Subgroups — C₃×#78552 #11859081

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5522	C₂	1	1	yes	maximal, characteristic
2	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5129	C₂	1	1	yes	maximal, characteristic
4	C₃×#5118	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5110	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4709	C₂	1	2	yes	maximal, complemented
9	C₃×#4705	C₂	1	2	yes	maximal, complemented
10	C₃×#4690	C₂	1	2	yes	maximal, complemented
11	C₃×#4685	C₂	1	2	yes	maximal, complemented
12	C₃×#2925	—	3	1	no	maximal
13	#78552	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#235	C₂²	1	1	yes	characteristic
15	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₃²×#117	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×#208	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×#893	C₄	1	1	yes	characteristic
22	C₃×#893	C₄	1	1	yes	characteristic
23	C₃×#887	C₄	1	1	yes	characteristic
24	C₃×#887	C₄	1	1	yes	characteristic
25	C₃×#67⋊C₄	C₄	1	2	yes	—
26	C₃×#67⋊C₄	C₄	1	2	yes	—
27	C₃×#872	C₂²	1	2	yes	—
28	C₃×C₄²×D₃	C₂²	1	2	yes	—
29	C₃²×#97	C₂²	1	2	yes	—
30	C₃²×C₄×C₈	C₂²	1	2	yes	—
31	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
32	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
33	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
34	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
35	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
37	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
39	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
41	C₃×#803	C₂²	1	2	yes	—
42	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
43	C₃×C₄×#41	—	3	1	no	—
44	#5522	C₂×C₃	1	1	yes	characteristic
45	C₃×#433	—	3	2	no	—
46	C₃×#433	—	3	2	no	—
47	C₃×#432	—	3	2	no	—
48	C₃×#431	—	3	2	no	—
49	C₃×#423	—	3	1	no	—
50	C₂×C₃×C₄⋊C₈	—	3	1	no	—
51	C₃×#408	—	3	1	no	—
52	C₃×#408	—	3	1	no	—
53	C₃×#405	—	2	1	no	—
54	C₃×#405	—	3	1	no	—
55	C₃×#405	D₃	1	1	yes	characteristic, complemented
56	C₃×#405	C₂×C₃	1	1	yes	characteristic, complemented
57	#5129	C₂×C₃	1	1	yes	characteristic
58	#5118	C₂×C₃	1	1	yes	characteristic, complemented
59	#5110	C₂×C₃	1	1	yes	characteristic
60	C₂×Dic₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
61	#4997	C₂×C₃	1	1	yes	characteristic, complemented
62	#4709	C₂×C₃	1	2	yes	complemented
63	#4705	C₂×C₃	1	2	yes	complemented
64	#4690	C₂×C₃	1	2	yes	complemented
65	#4685	C₂×C₃	1	2	yes	complemented
66	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃×#67	C₂×C₄	1	2	yes	—
68	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
70	C₃×#235	—	2	2	no	—
71	C₃×#235	—	2	2	no	—
72	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
74	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
75	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
76	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
77	C₃²×M₁₆	—	2	2	no	—
78	C₂×C₃²×C₈	—	2	2	no	—
79	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
80	C₂×C₃²×C₈	C₂³	1	2	yes	—
81	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
82	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
85	C₃²×C₄²	C₂³	1	2	yes	—
86	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
87	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
88	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
89	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
90	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
91	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
92	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
93	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
94	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
95	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
96	C₃×#208	—	2	2	no	—
97	C₂×C₃×C₃⋊C₈	—	2	2	no	—
98	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
101	#2925	—	3	1	no	Sylow
102	C₂×C₃×#41	—	3	1	no	—
103	C₂×#235	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×M₁₆	—	2	1	no	—
105	C₂×C₃×M₁₆	—	3	1	no	—
106	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
107	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₃×C₈	—	2	1	no	—
109	C₂²×C₃×C₈	—	3	1	no	—
110	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
111	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
112	C₃×C₄×Q₈	—	3	1	no	—
113	C₃×C₄×Q₈	—	3	1	no	—
114	C₃×C₄×D₄	—	3	1	no	—
115	C₃×C₄×D₄	—	3	1	no	—
116	C₃×C₄×D₄	—	3	2	no	—
117	C₃×C₄×D₄	—	3	2	no	—
118	C₃×#117	—	2	1	no	—
119	C₃×#117	—	3	2	no	—
120	C₃×#117	C₂×D₃	1	1	yes	characteristic
121	C₃×#117	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₄²	—	3	1	no	—
123	C₂×C₃×C₄²	—	3	2	no	—
124	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
125	C₂×#208	C₂²×C₃	1	1	yes	characteristic
126	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
127	#893	C₃×C₄	1	1	yes	characteristic
128	#893	C₃×C₄	1	1	yes	characteristic
129	#887	C₃×C₄	1	1	yes	characteristic
130	#887	C₃×C₄	1	1	yes	characteristic
131	#67⋊C₄	C₃×C₄	1	2	yes	—
132	#67⋊C₄	C₃×C₄	1	2	yes	—
133	#872	C₂²×C₃	1	2	yes	—
134	C₄²×D₃	C₂²×C₃	1	2	yes	—
135	C₃×C₄⋊C₈	—	3	1	no	—
136	C₃×C₄⋊C₈	—	3	1	no	—
137	C₃×C₄⋊C₈	—	3	1	no	—
138	C₃×C₄⋊C₈	—	3	1	no	—
139	C₃×C₄⋊C₈	—	3	2	no	—
140	C₃×C₄⋊C₈	—	3	2	no	—
141	C₃×C₂²⋊C₈	—	3	2	no	—
142	C₃×C₂²⋊C₈	—	3	2	no	—
143	C₃×C₂²⋊C₈	—	3	2	no	—
144	C₃×C₂²⋊C₈	—	3	2	no	—
145	C₃×#97	—	2	2	no	—
146	C₃×#97	—	3	2	no	—
147	C₃×#97	C₂×D₃	1	2	yes	—
148	C₃×#97	C₂²×C₃	1	2	yes	—
149	C₃×C₄×C₈	—	2	2	no	—
150	C₃×C₄×C₈	—	3	2	no	—
151	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
152	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
153	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
154	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
155	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
156	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
157	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
158	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
159	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
160	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
161	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
162	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
163	#803	C₂²×C₃	1	2	yes	—
164	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
165	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
167	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
168	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
169	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₃²×C₄	#41	1	2	yes	—
171	C₂×C₃²×C₄	#41	1	2	yes	—
172	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
173	C₃×#67	—	2	4	no	—
174	C₂×C₃×Dic₃	—	2	2	no	—
175	C₂×C₃×Dic₃	—	4	1	no	—
176	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
178	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
181	C₃×D₁₂	—	2	2	no	—
182	C₃×C₄×D₃	—	2	2	no	—
183	C₃×C₄×D₃	—	2	2	no	—
184	C₃×C₄×D₃	—	2	4	no	—
185	C₃×C₄×D₃	—	4	2	no	—
186	C₃×Dic₆	—	2	2	no	—
187	C₃²×C₈	—	2	1	no	—
188	C₃²×C₈	—	2	1	no	—
189	C₃²×C₈	—	2	2	no	—
190	C₃×C₃⋊C₈	—	2	1	no	—
191	C₃×C₃⋊C₈	—	2	1	no	—
192	C₃×C₃⋊C₈	—	2	2	no	—
193	C₄×#41	—	3	1	no	—
194	#433	—	3	2	no	—
195	#433	—	3	2	no	—
196	#432	—	3	2	no	—
197	#431	—	3	2	no	—
198	#423	—	3	1	no	—
199	C₂×C₄⋊C₈	—	3	1	no	—
200	#408	—	3	1	no	—
201	#408	—	3	1	no	—
202	#405	—	3	1	no	—
203	#405	C₃×D₃	1	1	yes	characteristic, complemented
204	C₃×#41	—	6	2	no	—
205	C₃×#41	—	6	2	no	—
206	C₂×C₃×Q₈	—	3	1	no	—
207	C₂×C₃×D₄	—	3	2	no	—
208	C₂×C₃×D₄	—	3	1	no	—
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	—	3	1	no	—
211	C₂²×C₃×C₄	—	3	1	no	—
212	C₂²×C₃×C₄	—	3	2	no	—
213	C₂²×C₃×C₄	—	3	2	no	—
214	C₂²×C₃×C₄	—	3	2	no	—
215	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
217	C₂×#67	C₂×C₃×C₄	1	2	yes	—
218	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
219	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
220	#235	—	2	2	no	—
221	#235	—	2	2	no	—
222	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
223	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
224	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
225	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
226	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
227	C₃×M₁₆	—	2	4	no	—
228	C₃×M₁₆	—	2	2	no	—
229	C₃×M₁₆	—	2	2	no	—
230	C₃×M₁₆	—	6	2	no	—
231	C₂×C₃×C₈	—	2	4	no	—
232	C₂×C₃×C₈	—	2	2	no	—
233	C₂×C₃×C₈	—	2	2	no	—
234	C₂×C₃×C₈	—	2	1	no	—
235	C₂×C₃×C₈	—	2	2	no	—
236	C₂×C₃×C₈	—	2	1	no	—
237	C₂×C₃×C₈	—	3	1	no	—
238	C₂×C₃×C₈	—	3	2	no	—
239	C₂×C₃×C₈	—	3	1	no	—
240	C₂×C₃×C₈	—	6	2	no	—
241	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
242	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
243	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
244	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
245	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
246	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
247	C₃×C₄⋊C₄	—	2	1	no	—
248	C₃×C₄⋊C₄	—	2	1	no	—
249	C₃×C₄⋊C₄	—	3	2	no	—
250	C₃×C₄⋊C₄	—	3	2	no	—
251	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
252	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
253	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
254	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₂²⋊C₄	—	3	2	no	—
257	C₃×C₂²⋊C₄	—	3	2	no	—
258	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
259	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
260	C₃×C₄²	—	2	2	no	—
261	C₃×C₄²	—	3	1	no	—
262	C₃×C₄²	—	3	2	no	—
263	C₃×C₄²	—	3	1	no	—
264	C₃×C₄²	—	3	2	no	—
265	C₃×C₄²	—	3	1	no	—
266	C₃×C₄²	—	3	1	no	—
267	C₃×C₄²	C₂²×D₃	1	2	yes	—
268	C₃×C₄²	C₂³×C₃	1	2	yes	—
269	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
270	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
271	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
272	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
273	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
274	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
275	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
276	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
277	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
278	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
279	#208	—	2	2	no	—
280	C₂×C₃⋊C₈	—	2	2	no	—
281	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
283	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
284	C₂²×C₃²	—	2	1	no	—
285	C₂²×C₃²	—	2	1	no	—
286	C₂²×C₃²	#117	1	2	yes	—
287	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
288	C₂×C₃×D₃	—	2	2	no	—
289	C₂×C₃×D₃	—	2	2	no	—
290	C₂×C₃×D₃	—	2	2	no	—
291	C₃²×C₄	—	2	2	no	—
292	C₃²×C₄	—	2	2	no	—
293	C₃²×C₄	#117	1	2	yes	—
294	C₃²×C₄	C₂×#41	1	1	yes	characteristic
295	C₃²×C₄	C₂×#41	1	1	yes	characteristic
296	C₃×Dic₃	—	2	2	no	—
297	C₃×Dic₃	—	2	1	no	—
298	C₃×Dic₃	—	2	1	no	—
299	C₃×Dic₃	—	2	1	no	—
300	C₃×Dic₃	#131	1	2	yes	—
301	C₂×#41	—	3	1	no	—
302	C₂×M₁₆	—	3	1	no	—
303	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
304	C₂²×C₈	—	3	1	no	—
305	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
306	C₄×Q₈	—	3	1	no	—
307	C₄×Q₈	—	3	1	no	—
308	C₄×D₄	—	3	1	no	—
309	C₄×D₄	—	3	1	no	—
310	C₄×D₄	—	3	2	no	—
311	C₄×D₄	—	3	2	no	—
312	#117	—	3	2	no	—
313	#117	C₂×C₃×D₃	1	1	yes	characteristic
314	C₂×C₄²	—	3	1	no	—
315	C₂×C₄²	—	3	2	no	—
316	C₄⋊C₈	—	3	1	no	—
317	C₄⋊C₈	—	3	1	no	—
318	C₄⋊C₈	—	3	1	no	—
319	C₄⋊C₈	—	3	1	no	—
320	C₄⋊C₈	—	3	2	no	—
321	C₄⋊C₈	—	3	2	no	—
322	C₂²⋊C₈	—	3	2	no	—
323	C₂²⋊C₈	—	3	2	no	—
324	C₂²⋊C₈	—	3	2	no	—
325	C₂²⋊C₈	—	3	2	no	—
326	#97	—	3	2	no	—
327	#97	C₂×C₃×D₃	1	2	yes	—
328	C₄×C₈	—	3	2	no	—
329	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
330	C₂³×C₃	—	2	1	no	—
331	C₂³×C₃	—	3	2	no	—
332	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
333	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
334	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
335	C₃×Q₈	—	6	2	no	—
336	C₃×D₄	—	6	4	no	—
337	C₃×D₄	—	6	2	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	3	1	no	—
345	C₂×C₃×C₄	—	3	1	no	—
346	C₂×C₃×C₄	—	3	1	no	—
347	C₂×C₃×C₄	—	3	1	no	—
348	C₂×C₃×C₄	—	3	2	no	—
349	C₂×C₃×C₄	—	6	4	no	—
350	C₂×C₃×C₄	—	6	2	no	—
351	C₂×C₃×C₄	—	6	2	no	—
352	C₂×C₃×C₄	—	6	2	no	—
353	C₂×C₃×C₄	—	12	2	no	—
354	C₂×C₃×C₄	—	12	1	no	—
355	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
356	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
357	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
358	C₂×C₃×C₄	#235	1	2	yes	—
359	C₂×C₃×C₄	#235	1	2	yes	—
360	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
361	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
362	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
363	C₂×C₃×C₄	C₃×#41	1	2	yes	—
364	C₂×C₃×C₄	C₃×#41	1	2	yes	—
365	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
367	#67	—	2	4	no	—
368	C₂×Dic₃	—	2	2	no	—
369	C₂×Dic₃	—	4	1	no	—
370	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
371	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
372	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
373	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
374	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
375	D₁₂	—	2	2	no	—
376	C₄×D₃	—	2	2	no	—
377	C₄×D₃	—	2	2	no	—
378	C₄×D₃	—	2	4	no	—
379	C₄×D₃	—	4	2	no	—
380	Dic₆	—	2	2	no	—
381	C₃×C₈	—	2	2	no	—
382	C₃×C₈	—	2	2	no	—
383	C₃×C₈	—	2	4	no	—
384	C₃×C₈	—	2	1	no	—
385	C₃×C₈	—	2	1	no	—
386	C₃×C₈	—	2	2	no	—
387	C₃×C₈	—	2	1	no	—
388	C₃×C₈	—	2	1	no	—
389	C₃×C₈	—	2	2	no	—
390	C₃×C₈	—	6	1	no	—
391	C₃×C₈	—	6	1	no	—
392	C₃×C₈	—	6	2	no	—
393	C₃⋊C₈	—	2	1	no	—
394	C₃⋊C₈	—	2	1	no	—
395	C₃⋊C₈	—	2	2	no	—
396	C₂×C₃²	—	2	2	no	—
397	C₂×C₃²	C₂×#117	1	1	yes	characteristic
398	C₂×C₃²	C₂×#131	1	1	yes	characteristic
399	C₂×C₃²	#568	1	1	yes	characteristic
400	C₃×D₃	—	4	2	no	—
401	#41	—	6	2	no	—
402	#41	—	6	2	no	—
403	C₂×Q₈	—	3	1	no	—
404	C₂×D₄	—	3	2	no	—
405	C₂×D₄	—	3	1	no	—
406	C₂²×C₄	—	3	1	no	—
407	C₂²×C₄	—	3	1	no	—
408	C₂²×C₄	—	3	2	no	—
409	C₂²×C₄	—	3	2	no	—
410	C₂²×C₄	—	3	2	no	—
411	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
412	M₁₆	—	2	2	no	—
413	M₁₆	—	6	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	3	1	no	—
416	C₂×C₈	—	3	2	no	—
417	C₂×C₈	—	3	1	no	—
418	C₂×C₈	—	6	2	no	—
419	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
420	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
421	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
422	C₄⋊C₄	—	3	2	no	—
423	C₄⋊C₄	—	3	2	no	—
424	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
425	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
426	C₂²⋊C₄	—	3	2	no	—
427	C₂²⋊C₄	—	3	2	no	—
428	C₂²⋊C₄	C₃×C₄×D₃	1	2	yes	—
429	C₄²	—	3	1	no	—
430	C₄²	—	3	1	no	—
431	C₄²	—	3	1	no	—
432	C₄²	—	3	2	no	—
433	C₄²	—	3	1	no	—
434	C₄²	—	3	2	no	—
435	C₄²	C₂²×C₃×D₃	1	2	yes	—
436	C₂²×C₃	—	2	1	no	—
437	C₂²×C₃	—	2	1	no	—
438	C₂²×C₃	—	2	1	no	—
439	C₂²×C₃	—	2	1	no	—
440	C₂²×C₃	—	2	1	no	—
441	C₂²×C₃	—	2	2	no	—
442	C₂²×C₃	—	4	1	no	—
443	C₂²×C₃	—	4	1	no	—
444	C₂²×C₃	—	6	2	no	—
445	C₂²×C₃	—	6	2	no	—
446	C₂²×C₃	—	6	2	no	—
447	C₂²×C₃	#872	1	2	yes	—
448	C₂²×C₃	C₃×#117	1	2	yes	—
449	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
450	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
451	C₂×D₃	—	2	2	no	—
452	C₂×D₃	—	2	2	no	—
453	C₂×D₃	—	2	2	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	2	2	no	—
456	C₃×C₄	—	2	2	no	—
457	C₃×C₄	—	2	2	no	—
458	C₃×C₄	—	2	1	no	—
459	C₃×C₄	—	2	1	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	3	2	no	—
462	C₃×C₄	—	4	2	no	—
463	C₃×C₄	—	4	2	no	—
464	C₃×C₄	—	6	2	no	—
465	C₃×C₄	—	6	1	no	—
466	C₃×C₄	—	6	1	no	—
467	C₃×C₄	—	6	1	no	—
468	C₃×C₄	#872	1	2	yes	—
469	C₃×C₄	C₃×#117	1	2	yes	—
470	C₃×C₄	C₂×#235	1	1	yes	characteristic
471	C₃×C₄	C₂×#235	1	1	yes	characteristic
472	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
473	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
474	Dic₃	—	2	1	no	—
475	Dic₃	—	2	1	no	—
476	Dic₃	—	2	1	no	—
477	Dic₃	—	2	2	no	—
478	Dic₃	C₃×#131	1	2	yes	—
479	C₃²	#2925	1	1	yes	characteristic, complemented, Sylow
480	C₂³	—	3	2	no	—
481	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
482	Q₈	—	6	2	no	—
483	D₄	—	6	4	no	—
484	D₄	—	6	2	no	—
485	C₂×C₄	—	3	1	no	—
486	C₂×C₄	—	3	1	no	—
487	C₂×C₄	—	3	1	no	—
488	C₂×C₄	—	3	1	no	—
489	C₂×C₄	—	3	2	no	—
490	C₂×C₄	—	6	4	no	—
491	C₂×C₄	—	6	2	no	—
492	C₂×C₄	—	6	2	no	—
493	C₂×C₄	—	6	2	no	—
494	C₂×C₄	—	12	2	no	—
495	C₂×C₄	—	12	1	no	—
496	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
497	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
498	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
499	C₂×C₄	C₃×#235	1	2	yes	—
500	C₂×C₄	C₃×#235	1	2	yes	—
501	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
502	C₈	—	2	1	no	—
503	C₈	—	2	1	no	—
504	C₈	—	2	2	no	—
505	C₈	—	6	1	no	—
506	C₈	—	6	1	no	—
507	C₈	—	6	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	—	2	2	no	—
510	C₂×C₃	—	2	1	no	—
511	C₂×C₃	—	2	1	no	—
512	C₂×C₃	—	2	1	no	—
513	C₂×C₃	—	4	2	no	—
514	C₂×C₃	—	12	2	no	—
515	C₂×C₃	C₂×#872	1	1	yes	characteristic
516	C₂×C₃	D₃×#131	1	1	yes	characteristic
517	C₂×C₃	#5750	1	1	yes	characteristic
518	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
519	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
520	C₂×C₃	C₃×#568	1	1	yes	characteristic
521	D₃	—	4	2	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	6	2	no	—
525	C₂²	—	6	2	no	—
526	C₂²	—	6	2	no	—
527	C₂²	C₃×#872	1	2	yes	—
528	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	3	2	no	—
532	C₄	—	6	1	no	—
533	C₄	—	6	1	no	—
534	C₄	—	6	1	no	—
535	C₄	—	6	2	no	—
536	C₄	C₃×#872	1	2	yes	—
537	C₄	C₂×C₃×#235	1	1	yes	characteristic
538	C₄	C₂×C₃×#235	1	1	yes	characteristic
539	C₃	—	2	1	no	—
540	C₃	#78552	1	1	yes	characteristic, direct product factor
541	C₃	C₃×#2925	1	1	yes	characteristic, complemented
542	C₂	—	2	2	no	—
543	C₂	—	12	2	no	—
544	C₂	C₂×C₃×#872	1	1	yes	characteristic
545	C₂	C₃×D₃×#131	1	1	yes	characteristic
546	C₂	C₃×#5750	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#2925
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
2. C₃²×#405	C₂	semidirect
4. C₃×#5118	C₂	semidirect
6. C₂×C₃×Dic₃⋊C₈	C₂	semidirect
7. C₃×#4997	C₂	semidirect
8. C₃×#4709	C₂	semidirect
9. C₃×#4705	C₂	semidirect
10. C₃×#4690	C₂	semidirect
11. C₃×#4685	C₂	semidirect
13. #78552	C₃	direct (N × H)
55. C₃×#405	D₃	semidirect
56. C₃×#405	C₂×C₃	semidirect
58. #5118	C₂×C₃	semidirect
60. C₂×Dic₃⋊C₈	C₂×C₃	semidirect
61. #4997	C₂×C₃	semidirect
62. #4709	C₂×C₃	semidirect
63. #4705	C₂×C₃	semidirect
64. #4690	C₂×C₃	semidirect
65. #4685	C₂×C₃	semidirect
203. #405	C₃×D₃	semidirect
479. C₃²	#2925	semidirect
540. C₃	#78552	direct (N × H)
541. C₃	C₃×#2925	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5522	2
C₃²×#405	2
C₃×#5129	2
C₃×#5118	2
C₃×#5110	2
C₂×C₃×Dic₃⋊C₈	2
C₃×#4997	2
C₃×#4709	2
C₃×#4705	2
C₃×#4690	2
C₃×#4685	2
C₃×#2925	3
#78552	3

Subgroups — C3×#78552 #11859081

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78552 #11859081