Subgroups — C₃×#79511 #11889352

Order 1152.

814 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5541	C₂	1	1	yes	maximal, characteristic
2	C₃×D₄×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₃²×#435	C₂	1	1	yes	maximal, characteristic
4	C₃×#5137	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5120	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5116	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#816	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4849	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4829	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4739	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4739	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4723	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4721	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4716	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#4703	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3312	—	3	1	no	maximal
17	#79511	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
19	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic
20	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
22	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
23	C₃×#935	—	2	1	no	—
24	C₃×D₄×Dic₃	—	2	1	no	—
25	C₃×#926	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₃×#924	C₂²	1	1	yes	characteristic
28	C₃×#924	C₂²	1	1	yes	characteristic
29	C₃×#924	C₂²	1	1	yes	characteristic
30	C₃×#924	C₂²	1	1	yes	characteristic
31	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
32	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
33	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
34	C₃×#889	—	2	1	no	—
35	C₃×#888	—	2	1	no	—
36	C₃×#879	—	2	1	no	—
37	C₃×#878	—	2	1	no	—
38	C₃×#878	—	2	1	no	—
39	C₃×#877	—	2	1	no	—
40	C₃×#870	C₂²	1	1	yes	characteristic
41	C₃×#869	C₂²	1	1	yes	characteristic
42	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
43	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
44	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₃²×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₃²×#97	C₂²	1	1	yes	characteristic
48	C₃×#818	C₂²	1	1	yes	characteristic
49	C₃×#817	C₂²	1	1	yes	characteristic
50	C₃×#817	C₂²	1	1	yes	characteristic
51	C₃×#816	C₂²	1	1	yes	characteristic
52	C₃×#816	C₂²	1	1	yes	characteristic
53	C₃×#816	C₂²	1	1	yes	characteristic
54	C₃×#816	C₂²	1	1	yes	characteristic
55	C₃×#816	C₂²	1	1	yes	characteristic
56	C₃×#816	C₂²	1	1	yes	characteristic
57	C₃×#816	C₂²	1	1	yes	characteristic
58	C₃×#816	C₂²	1	1	yes	characteristic
59	C₃×#816	C₂²	1	1	yes	characteristic
60	C₃×#816	C₂²	1	1	yes	characteristic
61	C₃×#552	—	3	1	no	—
62	C₃×D₄×Q₈	—	3	1	no	—
63	#5541	C₂×C₃	1	1	yes	characteristic
64	D₄×Dic₆	C₂×C₃	1	1	yes	characteristic
65	C₃×#491	—	3	1	no	—
66	C₃×#485	—	3	1	no	—
67	C₃×#483	—	3	1	no	—
68	C₃×#479	—	3	1	no	—
69	C₃×#470	—	3	1	no	—
70	C₃×#467	—	3	1	no	—
71	C₃×#462	—	3	1	no	—
72	C₃×#451	—	3	1	no	—
73	C₃×#451	—	3	1	no	—
74	C₃×#441	—	3	1	no	—
75	C₃×#435	—	2	1	no	—
76	C₃×#435	D₃	1	1	yes	characteristic
77	C₃×#435	C₂×C₃	1	1	yes	characteristic
78	C₃×#419	—	3	1	no	—
79	C₂×C₃×#103	—	3	1	no	—
80	#5137	C₂×C₃	1	1	yes	characteristic, complemented
81	#5120	C₂×C₃	1	1	yes	characteristic, complemented
82	#5116	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×#816	C₂×C₃	1	1	yes	characteristic, complemented
84	#4849	C₂×C₃	1	1	yes	characteristic, complemented
85	#4829	C₂×C₃	1	1	yes	characteristic, complemented
86	#4739	C₂×C₃	1	1	yes	characteristic, complemented
87	#4739	C₂×C₃	1	1	yes	characteristic, complemented
88	#4723	C₂×C₃	1	1	yes	characteristic, complemented
89	#4721	C₂×C₃	1	1	yes	characteristic, complemented
90	#4716	C₂×C₃	1	1	yes	characteristic, complemented
91	#4703	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×C₃²×D₄	D₄	1	1	yes	characteristic
93	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
94	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
95	C₂²×C₃×Dic₃	—	2	1	no	—
96	C₂²×C₃×Dic₃	—	2	1	no	—
97	C₂²×C₃×Dic₃	—	2	1	no	—
98	C₂×C₃×Dic₆	—	2	2	no	—
99	C₂×C₃×Dic₆	—	2	2	no	—
100	C₂×C₃×Dic₆	—	2	1	no	—
101	C₂×C₃×Dic₆	—	2	1	no	—
102	C₂×C₃×Dic₆	—	4	1	no	—
103	C₂×C₃×Dic₆	—	4	1	no	—
104	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
105	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
106	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
107	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
108	C₃²×M₁₆	—	4	1	no	—
109	C₂×C₃²×C₈	—	4	1	no	—
110	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
111	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
112	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
113	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
114	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
115	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₃²×C₂²⋊C₄	D₄	1	1	yes	characteristic
117	C₃²×C₄²	C₂³	1	1	yes	characteristic
118	C₃×#217	—	2	1	no	—
119	C₃×#217	—	2	1	no	—
120	C₃×#217	—	2	1	no	—
121	C₃×#217	—	2	1	no	—
122	C₃×#217	—	2	1	no	—
123	C₃×C₄⋊Dic₃	—	2	1	no	—
124	C₃×C₄⋊Dic₃	—	2	1	no	—
125	C₃×C₄⋊Dic₃	—	2	1	no	—
126	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
127	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
128	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
129	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
130	C₃×Dic₃⋊C₄	—	2	1	no	—
131	C₃×Dic₃⋊C₄	—	2	1	no	—
132	C₃×Dic₃⋊C₄	—	2	1	no	—
133	C₃×Dic₃⋊C₄	—	2	1	no	—
134	C₃×Dic₃⋊C₄	—	2	1	no	—
135	C₃×Dic₃⋊C₄	—	2	1	no	—
136	C₃×Dic₃⋊C₄	—	2	1	no	—
137	C₃×Dic₃⋊C₄	—	2	1	no	—
138	C₃×C₄×Dic₃	—	2	1	no	—
139	C₃×C₄×Dic₃	—	2	1	no	—
140	C₃×C₄×Dic₃	—	2	1	no	—
141	C₃×Dic₁₂	—	2	2	no	—
142	C₃×Dic₁₂	—	4	1	no	—
143	C₃×Dic₁₂	—	4	1	no	—
144	#3312	—	3	1	no	Sylow
145	C₂²×C₃×Q₈	—	3	1	no	—
146	C₂²×C₃×Q₈	—	3	1	no	—
147	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
148	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×Q₁₆	—	3	1	no	—
150	C₂×C₃×Q₁₆	—	3	1	no	—
151	C₂×C₃×Q₁₆	—	3	1	no	—
152	C₂×C₃×M₁₆	—	2	1	no	—
153	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
154	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
155	C₂²×C₃×C₈	—	2	1	no	—
156	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
157	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
158	C₃×C₄⋊Q₈	—	3	1	no	—
159	C₃×C₄⋊Q₈	—	6	1	no	—
160	C₃×#126	—	6	1	no	—
161	C₃×#125	—	3	1	no	—
162	C₃×#125	—	6	1	no	—
163	C₃×#123	—	6	1	no	—
164	C₃×C₂²⋊Q₈	—	3	1	no	—
165	C₃×C₂²⋊Q₈	—	3	1	no	—
166	C₃×C₂²⋊Q₈	—	3	1	no	—
167	C₃×C₂²⋊Q₈	—	3	1	no	—
168	C₃×C₂²⋊Q₈	—	6	1	no	—
169	C₃×C₂²⋊Q₈	—	6	1	no	—
170	C₃×C₄×Q₈	—	3	1	no	—
171	C₃×C₄×Q₈	—	3	1	no	—
172	C₃×C₄×D₄	—	2	1	no	—
173	C₃×C₄×D₄	—	6	1	no	—
174	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
175	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
176	C₃×#117	—	3	1	no	—
177	C₃×#117	—	6	1	no	—
178	C₂×C₃×C₄⋊C₄	—	3	1	no	—
179	#935	—	2	1	no	—
180	D₄×Dic₃	—	2	1	no	—
181	#926	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
183	#924	C₂²×C₃	1	1	yes	characteristic
184	#924	C₂²×C₃	1	1	yes	characteristic
185	#924	C₂²×C₃	1	1	yes	characteristic
186	#924	C₂²×C₃	1	1	yes	characteristic
187	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
188	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
189	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
190	#889	—	2	1	no	—
191	#888	—	2	1	no	—
192	#879	—	2	1	no	—
193	#878	—	2	1	no	—
194	#878	—	2	1	no	—
195	#877	—	2	1	no	—
196	#870	C₂²×C₃	1	1	yes	characteristic
197	#869	C₂²×C₃	1	1	yes	characteristic
198	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
199	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
200	C₃×#107	—	3	1	no	—
201	C₃×#106	—	3	1	no	—
202	C₃×#106	—	3	1	no	—
203	C₃×C₄⋊C₈	—	2	1	no	—
204	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
205	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
206	C₃×#103	—	3	1	no	—
207	C₃×#103	—	3	1	no	—
208	C₃×#103	—	3	1	no	—
209	C₃×#103	—	3	1	no	—
210	C₃×#103	—	3	1	no	—
211	C₃×#103	—	3	1	no	—
212	C₃×#103	—	3	1	no	—
213	C₃×#103	—	3	1	no	—
214	C₃×#103	—	3	1	no	—
215	C₃×#103	—	3	1	no	—
216	C₃×C₂²⋊C₈	—	2	1	no	—
217	C₃×C₂²⋊C₈	—	2	1	no	—
218	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
219	C₃×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
220	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
221	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
222	C₃×#97	—	2	1	no	—
223	C₃×#97	C₂×D₃	1	1	yes	characteristic
224	C₃×#97	C₂²×C₃	1	1	yes	characteristic
225	#818	C₂²×C₃	1	1	yes	characteristic
226	#817	C₂²×C₃	1	1	yes	characteristic
227	#817	C₂²×C₃	1	1	yes	characteristic
228	#816	C₂²×C₃	1	1	yes	characteristic
229	#816	C₂²×C₃	1	1	yes	characteristic
230	#816	C₂²×C₃	1	1	yes	characteristic
231	#816	C₂²×C₃	1	1	yes	characteristic
232	#816	C₂²×C₃	1	1	yes	characteristic
233	#816	C₂²×C₃	1	1	yes	characteristic
234	#816	C₂²×C₃	1	1	yes	characteristic
235	#816	C₂²×C₃	1	1	yes	characteristic
236	#816	C₂²×C₃	1	1	yes	characteristic
237	#816	C₂²×C₃	1	1	yes	characteristic
238	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
239	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
240	C₃²×D₄	—	2	2	no	—
241	C₂×C₃²×C₄	—	2	1	no	—
242	C₂×C₃²×C₄	—	2	1	no	—
243	C₂×C₃²×C₄	—	2	1	no	—
244	C₂×C₃²×C₄	—	2	1	no	—
245	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
246	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
247	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
248	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
249	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
250	C₂×C₃×Dic₃	—	2	1	no	—
251	C₂×C₃×Dic₃	—	2	1	no	—
252	C₂×C₃×Dic₃	—	2	1	no	—
253	C₂×C₃×Dic₃	—	2	1	no	—
254	C₂×C₃×Dic₃	—	2	1	no	—
255	C₂×C₃×Dic₃	—	2	1	no	—
256	C₂×C₃×Dic₃	—	2	1	no	—
257	C₂×C₃×Dic₃	—	2	1	no	—
258	C₂×C₃×Dic₃	—	4	2	no	—
259	C₂×C₃×Dic₃	—	4	2	no	—
260	C₂×C₃×Dic₃	—	4	2	no	—
261	C₃×Dic₆	—	2	1	no	—
262	C₃×Dic₆	—	2	1	no	—
263	C₃×Dic₆	—	2	1	no	—
264	C₃×Dic₆	—	2	1	no	—
265	C₃×Dic₆	—	2	1	no	—
266	C₃×Dic₆	—	2	1	no	—
267	C₃×Dic₆	—	2	1	no	—
268	C₃×Dic₆	—	4	2	no	—
269	C₃×Dic₆	—	4	2	no	—
270	C₃×Dic₆	#41	1	2	yes	—
271	C₃²×C₈	—	2	1	no	—
272	C₃²×C₈	—	2	1	no	—
273	C₃²×C₈	—	2	1	no	—
274	C₃²×C₈	—	2	1	no	—
275	#552	—	3	1	no	—
276	D₄×Q₈	—	3	1	no	—
277	#491	—	3	1	no	—
278	#485	—	3	1	no	—
279	#483	—	3	1	no	—
280	#479	—	3	1	no	—
281	#470	—	3	1	no	—
282	#467	—	3	1	no	—
283	#462	—	3	1	no	—
284	#451	—	3	1	no	—
285	#451	—	3	1	no	—
286	#441	—	3	1	no	—
287	#435	C₃×D₃	1	1	yes	characteristic
288	#419	—	3	1	no	—
289	C₂×#103	—	3	1	no	—
290	C₂×C₃×Q₈	—	3	1	no	—
291	C₂×C₃×Q₈	—	3	1	no	—
292	C₂×C₃×Q₈	—	3	1	no	—
293	C₂×C₃×Q₈	—	3	1	no	—
294	C₂×C₃×Q₈	—	6	2	no	—
295	C₂×C₃×Q₈	—	6	2	no	—
296	C₂×C₃×Q₈	—	6	1	no	—
297	C₂×C₃×Q₈	—	6	1	no	—
298	C₂×C₃×Q₈	—	12	1	no	—
299	C₂×C₃×Q₈	—	12	1	no	—
300	C₂×C₃×D₄	—	2	1	no	—
301	C₂×C₃×D₄	D₁₂	1	1	yes	characteristic
302	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
303	C₂²×C₃×C₄	—	2	1	no	—
304	C₂²×C₃×C₄	—	2	1	no	—
305	C₂²×C₃×C₄	—	6	1	no	—
306	C₂²×C₃×C₄	—	6	1	no	—
307	C₂²×C₃×C₄	—	6	1	no	—
308	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
310	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
312	C₂²×Dic₃	—	2	1	no	—
313	C₂²×Dic₃	—	2	1	no	—
314	C₂²×Dic₃	—	2	1	no	—
315	C₂×Dic₆	—	2	2	no	—
316	C₂×Dic₆	—	2	2	no	—
317	C₂×Dic₆	—	2	1	no	—
318	C₂×Dic₆	—	2	1	no	—
319	C₂×Dic₆	—	4	1	no	—
320	C₂×Dic₆	—	4	1	no	—
321	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
322	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
323	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
324	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
325	C₃×Q₁₆	—	6	2	no	—
326	C₃×Q₁₆	—	12	1	no	—
327	C₃×Q₁₆	—	12	1	no	—
328	C₃×M₁₆	—	4	1	no	—
329	C₃×M₁₆	—	4	1	no	—
330	C₃×M₁₆	—	4	2	no	—
331	C₂×C₃×C₈	—	2	1	no	—
332	C₂×C₃×C₈	—	2	1	no	—
333	C₂×C₃×C₈	—	2	1	no	—
334	C₂×C₃×C₈	—	2	1	no	—
335	C₂×C₃×C₈	—	4	1	no	—
336	C₂×C₃×C₈	—	4	1	no	—
337	C₂×C₃×C₈	—	4	2	no	—
338	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
339	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
340	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
341	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
342	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
343	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
344	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
345	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
346	C₃×C₄⋊C₄	—	2	1	no	—
347	C₃×C₄⋊C₄	—	3	1	no	—
348	C₃×C₄⋊C₄	—	3	1	no	—
349	C₃×C₄⋊C₄	—	3	1	no	—
350	C₃×C₄⋊C₄	—	3	1	no	—
351	C₃×C₄⋊C₄	—	6	1	no	—
352	C₃×C₄⋊C₄	—	6	1	no	—
353	C₃×C₄⋊C₄	—	6	1	no	—
354	C₃×C₄⋊C₄	—	6	1	no	—
355	C₃×C₄⋊C₄	—	6	1	no	—
356	C₃×C₄⋊C₄	—	6	1	no	—
357	C₃×C₄⋊C₄	—	6	1	no	—
358	C₃×C₄⋊C₄	—	6	1	no	—
359	C₃×C₄⋊C₄	—	6	1	no	—
360	C₃×C₄⋊C₄	—	6	1	no	—
361	C₃×C₄⋊C₄	—	6	1	no	—
362	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
363	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
364	C₃×C₂²⋊C₄	—	2	1	no	—
365	C₃×C₂²⋊C₄	—	2	1	no	—
366	C₃×C₂²⋊C₄	—	6	1	no	—
367	C₃×C₂²⋊C₄	—	6	1	no	—
368	C₃×C₂²⋊C₄	—	6	1	no	—
369	C₃×C₂²⋊C₄	—	6	1	no	—
370	C₃×C₂²⋊C₄	—	6	1	no	—
371	C₃×C₂²⋊C₄	D₁₂	1	1	yes	characteristic
372	C₃×C₂²⋊C₄	D₁₂	1	1	yes	characteristic
373	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
374	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
375	C₃×C₄²	—	2	1	no	—
376	C₃×C₄²	—	6	1	no	—
377	C₃×C₄²	—	6	1	no	—
378	C₃×C₄²	—	6	1	no	—
379	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
380	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
381	#217	—	2	1	no	—
382	#217	—	2	1	no	—
383	#217	—	2	1	no	—
384	#217	—	2	1	no	—
385	#217	—	2	1	no	—
386	C₄⋊Dic₃	—	2	1	no	—
387	C₄⋊Dic₃	—	2	1	no	—
388	C₄⋊Dic₃	—	2	1	no	—
389	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
390	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
391	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
392	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
393	Dic₃⋊C₄	—	2	1	no	—
394	Dic₃⋊C₄	—	2	1	no	—
395	Dic₃⋊C₄	—	2	1	no	—
396	Dic₃⋊C₄	—	2	1	no	—
397	Dic₃⋊C₄	—	2	1	no	—
398	Dic₃⋊C₄	—	2	1	no	—
399	Dic₃⋊C₄	—	2	1	no	—
400	Dic₃⋊C₄	—	2	1	no	—
401	C₄×Dic₃	—	2	1	no	—
402	C₄×Dic₃	—	2	1	no	—
403	C₄×Dic₃	—	2	1	no	—
404	Dic₁₂	—	2	2	no	—
405	Dic₁₂	—	4	1	no	—
406	Dic₁₂	—	4	1	no	—
407	C₂²×C₃²	—	2	1	no	—
408	C₂²×C₃²	—	2	1	no	—
409	C₂²×C₃²	—	2	1	no	—
410	C₂²×C₃²	—	2	1	no	—
411	C₂²×C₃²	—	2	1	no	—
412	C₂²×C₃²	#137	1	2	yes	—
413	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
414	C₃²×C₄	—	2	1	no	—
415	C₃²×C₄	—	2	1	no	—
416	C₃²×C₄	—	2	1	no	—
417	C₃²×C₄	—	2	1	no	—
418	C₃²×C₄	C₂×#41	1	1	yes	characteristic
419	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
420	C₃×Dic₃	—	2	2	no	—
421	C₃×Dic₃	—	4	1	no	—
422	C₃×Dic₃	—	4	1	no	—
423	C₃×Dic₃	—	4	1	no	—
424	C₃×Dic₃	—	4	1	no	—
425	C₃×Dic₃	—	4	1	no	—
426	C₃×Dic₃	—	4	1	no	—
427	C₃×Dic₃	—	4	1	no	—
428	C₂²×Q₈	—	3	1	no	—
429	C₂²×Q₈	—	3	1	no	—
430	C₂×Q₁₆	—	3	1	no	—
431	C₂×Q₁₆	—	3	1	no	—
432	C₂×Q₁₆	—	3	1	no	—
433	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
434	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
435	C₄⋊Q₈	—	3	1	no	—
436	C₄⋊Q₈	—	6	1	no	—
437	#126	—	6	1	no	—
438	#125	—	3	1	no	—
439	#125	—	6	1	no	—
440	#123	—	6	1	no	—
441	C₂²⋊Q₈	—	3	1	no	—
442	C₂²⋊Q₈	—	3	1	no	—
443	C₂²⋊Q₈	—	3	1	no	—
444	C₂²⋊Q₈	—	3	1	no	—
445	C₂²⋊Q₈	—	6	1	no	—
446	C₂²⋊Q₈	—	6	1	no	—
447	C₄×Q₈	—	3	1	no	—
448	C₄×Q₈	—	3	1	no	—
449	C₄×D₄	—	6	1	no	—
450	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
451	#117	—	3	1	no	—
452	#117	—	6	1	no	—
453	C₂×C₄⋊C₄	—	3	1	no	—
454	#107	—	3	1	no	—
455	#106	—	3	1	no	—
456	#106	—	3	1	no	—
457	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
458	#103	—	3	1	no	—
459	#103	—	3	1	no	—
460	#103	—	3	1	no	—
461	#103	—	3	1	no	—
462	#103	—	3	1	no	—
463	#103	—	3	1	no	—
464	#103	—	3	1	no	—
465	#103	—	3	1	no	—
466	#103	—	3	1	no	—
467	#103	—	3	1	no	—
468	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
469	C₂²⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
470	#97	C₂×C₃×D₃	1	1	yes	characteristic
471	C₂³×C₃	—	2	1	no	—
472	C₂³×C₃	—	2	1	no	—
473	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
474	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
475	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
476	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
477	C₃×Q₈	—	3	2	no	—
478	C₃×Q₈	—	6	1	no	—
479	C₃×Q₈	—	6	1	no	—
480	C₃×Q₈	—	6	1	no	—
481	C₃×Q₈	—	6	1	no	—
482	C₃×Q₈	—	6	1	no	—
483	C₃×Q₈	—	6	1	no	—
484	C₃×Q₈	—	6	1	no	—
485	C₃×Q₈	—	12	2	no	—
486	C₃×Q₈	—	12	2	no	—
487	C₃×D₄	—	2	2	no	—
488	C₃×D₄	—	2	2	no	—
489	C₃×D₄	—	4	2	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	4	1	no	—
504	C₂×C₃×C₄	—	4	1	no	—
505	C₂×C₃×C₄	—	4	1	no	—
506	C₂×C₃×C₄	—	4	1	no	—
507	C₂×C₃×C₄	—	6	1	no	—
508	C₂×C₃×C₄	—	6	1	no	—
509	C₂×C₃×C₄	—	6	1	no	—
510	C₂×C₃×C₄	—	6	1	no	—
511	C₂×C₃×C₄	—	6	1	no	—
512	C₂×C₃×C₄	—	6	1	no	—
513	C₂×C₃×C₄	—	6	1	no	—
514	C₂×C₃×C₄	—	6	1	no	—
515	C₂×C₃×C₄	—	12	2	no	—
516	C₂×C₃×C₄	—	12	2	no	—
517	C₂×C₃×C₄	—	12	2	no	—
518	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
519	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
520	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
521	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
522	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
523	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
524	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
525	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
526	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
528	C₂×Dic₃	—	2	1	no	—
529	C₂×Dic₃	—	2	1	no	—
530	C₂×Dic₃	—	2	1	no	—
531	C₂×Dic₃	—	2	1	no	—
532	C₂×Dic₃	—	2	1	no	—
533	C₂×Dic₃	—	2	1	no	—
534	C₂×Dic₃	—	2	1	no	—
535	C₂×Dic₃	—	2	1	no	—
536	C₂×Dic₃	—	4	2	no	—
537	C₂×Dic₃	—	4	2	no	—
538	C₂×Dic₃	—	4	2	no	—
539	Dic₆	—	2	1	no	—
540	Dic₆	—	2	1	no	—
541	Dic₆	—	2	1	no	—
542	Dic₆	—	2	1	no	—
543	Dic₆	—	2	1	no	—
544	Dic₆	—	2	1	no	—
545	Dic₆	—	2	1	no	—
546	Dic₆	—	4	2	no	—
547	Dic₆	—	4	2	no	—
548	Dic₆	C₃×#41	1	2	yes	—
549	C₃×C₈	—	2	2	no	—
550	C₃×C₈	—	2	1	no	—
551	C₃×C₈	—	2	1	no	—
552	C₃×C₈	—	2	1	no	—
553	C₃×C₈	—	2	1	no	—
554	C₃×C₈	—	2	1	no	—
555	C₃×C₈	—	2	1	no	—
556	C₃×C₈	—	2	1	no	—
557	C₃×C₈	—	2	1	no	—
558	C₃×C₈	—	4	1	no	—
559	C₃×C₈	—	4	1	no	—
560	C₃×C₈	—	4	1	no	—
561	C₂×C₃²	—	2	2	no	—
562	C₂×C₃²	—	4	1	no	—
563	C₂×C₃²	#546	1	1	yes	characteristic
564	C₂×C₃²	C₂×#137	1	1	yes	characteristic
565	C₂×C₃²	#578	1	1	yes	characteristic
566	C₂×Q₈	—	3	1	no	—
567	C₂×Q₈	—	3	1	no	—
568	C₂×Q₈	—	3	1	no	—
569	C₂×Q₈	—	3	1	no	—
570	C₂×Q₈	—	6	2	no	—
571	C₂×Q₈	—	6	2	no	—
572	C₂×Q₈	—	6	1	no	—
573	C₂×Q₈	—	6	1	no	—
574	C₂×Q₈	—	12	1	no	—
575	C₂×Q₈	—	12	1	no	—
576	C₂×D₄	C₃×D₁₂	1	1	yes	characteristic
577	C₂²×C₄	—	6	1	no	—
578	C₂²×C₄	—	6	1	no	—
579	C₂²×C₄	—	6	1	no	—
580	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
581	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
582	Q₁₆	—	6	2	no	—
583	Q₁₆	—	12	1	no	—
584	Q₁₆	—	12	1	no	—
585	M₁₆	—	4	1	no	—
586	C₂×C₈	—	4	1	no	—
587	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
588	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
589	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
590	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
591	C₄⋊C₄	—	3	1	no	—
592	C₄⋊C₄	—	3	1	no	—
593	C₄⋊C₄	—	3	1	no	—
594	C₄⋊C₄	—	3	1	no	—
595	C₄⋊C₄	—	6	1	no	—
596	C₄⋊C₄	—	6	1	no	—
597	C₄⋊C₄	—	6	1	no	—
598	C₄⋊C₄	—	6	1	no	—
599	C₄⋊C₄	—	6	1	no	—
600	C₄⋊C₄	—	6	1	no	—
601	C₄⋊C₄	—	6	1	no	—
602	C₄⋊C₄	—	6	1	no	—
603	C₄⋊C₄	—	6	1	no	—
604	C₄⋊C₄	—	6	1	no	—
605	C₄⋊C₄	—	6	1	no	—
606	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
607	C₂²⋊C₄	—	6	1	no	—
608	C₂²⋊C₄	—	6	1	no	—
609	C₂²⋊C₄	—	6	1	no	—
610	C₂²⋊C₄	—	6	1	no	—
611	C₂²⋊C₄	—	6	1	no	—
612	C₂²⋊C₄	C₃×D₁₂	1	1	yes	characteristic
613	C₂²⋊C₄	C₃×D₁₂	1	1	yes	characteristic
614	C₄²	—	6	1	no	—
615	C₄²	—	6	1	no	—
616	C₄²	—	6	1	no	—
617	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
618	C₂²×C₃	—	2	1	no	—
619	C₂²×C₃	—	2	1	no	—
620	C₂²×C₃	—	2	1	no	—
621	C₂²×C₃	—	2	1	no	—
622	C₂²×C₃	—	2	1	no	—
623	C₂²×C₃	—	2	1	no	—
624	C₂²×C₃	—	2	1	no	—
625	C₂²×C₃	—	2	1	no	—
626	C₂²×C₃	—	2	1	no	—
627	C₂²×C₃	—	2	1	no	—
628	C₂²×C₃	—	2	2	no	—
629	C₂²×C₃	—	2	1	no	—
630	C₂²×C₃	—	4	1	no	—
631	C₂²×C₃	—	4	1	no	—
632	C₂²×C₃	—	4	1	no	—
633	C₂²×C₃	—	4	1	no	—
634	C₂²×C₃	—	4	1	no	—
635	C₂²×C₃	#909	1	2	yes	—
636	C₂²×C₃	C₃×#137	1	2	yes	—
637	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
638	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
639	C₃×C₄	—	2	1	no	—
640	C₃×C₄	—	2	1	no	—
641	C₃×C₄	—	2	1	no	—
642	C₃×C₄	—	2	1	no	—
643	C₃×C₄	—	2	1	no	—
644	C₃×C₄	—	2	1	no	—
645	C₃×C₄	—	2	1	no	—
646	C₃×C₄	—	2	1	no	—
647	C₃×C₄	—	2	1	no	—
648	C₃×C₄	—	2	1	no	—
649	C₃×C₄	—	4	1	no	—
650	C₃×C₄	—	4	1	no	—
651	C₃×C₄	—	4	1	no	—
652	C₃×C₄	—	4	1	no	—
653	C₃×C₄	—	6	2	no	—
654	C₃×C₄	—	12	1	no	—
655	C₃×C₄	—	12	1	no	—
656	C₃×C₄	—	12	1	no	—
657	C₃×C₄	—	12	1	no	—
658	C₃×C₄	—	12	1	no	—
659	C₃×C₄	—	12	1	no	—
660	C₃×C₄	—	12	1	no	—
661	C₃×C₄	#1004	1	1	yes	characteristic
662	C₃×C₄	D₃×#41	1	1	yes	characteristic
663	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
664	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
665	Dic₃	—	2	2	no	—
666	Dic₃	—	4	1	no	—
667	Dic₃	—	4	1	no	—
668	Dic₃	—	4	1	no	—
669	Dic₃	—	4	1	no	—
670	Dic₃	—	4	1	no	—
671	Dic₃	—	4	1	no	—
672	Dic₃	—	4	1	no	—
673	C₃²	#3312	1	1	yes	characteristic, complemented, Sylow
674	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
675	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
676	Q₈	—	3	2	no	—
677	Q₈	—	6	1	no	—
678	Q₈	—	6	1	no	—
679	Q₈	—	6	1	no	—
680	Q₈	—	6	1	no	—
681	Q₈	—	6	1	no	—
682	Q₈	—	6	1	no	—
683	Q₈	—	6	1	no	—
684	Q₈	—	12	2	no	—
685	Q₈	—	12	2	no	—
686	D₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	6	1	no	—
692	C₂×C₄	—	6	1	no	—
693	C₂×C₄	—	6	1	no	—
694	C₂×C₄	—	6	1	no	—
695	C₂×C₄	—	6	1	no	—
696	C₂×C₄	—	6	1	no	—
697	C₂×C₄	—	6	1	no	—
698	C₂×C₄	—	6	1	no	—
699	C₂×C₄	—	12	2	no	—
700	C₂×C₄	—	12	2	no	—
701	C₂×C₄	—	12	2	no	—
702	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
703	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
704	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
705	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
706	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
707	C₈	—	2	1	no	—
708	C₈	—	2	1	no	—
709	C₈	—	2	1	no	—
710	C₈	—	2	1	no	—
711	C₂×C₃	—	2	2	no	—
712	C₂×C₃	—	2	2	no	—
713	C₂×C₃	—	2	1	no	—
714	C₂×C₃	—	2	1	no	—
715	C₂×C₃	—	2	1	no	—
716	C₂×C₃	—	4	2	no	—
717	C₂×C₃	—	4	1	no	—
718	C₂×C₃	—	4	1	no	—
719	C₂×C₃	—	8	1	no	—
720	C₂×C₃	#5554	1	1	yes	characteristic
721	C₂×C₃	C₂×#909	1	1	yes	characteristic
722	C₂×C₃	#5753	1	1	yes	characteristic
723	C₂×C₃	C₃×#546	1	1	yes	characteristic
724	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
725	C₂×C₃	C₃×#578	1	1	yes	characteristic
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	C₃×#909	1	2	yes	—
732	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	6	2	no	—
738	C₄	—	12	1	no	—
739	C₄	—	12	1	no	—
740	C₄	—	12	1	no	—
741	C₄	—	12	1	no	—
742	C₄	—	12	1	no	—
743	C₄	—	12	1	no	—
744	C₄	—	12	1	no	—
745	C₄	C₃×#1004	1	1	yes	characteristic
746	C₄	C₃×D₃×#41	1	1	yes	characteristic
747	C₃	—	2	1	no	—
748	C₃	#79511	1	1	yes	characteristic, direct product factor
749	C₃	C₃×#3312	1	1	yes	characteristic, complemented
750	C₂	—	2	2	no	—
751	C₂	—	4	1	no	—
752	C₂	C₃×#5554	1	1	yes	characteristic
753	C₂	C₂×C₃×#909	1	1	yes	characteristic
754	C₂	C₃×#5753	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#435	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃²×D₄	D₄
hypercenter	C₃×#435	D₃
hypocenter	C₃	C₃×#3312
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄ ◁ C₃×#435

Complements

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

N	H ≅ G/N	type
4. C₃×#5137	C₂	semidirect
5. C₃×#5120	C₂	semidirect
6. C₃×#5116	C₂	semidirect
7. C₂×C₃×#816	C₂	semidirect
8. C₃×#4849	C₂	semidirect
9. C₃×#4829	C₂	semidirect
10. C₃×#4739	C₂	semidirect
11. C₃×#4739	C₂	semidirect
12. C₃×#4723	C₂	semidirect
13. C₃×#4721	C₂	semidirect
14. C₃×#4716	C₂	semidirect
15. C₃×#4703	C₂	semidirect
17. #79511	C₃	direct (N × H)
80. #5137	C₂×C₃	semidirect
81. #5120	C₂×C₃	semidirect
82. #5116	C₂×C₃	semidirect
83. C₂×#816	C₂×C₃	semidirect
84. #4849	C₂×C₃	semidirect
85. #4829	C₂×C₃	semidirect
86. #4739	C₂×C₃	semidirect
87. #4739	C₂×C₃	semidirect
88. #4723	C₂×C₃	semidirect
89. #4721	C₂×C₃	semidirect
90. #4716	C₂×C₃	semidirect
91. #4703	C₂×C₃	semidirect
673. C₃²	#3312	semidirect
748. C₃	#79511	direct (N × H)
749. C₃	C₃×#3312	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5541	2
C₃×D₄×Dic₆	2
C₃²×#435	2
C₃×#5137	2
C₃×#5120	2
C₃×#5116	2
C₂×C₃×#816	2
C₃×#4849	2
C₃×#4829	2
C₃×#4739	2
C₃×#4723	2
C₃×#4721	2
C₃×#4716	2
C₃×#4703	2
C₃×#3312	3
#79511	3

Subgroups — C3×#79511 #11889352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79511 #11889352