Subgroups — C₃×D₃×#433 #11858765

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×#117	C₂	1	1	yes	maximal, characteristic
2	C₃²×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5000	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4840	C₂	1	2	yes	maximal, complemented
5	C₃×D₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₃×D₃×C₂²⋊C₈	C₂	1	2	yes	maximal
7	C₃×#4720	C₂	1	2	yes	maximal, complemented
8	C₃×#4709	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4690	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#433	—	3	1	no	maximal
13	D₃×#433	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
15	C₃²×#117	C₂²	1	1	yes	characteristic
16	C₃×#926	C₂²	1	1	yes	characteristic
17	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
18	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
19	C₃×#892	C₄	1	2	yes	—
20	C₃×D₃×C₄⋊C₄	C₄	1	2	yes	—
21	C₃×D₃×C₂²⋊C₄	C₄	1	2	yes	—
22	C₃×#877	C₄	1	2	yes	—
23	C₃×#872	C₂²	1	1	yes	characteristic
24	C₃×#872	C₂²	1	1	yes	characteristic
25	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
26	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
27	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
28	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃²×#97	C₂²	1	1	yes	characteristic, complemented
30	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×#830	C₂²	1	2	yes	—
32	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
33	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
34	C₃×#815	C₂²	1	2	yes	complemented
35	C₃×Dic₃⋊C₈	C₂²	1	2	yes	complemented
36	C₃×Dic₃⋊C₈	C₂²	1	2	yes	complemented
37	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
38	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
39	C₃×#803	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×#117	—	3	1	no	—
42	D₃×#117	C₂×C₃	1	1	yes	characteristic
43	C₃×#433	—	2	1	no	—
44	C₃×#433	—	3	1	no	—
45	C₃×#433	—	3	2	no	—
46	C₃×#433	—	3	2	no	—
47	C₃×#433	—	3	1	no	—
48	C₃×#433	—	3	1	no	—
49	C₃×#433	D₃	1	1	yes	characteristic, direct product factor
50	C₃×#433	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×C₃×C₄⋊C₈	—	3	2	no	—
52	C₂×C₃×C₂²⋊C₈	—	3	2	no	—
53	C₂×C₃×#97	—	3	1	no	—
54	C₂×C₃×C₄×C₈	—	3	1	no	—
55	#5000	C₂×C₃	1	1	yes	characteristic, complemented
56	#4840	C₂×C₃	1	2	yes	complemented
57	D₃×C₄⋊C₈	C₂×C₃	1	2	yes	complemented
58	D₃×C₂²⋊C₈	C₂×C₃	1	2	yes	—
59	#4720	C₂×C₃	1	2	yes	complemented
60	#4709	C₂×C₃	1	1	yes	characteristic, complemented
61	D₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
62	#4690	C₂×C₃	1	1	yes	characteristic, complemented
63	C₄×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
66	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄×D₃	—	2	4	no	—
68	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
69	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
70	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
74	C₂×C₃²×C₈	C₂³	1	2	yes	—
75	C₂×C₃²×C₈	C₂³	1	2	yes	—
76	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
77	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₃²×C₄²	C₂³	1	1	yes	characteristic
79	C₃²×C₄²	C₂³	1	1	yes	characteristic
80	C₃×#217	C₂×C₄	1	2	yes	—
81	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
82	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
83	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
84	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
85	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
86	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
87	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
88	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
89	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
91	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
92	C₃×D₃×C₈	—	2	4	no	—
93	C₃×D₃×C₈	—	2	4	no	—
94	C₂×#433	—	3	1	no	Sylow
95	C₂³×C₃×C₄	—	3	1	no	—
96	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
97	C₂²×C₃×C₈	—	3	2	no	—
98	C₂²×C₃×C₈	—	3	2	no	—
99	C₃×#117	—	2	1	no	—
100	C₃×#117	—	3	1	no	—
101	C₃×#117	—	3	2	no	—
102	C₃×#117	—	3	2	no	—
103	C₃×#117	—	3	1	no	—
104	C₃×#117	—	3	1	no	—
105	C₃×#117	C₂×D₃	1	1	yes	characteristic
106	C₃×#117	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₃×C₄⋊C₄	—	3	2	no	—
108	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
109	C₂×C₃×C₄²	—	3	1	no	—
110	C₂×C₃×C₄²	—	3	1	no	—
111	#926	C₂²×C₃	1	1	yes	characteristic
112	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
113	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
114	#892	C₃×C₄	1	2	yes	—
115	D₃×C₄⋊C₄	C₃×C₄	1	2	yes	—
116	D₃×C₂²⋊C₄	C₃×C₄	1	2	yes	—
117	#877	C₃×C₄	1	2	yes	—
118	#872	C₂²×C₃	1	1	yes	characteristic
119	#872	C₂²×C₃	1	1	yes	characteristic
120	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
121	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
122	C₃×C₄⋊C₈	—	2	2	no	—
123	C₃×C₄⋊C₈	—	3	2	no	—
124	C₃×C₄⋊C₈	—	3	2	no	—
125	C₃×C₄⋊C₈	—	3	2	no	—
126	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
127	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
128	C₃×C₂²⋊C₈	—	2	2	no	—
129	C₃×C₂²⋊C₈	—	3	2	no	—
130	C₃×C₂²⋊C₈	—	3	2	no	—
131	C₃×C₂²⋊C₈	—	3	2	no	—
132	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	—
133	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
134	C₃×#97	—	2	1	no	—
135	C₃×#97	—	3	2	no	—
136	C₃×#97	—	3	1	no	—
137	C₃×#97	C₂×D₃	1	1	yes	characteristic, complemented
138	C₃×#97	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₃×C₄×C₈	—	2	1	no	—
140	C₃×C₄×C₈	—	3	2	no	—
141	C₃×C₄×C₈	—	3	1	no	—
142	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
143	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
144	#830	C₂²×C₃	1	2	yes	—
145	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
146	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
147	#815	C₂²×C₃	1	2	yes	complemented
148	Dic₃⋊C₈	C₂²×C₃	1	2	yes	complemented
149	Dic₃⋊C₈	C₂²×C₃	1	2	yes	complemented
150	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
151	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	complemented
152	#803	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
154	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₃×D₃	—	2	2	no	—
156	C₂²×C₃×D₃	—	2	4	no	—
157	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₃²×C₄	—	2	2	no	—
160	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
161	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
162	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
164	C₂×C₃×Dic₃	—	2	2	no	—
165	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
166	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
167	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
169	C₃×C₄×D₃	—	2	2	no	—
170	C₃×C₄×D₃	—	2	4	no	—
171	C₃×C₄×D₃	—	2	4	no	—
172	C₃×C₄×D₃	—	2	2	no	—
173	C₃×C₄×D₃	—	2	2	no	—
174	C₃×C₄×D₃	#41	1	4	yes	—
175	C₃²×C₈	—	2	2	no	—
176	C₃²×C₈	—	2	2	no	—
177	C₃×C₃⋊C₈	—	2	2	no	—
178	C₃×C₃⋊C₈	—	2	2	no	—
179	C₂×#117	—	3	1	no	—
180	#433	—	3	1	no	—
181	#433	—	3	2	no	—
182	#433	—	3	2	no	—
183	#433	—	3	1	no	—
184	#433	—	3	1	no	—
185	#433	C₃×D₃	1	1	yes	characteristic, direct product factor
186	C₂×C₄⋊C₈	—	3	2	no	—
187	C₂×C₂²⋊C₈	—	3	2	no	—
188	C₂×#97	—	3	1	no	—
189	C₂×C₄×C₈	—	3	1	no	—
190	C₂⁴×C₃	—	3	1	no	—
191	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
192	C₂²×C₃×C₄	—	2	1	no	—
193	C₂²×C₃×C₄	—	3	1	no	—
194	C₂²×C₃×C₄	—	3	1	no	—
195	C₂²×C₃×C₄	—	3	2	no	—
196	C₂²×C₃×C₄	—	3	2	no	—
197	C₂²×C₃×C₄	—	3	1	no	—
198	C₂²×C₃×C₄	—	3	1	no	—
199	C₂²×C₃×C₄	—	3	1	no	—
200	C₂²×C₃×C₄	—	6	4	no	—
201	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
203	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂×C₄×D₃	—	2	4	no	—
205	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
206	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
207	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
208	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₃×C₈	—	2	2	no	—
212	C₂×C₃×C₈	—	2	2	no	—
213	C₂×C₃×C₈	—	3	2	no	—
214	C₂×C₃×C₈	—	3	2	no	—
215	C₂×C₃×C₈	—	6	4	no	—
216	C₂×C₃×C₈	—	6	4	no	—
217	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
218	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
219	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
220	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
221	C₃×C₄⋊C₄	—	2	2	no	—
222	C₃×C₄⋊C₄	—	3	2	no	—
223	C₃×C₄⋊C₄	—	3	2	no	—
224	C₃×C₄⋊C₄	—	3	2	no	—
225	C₃×C₄⋊C₄	C₄×D₃	1	2	yes	—
226	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
227	C₃×C₂²⋊C₄	—	2	2	no	—
228	C₃×C₂²⋊C₄	—	3	2	no	—
229	C₃×C₂²⋊C₄	—	3	2	no	—
230	C₃×C₂²⋊C₄	—	3	2	no	—
231	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
232	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
233	C₃×C₄²	—	2	1	no	—
234	C₃×C₄²	—	2	1	no	—
235	C₃×C₄²	—	3	2	no	—
236	C₃×C₄²	—	3	2	no	—
237	C₃×C₄²	—	3	1	no	—
238	C₃×C₄²	—	3	1	no	—
239	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
240	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
241	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
242	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
243	#217	C₂×C₃×C₄	1	2	yes	—
244	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
245	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
246	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
247	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
248	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
249	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
250	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
251	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
252	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
253	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
254	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
255	D₃×C₈	—	2	4	no	—
256	D₃×C₈	—	2	4	no	—
257	C₂²×C₃²	—	2	1	no	—
258	C₂²×C₃²	—	2	2	no	—
259	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₃×D₃	—	2	1	no	—
261	C₂×C₃×D₃	—	2	2	no	—
262	C₂×C₃×D₃	—	4	4	no	—
263	C₂×C₃×D₃	#117	1	2	yes	—
264	C₂×C₃×D₃	#131	1	4	yes	—
265	C₃²×C₄	—	2	1	no	—
266	C₃²×C₄	—	2	2	no	—
267	C₃²×C₄	—	2	2	no	—
268	C₃²×C₄	C₂×#41	1	2	yes	—
269	C₃×Dic₃	—	2	1	no	—
270	C₃×Dic₃	—	2	2	no	—
271	C₃×Dic₃	—	2	2	no	—
272	C₃×Dic₃	#117	1	2	yes	—
273	C₂³×C₄	—	3	1	no	—
274	C₂²×C₈	—	3	2	no	—
275	C₂²×C₈	—	3	2	no	—
276	#117	—	3	1	no	—
277	#117	—	3	2	no	—
278	#117	—	3	2	no	—
279	#117	—	3	1	no	—
280	#117	—	3	1	no	—
281	#117	C₂×C₃×D₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	—	3	2	no	—
283	C₂×C₂²⋊C₄	—	3	2	no	—
284	C₂×C₄²	—	3	1	no	—
285	C₂×C₄²	—	3	1	no	—
286	C₄⋊C₈	—	3	2	no	—
287	C₄⋊C₈	—	3	2	no	—
288	C₄⋊C₈	—	3	2	no	—
289	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
290	C₂²⋊C₈	—	3	2	no	—
291	C₂²⋊C₈	—	3	2	no	—
292	C₂²⋊C₈	—	3	2	no	—
293	C₂²⋊C₈	C₂×C₃×D₃	1	2	yes	—
294	#97	—	3	2	no	—
295	#97	—	3	1	no	—
296	#97	C₂×C₃×D₃	1	1	yes	characteristic, complemented
297	C₄×C₈	—	3	2	no	—
298	C₄×C₈	—	3	1	no	—
299	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
300	C₂³×C₃	—	2	1	no	—
301	C₂³×C₃	—	3	1	no	—
302	C₂³×C₃	—	3	1	no	—
303	C₂³×C₃	—	6	2	no	—
304	C₂³×C₃	—	6	4	no	—
305	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
306	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
307	C₂²×D₃	—	2	2	no	—
308	C₂²×D₃	—	2	4	no	—
309	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	3	1	no	—
318	C₂×C₃×C₄	—	3	4	no	—
319	C₂×C₃×C₄	—	3	2	no	—
320	C₂×C₃×C₄	—	3	2	no	—
321	C₂×C₃×C₄	—	3	1	no	—
322	C₂×C₃×C₄	—	4	2	no	—
323	C₂×C₃×C₄	—	6	2	no	—
324	C₂×C₃×C₄	—	6	4	no	—
325	C₂×C₃×C₄	—	6	4	no	—
326	C₂×C₃×C₄	—	6	2	no	—
327	C₂×C₃×C₄	—	6	2	no	—
328	C₂×C₃×C₄	—	6	2	no	—
329	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
330	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
331	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
333	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
334	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
337	C₂×Dic₃	—	2	2	no	—
338	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
339	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
340	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
341	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
342	C₄×D₃	—	2	2	no	—
343	C₄×D₃	—	2	4	no	—
344	C₄×D₃	—	2	4	no	—
345	C₄×D₃	—	2	2	no	—
346	C₄×D₃	—	2	2	no	—
347	C₄×D₃	C₃×#41	1	4	yes	—
348	C₃×C₈	—	2	2	no	—
349	C₃×C₈	—	2	2	no	—
350	C₃×C₈	—	2	2	no	—
351	C₃×C₈	—	2	2	no	—
352	C₃×C₈	—	4	2	no	—
353	C₃×C₈	—	4	2	no	—
354	C₃×C₈	—	6	2	no	—
355	C₃×C₈	—	6	2	no	—
356	C₃⋊C₈	—	2	2	no	—
357	C₃⋊C₈	—	2	2	no	—
358	C₂×C₃²	—	4	1	no	—
359	C₂×C₃²	C₂×#117	1	1	yes	characteristic
360	C₂×C₃²	C₂×#131	1	2	yes	—
361	C₃×D₃	—	4	1	no	—
362	C₃×D₃	#433	1	4	yes	direct product factor
363	C₂⁴	—	3	1	no	—
364	C₂²×C₄	—	3	1	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	3	1	no	—
367	C₂²×C₄	—	3	2	no	—
368	C₂²×C₄	—	3	2	no	—
369	C₂²×C₄	—	3	1	no	—
370	C₂²×C₄	—	3	1	no	—
371	C₂²×C₄	—	6	4	no	—
372	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
373	C₂×C₈	—	3	2	no	—
374	C₂×C₈	—	3	2	no	—
375	C₂×C₈	—	6	4	no	—
376	C₂×C₈	—	6	4	no	—
377	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
378	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
379	C₄⋊C₄	—	3	2	no	—
380	C₄⋊C₄	—	3	2	no	—
381	C₄⋊C₄	—	3	2	no	—
382	C₄⋊C₄	C₃×C₄×D₃	1	2	yes	—
383	C₂²⋊C₄	—	3	2	no	—
384	C₂²⋊C₄	—	3	2	no	—
385	C₂²⋊C₄	—	3	2	no	—
386	C₂²⋊C₄	C₃×C₄×D₃	1	2	yes	—
387	C₄²	—	3	1	no	—
388	C₄²	—	3	1	no	—
389	C₄²	—	3	2	no	—
390	C₄²	—	3	2	no	—
391	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
392	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
393	C₂²×C₃	—	2	2	no	—
394	C₂²×C₃	—	2	2	no	—
395	C₂²×C₃	—	2	1	no	—
396	C₂²×C₃	—	2	1	no	—
397	C₂²×C₃	—	2	1	no	—
398	C₂²×C₃	—	3	4	no	—
399	C₂²×C₃	—	3	2	no	—
400	C₂²×C₃	—	4	1	no	—
401	C₂²×C₃	—	4	2	no	—
402	C₂²×C₃	—	6	2	no	—
403	C₂²×C₃	—	6	1	no	—
404	C₂²×C₃	—	12	4	no	—
405	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
406	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
407	C₂×D₃	—	2	2	no	—
408	C₂×D₃	—	2	1	no	—
409	C₂×D₃	—	4	4	no	—
410	C₂×D₃	C₃×#117	1	2	yes	—
411	C₂×D₃	C₃×#131	1	4	yes	—
412	C₃×C₄	—	2	2	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	2	2	no	—
419	C₃×C₄	—	3	2	no	—
420	C₃×C₄	—	4	1	no	—
421	C₃×C₄	—	4	2	no	—
422	C₃×C₄	—	4	2	no	—
423	C₃×C₄	—	6	2	no	—
424	C₃×C₄	—	6	2	no	—
425	C₃×C₄	—	6	1	no	—
426	C₃×C₄	D₃×#41	1	2	yes	—
427	C₃×C₄	C₂×C₃×#41	1	2	yes	—
428	Dic₃	—	2	2	no	—
429	Dic₃	—	2	2	no	—
430	Dic₃	—	2	1	no	—
431	Dic₃	C₃×#117	1	2	yes	—
432	C₃²	C₂×#433	1	1	yes	characteristic, complemented, Sylow
433	C₂³	—	3	1	no	—
434	C₂³	—	3	1	no	—
435	C₂³	—	6	2	no	—
436	C₂³	—	6	4	no	—
437	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	3	1	no	—
440	C₂×C₄	—	3	4	no	—
441	C₂×C₄	—	3	2	no	—
442	C₂×C₄	—	3	2	no	—
443	C₂×C₄	—	3	1	no	—
444	C₂×C₄	—	6	2	no	—
445	C₂×C₄	—	6	2	no	—
446	C₂×C₄	—	6	4	no	—
447	C₂×C₄	—	6	4	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	2	no	—
450	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
451	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
452	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
453	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	6	2	no	—
457	C₈	—	6	2	no	—
458	C₂×C₃	—	2	2	no	—
459	C₂×C₃	—	2	1	no	—
460	C₂×C₃	—	3	4	no	—
461	C₂×C₃	—	4	1	no	—
462	C₂×C₃	—	4	1	no	—
463	C₂×C₃	—	8	1	no	—
464	C₂×C₃	—	12	1	no	—
465	C₂×C₃	D₃×#117	1	1	yes	characteristic
466	C₂×C₃	D₃×#131	1	2	yes	—
467	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
468	C₂×C₃	C₂×C₃×#131	1	2	yes	—
469	D₃	—	4	1	no	—
470	D₃	C₃×#433	1	4	yes	direct product factor
471	C₂²	—	2	2	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	3	4	no	—
474	C₂²	—	3	2	no	—
475	C₂²	—	6	2	no	—
476	C₂²	—	6	1	no	—
477	C₂²	—	12	4	no	—
478	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	1	no	—
482	C₄	—	3	2	no	—
483	C₄	—	6	2	no	—
484	C₄	—	6	2	no	—
485	C₄	—	6	1	no	—
486	C₄	C₃×D₃×#41	1	2	yes	—
487	C₃	—	2	1	no	—
488	C₃	D₃×#433	1	1	yes	characteristic, direct product factor
489	C₃	C₂×C₃×#433	1	1	yes	characteristic, complemented
490	C₂	—	3	4	no	—
491	C₂	—	4	1	no	—
492	C₂	—	12	1	no	—
493	C₂	C₃×D₃×#117	1	1	yes	characteristic
494	C₂	C₃×D₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#433	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#433	D₃
hypocenter	C₃	C₂×C₃×#433
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#433

Complements

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

N	H ≅ G/N	type
2. C₃²×#433	C₂	semidirect
3. C₃×#5000	C₂	semidirect
4. C₃×#4840	C₂	semidirect
5. C₃×D₃×C₄⋊C₈	C₂	semidirect
7. C₃×#4720	C₂	semidirect
8. C₃×#4709	C₂	semidirect
9. C₃×D₃×#97	C₂	semidirect
10. C₃×#4690	C₂	semidirect
11. C₃×C₄×D₃×C₈	C₂	semidirect
13. D₃×#433	C₃	direct (N × H)
27. C₃²×C₄⋊C₈	C₂²	semidirect
29. C₃²×#97	C₂²	semidirect
30. C₃²×C₄×C₈	C₂²	semidirect
34. C₃×#815	C₂²	semidirect
35. C₃×Dic₃⋊C₈	C₂²	semidirect
36. C₃×Dic₃⋊C₈	C₂²	semidirect
37. C₃×C₈×Dic₃	C₂²	semidirect
38. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
39. C₃×#803	C₂²	semidirect
40. C₃×C₄×C₃⋊C₈	C₂²	semidirect
49. C₃×#433	D₃	direct (N × H)
50. C₃×#433	C₂×C₃	semidirect
55. #5000	C₂×C₃	semidirect
56. #4840	C₂×C₃	semidirect
57. D₃×C₄⋊C₈	C₂×C₃	semidirect
59. #4720	C₂×C₃	semidirect
60. #4709	C₂×C₃	semidirect
61. D₃×#97	C₂×C₃	semidirect
62. #4690	C₂×C₃	semidirect
63. C₄×D₃×C₈	C₂×C₃	semidirect
126. C₃×C₄⋊C₈	C₂×D₃	semidirect
127. C₃×C₄⋊C₈	C₂²×C₃	semidirect
137. C₃×#97	C₂×D₃	semidirect
138. C₃×#97	C₂²×C₃	semidirect
142. C₃×C₄×C₈	C₂×D₃	semidirect
143. C₃×C₄×C₈	C₂²×C₃	semidirect
147. #815	C₂²×C₃	semidirect
148. Dic₃⋊C₈	C₂²×C₃	semidirect
149. Dic₃⋊C₈	C₂²×C₃	semidirect
150. C₈×Dic₃	C₂²×C₃	semidirect
151. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
152. #803	C₂²×C₃	semidirect
153. C₄×C₃⋊C₈	C₂²×C₃	semidirect
185. #433	C₃×D₃	direct (N × H)
289. C₄⋊C₈	C₂×C₃×D₃	semidirect
296. #97	C₂×C₃×D₃	semidirect
299. C₄×C₈	C₂×C₃×D₃	semidirect
362. C₃×D₃	#433	direct (N × H)
432. C₃²	C₂×#433	semidirect
470. D₃	C₃×#433	direct (N × H)
488. C₃	D₃×#433	direct (N × H)
489. C₃	C₂×C₃×#433	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×#117	2
C₃²×#433	2
C₃×#5000	2
C₃×#4840	2
C₃×D₃×C₄⋊C₈	2
C₃×D₃×C₂²⋊C₈	2
C₃×#4720	2
C₃×#4709	2
C₃×D₃×#97	2
C₃×#4690	2
C₃×C₄×D₃×C₈	2
C₂×C₃×#433	3
D₃×#433	3

Subgroups — C3×D3×#433 #11858765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#433 #11858765