Subgroups — C₃²×#5580 #13178957

Order 1728.

1684 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#898	C₂	1	2	yes	maximal, complemented
5	C₃²×#895	C₂	1	1	yes	maximal, characteristic
6	C₃²×#894	C₂	1	2	yes	maximal, complemented
7	C₃²×#890	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃²×C₄×D₁₂	C₂	1	2	yes	maximal, complemented
10	C₃²×#872	C₂	1	2	yes	maximal, complemented
11	C₃²×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#529	—	3	1	no	maximal
13	C₃×#5580	C₃	1	4	yes	maximal, direct product factor
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
17	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	—
21	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
23	C₃³×C₄²	C₂²	1	1	yes	characteristic
24	C₃³×C₄²	C₂²	1	2	yes	—
25	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
26	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
29	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
32	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
35	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
36	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
37	C₃²×#126	—	3	2	no	—
38	C₃²×#125	—	3	1	no	—
39	C₃²×#124	—	3	1	no	—
40	C₃²×#123	—	3	2	no	—
41	C₃²×C₂²⋊Q₈	—	3	1	no	—
42	C₃²×#121	—	3	1	no	—
43	C₃²×C₄×Q₈	—	2	4	no	—
44	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic, complemented
45	C₃²×C₄×Q₈	C₂×C₃	1	4	yes	complemented
46	C₃²×C₄×D₄	—	3	1	no	—
47	C₃²×C₄×D₄	—	3	2	no	—
48	C₃²×#117	—	3	2	no	—
49	C₂×C₃²×C₄²	—	3	1	no	—
50	C₃×#947	C₂×C₃	1	4	yes	complemented
51	C₃×#946	C₂×C₃	1	4	yes	complemented
52	C₃×#898	C₂×C₃	1	8	yes	complemented
53	C₃×#895	C₂×C₃	1	4	yes	—
54	C₃×#894	C₂×C₃	1	8	yes	complemented
55	C₃×#890	C₂×C₃	1	4	yes	complemented
56	C₃×C₄×D₁₂	C₂×C₃	1	8	yes	complemented
57	C₃×C₄×D₁₂	C₂×C₃	1	4	yes	complemented
58	C₃×#872	C₂×C₃	1	8	yes	complemented
59	C₃×C₄²×D₃	C₂×C₃	1	4	yes	complemented
60	C₂²×C₃²×D₃	C₂³	1	2	yes	—
61	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
62	C₃³×Q₈	—	2	2	no	—
63	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
64	C₂×C₃³×C₄	C₂³	1	2	yes	—
65	C₂×C₃³×C₄	C₂³	1	2	yes	—
66	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
68	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₃²×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
72	C₃²×D₁₂	—	2	4	no	—
73	C₃²×D₁₂	—	2	2	no	—
74	C₃²×C₄×D₃	—	2	2	no	—
75	C₃²×C₄×D₃	—	2	2	no	—
76	C₃²×C₄×D₃	—	2	2	no	—
77	C₃²×C₄×D₃	—	2	4	no	—
78	C₃×#529	—	3	4	no	—
79	#5580	C₃²	1	1	yes	characteristic, direct product factor
80	C₂×C₃²×Q₈	—	2	4	no	—
81	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
82	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
83	C₂×C₃²×D₄	—	3	2	no	—
84	C₂×C₃²×D₄	—	3	1	no	—
85	C₂²×C₃²×C₄	—	3	1	no	—
86	C₂²×C₃²×C₄	—	3	1	no	—
87	C₂²×C₃²×C₄	—	3	1	no	—
88	C₂²×C₃²×C₄	—	3	2	no	—
89	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
90	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
91	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
92	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
93	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
94	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
95	C₃²×C₄⋊C₄	—	2	4	no	—
96	C₃²×C₄⋊C₄	—	2	8	no	—
97	C₃²×C₄⋊C₄	—	3	2	no	—
98	C₃²×C₄⋊C₄	—	3	2	no	—
99	C₃²×C₄⋊C₄	—	3	1	no	—
100	C₃²×C₄⋊C₄	—	3	2	no	—
101	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
102	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
103	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
104	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
105	C₃²×C₂²⋊C₄	—	3	2	no	—
106	C₃²×C₂²⋊C₄	—	3	2	no	—
107	C₃²×C₂²⋊C₄	—	3	2	no	—
108	C₃²×C₂²⋊C₄	—	3	2	no	—
109	C₃²×C₂²⋊C₄	—	3	2	no	—
110	C₃²×C₄²	—	2	4	no	—
111	C₃²×C₄²	—	2	8	no	—
112	C₃²×C₄²	—	3	1	no	—
113	C₃²×C₄²	—	3	1	no	—
114	C₃²×C₄²	—	3	1	no	—
115	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
116	C₃²×C₄²	C₂×D₃	1	2	yes	—
117	C₃²×C₄²	C₂²×C₃	1	4	yes	—
118	C₃²×C₄²	C₂²×C₃	1	8	yes	—
119	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
120	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
121	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
122	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
123	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
124	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
125	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
126	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
127	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
128	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
129	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
130	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
131	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
132	C₂×C₃²×D₃	—	2	1	no	—
133	C₂×C₃²×D₃	—	2	1	no	—
134	C₂×C₃²×D₃	—	2	2	no	—
135	C₂×C₃²×D₃	—	2	2	no	—
136	C₂×C₃²×D₃	—	2	2	no	—
137	C₂×C₃²×D₃	#41	1	2	yes	—
138	C₃³×C₄	—	2	2	no	—
139	C₃³×C₄	—	2	1	no	—
140	C₃³×C₄	—	2	2	no	—
141	C₃³×C₄	#41	1	2	yes	—
142	C₃³×C₄	#41	1	2	yes	—
143	C₃²×Dic₃	—	2	1	no	—
144	C₃²×Dic₃	—	2	1	no	—
145	C₃²×Dic₃	—	2	2	no	—
146	C₃²×Dic₃	—	2	1	no	—
147	C₃×#126	—	3	8	no	—
148	C₃×#125	—	3	4	no	—
149	C₃×#124	—	3	4	no	—
150	C₃×#123	—	3	8	no	—
151	C₃×C₂²⋊Q₈	—	3	4	no	—
152	C₃×#121	—	3	4	no	—
153	C₃×C₄×Q₈	—	2	4	no	—
154	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
155	C₃×C₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
156	C₃×C₄×D₄	—	3	4	no	—
157	C₃×C₄×D₄	—	3	8	no	—
158	C₃×#117	—	3	8	no	—
159	C₂×C₃×C₄²	—	3	4	no	—
160	#947	C₂×C₃²	1	1	yes	characteristic, complemented
161	#946	C₂×C₃²	1	1	yes	characteristic, complemented
162	#898	C₂×C₃²	1	2	yes	complemented
163	#895	C₂×C₃²	1	1	yes	characteristic
164	#894	C₂×C₃²	1	2	yes	complemented
165	#890	C₂×C₃²	1	1	yes	characteristic, complemented
166	C₄×D₁₂	C₂×C₃²	1	2	yes	complemented
167	C₄×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
168	#872	C₂×C₃²	1	2	yes	complemented
169	C₄²×D₃	C₂×C₃²	1	1	yes	characteristic, complemented
170	C₂³×C₃²	—	3	1	no	—
171	C₂³×C₃²	—	3	2	no	—
172	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
173	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
174	C₃²×Q₈	—	2	16	no	—
175	C₃²×Q₈	—	2	2	no	—
176	C₃²×Q₈	—	2	8	no	—
177	C₃²×D₄	—	6	4	no	—
178	C₃²×D₄	—	6	2	no	—
179	C₂×C₃²×C₄	—	2	4	no	—
180	C₂×C₃²×C₄	—	2	8	no	—
181	C₂×C₃²×C₄	—	2	4	no	—
182	C₂×C₃²×C₄	—	2	4	no	—
183	C₂×C₃²×C₄	—	2	8	no	—
184	C₂×C₃²×C₄	—	3	1	no	—
185	C₂×C₃²×C₄	—	3	1	no	—
186	C₂×C₃²×C₄	—	3	1	no	—
187	C₂×C₃²×C₄	—	3	2	no	—
188	C₂×C₃²×C₄	—	6	2	no	—
189	C₂×C₃²×C₄	—	6	2	no	—
190	C₂×C₃²×C₄	—	6	2	no	—
191	C₂×C₃²×C₄	—	6	4	no	—
192	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
194	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
195	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
196	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
197	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
198	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
199	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
200	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
201	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
202	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
203	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
204	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
205	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
206	C₃×D₁₂	—	2	16	no	—
207	C₃×D₁₂	—	2	8	no	—
208	C₃×C₄×D₃	—	2	8	no	—
209	C₃×C₄×D₃	—	2	8	no	—
210	C₃×C₄×D₃	—	2	8	no	—
211	C₃×C₄×D₃	—	2	16	no	—
212	#529	—	3	1	no	Sylow
213	C₂×C₃³	C₂×#41	1	1	yes	characteristic
214	C₂×C₃³	C₂×#41	1	1	yes	characteristic
215	C₂×C₃³	C₂×#41	1	1	yes	characteristic
216	C₃²×D₃	—	2	2	no	—
217	C₃²×D₃	—	4	2	no	—
218	C₂×C₃×Q₈	—	2	4	no	—
219	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
220	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
221	C₂×C₃×D₄	—	3	8	no	—
222	C₂×C₃×D₄	—	3	4	no	—
223	C₂²×C₃×C₄	—	3	4	no	—
224	C₂²×C₃×C₄	—	3	4	no	—
225	C₂²×C₃×C₄	—	3	4	no	—
226	C₂²×C₃×C₄	—	3	8	no	—
227	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
228	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
229	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
230	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
231	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
232	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
233	C₃×C₄⋊C₄	—	2	4	no	—
234	C₃×C₄⋊C₄	—	2	8	no	—
235	C₃×C₄⋊C₄	—	3	8	no	—
236	C₃×C₄⋊C₄	—	3	8	no	—
237	C₃×C₄⋊C₄	—	3	4	no	—
238	C₃×C₄⋊C₄	—	3	8	no	—
239	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
240	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
241	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
242	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
243	C₃×C₂²⋊C₄	—	3	8	no	—
244	C₃×C₂²⋊C₄	—	3	8	no	—
245	C₃×C₂²⋊C₄	—	3	8	no	—
246	C₃×C₂²⋊C₄	—	3	8	no	—
247	C₃×C₂²⋊C₄	—	3	8	no	—
248	C₃×C₄²	—	2	4	no	—
249	C₃×C₄²	—	2	8	no	—
250	C₃×C₄²	—	3	4	no	—
251	C₃×C₄²	—	3	4	no	—
252	C₃×C₄²	—	3	4	no	—
253	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
254	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
255	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
256	C₃×C₄²	C₂²×C₃²	1	2	yes	—
257	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
258	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
259	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
260	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
261	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
262	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
263	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
264	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
265	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
266	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
267	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
268	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
269	C₂²×C₃²	—	2	4	no	—
270	C₂²×C₃²	—	3	2	no	—
271	C₂²×C₃²	—	6	1	no	—
272	C₂²×C₃²	—	6	1	no	—
273	C₂²×C₃²	—	6	2	no	—
274	C₂²×C₃²	—	6	2	no	—
275	C₂²×C₃²	—	6	2	no	—
276	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
277	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
278	C₂×C₃×D₃	—	2	4	no	—
279	C₂×C₃×D₃	—	2	4	no	—
280	C₂×C₃×D₃	—	2	8	no	—
281	C₂×C₃×D₃	—	2	8	no	—
282	C₂×C₃×D₃	—	2	8	no	—
283	C₂×C₃×D₃	C₃×#41	1	8	yes	—
284	C₃²×C₄	—	2	16	no	—
285	C₃²×C₄	—	2	2	no	—
286	C₃²×C₄	—	2	1	no	—
287	C₃²×C₄	—	2	2	no	—
288	C₃²×C₄	—	2	8	no	—
289	C₃²×C₄	—	2	8	no	—
290	C₃²×C₄	—	2	8	no	—
291	C₃²×C₄	—	2	4	no	—
292	C₃²×C₄	—	2	8	no	—
293	C₃²×C₄	—	4	4	no	—
294	C₃²×C₄	—	4	8	no	—
295	C₃²×C₄	—	6	1	no	—
296	C₃²×C₄	—	6	1	no	—
297	C₃²×C₄	—	6	2	no	—
298	C₃²×C₄	—	6	1	no	—
299	C₃²×C₄	#235	1	2	yes	—
300	C₃²×C₄	#239	1	2	yes	—
301	C₃²×C₄	C₃×#41	1	8	yes	—
302	C₃²×C₄	C₃×#41	1	8	yes	—
303	C₃×Dic₃	—	2	4	no	—
304	C₃×Dic₃	—	2	4	no	—
305	C₃×Dic₃	—	2	8	no	—
306	C₃×Dic₃	—	2	4	no	—
307	#126	—	3	2	no	—
308	#125	—	3	1	no	—
309	#124	—	3	1	no	—
310	#123	—	3	2	no	—
311	C₂²⋊Q₈	—	3	1	no	—
312	#121	—	3	1	no	—
313	C₄×Q₈	C₃²×D₃	1	1	yes	characteristic, complemented
314	C₄×D₄	—	3	1	no	—
315	C₄×D₄	—	3	2	no	—
316	#117	—	3	2	no	—
317	C₂×C₄²	—	3	1	no	—
318	C₃³	#529	1	1	yes	characteristic, complemented, Sylow
319	C₂³×C₃	—	3	4	no	—
320	C₂³×C₃	—	3	8	no	—
321	C₂²×D₃	C₂³×C₃²	1	2	yes	—
322	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
323	C₃×Q₈	—	2	16	no	—
324	C₃×Q₈	—	2	8	no	—
325	C₃×Q₈	—	2	2	no	—
326	C₃×D₄	—	6	16	no	—
327	C₃×D₄	—	6	8	no	—
328	C₂×C₃×C₄	—	2	4	no	—
329	C₂×C₃×C₄	—	2	8	no	—
330	C₂×C₃×C₄	—	2	4	no	—
331	C₂×C₃×C₄	—	2	4	no	—
332	C₂×C₃×C₄	—	2	8	no	—
333	C₂×C₃×C₄	—	3	4	no	—
334	C₂×C₃×C₄	—	3	4	no	—
335	C₂×C₃×C₄	—	3	4	no	—
336	C₂×C₃×C₄	—	3	8	no	—
337	C₂×C₃×C₄	—	6	8	no	—
338	C₂×C₃×C₄	—	6	8	no	—
339	C₂×C₃×C₄	—	6	8	no	—
340	C₂×C₃×C₄	—	6	16	no	—
341	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
342	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
343	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
344	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
345	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
346	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
348	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
349	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
351	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
352	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
353	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
354	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
355	D₁₂	—	2	4	no	—
356	D₁₂	—	2	2	no	—
357	C₄×D₃	—	2	2	no	—
358	C₄×D₃	—	2	2	no	—
359	C₄×D₃	—	2	2	no	—
360	C₄×D₃	—	2	4	no	—
361	C₂×C₃²	—	2	4	no	—
362	C₂×C₃²	—	2	4	no	—
363	C₂×C₃²	—	2	4	no	—
364	C₂×C₃²	—	6	2	no	—
365	C₂×C₃²	—	12	2	no	—
366	C₂×C₃²	C₂×#235	1	1	yes	characteristic
367	C₂×C₃²	C₂×#239	1	1	yes	characteristic
368	C₂×C₃²	D₃×#41	1	1	yes	characteristic
369	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
370	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
371	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
372	C₃×D₃	—	2	8	no	—
373	C₃×D₃	—	4	8	no	—
374	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
375	C₂×D₄	—	3	2	no	—
376	C₂×D₄	—	3	1	no	—
377	C₂²×C₄	—	3	1	no	—
378	C₂²×C₄	—	3	1	no	—
379	C₂²×C₄	—	3	1	no	—
380	C₂²×C₄	—	3	2	no	—
381	C₄⋊C₄	—	3	2	no	—
382	C₄⋊C₄	—	3	2	no	—
383	C₄⋊C₄	—	3	1	no	—
384	C₄⋊C₄	—	3	2	no	—
385	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
386	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	—
387	C₂²⋊C₄	—	3	2	no	—
388	C₂²⋊C₄	—	3	2	no	—
389	C₂²⋊C₄	—	3	2	no	—
390	C₂²⋊C₄	—	3	2	no	—
391	C₂²⋊C₄	—	3	2	no	—
392	C₄²	—	3	1	no	—
393	C₄²	—	3	1	no	—
394	C₄²	—	3	1	no	—
395	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
396	C₄²	C₂×C₃²×D₃	1	2	yes	—
397	C₂²×C₃	—	2	4	no	—
398	C₂²×C₃	—	3	8	no	—
399	C₂²×C₃	—	6	4	no	—
400	C₂²×C₃	—	6	4	no	—
401	C₂²×C₃	—	6	8	no	—
402	C₂²×C₃	—	6	8	no	—
403	C₂²×C₃	—	6	8	no	—
404	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
405	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
406	C₂×D₃	—	2	1	no	—
407	C₂×D₃	—	2	1	no	—
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	—	2	2	no	—
410	C₂×D₃	—	2	2	no	—
411	C₂×D₃	C₃²×#41	1	2	yes	—
412	C₃×C₄	—	2	16	no	—
413	C₃×C₄	—	2	8	no	—
414	C₃×C₄	—	2	4	no	—
415	C₃×C₄	—	2	8	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	2	no	—
419	C₃×C₄	—	2	8	no	—
420	C₃×C₄	—	2	8	no	—
421	C₃×C₄	—	4	4	no	—
422	C₃×C₄	—	4	8	no	—
423	C₃×C₄	—	6	4	no	—
424	C₃×C₄	—	6	4	no	—
425	C₃×C₄	—	6	8	no	—
426	C₃×C₄	—	6	4	no	—
427	C₃×C₄	C₃×#235	1	8	yes	—
428	C₃×C₄	C₃×#239	1	8	yes	—
429	C₃×C₄	C₃²×#41	1	2	yes	—
430	C₃×C₄	C₃²×#41	1	2	yes	—
431	Dic₃	—	2	1	no	—
432	Dic₃	—	2	1	no	—
433	Dic₃	—	2	2	no	—
434	Dic₃	—	2	1	no	—
435	C₃²	—	2	4	no	—
436	C₃²	#5580	1	1	yes	characteristic, direct product factor
437	C₃²	C₃×#529	1	4	yes	complemented
438	C₂³	—	3	1	no	—
439	C₂³	—	3	2	no	—
440	Q₈	—	2	2	no	—
441	D₄	—	6	4	no	—
442	D₄	—	6	2	no	—
443	C₂×C₄	—	3	1	no	—
444	C₂×C₄	—	3	1	no	—
445	C₂×C₄	—	3	1	no	—
446	C₂×C₄	—	3	2	no	—
447	C₂×C₄	—	6	2	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	2	no	—
450	C₂×C₄	—	6	4	no	—
451	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
453	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
454	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
455	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
456	C₂×C₃	—	2	4	no	—
457	C₂×C₃	—	2	4	no	—
458	C₂×C₃	—	2	4	no	—
459	C₂×C₃	—	6	8	no	—
460	C₂×C₃	—	12	8	no	—
461	C₂×C₃	C₂×C₃×#235	1	4	yes	—
462	C₂×C₃	C₂×C₃×#239	1	4	yes	—
463	C₂×C₃	C₃×D₃×#41	1	4	yes	—
464	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
465	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
466	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
467	D₃	—	2	2	no	—
468	D₃	—	4	2	no	—
469	C₂²	—	3	2	no	—
470	C₂²	—	6	1	no	—
471	C₂²	—	6	1	no	—
472	C₂²	—	6	2	no	—
473	C₂²	—	6	2	no	—
474	C₂²	—	6	2	no	—
475	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	6	1	no	—
480	C₄	—	6	1	no	—
481	C₄	—	6	2	no	—
482	C₄	—	6	1	no	—
483	C₄	C₃²×#235	1	2	yes	—
484	C₄	C₃²×#239	1	2	yes	—
485	C₃	—	2	4	no	—
486	C₃	C₃×#5580	1	4	yes	direct product factor
487	C₃	C₃²×#529	1	1	yes	characteristic, complemented
488	C₂	—	6	2	no	—
489	C₂	—	12	2	no	—
490	C₂	C₂×C₃²×#235	1	1	yes	characteristic
491	C₂	C₂×C₃²×#239	1	1	yes	characteristic
492	C₂	C₃²×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×C₄×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₃²×#895	C₂
hypercenter	C₃²×C₄×Q₈	D₃
hypocenter	C₃	C₃²×#529
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₃²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄×Q₈	C₂	semidirect
2. C₃²×#947	C₂	semidirect
3. C₃²×#946	C₂	semidirect
4. C₃²×#898	C₂	semidirect
6. C₃²×#894	C₂	semidirect
7. C₃²×#890	C₂	semidirect
8. C₃²×C₄×D₁₂	C₂	semidirect
9. C₃²×C₄×D₁₂	C₂	semidirect
10. C₃²×#872	C₂	semidirect
11. C₃²×C₄²×D₃	C₂	semidirect
13. C₃×#5580	C₃	direct (N × H)
44. C₃²×C₄×Q₈	D₃	semidirect
45. C₃²×C₄×Q₈	C₂×C₃	semidirect
50. C₃×#947	C₂×C₃	semidirect
51. C₃×#946	C₂×C₃	semidirect
52. C₃×#898	C₂×C₃	semidirect
54. C₃×#894	C₂×C₃	semidirect
55. C₃×#890	C₂×C₃	semidirect
56. C₃×C₄×D₁₂	C₂×C₃	semidirect
57. C₃×C₄×D₁₂	C₂×C₃	semidirect
58. C₃×#872	C₂×C₃	semidirect
59. C₃×C₄²×D₃	C₂×C₃	semidirect
79. #5580	C₃²	direct (N × H)
154. C₃×C₄×Q₈	C₃×D₃	semidirect
155. C₃×C₄×Q₈	C₂×C₃²	semidirect
160. #947	C₂×C₃²	semidirect
161. #946	C₂×C₃²	semidirect
162. #898	C₂×C₃²	semidirect
164. #894	C₂×C₃²	semidirect
165. #890	C₂×C₃²	semidirect
166. C₄×D₁₂	C₂×C₃²	semidirect
167. C₄×D₁₂	C₂×C₃²	semidirect
168. #872	C₂×C₃²	semidirect
169. C₄²×D₃	C₂×C₃²	semidirect
313. C₄×Q₈	C₃²×D₃	semidirect
318. C₃³	#529	semidirect
436. C₃²	#5580	direct (N × H)
437. C₃²	C₃×#529	semidirect
486. C₃	C₃×#5580	direct (N × H)
487. C₃	C₃²×#529	semidirect

Maximal subgroups

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

subgroup	index
C₃³×C₄×Q₈	2
C₃²×#947	2
C₃²×#946	2
C₃²×#898	2
C₃²×#895	2
C₃²×#894	2
C₃²×#890	2
C₃²×C₄×D₁₂	2
C₃²×#872	2
C₃²×C₄²×D₃	2
C₃²×#529	3
C₃×#5580	3

Subgroups — C32×#5580 #13178957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5580 #13178957