₂	—	2	2	no	—
207	C₃×D₁₂	—	2	1	no	—
208	C₃×D₁₂	C₂²×C₄	1	4	yes	—
209	C₃×D₁₂	C₂²×C₄	1	2	yes	complemented
210	C₃×C₄×D₃	—	2	4	no	—
211	C₃×C₄×D₃	—	4	2	no	—
212	C₃×C₄×D₃	—	4	4	no	—
213	C₃×C₄×D₃	—	4	2	no	—
214	C₃×C₄×D₃	—	4	4	no	—
215	C₃×Dic₆	—	2	1	no	—
216	C₃×Dic₆	C₂²×C₄	1	2	yes	complemented
217	C₃²×C₈	—	2	2	no	—
218	C₃²×C₈	C₂²×C₄	1	4	yes	complemented
219	C₂×AGL(1,ℤ/8)	—	3	1	no	—
220	C₄×#41	—	3	1	no	—
221	C₂×C₄×D₄	—	3	1	no	—
222	#442	—	3	2	no	—
223	#440	—	3	2	no	—
224	C₄×SD₁₆	—	3	2	no	—
225	C₄×D₈	—	3	2	no	—
226	#428	—	3	1	no	—
227	#418	—	3	1	no	—
228	#417	—	3	1	no	—
229	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic, complemented
230	C₂⁴×C₃	—	6	1	no	—
231	C₂³×D₃	—	2	1	no	—
232	C₃×#41	—	3	4	no	—
233	C₃×#41	—	6	2	no	—
234	C₂×C₃×Q₈	—	3	1	no	—
235	C₂×C₃×D₄	—	3	4	no	—
236	C₂×C₃×D₄	—	3	1	no	—
237	C₂×C₃×D₄	—	3	2	no	—
238	C₂×C₃×D₄	—	6	1	no	—
239	C₂×C₃×D₄	—	6	1	no	—
240	C₂×C₃×D₄	—	6	2	no	—
241	C₂²×C₃×C₄	—	2	1	no	—
242	C₂²×C₃×C₄	—	2	1	no	—
243	C₂²×C₃×C₄	—	2	1	no	—
244	C₂²×C₃×C₄	—	6	1	no	—
245	C₂²×C₃×C₄	—	6	1	no	—
246	C₂²×C₃×C₄	—	6	1	no	—
247	C₂²×C₃×C₄	—	6	2	no	—
248	C₂²×C₃×C₄	—	6	1	no	—
249	C₂²×C₃×C₄	—	6	2	no	—
250	C₂²×C₃×C₄	—	12	4	no	—
251	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
252	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
254	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
257	C₂×#67	—	2	1	no	—
258	C₂²×Dic₃	—	2	1	no	—
259	#235	—	2	2	no	—
260	#235	C₂×C₃×C₄	1	4	yes	complemented
261	C₂×D₁₂	—	2	1	no	—
262	C₂×D₁₂	—	2	2	no	—
263	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	complemented
264	C₂×D₁₂	C₂³×C₃	1	2	yes	—
265	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₄×D₃	—	2	1	no	—
267	C₂×C₄×D₃	—	2	1	no	—
268	C₂×C₄×D₃	—	2	1	no	—
269	C₂×C₄×D₃	—	2	2	no	—
270	C₂×C₄×D₃	—	2	2	no	—
271	C₂×C₄×D₃	—	4	4	no	—
272	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
273	C₃×SD₁₆	—	3	8	no	—
274	C₃×D₈	—	3	8	no	—
275	C₃×M₁₆	—	2	4	no	—
276	C₃×M₁₆	—	2	2	no	—
277	C₃×M₁₆	—	2	2	no	—
278	C₃×M₁₆	—	2	4	no	—
279	C₃×M₁₆	C₄×D₃	1	4	yes	complemented
280	C₃×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
281	C₂×C₃×C₈	—	2	2	no	—
282	C₂×C₃×C₈	—	2	2	no	—
283	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
284	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
285	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
286	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
287	C₃×C₄⋊C₄	—	3	1	no	—
288	C₃×C₄⋊C₄	—	3	1	no	—
289	C₃×C₄⋊C₄	—	3	2	no	—
290	C₃×C₄⋊C₄	—	6	1	no	—
291	C₃×C₄⋊C₄	—	6	1	no	—
292	C₃×C₄⋊C₄	—	6	1	no	—
293	C₃×C₂²⋊C₄	—	6	1	no	—
294	C₃×C₂²⋊C₄	—	6	2	no	—
295	C₃×C₂²⋊C₄	—	6	2	no	—
296	C₃×C₂²⋊C₄	—	6	1	no	—
297	C₃×C₂²⋊C₄	—	6	1	no	—
298	C₃×C₄²	—	2	1	no	—
299	C₃×C₄²	—	2	1	no	—
300	C₃×C₄²	—	2	1	no	—
301	C₃×C₄²	—	2	1	no	—
302	C₃×C₄²	—	6	1	no	—
303	C₃×C₄²	—	6	1	no	—
304	C₃×C₄²	—	6	1	no	—
305	C₃×C₄²	D₁₂	1	1	yes	characteristic
306	C₃×C₄²	D₁₂	1	1	yes	characteristic
307	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
308	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
309	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
310	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
311	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
312	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
313	#217	—	2	1	no	—
314	(C₂×D₃)⋊C₄	—	2	1	no	—
315	(C₂×D₃)⋊C₄	—	2	1	no	—
316	(C₂×D₃)⋊C₄	—	2	2	no	—
317	(C₂×D₃)⋊C₄	—	2	2	no	—
318	C₄⋊Dic₃	—	2	1	no	—
319	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
320	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
321	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
322	Dic₃⋊C₄	—	2	1	no	—
323	Dic₃⋊C₄	—	2	1	no	—
324	C₄×Dic₃	—	2	1	no	—
325	C₄×Dic₃	—	2	1	no	—
326	C₄×Dic₃	—	2	1	no	—
327	D₂₄	C₂×C₃×C₄	1	8	yes	complemented
328	#204	C₂×C₃×C₄	1	8	yes	complemented
329	C₂²×C₃²	—	2	1	no	—
330	C₂²×C₃²	—	2	1	no	—
331	C₂²×C₃²	C₄×D₄	1	2	yes	—
332	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₃×D₃	—	2	2	no	—
334	C₂×C₃×D₃	—	2	4	no	—
335	C₂×C₃×D₃	—	4	8	no	—
336	C₂×C₃×D₃	—	4	2	no	—
337	C₂×C₃×D₃	—	4	1	no	—
338	C₂×C₃×D₃	—	4	1	no	—
339	C₂×C₃×D₃	—	4	2	no	—
340	C₃²×C₄	—	2	1	no	—
341	C₃²×C₄	—	2	1	no	—
342	C₃²×C₄	—	2	1	no	—
343	C₃²×C₄	C₄×D₄	1	2	yes	—
344	C₃²×C₄	AGL(1,ℤ/8)	1	2	yes	complemented
345	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
346	C₃²×C₄	C₂×#41	1	1	yes	characteristic
347	C₃×Dic₃	—	2	2	no	—
348	C₃×Dic₃	—	4	2	no	—
349	C₃×Dic₃	—	4	1	no	—
350	C₃×Dic₃	—	4	1	no	—
351	C₂×#41	—	3	1	no	—
352	C₂²×D₄	—	3	1	no	—
353	C₂³×C₄	—	6	1	no	—
354	AGL(1,ℤ/8)	—	3	8	no	—
355	C₂×SD₁₆	—	3	2	no	—
356	C₂×D₈	—	3	2	no	—
357	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
358	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
359	C₄×Q₈	—	3	1	no	—
360	C₄×Q₈	—	3	1	no	—
361	C₄×D₄	—	3	2	no	—
362	C₄×D₄	—	3	2	no	—
363	C₄×D₄	—	3	1	no	—
364	C₄×D₄	—	3	1	no	—
365	C₄×D₄	—	6	1	no	—
366	C₄×D₄	—	6	1	no	—
367	C₄×D₄	—	6	1	no	—
368	C₄×D₄	—	6	1	no	—
369	#117	—	3	1	no	—
370	#117	—	6	1	no	—
371	C₂×C₄⋊C₄	—	3	1	no	—
372	C₂×C₂²⋊C₄	—	6	1	no	—
373	C₂×C₄²	—	6	1	no	—
374	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
375	#107	—	3	2	no	—
376	#106	—	3	2	no	—
377	#103	—	3	2	no	—
378	#102	—	3	2	no	—
379	#102	—	3	2	no	—
380	#102	—	3	2	no	—
381	#97	C₂×C₃×D₃	1	2	yes	complemented
382	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
383	C₂³×C₃	—	2	1	no	—
384	C₂³×C₃	—	6	4	no	—
385	C₂³×C₃	—	6	1	no	—
386	C₂³×C₃	—	6	2	no	—
387	C₂³×C₃	—	12	2	no	—
388	C₂³×C₃	—	12	2	no	—
389	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
390	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
391	C₂²×D₃	—	2	4	no	—
392	C₂²×D₃	—	2	1	no	—
393	C₂²×D₃	—	2	2	no	—
394	C₂²×D₃	—	4	2	no	—
395	C₂²×D₃	—	4	2	no	—
396	C₃×Q₈	—	3	2	no	—
397	C₃×Q₈	—	6	1	no	—
398	C₃×D₄	—	3	4	no	—
399	C₃×D₄	—	3	2	no	—
400	C₃×D₄	—	6	4	no	—
401	C₃×D₄	—	6	4	no	—
402	C₃×D₄	—	6	2	no	—
403	C₃×D₄	—	6	1	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	2	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	4	2	no	—
415	C₂×C₃×C₄	—	4	1	no	—
416	C₂×C₃×C₄	—	4	1	no	—
417	C₂×C₃×C₄	—	4	2	no	—
418	C₂×C₃×C₄	—	6	1	no	—
419	C₂×C₃×C₄	—	6	4	no	—
420	C₂×C₃×C₄	—	6	1	no	—
421	C₂×C₃×C₄	—	6	1	no	—
422	C₂×C₃×C₄	—	6	2	no	—
423	C₂×C₃×C₄	—	12	2	no	—
424	C₂×C₃×C₄	—	12	4	no	—
425	C₂×C₃×C₄	—	12	2	no	—
426	C₂×C₃×C₄	—	12	2	no	—
427	C₂×C₃×C₄	—	12	4	no	—
428	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
429	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
430	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
431	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
432	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
434	C₂×C₃×C₄	#235	1	2	yes	—
435	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
436	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
437	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
440	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
441	C₂×C₃×C₄	C₃×#41	1	2	yes	—
442	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
443	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
444	#67	—	2	4	no	—
445	C₂×Dic₃	—	2	1	no	—
446	C₂×Dic₃	—	2	1	no	—
447	C₂×Dic₃	—	2	1	no	—
448	C₂×Dic₃	—	2	2	no	—
449	C₂×Dic₃	—	4	2	no	—
450	D₁₂	—	2	4	no	—
451	D₁₂	—	2	2	no	—
452	D₁₂	—	2	1	no	—
453	D₁₂	C₂²×C₃×C₄	1	4	yes	—
454	D₁₂	C₂²×C₃×C₄	1	2	yes	complemented
455	C₄×D₃	—	2	4	no	—
456	C₄×D₃	—	4	2	no	—
457	C₄×D₃	—	4	4	no	—
458	C₄×D₃	—	4	2	no	—
459	C₄×D₃	—	4	4	no	—
460	Dic₆	—	2	1	no	—
461	Dic₆	C₂²×C₃×C₄	1	2	yes	complemented
462	C₃×C₈	—	2	4	no	—
463	C₃×C₈	—	2	2	no	—
464	C₃×C₈	—	2	2	no	—
465	C₃×C₈	—	2	4	no	—
466	C₃×C₈	C₂×C₄×D₃	1	4	yes	complemented
467	C₃×C₈	C₂²×C₃×C₄	1	4	yes	complemented
468	C₂×C₃²	—	2	2	no	—
469	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
470	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
471	C₂×C₃²	#575	1	1	yes	characteristic
472	C₃×D₃	—	4	2	no	—
473	C₃×D₃	—	4	4	no	—
474	C₂⁴	—	6	1	no	—
475	#41	—	3	4	no	—
476	#41	—	6	2	no	—
477	C₂×Q₈	—	3	1	no	—
478	C₂×D₄	—	3	1	no	—
479	C₂×D₄	—	3	2	no	—
480	C₂×D₄	—	3	4	no	—
481	C₂×D₄	—	6	1	no	—
482	C₂×D₄	—	6	1	no	—
483	C₂×D₄	—	6	2	no	—
484	C₂²×C₄	—	6	1	no	—
485	C₂²×C₄	—	6	1	no	—
486	C₂²×C₄	—	6	1	no	—
487	C₂²×C₄	—	6	1	no	—
488	C₂²×C₄	—	6	2	no	—
489	C₂²×C₄	—	6	2	no	—
490	C₂²×C₄	—	12	4	no	—
491	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
492	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
493	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
494	SD₁₆	—	3	8	no	—
495	D₈	—	3	8	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	C₃×C₄×D₃	1	4	yes	complemented
498	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
499	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
500	C₄⋊C₄	—	3	1	no	—
501	C₄⋊C₄	—	3	1	no	—
502	C₄⋊C₄	—	3	2	no	—
503	C₄⋊C₄	—	6	1	no	—
504	C₄⋊C₄	—	6	1	no	—
505	C₄⋊C₄	—	6	1	no	—
506	C₂²⋊C₄	—	6	1	no	—
507	C₂²⋊C₄	—	6	2	no	—
508	C₂²⋊C₄	—	6	2	no	—
509	C₂²⋊C₄	—	6	1	no	—
510	C₂²⋊C₄	—	6	1	no	—
511	C₄²	—	6	1	no	—
512	C₄²	—	6	1	no	—
513	C₄²	—	6	1	no	—
514	C₄²	C₃×D₁₂	1	1	yes	characteristic
515	C₄²	C₃×D₁₂	1	1	yes	characteristic
516	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
517	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	1	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	4	1	no	—
525	C₂²×C₃	—	4	1	no	—
526	C₂²×C₃	—	6	2	no	—
527	C₂²×C₃	—	6	4	no	—
528	C₂²×C₃	—	12	8	no	—
529	C₂²×C₃	—	12	2	no	—
530	C₂²×C₃	—	12	1	no	—
531	C₂²×C₃	—	12	1	no	—
532	C₂²×C₃	—	12	2	no	—
533	C₂²×C₃	C₄×D₁₂	1	2	yes	—
534	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
535	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
536	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
537	C₂×D₃	—	2	2	no	—
538	C₂×D₃	—	2	4	no	—
539	C₂×D₃	—	4	8	no	—
540	C₂×D₃	—	4	2	no	—
541	C₂×D₃	—	4	1	no	—
542	C₂×D₃	—	4	1	no	—
543	C₂×D₃	—	4	2	no	—
544	C₃×C₄	—	2	2	no	—
545	C₃×C₄	—	2	1	no	—
546	C₃×C₄	—	2	1	no	—
547	C₃×C₄	—	2	1	no	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	—	2	1	no	—
550	C₃×C₄	—	2	1	no	—
551	C₃×C₄	—	2	2	no	—
552	C₃×C₄	—	2	1	no	—
553	C₃×C₄	—	2	1	no	—
554	C₃×C₄	—	2	2	no	—
555	C₃×C₄	—	4	1	no	—
556	C₃×C₄	—	4	1	no	—
557	C₃×C₄	—	6	2	no	—
558	C₃×C₄	—	12	2	no	—
559	C₃×C₄	—	12	1	no	—
560	C₃×C₄	—	12	1	no	—
561	C₃×C₄	C₄×D₁₂	1	2	yes	—
562	C₃×C₄	#908	1	2	yes	direct product factor
563	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
564	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
565	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
566	C₃×C₄	C₂×#235	1	1	yes	characteristic
567	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
568	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
569	Dic₃	—	2	2	no	—
570	Dic₃	—	4	2	no	—
571	Dic₃	—	4	1	no	—
572	Dic₃	—	4	1	no	—
573	C₃²	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
574	C₂³	—	6	1	no	—
575	C₂³	—	6	2	no	—
576	C₂³	—	6	4	no	—
577	C₂³	—	12	2	no	—
578	C₂³	—	12	2	no	—
579	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
580	Q₈	—	3	2	no	—
581	Q₈	—	6	1	no	—
582	D₄	—	3	2	no	—
583	D₄	—	3	4	no	—
584	D₄	—	6	4	no	—
585	D₄	—	6	2	no	—
586	D₄	—	6	1	no	—
587	D₄	—	6	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	6	1	no	—
591	C₂×C₄	—	6	4	no	—
592	C₂×C₄	—	6	1	no	—
593	C₂×C₄	—	6	1	no	—
594	C₂×C₄	—	6	2	no	—
595	C₂×C₄	—	12	4	no	—
596	C₂×C₄	—	12	2	no	—
597	C₂×C₄	—	12	2	no	—
598	C₂×C₄	—	12	4	no	—
599	C₂×C₄	—	12	2	no	—
600	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
601	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
602	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
603	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
604	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
605	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
606	C₂×C₄	C₃×#235	1	2	yes	—
607	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
608	C₈	—	2	2	no	—
609	C₈	C₂×C₃×C₄×D₃	1	4	yes	complemented
610	C₂×C₃	—	2	2	no	—
611	C₂×C₃	—	2	2	no	—
612	C₂×C₃	—	2	1	no	—
613	C₂×C₃	—	2	1	no	—
614	C₂×C₃	—	2	1	no	—
615	C₂×C₃	—	4	2	no	—
616	C₂×C₃	—	12	4	no	—
617	C₂×C₃	—	12	2	no	—
618	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
619	C₂×C₃	C₂×#908	1	1	yes	characteristic
620	C₂×C₃	#5748	1	1	yes	characteristic
621	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
622	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
623	C₂×C₃	C₃×#575	1	1	yes	characteristic
624	D₃	—	4	4	no	—
625	D₃	—	4	2	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	6	2	no	—
629	C₂²	—	6	4	no	—
630	C₂²	—	12	8	no	—
631	C₂²	—	12	2	no	—
632	C₂²	—	12	1	no	—
633	C₂²	—	12	1	no	—
634	C₂²	—	12	2	no	—
635	C₂²	C₃×C₄×D₁₂	1	2	yes	—
636	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	6	2	no	—
641	C₄	—	12	2	no	—
642	C₄	—	12	1	no	—
643	C₄	—	12	1	no	—
644	C₄	C₃×C₄×D₁₂	1	2	yes	—
645	C₄	C₃×#908	1	2	yes	direct product factor
646	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
647	C₄	C₂×C₃×#235	1	1	yes	characteristic
648	C₃	—	2	1	no	—
649	C₃	C₄×#908	1	1	yes	characteristic, direct product factor
650	C₃	C₃×C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
651	C₂	—	2	2	no	—
652	C₂	—	12	4	no	—
653	C₂	—	12	2	no	—
654	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
655	C₂	C₂×C₃×#908	1	1	yes	characteristic
656	C₂	C₃×#5748	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₁₂
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×#908	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₃×C₄×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×#235	C₂	semidirect
3. C₂×C₃×C₄×D₁₂	C₂	semidirect
4. C₃²×C₄×M₁₆	C₂	semidirect
5. C₃×#5133	C₂	semidirect
6. C₃×#5131	C₂	semidirect
7. C₃×#5121	C₂	semidirect
8. C₃×#4711	C₂	semidirect
9. C₃×#4710	C₂	semidirect
10. C₃×C₄×D₂₄	C₂	semidirect
11. C₃×C₄×#204	C₂	semidirect
13. C₄×#908	C₃	direct (N × H)
25. C₃×#908	C₄	direct (N × H)
32. C₃×C₄×D₁₂	C₂²	semidirect
33. C₃×C₄×D₁₂	C₂²	semidirect
36. C₃×C₄×Dic₆	C₂²	semidirect
37. C₃×C₄×Dic₆	C₂²	semidirect
38. C₃²×#97	C₂²	semidirect
39. C₃²×C₄×C₈	C₂²	semidirect
42. C₃×#821	C₂²	semidirect
43. C₃×#818	C₂²	semidirect
44. C₃×#817	C₂²	semidirect
45. C₃×#816	C₂²	semidirect
50. C₄×#235	C₂×C₃	semidirect
51. C₂×C₄×D₁₂	C₂×C₃	semidirect
60. C₃×C₄×M₁₆	D₃	semidirect
61. C₃×C₄×M₁₆	C₂×C₃	semidirect
62. #5133	C₂×C₃	semidirect
63. #5131	C₂×C₃	semidirect
64. #5121	C₂×C₃	semidirect
65. #4711	C₂×C₃	semidirect
66. #4710	C₂×C₃	semidirect
67. C₄×D₂₄	C₂×C₃	semidirect
68. C₄×#204	C₂×C₃	semidirect
76. C₃×#235	C₂×C₄	semidirect
79. C₂×C₃×D₁₂	C₂×C₄	semidirect
90. C₃²×M₁₆	C₂×C₄	semidirect
111. C₃×D₂₄	C₂×C₄	semidirect
112. C₃×#204	C₂×C₄	semidirect
152. #908	C₃×C₄	direct (N × H)
159. C₄×D₁₂	C₂²×C₃	semidirect
160. C₄×D₁₂	C₂²×C₃	semidirect
163. C₄×Dic₆	C₂²×C₃	semidirect
164. C₄×Dic₆	C₂²×C₃	semidirect
172. C₃×#97	C₂×D₃	semidirect
173. C₃×#97	C₂²×C₃	semidirect
175. C₃×C₄×C₈	C₂×D₃	semidirect
176. C₃×C₄×C₈	C₂²×C₃	semidirect
179. #821	C₂²×C₃	semidirect
180. #818	C₂²×C₃	semidirect
181. #817	C₂²×C₃	semidirect
182. #816	C₂²×C₃	semidirect
209. C₃×D₁₂	C₂²×C₄	semidirect
216. C₃×Dic₆	C₂²×C₄	semidirect
218. C₃²×C₈	C₂²×C₄	semidirect
229. C₄×M₁₆	C₃×D₃	semidirect
260. #235	C₂×C₃×C₄	semidirect
263. C₂×D₁₂	C₂×C₃×C₄	semidirect
279. C₃×M₁₆	C₄×D₃	semidirect
280. C₃×M₁₆	C₂×C₃×C₄	semidirect
327. D₂₄	C₂×C₃×C₄	semidirect
328. #204	C₂×C₃×C₄	semidirect
344. C₃²×C₄	AGL(1,ℤ/8)	semidirect
381. #97	C₂×C₃×D₃	semidirect
382. C₄×C₈	C₂×C₃×D₃	semidirect
454. D₁₂	C₂²×C₃×C₄	semidirect
461. Dic₆	C₂²×C₃×C₄	semidirect
466. C₃×C₈	C₂×C₄×D₃	semidirect
467. C₃×C₈	C₂²×C₃×C₄	semidirect
497. M₁₆	C₃×C₄×D₃	semidirect
562. C₃×C₄	#908	direct (N × H)
564. C₃×C₄	C₃×AGL(1,ℤ/8)	semidirect
573. C₃²	C₄×AGL(1,ℤ/8)	semidirect
609. C₈	C₂×C₃×C₄×D₃	semidirect
645. C₄	C₃×#908	direct (N × H)
649. C₃	C₄×#908	direct (N × H)
650. C₃	C₃×C₄×AGL(1,ℤ/8)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#908	2
C₃×C₄×#235	2
C₂×C₃×C₄×D₁₂	2
C₃²×C₄×M₁₆	2
C₃×#5133	2
C₃×#5131	2
C₃×#5121	2
C₃×#4711	2
C₃×#4710	2
C₃×C₄×D₂₄	2
C₃×C₄×#204	2
C₃×C₄×AGL(1,ℤ/8)	3
C₄×#908	3

Subgroups — C3×C4×#908 #11860277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#908 #11860277