Subgroups — C₃²×#5568 #13178945

Order 1728.

1552 conjugacy classes of subgroups.

The subgroup lattice has 464 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
3	C₃²×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#898	C₂	1	2	yes	maximal, complemented
5	C₃²×#896	C₂	1	2	yes	maximal, complemented
6	C₃²×#893	C₂	1	1	yes	maximal, characteristic
7	C₃²×#887	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#876	C₂	1	2	yes	maximal, complemented
9	C₃²×#875	C₂	1	1	yes	maximal, characteristic
10	C₃²×#872	C₂	1	2	yes	maximal, complemented
11	C₃²×C₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#556	—	3	1	no	maximal
13	C₃×#5568	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×C₄×D₃	C₂²	1	2	yes	—
17	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
18	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
19	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃³×C₄²	C₂²	1	1	yes	characteristic
22	C₃³×C₄²	C₂²	1	2	yes	—
23	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₃²×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
30	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₃²×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₃²×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
37	C₃²×C₄⋊Q₈	—	3	1	no	—
38	C₃²×#126	—	3	2	no	—
39	C₃²×#126	—	3	2	no	—
40	C₃²×#124	—	3	1	no	—
41	C₃²×#124	—	3	1	no	—
42	C₃²×C₂²⋊Q₈	—	3	2	no	—
43	C₃²×C₄×Q₈	—	2	4	no	—
44	C₃²×C₄×Q₈	—	3	1	no	—
45	C₃²×C₄×Q₈	—	3	1	no	—
46	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic, complemented
47	C₃²×C₄×Q₈	C₂×C₃	1	4	yes	complemented
48	C₃²×C₄×D₄	—	3	1	no	—
49	C₃²×#117	—	3	2	no	—
50	C₃×#947	C₂×C₃	1	4	yes	—
51	C₃×#944	C₂×C₃	1	4	yes	complemented
52	C₃×#898	C₂×C₃	1	8	yes	complemented
53	C₃×#896	C₂×C₃	1	8	yes	complemented
54	C₃×#893	C₂×C₃	1	4	yes	—
55	C₃×#887	C₂×C₃	1	4	yes	complemented
56	C₃×#876	C₂×C₃	1	8	yes	complemented
57	C₃×#875	C₂×C₃	1	4	yes	—
58	C₃×#872	C₂×C₃	1	8	yes	complemented
59	C₃×C₄×Dic₆	C₂×C₃	1	4	yes	complemented
60	C₂²×C₃²×D₃	C₂³	1	2	yes	—
61	C₃³×Q₈	—	2	2	no	—
62	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
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×C₃²×Dic₃	C₂³	1	2	yes	—
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	1	yes	characteristic
72	C₃²×D₁₂	—	2	2	no	—
73	C₃²×C₄×D₃	—	2	4	no	—
74	C₃²×Dic₆	—	2	2	no	—
75	C₃²×Dic₆	—	2	2	no	—
76	C₃×#556	—	3	4	no	—
77	#5568	C₃²	1	1	yes	characteristic, direct product factor
78	C₂×C₃²×Q₈	—	2	4	no	—
79	C₂×C₃²×Q₈	—	3	1	no	—
80	C₂×C₃²×Q₈	—	3	1	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	1	no	—
84	C₂²×C₃²×C₄	—	3	2	no	—
85	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
86	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
87	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
88	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
89	C₃²×C₄⋊C₄	—	2	4	no	—
90	C₃²×C₄⋊C₄	—	2	8	no	—
91	C₃²×C₄⋊C₄	—	3	1	no	—
92	C₃²×C₄⋊C₄	—	3	2	no	—
93	C₃²×C₄⋊C₄	—	3	2	no	—
94	C₃²×C₄⋊C₄	—	3	1	no	—
95	C₃²×C₄⋊C₄	—	3	1	no	—
96	C₃²×C₄⋊C₄	—	3	2	no	—
97	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
98	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
99	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
100	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
101	C₃²×C₂²⋊C₄	—	3	2	no	—
102	C₃²×C₂²⋊C₄	—	3	2	no	—
103	C₃²×C₂²⋊C₄	—	3	2	no	—
104	C₃²×C₂²⋊C₄	—	3	2	no	—
105	C₃²×C₂²⋊C₄	—	3	2	no	—
106	C₃²×C₄²	—	2	8	no	—
107	C₃²×C₄²	—	2	4	no	—
108	C₃²×C₄²	—	3	2	no	—
109	C₃²×C₄²	—	3	1	no	—
110	C₃²×C₄²	—	3	1	no	—
111	C₃²×C₄²	C₂×D₃	1	2	yes	—
112	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
113	C₃²×C₄²	C₂²×C₃	1	4	yes	—
114	C₃²×C₄²	C₂²×C₃	1	8	yes	—
115	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
116	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
117	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
118	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
119	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
120	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
121	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
122	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
123	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
124	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
125	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
126	C₃×C₄×Dic₃	C₂²×C₃	1	8	yes	—
127	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
128	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
129	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
130	C₂×C₃²×D₃	—	2	2	no	—
131	C₂×C₃²×D₃	—	2	2	no	—
132	C₂×C₃²×D₃	—	2	2	no	—
133	C₃³×C₄	—	2	2	no	—
134	C₃³×C₄	—	2	1	no	—
135	C₃³×C₄	—	2	2	no	—
136	C₃³×C₄	—	2	1	no	—
137	C₃³×C₄	#41	1	2	yes	—
138	C₃²×Dic₃	—	2	2	no	—
139	C₃²×Dic₃	—	2	1	no	—
140	C₃²×Dic₃	—	2	1	no	—
141	C₃²×Dic₃	—	2	1	no	—
142	C₃²×Dic₃	#41	1	2	yes	—
143	C₃×C₄⋊Q₈	—	3	4	no	—
144	C₃×#126	—	3	8	no	—
145	C₃×#126	—	3	8	no	—
146	C₃×#124	—	3	4	no	—
147	C₃×#124	—	3	4	no	—
148	C₃×C₂²⋊Q₈	—	3	8	no	—
149	C₃×C₄×Q₈	—	2	4	no	—
150	C₃×C₄×Q₈	—	3	4	no	—
151	C₃×C₄×Q₈	—	3	4	no	—
152	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
153	C₃×C₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
154	C₃×C₄×D₄	—	3	4	no	—
155	C₃×#117	—	3	8	no	—
156	#947	C₂×C₃²	1	1	yes	characteristic
157	#944	C₂×C₃²	1	1	yes	characteristic, complemented
158	#898	C₂×C₃²	1	2	yes	complemented
159	#896	C₂×C₃²	1	2	yes	complemented
160	#893	C₂×C₃²	1	1	yes	characteristic
161	#887	C₂×C₃²	1	1	yes	characteristic, complemented
162	#876	C₂×C₃²	1	2	yes	complemented
163	#875	C₂×C₃²	1	1	yes	characteristic
164	#872	C₂×C₃²	1	2	yes	complemented
165	C₄×Dic₆	C₂×C₃²	1	1	yes	characteristic, complemented
166	C₂³×C₃²	—	3	2	no	—
167	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
168	C₃²×Q₈	—	2	16	no	—
169	C₃²×Q₈	—	2	2	no	—
170	C₃²×Q₈	—	2	8	no	—
171	C₃²×Q₈	—	6	2	no	—
172	C₃²×Q₈	—	6	2	no	—
173	C₃²×D₄	—	6	2	no	—
174	C₂×C₃²×C₄	—	2	4	no	—
175	C₂×C₃²×C₄	—	2	8	no	—
176	C₂×C₃²×C₄	—	2	4	no	—
177	C₂×C₃²×C₄	—	2	8	no	—
178	C₂×C₃²×C₄	—	2	4	no	—
179	C₂×C₃²×C₄	—	3	1	no	—
180	C₂×C₃²×C₄	—	3	1	no	—
181	C₂×C₃²×C₄	—	3	1	no	—
182	C₂×C₃²×C₄	—	3	2	no	—
183	C₂×C₃²×C₄	—	3	1	no	—
184	C₂×C₃²×C₄	—	6	4	no	—
185	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
186	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
187	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
188	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
190	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
191	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
192	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
193	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
194	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
195	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
196	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
197	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
198	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
199	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
200	C₃×D₁₂	—	2	8	no	—
201	C₃×C₄×D₃	—	2	16	no	—
202	C₃×Dic₆	—	2	8	no	—
203	C₃×Dic₆	—	2	8	no	—
204	#556	—	3	1	no	Sylow
205	C₂×C₃³	C₂×#41	1	1	yes	characteristic
206	C₂×C₃³	C₂×#41	1	1	yes	characteristic
207	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
208	C₃²×D₃	—	4	2	no	—
209	C₂×C₃×Q₈	—	2	4	no	—
210	C₂×C₃×Q₈	—	3	4	no	—
211	C₂×C₃×Q₈	—	3	4	no	—
212	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
213	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
214	C₂×C₃×D₄	—	3	4	no	—
215	C₂²×C₃×C₄	—	3	8	no	—
216	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
217	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	—
218	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
219	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
220	C₃×C₄⋊C₄	—	2	4	no	—
221	C₃×C₄⋊C₄	—	2	8	no	—
222	C₃×C₄⋊C₄	—	3	4	no	—
223	C₃×C₄⋊C₄	—	3	8	no	—
224	C₃×C₄⋊C₄	—	3	8	no	—
225	C₃×C₄⋊C₄	—	3	4	no	—
226	C₃×C₄⋊C₄	—	3	8	no	—
227	C₃×C₄⋊C₄	—	3	4	no	—
228	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
229	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
230	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
231	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
232	C₃×C₂²⋊C₄	—	3	8	no	—
233	C₃×C₂²⋊C₄	—	3	8	no	—
234	C₃×C₂²⋊C₄	—	3	8	no	—
235	C₃×C₂²⋊C₄	—	3	8	no	—
236	C₃×C₂²⋊C₄	—	3	8	no	—
237	C₃×C₄²	—	2	8	no	—
238	C₃×C₄²	—	2	4	no	—
239	C₃×C₄²	—	3	8	no	—
240	C₃×C₄²	—	3	4	no	—
241	C₃×C₄²	—	3	4	no	—
242	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
243	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
244	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
245	C₃×C₄²	C₂²×C₃²	1	2	yes	—
246	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
247	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
248	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
249	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
250	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
251	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
252	Dic₃⋊C₄	C₂²×C₃²	1	1	yes	characteristic
253	Dic₃⋊C₄	C₂²×C₃²	1	1	yes	characteristic
254	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
255	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
256	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
257	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
258	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
259	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
260	C₂²×C₃²	—	2	4	no	—
261	C₂²×C₃²	—	6	2	no	—
262	C₂²×C₃²	—	6	2	no	—
263	C₂²×C₃²	—	6	2	no	—
264	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
265	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
266	C₂×C₃×D₃	—	2	8	no	—
267	C₂×C₃×D₃	—	2	8	no	—
268	C₂×C₃×D₃	—	2	8	no	—
269	C₃²×C₄	—	2	8	no	—
270	C₃²×C₄	—	2	16	no	—
271	C₃²×C₄	—	2	2	no	—
272	C₃²×C₄	—	2	1	no	—
273	C₃²×C₄	—	2	2	no	—
274	C₃²×C₄	—	2	1	no	—
275	C₃²×C₄	—	2	8	no	—
276	C₃²×C₄	—	2	4	no	—
277	C₃²×C₄	—	2	8	no	—
278	C₃²×C₄	—	2	4	no	—
279	C₃²×C₄	—	2	8	no	—
280	C₃²×C₄	—	3	2	no	—
281	C₃²×C₄	—	4	8	no	—
282	C₃²×C₄	—	4	4	no	—
283	C₃²×C₄	—	6	2	no	—
284	C₃²×C₄	—	6	1	no	—
285	C₃²×C₄	—	6	1	no	—
286	C₃²×C₄	—	6	1	no	—
287	C₃²×C₄	#235	1	2	yes	—
288	C₃²×C₄	C₃×#41	1	8	yes	—
289	C₃×Dic₃	—	2	8	no	—
290	C₃×Dic₃	—	2	4	no	—
291	C₃×Dic₃	—	2	4	no	—
292	C₃×Dic₃	—	2	4	no	—
293	C₃×Dic₃	C₃×#41	1	8	yes	—
294	C₄⋊Q₈	—	3	1	no	—
295	#126	—	3	2	no	—
296	#126	—	3	2	no	—
297	#124	—	3	1	no	—
298	#124	—	3	1	no	—
299	C₂²⋊Q₈	—	3	2	no	—
300	C₄×Q₈	—	3	1	no	—
301	C₄×Q₈	—	3	1	no	—
302	C₄×Q₈	C₃²×D₃	1	1	yes	characteristic, complemented
303	C₄×D₄	—	3	1	no	—
304	#117	—	3	2	no	—
305	C₃³	#556	1	1	yes	characteristic, complemented, Sylow
306	C₂³×C₃	—	3	8	no	—
307	C₂²×D₃	C₂³×C₃²	1	2	yes	—
308	C₃×Q₈	—	2	16	no	—
309	C₃×Q₈	—	2	8	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	6	8	no	—
312	C₃×Q₈	—	6	8	no	—
313	C₃×D₄	—	6	8	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	8	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	8	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	3	4	no	—
320	C₂×C₃×C₄	—	3	4	no	—
321	C₂×C₃×C₄	—	3	4	no	—
322	C₂×C₃×C₄	—	3	8	no	—
323	C₂×C₃×C₄	—	3	4	no	—
324	C₂×C₃×C₄	—	6	16	no	—
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
327	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
328	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
330	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
331	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
333	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
335	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
336	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
337	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
338	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
339	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
340	D₁₂	—	2	2	no	—
341	C₄×D₃	—	2	4	no	—
342	Dic₆	—	2	2	no	—
343	Dic₆	—	2	2	no	—
344	C₂×C₃²	—	2	4	no	—
345	C₂×C₃²	—	2	4	no	—
346	C₂×C₃²	—	2	4	no	—
347	C₂×C₃²	—	12	2	no	—
348	C₂×C₃²	C₂×#235	1	1	yes	characteristic
349	C₂×C₃²	#1007	1	1	yes	characteristic
350	C₂×C₃²	D₃×#41	1	1	yes	characteristic
351	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
352	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
353	C₂×C₃²	C₃×2₋¹⁺⁴	1	4	yes	—
354	C₃×D₃	—	4	8	no	—
355	C₂×Q₈	—	3	1	no	—
356	C₂×Q₈	—	3	1	no	—
357	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
358	C₂×D₄	—	3	1	no	—
359	C₂²×C₄	—	3	2	no	—
360	C₄⋊C₄	—	3	1	no	—
361	C₄⋊C₄	—	3	2	no	—
362	C₄⋊C₄	—	3	2	no	—
363	C₄⋊C₄	—	3	1	no	—
364	C₄⋊C₄	—	3	1	no	—
365	C₄⋊C₄	—	3	2	no	—
366	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
367	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	—
368	C₂²⋊C₄	—	3	2	no	—
369	C₂²⋊C₄	—	3	2	no	—
370	C₂²⋊C₄	—	3	2	no	—
371	C₂²⋊C₄	—	3	2	no	—
372	C₂²⋊C₄	—	3	2	no	—
373	C₄²	—	3	2	no	—
374	C₄²	—	3	1	no	—
375	C₄²	—	3	1	no	—
376	C₄²	C₂×C₃²×D₃	1	2	yes	—
377	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
378	C₂²×C₃	—	2	4	no	—
379	C₂²×C₃	—	6	8	no	—
380	C₂²×C₃	—	6	8	no	—
381	C₂²×C₃	—	6	8	no	—
382	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
383	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
384	C₂×D₃	—	2	2	no	—
385	C₂×D₃	—	2	2	no	—
386	C₂×D₃	—	2	2	no	—
387	C₃×C₄	—	2	16	no	—
388	C₃×C₄	—	2	8	no	—
389	C₃×C₄	—	2	8	no	—
390	C₃×C₄	—	2	4	no	—
391	C₃×C₄	—	2	8	no	—
392	C₃×C₄	—	2	4	no	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	8	no	—
398	C₃×C₄	—	3	8	no	—
399	C₃×C₄	—	4	8	no	—
400	C₃×C₄	—	4	4	no	—
401	C₃×C₄	—	6	8	no	—
402	C₃×C₄	—	6	4	no	—
403	C₃×C₄	—	6	4	no	—
404	C₃×C₄	—	6	4	no	—
405	C₃×C₄	C₃×#235	1	8	yes	—
406	C₃×C₄	C₃²×#41	1	2	yes	—
407	Dic₃	—	2	2	no	—
408	Dic₃	—	2	1	no	—
409	Dic₃	—	2	1	no	—
410	Dic₃	—	2	1	no	—
411	Dic₃	C₃²×#41	1	2	yes	—
412	C₃²	—	2	4	no	—
413	C₃²	#5568	1	1	yes	characteristic, direct product factor
414	C₃²	C₃×#556	1	4	yes	complemented
415	C₂³	—	3	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	6	2	no	—
418	Q₈	—	6	2	no	—
419	D₄	—	6	2	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	2	no	—
424	C₂×C₄	—	3	1	no	—
425	C₂×C₄	—	6	4	no	—
426	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
427	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
429	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
431	C₂×C₃	—	2	4	no	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	—	2	4	no	—
434	C₂×C₃	—	12	8	no	—
435	C₂×C₃	C₂×C₃×#235	1	4	yes	—
436	C₂×C₃	C₃×#1007	1	4	yes	—
437	C₂×C₃	C₃×D₃×#41	1	4	yes	—
438	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
439	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
440	C₂×C₃	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
441	D₃	—	4	2	no	—
442	C₂²	—	6	2	no	—
443	C₂²	—	6	2	no	—
444	C₂²	—	6	2	no	—
445	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	3	2	no	—
451	C₄	—	6	2	no	—
452	C₄	—	6	1	no	—
453	C₄	—	6	1	no	—
454	C₄	—	6	1	no	—
455	C₄	C₃²×#235	1	2	yes	—
456	C₃	—	2	4	no	—
457	C₃	C₃×#5568	1	4	yes	direct product factor
458	C₃	C₃²×#556	1	1	yes	characteristic, complemented
459	C₂	—	12	2	no	—
460	C₂	C₂×C₃²×#235	1	1	yes	characteristic
461	C₂	C₃²×#1007	1	1	yes	characteristic
462	C₂	C₃²×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×C₄×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃²×D₁₂	C₂²
hypercenter	C₃²×C₄×Q₈	D₃
hypocenter	C₃	C₃²×#556
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ 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
3. C₃²×#944	C₂	semidirect
4. C₃²×#898	C₂	semidirect
5. C₃²×#896	C₂	semidirect
7. C₃²×#887	C₂	semidirect
8. C₃²×#876	C₂	semidirect
10. C₃²×#872	C₂	semidirect
11. C₃²×C₄×Dic₆	C₂	semidirect
13. C₃×#5568	C₃	direct (N × H)
46. C₃²×C₄×Q₈	D₃	semidirect
47. C₃²×C₄×Q₈	C₂×C₃	semidirect
51. C₃×#944	C₂×C₃	semidirect
52. C₃×#898	C₂×C₃	semidirect
53. C₃×#896	C₂×C₃	semidirect
55. C₃×#887	C₂×C₃	semidirect
56. C₃×#876	C₂×C₃	semidirect
58. C₃×#872	C₂×C₃	semidirect
59. C₃×C₄×Dic₆	C₂×C₃	semidirect
77. #5568	C₃²	direct (N × H)
152. C₃×C₄×Q₈	C₃×D₃	semidirect
153. C₃×C₄×Q₈	C₂×C₃²	semidirect
157. #944	C₂×C₃²	semidirect
158. #898	C₂×C₃²	semidirect
159. #896	C₂×C₃²	semidirect
161. #887	C₂×C₃²	semidirect
162. #876	C₂×C₃²	semidirect
164. #872	C₂×C₃²	semidirect
165. C₄×Dic₆	C₂×C₃²	semidirect
302. C₄×Q₈	C₃²×D₃	semidirect
305. C₃³	#556	semidirect
413. C₃²	#5568	direct (N × H)
414. C₃²	C₃×#556	semidirect
457. C₃	C₃×#5568	direct (N × H)
458. C₃	C₃²×#556	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×#944	2
C₃²×#898	2
C₃²×#896	2
C₃²×#893	2
C₃²×#887	2
C₃²×#876	2
C₃²×#875	2
C₃²×#872	2
C₃²×C₄×Dic₆	2
C₃²×#556	3
C₃×#5568	3

Subgroups — C32×#5568 #13178945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5568 #13178945