Subgroups — C₃×D₄×#239 #11902769

Order 1152.

3436 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#239	C₂	1	2	yes	maximal, complemented
2	C₃²×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5817	C₂	1	2	yes	maximal, complemented
4	C₃×#5726	C₂	1	3	yes	maximal, complemented
5	C₃×#5725	C₂	1	3	yes	maximal, complemented
6	C₃×#5630	C₂	1	6	yes	maximal, complemented
7	C₃×#5627	C₂	1	6	yes	maximal, complemented
8	C₃×#5577	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×#239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₄×D₁₂	C₂	1	3	yes	maximal, complemented
11	C₃×C₄×D₃×D₄	C₂	1	3	yes	maximal, complemented
12	C₃×D₄×#41	—	3	1	no	maximal
13	D₄×#239	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃²×Q₈	C₂²	1	2	yes	complemented
15	C₂×C₃×#239	—	2	16	no	—
16	C₂×C₃×#239	C₂²	1	1	yes	characteristic
17	C₂×C₃×#239	C₂²	1	2	yes	complemented
18	C₂×C₃×#239	C₂²	1	6	yes	complemented
19	C₂×C₃×#239	C₂²	1	6	yes	complemented
20	C₂×C₃×D₃×D₄	C₂²	1	3	yes	—
21	C₂²×C₃×D₁₂	C₂²	1	6	yes	complemented
22	C₂²×C₃×C₄×D₃	C₂²	1	6	yes	complemented
23	C₃²×C₄⋊Q₈	C₂²	1	3	yes	complemented
24	C₃²×C₂²⋊Q₈	C₂²	1	6	yes	complemented
25	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃²×C₄×D₄	C₂²	1	3	yes	—
27	C₃×#947	C₂²	1	6	yes	complemented
28	C₃×#946	C₂²	1	6	yes	complemented
29	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
30	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
31	C₃×#930	C₂²	1	6	yes	complemented
32	C₃×C₄×#67	C₂²	1	6	yes	complemented
33	C₃×#895	C₂²	1	6	yes	complemented
34	C₃×#895	C₂²	1	6	yes	complemented
35	C₃×#895	C₂²	1	6	yes	complemented
36	C₃×#894	C₂²	1	12	yes	complemented
37	C₃×#893	C₂²	1	3	yes	complemented
38	C₃×#893	C₂²	1	3	yes	complemented
39	C₃×#893	C₂²	1	6	yes	complemented
40	C₃×#892	C₂²	1	3	yes	complemented
41	C₃×D₃×C₄⋊C₄	C₂²	1	3	yes	complemented
42	C₃×#882	C₂²	1	12	yes	complemented
43	C₃×#67⋊C₄	C₂²	1	6	yes	complemented
44	C₃×D₃×C₂²⋊C₄	C₂²	1	6	yes	complemented
45	C₃×#874	C₂²	1	3	yes	complemented
46	C₃×C₄×D₁₂	C₂²	1	3	yes	complemented
47	C₃×C₄×D₁₂	C₂²	1	3	yes	complemented
48	C₃×C₄²×D₃	C₂²	1	3	yes	complemented
49	C₂²×C₃×#41	—	3	2	no	—
50	C₂²×#239	C₂×C₃	1	2	yes	complemented
51	C₃×#550	—	3	1	no	—
52	C₃×D₄×Q₈	—	2	1	no	—
53	C₃×D₄×Q₈	D₃	1	1	yes	characteristic, complemented
54	C₃×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#548	—	3	2	no	—
56	C₃×#547	—	3	3	no	—
57	C₃×#546	—	3	6	no	—
58	C₃×D₄²	—	3	3	no	—
59	C₃×#532	—	3	3	no	—
60	C₃×#525	—	3	6	no	—
61	C₃×C₄×#41	—	3	1	no	—
62	C₂×C₃×C₄×D₄	—	3	3	no	—
63	#5817	C₂×C₃	1	2	yes	complemented
64	#5726	C₂×C₃	1	3	yes	complemented
65	#5725	C₂×C₃	1	3	yes	complemented
66	#5630	C₂×C₃	1	6	yes	complemented
67	#5627	C₂×C₃	1	6	yes	complemented
68	#5577	C₂×C₃	1	1	yes	characteristic, complemented
69	C₄×#239	C₂×C₃	1	1	yes	characteristic, complemented
70	D₄×D₁₂	C₂×C₃	1	3	yes	complemented
71	C₄×D₃×D₄	C₂×C₃	1	3	yes	complemented
72	C₂³×C₃×D₃	C₂³	1	6	yes	—
73	C₂×C₃²×Q₈	—	2	8	no	—
74	C₂×C₃²×Q₈	C₂³	1	6	yes	—
75	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
76	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
77	C₂²×C₃²×C₄	C₂³	1	6	yes	—
78	C₂×C₃×#67	C₂³	1	6	yes	—
79	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
80	C₃×#239	—	2	8	no	—
81	C₃×#239	—	2	24	no	—
82	C₃×#239	—	2	24	no	—
83	C₃×#239	D₄	1	8	yes	direct product factor
84	C₃×D₃×D₄	—	2	12	no	—
85	C₂×C₃×D₁₂	—	2	24	no	—
86	C₂×C₃×D₁₂	C₂³	1	12	yes	—
87	C₂×C₃×D₁₂	C₂³	1	3	yes	—
88	C₂×C₃×D₁₂	C₂³	1	6	yes	—
89	C₂×C₃×D₁₂	C₂³	1	6	yes	—
90	C₂×C₃×D₁₂	C₂³	1	3	yes	—
91	C₂×C₃×C₄×D₃	—	2	24	no	—
92	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
93	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
94	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
95	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
96	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
97	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
98	C₃²×C₄⋊C₄	C₂³	1	3	yes	—
99	C₃²×C₄⋊C₄	C₂³	1	3	yes	—
100	C₃²×C₄⋊C₄	C₂³	1	6	yes	—
101	C₃²×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₃²×C₄²	C₂³	1	3	yes	—
103	C₃×#217	C₂³	1	2	yes	—
104	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
105	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
106	C₃×(C₂×D₃)⋊C₄	C₂³	1	6	yes	—
107	C₃×(C₂×D₃)⋊C₄	C₂³	1	12	yes	—
108	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
109	C₃×C₄⋊Dic₃	C₂³	1	3	yes	—
110	C₃×Dic₃⋊C₄	C₂³	1	6	yes	—
111	C₃×C₄×Dic₃	C₂³	1	3	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	—	3	1	no	—
116	C₂×C₃×#41	—	3	6	no	—
117	C₂×C₃×#41	—	3	6	no	—
118	C₂×C₃×#41	—	3	2	no	—
119	C₂×C₃×#41	—	6	16	no	—
120	C₂²×C₃×Q₈	—	2	2	no	—
121	C₂²×C₃×Q₈	C₂×D₃	1	2	yes	complemented
122	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	complemented
123	C₂²×C₃×D₄	—	3	3	no	—
124	C₂²×C₃×D₄	—	3	6	no	—
125	C₂³×C₃×C₄	—	3	6	no	—
126	C₂×#239	—	2	16	no	—
127	C₂×#239	C₂²×C₃	1	1	yes	characteristic
128	C₂×#239	C₂²×C₃	1	6	yes	complemented
129	C₂×#239	C₂²×C₃	1	6	yes	complemented
130	C₂×#239	C₂²×C₃	1	2	yes	complemented
131	C₂×D₃×D₄	C₂²×C₃	1	3	yes	—
132	C₂²×D₁₂	C₂²×C₃	1	6	yes	complemented
133	C₂²×C₄×D₃	C₂²×C₃	1	6	yes	complemented
134	C₃×C₄⋊Q₈	—	2	3	no	—
135	C₃×C₄⋊Q₈	C₂×D₃	1	3	yes	complemented
136	C₃×C₄⋊Q₈	C₂²×C₃	1	3	yes	complemented
137	C₃×#127	—	3	3	no	—
138	C₃×#124	—	3	6	no	—
139	C₃×#123	—	3	12	no	—
140	C₃×C₂²⋊Q₈	—	2	6	no	—
141	C₃×C₂²⋊Q₈	—	3	6	no	—
142	C₃×C₂²⋊Q₈	C₂×D₃	1	6	yes	complemented
143	C₃×C₂²⋊Q₈	C₂²×C₃	1	6	yes	complemented
144	C₃×#121	—	3	6	no	—
145	C₃×#121	—	3	6	no	—
146	C₃×#121	—	3	6	no	—
147	C₃×#121	—	3	6	no	—
148	C₃×#120	—	3	12	no	—
149	C₃×C₄×Q₈	—	2	1	no	—
150	C₃×C₄×Q₈	—	3	1	no	—
151	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
152	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₃×C₄×D₄	—	2	3	no	—
154	C₃×C₄×D₄	—	3	1	no	—
155	C₃×C₄×D₄	—	3	6	no	—
156	C₃×C₄×D₄	—	3	3	no	—
157	C₃×C₄×D₄	—	3	3	no	—
158	C₃×C₄×D₄	—	3	6	no	—
159	C₃×C₄×D₄	—	3	6	no	—
160	C₃×C₄×D₄	—	3	3	no	—
161	C₃×C₄×D₄	—	3	3	no	—
162	C₃×C₄×D₄	C₂×D₃	1	3	yes	—
163	C₃×C₄×D₄	C₂²×C₃	1	3	yes	—
164	C₃×#117	—	3	3	no	—
165	C₂×C₃×C₄⋊C₄	—	3	3	no	—
166	C₂×C₃×C₂²⋊C₄	—	3	6	no	—
167	C₂×C₃×C₄²	—	3	3	no	—
168	#947	C₂²×C₃	1	6	yes	complemented
169	#946	C₂²×C₃	1	6	yes	complemented
170	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
171	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
172	#930	C₂²×C₃	1	6	yes	complemented
173	C₄×#67	C₂²×C₃	1	6	yes	complemented
174	#895	C₂²×C₃	1	6	yes	complemented
175	#895	C₂²×C₃	1	6	yes	complemented
176	#895	C₂²×C₃	1	6	yes	complemented
177	#894	C₂²×C₃	1	12	yes	complemented
178	#893	C₂²×C₃	1	3	yes	complemented
179	#893	C₂²×C₃	1	6	yes	complemented
180	#893	C₂²×C₃	1	3	yes	complemented
181	#892	C₂²×C₃	1	3	yes	complemented
182	D₃×C₄⋊C₄	C₂²×C₃	1	3	yes	complemented
183	#882	C₂²×C₃	1	12	yes	complemented
184	#67⋊C₄	C₂²×C₃	1	6	yes	complemented
185	D₃×C₂²⋊C₄	C₂²×C₃	1	6	yes	complemented
186	#874	C₂²×C₃	1	3	yes	complemented
187	C₄×D₁₂	C₂²×C₃	1	3	yes	complemented
188	C₄×D₁₂	C₂²×C₃	1	3	yes	complemented
189	C₄²×D₃	C₂²×C₃	1	3	yes	complemented
190	C₂³×C₃²	C₂⁴	1	2	yes	—
191	C₂²×C₃×D₃	—	2	12	no	—
192	C₂²×C₃×D₃	—	2	12	no	—
193	C₂²×C₃×D₃	—	4	6	no	—
194	C₂²×C₃×D₃	C₂⁴	1	6	yes	—
195	C₂²×C₃×D₃	C₂⁴	1	3	yes	—
196	C₃²×Q₈	—	2	12	no	—
197	C₃²×Q₈	C₂×D₄	1	4	yes	complemented
198	C₃²×D₄	#41	1	4	yes	complemented
199	C₂×C₃²×C₄	—	2	12	no	—
200	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
201	C₂×C₃²×C₄	C₂⁴	1	6	yes	—
202	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
203	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
204	C₃×#67	—	2	12	no	—
205	C₂×C₃×Dic₃	—	2	4	no	—
206	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
207	C₂×C₃×Dic₃	C₂⁴	1	3	yes	—
208	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
209	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
210	C₃×D₁₂	—	2	24	no	—
211	C₃×D₁₂	—	2	12	no	—
212	C₃×D₁₂	—	2	6	no	—
213	C₃×D₁₂	—	4	6	no	—
214	C₃×D₁₂	C₂×D₄	1	12	yes	complemented
215	C₃×C₄×D₃	—	2	12	no	—
216	C₃×C₄×D₃	—	2	12	no	—
217	C₃×C₄×D₃	—	2	6	no	—
218	C₃×C₄×D₃	—	2	12	no	—
219	C₃×C₄×D₃	—	4	3	no	—
220	C₃×C₄×D₃	C₂×D₄	1	12	yes	complemented
221	C₂²×#41	—	3	2	no	—
222	#550	—	3	1	no	—
223	D₄×Q₈	C₃×D₃	1	1	yes	characteristic, complemented
224	#548	—	3	2	no	—
225	#547	—	3	3	no	—
226	#546	—	3	6	no	—
227	D₄²	—	3	3	no	—
228	#532	—	3	3	no	—
229	#525	—	3	6	no	—
230	C₄×#41	—	3	1	no	—
231	C₂×C₄×D₄	—	3	3	no	—
232	C₂⁴×C₃	—	3	6	no	—
233	C₂³×D₃	C₂³×C₃	1	6	yes	—
234	C₃×#41	—	3	8	no	—
235	C₃×#41	—	6	24	no	—
236	C₃×#41	—	6	24	no	—
237	C₃×#41	—	6	8	no	—
238	C₂×C₃×Q₈	—	2	8	no	—
239	C₂×C₃×Q₈	—	2	8	no	—
240	C₂×C₃×Q₈	—	2	1	no	—
241	C₂×C₃×Q₈	—	2	6	no	—
242	C₂×C₃×Q₈	—	4	8	no	—
243	C₂×C₃×Q₈	C₂²×D₃	1	6	yes	—
244	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
245	C₂×C₃×Q₈	C₂³×C₃	1	6	yes	—
246	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
247	C₂×C₃×D₄	—	2	1	no	—
248	C₂×C₃×D₄	—	3	6	no	—
249	C₂×C₃×D₄	—	3	3	no	—
250	C₂×C₃×D₄	—	3	3	no	—
251	C₂×C₃×D₄	—	3	12	no	—
252	C₂×C₃×D₄	—	3	6	no	—
253	C₂×C₃×D₄	—	3	6	no	—
254	C₂×C₃×D₄	—	6	24	no	—
255	C₂×C₃×D₄	—	6	12	no	—
256	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
257	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₃×C₄	—	2	6	no	—
259	C₂²×C₃×C₄	—	3	3	no	—
260	C₂²×C₃×C₄	—	3	2	no	—
261	C₂²×C₃×C₄	—	3	3	no	—
262	C₂²×C₃×C₄	—	3	6	no	—
263	C₂²×C₃×C₄	—	3	6	no	—
264	C₂²×C₃×C₄	—	3	6	no	—
265	C₂²×C₃×C₄	—	3	3	no	—
266	C₂²×C₃×C₄	—	6	24	no	—
267	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
268	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
269	C₂×#67	C₂³×C₃	1	6	yes	—
270	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
271	#239	—	2	8	no	—
272	#239	—	2	24	no	—
273	#239	—	2	24	no	—
274	#239	C₃×D₄	1	8	yes	direct product factor
275	D₃×D₄	—	2	12	no	—
276	C₂×D₁₂	—	2	24	no	—
277	C₂×D₁₂	C₂³×C₃	1	3	yes	—
278	C₂×D₁₂	C₂³×C₃	1	6	yes	—
279	C₂×D₁₂	C₂³×C₃	1	12	yes	—
280	C₂×D₁₂	C₂³×C₃	1	6	yes	—
281	C₂×D₁₂	C₂³×C₃	1	3	yes	—
282	C₂×C₄×D₃	—	2	24	no	—
283	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
284	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
285	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
286	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
287	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
288	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
289	C₃×C₄⋊C₄	—	2	3	no	—
290	C₃×C₄⋊C₄	—	2	3	no	—
291	C₃×C₄⋊C₄	—	2	6	no	—
292	C₃×C₄⋊C₄	—	3	6	no	—
293	C₃×C₄⋊C₄	—	3	1	no	—
294	C₃×C₄⋊C₄	—	3	3	no	—
295	C₃×C₄⋊C₄	C₂²×D₃	1	3	yes	—
296	C₃×C₄⋊C₄	C₂²×D₃	1	3	yes	—
297	C₃×C₄⋊C₄	C₂²×D₃	1	6	yes	—
298	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
299	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
300	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
301	C₃×C₂²⋊C₄	—	2	6	no	—
302	C₃×C₂²⋊C₄	—	3	2	no	—
303	C₃×C₂²⋊C₄	—	3	6	no	—
304	C₃×C₂²⋊C₄	—	3	6	no	—
305	C₃×C₂²⋊C₄	—	3	6	no	—
306	C₃×C₂²⋊C₄	—	3	12	no	—
307	C₃×C₂²⋊C₄	C₂²×D₃	1	6	yes	—
308	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
309	C₃×C₄²	—	2	3	no	—
310	C₃×C₄²	—	3	1	no	—
311	C₃×C₄²	—	3	3	no	—
312	C₃×C₄²	—	3	3	no	—
313	C₃×C₄²	C₂²×D₃	1	3	yes	—
314	C₃×C₄²	C₂³×C₃	1	3	yes	—
315	#217	C₂³×C₃	1	2	yes	—
316	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
317	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
318	(C₂×D₃)⋊C₄	C₂³×C₃	1	6	yes	—
319	(C₂×D₃)⋊C₄	C₂³×C₃	1	12	yes	—
320	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
321	C₄⋊Dic₃	C₂³×C₃	1	3	yes	—
322	Dic₃⋊C₄	C₂³×C₃	1	6	yes	—
323	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
324	C₄×Dic₃	C₂³×C₃	1	3	yes	—
325	C₄×Dic₃	C₂³×C₃	1	3	yes	—
326	C₂²×C₃²	—	2	2	no	—
327	C₂²×C₃²	—	2	2	no	—
328	C₂²×C₃²	C₂×#41	1	4	yes	complemented
329	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
330	C₂×C₃×D₃	—	2	3	no	—
331	C₂×C₃×D₃	—	2	3	no	—
332	C₂×C₃×D₃	—	2	6	no	—
333	C₂×C₃×D₃	—	2	6	no	—
334	C₂×C₃×D₃	—	2	6	no	—
335	C₂×C₃×D₃	—	4	24	no	—
336	C₂×C₃×D₃	C₂²×D₄	1	6	yes	—
337	C₃²×C₄	—	2	6	no	—
338	C₃²×C₄	—	2	3	no	—
339	C₃²×C₄	C₂²×D₄	1	6	yes	—
340	C₃²×C₄	C₂×#41	1	2	yes	complemented
341	C₃×Dic₃	—	2	2	no	—
342	C₃×Dic₃	—	2	3	no	—
343	C₃×Dic₃	—	2	1	no	—
344	C₃×Dic₃	C₂²×D₄	1	2	yes	—
345	C₂×#41	—	3	1	no	—
346	C₂×#41	—	3	6	no	—
347	C₂×#41	—	3	6	no	—
348	C₂×#41	—	3	2	no	—
349	C₂×#41	—	6	16	no	—
350	C₂²×Q₈	C₂×C₃×D₃	1	2	yes	complemented
351	C₂²×D₄	—	3	3	no	—
352	C₂²×D₄	—	3	6	no	—
353	C₂³×C₄	—	3	6	no	—
354	C₄⋊Q₈	C₂×C₃×D₃	1	3	yes	complemented
355	#127	—	3	3	no	—
356	#124	—	3	6	no	—
357	#123	—	3	12	no	—
358	C₂²⋊Q₈	—	3	6	no	—
359	C₂²⋊Q₈	C₂×C₃×D₃	1	6	yes	complemented
360	#121	—	3	6	no	—
361	#121	—	3	6	no	—
362	#121	—	3	6	no	—
363	#121	—	3	6	no	—
364	#120	—	3	12	no	—
365	C₄×Q₈	—	3	1	no	—
366	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
367	C₄×D₄	—	3	1	no	—
368	C₄×D₄	—	3	6	no	—
369	C₄×D₄	—	3	3	no	—
370	C₄×D₄	—	3	3	no	—
371	C₄×D₄	—	3	6	no	—
372	C₄×D₄	—	3	6	no	—
373	C₄×D₄	—	3	3	no	—
374	C₄×D₄	—	3	3	no	—
375	C₄×D₄	C₂×C₃×D₃	1	3	yes	—
376	#117	—	3	3	no	—
377	C₂×C₄⋊C₄	—	3	3	no	—
378	C₂×C₂²⋊C₄	—	3	6	no	—
379	C₂×C₄²	—	3	3	no	—
380	C₂³×C₃	—	2	2	no	—
381	C₂³×C₃	—	3	3	no	—
382	C₂³×C₃	—	3	6	no	—
383	C₂³×C₃	—	6	12	no	—
384	C₂³×C₃	—	6	12	no	—
385	C₂³×C₃	—	12	6	no	—
386	C₂³×C₃	C₂³×D₃	1	2	yes	—
387	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
388	C₂²×D₃	—	2	12	no	—
389	C₂²×D₃	—	2	12	no	—
390	C₂²×D₃	—	4	6	no	—
391	C₂²×D₃	C₂⁴×C₃	1	6	yes	—
392	C₂²×D₃	C₂⁴×C₃	1	3	yes	—
393	C₃×Q₈	—	2	12	no	—
394	C₃×Q₈	—	2	12	no	—
395	C₃×Q₈	—	2	4	no	—
396	C₃×Q₈	—	4	12	no	—
397	C₃×Q₈	D₃×D₄	1	4	yes	complemented
398	C₃×Q₈	C₂×C₃×D₄	1	4	yes	complemented
399	C₃×D₄	—	2	4	no	—
400	C₃×D₄	—	3	12	no	—
401	C₃×D₄	—	6	24	no	—
402	C₃×D₄	—	6	12	no	—
403	C₃×D₄	—	6	12	no	—
404	C₃×D₄	—	6	6	no	—
405	C₃×D₄	—	12	6	no	—
406	C₃×D₄	#239	1	4	yes	direct product factor
407	C₃×D₄	C₃×#41	1	4	yes	complemented
408	C₂×C₃×C₄	—	2	12	no	—
409	C₂×C₃×C₄	—	2	12	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	3	no	—
412	C₂×C₃×C₄	—	2	3	no	—
413	C₂×C₃×C₄	—	2	6	no	—
414	C₂×C₃×C₄	—	3	1	no	—
415	C₂×C₃×C₄	—	3	12	no	—
416	C₂×C₃×C₄	—	3	1	no	—
417	C₂×C₃×C₄	—	3	3	no	—
418	C₂×C₃×C₄	—	3	2	no	—
419	C₂×C₃×C₄	—	4	12	no	—
420	C₂×C₃×C₄	—	6	12	no	—
421	C₂×C₃×C₄	—	6	12	no	—
422	C₂×C₃×C₄	—	6	4	no	—
423	C₂×C₃×C₄	—	6	12	no	—
424	C₂×C₃×C₄	—	6	6	no	—
425	C₂×C₃×C₄	—	12	3	no	—
426	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
427	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
428	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
429	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
430	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
431	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
432	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
433	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
434	#67	—	2	12	no	—
435	C₂×Dic₃	—	2	4	no	—
436	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
437	C₂×Dic₃	C₂⁴×C₃	1	3	yes	—
438	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
439	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
440	D₁₂	—	2	24	no	—
441	D₁₂	—	2	12	no	—
442	D₁₂	—	2	6	no	—
443	D₁₂	—	4	6	no	—
444	D₁₂	C₂×C₃×D₄	1	12	yes	complemented
445	C₄×D₃	—	2	12	no	—
446	C₄×D₃	—	2	12	no	—
447	C₄×D₃	—	2	6	no	—
448	C₄×D₃	—	2	12	no	—
449	C₄×D₃	—	4	3	no	—
450	C₄×D₃	C₂×C₃×D₄	1	12	yes	complemented
451	C₂×C₃²	—	2	4	no	—
452	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
453	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
454	C₂×C₃²	#585	1	1	yes	characteristic
455	C₃×D₃	—	2	6	no	—
456	C₃×D₃	—	4	6	no	—
457	C₂⁴	—	3	6	no	—
458	#41	—	3	8	no	—
459	#41	—	6	24	no	—
460	#41	—	6	24	no	—
461	#41	—	6	8	no	—
462	C₂×Q₈	—	2	8	no	—
463	C₂×Q₈	C₂²×C₃×D₃	1	6	yes	—
464	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
465	C₂×D₄	—	3	6	no	—
466	C₂×D₄	—	3	3	no	—
467	C₂×D₄	—	3	3	no	—
468	C₂×D₄	—	3	12	no	—
469	C₂×D₄	—	3	6	no	—
470	C₂×D₄	—	3	6	no	—
471	C₂×D₄	—	6	24	no	—
472	C₂×D₄	—	6	12	no	—
473	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
474	C₂²×C₄	—	3	3	no	—
475	C₂²×C₄	—	3	2	no	—
476	C₂²×C₄	—	3	3	no	—
477	C₂²×C₄	—	3	6	no	—
478	C₂²×C₄	—	3	6	no	—
479	C₂²×C₄	—	3	6	no	—
480	C₂²×C₄	—	3	3	no	—
481	C₂²×C₄	—	6	24	no	—
482	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
483	C₄⋊C₄	—	3	1	no	—
484	C₄⋊C₄	—	3	6	no	—
485	C₄⋊C₄	—	3	3	no	—
486	C₄⋊C₄	C₂²×C₃×D₃	1	3	yes	—
487	C₄⋊C₄	C₂²×C₃×D₃	1	3	yes	—
488	C₄⋊C₄	C₂²×C₃×D₃	1	6	yes	—
489	C₂²⋊C₄	—	3	2	no	—
490	C₂²⋊C₄	—	3	6	no	—
491	C₂²⋊C₄	—	3	6	no	—
492	C₂²⋊C₄	—	3	6	no	—
493	C₂²⋊C₄	—	3	12	no	—
494	C₂²⋊C₄	C₂²×C₃×D₃	1	6	yes	—
495	C₄²	—	3	1	no	—
496	C₄²	—	3	3	no	—
497	C₄²	—	3	3	no	—
498	C₄²	C₂²×C₃×D₃	1	3	yes	—
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	2	2	no	—
501	C₂²×C₃	—	2	2	no	—
502	C₂²×C₃	—	2	2	no	—
503	C₂²×C₃	—	2	4	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	3	6	no	—
506	C₂²×C₃	—	4	2	no	—
507	C₂²×C₃	—	4	2	no	—
508	C₂²×C₃	—	6	3	no	—
509	C₂²×C₃	—	6	3	no	—
510	C₂²×C₃	—	6	6	no	—
511	C₂²×C₃	—	6	6	no	—
512	C₂²×C₃	—	6	6	no	—
513	C₂²×C₃	—	12	24	no	—
514	C₂²×C₃	C₂×#239	1	4	yes	complemented
515	C₂²×C₃	C₂×C₃×#41	1	4	yes	complemented
516	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
517	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
518	C₂×D₃	—	2	3	no	—
519	C₂×D₃	—	2	3	no	—
520	C₂×D₃	—	2	6	no	—
521	C₂×D₃	—	2	6	no	—
522	C₂×D₃	—	2	6	no	—
523	C₂×D₃	—	4	24	no	—
524	C₂×D₃	C₂²×C₃×D₄	1	6	yes	—
525	C₃×C₄	—	2	6	no	—
526	C₃×C₄	—	2	3	no	—
527	C₃×C₄	—	2	6	no	—
528	C₃×C₄	—	2	3	no	—
529	C₃×C₄	—	2	6	no	—
530	C₃×C₄	—	2	2	no	—
531	C₃×C₄	—	3	2	no	—
532	C₃×C₄	—	4	6	no	—
533	C₃×C₄	—	4	3	no	—
534	C₃×C₄	—	6	2	no	—
535	C₃×C₄	—	6	3	no	—
536	C₃×C₄	—	6	1	no	—
537	C₃×C₄	C₂×D₃×D₄	1	6	yes	—
538	C₃×C₄	C₂×#239	1	2	yes	complemented
539	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
540	C₃×C₄	C₂×C₃×#41	1	2	yes	complemented
541	Dic₃	—	2	2	no	—
542	Dic₃	—	2	3	no	—
543	Dic₃	—	2	1	no	—
544	Dic₃	C₂²×C₃×D₄	1	2	yes	—
545	C₃²	D₄×#41	1	1	yes	characteristic, complemented, Sylow
546	C₂³	—	3	3	no	—
547	C₂³	—	3	6	no	—
548	C₂³	—	6	12	no	—
549	C₂³	—	6	12	no	—
550	C₂³	—	12	6	no	—
551	C₂³	C₂³×C₃×D₃	1	2	yes	—
552	Q₈	—	2	12	no	—
553	Q₈	C₃×D₃×D₄	1	4	yes	complemented
554	D₄	—	3	12	no	—
555	D₄	—	6	24	no	—
556	D₄	—	6	12	no	—
557	D₄	—	6	12	no	—
558	D₄	—	6	6	no	—
559	D₄	—	12	6	no	—
560	D₄	C₃×#239	1	4	yes	direct product factor
561	C₂×C₄	—	2	12	no	—
562	C₂×C₄	—	3	1	no	—
563	C₂×C₄	—	3	12	no	—
564	C₂×C₄	—	3	1	no	—
565	C₂×C₄	—	3	3	no	—
566	C₂×C₄	—	3	2	no	—
567	C₂×C₄	—	6	12	no	—
568	C₂×C₄	—	6	12	no	—
569	C₂×C₄	—	6	4	no	—
570	C₂×C₄	—	6	12	no	—
571	C₂×C₄	—	6	6	no	—
572	C₂×C₄	—	12	3	no	—
573	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
574	C₂×C₄	C₂³×C₃×D₃	1	6	yes	—
575	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
576	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
577	C₂×C₃	—	2	4	no	—
578	C₂×C₃	—	2	4	no	—
579	C₂×C₃	—	2	1	no	—
580	C₂×C₃	—	2	1	no	—
581	C₂×C₃	—	2	1	no	—
582	C₂×C₃	—	4	4	no	—
583	C₂×C₃	—	6	6	no	—
584	C₂×C₃	—	12	6	no	—
585	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
586	C₂×C₃	C₂²×#239	1	1	yes	characteristic
587	C₂×C₃	#5968	1	1	yes	characteristic
588	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
589	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
590	C₂×C₃	C₃×#585	1	1	yes	characteristic
591	D₃	—	2	6	no	—
592	D₃	—	4	6	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	3	6	no	—
596	C₂²	—	6	3	no	—
597	C₂²	—	6	3	no	—
598	C₂²	—	6	6	no	—
599	C₂²	—	6	6	no	—
600	C₂²	—	6	6	no	—
601	C₂²	—	12	24	no	—
602	C₂²	C₂×C₃×#239	1	4	yes	complemented
603	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
604	C₄	—	2	6	no	—
605	C₄	—	2	3	no	—
606	C₄	—	3	2	no	—
607	C₄	—	6	2	no	—
608	C₄	—	6	3	no	—
609	C₄	—	6	1	no	—
610	C₄	C₂×C₃×D₃×D₄	1	6	yes	—
611	C₄	C₂×C₃×#239	1	2	yes	complemented
612	C₃	—	2	1	no	—
613	C₃	D₄×#239	1	1	yes	characteristic, direct product factor
614	C₃	C₃×D₄×#41	1	1	yes	characteristic, complemented
615	C₂	—	2	4	no	—
616	C₂	—	6	6	no	—
617	C₂	—	12	6	no	—
618	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
619	C₂	C₂²×C₃×#239	1	1	yes	characteristic
620	C₂	C₃×#5968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×D₄×Q₈	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×D₄×Q₈	D₃
hypocenter	C₃	C₃×D₄×#41
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#239	C₂	semidirect
2. C₃²×D₄×Q₈	C₂	semidirect
3. C₃×#5817	C₂	semidirect
4. C₃×#5726	C₂	semidirect
5. C₃×#5725	C₂	semidirect
6. C₃×#5630	C₂	semidirect
7. C₃×#5627	C₂	semidirect
8. C₃×#5577	C₂	semidirect
9. C₃×C₄×#239	C₂	semidirect
10. C₃×D₄×D₁₂	C₂	semidirect
11. C₃×C₄×D₃×D₄	C₂	semidirect
13. D₄×#239	C₃	direct (N × H)
14. C₂²×C₃²×Q₈	C₂²	semidirect
17. C₂×C₃×#239	C₂²	semidirect
18. C₂×C₃×#239	C₂²	semidirect
19. C₂×C₃×#239	C₂²	semidirect
21. C₂²×C₃×D₁₂	C₂²	semidirect
22. C₂²×C₃×C₄×D₃	C₂²	semidirect
23. C₃²×C₄⋊Q₈	C₂²	semidirect
24. C₃²×C₂²⋊Q₈	C₂²	semidirect
25. C₃²×C₄×Q₈	C₂²	semidirect
27. C₃×#947	C₂²	semidirect
28. C₃×#946	C₂²	semidirect
29. C₃×Q₈×Dic₃	C₂²	semidirect
31. C₃×#930	C₂²	semidirect
32. C₃×C₄×#67	C₂²	semidirect
33. C₃×#895	C₂²	semidirect
34. C₃×#895	C₂²	semidirect
35. C₃×#895	C₂²	semidirect
36. C₃×#894	C₂²	semidirect
37. C₃×#893	C₂²	semidirect
38. C₃×#893	C₂²	semidirect
39. C₃×#893	C₂²	semidirect
40. C₃×#892	C₂²	semidirect
41. C₃×D₃×C₄⋊C₄	C₂²	semidirect
42. C₃×#882	C₂²	semidirect
43. C₃×#67⋊C₄	C₂²	semidirect
44. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
45. C₃×#874	C₂²	semidirect
46. C₃×C₄×D₁₂	C₂²	semidirect
47. C₃×C₄×D₁₂	C₂²	semidirect
48. C₃×C₄²×D₃	C₂²	semidirect
50. C₂²×#239	C₂×C₃	semidirect
53. C₃×D₄×Q₈	D₃	semidirect
54. C₃×D₄×Q₈	C₂×C₃	semidirect
63. #5817	C₂×C₃	semidirect
64. #5726	C₂×C₃	semidirect
65. #5725	C₂×C₃	semidirect
66. #5630	C₂×C₃	semidirect
67. #5627	C₂×C₃	semidirect
68. #5577	C₂×C₃	semidirect
69. C₄×#239	C₂×C₃	semidirect
70. D₄×D₁₂	C₂×C₃	semidirect
71. C₄×D₃×D₄	C₂×C₃	semidirect
83. C₃×#239	D₄	direct (N × H)
121. C₂²×C₃×Q₈	C₂×D₃	semidirect
122. C₂²×C₃×Q₈	C₂²×C₃	semidirect
128. C₂×#239	C₂²×C₃	semidirect
129. C₂×#239	C₂²×C₃	semidirect
130. C₂×#239	C₂²×C₃	semidirect
132. C₂²×D₁₂	C₂²×C₃	semidirect
133. C₂²×C₄×D₃	C₂²×C₃	semidirect
135. C₃×C₄⋊Q₈	C₂×D₃	semidirect
136. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
142. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
143. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
151. C₃×C₄×Q₈	C₂×D₃	semidirect
152. C₃×C₄×Q₈	C₂²×C₃	semidirect
168. #947	C₂²×C₃	semidirect
169. #946	C₂²×C₃	semidirect
170. Q₈×Dic₃	C₂²×C₃	semidirect
172. #930	C₂²×C₃	semidirect
173. C₄×#67	C₂²×C₃	semidirect
174. #895	C₂²×C₃	semidirect
175. #895	C₂²×C₃	semidirect
176. #895	C₂²×C₃	semidirect
177. #894	C₂²×C₃	semidirect
178. #893	C₂²×C₃	semidirect
179. #893	C₂²×C₃	semidirect
180. #893	C₂²×C₃	semidirect
181. #892	C₂²×C₃	semidirect
182. D₃×C₄⋊C₄	C₂²×C₃	semidirect
183. #882	C₂²×C₃	semidirect
184. #67⋊C₄	C₂²×C₃	semidirect
185. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
186. #874	C₂²×C₃	semidirect
187. C₄×D₁₂	C₂²×C₃	semidirect
188. C₄×D₁₂	C₂²×C₃	semidirect
189. C₄²×D₃	C₂²×C₃	semidirect
197. C₃²×Q₈	C₂×D₄	semidirect
198. C₃²×D₄	#41	semidirect
214. C₃×D₁₂	C₂×D₄	semidirect
220. C₃×C₄×D₃	C₂×D₄	semidirect
223. D₄×Q₈	C₃×D₃	semidirect
274. #239	C₃×D₄	direct (N × H)
328. C₂²×C₃²	C₂×#41	semidirect
340. C₃²×C₄	C₂×#41	semidirect
350. C₂²×Q₈	C₂×C₃×D₃	semidirect
354. C₄⋊Q₈	C₂×C₃×D₃	semidirect
359. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
366. C₄×Q₈	C₂×C₃×D₃	semidirect
397. C₃×Q₈	D₃×D₄	semidirect
398. C₃×Q₈	C₂×C₃×D₄	semidirect
406. C₃×D₄	#239	direct (N × H)
407. C₃×D₄	C₃×#41	semidirect
444. D₁₂	C₂×C₃×D₄	semidirect
450. C₄×D₃	C₂×C₃×D₄	semidirect
514. C₂²×C₃	C₂×#239	semidirect
515. C₂²×C₃	C₂×C₃×#41	semidirect
538. C₃×C₄	C₂×#239	semidirect
540. C₃×C₄	C₂×C₃×#41	semidirect
545. C₃²	D₄×#41	semidirect
553. Q₈	C₃×D₃×D₄	semidirect
560. D₄	C₃×#239	direct (N × H)
602. C₂²	C₂×C₃×#239	semidirect
611. C₄	C₂×C₃×#239	semidirect
613. C₃	D₄×#239	direct (N × H)
614. 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
C₂²×C₃×#239	2
C₃²×D₄×Q₈	2
C₃×#5817	2
C₃×#5726	2
C₃×#5725	2
C₃×#5630	2
C₃×#5627	2
C₃×#5577	2
C₃×C₄×#239	2
C₃×D₄×D₁₂	2
C₃×C₄×D₃×D₄	2
C₃×D₄×#41	3
D₄×#239	3

Subgroups — C3×D4×#239 #11902769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×#239 #11902769