Subgroups — C₃×C₄×D₃×#41 #11899944

Order 1152.

3611 conjugacy classes of subgroups.

The subgroup lattice has 600 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	1	yes	maximal, characteristic
2	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×#239	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×D₃×Q₈	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×D₃×D₄	C₂	1	6	yes	maximal, complemented
7	C₃×C₄×#237	C₂	1	6	yes	maximal, complemented
8	C₃×#5522	C₂	1	3	yes	maximal, complemented
9	C₃×D₃×#117	C₂	1	3	yes	maximal, complemented
10	C₃×C₄×#235	C₂	1	3	yes	maximal, complemented
11	C₂×C₃×C₄²×D₃	C₂	1	3	yes	maximal, complemented
12	C₂×C₃×C₄×#41	—	3	1	no	maximal
13	C₄×D₃×#41	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
15	C₃×D₃×#41	C₄	1	16	yes	direct product factor
16	C₂×C₃×#239	C₂²	1	1	yes	characteristic
17	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×#237	C₂²	1	3	yes	—
19	C₂×C₃×D₃×D₄	C₂²	1	3	yes	—
20	C₂×C₃×#235	C₂²	1	3	yes	—
21	C₂²×C₃×C₄×D₃	C₂²	1	6	yes	—
22	C₂²×C₃×C₄×D₃	C₂²	1	3	yes	—
23	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
24	C₃²×C₄×D₄	C₂²	1	6	yes	complemented
25	C₃²×#117	C₂²	1	3	yes	complemented
26	C₂×C₃²×C₄²	C₂²	1	3	yes	complemented
27	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
28	C₃×D₄×Dic₃	C₂²	1	6	yes	complemented
29	C₃×C₄×#67	C₂²	1	12	yes	complemented
30	C₃×#926	C₂²	1	3	yes	complemented
31	C₂×C₃×C₄×Dic₃	C₂²	1	3	yes	complemented
32	C₂×C₃×C₄×Dic₃	C₂²	1	6	yes	complemented
33	C₃×#893	C₂²	1	6	yes	complemented
34	C₃×#892	C₂²	1	6	yes	complemented
35	C₃×D₃×C₄⋊C₄	C₂²	1	6	yes	—
36	C₃×#887	C₂²	1	6	yes	complemented
37	C₃×#67⋊C₄	C₂²	1	12	yes	complemented
38	C₃×D₃×C₂²⋊C₄	C₂²	1	6	yes	—
39	C₃×#877	C₂²	1	6	yes	complemented
40	C₃×C₄×D₁₂	C₂²	1	6	yes	complemented
41	C₃×#872	C₂²	1	6	yes	complemented
42	C₃×C₄²×D₃	C₂²	1	3	yes	—
43	C₃×C₄²×D₃	C₂²	1	6	yes	—
44	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
45	C₃×C₄²×D₃	C₂²	1	3	yes	complemented
46	C₃×C₄²×D₃	C₂²	1	6	yes	complemented
47	C₃×C₄²×D₃	C₂²	1	3	yes	complemented
48	C₃×C₄×Dic₆	C₂²	1	6	yes	complemented
49	C₂²×C₃×#41	—	3	1	no	—
50	C₂×D₃×#41	C₂×C₃	1	1	yes	characteristic
51	C₃×C₄×#41	—	2	1	no	—
52	C₃×C₄×#41	—	3	1	no	—
53	C₃×C₄×#41	—	3	2	no	—
54	C₃×C₄×#41	—	3	6	no	—
55	C₃×C₄×#41	—	3	3	no	—
56	C₃×C₄×#41	—	3	3	no	—
57	C₃×C₄×#41	D₃	1	1	yes	characteristic, direct product factor
58	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×C₄×Q₈	—	3	2	no	—
60	C₂×C₃×C₄×D₄	—	3	6	no	—
61	C₂×C₃×#117	—	3	3	no	—
62	C₂²×C₃×C₄²	—	3	3	no	—
63	Dic₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
64	C₄×#239	C₂×C₃	1	2	yes	complemented
65	C₄×D₃×Q₈	C₂×C₃	1	2	yes	complemented
66	C₄×D₃×D₄	C₂×C₃	1	6	yes	complemented
67	C₄×#237	C₂×C₃	1	6	yes	complemented
68	#5522	C₂×C₃	1	3	yes	complemented
69	D₃×#117	C₂×C₃	1	3	yes	complemented
70	C₄×#235	C₂×C₃	1	3	yes	complemented
71	C₂×C₄²×D₃	C₂×C₃	1	3	yes	complemented
72	C₂³×C₃×D₃	C₂³	1	3	yes	—
73	C₃²×#41	C₂×C₄	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	6	yes	—
77	C₂²×C₃²×C₄	C₂³	1	3	yes	—
78	C₂×C₃×#67	C₂³	1	6	yes	—
79	C₂²×C₃×Dic₃	C₂³	1	6	yes	—
80	C₂²×C₃×Dic₃	C₂³	1	3	yes	—
81	C₃×#239	C₂×C₄	1	8	yes	complemented
82	C₃×D₃×Q₈	C₂×C₄	1	8	yes	complemented
83	C₃×#237	C₂×C₄	1	24	yes	complemented
84	C₃×D₃×D₄	C₂×C₄	1	24	yes	complemented
85	C₃×#235	C₂×C₄	1	24	yes	complemented
86	C₂×C₃×D₁₂	C₂³	1	3	yes	—
87	C₂×C₃×C₄×D₃	—	2	24	no	—
88	C₂×C₃×C₄×D₃	C₂×C₄	1	24	yes	complemented
89	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
90	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
91	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
92	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
93	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
95	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
96	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
97	C₂×C₃×Dic₆	C₂³	1	3	yes	—
98	C₃²×C₄⋊C₄	C₂³	1	6	yes	—
99	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
100	C₃²×C₄²	C₂³	1	3	yes	—
101	C₃²×C₄²	C₂³	1	6	yes	—
102	C₃²×C₄²	C₂³	1	1	yes	characteristic
103	C₃×#217	C₂³	1	6	yes	—
104	C₃×(C₂×D₃)⋊C₄	C₂³	1	12	yes	—
105	C₃×C₄⋊Dic₃	C₂³	1	6	yes	—
106	C₃×Dic₃⋊C₄	C₂³	1	12	yes	—
107	C₃×C₄×Dic₃	C₂³	1	6	yes	—
108	C₃×C₄×Dic₃	C₂³	1	6	yes	—
109	C₃×C₄×Dic₃	C₂³	1	6	yes	—
110	C₃×C₄×Dic₃	C₂³	1	2	yes	—
111	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
112	C₃×C₄×Dic₃	C₂³	1	3	yes	—
113	C₃×C₄×Dic₃	C₂³	1	6	yes	—
114	C₂×C₄×#41	—	3	1	no	Sylow
115	C₂×C₃×#41	—	2	1	no	—
116	C₂×C₃×#41	—	3	16	no	—
117	C₂×C₃×#41	—	3	1	no	—
118	C₂×C₃×#41	—	3	3	no	—
119	C₂×C₃×#41	—	3	3	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	1	no	—
123	C₂²×C₃×D₄	—	3	3	no	—
124	C₂³×C₃×C₄	—	3	3	no	—
125	C₂³×C₃×C₄	—	3	6	no	—
126	D₃×#41	C₃×C₄	1	16	yes	direct product factor
127	C₂×#239	C₂²×C₃	1	1	yes	characteristic
128	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
129	C₂×#237	C₂²×C₃	1	3	yes	—
130	C₂×D₃×D₄	C₂²×C₃	1	3	yes	—
131	C₂×#235	C₂²×C₃	1	3	yes	—
132	C₂²×C₄×D₃	C₂²×C₃	1	6	yes	—
133	C₂²×C₄×D₃	C₂²×C₃	1	3	yes	—
134	C₃×C₄×Q₈	—	2	2	no	—
135	C₃×C₄×Q₈	—	3	2	no	—
136	C₃×C₄×Q₈	—	3	6	no	—
137	C₃×C₄×Q₈	—	3	6	no	—
138	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
139	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
140	C₃×C₄×D₄	—	2	6	no	—
141	C₃×C₄×D₄	—	3	6	no	—
142	C₃×C₄×D₄	—	3	12	no	—
143	C₃×C₄×D₄	—	3	6	no	—
144	C₃×C₄×D₄	—	3	12	no	—
145	C₃×C₄×D₄	—	3	6	no	—
146	C₃×C₄×D₄	C₂×D₃	1	6	yes	complemented
147	C₃×C₄×D₄	C₂²×C₃	1	6	yes	complemented
148	C₃×#117	—	2	3	no	—
149	C₃×#117	—	3	3	no	—
150	C₃×#117	—	3	6	no	—
151	C₃×#117	—	3	6	no	—
152	C₃×#117	—	3	6	no	—
153	C₃×#117	C₂×D₃	1	3	yes	complemented
154	C₃×#117	C₂²×C₃	1	3	yes	complemented
155	C₂×C₃×C₄⋊C₄	—	3	6	no	—
156	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
157	C₂×C₃×C₄²	—	2	3	no	—
158	C₂×C₃×C₄²	—	3	6	no	—
159	C₂×C₃×C₄²	—	3	3	no	—
160	C₂×C₃×C₄²	—	3	3	no	—
161	C₂×C₃×C₄²	—	3	6	no	—
162	C₂×C₃×C₄²	—	3	6	no	—
163	C₂×C₃×C₄²	—	3	3	no	—
164	C₂×C₃×C₄²	—	3	1	no	—
165	C₂×C₃×C₄²	—	3	3	no	—
166	C₂×C₃×C₄²	C₂×D₃	1	3	yes	complemented
167	C₂×C₃×C₄²	C₂²×C₃	1	3	yes	complemented
168	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
169	D₄×Dic₃	C₂²×C₃	1	6	yes	complemented
170	C₄×#67	C₂²×C₃	1	12	yes	complemented
171	#926	C₂²×C₃	1	3	yes	complemented
172	C₂×C₄×Dic₃	C₂²×C₃	1	3	yes	complemented
173	C₂×C₄×Dic₃	C₂²×C₃	1	6	yes	complemented
174	#893	C₂²×C₃	1	6	yes	complemented
175	#892	C₂²×C₃	1	6	yes	complemented
176	D₃×C₄⋊C₄	C₂²×C₃	1	6	yes	—
177	#887	C₂²×C₃	1	6	yes	complemented
178	#67⋊C₄	C₂²×C₃	1	12	yes	complemented
179	D₃×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
180	#877	C₂²×C₃	1	6	yes	complemented
181	C₄×D₁₂	C₂²×C₃	1	6	yes	complemented
182	#872	C₂²×C₃	1	6	yes	complemented
183	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
184	C₄²×D₃	C₂²×C₃	1	3	yes	—
185	C₄²×D₃	C₂²×C₃	1	6	yes	—
186	C₄²×D₃	C₂²×C₃	1	3	yes	complemented
187	C₄²×D₃	C₂²×C₃	1	3	yes	complemented
188	C₄²×D₃	C₂²×C₃	1	6	yes	complemented
189	C₄×Dic₆	C₂²×C₃	1	6	yes	complemented
190	C₂³×C₃²	C₂⁴	1	3	yes	—
191	C₂²×C₃×D₃	—	2	12	no	—
192	C₂²×C₃×D₃	C₂²×C₄	1	12	yes	—
193	C₂²×C₃×D₃	C₂⁴	1	3	yes	—
194	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
195	C₃²×Q₈	C₂²×C₄	1	4	yes	complemented
196	C₃²×D₄	C₂²×C₄	1	12	yes	complemented
197	C₂×C₃²×C₄	—	2	12	no	—
198	C₂×C₃²×C₄	C₂²×C₄	1	12	yes	complemented
199	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
200	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
201	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
202	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
203	C₃×#67	C₂²×C₄	1	24	yes	complemented
204	C₂×C₃×Dic₃	—	2	12	no	—
205	C₂×C₃×Dic₃	C₂²×C₄	1	12	yes	complemented
206	C₂×C₃×Dic₃	C₂⁴	1	6	yes	—
207	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
208	C₂×C₃×Dic₃	C₂⁴	1	3	yes	—
209	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
210	C₃×D₁₂	C₂²×C₄	1	12	yes	complemented
211	C₃×C₄×D₃	—	2	12	no	—
212	C₃×C₄×D₃	—	2	12	no	—
213	C₃×C₄×D₃	—	2	12	no	—
214	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
215	C₃×C₄×D₃	C₂²×C₄	1	12	yes	—
216	C₃×C₄×D₃	C₂²×C₄	1	12	yes	complemented
217	C₃×C₄×D₃	C₂²×C₄	1	12	yes	complemented
218	C₃×C₄×D₃	#41	1	8	yes	direct product factor
219	C₃×Dic₆	C₂²×C₄	1	12	yes	complemented
220	C₂²×#41	—	3	1	no	—
221	C₄×#41	—	3	1	no	—
222	C₄×#41	—	3	2	no	—
223	C₄×#41	—	3	6	no	—
224	C₄×#41	—	3	3	no	—
225	C₄×#41	—	3	3	no	—
226	C₄×#41	C₃×D₃	1	1	yes	characteristic, direct product factor
227	C₂×C₄×Q₈	—	3	2	no	—
228	C₂×C₄×D₄	—	3	6	no	—
229	C₂×#117	—	3	3	no	—
230	C₂²×C₄²	—	3	3	no	—
231	C₂⁴×C₃	—	3	3	no	—
232	C₂³×D₃	C₂³×C₃	1	3	yes	—
233	C₃×#41	—	2	8	no	—
234	C₃×#41	—	3	8	no	—
235	C₃×#41	—	3	24	no	—
236	C₃×#41	—	3	24	no	—
237	C₃×#41	C₄×D₃	1	8	yes	direct product factor
238	C₃×#41	C₂×C₃×C₄	1	8	yes	complemented
239	C₂×C₃×Q₈	—	2	1	no	—
240	C₂×C₃×Q₈	—	3	8	no	—
241	C₂×C₃×Q₈	—	3	3	no	—
242	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
243	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₃×D₄	—	2	3	no	—
245	C₂×C₃×D₄	—	3	6	no	—
246	C₂×C₃×D₄	—	3	24	no	—
247	C₂×C₃×D₄	—	3	3	no	—
248	C₂×C₃×D₄	C₂²×D₃	1	3	yes	—
249	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
250	C₂²×C₃×C₄	—	2	3	no	—
251	C₂²×C₃×C₄	—	2	6	no	—
252	C₂²×C₃×C₄	—	3	3	no	—
253	C₂²×C₃×C₄	—	3	24	no	—
254	C₂²×C₃×C₄	—	3	1	no	—
255	C₂²×C₃×C₄	—	3	2	no	—
256	C₂²×C₃×C₄	—	3	3	no	—
257	C₂²×C₃×C₄	—	3	3	no	—
258	C₂²×C₃×C₄	—	3	3	no	—
259	C₂²×C₃×C₄	—	3	6	no	—
260	C₂²×C₃×C₄	—	3	6	no	—
261	C₂²×C₃×C₄	—	3	6	no	—
262	C₂²×C₃×C₄	—	3	6	no	—
263	C₂²×C₃×C₄	—	6	24	no	—
264	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
265	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
266	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
267	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
268	C₂×#67	C₂³×C₃	1	6	yes	—
269	C₂²×Dic₃	C₂³×C₃	1	6	yes	—
270	C₂²×Dic₃	C₂³×C₃	1	3	yes	—
271	#239	C₂×C₃×C₄	1	8	yes	complemented
272	D₃×Q₈	C₂×C₃×C₄	1	8	yes	complemented
273	#237	C₂×C₃×C₄	1	24	yes	complemented
274	D₃×D₄	C₂×C₃×C₄	1	24	yes	complemented
275	#235	C₂×C₃×C₄	1	24	yes	complemented
276	C₂×D₁₂	C₂³×C₃	1	3	yes	—
277	C₂×C₄×D₃	—	2	24	no	—
278	C₂×C₄×D₃	C₂×C₃×C₄	1	24	yes	complemented
279	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
280	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
281	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
282	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
284	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
285	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
286	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
287	C₂×Dic₆	C₂³×C₃	1	3	yes	—
288	C₃×C₄⋊C₄	—	2	6	no	—
289	C₃×C₄⋊C₄	—	3	12	no	—
290	C₃×C₄⋊C₄	—	3	6	no	—
291	C₃×C₄⋊C₄	C₂²×D₃	1	6	yes	—
292	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
293	C₃×C₂²⋊C₄	—	2	6	no	—
294	C₃×C₂²⋊C₄	—	3	6	no	—
295	C₃×C₂²⋊C₄	—	3	12	no	—
296	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
297	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
298	C₃×C₄²	—	2	1	no	—
299	C₃×C₄²	—	2	3	no	—
300	C₃×C₄²	—	2	6	no	—
301	C₃×C₄²	—	3	1	no	—
302	C₃×C₄²	—	3	2	no	—
303	C₃×C₄²	—	3	6	no	—
304	C₃×C₄²	—	3	3	no	—
305	C₃×C₄²	—	3	6	no	—
306	C₃×C₄²	—	3	6	no	—
307	C₃×C₄²	—	3	6	no	—
308	C₃×C₄²	C₂²×D₃	1	3	yes	—
309	C₃×C₄²	C₂²×D₃	1	6	yes	—
310	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
311	C₃×C₄²	C₂³×C₃	1	6	yes	—
312	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
313	C₃×C₄²	C₂³×C₃	1	3	yes	—
314	#217	C₂³×C₃	1	6	yes	—
315	(C₂×D₃)⋊C₄	C₂³×C₃	1	12	yes	—
316	C₄⋊Dic₃	C₂³×C₃	1	6	yes	—
317	Dic₃⋊C₄	C₂³×C₃	1	12	yes	—
318	C₄×Dic₃	C₂³×C₃	1	6	yes	—
319	C₄×Dic₃	C₂³×C₃	1	2	yes	—
320	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
321	C₄×Dic₃	C₂³×C₃	1	3	yes	—
322	C₄×Dic₃	C₂³×C₃	1	6	yes	—
323	C₄×Dic₃	C₂³×C₃	1	6	yes	—
324	C₄×Dic₃	C₂³×C₃	1	6	yes	—
325	C₂²×C₃²	—	2	6	no	—
326	C₂²×C₃²	C₂³×C₄	1	6	yes	—
327	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
328	C₂×C₃×D₃	—	2	6	no	—
329	C₂×C₃×D₃	—	2	24	no	—
330	C₂×C₃×D₃	C₂³×C₄	1	6	yes	—
331	C₂×C₃×D₃	C₂³×C₄	1	2	yes	—
332	C₂×C₃×D₃	C₂×#41	1	4	yes	—
333	C₃²×C₄	—	2	6	no	—
334	C₃²×C₄	C₂³×C₄	1	6	yes	—
335	C₃²×C₄	C₂³×C₄	1	2	yes	—
336	C₃²×C₄	C₂×#41	1	4	yes	complemented
337	C₃×Dic₃	—	2	6	no	—
338	C₃×Dic₃	C₂³×C₄	1	6	yes	—
339	C₃×Dic₃	C₂³×C₄	1	2	yes	—
340	C₃×Dic₃	C₂×#41	1	4	yes	complemented
341	C₂×#41	—	3	16	no	—
342	C₂×#41	—	3	1	no	—
343	C₂×#41	—	3	3	no	—
344	C₂×#41	—	3	3	no	—
345	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
346	C₂²×Q₈	—	3	1	no	—
347	C₂²×D₄	—	3	3	no	—
348	C₂³×C₄	—	3	3	no	—
349	C₂³×C₄	—	3	6	no	—
350	C₄×Q₈	—	3	2	no	—
351	C₄×Q₈	—	3	6	no	—
352	C₄×Q₈	—	3	6	no	—
353	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
354	C₄×D₄	—	3	6	no	—
355	C₄×D₄	—	3	12	no	—
356	C₄×D₄	—	3	6	no	—
357	C₄×D₄	—	3	12	no	—
358	C₄×D₄	—	3	6	no	—
359	C₄×D₄	C₂×C₃×D₃	1	6	yes	complemented
360	#117	—	3	3	no	—
361	#117	—	3	6	no	—
362	#117	—	3	6	no	—
363	#117	—	3	6	no	—
364	#117	C₂×C₃×D₃	1	3	yes	complemented
365	C₂×C₄⋊C₄	—	3	6	no	—
366	C₂×C₂²⋊C₄	—	3	6	no	—
367	C₂×C₄²	—	3	6	no	—
368	C₂×C₄²	—	3	3	no	—
369	C₂×C₄²	—	3	3	no	—
370	C₂×C₄²	—	3	6	no	—
371	C₂×C₄²	—	3	6	no	—
372	C₂×C₄²	—	3	3	no	—
373	C₂×C₄²	—	3	3	no	—
374	C₂×C₄²	—	3	1	no	—
375	C₂×C₄²	C₂×C₃×D₃	1	3	yes	complemented
376	C₂³×C₃	—	2	3	no	—
377	C₂³×C₃	—	3	1	no	—
378	C₂³×C₃	—	3	12	no	—
379	C₂³×C₃	—	3	3	no	—
380	C₂³×C₃	—	6	12	no	—
381	C₂³×C₃	C₂³×D₃	1	3	yes	—
382	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
383	C₂²×D₃	—	2	12	no	—
384	C₂²×D₃	C₂²×C₃×C₄	1	12	yes	—
385	C₂²×D₃	C₂⁴×C₃	1	3	yes	—
386	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
387	C₃×Q₈	—	2	4	no	—
388	C₃×Q₈	—	3	12	no	—
389	C₃×Q₈	C₂×C₄×D₃	1	4	yes	complemented
390	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	complemented
391	C₃×D₄	—	2	12	no	—
392	C₃×D₄	—	3	24	no	—
393	C₃×D₄	—	3	12	no	—
394	C₃×D₄	C₂×C₄×D₃	1	12	yes	complemented
395	C₃×D₄	C₂²×C₃×C₄	1	12	yes	complemented
396	C₂×C₃×C₄	—	2	12	no	—
397	C₂×C₃×C₄	—	2	12	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	3	no	—
401	C₂×C₃×C₄	—	2	6	no	—
402	C₂×C₃×C₄	—	2	12	no	—
403	C₂×C₃×C₄	—	3	12	no	—
404	C₂×C₃×C₄	—	3	1	no	—
405	C₂×C₃×C₄	—	3	2	no	—
406	C₂×C₃×C₄	—	3	3	no	—
407	C₂×C₃×C₄	—	3	4	no	—
408	C₂×C₃×C₄	—	3	12	no	—
409	C₂×C₃×C₄	—	3	12	no	—
410	C₂×C₃×C₄	—	3	12	no	—
411	C₂×C₃×C₄	—	3	8	no	—
412	C₂×C₃×C₄	—	3	6	no	—
413	C₂×C₃×C₄	—	4	12	no	—
414	C₂×C₃×C₄	—	6	12	no	—
415	C₂×C₃×C₄	—	6	12	no	—
416	C₂×C₃×C₄	—	6	12	no	—
417	C₂×C₃×C₄	—	6	12	no	—
418	C₂×C₃×C₄	C₂×C₄×D₃	1	12	yes	complemented
419	C₂×C₃×C₄	C₂²×C₃×C₄	1	12	yes	complemented
420	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
421	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
423	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
424	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
425	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
426	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
427	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
428	#67	C₂²×C₃×C₄	1	24	yes	complemented
429	C₂×Dic₃	—	2	12	no	—
430	C₂×Dic₃	C₂²×C₃×C₄	1	12	yes	complemented
431	C₂×Dic₃	C₂⁴×C₃	1	6	yes	—
432	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
433	C₂×Dic₃	C₂⁴×C₃	1	3	yes	—
434	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
435	D₁₂	C₂²×C₃×C₄	1	12	yes	complemented
436	C₄×D₃	—	2	12	no	—
437	C₄×D₃	—	2	12	no	—
438	C₄×D₃	—	2	12	no	—
439	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
440	C₄×D₃	C₂²×C₃×C₄	1	12	yes	—
441	C₄×D₃	C₂²×C₃×C₄	1	12	yes	complemented
442	C₄×D₃	C₂²×C₃×C₄	1	12	yes	complemented
443	C₄×D₃	C₃×#41	1	8	yes	direct product factor
444	Dic₆	C₂²×C₃×C₄	1	12	yes	complemented
445	C₂×C₃²	—	2	6	no	—
446	C₂×C₃²	C₂⁴×C₄	1	1	yes	characteristic
447	C₂×C₃²	C₂²×#41	1	2	yes	—
448	C₃×D₃	—	2	6	no	—
449	C₃×D₃	C₄×#41	1	4	yes	direct product factor
450	C₂⁴	—	3	3	no	—
451	#41	—	3	8	no	—
452	#41	—	3	24	no	—
453	#41	—	3	24	no	—
454	#41	C₃×C₄×D₃	1	8	yes	direct product factor
455	C₂×Q₈	—	3	8	no	—
456	C₂×Q₈	—	3	3	no	—
457	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
458	C₂×D₄	—	3	6	no	—
459	C₂×D₄	—	3	24	no	—
460	C₂×D₄	—	3	3	no	—
461	C₂×D₄	C₂²×C₃×D₃	1	3	yes	—
462	C₂²×C₄	—	3	3	no	—
463	C₂²×C₄	—	3	1	no	—
464	C₂²×C₄	—	3	2	no	—
465	C₂²×C₄	—	3	3	no	—
466	C₂²×C₄	—	3	3	no	—
467	C₂²×C₄	—	3	3	no	—
468	C₂²×C₄	—	3	24	no	—
469	C₂²×C₄	—	3	6	no	—
470	C₂²×C₄	—	3	6	no	—
471	C₂²×C₄	—	3	6	no	—
472	C₂²×C₄	—	3	6	no	—
473	C₂²×C₄	—	6	24	no	—
474	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
475	C₂²×C₄	C₂²×C₃×D₃	1	3	yes	—
476	C₄⋊C₄	—	3	12	no	—
477	C₄⋊C₄	—	3	6	no	—
478	C₄⋊C₄	C₂²×C₃×D₃	1	6	yes	—
479	C₂²⋊C₄	—	3	6	no	—
480	C₂²⋊C₄	—	3	12	no	—
481	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
482	C₄²	—	3	1	no	—
483	C₄²	—	3	2	no	—
484	C₄²	—	3	6	no	—
485	C₄²	—	3	3	no	—
486	C₄²	—	3	6	no	—
487	C₄²	—	3	6	no	—
488	C₄²	—	3	6	no	—
489	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
490	C₄²	C₂²×C₃×D₃	1	3	yes	—
491	C₄²	C₂²×C₃×D₃	1	6	yes	—
492	C₂²×C₃	—	2	6	no	—
493	C₂²×C₃	—	2	6	no	—
494	C₂²×C₃	—	2	6	no	—
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	3	2	no	—
497	C₂²×C₃	—	3	4	no	—
498	C₂²×C₃	—	3	6	no	—
499	C₂²×C₃	—	4	6	no	—
500	C₂²×C₃	—	6	24	no	—
501	C₂²×C₃	—	6	6	no	—
502	C₂²×C₃	C₂²×C₄×D₃	1	6	yes	—
503	C₂²×C₃	C₂³×C₃×C₄	1	6	yes	—
504	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
505	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
506	C₂×D₃	—	2	6	no	—
507	C₂×D₃	—	2	24	no	—
508	C₂×D₃	C₂³×C₃×C₄	1	6	yes	—
509	C₂×D₃	C₂³×C₃×C₄	1	2	yes	—
510	C₂×D₃	C₂×C₃×#41	1	4	yes	—
511	C₃×C₄	—	2	6	no	—
512	C₃×C₄	—	2	6	no	—
513	C₃×C₄	—	2	2	no	—
514	C₃×C₄	—	2	6	no	—
515	C₃×C₄	—	2	4	no	—
516	C₃×C₄	—	3	2	no	—
517	C₃×C₄	—	3	6	no	—
518	C₃×C₄	—	3	4	no	—
519	C₃×C₄	—	4	6	no	—
520	C₃×C₄	—	6	6	no	—
521	C₃×C₄	C₂²×C₄×D₃	1	2	yes	—
522	C₃×C₄	C₂²×C₄×D₃	1	6	yes	—
523	C₃×C₄	D₃×#41	1	4	yes	direct product factor
524	C₃×C₄	C₂³×C₃×C₄	1	6	yes	—
525	C₃×C₄	C₂³×C₃×C₄	1	2	yes	—
526	C₃×C₄	C₂×C₃×#41	1	4	yes	complemented
527	Dic₃	—	2	6	no	—
528	Dic₃	C₂³×C₃×C₄	1	6	yes	—
529	Dic₃	C₂³×C₃×C₄	1	2	yes	—
530	Dic₃	C₂×C₃×#41	1	4	yes	complemented
531	C₃²	C₂×C₄×#41	1	1	yes	characteristic, complemented, Sylow
532	C₂³	—	3	1	no	—
533	C₂³	—	3	12	no	—
534	C₂³	—	3	3	no	—
535	C₂³	—	6	12	no	—
536	C₂³	C₂³×C₃×D₃	1	3	yes	—
537	Q₈	—	3	12	no	—
538	Q₈	C₂×C₃×C₄×D₃	1	4	yes	complemented
539	D₄	—	3	24	no	—
540	D₄	—	3	12	no	—
541	D₄	C₂×C₃×C₄×D₃	1	12	yes	complemented
542	C₂×C₄	—	2	12	no	—
543	C₂×C₄	—	3	12	no	—
544	C₂×C₄	—	3	1	no	—
545	C₂×C₄	—	3	2	no	—
546	C₂×C₄	—	3	3	no	—
547	C₂×C₄	—	3	4	no	—
548	C₂×C₄	—	3	12	no	—
549	C₂×C₄	—	3	12	no	—
550	C₂×C₄	—	3	12	no	—
551	C₂×C₄	—	3	8	no	—
552	C₂×C₄	—	3	6	no	—
553	C₂×C₄	—	6	12	no	—
554	C₂×C₄	—	6	12	no	—
555	C₂×C₄	—	6	12	no	—
556	C₂×C₄	—	6	12	no	—
557	C₂×C₄	C₂×C₃×C₄×D₃	1	12	yes	complemented
558	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
559	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
560	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
561	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
562	C₂×C₃	—	2	6	no	—
563	C₂×C₃	—	2	6	no	—
564	C₂×C₃	—	2	1	no	—
565	C₂×C₃	—	2	2	no	—
566	C₂×C₃	—	3	4	no	—
567	C₂×C₃	—	4	6	no	—
568	C₂×C₃	—	6	6	no	—
569	C₂×C₃	C₂³×C₄×D₃	1	1	yes	characteristic
570	C₂×C₃	C₂×D₃×#41	1	2	yes	—
571	C₂×C₃	C₂⁴×C₃×C₄	1	1	yes	characteristic
572	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
573	D₃	—	2	6	no	—
574	D₃	C₃×C₄×#41	1	4	yes	direct product factor
575	C₂²	—	2	6	no	—
576	C₂²	—	3	2	no	—
577	C₂²	—	3	4	no	—
578	C₂²	—	3	6	no	—
579	C₂²	—	6	24	no	—
580	C₂²	—	6	6	no	—
581	C₂²	C₂²×C₃×C₄×D₃	1	6	yes	—
582	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
583	C₄	—	2	6	no	—
584	C₄	—	3	2	no	—
585	C₄	—	3	6	no	—
586	C₄	—	3	4	no	—
587	C₄	—	6	6	no	—
588	C₄	C₂²×C₃×C₄×D₃	1	2	yes	—
589	C₄	C₂²×C₃×C₄×D₃	1	6	yes	—
590	C₄	C₃×D₃×#41	1	4	yes	direct product factor
591	C₃	—	2	1	no	—
592	C₃	C₄×D₃×#41	1	1	yes	characteristic, direct product factor
593	C₃	C₂×C₃×C₄×#41	1	1	yes	characteristic, complemented
594	C₂	—	2	6	no	—
595	C₂	—	3	4	no	—
596	C₂	—	6	6	no	—
597	C₂	C₂³×C₃×C₄×D₃	1	1	yes	characteristic
598	C₂	C₂×C₃×D₃×#41	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂²×D₃
commutator	C₂×C₃	C₂⁴×C₃×C₄
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×C₄×#41	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂×C₃×D₃×#41	C₂
cosocle	C₂²×C₃	C₂⁵×C₃
hypercenter	C₃×C₄×#41	D₃
hypocenter	C₃	C₂×C₃×C₄×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄² ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×#41	C₂	semidirect
3. C₃×Dic₃×#41	C₂	semidirect
4. C₃×C₄×#239	C₂	semidirect
5. C₃×C₄×D₃×Q₈	C₂	semidirect
6. C₃×C₄×D₃×D₄	C₂	semidirect
7. C₃×C₄×#237	C₂	semidirect
8. C₃×#5522	C₂	semidirect
9. C₃×D₃×#117	C₂	semidirect
10. C₃×C₄×#235	C₂	semidirect
11. C₂×C₃×C₄²×D₃	C₂	semidirect
13. C₄×D₃×#41	C₃	direct (N × H)
15. C₃×D₃×#41	C₄	direct (N × H)
23. C₃²×C₄×Q₈	C₂²	semidirect
24. C₃²×C₄×D₄	C₂²	semidirect
25. C₃²×#117	C₂²	semidirect
26. C₂×C₃²×C₄²	C₂²	semidirect
27. C₃×Q₈×Dic₃	C₂²	semidirect
28. C₃×D₄×Dic₃	C₂²	semidirect
29. C₃×C₄×#67	C₂²	semidirect
30. C₃×#926	C₂²	semidirect
31. C₂×C₃×C₄×Dic₃	C₂²	semidirect
32. C₂×C₃×C₄×Dic₃	C₂²	semidirect
33. C₃×#893	C₂²	semidirect
34. C₃×#892	C₂²	semidirect
36. C₃×#887	C₂²	semidirect
37. C₃×#67⋊C₄	C₂²	semidirect
39. C₃×#877	C₂²	semidirect
40. C₃×C₄×D₁₂	C₂²	semidirect
41. C₃×#872	C₂²	semidirect
45. C₃×C₄²×D₃	C₂²	semidirect
46. C₃×C₄²×D₃	C₂²	semidirect
47. C₃×C₄²×D₃	C₂²	semidirect
48. C₃×C₄×Dic₆	C₂²	semidirect
57. C₃×C₄×#41	D₃	direct (N × H)
58. C₃×C₄×#41	C₂×C₃	semidirect
63. Dic₃×#41	C₂×C₃	semidirect
64. C₄×#239	C₂×C₃	semidirect
65. C₄×D₃×Q₈	C₂×C₃	semidirect
66. C₄×D₃×D₄	C₂×C₃	semidirect
67. C₄×#237	C₂×C₃	semidirect
68. #5522	C₂×C₃	semidirect
69. D₃×#117	C₂×C₃	semidirect
70. C₄×#235	C₂×C₃	semidirect
71. C₂×C₄²×D₃	C₂×C₃	semidirect
73. C₃²×#41	C₂×C₄	semidirect
81. C₃×#239	C₂×C₄	semidirect
82. C₃×D₃×Q₈	C₂×C₄	semidirect
83. C₃×#237	C₂×C₄	semidirect
84. C₃×D₃×D₄	C₂×C₄	semidirect
85. C₃×#235	C₂×C₄	semidirect
88. C₂×C₃×C₄×D₃	C₂×C₄	semidirect
126. D₃×#41	C₃×C₄	direct (N × H)
138. C₃×C₄×Q₈	C₂×D₃	semidirect
139. C₃×C₄×Q₈	C₂²×C₃	semidirect
146. C₃×C₄×D₄	C₂×D₃	semidirect
147. C₃×C₄×D₄	C₂²×C₃	semidirect
153. C₃×#117	C₂×D₃	semidirect
154. C₃×#117	C₂²×C₃	semidirect
166. C₂×C₃×C₄²	C₂×D₃	semidirect
167. C₂×C₃×C₄²	C₂²×C₃	semidirect
168. Q₈×Dic₃	C₂²×C₃	semidirect
169. D₄×Dic₃	C₂²×C₃	semidirect
170. C₄×#67	C₂²×C₃	semidirect
171. #926	C₂²×C₃	semidirect
172. C₂×C₄×Dic₃	C₂²×C₃	semidirect
173. C₂×C₄×Dic₃	C₂²×C₃	semidirect
174. #893	C₂²×C₃	semidirect
175. #892	C₂²×C₃	semidirect
177. #887	C₂²×C₃	semidirect
178. #67⋊C₄	C₂²×C₃	semidirect
180. #877	C₂²×C₃	semidirect
181. C₄×D₁₂	C₂²×C₃	semidirect
182. #872	C₂²×C₃	semidirect
186. C₄²×D₃	C₂²×C₃	semidirect
187. C₄²×D₃	C₂²×C₃	semidirect
188. C₄²×D₃	C₂²×C₃	semidirect
189. C₄×Dic₆	C₂²×C₃	semidirect
195. C₃²×Q₈	C₂²×C₄	semidirect
196. C₃²×D₄	C₂²×C₄	semidirect
198. C₂×C₃²×C₄	C₂²×C₄	semidirect
203. C₃×#67	C₂²×C₄	semidirect
205. C₂×C₃×Dic₃	C₂²×C₄	semidirect
210. C₃×D₁₂	C₂²×C₄	semidirect
216. C₃×C₄×D₃	C₂²×C₄	semidirect
217. C₃×C₄×D₃	C₂²×C₄	semidirect
218. C₃×C₄×D₃	#41	direct (N × H)
219. C₃×Dic₆	C₂²×C₄	semidirect
226. C₄×#41	C₃×D₃	direct (N × H)
237. C₃×#41	C₄×D₃	direct (N × H)
238. C₃×#41	C₂×C₃×C₄	semidirect
271. #239	C₂×C₃×C₄	semidirect
272. D₃×Q₈	C₂×C₃×C₄	semidirect
273. #237	C₂×C₃×C₄	semidirect
274. D₃×D₄	C₂×C₃×C₄	semidirect
275. #235	C₂×C₃×C₄	semidirect
278. C₂×C₄×D₃	C₂×C₃×C₄	semidirect
336. C₃²×C₄	C₂×#41	semidirect
340. C₃×Dic₃	C₂×#41	semidirect
353. C₄×Q₈	C₂×C₃×D₃	semidirect
359. C₄×D₄	C₂×C₃×D₃	semidirect
364. #117	C₂×C₃×D₃	semidirect
375. C₂×C₄²	C₂×C₃×D₃	semidirect
389. C₃×Q₈	C₂×C₄×D₃	semidirect
390. C₃×Q₈	C₂²×C₃×C₄	semidirect
394. C₃×D₄	C₂×C₄×D₃	semidirect
395. C₃×D₄	C₂²×C₃×C₄	semidirect
418. C₂×C₃×C₄	C₂×C₄×D₃	semidirect
419. C₂×C₃×C₄	C₂²×C₃×C₄	semidirect
428. #67	C₂²×C₃×C₄	semidirect
430. C₂×Dic₃	C₂²×C₃×C₄	semidirect
435. D₁₂	C₂²×C₃×C₄	semidirect
441. C₄×D₃	C₂²×C₃×C₄	semidirect
442. C₄×D₃	C₂²×C₃×C₄	semidirect
443. C₄×D₃	C₃×#41	direct (N × H)
444. Dic₆	C₂²×C₃×C₄	semidirect
449. C₃×D₃	C₄×#41	direct (N × H)
454. #41	C₃×C₄×D₃	direct (N × H)
523. C₃×C₄	D₃×#41	direct (N × H)
526. C₃×C₄	C₂×C₃×#41	semidirect
530. Dic₃	C₂×C₃×#41	semidirect
531. C₃²	C₂×C₄×#41	semidirect
538. Q₈	C₂×C₃×C₄×D₃	semidirect
541. D₄	C₂×C₃×C₄×D₃	semidirect
557. C₂×C₄	C₂×C₃×C₄×D₃	semidirect
574. D₃	C₃×C₄×#41	direct (N × H)
590. C₄	C₃×D₃×#41	direct (N × H)
592. C₃	C₄×D₃×#41	direct (N × H)
593. C₃	C₂×C₃×C₄×#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×Dic₃×#41	2
C₃×C₄×#239	2
C₃×C₄×D₃×Q₈	2
C₃×C₄×D₃×D₄	2
C₃×C₄×#237	2
C₃×#5522	2
C₃×D₃×#117	2
C₃×C₄×#235	2
C₂×C₃×C₄²×D₃	2
C₂×C₃×C₄×#41	3
C₄×D₃×#41	3

Subgroups — C3×C4×D3×#41 #11899944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₃×#41 #11899944