Subgroups — C₃×D₃×#533 #11900806

Order 1152.

2447 conjugacy classes of subgroups.

The subgroup lattice has 671 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5728	C₂	1	2	yes	maximal, complemented
3	C₃×D₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
4	C₃×#5688	C₂	1	2	yes	maximal, complemented
5	C₃×D₃×#125	C₂	1	2	yes	maximal, complemented
6	C₃×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal
7	C₃×#5622	C₂	1	4	yes	maximal, complemented
8	C₃×#5578	C₂	1	4	yes	maximal, complemented
9	C₃×C₄×D₃×Q₈	C₂	1	4	yes	maximal, complemented
10	C₃×D₃×#117	C₂	1	2	yes	maximal
11	C₃×#5517	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic
13	C₃×#5470	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#533	—	3	1	no	maximal
15	D₃×#533	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂×C₃×D₃×Q₈	C₂²	1	4	yes	—
17	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
18	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
19	C₃²×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₃²×#125	C₂²	1	2	yes	complemented
21	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₃²×C₄×Q₈	C₂²	1	4	yes	complemented
23	C₃²×#117	C₂²	1	2	yes	—
24	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
25	C₃×#946	C₂²	1	4	yes	—
26	C₃×Q₈×Dic₃	C₂²	1	4	yes	complemented
27	C₃×#944	C₂²	1	4	yes	complemented
28	C₃×#926	C₂²	1	2	yes	—
29	C₃×#924	C₂²	1	4	yes	—
30	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
32	C₃×#897	C₂²	1	4	yes	—
33	C₃×#896	C₂²	1	8	yes	—
34	C₃×#892	C₂²	1	4	yes	—
35	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
36	C₃×D₃×C₄⋊C₄	C₂²	1	8	yes	—
37	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
38	C₃×#890	C₂²	1	4	yes	complemented
39	C₃×#889	C₂²	1	8	yes	complemented
40	C₃×#888	C₂²	1	4	yes	complemented
41	C₃×#888	C₂²	1	4	yes	complemented
42	C₃×#887	C₂²	1	8	yes	complemented
43	C₃×#887	C₂²	1	4	yes	complemented
44	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
45	C₃×#878	C₂²	1	8	yes	—
46	C₃×#877	C₂²	1	4	yes	—
47	C₃×#872	C₂²	1	4	yes	—
48	C₃×C₄²×D₃	C₂²	1	4	yes	—
49	C₃×C₄²×D₃	C₂²	1	2	yes	—
50	C₃×C₄²×D₃	C₂²	1	2	yes	—
51	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
52	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
53	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
54	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
55	C₃×#870	C₂²	1	2	yes	complemented
56	C₃×#869	C₂²	1	2	yes	complemented
57	C₃×C₄×Dic₆	C₂²	1	8	yes	complemented
58	C₃×C₄×Dic₆	C₂²	1	4	yes	complemented
59	C₃×#533	—	2	1	no	—
60	C₃×#533	—	3	2	no	—
61	C₃×#533	—	3	2	no	—
62	C₃×#533	—	3	4	no	—
63	C₃×#533	—	3	4	no	—
64	C₃×#533	—	3	2	no	—
65	C₃×#533	—	3	1	no	—
66	C₃×#533	D₃	1	1	yes	characteristic, direct product factor
67	C₃×#533	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×C₃×C₄⋊Q₈	—	3	2	no	—
69	C₂×C₃×#125	—	3	2	no	—
70	C₂×C₃×C₂²⋊Q₈	—	3	4	no	—
71	C₂×C₃×C₄×Q₈	—	3	4	no	—
72	C₂×C₃×#117	—	3	2	no	—
73	C₂²×C₃×C₄²	—	3	1	no	—
74	#5728	C₂×C₃	1	2	yes	complemented
75	D₃×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
76	#5688	C₂×C₃	1	2	yes	complemented
77	D₃×#125	C₂×C₃	1	2	yes	complemented
78	D₃×C₂²⋊Q₈	C₂×C₃	1	4	yes	—
79	#5622	C₂×C₃	1	4	yes	complemented
80	#5578	C₂×C₃	1	4	yes	complemented
81	C₄×D₃×Q₈	C₂×C₃	1	4	yes	complemented
82	D₃×#117	C₂×C₃	1	2	yes	—
83	#5517	C₂×C₃	1	2	yes	complemented
84	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
85	#5470	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
87	C₂×C₃²×Q₈	C₂³	1	4	yes	—
88	C₂²×C₃²×C₄	C₂³	1	2	yes	—
89	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
90	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
91	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
92	C₃×D₃×Q₈	—	2	16	no	—
93	C₂×C₃×C₄×D₃	—	2	8	no	—
94	C₂×C₃×C₄×D₃	Q₈	1	8	yes	complemented
95	C₂×C₃×C₄×D₃	C₂³	1	8	yes	—
96	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
97	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
98	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
99	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
104	C₂×C₃×Dic₆	C₂³	1	8	yes	—
105	C₂×C₃×Dic₆	C₂³	1	4	yes	—
106	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
107	C₃²×C₄⋊C₄	C₂³	1	8	yes	—
108	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
109	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₃²×C₄²	C₂³	1	2	yes	—
111	C₃²×C₄²	C₂³	1	1	yes	characteristic
112	C₃²×C₄²	C₂³	1	1	yes	characteristic
113	C₃²×C₄²	C₂³	1	4	yes	—
114	C₃×#217	C₂³	1	4	yes	—
115	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
116	C₃×C₄⋊Dic₃	C₂³	1	8	yes	—
117	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
118	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
119	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
120	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
121	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
122	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
123	C₃×C₄×Dic₃	C₂³	1	8	yes	—
124	C₃×C₄×Dic₃	C₂³	1	2	yes	—
125	C₃×C₄×Dic₃	C₂³	1	2	yes	—
126	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
127	C₃×C₄×Dic₃	C₂³	1	2	yes	—
128	C₃×C₄×Dic₃	C₂³	1	2	yes	—
129	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
130	C₃×C₄×Dic₃	C₂³	1	2	yes	—
131	C₃×C₄×Dic₃	C₂³	1	4	yes	—
132	C₂×#533	—	3	1	no	Sylow
133	C₂²×C₃×Q₈	—	3	4	no	—
134	C₂³×C₃×C₄	—	3	1	no	—
135	C₂³×C₃×C₄	—	3	2	no	—
136	C₂×D₃×Q₈	C₂²×C₃	1	4	yes	—
137	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
138	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
139	C₃×C₄⋊Q₈	—	2	2	no	—
140	C₃×C₄⋊Q₈	—	3	4	no	—
141	C₃×C₄⋊Q₈	—	3	4	no	—
142	C₃×C₄⋊Q₈	—	3	4	no	—
143	C₃×C₄⋊Q₈	—	3	2	no	—
144	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
145	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
146	C₃×#125	—	2	2	no	—
147	C₃×#125	—	3	8	no	—
148	C₃×#125	—	3	4	no	—
149	C₃×#125	—	3	2	no	—
150	C₃×#125	C₂×D₃	1	2	yes	complemented
151	C₃×#125	C₂²×C₃	1	2	yes	complemented
152	C₃×C₂²⋊Q₈	—	2	4	no	—
153	C₃×C₂²⋊Q₈	—	3	4	no	—
154	C₃×C₂²⋊Q₈	—	3	4	no	—
155	C₃×C₂²⋊Q₈	—	3	8	no	—
156	C₃×C₂²⋊Q₈	—	3	4	no	—
157	C₃×C₂²⋊Q₈	—	3	8	no	—
158	C₃×C₂²⋊Q₈	C₂×D₃	1	4	yes	—
159	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
160	C₃×C₄×Q₈	—	2	4	no	—
161	C₃×C₄×Q₈	—	3	4	no	—
162	C₃×C₄×Q₈	—	3	4	no	—
163	C₃×C₄×Q₈	—	3	8	no	—
164	C₃×C₄×Q₈	—	3	8	no	—
165	C₃×C₄×Q₈	—	3	4	no	—
166	C₃×C₄×Q₈	C₂×D₃	1	4	yes	complemented
167	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	complemented
168	C₃×#117	—	2	2	no	—
169	C₃×#117	—	3	2	no	—
170	C₃×#117	—	3	4	no	—
171	C₃×#117	—	3	4	no	—
172	C₃×#117	—	3	4	no	—
173	C₃×#117	C₂×D₃	1	2	yes	—
174	C₃×#117	C₂²×C₃	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	—	3	4	no	—
176	C₂×C₃×C₄⋊C₄	—	3	8	no	—
177	C₂×C₃×C₄⋊C₄	—	3	4	no	—
178	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
179	C₂×C₃×C₄²	—	2	1	no	—
180	C₂×C₃×C₄²	—	3	2	no	—
181	C₂×C₃×C₄²	—	3	1	no	—
182	C₂×C₃×C₄²	—	3	2	no	—
183	C₂×C₃×C₄²	—	3	1	no	—
184	C₂×C₃×C₄²	—	3	1	no	—
185	C₂×C₃×C₄²	—	3	1	no	—
186	C₂×C₃×C₄²	—	3	1	no	—
187	C₂×C₃×C₄²	—	3	2	no	—
188	C₂×C₃×C₄²	—	3	4	no	—
189	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
190	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
191	#946	C₂²×C₃	1	4	yes	—
192	Q₈×Dic₃	C₂²×C₃	1	4	yes	complemented
193	#944	C₂²×C₃	1	4	yes	complemented
194	#926	C₂²×C₃	1	2	yes	—
195	#924	C₂²×C₃	1	4	yes	—
196	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
197	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
198	#897	C₂²×C₃	1	4	yes	—
199	#896	C₂²×C₃	1	8	yes	—
200	#892	C₂²×C₃	1	4	yes	—
201	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
202	D₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
203	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
204	#890	C₂²×C₃	1	4	yes	complemented
205	#889	C₂²×C₃	1	8	yes	complemented
206	#888	C₂²×C₃	1	4	yes	complemented
207	#888	C₂²×C₃	1	4	yes	complemented
208	#887	C₂²×C₃	1	8	yes	complemented
209	#887	C₂²×C₃	1	4	yes	complemented
210	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
211	#878	C₂²×C₃	1	8	yes	—
212	#877	C₂²×C₃	1	4	yes	—
213	#872	C₂²×C₃	1	4	yes	—
214	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
215	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
216	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
217	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
218	C₄²×D₃	C₂²×C₃	1	2	yes	—
219	C₄²×D₃	C₂²×C₃	1	2	yes	—
220	C₄²×D₃	C₂²×C₃	1	4	yes	—
221	#870	C₂²×C₃	1	2	yes	complemented
222	#869	C₂²×C₃	1	2	yes	complemented
223	C₄×Dic₆	C₂²×C₃	1	4	yes	complemented
224	C₄×Dic₆	C₂²×C₃	1	8	yes	complemented
225	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
226	C₂²×C₃×D₃	—	2	4	no	—
227	C₂²×C₃×D₃	C₂×Q₈	1	4	yes	—
228	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
230	C₃²×Q₈	—	2	8	no	—
231	C₂×C₃²×C₄	—	2	4	no	—
232	C₂×C₃²×C₄	C₂×Q₈	1	4	yes	complemented
233	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
234	C₂×C₃²×C₄	C₂⁴	1	8	yes	—
235	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
236	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
237	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
238	C₂×C₃×Dic₃	—	2	4	no	—
239	C₂×C₃×Dic₃	C₂×Q₈	1	4	yes	complemented
240	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
241	C₂×C₃×Dic₃	C₂⁴	1	8	yes	—
242	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
245	C₃×C₄×D₃	—	2	4	no	—
246	C₃×C₄×D₃	—	2	16	no	—
247	C₃×C₄×D₃	—	2	4	no	—
248	C₃×C₄×D₃	—	2	4	no	—
249	C₃×C₄×D₃	C₂×Q₈	1	4	yes	—
250	C₃×C₄×D₃	C₂×Q₈	1	4	yes	—
251	C₃×C₄×D₃	C₂×Q₈	1	4	yes	complemented
252	C₃×C₄×D₃	C₂×Q₈	1	4	yes	complemented
253	C₃×C₄×D₃	#41	1	8	yes	—
254	C₃×Dic₆	—	2	8	no	—
255	C₃×Dic₆	—	2	16	no	—
256	#533	—	3	2	no	—
257	#533	—	3	2	no	—
258	#533	—	3	4	no	—
259	#533	—	3	4	no	—
260	#533	—	3	2	no	—
261	#533	—	3	1	no	—
262	#533	C₃×D₃	1	1	yes	characteristic, direct product factor
263	C₂×C₄⋊Q₈	—	3	2	no	—
264	C₂×#125	—	3	2	no	—
265	C₂×C₂²⋊Q₈	—	3	4	no	—
266	C₂×C₄×Q₈	—	3	4	no	—
267	C₂×#117	—	3	2	no	—
268	C₂²×C₄²	—	3	1	no	—
269	C₂⁴×C₃	—	3	1	no	—
270	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
271	C₂×C₃×Q₈	—	2	4	no	—
272	C₂×C₃×Q₈	—	3	8	no	—
273	C₂×C₃×Q₈	—	3	4	no	—
274	C₂×C₃×Q₈	—	6	16	no	—
275	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
276	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
277	C₂²×C₃×C₄	—	2	1	no	—
278	C₂²×C₃×C₄	—	2	2	no	—
279	C₂²×C₃×C₄	—	3	1	no	—
280	C₂²×C₃×C₄	—	3	8	no	—
281	C₂²×C₃×C₄	—	3	1	no	—
282	C₂²×C₃×C₄	—	3	2	no	—
283	C₂²×C₃×C₄	—	3	1	no	—
284	C₂²×C₃×C₄	—	3	1	no	—
285	C₂²×C₃×C₄	—	3	1	no	—
286	C₂²×C₃×C₄	—	3	2	no	—
287	C₂²×C₃×C₄	—	3	2	no	—
288	C₂²×C₃×C₄	—	3	2	no	—
289	C₂²×C₃×C₄	—	3	2	no	—
290	C₂²×C₃×C₄	—	3	8	no	—
291	C₂²×C₃×C₄	—	6	8	no	—
292	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
293	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
294	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
295	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
296	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
297	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
298	D₃×Q₈	—	2	16	no	—
299	C₂×C₄×D₃	—	2	8	no	—
300	C₂×C₄×D₃	C₃×Q₈	1	8	yes	complemented
301	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
302	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
303	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
304	C₂×C₄×D₃	C₂³×C₃	1	8	yes	—
305	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
306	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
308	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
310	C₂×Dic₆	C₂³×C₃	1	4	yes	—
311	C₂×Dic₆	C₂³×C₃	1	8	yes	—
312	C₃×C₄⋊C₄	—	2	4	no	—
313	C₃×C₄⋊C₄	—	2	8	no	—
314	C₃×C₄⋊C₄	—	2	4	no	—
315	C₃×C₄⋊C₄	—	3	8	no	—
316	C₃×C₄⋊C₄	—	3	8	no	—
317	C₃×C₄⋊C₄	—	3	8	no	—
318	C₃×C₄⋊C₄	—	3	8	no	—
319	C₃×C₄⋊C₄	—	3	4	no	—
320	C₃×C₄⋊C₄	—	3	8	no	—
321	C₃×C₄⋊C₄	—	3	4	no	—
322	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
323	C₃×C₄⋊C₄	C₂²×D₃	1	8	yes	—
324	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
325	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
326	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
327	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
328	C₃×C₂²⋊C₄	—	2	4	no	—
329	C₃×C₂²⋊C₄	—	3	4	no	—
330	C₃×C₂²⋊C₄	—	3	8	no	—
331	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
332	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
333	C₃×C₄²	—	2	2	no	—
334	C₃×C₄²	—	2	1	no	—
335	C₃×C₄²	—	2	1	no	—
336	C₃×C₄²	—	2	4	no	—
337	C₃×C₄²	—	3	2	no	—
338	C₃×C₄²	—	3	2	no	—
339	C₃×C₄²	—	3	2	no	—
340	C₃×C₄²	—	3	1	no	—
341	C₃×C₄²	—	3	2	no	—
342	C₃×C₄²	—	3	1	no	—
343	C₃×C₄²	—	3	8	no	—
344	C₃×C₄²	—	3	2	no	—
345	C₃×C₄²	—	3	4	no	—
346	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
347	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
348	C₃×C₄²	C₂²×D₃	1	2	yes	—
349	C₃×C₄²	C₂²×D₃	1	4	yes	—
350	C₃×C₄²	C₂³×C₃	1	2	yes	—
351	C₃×C₄²	C₂³×C₃	1	4	yes	—
352	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
353	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
354	#217	C₂³×C₃	1	4	yes	—
355	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
356	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
357	C₄⋊Dic₃	C₂³×C₃	1	8	yes	—
358	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
359	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
360	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
361	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
362	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
363	C₄×Dic₃	C₂³×C₃	1	2	yes	—
364	C₄×Dic₃	C₂³×C₃	1	4	yes	—
365	C₄×Dic₃	C₂³×C₃	1	2	yes	—
366	C₄×Dic₃	C₂³×C₃	1	2	yes	—
367	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
368	C₄×Dic₃	C₂³×C₃	1	2	yes	—
369	C₄×Dic₃	C₂³×C₃	1	2	yes	—
370	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
371	C₄×Dic₃	C₂³×C₃	1	8	yes	—
372	C₂²×C₃²	—	2	2	no	—
373	C₂²×C₃²	C₂²×Q₈	1	2	yes	—
374	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
375	C₂×C₃×D₃	—	2	2	no	—
376	C₂×C₃×D₃	—	2	8	no	—
377	C₂×C₃×D₃	C₂²×Q₈	1	2	yes	—
378	C₂×C₃×D₃	C₂²×Q₈	1	2	yes	—
379	C₂×C₃×D₃	C₂×#41	1	4	yes	—
380	C₃²×C₄	—	2	8	no	—
381	C₃²×C₄	—	2	2	no	—
382	C₃²×C₄	C₂²×Q₈	1	2	yes	—
383	C₃²×C₄	C₂²×Q₈	1	2	yes	—
384	C₃²×C₄	C₂×#41	1	4	yes	—
385	C₃×Dic₃	—	2	8	no	—
386	C₃×Dic₃	—	2	2	no	—
387	C₃×Dic₃	C₂²×Q₈	1	2	yes	—
388	C₃×Dic₃	C₂²×Q₈	1	2	yes	—
389	C₃×Dic₃	C₂×#41	1	4	yes	—
390	C₂²×Q₈	—	3	4	no	—
391	C₂³×C₄	—	3	1	no	—
392	C₂³×C₄	—	3	2	no	—
393	C₄⋊Q₈	—	3	4	no	—
394	C₄⋊Q₈	—	3	4	no	—
395	C₄⋊Q₈	—	3	4	no	—
396	C₄⋊Q₈	—	3	2	no	—
397	C₄⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
398	#125	—	3	8	no	—
399	#125	—	3	4	no	—
400	#125	—	3	2	no	—
401	#125	C₂×C₃×D₃	1	2	yes	complemented
402	C₂²⋊Q₈	—	3	4	no	—
403	C₂²⋊Q₈	—	3	4	no	—
404	C₂²⋊Q₈	—	3	8	no	—
405	C₂²⋊Q₈	—	3	4	no	—
406	C₂²⋊Q₈	—	3	8	no	—
407	C₂²⋊Q₈	C₂×C₃×D₃	1	4	yes	—
408	C₄×Q₈	—	3	4	no	—
409	C₄×Q₈	—	3	4	no	—
410	C₄×Q₈	—	3	8	no	—
411	C₄×Q₈	—	3	8	no	—
412	C₄×Q₈	—	3	4	no	—
413	C₄×Q₈	C₂×C₃×D₃	1	4	yes	complemented
414	#117	—	3	2	no	—
415	#117	—	3	4	no	—
416	#117	—	3	4	no	—
417	#117	—	3	4	no	—
418	#117	C₂×C₃×D₃	1	2	yes	—
419	C₂×C₄⋊C₄	—	3	4	no	—
420	C₂×C₄⋊C₄	—	3	8	no	—
421	C₂×C₄⋊C₄	—	3	4	no	—
422	C₂×C₂²⋊C₄	—	3	4	no	—
423	C₂×C₄²	—	3	2	no	—
424	C₂×C₄²	—	3	1	no	—
425	C₂×C₄²	—	3	4	no	—
426	C₂×C₄²	—	3	2	no	—
427	C₂×C₄²	—	3	1	no	—
428	C₂×C₄²	—	3	1	no	—
429	C₂×C₄²	—	3	1	no	—
430	C₂×C₄²	—	3	1	no	—
431	C₂×C₄²	—	3	2	no	—
432	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
433	C₂³×C₃	—	2	1	no	—
434	C₂³×C₃	—	3	1	no	—
435	C₂³×C₃	—	3	4	no	—
436	C₂³×C₃	—	3	1	no	—
437	C₂³×C₃	—	6	4	no	—
438	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
439	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
440	C₂²×D₃	—	2	4	no	—
441	C₂²×D₃	C₂×C₃×Q₈	1	4	yes	—
442	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
443	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
444	C₃×Q₈	—	2	8	no	—
445	C₃×Q₈	—	2	8	no	—
446	C₃×Q₈	—	4	8	no	—
447	C₃×Q₈	—	6	16	no	—
448	C₃×Q₈	—	6	8	no	—
449	C₂×C₃×C₄	—	2	4	no	—
450	C₂×C₃×C₄	—	2	4	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	2	2	no	—
454	C₂×C₃×C₄	—	2	2	no	—
455	C₂×C₃×C₄	—	2	8	no	—
456	C₂×C₃×C₄	—	2	4	no	—
457	C₂×C₃×C₄	—	3	4	no	—
458	C₂×C₃×C₄	—	3	1	no	—
459	C₂×C₃×C₄	—	3	1	no	—
460	C₂×C₃×C₄	—	3	2	no	—
461	C₂×C₃×C₄	—	3	4	no	—
462	C₂×C₃×C₄	—	3	4	no	—
463	C₂×C₃×C₄	—	3	4	no	—
464	C₂×C₃×C₄	—	3	4	no	—
465	C₂×C₃×C₄	—	3	8	no	—
466	C₂×C₃×C₄	—	3	2	no	—
467	C₂×C₃×C₄	—	3	8	no	—
468	C₂×C₃×C₄	—	4	4	no	—
469	C₂×C₃×C₄	—	6	4	no	—
470	C₂×C₃×C₄	—	6	4	no	—
471	C₂×C₃×C₄	—	6	16	no	—
472	C₂×C₃×C₄	—	6	4	no	—
473	C₂×C₃×C₄	—	6	4	no	—
474	C₂×C₃×C₄	D₃×Q₈	1	4	yes	complemented
475	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	complemented
476	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
477	C₂×C₃×C₄	C₂³×D₃	1	8	yes	—
478	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
479	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
480	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
481	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
482	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
483	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
484	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
485	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
486	C₂×Dic₃	—	2	4	no	—
487	C₂×Dic₃	C₂×C₃×Q₈	1	4	yes	complemented
488	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
489	C₂×Dic₃	C₂⁴×C₃	1	8	yes	—
490	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
491	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
492	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
493	C₄×D₃	—	2	4	no	—
494	C₄×D₃	—	2	16	no	—
495	C₄×D₃	—	2	4	no	—
496	C₄×D₃	—	2	4	no	—
497	C₄×D₃	C₂×C₃×Q₈	1	4	yes	—
498	C₄×D₃	C₂×C₃×Q₈	1	4	yes	—
499	C₄×D₃	C₂×C₃×Q₈	1	4	yes	complemented
500	C₄×D₃	C₂×C₃×Q₈	1	4	yes	complemented
501	C₄×D₃	C₃×#41	1	8	yes	—
502	Dic₆	—	2	8	no	—
503	Dic₆	—	2	16	no	—
504	C₂×C₃²	—	2	2	no	—
505	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
506	C₂×C₃²	C₂²×#41	1	2	yes	—
507	C₃×D₃	—	2	2	no	—
508	C₃×D₃	#533	1	4	yes	direct product factor
509	C₂⁴	—	3	1	no	—
510	C₂×Q₈	—	3	8	no	—
511	C₂×Q₈	—	3	4	no	—
512	C₂×Q₈	—	6	16	no	—
513	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
514	C₂²×C₄	—	3	1	no	—
515	C₂²×C₄	—	3	1	no	—
516	C₂²×C₄	—	3	1	no	—
517	C₂²×C₄	—	3	2	no	—
518	C₂²×C₄	—	3	1	no	—
519	C₂²×C₄	—	3	1	no	—
520	C₂²×C₄	—	3	8	no	—
521	C₂²×C₄	—	3	2	no	—
522	C₂²×C₄	—	3	2	no	—
523	C₂²×C₄	—	3	2	no	—
524	C₂²×C₄	—	3	2	no	—
525	C₂²×C₄	—	3	8	no	—
526	C₂²×C₄	—	6	8	no	—
527	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
528	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
529	C₄⋊C₄	—	3	8	no	—
530	C₄⋊C₄	—	3	4	no	—
531	C₄⋊C₄	—	3	8	no	—
532	C₄⋊C₄	—	3	8	no	—
533	C₄⋊C₄	—	3	8	no	—
534	C₄⋊C₄	—	3	8	no	—
535	C₄⋊C₄	—	3	4	no	—
536	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
537	C₄⋊C₄	C₂²×C₃×D₃	1	8	yes	—
538	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
539	C₂²⋊C₄	—	3	4	no	—
540	C₂²⋊C₄	—	3	8	no	—
541	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
542	C₄²	—	3	2	no	—
543	C₄²	—	3	2	no	—
544	C₄²	—	3	2	no	—
545	C₄²	—	3	2	no	—
546	C₄²	—	3	1	no	—
547	C₄²	—	3	2	no	—
548	C₄²	—	3	1	no	—
549	C₄²	—	3	8	no	—
550	C₄²	—	3	4	no	—
551	C₄²	C₂²×C₃×D₃	1	2	yes	—
552	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
553	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
554	C₄²	C₂²×C₃×D₃	1	4	yes	—
555	C₂²×C₃	—	2	2	no	—
556	C₂²×C₃	—	2	2	no	—
557	C₂²×C₃	—	2	2	no	—
558	C₂²×C₃	—	2	1	no	—
559	C₂²×C₃	—	3	2	no	—
560	C₂²×C₃	—	3	4	no	—
561	C₂²×C₃	—	3	2	no	—
562	C₂²×C₃	—	4	2	no	—
563	C₂²×C₃	—	6	8	no	—
564	C₂²×C₃	—	6	2	no	—
565	C₂²×C₃	C₂×D₃×Q₈	1	2	yes	—
566	C₂²×C₃	C₂²×C₃×Q₈	1	2	yes	—
567	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
568	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
569	C₂×D₃	—	2	2	no	—
570	C₂×D₃	—	2	8	no	—
571	C₂×D₃	C₂²×C₃×Q₈	1	2	yes	—
572	C₂×D₃	C₂²×C₃×Q₈	1	2	yes	—
573	C₂×D₃	C₂×C₃×#41	1	4	yes	—
574	C₃×C₄	—	2	2	no	—
575	C₃×C₄	—	2	8	no	—
576	C₃×C₄	—	2	8	no	—
577	C₃×C₄	—	2	2	no	—
578	C₃×C₄	—	2	2	no	—
579	C₃×C₄	—	2	2	no	—
580	C₃×C₄	—	2	4	no	—
581	C₃×C₄	—	3	2	no	—
582	C₃×C₄	—	3	2	no	—
583	C₃×C₄	—	3	4	no	—
584	C₃×C₄	—	4	2	no	—
585	C₃×C₄	—	4	8	no	—
586	C₃×C₄	—	6	2	no	—
587	C₃×C₄	—	6	8	no	—
588	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
589	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
590	C₃×C₄	D₃×#41	1	4	yes	—
591	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
592	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
593	C₃×C₄	C₂×C₃×#41	1	4	yes	—
594	Dic₃	—	2	8	no	—
595	Dic₃	—	2	2	no	—
596	Dic₃	C₂²×C₃×Q₈	1	2	yes	—
597	Dic₃	C₂²×C₃×Q₈	1	2	yes	—
598	Dic₃	C₂×C₃×#41	1	4	yes	—
599	C₃²	C₂×#533	1	1	yes	characteristic, complemented, Sylow
600	C₂³	—	3	1	no	—
601	C₂³	—	3	4	no	—
602	C₂³	—	3	1	no	—
603	C₂³	—	6	4	no	—
604	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
605	Q₈	—	2	8	no	—
606	Q₈	—	6	16	no	—
607	Q₈	—	6	8	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	3	4	no	—
610	C₂×C₄	—	3	1	no	—
611	C₂×C₄	—	3	1	no	—
612	C₂×C₄	—	3	2	no	—
613	C₂×C₄	—	3	4	no	—
614	C₂×C₄	—	3	4	no	—
615	C₂×C₄	—	3	4	no	—
616	C₂×C₄	—	3	4	no	—
617	C₂×C₄	—	3	8	no	—
618	C₂×C₄	—	3	2	no	—
619	C₂×C₄	—	3	8	no	—
620	C₂×C₄	—	6	4	no	—
621	C₂×C₄	—	6	4	no	—
622	C₂×C₄	—	6	16	no	—
623	C₂×C₄	—	6	4	no	—
624	C₂×C₄	—	6	4	no	—
625	C₂×C₄	C₃×D₃×Q₈	1	4	yes	complemented
626	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
627	C₂×C₄	C₂³×C₃×D₃	1	8	yes	—
628	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
629	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
630	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
631	C₂×C₃	—	2	2	no	—
632	C₂×C₃	—	2	2	no	—
633	C₂×C₃	—	2	1	no	—
634	C₂×C₃	—	2	2	no	—
635	C₂×C₃	—	3	4	no	—
636	C₂×C₃	—	4	2	no	—
637	C₂×C₃	—	6	2	no	—
638	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
639	C₂×C₃	C₂×D₃×#41	1	2	yes	—
640	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
641	C₂×C₃	C₂²×C₃×#41	1	2	yes	—
642	D₃	—	2	2	no	—
643	D₃	C₃×#533	1	4	yes	direct product factor
644	C₂²	—	2	2	no	—
645	C₂²	—	3	2	no	—
646	C₂²	—	3	4	no	—
647	C₂²	—	3	2	no	—
648	C₂²	—	6	8	no	—
649	C₂²	—	6	2	no	—
650	C₂²	C₂×C₃×D₃×Q₈	1	2	yes	—
651	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	8	no	—
654	C₄	—	3	2	no	—
655	C₄	—	3	2	no	—
656	C₄	—	3	4	no	—
657	C₄	—	6	2	no	—
658	C₄	—	6	8	no	—
659	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
660	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
661	C₄	C₃×D₃×#41	1	4	yes	—
662	C₃	—	2	1	no	—
663	C₃	D₃×#533	1	1	yes	characteristic, direct product factor
664	C₃	C₂×C₃×#533	1	1	yes	characteristic, complemented
665	C₂	—	2	2	no	—
666	C₂	—	3	4	no	—
667	C₂	—	6	2	no	—
668	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
669	C₂	C₂×C₃×D₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#533	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂³×C₃×D₃	C₂³
hypercenter	C₃×#533	D₃
hypocenter	C₃	C₂×C₃×#533
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#533

Complements

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

N	H ≅ G/N	type
1. C₃²×#533	C₂	semidirect
2. C₃×#5728	C₂	semidirect
3. C₃×D₃×C₄⋊Q₈	C₂	semidirect
4. C₃×#5688	C₂	semidirect
5. C₃×D₃×#125	C₂	semidirect
7. C₃×#5622	C₂	semidirect
8. C₃×#5578	C₂	semidirect
9. C₃×C₄×D₃×Q₈	C₂	semidirect
11. C₃×#5517	C₂	semidirect
13. C₃×#5470	C₂	semidirect
15. D₃×#533	C₃	direct (N × H)
19. C₃²×C₄⋊Q₈	C₂²	semidirect
20. C₃²×#125	C₂²	semidirect
22. C₃²×C₄×Q₈	C₂²	semidirect
26. C₃×Q₈×Dic₃	C₂²	semidirect
27. C₃×#944	C₂²	semidirect
38. C₃×#890	C₂²	semidirect
39. C₃×#889	C₂²	semidirect
40. C₃×#888	C₂²	semidirect
41. C₃×#888	C₂²	semidirect
42. C₃×#887	C₂²	semidirect
43. C₃×#887	C₂²	semidirect
55. C₃×#870	C₂²	semidirect
56. C₃×#869	C₂²	semidirect
57. C₃×C₄×Dic₆	C₂²	semidirect
58. C₃×C₄×Dic₆	C₂²	semidirect
66. C₃×#533	D₃	direct (N × H)
67. C₃×#533	C₂×C₃	semidirect
74. #5728	C₂×C₃	semidirect
75. D₃×C₄⋊Q₈	C₂×C₃	semidirect
76. #5688	C₂×C₃	semidirect
77. D₃×#125	C₂×C₃	semidirect
79. #5622	C₂×C₃	semidirect
80. #5578	C₂×C₃	semidirect
81. C₄×D₃×Q₈	C₂×C₃	semidirect
83. #5517	C₂×C₃	semidirect
85. #5470	C₂×C₃	semidirect
94. C₂×C₃×C₄×D₃	Q₈	semidirect
144. C₃×C₄⋊Q₈	C₂×D₃	semidirect
145. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
150. C₃×#125	C₂×D₃	semidirect
151. C₃×#125	C₂²×C₃	semidirect
166. C₃×C₄×Q₈	C₂×D₃	semidirect
167. C₃×C₄×Q₈	C₂²×C₃	semidirect
192. Q₈×Dic₃	C₂²×C₃	semidirect
193. #944	C₂²×C₃	semidirect
204. #890	C₂²×C₃	semidirect
205. #889	C₂²×C₃	semidirect
206. #888	C₂²×C₃	semidirect
207. #888	C₂²×C₃	semidirect
208. #887	C₂²×C₃	semidirect
209. #887	C₂²×C₃	semidirect
221. #870	C₂²×C₃	semidirect
222. #869	C₂²×C₃	semidirect
223. C₄×Dic₆	C₂²×C₃	semidirect
224. C₄×Dic₆	C₂²×C₃	semidirect
232. C₂×C₃²×C₄	C₂×Q₈	semidirect
239. C₂×C₃×Dic₃	C₂×Q₈	semidirect
251. C₃×C₄×D₃	C₂×Q₈	semidirect
252. C₃×C₄×D₃	C₂×Q₈	semidirect
262. #533	C₃×D₃	direct (N × H)
300. C₂×C₄×D₃	C₃×Q₈	semidirect
397. C₄⋊Q₈	C₂×C₃×D₃	semidirect
401. #125	C₂×C₃×D₃	semidirect
413. C₄×Q₈	C₂×C₃×D₃	semidirect
474. C₂×C₃×C₄	D₃×Q₈	semidirect
475. C₂×C₃×C₄	C₂×C₃×Q₈	semidirect
487. C₂×Dic₃	C₂×C₃×Q₈	semidirect
499. C₄×D₃	C₂×C₃×Q₈	semidirect
500. C₄×D₃	C₂×C₃×Q₈	semidirect
508. C₃×D₃	#533	direct (N × H)
599. C₃²	C₂×#533	semidirect
625. C₂×C₄	C₃×D₃×Q₈	semidirect
643. D₃	C₃×#533	direct (N × H)
663. C₃	D₃×#533	direct (N × H)
664. C₃	C₂×C₃×#533	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#533	2
C₃×#5728	2
C₃×D₃×C₄⋊Q₈	2
C₃×#5688	2
C₃×D₃×#125	2
C₃×D₃×C₂²⋊Q₈	2
C₃×#5622	2
C₃×#5578	2
C₃×C₄×D₃×Q₈	2
C₃×D₃×#117	2
C₃×#5517	2
C₂×C₃×C₄²×D₃	2
C₃×#5470	2
C₂×C₃×#533	3
D₃×#533	3

Subgroups — C3×D3×#533 #11900806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#533 #11900806