Subgroups — C₃²×#5583 #13178960

Order 1728.

1432 conjugacy classes of subgroups.

The subgroup lattice has 452 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×#946	C₂	1	1	yes	maximal, characteristic
3	C₃²×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#898	C₂	1	2	yes	maximal
5	C₃²×#897	C₂	1	1	yes	maximal, characteristic
6	C₃²×#890	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#889	C₂	1	2	yes	maximal, complemented
8	C₃²×#876	C₂	1	2	yes	maximal
9	C₃²×#872	C₂	1	1	yes	maximal, characteristic
10	C₃²×#870	C₂	1	2	yes	maximal, complemented
11	C₃²×C₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#541	—	3	1	no	maximal
13	C₃×#5583	C₃	1	4	yes	maximal, direct product factor
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
16	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
17	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₃³×C₄²	C₂²	1	1	yes	characteristic
20	C₃³×C₄²	C₂²	1	2	yes	—
21	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
22	C₃²×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
23	C₃²×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
24	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
27	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
28	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
29	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
30	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₃²×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₃²×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	—
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×#125	—	3	2	no	—
41	C₃²×#125	—	3	1	no	—
42	C₃²×#125	—	3	2	no	—
43	C₃²×C₂²⋊Q₈	—	3	1	no	—
44	C₃²×C₂²⋊Q₈	—	3	1	no	—
45	C₃²×C₄×Q₈	—	2	4	no	—
46	C₃²×C₄×Q₈	—	3	1	no	—
47	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic, complemented
48	C₃²×C₄×Q₈	C₂×C₃	1	4	yes	complemented
49	C₃²×#117	—	3	1	no	—
50	C₃×#946	C₂×C₃	1	4	yes	—
51	C₃×#944	C₂×C₃	1	4	yes	complemented
52	C₃×#898	C₂×C₃	1	8	yes	—
53	C₃×#897	C₂×C₃	1	4	yes	—
54	C₃×#890	C₂×C₃	1	4	yes	complemented
55	C₃×#889	C₂×C₃	1	8	yes	complemented
56	C₃×#876	C₂×C₃	1	8	yes	—
57	C₃×#872	C₂×C₃	1	4	yes	—
58	C₃×#870	C₂×C₃	1	8	yes	complemented
59	C₃×C₄×Dic₆	C₂×C₃	1	4	yes	complemented
60	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
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	2	yes	—
72	C₃²×C₄×D₃	—	2	2	no	—
73	C₃²×Dic₆	—	2	2	no	—
74	C₃×#541	—	3	4	no	—
75	#5583	C₃²	1	1	yes	characteristic, direct product factor
76	C₂×C₃²×Q₈	—	2	4	no	—
77	C₂×C₃²×Q₈	—	3	1	no	—
78	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
80	C₂²×C₃²×C₄	—	3	1	no	—
81	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
82	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
83	C₃²×C₄⋊C₄	—	2	4	no	—
84	C₃²×C₄⋊C₄	—	2	8	no	—
85	C₃²×C₄⋊C₄	—	3	1	no	—
86	C₃²×C₄⋊C₄	—	3	1	no	—
87	C₃²×C₄⋊C₄	—	3	1	no	—
88	C₃²×C₄⋊C₄	—	3	2	no	—
89	C₃²×C₄⋊C₄	—	3	2	no	—
90	C₃²×C₄⋊C₄	—	3	2	no	—
91	C₃²×C₄⋊C₄	—	3	2	no	—
92	C₃²×C₄⋊C₄	—	3	2	no	—
93	C₃²×C₄⋊C₄	—	3	2	no	—
94	C₃²×C₄⋊C₄	—	3	2	no	—
95	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
96	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
97	C₃²×C₄⋊C₄	C₂²×C₃	1	8	yes	—
98	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
99	C₃²×C₂²⋊C₄	—	3	1	no	—
100	C₃²×C₂²⋊C₄	—	3	1	no	—
101	C₃²×C₂²⋊C₄	—	3	2	no	—
102	C₃²×C₂²⋊C₄	—	3	2	no	—
103	C₃²×C₄²	—	2	4	no	—
104	C₃²×C₄²	—	2	8	no	—
105	C₃²×C₄²	—	3	1	no	—
106	C₃²×C₄²	—	3	2	no	—
107	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
108	C₃²×C₄²	C₂×D₃	1	2	yes	—
109	C₃²×C₄²	C₂²×C₃	1	4	yes	—
110	C₃²×C₄²	C₂²×C₃	1	8	yes	—
111	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
112	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
113	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
114	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
115	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
116	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
117	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
118	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
119	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	—
120	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	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×C₄×Dic₃	C₂²×C₃	1	8	yes	—
126	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
127	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
128	C₂×C₃²×D₃	—	2	1	no	—
129	C₂×C₃²×D₃	—	2	1	no	—
130	C₂×C₃²×D₃	—	2	1	no	—
131	C₃³×C₄	—	2	2	no	—
132	C₃³×C₄	—	2	1	no	—
133	C₃³×C₄	—	2	1	no	—
134	C₃³×C₄	—	2	2	no	—
135	C₃³×C₄	#41	1	2	yes	—
136	C₃²×Dic₃	—	2	2	no	—
137	C₃²×Dic₃	—	2	1	no	—
138	C₃²×Dic₃	—	2	1	no	—
139	C₃²×Dic₃	—	2	2	no	—
140	C₃²×Dic₃	—	2	1	no	—
141	C₃×C₄⋊Q₈	—	3	4	no	—
142	C₃×#126	—	3	8	no	—
143	C₃×#126	—	3	8	no	—
144	C₃×#125	—	3	8	no	—
145	C₃×#125	—	3	4	no	—
146	C₃×#125	—	3	8	no	—
147	C₃×C₂²⋊Q₈	—	3	4	no	—
148	C₃×C₂²⋊Q₈	—	3	4	no	—
149	C₃×C₄×Q₈	—	2	4	no	—
150	C₃×C₄×Q₈	—	3	4	no	—
151	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
152	C₃×C₄×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
153	C₃×#117	—	3	4	no	—
154	#946	C₂×C₃²	1	1	yes	characteristic
155	#944	C₂×C₃²	1	1	yes	characteristic, complemented
156	#898	C₂×C₃²	1	2	yes	—
157	#897	C₂×C₃²	1	1	yes	characteristic
158	#890	C₂×C₃²	1	1	yes	characteristic, complemented
159	#889	C₂×C₃²	1	2	yes	complemented
160	#876	C₂×C₃²	1	2	yes	—
161	#872	C₂×C₃²	1	1	yes	characteristic
162	#870	C₂×C₃²	1	2	yes	complemented
163	C₄×Dic₆	C₂×C₃²	1	1	yes	characteristic, complemented
164	C₂³×C₃²	—	3	1	no	—
165	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
166	C₃²×Q₈	—	2	16	no	—
167	C₃²×Q₈	—	2	2	no	—
168	C₃²×Q₈	—	2	8	no	—
169	C₃²×Q₈	—	6	2	no	—
170	C₂×C₃²×C₄	—	2	4	no	—
171	C₂×C₃²×C₄	—	2	8	no	—
172	C₂×C₃²×C₄	—	2	4	no	—
173	C₂×C₃²×C₄	—	2	4	no	—
174	C₂×C₃²×C₄	—	2	8	no	—
175	C₂×C₃²×C₄	—	3	1	no	—
176	C₂×C₃²×C₄	—	3	2	no	—
177	C₂×C₃²×C₄	—	3	1	no	—
178	C₂×C₃²×C₄	—	3	2	no	—
179	C₂×C₃²×C₄	—	3	1	no	—
180	C₂×C₃²×C₄	—	6	2	no	—
181	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
182	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
183	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
184	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
185	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
186	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
187	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
188	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
189	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
190	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
191	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
192	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
193	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
194	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
195	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
196	C₃×C₄×D₃	—	2	8	no	—
197	C₃×Dic₆	—	2	8	no	—
198	#541	—	3	1	no	Sylow
199	C₂×C₃³	C₂×#41	1	1	yes	characteristic
200	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
202	C₃²×D₃	—	4	1	no	—
203	C₂×C₃×Q₈	—	2	4	no	—
204	C₂×C₃×Q₈	—	3	4	no	—
205	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
206	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
207	C₂²×C₃×C₄	—	3	4	no	—
208	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
209	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
210	C₃×C₄⋊C₄	—	2	4	no	—
211	C₃×C₄⋊C₄	—	2	8	no	—
212	C₃×C₄⋊C₄	—	3	4	no	—
213	C₃×C₄⋊C₄	—	3	4	no	—
214	C₃×C₄⋊C₄	—	3	8	no	—
215	C₃×C₄⋊C₄	—	3	8	no	—
216	C₃×C₄⋊C₄	—	3	8	no	—
217	C₃×C₄⋊C₄	—	3	8	no	—
218	C₃×C₄⋊C₄	—	3	8	no	—
219	C₃×C₄⋊C₄	—	3	4	no	—
220	C₃×C₄⋊C₄	—	3	8	no	—
221	C₃×C₄⋊C₄	—	3	8	no	—
222	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
223	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
224	C₃×C₄⋊C₄	C₂²×C₃²	1	2	yes	—
225	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
226	C₃×C₂²⋊C₄	—	3	4	no	—
227	C₃×C₂²⋊C₄	—	3	4	no	—
228	C₃×C₂²⋊C₄	—	3	8	no	—
229	C₃×C₂²⋊C₄	—	3	8	no	—
230	C₃×C₄²	—	2	4	no	—
231	C₃×C₄²	—	2	8	no	—
232	C₃×C₄²	—	3	4	no	—
233	C₃×C₄²	—	3	8	no	—
234	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
235	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
236	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic
237	C₃×C₄²	C₂²×C₃²	1	2	yes	—
238	(C₂×D₃)⋊C₄	C₂²×C₃²	1	1	yes	characteristic
239	(C₂×D₃)⋊C₄	C₂²×C₃²	1	1	yes	characteristic
240	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
241	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	—
242	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic
243	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
244	C₄⋊Dic₃	C₂²×C₃²	1	2	yes	—
245	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
246	Dic₃⋊C₄	C₂²×C₃²	1	1	yes	characteristic
247	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
248	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
249	Dic₃⋊C₄	C₂²×C₃²	1	1	yes	characteristic
250	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
251	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	—
252	C₄×Dic₃	C₂²×C₃²	1	2	yes	—
253	C₄×Dic₃	C₂²×C₃²	1	1	yes	characteristic
254	C₂²×C₃²	—	2	4	no	—
255	C₂²×C₃²	—	6	1	no	—
256	C₂²×C₃²	—	6	1	no	—
257	C₂²×C₃²	—	6	1	no	—
258	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
259	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
260	C₂×C₃×D₃	—	2	4	no	—
261	C₂×C₃×D₃	—	2	4	no	—
262	C₂×C₃×D₃	—	2	4	no	—
263	C₃²×C₄	—	2	8	no	—
264	C₃²×C₄	—	2	16	no	—
265	C₃²×C₄	—	2	2	no	—
266	C₃²×C₄	—	2	1	no	—
267	C₃²×C₄	—	2	1	no	—
268	C₃²×C₄	—	2	2	no	—
269	C₃²×C₄	—	2	8	no	—
270	C₃²×C₄	—	2	4	no	—
271	C₃²×C₄	—	2	8	no	—
272	C₃²×C₄	—	2	4	no	—
273	C₃²×C₄	—	2	8	no	—
274	C₃²×C₄	—	4	4	no	—
275	C₃²×C₄	—	4	8	no	—
276	C₃²×C₄	—	6	1	no	—
277	C₃²×C₄	—	6	2	no	—
278	C₃²×C₄	—	6	1	no	—
279	C₃²×C₄	—	6	2	no	—
280	C₃²×C₄	—	6	1	no	—
281	C₃²×C₄	#235	1	2	yes	—
282	C₃²×C₄	C₃×#41	1	8	yes	—
283	C₃×Dic₃	—	2	8	no	—
284	C₃×Dic₃	—	2	4	no	—
285	C₃×Dic₃	—	2	8	no	—
286	C₃×Dic₃	—	2	4	no	—
287	C₃×Dic₃	—	2	4	no	—
288	C₄⋊Q₈	—	3	1	no	—
289	#126	—	3	2	no	—
290	#126	—	3	2	no	—
291	#125	—	3	2	no	—
292	#125	—	3	1	no	—
293	#125	—	3	2	no	—
294	C₂²⋊Q₈	—	3	1	no	—
295	C₂²⋊Q₈	—	3	1	no	—
296	C₄×Q₈	—	3	1	no	—
297	C₄×Q₈	C₃²×D₃	1	1	yes	characteristic, complemented
298	#117	—	3	1	no	—
299	C₃³	#541	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₃	—	3	4	no	—
301	C₂²×D₃	C₂³×C₃²	1	1	yes	characteristic
302	C₃×Q₈	—	2	16	no	—
303	C₃×Q₈	—	2	8	no	—
304	C₃×Q₈	—	2	2	no	—
305	C₃×Q₈	—	6	8	no	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	8	no	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	2	4	no	—
310	C₂×C₃×C₄	—	2	8	no	—
311	C₂×C₃×C₄	—	3	4	no	—
312	C₂×C₃×C₄	—	3	8	no	—
313	C₂×C₃×C₄	—	3	4	no	—
314	C₂×C₃×C₄	—	3	8	no	—
315	C₂×C₃×C₄	—	3	4	no	—
316	C₂×C₃×C₄	—	6	8	no	—
317	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
318	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
320	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
321	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
322	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
325	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
326	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
327	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
328	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
329	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
330	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
331	C₂×Dic₃	C₂³×C₃²	1	1	yes	characteristic
332	C₄×D₃	—	2	2	no	—
333	Dic₆	—	2	2	no	—
334	C₂×C₃²	—	2	4	no	—
335	C₂×C₃²	—	2	4	no	—
336	C₂×C₃²	—	2	4	no	—
337	C₂×C₃²	—	12	1	no	—
338	C₂×C₃²	C₂×#235	1	1	yes	characteristic
339	C₂×C₃²	#1007	1	1	yes	characteristic
340	C₂×C₃²	#1010	1	1	yes	characteristic
341	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
342	C₂×C₃²	C₃×2₋¹⁺⁴	1	4	yes	—
343	C₂×C₃²	C₃×2₋¹⁺⁴	1	4	yes	—
344	C₃×D₃	—	4	4	no	—
345	C₂×Q₈	—	3	1	no	—
346	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
347	C₂²×C₄	—	3	1	no	—
348	C₄⋊C₄	—	3	1	no	—
349	C₄⋊C₄	—	3	1	no	—
350	C₄⋊C₄	—	3	1	no	—
351	C₄⋊C₄	—	3	2	no	—
352	C₄⋊C₄	—	3	2	no	—
353	C₄⋊C₄	—	3	2	no	—
354	C₄⋊C₄	—	3	2	no	—
355	C₄⋊C₄	—	3	2	no	—
356	C₄⋊C₄	—	3	2	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
359	C₄⋊C₄	C₂×C₃²×D₃	1	2	yes	—
360	C₂²⋊C₄	—	3	1	no	—
361	C₂²⋊C₄	—	3	1	no	—
362	C₂²⋊C₄	—	3	2	no	—
363	C₂²⋊C₄	—	3	2	no	—
364	C₄²	—	3	1	no	—
365	C₄²	—	3	2	no	—
366	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic
367	C₄²	C₂×C₃²×D₃	1	2	yes	—
368	C₂²×C₃	—	2	4	no	—
369	C₂²×C₃	—	6	4	no	—
370	C₂²×C₃	—	6	4	no	—
371	C₂²×C₃	—	6	4	no	—
372	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
373	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
374	C₂×D₃	—	2	1	no	—
375	C₂×D₃	—	2	1	no	—
376	C₂×D₃	—	2	1	no	—
377	C₃×C₄	—	2	16	no	—
378	C₃×C₄	—	2	8	no	—
379	C₃×C₄	—	2	8	no	—
380	C₃×C₄	—	2	4	no	—
381	C₃×C₄	—	2	4	no	—
382	C₃×C₄	—	2	8	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	8	no	—
388	C₃×C₄	—	4	4	no	—
389	C₃×C₄	—	4	8	no	—
390	C₃×C₄	—	6	4	no	—
391	C₃×C₄	—	6	8	no	—
392	C₃×C₄	—	6	4	no	—
393	C₃×C₄	—	6	8	no	—
394	C₃×C₄	—	6	4	no	—
395	C₃×C₄	C₃×#235	1	8	yes	—
396	C₃×C₄	C₃²×#41	1	2	yes	—
397	Dic₃	—	2	2	no	—
398	Dic₃	—	2	1	no	—
399	Dic₃	—	2	2	no	—
400	Dic₃	—	2	1	no	—
401	Dic₃	—	2	1	no	—
402	C₃²	—	2	4	no	—
403	C₃²	#5583	1	1	yes	characteristic, direct product factor
404	C₃²	C₃×#541	1	4	yes	complemented
405	C₂³	—	3	1	no	—
406	Q₈	—	2	2	no	—
407	Q₈	—	6	2	no	—
408	C₂×C₄	—	3	1	no	—
409	C₂×C₄	—	3	2	no	—
410	C₂×C₄	—	3	1	no	—
411	C₂×C₄	—	3	2	no	—
412	C₂×C₄	—	3	1	no	—
413	C₂×C₄	—	6	2	no	—
414	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
417	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
418	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
419	C₂×C₃	—	2	4	no	—
420	C₂×C₃	—	2	4	no	—
421	C₂×C₃	—	2	4	no	—
422	C₂×C₃	—	12	4	no	—
423	C₂×C₃	C₂×C₃×#235	1	4	yes	—
424	C₂×C₃	C₃×#1007	1	4	yes	—
425	C₂×C₃	C₃×#1010	1	4	yes	—
426	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
427	C₂×C₃	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
428	C₂×C₃	C₃²×2₋¹⁺⁴	1	1	yes	characteristic
429	D₃	—	4	1	no	—
430	C₂²	—	6	1	no	—
431	C₂²	—	6	1	no	—
432	C₂²	—	6	1	no	—
433	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	6	1	no	—
439	C₄	—	6	2	no	—
440	C₄	—	6	1	no	—
441	C₄	—	6	2	no	—
442	C₄	—	6	1	no	—
443	C₄	C₃²×#235	1	2	yes	—
444	C₃	—	2	4	no	—
445	C₃	C₃×#5583	1	4	yes	direct product factor
446	C₃	C₃²×#541	1	1	yes	characteristic, complemented
447	C₂	—	12	1	no	—
448	C₂	C₂×C₃²×#235	1	1	yes	characteristic
449	C₂	C₃²×#1007	1	1	yes	characteristic
450	C₂	C₃²×#1010	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	C₂²×C₃²×D₃	C₂³
hypercenter	C₃²×C₄×Q₈	D₃
hypocenter	C₃	C₃²×#541
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
6. C₃²×#890	C₂	semidirect
7. C₃²×#889	C₂	semidirect
10. C₃²×#870	C₂	semidirect
11. C₃²×C₄×Dic₆	C₂	semidirect
13. C₃×#5583	C₃	direct (N × H)
47. C₃²×C₄×Q₈	D₃	semidirect
48. C₃²×C₄×Q₈	C₂×C₃	semidirect
51. C₃×#944	C₂×C₃	semidirect
54. C₃×#890	C₂×C₃	semidirect
55. C₃×#889	C₂×C₃	semidirect
58. C₃×#870	C₂×C₃	semidirect
59. C₃×C₄×Dic₆	C₂×C₃	semidirect
75. #5583	C₃²	direct (N × H)
151. C₃×C₄×Q₈	C₃×D₃	semidirect
152. C₃×C₄×Q₈	C₂×C₃²	semidirect
155. #944	C₂×C₃²	semidirect
158. #890	C₂×C₃²	semidirect
159. #889	C₂×C₃²	semidirect
162. #870	C₂×C₃²	semidirect
163. C₄×Dic₆	C₂×C₃²	semidirect
297. C₄×Q₈	C₃²×D₃	semidirect
299. C₃³	#541	semidirect
403. C₃²	#5583	direct (N × H)
404. C₃²	C₃×#541	semidirect
445. C₃	C₃×#5583	direct (N × H)
446. C₃	C₃²×#541	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×#946	2
C₃²×#944	2
C₃²×#898	2
C₃²×#897	2
C₃²×#890	2
C₃²×#889	2
C₃²×#876	2
C₃²×#872	2
C₃²×#870	2
C₃²×C₄×Dic₆	2
C₃²×#541	3
C₃×#5583	3

Subgroups — C32×#5583 #13178960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5583 #13178960