Subgroups — C₃×#79721 #11860860

Order 1152.

1023 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#919	C₂	1	1	yes	maximal, characteristic
2	C₃×#5574	C₂	1	2	yes	maximal, complemented
3	C₃²×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Dic₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5026	C₂	1	2	yes	maximal, complemented
6	C₃×D₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4872	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4817	C₂	1	2	yes	maximal, complemented
9	C₃×#4803	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4689	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2951	—	3	1	no	maximal
13	#79721	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#239	C₂²	1	2	yes	—
15	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
16	C₃²×C₄×Q₈	C₂²	1	2	yes	—
17	C₃×Q₈×Dic₃	C₂²	1	2	yes	—
18	C₂×C₃×#215	C₂²	1	2	yes	—
19	C₃×#919	C₄	1	8	yes	complemented
20	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₃×#893	—	2	2	no	—
24	C₃×#893	C₂²	1	2	yes	—
25	C₃×D₃×C₄⋊C₄	—	2	2	no	—
26	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₃×C₄×D₁₂	—	2	2	no	—
28	C₃×C₄×D₁₂	C₂²	1	2	yes	—
29	C₃×#872	—	2	2	no	—
30	C₃×#872	C₂²	1	1	yes	characteristic
31	C₃²×#107	C₂²	1	1	yes	characteristic
32	C₃²×#103	C₂²	1	2	yes	—
33	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
34	C₃×#835	C₂²	1	2	yes	—
35	C₃×#821	C₂²	1	2	yes	—
36	C₃×#818	C₂²	1	1	yes	characteristic
37	C₃×#815	C₂²	1	1	yes	characteristic
38	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×#809	C₂²	1	2	yes	—
40	C₃×#807	C₂²	1	2	yes	—
41	C₃×#803	C₂²	1	1	yes	characteristic
42	C₂×C₃×#135	—	3	1	no	—
43	C₃×#520	—	3	2	no	—
44	C₂×#919	C₂×C₃	1	1	yes	characteristic
45	#5574	C₂×C₃	1	2	yes	complemented
46	C₃×#440	—	3	2	no	—
47	C₃×#440	—	3	2	no	—
48	C₃×C₄×Q₁₆	—	2	1	no	—
49	C₃×C₄×Q₁₆	—	3	1	no	—
50	C₃×C₄×Q₁₆	D₃	1	1	yes	characteristic, complemented
51	C₃×C₄×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
52	C₃×C₄×D₈	—	3	1	no	—
53	C₃×C₄×D₈	—	3	1	no	—
54	C₂×C₃×#107	—	3	1	no	—
55	C₃×#417	—	3	2	no	—
56	C₃×#405	—	3	1	no	—
57	Dic₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
58	#5026	C₂×C₃	1	2	yes	complemented
59	D₃×#107	C₂×C₃	1	1	yes	characteristic, complemented
60	#4872	C₂×C₃	1	1	yes	characteristic, complemented
61	#4817	C₂×C₃	1	2	yes	complemented
62	#4803	C₂×C₃	1	2	yes	complemented
63	C₄×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
64	#4689	C₂×C₃	1	1	yes	characteristic, complemented
65	C₂×C₃²×Q₈	C₂³	1	2	yes	—
66	C₃×#239	—	2	4	no	—
67	C₃×#239	C₂×C₄	1	8	yes	complemented
68	C₂×C₃×D₁₂	—	2	2	no	—
69	C₂×C₃×D₁₂	C₂³	1	2	yes	—
70	C₂×C₃×C₄×D₃	—	2	2	no	—
71	C₂×C₃×C₄×D₃	—	2	2	no	—
72	C₂×C₃×C₄×D₃	—	2	2	no	—
73	C₂×C₃×C₄×D₃	—	2	2	no	—
74	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
75	C₃²×Q₁₆	C₂×C₄	1	4	yes	complemented
76	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	—	2	2	no	—
79	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃²×C₄²	—	2	2	no	—
81	C₃²×C₄²	C₂³	1	1	yes	characteristic
82	C₃×#215	C₂×C₄	1	8	yes	complemented
83	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
84	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
85	C₃×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
86	C₃×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
87	C₃×C₄⋊Dic₃	—	2	2	no	—
88	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
89	C₃×Dic₃⋊C₄	—	2	2	no	—
90	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
91	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
92	C₃×C₄×Dic₃	—	2	2	no	—
93	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
96	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
97	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
98	C₃×D₃×C₈	C₂×C₄	1	4	yes	complemented
99	#2951	—	3	1	no	Sylow
100	C₂×C₃×#41	—	3	2	no	—
101	C₂×#239	C₂²×C₃	1	2	yes	—
102	C₃×#135	—	3	8	no	—
103	C₂×C₃×Q₁₆	—	2	1	no	—
104	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
105	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×SD₁₆	—	3	2	no	—
107	C₂×C₃×D₈	—	3	1	no	—
108	C₂×C₃×M₁₆	—	3	1	no	—
109	C₂²×C₃×C₈	—	3	1	no	—
110	C₃×C₄×Q₈	—	2	2	no	—
111	C₃×C₄×Q₈	—	3	2	no	—
112	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
113	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
114	C₃×C₄×D₄	—	3	2	no	—
115	C₃×C₄×D₄	—	3	2	no	—
116	C₃×C₄×D₄	—	6	2	no	—
117	C₃×C₄×D₄	—	6	2	no	—
118	C₃×#117	—	3	1	no	—
119	C₃×#117	—	6	2	no	—
120	C₂×C₃×C₄⋊C₄	—	3	2	no	—
121	C₂×C₃×C₄⋊C₄	—	6	2	no	—
122	Q₈×Dic₃	C₂²×C₃	1	2	yes	—
123	C₂×#215	C₂²×C₃	1	2	yes	—
124	#919	C₃×C₄	1	8	yes	complemented
125	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
127	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
128	#893	—	2	2	no	—
129	#893	C₂²×C₃	1	2	yes	—
130	D₃×C₄⋊C₄	—	2	2	no	—
131	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
132	C₄×D₁₂	—	2	2	no	—
133	C₄×D₁₂	C₂²×C₃	1	2	yes	—
134	#872	—	2	2	no	—
135	#872	C₂²×C₃	1	1	yes	characteristic
136	C₃×#107	—	2	1	no	—
137	C₃×#107	—	3	1	no	—
138	C₃×#107	—	3	2	no	—
139	C₃×#107	C₂×D₃	1	1	yes	characteristic
140	C₃×#107	C₂²×C₃	1	1	yes	characteristic
141	C₃×#103	—	2	2	no	—
142	C₃×#103	—	3	2	no	—
143	C₃×#103	C₂×D₃	1	2	yes	—
144	C₃×#103	C₂²×C₃	1	2	yes	—
145	C₃×#102	—	3	2	no	—
146	C₃×#102	—	3	2	no	—
147	C₃×#97	—	3	1	no	—
148	C₃×#97	—	3	1	no	—
149	C₃×C₄×C₈	—	2	1	no	—
150	C₃×C₄×C₈	—	3	1	no	—
151	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
152	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
153	#835	C₂²×C₃	1	2	yes	—
154	#821	C₂²×C₃	1	2	yes	—
155	#818	C₂²×C₃	1	1	yes	characteristic
156	#815	C₂²×C₃	1	1	yes	characteristic
157	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
158	#809	C₂²×C₃	1	2	yes	—
159	#807	C₂²×C₃	1	2	yes	—
160	#803	C₂²×C₃	1	1	yes	characteristic
161	C₂²×C₃×D₃	—	2	2	no	—
162	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
163	C₃²×Q₈	—	2	2	no	—
164	C₃²×Q₈	C₂²×C₄	1	4	yes	—
165	C₂×C₃²×C₄	—	2	2	no	—
166	C₂×C₃²×C₄	—	2	2	no	—
167	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
170	C₂×C₃×Dic₃	—	2	2	no	—
171	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
172	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
174	C₃×D₁₂	—	2	8	no	—
175	C₃×D₁₂	—	2	2	no	—
176	C₃×D₁₂	C₂²×C₄	1	4	yes	—
177	C₃×C₄×D₃	—	2	8	no	—
178	C₃×C₄×D₃	—	8	2	no	—
179	C₃×C₄×D₃	—	8	2	no	—
180	C₃×C₄×D₃	—	8	2	no	—
181	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
182	C₃×C₄×D₃	#41	1	2	yes	—
183	C₃²×C₈	—	2	1	no	—
184	C₃²×C₈	C₂²×C₄	1	2	yes	—
185	C₃×C₃⋊C₈	—	2	1	no	—
186	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
187	C₂×#135	—	3	1	no	—
188	#520	—	3	2	no	—
189	#440	—	3	2	no	—
190	#440	—	3	2	no	—
191	C₄×Q₁₆	—	3	1	no	—
192	C₄×Q₁₆	C₃×D₃	1	1	yes	characteristic, complemented
193	C₄×D₈	—	3	1	no	—
194	C₄×D₈	—	3	1	no	—
195	C₂×#107	—	3	1	no	—
196	#417	—	3	2	no	—
197	#405	—	3	1	no	—
198	C₃×#41	—	3	8	no	—
199	C₃×#41	—	6	4	no	—
200	C₂×C₃×Q₈	—	2	2	no	—
201	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
202	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
203	C₂×C₃×D₄	—	3	2	no	—
204	C₂×C₃×D₄	—	6	2	no	—
205	C₂²×C₃×C₄	—	3	1	no	—
206	C₂²×C₃×C₄	—	6	2	no	—
207	C₂²×C₃×C₄	—	6	2	no	—
208	C₂²×C₃×C₄	—	6	2	no	—
209	C₂²×C₃×C₄	—	6	2	no	—
210	#239	—	2	4	no	—
211	#239	C₂×C₃×C₄	1	8	yes	complemented
212	C₂×D₁₂	—	2	2	no	—
213	C₂×D₁₂	C₂³×C₃	1	2	yes	—
214	C₂×C₄×D₃	—	2	2	no	—
215	C₂×C₄×D₃	—	2	2	no	—
216	C₂×C₄×D₃	—	2	2	no	—
217	C₂×C₄×D₃	—	2	2	no	—
218	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
219	C₃×Q₁₆	—	2	4	no	—
220	C₃×Q₁₆	C₄×D₃	1	4	yes	complemented
221	C₃×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
222	C₃×SD₁₆	—	3	8	no	—
223	C₃×D₈	—	3	4	no	—
224	C₃×M₁₆	—	6	2	no	—
225	C₂×C₃×C₈	—	2	1	no	—
226	C₂×C₃×C₈	—	2	1	no	—
227	C₂×C₃×C₈	—	3	1	no	—
228	C₂×C₃×C₈	—	3	4	no	—
229	C₂×C₃×C₈	—	3	1	no	—
230	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
233	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
234	C₃×C₄⋊C₄	—	2	2	no	—
235	C₃×C₄⋊C₄	—	2	2	no	—
236	C₃×C₄⋊C₄	—	2	2	no	—
237	C₃×C₄⋊C₄	—	3	1	no	—
238	C₃×C₄⋊C₄	—	3	1	no	—
239	C₃×C₄⋊C₄	—	3	2	no	—
240	C₃×C₄⋊C₄	—	4	2	no	—
241	C₃×C₄⋊C₄	—	6	2	no	—
242	C₃×C₄⋊C₄	—	6	2	no	—
243	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
244	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
245	C₃×C₂²⋊C₄	—	3	1	no	—
246	C₃×C₂²⋊C₄	—	3	1	no	—
247	C₃×C₂²⋊C₄	—	6	2	no	—
248	C₃×C₂²⋊C₄	—	6	2	no	—
249	C₃×C₄²	—	2	2	no	—
250	C₃×C₄²	—	2	2	no	—
251	C₃×C₄²	—	2	1	no	—
252	C₃×C₄²	—	3	1	no	—
253	C₃×C₄²	—	4	2	no	—
254	C₃×C₄²	—	6	2	no	—
255	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
256	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
257	#215	C₂×C₃×C₄	1	8	yes	complemented
258	(C₂×D₃)⋊C₄	—	2	2	no	—
259	(C₂×D₃)⋊C₄	—	2	2	no	—
260	(C₂×D₃)⋊C₄	C₃×D₄	1	1	yes	characteristic
261	(C₂×D₃)⋊C₄	C₃×D₄	1	1	yes	characteristic
262	C₄⋊Dic₃	—	2	2	no	—
263	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
264	Dic₃⋊C₄	—	2	2	no	—
265	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
266	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
267	C₄×Dic₃	—	2	2	no	—
268	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
271	D₂₄	C₂×C₃×C₄	1	4	yes	complemented
272	ΓL(1,𝔽₂₅)	—	2	2	no	—
273	D₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
274	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₃×D₃	—	2	1	no	—
276	C₂×C₃×D₃	—	2	1	no	—
277	C₂×C₃×D₃	—	2	4	no	—
278	C₂×C₃×D₃	—	4	2	no	—
279	C₂×C₃×D₃	—	4	2	no	—
280	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
281	C₃²×C₄	—	2	1	no	—
282	C₃²×C₄	—	2	4	no	—
283	C₃²×C₄	—	2	1	no	—
284	C₃²×C₄	—	4	2	no	—
285	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
286	C₃²×C₄	C₂×#41	1	1	yes	characteristic
287	C₃×Dic₃	—	2	1	no	—
288	C₃×Dic₃	—	2	1	no	—
289	C₃×Dic₃	—	4	2	no	—
290	C₃×Dic₃	C₄×D₄	1	2	yes	—
291	C₂×#41	—	3	2	no	—
292	#135	—	3	8	no	—
293	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
294	C₂×SD₁₆	—	3	2	no	—
295	C₂×D₈	—	3	1	no	—
296	C₂×M₁₆	—	3	1	no	—
297	C₂²×C₈	—	3	1	no	—
298	C₄×Q₈	—	3	2	no	—
299	C₄×Q₈	C₂×C₃×D₃	1	2	yes	—
300	C₄×D₄	—	3	2	no	—
301	C₄×D₄	—	3	2	no	—
302	C₄×D₄	—	6	2	no	—
303	C₄×D₄	—	6	2	no	—
304	#117	—	3	1	no	—
305	#117	—	6	2	no	—
306	C₂×C₄⋊C₄	—	3	2	no	—
307	C₂×C₄⋊C₄	—	6	2	no	—
308	#107	—	3	1	no	—
309	#107	—	3	2	no	—
310	#107	C₂×C₃×D₃	1	1	yes	characteristic
311	#103	—	3	2	no	—
312	#103	C₂×C₃×D₃	1	2	yes	—
313	#102	—	3	2	no	—
314	#102	—	3	2	no	—
315	#97	—	3	1	no	—
316	#97	—	3	1	no	—
317	C₄×C₈	—	3	1	no	—
318	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
319	C₂³×C₃	—	3	1	no	—
320	C₂³×C₃	—	6	2	no	—
321	C₂²×D₃	—	2	2	no	—
322	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
323	C₃×Q₈	—	2	2	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	2	4	no	—
326	C₃×Q₈	—	4	2	no	—
327	C₃×Q₈	C₂×C₄×D₃	1	4	yes	—
328	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
329	C₃×D₄	—	3	4	no	—
330	C₃×D₄	—	6	8	no	—
331	C₃×D₄	—	6	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	3	1	no	—
340	C₂×C₃×C₄	—	3	2	no	—
341	C₂×C₃×C₄	—	3	2	no	—
342	C₂×C₃×C₄	—	3	1	no	—
343	C₂×C₃×C₄	—	3	1	no	—
344	C₂×C₃×C₄	—	4	2	no	—
345	C₂×C₃×C₄	—	4	2	no	—
346	C₂×C₃×C₄	—	6	8	no	—
347	C₂×C₃×C₄	—	6	2	no	—
348	C₂×C₃×C₄	—	24	2	no	—
349	C₂×C₃×C₄	—	24	2	no	—
350	C₂×C₃×C₄	—	24	2	no	—
351	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
352	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
356	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
357	C₂×Dic₃	—	2	2	no	—
358	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
359	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
360	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
361	D₁₂	—	2	8	no	—
362	D₁₂	—	2	2	no	—
363	D₁₂	C₂²×C₃×C₄	1	4	yes	—
364	C₄×D₃	—	2	8	no	—
365	C₄×D₃	—	8	2	no	—
366	C₄×D₃	—	8	2	no	—
367	C₄×D₃	—	8	2	no	—
368	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
369	C₄×D₃	C₃×#41	1	2	yes	—
370	C₃×C₈	—	2	1	no	—
371	C₃×C₈	—	2	1	no	—
372	C₃×C₈	—	2	2	no	—
373	C₃×C₈	—	3	2	no	—
374	C₃×C₈	—	4	1	no	—
375	C₃×C₈	—	6	1	no	—
376	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
377	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
378	C₃⋊C₈	—	2	1	no	—
379	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
380	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
381	C₂×C₃²	#576	1	1	yes	characteristic
382	C₂×C₃²	#578	1	1	yes	characteristic
383	C₃×D₃	—	2	2	no	—
384	C₃×D₃	—	4	4	no	—
385	#41	—	3	8	no	—
386	#41	—	6	4	no	—
387	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
388	C₂×D₄	—	3	2	no	—
389	C₂×D₄	—	6	2	no	—
390	C₂²×C₄	—	3	1	no	—
391	C₂²×C₄	—	6	2	no	—
392	C₂²×C₄	—	6	2	no	—
393	C₂²×C₄	—	6	2	no	—
394	C₂²×C₄	—	6	2	no	—
395	Q₁₆	C₃×C₄×D₃	1	4	yes	complemented
396	SD₁₆	—	3	8	no	—
397	D₈	—	3	4	no	—
398	M₁₆	—	6	2	no	—
399	C₂×C₈	—	3	1	no	—
400	C₂×C₈	—	3	4	no	—
401	C₂×C₈	—	3	1	no	—
402	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
403	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	3	1	no	—
406	C₄⋊C₄	—	3	1	no	—
407	C₄⋊C₄	—	3	2	no	—
408	C₄⋊C₄	—	6	2	no	—
409	C₄⋊C₄	—	6	2	no	—
410	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
411	C₂²⋊C₄	—	3	1	no	—
412	C₂²⋊C₄	—	3	1	no	—
413	C₂²⋊C₄	—	6	2	no	—
414	C₂²⋊C₄	—	6	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	3	1	no	—
417	C₄²	—	6	2	no	—
418	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
419	C₂²×C₃	—	2	1	no	—
420	C₂²×C₃	—	3	2	no	—
421	C₂²×C₃	—	6	1	no	—
422	C₂²×C₃	—	6	1	no	—
423	C₂²×C₃	—	6	4	no	—
424	C₂²×C₃	—	12	2	no	—
425	C₂²×C₃	—	12	2	no	—
426	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
427	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
428	C₂×D₃	—	2	1	no	—
429	C₂×D₃	—	2	1	no	—
430	C₂×D₃	—	2	4	no	—
431	C₂×D₃	—	4	2	no	—
432	C₂×D₃	—	4	2	no	—
433	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	2	1	no	—
436	C₃×C₄	—	2	1	no	—
437	C₃×C₄	—	2	1	no	—
438	C₃×C₄	—	2	1	no	—
439	C₃×C₄	—	2	4	no	—
440	C₃×C₄	—	2	4	no	—
441	C₃×C₄	—	2	1	no	—
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	3	2	no	—
444	C₃×C₄	—	4	1	no	—
445	C₃×C₄	—	4	4	no	—
446	C₃×C₄	—	4	2	no	—
447	C₃×C₄	—	4	2	no	—
448	C₃×C₄	—	6	1	no	—
449	C₃×C₄	—	6	1	no	—
450	C₃×C₄	—	8	2	no	—
451	C₃×C₄	—	12	2	no	—
452	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
453	C₃×C₄	D₃×#41	1	1	yes	characteristic
454	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
455	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
456	Dic₃	—	2	1	no	—
457	Dic₃	—	2	1	no	—
458	Dic₃	—	4	2	no	—
459	Dic₃	C₃×C₄×D₄	1	2	yes	—
460	C₃²	#2951	1	1	yes	characteristic, complemented, Sylow
461	C₂³	—	3	1	no	—
462	C₂³	—	6	2	no	—
463	Q₈	—	2	2	no	—
464	Q₈	C₂×C₃×C₄×D₃	1	4	yes	—
465	D₄	—	3	4	no	—
466	D₄	—	6	8	no	—
467	D₄	—	6	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	3	1	no	—
471	C₂×C₄	—	3	2	no	—
472	C₂×C₄	—	3	2	no	—
473	C₂×C₄	—	3	1	no	—
474	C₂×C₄	—	3	1	no	—
475	C₂×C₄	—	6	8	no	—
476	C₂×C₄	—	6	2	no	—
477	C₂×C₄	—	24	2	no	—
478	C₂×C₄	—	24	2	no	—
479	C₂×C₄	—	24	2	no	—
480	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
481	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
483	C₈	—	2	1	no	—
484	C₈	—	3	2	no	—
485	C₈	—	6	1	no	—
486	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
487	C₂×C₃	—	2	1	no	—
488	C₂×C₃	—	2	1	no	—
489	C₂×C₃	—	2	1	no	—
490	C₂×C₃	—	6	2	no	—
491	C₂×C₃	—	12	4	no	—
492	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
493	C₂×C₃	#5766	1	1	yes	characteristic
494	C₂×C₃	#5769	1	1	yes	characteristic
495	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
496	C₂×C₃	C₃×#576	1	1	yes	characteristic
497	C₂×C₃	C₃×#578	1	1	yes	characteristic
498	D₃	—	2	2	no	—
499	D₃	—	4	4	no	—
500	C₂²	—	3	2	no	—
501	C₂²	—	6	1	no	—
502	C₂²	—	6	1	no	—
503	C₂²	—	6	4	no	—
504	C₂²	—	12	2	no	—
505	C₂²	—	12	2	no	—
506	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	4	no	—
510	C₄	—	3	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	6	1	no	—
513	C₄	—	6	1	no	—
514	C₄	—	12	2	no	—
515	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
516	C₄	C₃×D₃×#41	1	1	yes	characteristic
517	C₃	—	2	1	no	—
518	C₃	#79721	1	1	yes	characteristic, direct product factor
519	C₃	C₃×#2951	1	1	yes	characteristic, complemented
520	C₂	—	6	2	no	—
521	C₂	—	12	4	no	—
522	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
523	C₂	C₃×#5766	1	1	yes	characteristic
524	C₂	C₃×#5769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×Q₁₆	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×#919	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×Q₁₆	D₃
hypocenter	C₃	C₃×#2951
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×#5574	C₂	semidirect
3. C₃²×C₄×Q₁₆	C₂	semidirect
4. C₃×Dic₃×Q₁₆	C₂	semidirect
5. C₃×#5026	C₂	semidirect
6. C₃×D₃×#107	C₂	semidirect
7. C₃×#4872	C₂	semidirect
8. C₃×#4817	C₂	semidirect
9. C₃×#4803	C₂	semidirect
10. C₃×C₄×D₂₄	C₂	semidirect
11. C₃×#4689	C₂	semidirect
13. #79721	C₃	direct (N × H)
19. C₃×#919	C₄	semidirect
45. #5574	C₂×C₃	semidirect
50. C₃×C₄×Q₁₆	D₃	semidirect
51. C₃×C₄×Q₁₆	C₂×C₃	semidirect
57. Dic₃×Q₁₆	C₂×C₃	semidirect
58. #5026	C₂×C₃	semidirect
59. D₃×#107	C₂×C₃	semidirect
60. #4872	C₂×C₃	semidirect
61. #4817	C₂×C₃	semidirect
62. #4803	C₂×C₃	semidirect
63. C₄×D₂₄	C₂×C₃	semidirect
64. #4689	C₂×C₃	semidirect
67. C₃×#239	C₂×C₄	semidirect
75. C₃²×Q₁₆	C₂×C₄	semidirect
82. C₃×#215	C₂×C₄	semidirect
96. C₃×D₂₄	C₂×C₄	semidirect
98. C₃×D₃×C₈	C₂×C₄	semidirect
124. #919	C₃×C₄	semidirect
192. C₄×Q₁₆	C₃×D₃	semidirect
211. #239	C₂×C₃×C₄	semidirect
220. C₃×Q₁₆	C₄×D₃	semidirect
221. C₃×Q₁₆	C₂×C₃×C₄	semidirect
257. #215	C₂×C₃×C₄	semidirect
271. D₂₄	C₂×C₃×C₄	semidirect
273. D₃×C₈	C₂×C₃×C₄	semidirect
395. Q₁₆	C₃×C₄×D₃	semidirect
460. C₃²	#2951	semidirect
518. C₃	#79721	direct (N × H)
519. C₃	C₃×#2951	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#919	2
C₃×#5574	2
C₃²×C₄×Q₁₆	2
C₃×Dic₃×Q₁₆	2
C₃×#5026	2
C₃×D₃×#107	2
C₃×#4872	2
C₃×#4817	2
C₃×#4803	2
C₃×C₄×D₂₄	2
C₃×#4689	2
C₃×#2951	3
#79721	3

Subgroups — C3×#79721 #11860860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79721 #11860860