Subgroups — C₃×#41×D₁₂ #11902766

Order 1152.

3451 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×#41	C₂	1	2	yes	maximal, complemented
2	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5577	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5576	C₂	1	2	yes	maximal, complemented
5	C₃×Q₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5555	C₂	1	3	yes	maximal, complemented
7	C₃×#5554	C₂	1	6	yes	maximal, complemented
8	C₃×D₄×D₁₂	C₂	1	3	yes	maximal, complemented
9	C₃×#5524	C₂	1	6	yes	maximal, complemented
10	C₃×#5477	C₂	1	3	yes	maximal, complemented
11	C₂×C₃×C₄×D₁₂	C₂	1	3	yes	maximal, complemented
12	C₃×D₄×#41	—	3	1	no	maximal
13	#41×D₁₂	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
15	C₃×D₃×#41	—	2	16	no	—
16	C₂×C₃×#239	C₂²	1	2	yes	complemented
17	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	complemented
18	C₂×C₃×#237	C₂²	1	6	yes	complemented
19	C₂×C₃×D₃×D₄	C₂²	1	6	yes	complemented
20	C₂×C₃×#235	C₂²	1	6	yes	complemented
21	C₂²×C₃×D₁₂	C₂²	1	3	yes	—
22	C₂²×C₃×C₄×D₃	C₂²	1	6	yes	complemented
23	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃²×C₄×D₄	C₂²	1	3	yes	complemented
26	C₃²×C₄×D₄	C₂²	1	3	yes	complemented
27	C₃²×#117	C₂²	1	3	yes	complemented
28	C₂×C₃²×C₄²	C₂²	1	3	yes	complemented
29	C₃×#930	C₂²	1	6	yes	complemented
30	C₃×#930	C₂²	1	6	yes	complemented
31	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	6	yes	complemented
32	C₂×C₃×C₄⋊Dic₃	C₂²	1	3	yes	complemented
33	C₃×#897	C₂²	1	6	yes	complemented
34	C₃×#897	C₂²	1	6	yes	complemented
35	C₃×#895	C₂²	1	6	yes	complemented
36	C₃×#895	C₂²	1	6	yes	complemented
37	C₃×#886	C₂²	1	12	yes	complemented
38	C₃×#882	C₂²	1	12	yes	complemented
39	C₃×#875	C₂²	1	6	yes	complemented
40	C₃×#874	C₂²	1	3	yes	complemented
41	C₃×C₄×D₁₂	C₂²	1	3	yes	—
42	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
43	C₃×C₄×D₁₂	C₂²	1	6	yes	complemented
44	C₃×C₄×D₁₂	C₂²	1	6	yes	complemented
45	C₃×C₄×D₁₂	C₂²	1	6	yes	complemented
46	C₃×C₄×D₁₂	C₂²	1	3	yes	complemented
47	C₃×C₄×D₁₂	C₂²	1	3	yes	complemented
48	C₃×#869	C₂²	1	3	yes	complemented
49	C₂²×C₃×#41	—	3	2	no	—
50	C₂×D₃×#41	C₂×C₃	1	2	yes	complemented
51	C₃×#550	—	3	1	no	—
52	C₃×D₄×Q₈	—	3	1	no	—
53	C₃×#548	—	3	2	no	—
54	C₃×#547	—	3	3	no	—
55	C₃×#546	—	3	6	no	—
56	C₃×D₄²	—	3	3	no	—
57	C₃×#532	—	3	3	no	—
58	C₃×#525	—	3	6	no	—
59	C₃×C₄×#41	—	2	1	no	—
60	C₃×C₄×#41	D₃	1	1	yes	characteristic, complemented
61	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×C₃×C₄×D₄	—	3	3	no	—
63	#5577	C₂×C₃	1	1	yes	characteristic, complemented
64	#5576	C₂×C₃	1	2	yes	complemented
65	Q₈×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
66	#5555	C₂×C₃	1	3	yes	complemented
67	#5554	C₂×C₃	1	6	yes	complemented
68	D₄×D₁₂	C₂×C₃	1	3	yes	complemented
69	#5524	C₂×C₃	1	6	yes	complemented
70	#5477	C₂×C₃	1	3	yes	complemented
71	C₂×C₄×D₁₂	C₂×C₃	1	3	yes	complemented
72	C₂³×C₃×D₃	C₂³	1	6	yes	—
73	C₃²×#41	D₄	1	8	yes	complemented
74	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
75	C₂×C₃²×D₄	C₂³	1	3	yes	—
76	C₂²×C₃²×C₄	C₂³	1	3	yes	—
77	C₂²×C₃²×C₄	C₂³	1	3	yes	—
78	C₂²×C₃²×C₄	C₂³	1	3	yes	—
79	C₂×C₃×#67	C₂³	1	12	yes	—
80	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
81	C₃×#239	—	2	8	no	—
82	C₃×D₃×Q₈	—	2	8	no	—
83	C₃×#237	—	2	24	no	—
84	C₃×D₃×D₄	—	2	24	no	—
85	C₃×#235	—	2	24	no	—
86	C₂×C₃×D₁₂	—	2	12	no	—
87	C₂×C₃×D₁₂	C₂³	1	6	yes	—
88	C₂×C₃×D₁₂	C₂³	1	6	yes	—
89	C₂×C₃×D₁₂	C₂³	1	3	yes	—
90	C₂×C₃×D₁₂	C₂³	1	6	yes	—
91	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₄×D₃	—	2	24	no	—
93	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
94	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
95	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
96	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
97	C₂×C₃×Dic₆	C₂³	1	6	yes	—
98	C₃²×C₄⋊C₄	C₂³	1	3	yes	—
99	C₃²×C₄⋊C₄	C₂³	1	3	yes	—
100	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
101	C₃²×C₄²	C₂³	1	1	yes	characteristic
102	C₃²×C₄²	C₂³	1	3	yes	—
103	C₃²×C₄²	C₂³	1	3	yes	—
104	C₃²×C₄²	C₂³	1	3	yes	—
105	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
106	C₃×(C₂×D₃)⋊C₄	C₂³	1	12	yes	—
107	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
108	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
109	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
110	C₃×C₄⋊Dic₃	C₂³	1	6	yes	—
111	C₃×C₄⋊Dic₃	C₂³	1	6	yes	—
112	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
113	C₃×C₄⋊Dic₃	C₂³	1	3	yes	—
114	D₄×#41	—	3	1	no	Sylow
115	C₂×C₃×#41	—	2	1	no	—
116	C₂×C₃×#41	—	3	2	no	—
117	C₂×C₃×#41	—	3	6	no	—
118	C₂×C₃×#41	—	3	6	no	—
119	C₂×C₃×#41	—	6	16	no	—
120	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
121	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
122	C₂²×C₃×Q₈	—	3	2	no	—
123	C₂²×C₃×D₄	—	3	6	no	—
124	C₂²×C₃×D₄	—	3	3	no	—
125	C₂³×C₃×C₄	—	3	6	no	—
126	D₃×#41	—	2	16	no	—
127	C₂×#239	C₂²×C₃	1	2	yes	complemented
128	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	complemented
129	C₂×#237	C₂²×C₃	1	6	yes	complemented
130	C₂×D₃×D₄	C₂²×C₃	1	6	yes	complemented
131	C₂×#235	C₂²×C₃	1	6	yes	complemented
132	C₂²×D₁₂	C₂²×C₃	1	3	yes	—
133	C₂²×C₄×D₃	C₂²×C₃	1	6	yes	complemented
134	C₃×C₄⋊Q₈	—	3	3	no	—
135	C₃×#127	—	3	3	no	—
136	C₃×#124	—	3	6	no	—
137	C₃×#123	—	3	12	no	—
138	C₃×C₂²⋊Q₈	—	3	6	no	—
139	C₃×C₂²⋊Q₈	—	3	6	no	—
140	C₃×#121	—	3	6	no	—
141	C₃×#121	—	3	6	no	—
142	C₃×#121	—	3	6	no	—
143	C₃×#121	—	3	6	no	—
144	C₃×#120	—	3	12	no	—
145	C₃×C₄×Q₈	—	2	1	no	—
146	C₃×C₄×Q₈	—	2	1	no	—
147	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
148	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
149	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₃×C₄×D₄	—	2	3	no	—
152	C₃×C₄×D₄	—	2	3	no	—
153	C₃×C₄×D₄	—	3	1	no	—
154	C₃×C₄×D₄	—	3	6	no	—
155	C₃×C₄×D₄	—	3	3	no	—
156	C₃×C₄×D₄	—	3	3	no	—
157	C₃×C₄×D₄	—	3	6	no	—
158	C₃×C₄×D₄	—	3	3	no	—
159	C₃×C₄×D₄	—	3	6	no	—
160	C₃×C₄×D₄	C₂×D₃	1	3	yes	complemented
161	C₃×C₄×D₄	C₂×D₃	1	3	yes	complemented
162	C₃×C₄×D₄	C₂²×C₃	1	3	yes	complemented
163	C₃×C₄×D₄	C₂²×C₃	1	3	yes	complemented
164	C₃×#117	—	2	3	no	—
165	C₃×#117	C₂×D₃	1	3	yes	complemented
166	C₃×#117	C₂²×C₃	1	3	yes	complemented
167	C₂×C₃×C₄⋊C₄	—	3	3	no	—
168	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
169	C₂×C₃×C₄²	—	2	3	no	—
170	C₂×C₃×C₄²	C₂×D₃	1	3	yes	complemented
171	C₂×C₃×C₄²	C₂²×C₃	1	3	yes	complemented
172	#930	C₂²×C₃	1	6	yes	complemented
173	#930	C₂²×C₃	1	6	yes	complemented
174	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	6	yes	complemented
175	C₂×C₄⋊Dic₃	C₂²×C₃	1	3	yes	complemented
176	#897	C₂²×C₃	1	6	yes	complemented
177	#897	C₂²×C₃	1	6	yes	complemented
178	#895	C₂²×C₃	1	6	yes	complemented
179	#895	C₂²×C₃	1	6	yes	complemented
180	#886	C₂²×C₃	1	12	yes	complemented
181	#882	C₂²×C₃	1	12	yes	complemented
182	#875	C₂²×C₃	1	6	yes	complemented
183	#874	C₂²×C₃	1	3	yes	complemented
184	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
185	C₄×D₁₂	C₂²×C₃	1	3	yes	—
186	C₄×D₁₂	C₂²×C₃	1	3	yes	complemented
187	C₄×D₁₂	C₂²×C₃	1	6	yes	complemented
188	C₄×D₁₂	C₂²×C₃	1	6	yes	complemented
189	C₄×D₁₂	C₂²×C₃	1	3	yes	complemented
190	C₄×D₁₂	C₂²×C₃	1	6	yes	complemented
191	#869	C₂²×C₃	1	3	yes	complemented
192	C₂³×C₃²	C₂⁴	1	3	yes	—
193	C₂²×C₃×D₃	—	2	12	no	—
194	C₂²×C₃×D₃	—	2	12	no	—
195	C₂²×C₃×D₃	—	4	6	no	—
196	C₂²×C₃×D₃	C₂⁴	1	6	yes	—
197	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
198	C₃²×Q₈	C₂×D₄	1	4	yes	complemented
199	C₃²×D₄	C₂×D₄	1	12	yes	complemented
200	C₂×C₃²×C₄	—	2	6	no	—
201	C₂×C₃²×C₄	—	4	3	no	—
202	C₂×C₃²×C₄	C₂×D₄	1	12	yes	complemented
203	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
204	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
205	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
206	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
207	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
208	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
209	C₃×#67	—	2	24	no	—
210	C₂×C₃×Dic₃	—	2	12	no	—
211	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
212	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
213	C₃×D₁₂	—	2	12	no	—
214	C₃×D₁₂	—	2	12	no	—
215	C₃×D₁₂	—	2	6	no	—
216	C₃×D₁₂	—	4	6	no	—
217	C₃×D₁₂	#41	1	4	yes	direct product factor
218	C₃×C₄×D₃	—	2	4	no	—
219	C₃×C₄×D₃	—	2	12	no	—
220	C₃×C₄×D₃	—	2	12	no	—
221	C₃×C₄×D₃	—	2	12	no	—
222	C₃×Dic₆	—	2	12	no	—
223	C₂²×#41	—	3	2	no	—
224	#550	—	3	1	no	—
225	D₄×Q₈	—	3	1	no	—
226	#548	—	3	2	no	—
227	#547	—	3	3	no	—
228	#546	—	3	6	no	—
229	D₄²	—	3	3	no	—
230	#532	—	3	3	no	—
231	#525	—	3	6	no	—
232	C₄×#41	C₃×D₃	1	1	yes	characteristic, complemented
233	C₂×C₄×D₄	—	3	3	no	—
234	C₂⁴×C₃	—	3	6	no	—
235	C₂³×D₃	C₂³×C₃	1	6	yes	—
236	C₃×#41	—	2	8	no	—
237	C₃×#41	—	6	8	no	—
238	C₃×#41	—	6	24	no	—
239	C₃×#41	—	6	24	no	—
240	C₃×#41	D₁₂	1	8	yes	direct product factor
241	C₃×#41	C₃×D₄	1	8	yes	complemented
242	C₂×C₃×Q₈	—	2	1	no	—
243	C₂×C₃×Q₈	—	3	6	no	—
244	C₂×C₃×Q₈	—	6	8	no	—
245	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
246	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
247	C₂×C₃×D₄	—	2	3	no	—
248	C₂×C₃×D₄	—	3	12	no	—
249	C₂×C₃×D₄	—	3	1	no	—
250	C₂×C₃×D₄	—	3	6	no	—
251	C₂×C₃×D₄	—	3	3	no	—
252	C₂×C₃×D₄	—	3	6	no	—
253	C₂×C₃×D₄	—	3	6	no	—
254	C₂×C₃×D₄	—	6	12	no	—
255	C₂×C₃×D₄	—	6	24	no	—
256	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
257	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
258	C₂²×C₃×C₄	—	2	3	no	—
259	C₂²×C₃×C₄	—	2	3	no	—
260	C₂²×C₃×C₄	—	2	3	no	—
261	C₂²×C₃×C₄	—	3	6	no	—
262	C₂²×C₃×C₄	—	3	6	no	—
263	C₂²×C₃×C₄	—	3	6	no	—
264	C₂²×C₃×C₄	—	3	2	no	—
265	C₂²×C₃×C₄	—	3	6	no	—
266	C₂²×C₃×C₄	—	6	24	no	—
267	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
268	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
269	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
270	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
271	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
272	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
273	C₂×#67	C₂³×C₃	1	12	yes	—
274	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
275	#239	—	2	8	no	—
276	D₃×Q₈	—	2	8	no	—
277	#237	—	2	24	no	—
278	D₃×D₄	—	2	24	no	—
279	#235	—	2	24	no	—
280	C₂×D₁₂	—	2	12	no	—
281	C₂×D₁₂	C₂³×C₃	1	3	yes	—
282	C₂×D₁₂	C₂³×C₃	1	6	yes	—
283	C₂×D₁₂	C₂³×C₃	1	6	yes	—
284	C₂×D₁₂	C₂³×C₃	1	6	yes	—
285	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₄×D₃	—	2	24	no	—
287	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
288	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
289	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
290	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
291	C₂×Dic₆	C₂³×C₃	1	6	yes	—
292	C₃×C₄⋊C₄	—	2	3	no	—
293	C₃×C₄⋊C₄	—	2	3	no	—
294	C₃×C₄⋊C₄	—	3	1	no	—
295	C₃×C₄⋊C₄	—	3	3	no	—
296	C₃×C₄⋊C₄	—	3	6	no	—
297	C₃×C₄⋊C₄	—	3	6	no	—
298	C₃×C₄⋊C₄	C₂²×D₃	1	3	yes	—
299	C₃×C₄⋊C₄	C₂²×D₃	1	3	yes	—
300	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
301	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
302	C₃×C₂²⋊C₄	—	2	6	no	—
303	C₃×C₂²⋊C₄	—	3	2	no	—
304	C₃×C₂²⋊C₄	—	3	6	no	—
305	C₃×C₂²⋊C₄	—	3	6	no	—
306	C₃×C₂²⋊C₄	—	3	6	no	—
307	C₃×C₂²⋊C₄	—	3	12	no	—
308	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
309	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
310	C₃×C₄²	—	2	1	no	—
311	C₃×C₄²	—	2	3	no	—
312	C₃×C₄²	—	2	3	no	—
313	C₃×C₄²	—	2	3	no	—
314	C₃×C₄²	C₂²×D₃	1	3	yes	—
315	C₃×C₄²	C₂²×D₃	1	3	yes	—
316	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
317	C₃×C₄²	C₂²×D₃	1	3	yes	—
318	C₃×C₄²	C₂³×C₃	1	3	yes	—
319	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
320	C₃×C₄²	C₂³×C₃	1	3	yes	—
321	C₃×C₄²	C₂³×C₃	1	3	yes	—
322	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
323	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
324	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
325	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
326	(C₂×D₃)⋊C₄	C₂³×C₃	1	12	yes	—
327	C₄⋊Dic₃	C₂³×C₃	1	3	yes	—
328	C₄⋊Dic₃	C₂³×C₃	1	6	yes	—
329	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
330	C₄⋊Dic₃	C₂³×C₃	1	6	yes	—
331	C₂²×C₃²	—	2	3	no	—
332	C₂²×C₃²	—	2	3	no	—
333	C₂²×C₃²	C₂²×D₄	1	6	yes	—
334	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
335	C₂×C₃×D₃	—	2	2	no	—
336	C₂×C₃×D₃	—	2	2	no	—
337	C₂×C₃×D₃	—	2	6	no	—
338	C₂×C₃×D₃	—	2	6	no	—
339	C₂×C₃×D₃	—	2	6	no	—
340	C₂×C₃×D₃	—	4	24	no	—
341	C₂×C₃×D₃	C₂×#41	1	4	yes	complemented
342	C₃²×C₄	—	2	1	no	—
343	C₃²×C₄	—	2	3	no	—
344	C₃²×C₄	—	2	3	no	—
345	C₃²×C₄	C₂²×D₄	1	6	yes	—
346	C₃²×C₄	C₂²×D₄	1	2	yes	—
347	C₃²×C₄	C₂×#41	1	2	yes	complemented
348	C₃×Dic₃	—	2	6	no	—
349	C₃×Dic₃	—	2	2	no	—
350	C₂×#41	—	3	2	no	—
351	C₂×#41	—	3	6	no	—
352	C₂×#41	—	3	6	no	—
353	C₂×#41	—	6	16	no	—
354	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
355	C₂²×Q₈	—	3	2	no	—
356	C₂²×D₄	—	3	6	no	—
357	C₂²×D₄	—	3	3	no	—
358	C₂³×C₄	—	3	6	no	—
359	C₄⋊Q₈	—	3	3	no	—
360	#127	—	3	3	no	—
361	#124	—	3	6	no	—
362	#123	—	3	12	no	—
363	C₂²⋊Q₈	—	3	6	no	—
364	C₂²⋊Q₈	—	3	6	no	—
365	#121	—	3	6	no	—
366	#121	—	3	6	no	—
367	#121	—	3	6	no	—
368	#121	—	3	6	no	—
369	#120	—	3	12	no	—
370	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
371	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
372	C₄×D₄	—	3	1	no	—
373	C₄×D₄	—	3	6	no	—
374	C₄×D₄	—	3	3	no	—
375	C₄×D₄	—	3	3	no	—
376	C₄×D₄	—	3	6	no	—
377	C₄×D₄	—	3	3	no	—
378	C₄×D₄	—	3	6	no	—
379	C₄×D₄	C₂×C₃×D₃	1	3	yes	complemented
380	C₄×D₄	C₂×C₃×D₃	1	3	yes	complemented
381	#117	C₂×C₃×D₃	1	3	yes	complemented
382	C₂×C₄⋊C₄	—	3	3	no	—
383	C₂×C₂²⋊C₄	—	3	6	no	—
384	C₂×C₄²	C₂×C₃×D₃	1	3	yes	complemented
385	C₂³×C₃	—	2	3	no	—
386	C₂³×C₃	—	3	2	no	—
387	C₂³×C₃	—	3	6	no	—
388	C₂³×C₃	—	6	12	no	—
389	C₂³×C₃	—	6	12	no	—
390	C₂³×C₃	—	12	6	no	—
391	C₂³×C₃	C₂³×D₃	1	3	yes	—
392	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
393	C₂²×D₃	—	2	12	no	—
394	C₂²×D₃	—	2	12	no	—
395	C₂²×D₃	—	4	6	no	—
396	C₂²×D₃	C₂⁴×C₃	1	6	yes	—
397	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
398	C₃×Q₈	—	2	4	no	—
399	C₃×Q₈	—	6	12	no	—
400	C₃×Q₈	C₂×D₁₂	1	4	yes	complemented
401	C₃×Q₈	C₂×C₃×D₄	1	4	yes	complemented
402	C₃×D₄	—	2	12	no	—
403	C₃×D₄	—	3	4	no	—
404	C₃×D₄	—	6	12	no	—
405	C₃×D₄	—	6	24	no	—
406	C₃×D₄	—	6	12	no	—
407	C₃×D₄	—	6	6	no	—
408	C₃×D₄	—	12	6	no	—
409	C₃×D₄	C₂×D₁₂	1	12	yes	complemented
410	C₃×D₄	C₂×C₃×D₄	1	12	yes	complemented
411	C₂×C₃×C₄	—	2	6	no	—
412	C₂×C₃×C₄	—	2	6	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	3	no	—
417	C₂×C₃×C₄	—	2	3	no	—
418	C₂×C₃×C₄	—	2	3	no	—
419	C₂×C₃×C₄	—	2	12	no	—
420	C₂×C₃×C₄	—	3	2	no	—
421	C₂×C₃×C₄	—	3	6	no	—
422	C₂×C₃×C₄	—	4	6	no	—
423	C₂×C₃×C₄	—	4	3	no	—
424	C₂×C₃×C₄	—	4	3	no	—
425	C₂×C₃×C₄	—	4	6	no	—
426	C₂×C₃×C₄	—	6	12	no	—
427	C₂×C₃×C₄	—	6	4	no	—
428	C₂×C₃×C₄	—	6	12	no	—
429	C₂×C₃×C₄	—	6	12	no	—
430	C₂×C₃×C₄	—	6	12	no	—
431	C₂×C₃×C₄	C₂×D₁₂	1	12	yes	complemented
432	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	complemented
433	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
434	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
435	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
436	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
437	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
438	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
439	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
440	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
441	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
442	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
443	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
444	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
445	#67	—	2	24	no	—
446	C₂×Dic₃	—	2	12	no	—
447	C₂×Dic₃	C₂⁴×C₃	1	6	yes	—
448	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
449	D₁₂	—	2	12	no	—
450	D₁₂	—	2	12	no	—
451	D₁₂	—	2	6	no	—
452	D₁₂	—	4	6	no	—
453	D₁₂	C₃×#41	1	4	yes	direct product factor
454	C₄×D₃	—	2	4	no	—
455	C₄×D₃	—	2	12	no	—
456	C₄×D₃	—	2	12	no	—
457	C₄×D₃	—	2	12	no	—
458	Dic₆	—	2	12	no	—
459	C₂×C₃²	—	2	6	no	—
460	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
461	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
462	C₂×C₃²	#585	1	1	yes	characteristic
463	C₃×D₃	—	2	4	no	—
464	C₃×D₃	—	4	6	no	—
465	C₂⁴	—	3	6	no	—
466	#41	—	6	8	no	—
467	#41	—	6	24	no	—
468	#41	—	6	24	no	—
469	#41	C₃×D₁₂	1	8	yes	direct product factor
470	C₂×Q₈	—	3	6	no	—
471	C₂×Q₈	—	6	8	no	—
472	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
473	C₂×D₄	—	3	12	no	—
474	C₂×D₄	—	3	1	no	—
475	C₂×D₄	—	3	6	no	—
476	C₂×D₄	—	3	3	no	—
477	C₂×D₄	—	3	6	no	—
478	C₂×D₄	—	3	6	no	—
479	C₂×D₄	—	6	12	no	—
480	C₂×D₄	—	6	24	no	—
481	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
482	C₂²×C₄	—	3	6	no	—
483	C₂²×C₄	—	3	2	no	—
484	C₂²×C₄	—	3	6	no	—
485	C₂²×C₄	—	3	6	no	—
486	C₂²×C₄	—	3	6	no	—
487	C₂²×C₄	—	6	24	no	—
488	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
489	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
490	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
491	C₄⋊C₄	—	3	1	no	—
492	C₄⋊C₄	—	3	3	no	—
493	C₄⋊C₄	—	3	6	no	—
494	C₄⋊C₄	—	3	6	no	—
495	C₄⋊C₄	C₂²×C₃×D₃	1	3	yes	—
496	C₄⋊C₄	C₂²×C₃×D₃	1	3	yes	—
497	C₂²⋊C₄	—	3	2	no	—
498	C₂²⋊C₄	—	3	6	no	—
499	C₂²⋊C₄	—	3	6	no	—
500	C₂²⋊C₄	—	3	6	no	—
501	C₂²⋊C₄	—	3	12	no	—
502	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
503	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
504	C₄²	C₂²×C₃×D₃	1	3	yes	—
505	C₄²	C₂²×C₃×D₃	1	3	yes	—
506	C₄²	C₂²×C₃×D₃	1	3	yes	—
507	C₂²×C₃	—	2	3	no	—
508	C₂²×C₃	—	2	3	no	—
509	C₂²×C₃	—	2	3	no	—
510	C₂²×C₃	—	2	3	no	—
511	C₂²×C₃	—	2	6	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	—	3	4	no	—
514	C₂²×C₃	—	4	3	no	—
515	C₂²×C₃	—	4	3	no	—
516	C₂²×C₃	—	6	2	no	—
517	C₂²×C₃	—	6	2	no	—
518	C₂²×C₃	—	6	6	no	—
519	C₂²×C₃	—	6	6	no	—
520	C₂²×C₃	—	6	6	no	—
521	C₂²×C₃	—	12	24	no	—
522	C₂²×C₃	C₂²×D₁₂	1	6	yes	—
523	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
524	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
525	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
526	C₂×D₃	—	2	2	no	—
527	C₂×D₃	—	2	2	no	—
528	C₂×D₃	—	2	6	no	—
529	C₂×D₃	—	2	6	no	—
530	C₂×D₃	—	2	6	no	—
531	C₂×D₃	—	4	24	no	—
532	C₂×D₃	C₂×C₃×#41	1	4	yes	complemented
533	C₃×C₄	—	2	2	no	—
534	C₃×C₄	—	2	3	no	—
535	C₃×C₄	—	2	1	no	—
536	C₃×C₄	—	2	3	no	—
537	C₃×C₄	—	2	3	no	—
538	C₃×C₄	—	2	3	no	—
539	C₃×C₄	—	2	1	no	—
540	C₃×C₄	—	2	2	no	—
541	C₃×C₄	—	2	6	no	—
542	C₃×C₄	—	2	2	no	—
543	C₃×C₄	—	4	3	no	—
544	C₃×C₄	—	4	3	no	—
545	C₃×C₄	—	6	2	no	—
546	C₃×C₄	—	6	6	no	—
547	C₃×C₄	C₂²×D₁₂	1	2	yes	—
548	C₃×C₄	C₂²×D₁₂	1	6	yes	—
549	C₃×C₄	D₃×#41	1	2	yes	complemented
550	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
551	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
552	C₃×C₄	C₂×C₃×#41	1	2	yes	complemented
553	Dic₃	—	2	6	no	—
554	Dic₃	—	2	2	no	—
555	C₃²	D₄×#41	1	1	yes	characteristic, complemented, Sylow
556	C₂³	—	3	2	no	—
557	C₂³	—	3	6	no	—
558	C₂³	—	6	12	no	—
559	C₂³	—	6	12	no	—
560	C₂³	—	12	6	no	—
561	C₂³	C₂³×C₃×D₃	1	3	yes	—
562	Q₈	—	6	12	no	—
563	Q₈	C₂×C₃×D₁₂	1	4	yes	complemented
564	D₄	—	3	4	no	—
565	D₄	—	6	12	no	—
566	D₄	—	6	24	no	—
567	D₄	—	6	12	no	—
568	D₄	—	6	6	no	—
569	D₄	—	12	6	no	—
570	D₄	C₂×C₃×D₁₂	1	12	yes	complemented
571	C₂×C₄	—	2	6	no	—
572	C₂×C₄	—	3	2	no	—
573	C₂×C₄	—	3	6	no	—
574	C₂×C₄	—	4	3	no	—
575	C₂×C₄	—	6	12	no	—
576	C₂×C₄	—	6	4	no	—
577	C₂×C₄	—	6	12	no	—
578	C₂×C₄	—	6	12	no	—
579	C₂×C₄	—	6	12	no	—
580	C₂×C₄	C₂×C₃×D₁₂	1	12	yes	complemented
581	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
582	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
583	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
584	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
586	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
587	C₂×C₃	—	2	6	no	—
588	C₂×C₃	—	2	6	no	—
589	C₂×C₃	—	2	1	no	—
590	C₂×C₃	—	2	1	no	—
591	C₂×C₃	—	2	1	no	—
592	C₂×C₃	—	4	6	no	—
593	C₂×C₃	—	6	4	no	—
594	C₂×C₃	—	12	6	no	—
595	C₂×C₃	C₂³×D₁₂	1	1	yes	characteristic
596	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
597	C₂×C₃	#5964	1	1	yes	characteristic
598	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
599	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
600	C₂×C₃	C₃×#585	1	1	yes	characteristic
601	D₃	—	2	4	no	—
602	D₃	—	4	6	no	—
603	C₂²	—	2	3	no	—
604	C₂²	—	2	3	no	—
605	C₂²	—	3	4	no	—
606	C₂²	—	6	2	no	—
607	C₂²	—	6	2	no	—
608	C₂²	—	6	6	no	—
609	C₂²	—	6	6	no	—
610	C₂²	—	6	6	no	—
611	C₂²	—	12	24	no	—
612	C₂²	C₂²×C₃×D₁₂	1	6	yes	—
613	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
614	C₄	—	2	3	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	3	no	—
617	C₄	—	6	2	no	—
618	C₄	—	6	6	no	—
619	C₄	C₂²×C₃×D₁₂	1	2	yes	—
620	C₄	C₂²×C₃×D₁₂	1	6	yes	—
621	C₄	C₃×D₃×#41	1	2	yes	complemented
622	C₃	—	2	1	no	—
623	C₃	#41×D₁₂	1	1	yes	characteristic, direct product factor
624	C₃	C₃×D₄×#41	1	1	yes	characteristic, complemented
625	C₂	—	2	6	no	—
626	C₂	—	6	4	no	—
627	C₂	—	12	6	no	—
628	C₂	C₂³×C₃×D₁₂	1	1	yes	characteristic
629	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
630	C₂	C₃×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×C₄×#41	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×C₄×#41	D₃
hypocenter	C₃	C₃×D₄×#41
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×#41	C₂	semidirect
2. C₃²×C₄×#41	C₂	semidirect
3. C₃×#5577	C₂	semidirect
4. C₃×#5576	C₂	semidirect
5. C₃×Q₈×D₁₂	C₂	semidirect
6. C₃×#5555	C₂	semidirect
7. C₃×#5554	C₂	semidirect
8. C₃×D₄×D₁₂	C₂	semidirect
9. C₃×#5524	C₂	semidirect
10. C₃×#5477	C₂	semidirect
11. C₂×C₃×C₄×D₁₂	C₂	semidirect
13. #41×D₁₂	C₃	direct (N × H)
16. C₂×C₃×#239	C₂²	semidirect
17. C₂×C₃×D₃×Q₈	C₂²	semidirect
18. C₂×C₃×#237	C₂²	semidirect
19. C₂×C₃×D₃×D₄	C₂²	semidirect
20. C₂×C₃×#235	C₂²	semidirect
22. C₂²×C₃×C₄×D₃	C₂²	semidirect
23. C₃²×C₄×Q₈	C₂²	semidirect
24. C₃²×C₄×Q₈	C₂²	semidirect
25. C₃²×C₄×D₄	C₂²	semidirect
26. C₃²×C₄×D₄	C₂²	semidirect
27. C₃²×#117	C₂²	semidirect
28. C₂×C₃²×C₄²	C₂²	semidirect
29. C₃×#930	C₂²	semidirect
30. C₃×#930	C₂²	semidirect
31. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
32. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
33. C₃×#897	C₂²	semidirect
34. C₃×#897	C₂²	semidirect
35. C₃×#895	C₂²	semidirect
36. C₃×#895	C₂²	semidirect
37. C₃×#886	C₂²	semidirect
38. C₃×#882	C₂²	semidirect
39. C₃×#875	C₂²	semidirect
40. C₃×#874	C₂²	semidirect
43. C₃×C₄×D₁₂	C₂²	semidirect
44. C₃×C₄×D₁₂	C₂²	semidirect
45. C₃×C₄×D₁₂	C₂²	semidirect
46. C₃×C₄×D₁₂	C₂²	semidirect
47. C₃×C₄×D₁₂	C₂²	semidirect
48. C₃×#869	C₂²	semidirect
50. C₂×D₃×#41	C₂×C₃	semidirect
60. C₃×C₄×#41	D₃	semidirect
61. C₃×C₄×#41	C₂×C₃	semidirect
63. #5577	C₂×C₃	semidirect
64. #5576	C₂×C₃	semidirect
65. Q₈×D₁₂	C₂×C₃	semidirect
66. #5555	C₂×C₃	semidirect
67. #5554	C₂×C₃	semidirect
68. D₄×D₁₂	C₂×C₃	semidirect
69. #5524	C₂×C₃	semidirect
70. #5477	C₂×C₃	semidirect
71. C₂×C₄×D₁₂	C₂×C₃	semidirect
73. C₃²×#41	D₄	semidirect
127. C₂×#239	C₂²×C₃	semidirect
128. C₂×D₃×Q₈	C₂²×C₃	semidirect
129. C₂×#237	C₂²×C₃	semidirect
130. C₂×D₃×D₄	C₂²×C₃	semidirect
131. C₂×#235	C₂²×C₃	semidirect
133. C₂²×C₄×D₃	C₂²×C₃	semidirect
147. C₃×C₄×Q₈	C₂×D₃	semidirect
148. C₃×C₄×Q₈	C₂×D₃	semidirect
149. C₃×C₄×Q₈	C₂²×C₃	semidirect
150. C₃×C₄×Q₈	C₂²×C₃	semidirect
160. C₃×C₄×D₄	C₂×D₃	semidirect
161. C₃×C₄×D₄	C₂×D₃	semidirect
162. C₃×C₄×D₄	C₂²×C₃	semidirect
163. C₃×C₄×D₄	C₂²×C₃	semidirect
165. C₃×#117	C₂×D₃	semidirect
166. C₃×#117	C₂²×C₃	semidirect
170. C₂×C₃×C₄²	C₂×D₃	semidirect
171. C₂×C₃×C₄²	C₂²×C₃	semidirect
172. #930	C₂²×C₃	semidirect
173. #930	C₂²×C₃	semidirect
174. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
175. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
176. #897	C₂²×C₃	semidirect
177. #897	C₂²×C₃	semidirect
178. #895	C₂²×C₃	semidirect
179. #895	C₂²×C₃	semidirect
180. #886	C₂²×C₃	semidirect
181. #882	C₂²×C₃	semidirect
182. #875	C₂²×C₃	semidirect
183. #874	C₂²×C₃	semidirect
186. C₄×D₁₂	C₂²×C₃	semidirect
187. C₄×D₁₂	C₂²×C₃	semidirect
188. C₄×D₁₂	C₂²×C₃	semidirect
189. C₄×D₁₂	C₂²×C₃	semidirect
190. C₄×D₁₂	C₂²×C₃	semidirect
191. #869	C₂²×C₃	semidirect
198. C₃²×Q₈	C₂×D₄	semidirect
199. C₃²×D₄	C₂×D₄	semidirect
202. C₂×C₃²×C₄	C₂×D₄	semidirect
217. C₃×D₁₂	#41	direct (N × H)
232. C₄×#41	C₃×D₃	semidirect
240. C₃×#41	D₁₂	direct (N × H)
241. C₃×#41	C₃×D₄	semidirect
341. C₂×C₃×D₃	C₂×#41	semidirect
347. C₃²×C₄	C₂×#41	semidirect
370. C₄×Q₈	C₂×C₃×D₃	semidirect
371. C₄×Q₈	C₂×C₃×D₃	semidirect
379. C₄×D₄	C₂×C₃×D₃	semidirect
380. C₄×D₄	C₂×C₃×D₃	semidirect
381. #117	C₂×C₃×D₃	semidirect
384. C₂×C₄²	C₂×C₃×D₃	semidirect
400. C₃×Q₈	C₂×D₁₂	semidirect
401. C₃×Q₈	C₂×C₃×D₄	semidirect
409. C₃×D₄	C₂×D₁₂	semidirect
410. C₃×D₄	C₂×C₃×D₄	semidirect
431. C₂×C₃×C₄	C₂×D₁₂	semidirect
432. C₂×C₃×C₄	C₂×C₃×D₄	semidirect
453. D₁₂	C₃×#41	direct (N × H)
469. #41	C₃×D₁₂	direct (N × H)
532. C₂×D₃	C₂×C₃×#41	semidirect
549. C₃×C₄	D₃×#41	semidirect
552. C₃×C₄	C₂×C₃×#41	semidirect
555. C₃²	D₄×#41	semidirect
563. Q₈	C₂×C₃×D₁₂	semidirect
570. D₄	C₂×C₃×D₁₂	semidirect
580. C₂×C₄	C₂×C₃×D₁₂	semidirect
621. C₄	C₃×D₃×#41	semidirect
623. C₃	#41×D₁₂	direct (N × H)
624. C₃	C₃×D₄×#41	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×#41	2
C₃²×C₄×#41	2
C₃×#5577	2
C₃×#5576	2
C₃×Q₈×D₁₂	2
C₃×#5555	2
C₃×#5554	2
C₃×D₄×D₁₂	2
C₃×#5524	2
C₃×#5477	2
C₂×C₃×C₄×D₁₂	2
C₃×D₄×#41	3
#41×D₁₂	3

Subgroups — C3×#41×D12 #11902766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#41×D₁₂ #11902766