Subgroups — C₃×#86257 #11900881

Order 1152.

2535 conjugacy classes of subgroups.

The subgroup lattice has 667 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5728	C₂	1	2	yes	maximal, complemented
3	C₃×#5725	C₂	1	2	yes	maximal, complemented
4	C₃×#5691	C₂	1	4	yes	maximal, complemented
5	C₃×#5627	C₂	1	4	yes	maximal, complemented
6	C₃×#5624	C₂	1	4	yes	maximal, complemented
7	C₃×#5580	C₂	1	4	yes	maximal, complemented
8	C₃×C₄×#239	C₂	1	4	yes	maximal, complemented
9	C₃×#5524	C₂	1	2	yes	maximal, complemented
10	C₃×#5522	C₂	1	2	yes	maximal, complemented
11	C₃×#5477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3444	—	3	1	no	maximal
14	#86257	C₃	1	1	yes	maximal, characteristic, direct product factor
15	C₂×C₃×#239	C₂²	1	4	yes	—
16	C₂×C₃×#235	C₂²	1	2	yes	—
17	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
19	C₃²×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₃²×#125	C₂²	1	2	yes	complemented
21	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₃²×C₄×Q₈	C₂²	1	4	yes	complemented
23	C₃²×#117	C₂²	1	2	yes	—
24	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
25	C₃×#947	C₂²	1	4	yes	complemented
26	C₃×#946	C₂²	1	4	yes	—
27	C₃×Q₈×Dic₃	C₂²	1	4	yes	complemented
28	C₃×#930	C₂²	1	4	yes	—
29	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
31	C₃×#898	C₂²	1	8	yes	complemented
32	C₃×#897	C₂²	1	4	yes	—
33	C₃×#895	C₂²	1	4	yes	—
34	C₃×#895	C₂²	1	4	yes	—
35	C₃×#894	C₂²	1	8	yes	—
36	C₃×#893	C₂²	1	8	yes	—
37	C₃×#893	C₂²	1	4	yes	complemented
38	C₃×#893	C₂²	1	4	yes	complemented
39	C₃×#892	C₂²	1	4	yes	—
40	C₃×#892	C₂²	1	8	yes	complemented
41	C₃×#890	C₂²	1	4	yes	complemented
42	C₃×#887	C₂²	1	4	yes	complemented
43	C₃×#886	C₂²	1	4	yes	—
44	C₃×#882	C₂²	1	4	yes	—
45	C₃×#67⋊C₄	C₂²	1	8	yes	—
46	C₃×#875	C₂²	1	2	yes	complemented
47	C₃×#874	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₄×D₁₂	C₂²	1	8	yes	—
49	C₃×C₄×D₁₂	C₂²	1	4	yes	complemented
50	C₃×#872	C₂²	1	4	yes	complemented
51	C₃×C₄²×D₃	C₂²	1	2	yes	—
52	C₃×C₄²×D₃	C₂²	1	2	yes	—
53	C₃×C₄²×D₃	C₂²	1	2	yes	—
54	C₃×C₄²×D₃	C₂²	1	2	yes	—
55	C₃×C₄²×D₃	C₂²	1	4	yes	complemented
56	C₃×#869	C₂²	1	1	yes	characteristic, complemented
57	C₃×#533	—	2	1	no	—
58	C₃×#533	—	3	2	no	—
59	C₃×#533	D₃	1	1	yes	characteristic, complemented
60	C₃×#533	C₂×C₃	1	1	yes	characteristic, complemented
61	C₃×#532	—	3	2	no	—
62	C₃×#532	—	3	1	no	—
63	C₃×#529	—	3	4	no	—
64	C₃×#529	—	3	4	no	—
65	C₃×#529	—	3	4	no	—
66	C₃×#525	—	3	4	no	—
67	C₃×#525	—	3	2	no	—
68	C₃×C₄×#41	—	3	4	no	—
69	C₃×C₄×#41	—	3	2	no	—
70	C₂²×C₃×C₄²	—	3	1	no	—
71	#5728	C₂×C₃	1	2	yes	complemented
72	#5725	C₂×C₃	1	2	yes	complemented
73	#5691	C₂×C₃	1	4	yes	complemented
74	#5627	C₂×C₃	1	4	yes	complemented
75	#5624	C₂×C₃	1	4	yes	complemented
76	#5580	C₂×C₃	1	4	yes	complemented
77	C₄×#239	C₂×C₃	1	4	yes	complemented
78	#5524	C₂×C₃	1	2	yes	complemented
79	#5522	C₂×C₃	1	2	yes	complemented
80	#5477	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
83	C₂×C₃²×Q₈	C₂³	1	4	yes	—
84	C₂²×C₃²×C₄	C₂³	1	2	yes	—
85	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
86	C₂×C₃×#67	C₂³	1	4	yes	—
87	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
88	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
89	C₃×#239	—	2	16	no	—
90	C₃×#235	—	2	8	no	—
91	C₂×C₃×D₁₂	C₂³	1	8	yes	—
92	C₂×C₃×D₁₂	C₂³	1	2	yes	—
93	C₂×C₃×D₁₂	C₂³	1	4	yes	—
94	C₂×C₃×C₄×D₃	—	2	4	no	—
95	C₂×C₃×C₄×D₃	—	2	8	no	—
96	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
97	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
98	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
99	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
100	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
101	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
102	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
103	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
104	C₂×C₃×Dic₆	C₂³	1	2	yes	—
105	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
106	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
107	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
108	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₃²×C₄²	C₂³	1	2	yes	—
110	C₃²×C₄²	C₂³	1	1	yes	characteristic
111	C₃²×C₄²	C₂³	1	1	yes	characteristic
112	C₃²×C₄²	C₂³	1	4	yes	—
113	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
114	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
115	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
116	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
117	C₃×C₄⋊Dic₃	C₂³	1	8	yes	—
118	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
119	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
120	C₃×C₄×Dic₃	C₂³	1	8	yes	—
121	C₃×C₄×Dic₃	C₂³	1	2	yes	—
122	C₃×C₄×Dic₃	C₂³	1	2	yes	—
123	C₃×C₄×Dic₃	C₂³	1	2	yes	—
124	C₃×C₄×Dic₃	C₂³	1	2	yes	—
125	C₃×C₄×Dic₃	C₂³	1	2	yes	—
126	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
127	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
128	#3444	—	3	1	no	Sylow
129	C₂×C₃×#41	—	3	4	no	—
130	C₂×C₃×#41	—	3	2	no	—
131	C₂³×C₃×C₄	—	3	2	no	—
132	C₂³×C₃×C₄	—	3	1	no	—
133	C₂×#239	C₂²×C₃	1	4	yes	—
134	C₂×#235	C₂²×C₃	1	2	yes	—
135	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
136	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
137	C₃×C₄⋊Q₈	—	2	2	no	—
138	C₃×C₄⋊Q₈	—	3	1	no	—
139	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
140	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
141	C₃×#127	—	3	1	no	—
142	C₃×#126	—	3	8	no	—
143	C₃×#125	—	2	2	no	—
144	C₃×#125	—	3	4	no	—
145	C₃×#125	C₂×D₃	1	2	yes	complemented
146	C₃×#125	C₂²×C₃	1	2	yes	complemented
147	C₃×#124	—	3	4	no	—
148	C₃×#124	—	3	2	no	—
149	C₃×#123	—	3	8	no	—
150	C₃×#123	—	3	4	no	—
151	C₃×C₂²⋊Q₈	—	2	4	no	—
152	C₃×C₂²⋊Q₈	—	3	4	no	—
153	C₃×C₂²⋊Q₈	—	3	4	no	—
154	C₃×C₂²⋊Q₈	C₂×D₃	1	4	yes	—
155	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
156	C₃×#121	—	3	4	no	—
157	C₃×#121	—	3	4	no	—
158	C₃×#121	—	3	4	no	—
159	C₃×#120	—	3	4	no	—
160	C₃×C₄×Q₈	—	2	4	no	—
161	C₃×C₄×Q₈	—	3	4	no	—
162	C₃×C₄×Q₈	—	3	4	no	—
163	C₃×C₄×Q₈	C₂×D₃	1	4	yes	complemented
164	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
165	C₃×C₄×D₄	—	3	8	no	—
166	C₃×C₄×D₄	—	3	4	no	—
167	C₃×C₄×D₄	—	3	4	no	—
168	C₃×C₄×D₄	—	3	8	no	—
169	C₃×C₄×D₄	—	3	8	no	—
170	C₃×C₄×D₄	—	3	4	no	—
171	C₃×#117	—	2	2	no	—
172	C₃×#117	—	3	4	no	—
173	C₃×#117	—	3	8	no	—
174	C₃×#117	—	3	4	no	—
175	C₃×#117	C₂×D₃	1	2	yes	—
176	C₃×#117	C₂²×C₃	1	2	yes	—
177	C₂×C₃×C₄²	—	2	1	no	—
178	C₂×C₃×C₄²	—	3	1	no	—
179	C₂×C₃×C₄²	—	3	2	no	—
180	C₂×C₃×C₄²	—	3	2	no	—
181	C₂×C₃×C₄²	—	3	2	no	—
182	C₂×C₃×C₄²	—	3	2	no	—
183	C₂×C₃×C₄²	—	3	2	no	—
184	C₂×C₃×C₄²	—	3	4	no	—
185	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
186	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
187	#947	C₂²×C₃	1	4	yes	complemented
188	#946	C₂²×C₃	1	4	yes	—
189	Q₈×Dic₃	C₂²×C₃	1	4	yes	complemented
190	#930	C₂²×C₃	1	4	yes	—
191	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
192	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
193	#898	C₂²×C₃	1	8	yes	complemented
194	#897	C₂²×C₃	1	4	yes	—
195	#895	C₂²×C₃	1	4	yes	—
196	#895	C₂²×C₃	1	4	yes	—
197	#894	C₂²×C₃	1	8	yes	—
198	#893	C₂²×C₃	1	8	yes	—
199	#893	C₂²×C₃	1	4	yes	complemented
200	#893	C₂²×C₃	1	4	yes	complemented
201	#892	C₂²×C₃	1	4	yes	—
202	#892	C₂²×C₃	1	8	yes	complemented
203	#890	C₂²×C₃	1	4	yes	complemented
204	#887	C₂²×C₃	1	4	yes	complemented
205	#886	C₂²×C₃	1	4	yes	—
206	#882	C₂²×C₃	1	4	yes	—
207	#67⋊C₄	C₂²×C₃	1	8	yes	—
208	#875	C₂²×C₃	1	2	yes	complemented
209	#874	C₂²×C₃	1	1	yes	characteristic, complemented
210	C₄×D₁₂	C₂²×C₃	1	8	yes	—
211	C₄×D₁₂	C₂²×C₃	1	4	yes	complemented
212	#872	C₂²×C₃	1	4	yes	complemented
213	C₄²×D₃	C₂²×C₃	1	2	yes	—
214	C₄²×D₃	C₂²×C₃	1	2	yes	—
215	C₄²×D₃	C₂²×C₃	1	2	yes	—
216	C₄²×D₃	C₂²×C₃	1	2	yes	—
217	C₄²×D₃	C₂²×C₃	1	4	yes	complemented
218	#869	C₂²×C₃	1	1	yes	characteristic, complemented
219	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
220	C₂²×C₃×D₃	—	2	2	no	—
221	C₂²×C₃×D₃	—	2	4	no	—
222	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
223	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
224	C₃²×Q₈	—	2	8	no	—
225	C₂×C₃²×C₄	—	2	4	no	—
226	C₂×C₃²×C₄	#41	1	4	yes	complemented
227	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
228	C₂×C₃²×C₄	C₂⁴	1	8	yes	—
229	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
230	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
231	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
232	C₃×#67	—	2	8	no	—
233	C₂×C₃×Dic₃	—	2	2	no	—
234	C₂×C₃×Dic₃	—	2	4	no	—
235	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
236	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
237	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
238	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
239	C₃×D₁₂	—	2	16	no	—
240	C₃×D₁₂	—	2	4	no	—
241	C₃×D₁₂	—	2	8	no	—
242	C₃×C₄×D₃	—	2	4	no	—
243	C₃×C₄×D₃	—	2	4	no	—
244	C₃×C₄×D₃	—	2	4	no	—
245	C₃×C₄×D₃	—	2	4	no	—
246	C₃×C₄×D₃	—	2	8	no	—
247	C₃×C₄×D₃	—	2	4	no	—
248	C₃×C₄×D₃	—	2	16	no	—
249	C₃×C₄×D₃	#41	1	8	yes	complemented
250	C₃×Dic₆	—	2	4	no	—
251	#533	—	3	2	no	—
252	#533	C₃×D₃	1	1	yes	characteristic, complemented
253	#532	—	3	2	no	—
254	#532	—	3	1	no	—
255	#529	—	3	4	no	—
256	#529	—	3	4	no	—
257	#529	—	3	4	no	—
258	#525	—	3	4	no	—
259	#525	—	3	2	no	—
260	C₄×#41	—	3	4	no	—
261	C₄×#41	—	3	2	no	—
262	C₂²×C₄²	—	3	1	no	—
263	C₂⁴×C₃	—	3	1	no	—
264	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
265	C₃×#41	—	6	16	no	—
266	C₃×#41	—	6	8	no	—
267	C₂×C₃×Q₈	—	2	4	no	—
268	C₂×C₃×Q₈	—	3	2	no	—
269	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
270	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
271	C₂×C₃×D₄	—	3	4	no	—
272	C₂×C₃×D₄	—	3	8	no	—
273	C₂×C₃×D₄	—	3	2	no	—
274	C₂×C₃×D₄	—	3	4	no	—
275	C₂²×C₃×C₄	—	2	1	no	—
276	C₂²×C₃×C₄	—	2	2	no	—
277	C₂²×C₃×C₄	—	3	2	no	—
278	C₂²×C₃×C₄	—	3	2	no	—
279	C₂²×C₃×C₄	—	3	1	no	—
280	C₂²×C₃×C₄	—	3	2	no	—
281	C₂²×C₃×C₄	—	3	2	no	—
282	C₂²×C₃×C₄	—	3	2	no	—
283	C₂²×C₃×C₄	—	3	2	no	—
284	C₂²×C₃×C₄	—	3	8	no	—
285	C₂²×C₃×C₄	—	3	2	no	—
286	C₂²×C₃×C₄	—	3	4	no	—
287	C₂²×C₃×C₄	—	6	8	no	—
288	C₂²×C₃×C₄	—	6	4	no	—
289	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
290	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
291	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
292	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
293	C₂×#67	C₂³×C₃	1	4	yes	—
294	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
295	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
296	#239	—	2	16	no	—
297	#235	—	2	8	no	—
298	C₂×D₁₂	C₂³×C₃	1	8	yes	—
299	C₂×D₁₂	C₂³×C₃	1	4	yes	—
300	C₂×D₁₂	C₂³×C₃	1	2	yes	—
301	C₂×C₄×D₃	—	2	4	no	—
302	C₂×C₄×D₃	—	2	8	no	—
303	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
304	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
305	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
306	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
307	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
308	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
309	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
310	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
311	C₂×Dic₆	C₂³×C₃	1	2	yes	—
312	C₃×C₄⋊C₄	—	2	4	no	—
313	C₃×C₄⋊C₄	—	2	8	no	—
314	C₃×C₄⋊C₄	—	2	4	no	—
315	C₃×C₄⋊C₄	—	3	8	no	—
316	C₃×C₄⋊C₄	—	3	4	no	—
317	C₃×C₄⋊C₄	—	3	8	no	—
318	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
319	C₃×C₄⋊C₄	C₂²×D₃	1	8	yes	—
320	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
321	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
322	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
323	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
324	C₃×C₂²⋊C₄	—	2	4	no	—
325	C₃×C₂²⋊C₄	—	3	8	no	—
326	C₃×C₂²⋊C₄	—	3	8	no	—
327	C₃×C₂²⋊C₄	—	3	8	no	—
328	C₃×C₂²⋊C₄	—	3	8	no	—
329	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
330	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
331	C₃×C₄²	—	2	2	no	—
332	C₃×C₄²	—	2	1	no	—
333	C₃×C₄²	—	2	1	no	—
334	C₃×C₄²	—	2	4	no	—
335	C₃×C₄²	—	3	2	no	—
336	C₃×C₄²	—	3	2	no	—
337	C₃×C₄²	—	3	2	no	—
338	C₃×C₄²	—	3	2	no	—
339	C₃×C₄²	—	3	2	no	—
340	C₃×C₄²	—	3	8	no	—
341	C₃×C₄²	—	3	1	no	—
342	C₃×C₄²	—	3	1	no	—
343	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
344	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
345	C₃×C₄²	C₂²×D₃	1	2	yes	—
346	C₃×C₄²	C₂²×D₃	1	4	yes	—
347	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
348	C₃×C₄²	C₂³×C₃	1	2	yes	—
349	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
350	C₃×C₄²	C₂³×C₃	1	4	yes	—
351	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
352	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
353	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
354	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
355	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
356	C₄⋊Dic₃	C₂³×C₃	1	8	yes	—
357	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
358	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
359	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
360	C₄×Dic₃	C₂³×C₃	1	2	yes	—
361	C₄×Dic₃	C₂³×C₃	1	2	yes	—
362	C₄×Dic₃	C₂³×C₃	1	2	yes	—
363	C₄×Dic₃	C₂³×C₃	1	2	yes	—
364	C₄×Dic₃	C₂³×C₃	1	2	yes	—
365	C₄×Dic₃	C₂³×C₃	1	8	yes	—
366	C₂²×C₃²	—	2	2	no	—
367	C₂²×C₃²	C₂×#41	1	2	yes	—
368	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
369	C₂×C₃×D₃	—	2	8	no	—
370	C₂×C₃×D₃	—	2	2	no	—
371	C₂×C₃×D₃	—	2	2	no	—
372	C₂×C₃×D₃	—	2	8	no	—
373	C₂×C₃×D₃	—	2	4	no	—
374	C₂×C₃×D₃	C₂×#41	1	4	yes	—
375	C₃²×C₄	—	2	2	no	—
376	C₃²×C₄	—	2	8	no	—
377	C₃²×C₄	C₂×#41	1	2	yes	—
378	C₃²×C₄	C₂×#41	1	2	yes	—
379	C₃²×C₄	C₂×#41	1	4	yes	—
380	C₃×Dic₃	—	2	4	no	—
381	C₃×Dic₃	—	2	2	no	—
382	C₃×Dic₃	—	2	2	no	—
383	C₃×Dic₃	C₂×#41	1	4	yes	—
384	C₂×#41	—	3	4	no	—
385	C₂×#41	—	3	2	no	—
386	C₂³×C₄	—	3	2	no	—
387	C₂³×C₄	—	3	1	no	—
388	C₄⋊Q₈	—	3	1	no	—
389	C₄⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
390	#127	—	3	1	no	—
391	#126	—	3	8	no	—
392	#125	—	3	4	no	—
393	#125	C₂×C₃×D₃	1	2	yes	complemented
394	#124	—	3	4	no	—
395	#124	—	3	2	no	—
396	#123	—	3	8	no	—
397	#123	—	3	4	no	—
398	C₂²⋊Q₈	—	3	4	no	—
399	C₂²⋊Q₈	—	3	4	no	—
400	C₂²⋊Q₈	C₂×C₃×D₃	1	4	yes	—
401	#121	—	3	4	no	—
402	#121	—	3	4	no	—
403	#121	—	3	4	no	—
404	#120	—	3	4	no	—
405	C₄×Q₈	—	3	4	no	—
406	C₄×Q₈	—	3	4	no	—
407	C₄×Q₈	C₂×C₃×D₃	1	4	yes	complemented
408	C₄×D₄	—	3	8	no	—
409	C₄×D₄	—	3	4	no	—
410	C₄×D₄	—	3	4	no	—
411	C₄×D₄	—	3	8	no	—
412	C₄×D₄	—	3	8	no	—
413	C₄×D₄	—	3	4	no	—
414	#117	—	3	4	no	—
415	#117	—	3	8	no	—
416	#117	—	3	4	no	—
417	#117	C₂×C₃×D₃	1	2	yes	—
418	C₂×C₄²	—	3	1	no	—
419	C₂×C₄²	—	3	2	no	—
420	C₂×C₄²	—	3	4	no	—
421	C₂×C₄²	—	3	2	no	—
422	C₂×C₄²	—	3	2	no	—
423	C₂×C₄²	—	3	2	no	—
424	C₂×C₄²	—	3	2	no	—
425	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
426	C₂³×C₃	—	2	1	no	—
427	C₂³×C₃	—	3	2	no	—
428	C₂³×C₃	—	3	4	no	—
429	C₂³×C₃	—	6	4	no	—
430	C₂³×C₃	—	6	2	no	—
431	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
432	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
433	C₂²×D₃	—	2	2	no	—
434	C₂²×D₃	—	2	4	no	—
435	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
436	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
437	C₃×Q₈	—	2	8	no	—
438	C₃×Q₈	—	2	8	no	—
439	C₃×Q₈	—	4	8	no	—
440	C₃×Q₈	—	6	4	no	—
441	C₃×D₄	—	6	16	no	—
442	C₃×D₄	—	6	8	no	—
443	C₃×D₄	—	6	4	no	—
444	C₃×D₄	—	6	8	no	—
445	C₂×C₃×C₄	—	2	4	no	—
446	C₂×C₃×C₄	—	2	4	no	—
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	2	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	8	no	—
452	C₂×C₃×C₄	—	2	4	no	—
453	C₂×C₃×C₄	—	3	2	no	—
454	C₂×C₃×C₄	—	3	8	no	—
455	C₂×C₃×C₄	—	3	2	no	—
456	C₂×C₃×C₄	—	3	2	no	—
457	C₂×C₃×C₄	—	3	4	no	—
458	C₂×C₃×C₄	—	4	4	no	—
459	C₂×C₃×C₄	—	6	4	no	—
460	C₂×C₃×C₄	—	6	16	no	—
461	C₂×C₃×C₄	—	6	4	no	—
462	C₂×C₃×C₄	—	6	4	no	—
463	C₂×C₃×C₄	—	6	2	no	—
464	C₂×C₃×C₄	—	6	4	no	—
465	C₂×C₃×C₄	—	6	4	no	—
466	C₂×C₃×C₄	—	6	8	no	—
467	C₂×C₃×C₄	—	6	4	no	—
468	C₂×C₃×C₄	#239	1	4	yes	complemented
469	C₂×C₃×C₄	C₃×#41	1	4	yes	complemented
470	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
471	C₂×C₃×C₄	C₂³×D₃	1	8	yes	—
472	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
473	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
474	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
475	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
476	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
477	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
478	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
479	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
480	#67	—	2	8	no	—
481	C₂×Dic₃	—	2	2	no	—
482	C₂×Dic₃	—	2	4	no	—
483	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
484	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
485	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
486	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
487	D₁₂	—	2	16	no	—
488	D₁₂	—	2	4	no	—
489	D₁₂	—	2	8	no	—
490	C₄×D₃	—	2	4	no	—
491	C₄×D₃	—	2	4	no	—
492	C₄×D₃	—	2	4	no	—
493	C₄×D₃	—	2	4	no	—
494	C₄×D₃	—	2	8	no	—
495	C₄×D₃	—	2	4	no	—
496	C₄×D₃	—	2	16	no	—
497	C₄×D₃	C₃×#41	1	8	yes	complemented
498	Dic₆	—	2	4	no	—
499	C₂×C₃²	—	2	2	no	—
500	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
501	C₂×C₃²	C₂²×#41	1	2	yes	—
502	C₃×D₃	—	2	4	no	—
503	C₃×D₃	—	4	4	no	—
504	C₂⁴	—	3	1	no	—
505	#41	—	6	16	no	—
506	#41	—	6	8	no	—
507	C₂×Q₈	—	3	2	no	—
508	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
509	C₂×D₄	—	3	4	no	—
510	C₂×D₄	—	3	8	no	—
511	C₂×D₄	—	3	2	no	—
512	C₂×D₄	—	3	4	no	—
513	C₂²×C₄	—	3	2	no	—
514	C₂²×C₄	—	3	2	no	—
515	C₂²×C₄	—	3	1	no	—
516	C₂²×C₄	—	3	2	no	—
517	C₂²×C₄	—	3	2	no	—
518	C₂²×C₄	—	3	2	no	—
519	C₂²×C₄	—	3	2	no	—
520	C₂²×C₄	—	3	2	no	—
521	C₂²×C₄	—	3	8	no	—
522	C₂²×C₄	—	3	4	no	—
523	C₂²×C₄	—	6	8	no	—
524	C₂²×C₄	—	6	4	no	—
525	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
526	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
527	C₄⋊C₄	—	3	4	no	—
528	C₄⋊C₄	—	3	8	no	—
529	C₄⋊C₄	—	3	8	no	—
530	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
531	C₄⋊C₄	C₂²×C₃×D₃	1	8	yes	—
532	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
533	C₂²⋊C₄	—	3	8	no	—
534	C₂²⋊C₄	—	3	8	no	—
535	C₂²⋊C₄	—	3	8	no	—
536	C₂²⋊C₄	—	3	8	no	—
537	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
538	C₄²	—	3	1	no	—
539	C₄²	—	3	2	no	—
540	C₄²	—	3	1	no	—
541	C₄²	—	3	2	no	—
542	C₄²	—	3	2	no	—
543	C₄²	—	3	2	no	—
544	C₄²	—	3	2	no	—
545	C₄²	—	3	8	no	—
546	C₄²	C₂²×C₃×D₃	1	2	yes	—
547	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
548	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
549	C₄²	C₂²×C₃×D₃	1	4	yes	—
550	C₂²×C₃	—	2	2	no	—
551	C₂²×C₃	—	2	2	no	—
552	C₂²×C₃	—	2	2	no	—
553	C₂²×C₃	—	2	1	no	—
554	C₂²×C₃	—	3	4	no	—
555	C₂²×C₃	—	4	2	no	—
556	C₂²×C₃	—	6	8	no	—
557	C₂²×C₃	—	6	2	no	—
558	C₂²×C₃	—	6	2	no	—
559	C₂²×C₃	—	6	4	no	—
560	C₂²×C₃	—	6	8	no	—
561	C₂²×C₃	C₂×#239	1	2	yes	—
562	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
563	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
564	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
565	C₂×D₃	—	2	8	no	—
566	C₂×D₃	—	2	2	no	—
567	C₂×D₃	—	2	2	no	—
568	C₂×D₃	—	2	8	no	—
569	C₂×D₃	—	2	4	no	—
570	C₂×D₃	C₂×C₃×#41	1	4	yes	—
571	C₃×C₄	—	2	2	no	—
572	C₃×C₄	—	2	8	no	—
573	C₃×C₄	—	2	2	no	—
574	C₃×C₄	—	2	8	no	—
575	C₃×C₄	—	2	2	no	—
576	C₃×C₄	—	2	2	no	—
577	C₃×C₄	—	2	4	no	—
578	C₃×C₄	—	3	4	no	—
579	C₃×C₄	—	4	2	no	—
580	C₃×C₄	—	4	8	no	—
581	C₃×C₄	—	6	2	no	—
582	C₃×C₄	—	6	4	no	—
583	C₃×C₄	—	6	2	no	—
584	C₃×C₄	C₂×#239	1	2	yes	—
585	C₃×C₄	C₂×#239	1	2	yes	—
586	C₃×C₄	D₃×#41	1	4	yes	—
587	C₃×C₄	C₂×C₃×#41	1	2	yes	—
588	C₃×C₄	C₂×C₃×#41	1	2	yes	—
589	C₃×C₄	C₂×C₃×#41	1	4	yes	—
590	Dic₃	—	2	4	no	—
591	Dic₃	—	2	2	no	—
592	Dic₃	—	2	2	no	—
593	Dic₃	C₂×C₃×#41	1	4	yes	—
594	C₃²	#3444	1	1	yes	characteristic, complemented, Sylow
595	C₂³	—	3	2	no	—
596	C₂³	—	3	4	no	—
597	C₂³	—	6	4	no	—
598	C₂³	—	6	2	no	—
599	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
600	Q₈	—	2	8	no	—
601	Q₈	—	6	4	no	—
602	D₄	—	6	16	no	—
603	D₄	—	6	8	no	—
604	D₄	—	6	4	no	—
605	D₄	—	6	8	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	3	2	no	—
608	C₂×C₄	—	3	8	no	—
609	C₂×C₄	—	3	2	no	—
610	C₂×C₄	—	3	2	no	—
611	C₂×C₄	—	3	4	no	—
612	C₂×C₄	—	6	4	no	—
613	C₂×C₄	—	6	16	no	—
614	C₂×C₄	—	6	4	no	—
615	C₂×C₄	—	6	4	no	—
616	C₂×C₄	—	6	2	no	—
617	C₂×C₄	—	6	4	no	—
618	C₂×C₄	—	6	4	no	—
619	C₂×C₄	—	6	8	no	—
620	C₂×C₄	—	6	4	no	—
621	C₂×C₄	C₃×#239	1	4	yes	complemented
622	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
623	C₂×C₄	C₂³×C₃×D₃	1	8	yes	—
624	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
626	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
627	C₂×C₃	—	2	2	no	—
628	C₂×C₃	—	2	2	no	—
629	C₂×C₃	—	2	1	no	—
630	C₂×C₃	—	2	2	no	—
631	C₂×C₃	—	4	2	no	—
632	C₂×C₃	—	6	4	no	—
633	C₂×C₃	—	12	4	no	—
634	C₂×C₃	C₂²×#239	1	1	yes	characteristic
635	C₂×C₃	C₂×D₃×#41	1	2	yes	—
636	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
637	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
638	D₃	—	2	4	no	—
639	D₃	—	4	4	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	3	4	no	—
642	C₂²	—	6	8	no	—
643	C₂²	—	6	2	no	—
644	C₂²	—	6	2	no	—
645	C₂²	—	6	4	no	—
646	C₂²	—	6	8	no	—
647	C₂²	C₂×C₃×#239	1	2	yes	—
648	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
649	C₄	—	2	2	no	—
650	C₄	—	2	8	no	—
651	C₄	—	3	4	no	—
652	C₄	—	6	2	no	—
653	C₄	—	6	4	no	—
654	C₄	—	6	2	no	—
655	C₄	C₂×C₃×#239	1	2	yes	—
656	C₄	C₂×C₃×#239	1	2	yes	—
657	C₄	C₃×D₃×#41	1	4	yes	—
658	C₃	—	2	1	no	—
659	C₃	#86257	1	1	yes	characteristic, direct product factor
660	C₃	C₃×#3444	1	1	yes	characteristic, complemented
661	C₂	—	2	2	no	—
662	C₂	—	6	4	no	—
663	C₂	—	12	4	no	—
664	C₂	C₂²×C₃×#239	1	1	yes	characteristic
665	C₂	C₂×C₃×D₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#533	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#533	D₃
hypocenter	C₃	C₃×#3444
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#533

Complements

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

N	H ≅ G/N	type
1. C₃²×#533	C₂	semidirect
2. C₃×#5728	C₂	semidirect
3. C₃×#5725	C₂	semidirect
4. C₃×#5691	C₂	semidirect
5. C₃×#5627	C₂	semidirect
6. C₃×#5624	C₂	semidirect
7. C₃×#5580	C₂	semidirect
8. C₃×C₄×#239	C₂	semidirect
9. C₃×#5524	C₂	semidirect
10. C₃×#5522	C₂	semidirect
11. C₃×#5477	C₂	semidirect
12. C₂×C₃×C₄²×D₃	C₂	semidirect
14. #86257	C₃	direct (N × H)
19. C₃²×C₄⋊Q₈	C₂²	semidirect
20. C₃²×#125	C₂²	semidirect
22. C₃²×C₄×Q₈	C₂²	semidirect
25. C₃×#947	C₂²	semidirect
27. C₃×Q₈×Dic₃	C₂²	semidirect
31. C₃×#898	C₂²	semidirect
37. C₃×#893	C₂²	semidirect
38. C₃×#893	C₂²	semidirect
40. C₃×#892	C₂²	semidirect
41. C₃×#890	C₂²	semidirect
42. C₃×#887	C₂²	semidirect
46. C₃×#875	C₂²	semidirect
47. C₃×#874	C₂²	semidirect
49. C₃×C₄×D₁₂	C₂²	semidirect
50. C₃×#872	C₂²	semidirect
55. C₃×C₄²×D₃	C₂²	semidirect
56. C₃×#869	C₂²	semidirect
59. C₃×#533	D₃	semidirect
60. C₃×#533	C₂×C₃	semidirect
71. #5728	C₂×C₃	semidirect
72. #5725	C₂×C₃	semidirect
73. #5691	C₂×C₃	semidirect
74. #5627	C₂×C₃	semidirect
75. #5624	C₂×C₃	semidirect
76. #5580	C₂×C₃	semidirect
77. C₄×#239	C₂×C₃	semidirect
78. #5524	C₂×C₃	semidirect
79. #5522	C₂×C₃	semidirect
80. #5477	C₂×C₃	semidirect
81. C₂×C₄²×D₃	C₂×C₃	semidirect
139. C₃×C₄⋊Q₈	C₂×D₃	semidirect
140. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
145. C₃×#125	C₂×D₃	semidirect
146. C₃×#125	C₂²×C₃	semidirect
163. C₃×C₄×Q₈	C₂×D₃	semidirect
164. C₃×C₄×Q₈	C₂²×C₃	semidirect
187. #947	C₂²×C₃	semidirect
189. Q₈×Dic₃	C₂²×C₃	semidirect
193. #898	C₂²×C₃	semidirect
199. #893	C₂²×C₃	semidirect
200. #893	C₂²×C₃	semidirect
202. #892	C₂²×C₃	semidirect
203. #890	C₂²×C₃	semidirect
204. #887	C₂²×C₃	semidirect
208. #875	C₂²×C₃	semidirect
209. #874	C₂²×C₃	semidirect
211. C₄×D₁₂	C₂²×C₃	semidirect
212. #872	C₂²×C₃	semidirect
217. C₄²×D₃	C₂²×C₃	semidirect
218. #869	C₂²×C₃	semidirect
226. C₂×C₃²×C₄	#41	semidirect
249. C₃×C₄×D₃	#41	semidirect
252. #533	C₃×D₃	semidirect
389. C₄⋊Q₈	C₂×C₃×D₃	semidirect
393. #125	C₂×C₃×D₃	semidirect
407. C₄×Q₈	C₂×C₃×D₃	semidirect
468. C₂×C₃×C₄	#239	semidirect
469. C₂×C₃×C₄	C₃×#41	semidirect
497. C₄×D₃	C₃×#41	semidirect
594. C₃²	#3444	semidirect
621. C₂×C₄	C₃×#239	semidirect
659. C₃	#86257	direct (N × H)
660. C₃	C₃×#3444	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#533	2
C₃×#5728	2
C₃×#5725	2
C₃×#5691	2
C₃×#5627	2
C₃×#5624	2
C₃×#5580	2
C₃×C₄×#239	2
C₃×#5524	2
C₃×#5522	2
C₃×#5477	2
C₂×C₃×C₄²×D₃	2
C₃×#3444	3
#86257	3

Subgroups — C3×#86257 #11900881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86257 #11900881