Subgroups — C₃×D₃×#563 #11910280

Order 1152.

2146 conjugacy classes of subgroups.

The subgroup lattice has 763 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5735	C₂	1	2	yes	maximal, complemented
3	C₃×D₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
4	C₃×#5712	C₂	1	4	yes	maximal, complemented
5	C₃×D₃×#126	C₂	1	4	yes	maximal, complemented
6	C₃×#5699	C₂	1	2	yes	maximal, complemented
7	C₃×D₃×#125	C₂	1	2	yes	maximal, complemented
8	C₃×D₃×#124	C₂	1	1	yes	maximal, characteristic
9	C₃×#5672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₃×#123	C₂	1	2	yes	maximal
11	C₃×#5651	C₂	1	2	yes	maximal, complemented
12	C₃×#5646	C₂	1	4	yes	maximal, complemented
13	C₃×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
14	C₂×C₃×#563	—	3	1	no	maximal
15	D₃×#563	C₃	1	1	yes	maximal, characteristic, direct product factor
16	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	—
17	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
20	C₃²×C₄⋊Q₈	C₂²	1	2	yes	complemented
21	C₃²×#126	C₂²	1	4	yes	complemented
22	C₃²×#125	C₂²	1	2	yes	complemented
23	C₃²×#124	C₂²	1	1	yes	characteristic
24	C₃²×#123	C₂²	1	2	yes	—
25	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
26	C₃×#947	C₂²	1	1	yes	characteristic
27	C₃×#946	C₂²	1	4	yes	complemented
28	C₃×#944	C₂²	1	2	yes	complemented
29	C₃×#944	C₂²	1	2	yes	complemented
30	C₃×#936	C₂²	1	1	yes	characteristic
31	C₃×#935	C₂²	1	2	yes	—
32	C₃×#929	C₂²	1	2	yes	—
33	C₃×#924	C₂²	1	4	yes	complemented
34	C₃×#898	C₂²	1	4	yes	complemented
35	C₃×#898	C₂²	1	4	yes	complemented
36	C₃×#898	C₂²	1	4	yes	complemented
37	C₃×#897	C₂²	1	4	yes	complemented
38	C₃×#896	C₂²	1	4	yes	complemented
39	C₃×#896	C₂²	1	4	yes	complemented
40	C₃×#894	C₂²	1	4	yes	—
41	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
42	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
43	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
44	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
45	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
46	C₃×#890	C₂²	1	2	yes	complemented
47	C₃×#890	C₂²	1	2	yes	complemented
48	C₃×#889	C₂²	1	4	yes	complemented
49	C₃×#889	C₂²	1	4	yes	complemented
50	C₃×#888	C₂²	1	4	yes	complemented
51	C₃×#888	C₂²	1	4	yes	complemented
52	C₃×#886	C₂²	1	2	yes	—
53	C₃×#885	C₂²	1	4	yes	—
54	C₃×#883	C₂²	1	4	yes	—
55	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
56	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
57	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₃×#879	C₂²	1	4	yes	complemented
59	C₃×#879	C₂²	1	4	yes	complemented
60	C₃×#879	C₂²	1	4	yes	complemented
61	C₃×#878	C₂²	1	4	yes	complemented
62	C₃×#878	C₂²	1	4	yes	complemented
63	C₃×#876	C₂²	1	4	yes	complemented
64	C₃×#875	C₂²	1	1	yes	characteristic
65	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
66	C₃×C₄²×D₃	C₂²	1	2	yes	—
67	C₃×#870	C₂²	1	2	yes	complemented
68	C₃×#869	C₂²	1	2	yes	complemented
69	C₃×#563	—	2	1	no	—
70	C₃×#563	—	3	2	no	—
71	C₃×#563	—	3	4	no	—
72	C₃×#563	—	3	2	no	—
73	C₃×#563	—	3	1	no	—
74	C₃×#563	—	3	2	no	—
75	C₃×#563	—	3	4	no	—
76	C₃×#563	D₃	1	1	yes	characteristic, direct product factor
77	C₃×#563	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂×C₃×C₄⋊Q₈	—	3	2	no	—
79	C₂×C₃×#126	—	3	4	no	—
80	C₂×C₃×#125	—	3	2	no	—
81	C₂×C₃×#124	—	3	1	no	—
82	C₂×C₃×#123	—	3	2	no	—
83	C₂×C₃×C₂²⋊Q₈	—	3	4	no	—
84	#5735	C₂×C₃	1	2	yes	complemented
85	D₃×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
86	#5712	C₂×C₃	1	4	yes	complemented
87	D₃×#126	C₂×C₃	1	4	yes	complemented
88	#5699	C₂×C₃	1	2	yes	complemented
89	D₃×#125	C₂×C₃	1	2	yes	complemented
90	D₃×#124	C₂×C₃	1	1	yes	characteristic
91	#5672	C₂×C₃	1	1	yes	characteristic, complemented
92	D₃×#123	C₂×C₃	1	2	yes	—
93	#5651	C₂×C₃	1	2	yes	complemented
94	#5646	C₂×C₃	1	4	yes	complemented
95	D₃×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
96	C₂³×C₃×D₃	C₂³	1	2	yes	—
97	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
98	C₂×C₃²×Q₈	C₂³	1	2	yes	—
99	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
100	C₂²×C₃²×C₄	C₂³	1	2	yes	—
101	C₂×C₃×#67	C₂³	1	2	yes	—
102	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
103	C₃×D₃×Q₈	—	4	4	no	—
104	C₃×D₃×Q₈	—	4	2	no	—
105	C₃×D₃×D₄	—	4	2	no	—
106	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₄×D₃	—	4	4	no	—
108	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
109	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
110	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
111	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
112	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
113	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
114	C₂×C₃×Dic₆	C₂³	1	2	yes	—
115	C₂×C₃×Dic₆	C₂³	1	4	yes	—
116	C₂×C₃×Dic₆	C₂³	1	2	yes	—
117	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
118	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
119	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
120	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
121	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
122	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
123	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₃²×C₄²	C₂³	1	1	yes	characteristic
127	C₃²×C₄²	C₂³	1	2	yes	—
128	C₃×#217	C₂³	1	4	yes	—
129	C₃×#217	C₂³	1	4	yes	—
130	C₃×#217	C₂³	1	2	yes	—
131	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
132	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
133	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
134	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
135	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
136	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
137	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
138	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
139	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
140	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
141	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
142	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
143	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
144	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
145	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
146	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
147	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
148	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
149	C₃×C₄×Dic₃	C₂³	1	4	yes	—
150	C₃×C₄×Dic₃	C₂³	1	2	yes	—
151	C₃×C₄×Dic₃	C₂³	1	2	yes	—
152	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
153	C₂×#563	—	3	1	no	Sylow
154	C₂²×C₃×Q₈	—	3	2	no	—
155	C₂²×C₃×Q₈	—	3	1	no	—
156	C₂²×C₃×D₄	—	3	1	no	—
157	C₂³×C₃×C₄	—	3	2	no	—
158	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	—
160	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
161	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
162	C₃×C₄⋊Q₈	—	2	2	no	—
163	C₃×C₄⋊Q₈	—	3	2	no	—
164	C₃×C₄⋊Q₈	—	3	2	no	—
165	C₃×C₄⋊Q₈	—	3	4	no	—
166	C₃×C₄⋊Q₈	—	3	4	no	—
167	C₃×C₄⋊Q₈	—	3	2	no	—
168	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
169	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
170	C₃×#126	—	2	4	no	—
171	C₃×#126	—	3	4	no	—
172	C₃×#126	—	3	4	no	—
173	C₃×#126	—	3	4	no	—
174	C₃×#126	—	3	4	no	—
175	C₃×#126	—	3	4	no	—
176	C₃×#126	—	3	4	no	—
177	C₃×#126	—	3	4	no	—
178	C₃×#126	C₂×D₃	1	4	yes	complemented
179	C₃×#126	C₂²×C₃	1	4	yes	complemented
180	C₃×#125	—	2	2	no	—
181	C₃×#125	—	3	4	no	—
182	C₃×#125	—	3	4	no	—
183	C₃×#125	—	3	2	no	—
184	C₃×#125	—	3	2	no	—
185	C₃×#125	—	3	2	no	—
186	C₃×#125	C₂×D₃	1	2	yes	complemented
187	C₃×#125	C₂²×C₃	1	2	yes	complemented
188	C₃×#124	—	2	1	no	—
189	C₃×#124	—	3	1	no	—
190	C₃×#124	—	3	1	no	—
191	C₃×#124	—	3	4	no	—
192	C₃×#124	—	3	1	no	—
193	C₃×#124	C₂×D₃	1	1	yes	characteristic
194	C₃×#124	C₂²×C₃	1	1	yes	characteristic
195	C₃×#123	—	2	2	no	—
196	C₃×#123	—	3	2	no	—
197	C₃×#123	—	3	2	no	—
198	C₃×#123	—	3	4	no	—
199	C₃×#123	—	3	4	no	—
200	C₃×#123	—	3	2	no	—
201	C₃×#123	C₂×D₃	1	2	yes	—
202	C₃×#123	C₂²×C₃	1	2	yes	—
203	C₃×C₂²⋊Q₈	—	2	4	no	—
204	C₃×C₂²⋊Q₈	—	3	4	no	—
205	C₃×C₂²⋊Q₈	—	3	4	no	—
206	C₃×C₂²⋊Q₈	—	3	4	no	—
207	C₃×C₂²⋊Q₈	—	3	4	no	—
208	C₃×C₂²⋊Q₈	—	3	4	no	—
209	C₃×C₂²⋊Q₈	—	3	4	no	—
210	C₃×C₂²⋊Q₈	—	3	4	no	—
211	C₃×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
212	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
213	C₂×C₃×C₄⋊C₄	—	3	2	no	—
214	C₂×C₃×C₄⋊C₄	—	3	4	no	—
215	C₂×C₃×C₄⋊C₄	—	3	4	no	—
216	C₂×C₃×C₄⋊C₄	—	3	4	no	—
217	C₂×C₃×C₄⋊C₄	—	3	2	no	—
218	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
219	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
220	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
221	C₂×C₃×C₄²	—	3	1	no	—
222	C₂×C₃×C₄²	—	3	2	no	—
223	#947	C₂²×C₃	1	1	yes	characteristic
224	#946	C₂²×C₃	1	4	yes	complemented
225	#944	C₂²×C₃	1	2	yes	complemented
226	#944	C₂²×C₃	1	2	yes	complemented
227	#936	C₂²×C₃	1	1	yes	characteristic
228	#935	C₂²×C₃	1	2	yes	—
229	#929	C₂²×C₃	1	2	yes	—
230	#924	C₂²×C₃	1	4	yes	complemented
231	#898	C₂²×C₃	1	4	yes	complemented
232	#898	C₂²×C₃	1	4	yes	complemented
233	#898	C₂²×C₃	1	4	yes	complemented
234	#897	C₂²×C₃	1	4	yes	complemented
235	#896	C₂²×C₃	1	4	yes	complemented
236	#896	C₂²×C₃	1	4	yes	complemented
237	#894	C₂²×C₃	1	4	yes	—
238	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
239	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
240	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
241	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
242	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
243	#890	C₂²×C₃	1	2	yes	complemented
244	#890	C₂²×C₃	1	2	yes	complemented
245	#889	C₂²×C₃	1	4	yes	complemented
246	#889	C₂²×C₃	1	4	yes	complemented
247	#888	C₂²×C₃	1	4	yes	complemented
248	#888	C₂²×C₃	1	4	yes	complemented
249	#886	C₂²×C₃	1	2	yes	—
250	#885	C₂²×C₃	1	4	yes	—
251	#883	C₂²×C₃	1	4	yes	—
252	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
253	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
254	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
255	#879	C₂²×C₃	1	4	yes	complemented
256	#879	C₂²×C₃	1	4	yes	complemented
257	#879	C₂²×C₃	1	4	yes	complemented
258	#878	C₂²×C₃	1	4	yes	complemented
259	#878	C₂²×C₃	1	4	yes	complemented
260	#876	C₂²×C₃	1	4	yes	complemented
261	#875	C₂²×C₃	1	1	yes	characteristic
262	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
263	C₄²×D₃	C₂²×C₃	1	2	yes	—
264	#870	C₂²×C₃	1	2	yes	complemented
265	#869	C₂²×C₃	1	2	yes	complemented
266	C₂³×C₃²	C₂⁴	1	2	yes	—
267	C₂²×C₃×D₃	—	2	4	no	—
268	C₂²×C₃×D₃	—	2	8	no	—
269	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
270	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
271	C₃²×Q₈	—	4	1	no	—
272	C₃²×Q₈	—	4	2	no	—
273	C₃²×D₄	—	4	1	no	—
274	C₂×C₃²×C₄	—	4	2	no	—
275	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
276	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
277	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
278	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
279	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
280	C₃×#67	—	4	2	no	—
281	C₂×C₃×Dic₃	—	4	2	no	—
282	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
283	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
284	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
285	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
286	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
287	C₃×D₁₂	—	4	1	no	—
288	C₃×C₄×D₃	—	2	8	no	—
289	C₃×C₄×D₃	—	2	2	no	—
290	C₃×C₄×D₃	—	2	4	no	—
291	C₃×C₄×D₃	—	2	8	no	—
292	C₃×C₄×D₃	—	2	4	no	—
293	C₃×C₄×D₃	—	4	4	no	—
294	C₃×Dic₆	—	4	1	no	—
295	C₃×Dic₆	—	4	4	no	—
296	C₃×Dic₆	—	4	2	no	—
297	C₃×Dic₆	—	4	2	no	—
298	#563	—	3	2	no	—
299	#563	—	3	4	no	—
300	#563	—	3	2	no	—
301	#563	—	3	1	no	—
302	#563	—	3	2	no	—
303	#563	—	3	4	no	—
304	#563	C₃×D₃	1	1	yes	characteristic, direct product factor
305	C₂×C₄⋊Q₈	—	3	2	no	—
306	C₂×#126	—	3	4	no	—
307	C₂×#125	—	3	2	no	—
308	C₂×#124	—	3	1	no	—
309	C₂×#123	—	3	2	no	—
310	C₂×C₂²⋊Q₈	—	3	4	no	—
311	C₂⁴×C₃	—	3	2	no	—
312	C₂³×D₃	C₂³×C₃	1	2	yes	—
313	C₂×C₃×Q₈	—	2	2	no	—
314	C₂×C₃×Q₈	—	2	1	no	—
315	C₂×C₃×Q₈	—	3	4	no	—
316	C₂×C₃×Q₈	—	3	2	no	—
317	C₂×C₃×Q₈	—	3	1	no	—
318	C₂×C₃×Q₈	—	3	2	no	—
319	C₂×C₃×Q₈	—	12	4	no	—
320	C₂×C₃×Q₈	—	12	2	no	—
321	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
322	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
323	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
324	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
325	C₂×C₃×D₄	—	2	1	no	—
326	C₂×C₃×D₄	—	3	2	no	—
327	C₂×C₃×D₄	—	3	1	no	—
328	C₂×C₃×D₄	—	12	2	no	—
329	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
330	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
331	C₂²×C₃×C₄	—	2	2	no	—
332	C₂²×C₃×C₄	—	3	2	no	—
333	C₂²×C₃×C₄	—	3	2	no	—
334	C₂²×C₃×C₄	—	3	4	no	—
335	C₂²×C₃×C₄	—	3	2	no	—
336	C₂²×C₃×C₄	—	3	1	no	—
337	C₂²×C₃×C₄	—	3	4	no	—
338	C₂²×C₃×C₄	—	3	4	no	—
339	C₂²×C₃×C₄	—	12	4	no	—
340	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
341	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
342	C₂×#67	C₂³×C₃	1	2	yes	—
343	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
344	D₃×Q₈	—	4	4	no	—
345	D₃×Q₈	—	4	2	no	—
346	D₃×D₄	—	4	2	no	—
347	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
348	C₂×C₄×D₃	—	4	4	no	—
349	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
350	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
351	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
352	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
353	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
354	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
355	C₂×Dic₆	C₂³×C₃	1	2	yes	—
356	C₂×Dic₆	C₂³×C₃	1	2	yes	—
357	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
358	C₂×Dic₆	C₂³×C₃	1	4	yes	—
359	C₃×C₄⋊C₄	—	2	2	no	—
360	C₃×C₄⋊C₄	—	2	4	no	—
361	C₃×C₄⋊C₄	—	2	4	no	—
362	C₃×C₄⋊C₄	—	2	4	no	—
363	C₃×C₄⋊C₄	—	2	2	no	—
364	C₃×C₄⋊C₄	—	3	4	no	—
365	C₃×C₄⋊C₄	—	3	4	no	—
366	C₃×C₄⋊C₄	—	3	4	no	—
367	C₃×C₄⋊C₄	—	3	4	no	—
368	C₃×C₄⋊C₄	—	3	4	no	—
369	C₃×C₄⋊C₄	—	3	4	no	—
370	C₃×C₄⋊C₄	—	3	4	no	—
371	C₃×C₄⋊C₄	—	3	4	no	—
372	C₃×C₄⋊C₄	—	3	2	no	—
373	C₃×C₄⋊C₄	—	3	4	no	—
374	C₃×C₄⋊C₄	—	3	4	no	—
375	C₃×C₄⋊C₄	—	3	4	no	—
376	C₃×C₄⋊C₄	—	3	2	no	—
377	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
378	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
379	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
380	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
381	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
382	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
383	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
384	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
385	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
386	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
387	C₃×C₂²⋊C₄	—	2	4	no	—
388	C₃×C₂²⋊C₄	—	2	4	no	—
389	C₃×C₂²⋊C₄	—	2	2	no	—
390	C₃×C₂²⋊C₄	—	3	4	no	—
391	C₃×C₂²⋊C₄	—	3	4	no	—
392	C₃×C₂²⋊C₄	—	3	2	no	—
393	C₃×C₂²⋊C₄	—	3	4	no	—
394	C₃×C₂²⋊C₄	—	3	4	no	—
395	C₃×C₂²⋊C₄	—	3	4	no	—
396	C₃×C₂²⋊C₄	—	3	4	no	—
397	C₃×C₂²⋊C₄	—	3	4	no	—
398	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
399	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
400	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
401	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
402	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
403	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
404	C₃×C₄²	—	2	1	no	—
405	C₃×C₄²	—	2	2	no	—
406	C₃×C₄²	—	3	1	no	—
407	C₃×C₄²	—	3	2	no	—
408	C₃×C₄²	—	3	2	no	—
409	C₃×C₄²	—	3	4	no	—
410	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
411	C₃×C₄²	C₂²×D₃	1	2	yes	—
412	C₃×C₄²	C₂³×C₃	1	2	yes	—
413	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
414	#217	C₂³×C₃	1	4	yes	—
415	#217	C₂³×C₃	1	4	yes	—
416	#217	C₂³×C₃	1	2	yes	—
417	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
418	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
419	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
420	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
421	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
422	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
423	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
424	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
425	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
426	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
427	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
428	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
429	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
430	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
431	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
432	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
433	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
434	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
435	C₄×Dic₃	C₂³×C₃	1	4	yes	—
436	C₄×Dic₃	C₂³×C₃	1	2	yes	—
437	C₄×Dic₃	C₂³×C₃	1	2	yes	—
438	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
439	C₂²×C₃²	—	2	2	no	—
440	C₂²×C₃²	—	2	4	no	—
441	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
442	C₂×C₃×D₃	—	2	2	no	—
443	C₂×C₃×D₃	—	2	4	no	—
444	C₂×C₃×D₃	—	4	8	no	—
445	C₂×C₃×D₃	H(5,𝔽₂)	1	2	yes	—
446	C₂×C₃×D₃	2₋¹⁺⁴	1	4	yes	—
447	C₃²×C₄	—	2	2	no	—
448	C₃²×C₄	—	2	4	no	—
449	C₃²×C₄	—	2	1	no	—
450	C₃²×C₄	—	2	4	no	—
451	C₃²×C₄	—	2	2	no	—
452	C₃×Dic₃	—	2	2	no	—
453	C₃×Dic₃	—	2	4	no	—
454	C₃×Dic₃	—	2	1	no	—
455	C₃×Dic₃	—	2	4	no	—
456	C₃×Dic₃	—	2	2	no	—
457	C₂²×Q₈	—	3	2	no	—
458	C₂²×Q₈	—	3	1	no	—
459	C₂²×D₄	—	3	1	no	—
460	C₂³×C₄	—	3	2	no	—
461	C₄⋊Q₈	—	3	2	no	—
462	C₄⋊Q₈	—	3	2	no	—
463	C₄⋊Q₈	—	3	4	no	—
464	C₄⋊Q₈	—	3	4	no	—
465	C₄⋊Q₈	—	3	2	no	—
466	C₄⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
467	#126	—	3	4	no	—
468	#126	—	3	4	no	—
469	#126	—	3	4	no	—
470	#126	—	3	4	no	—
471	#126	—	3	4	no	—
472	#126	—	3	4	no	—
473	#126	—	3	4	no	—
474	#126	C₂×C₃×D₃	1	4	yes	complemented
475	#125	—	3	4	no	—
476	#125	—	3	4	no	—
477	#125	—	3	2	no	—
478	#125	—	3	2	no	—
479	#125	—	3	2	no	—
480	#125	C₂×C₃×D₃	1	2	yes	complemented
481	#124	—	3	1	no	—
482	#124	—	3	1	no	—
483	#124	—	3	4	no	—
484	#124	—	3	1	no	—
485	#124	C₂×C₃×D₃	1	1	yes	characteristic
486	#123	—	3	2	no	—
487	#123	—	3	2	no	—
488	#123	—	3	4	no	—
489	#123	—	3	4	no	—
490	#123	—	3	2	no	—
491	#123	C₂×C₃×D₃	1	2	yes	—
492	C₂²⋊Q₈	—	3	4	no	—
493	C₂²⋊Q₈	—	3	4	no	—
494	C₂²⋊Q₈	—	3	4	no	—
495	C₂²⋊Q₈	—	3	4	no	—
496	C₂²⋊Q₈	—	3	4	no	—
497	C₂²⋊Q₈	—	3	4	no	—
498	C₂²⋊Q₈	—	3	4	no	—
499	C₂²⋊Q₈	C₂×C₃×D₃	1	4	yes	complemented
500	C₂×C₄⋊C₄	—	3	2	no	—
501	C₂×C₄⋊C₄	—	3	4	no	—
502	C₂×C₄⋊C₄	—	3	4	no	—
503	C₂×C₄⋊C₄	—	3	4	no	—
504	C₂×C₄⋊C₄	—	3	2	no	—
505	C₂×C₂²⋊C₄	—	3	4	no	—
506	C₂×C₂²⋊C₄	—	3	4	no	—
507	C₂×C₂²⋊C₄	—	3	2	no	—
508	C₂×C₄²	—	3	1	no	—
509	C₂×C₄²	—	3	2	no	—
510	C₂³×C₃	—	2	2	no	—
511	C₂³×C₃	—	3	1	no	—
512	C₂³×C₃	—	3	2	no	—
513	C₂³×C₃	—	6	4	no	—
514	C₂³×C₃	—	6	8	no	—
515	C₂³×C₃	C₂³×D₃	1	2	yes	—
516	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
517	C₂²×D₃	—	2	4	no	—
518	C₂²×D₃	—	2	8	no	—
519	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
520	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
521	C₃×Q₈	—	4	1	no	—
522	C₃×Q₈	—	4	2	no	—
523	C₃×Q₈	—	4	2	no	—
524	C₃×Q₈	—	4	1	no	—
525	C₃×Q₈	—	8	2	no	—
526	C₃×Q₈	—	8	1	no	—
527	C₃×Q₈	—	12	4	no	—
528	C₃×Q₈	—	12	1	no	—
529	C₃×Q₈	—	12	2	no	—
530	C₃×Q₈	—	12	2	no	—
531	C₃×D₄	—	4	1	no	—
532	C₃×D₄	—	4	1	no	—
533	C₃×D₄	—	8	1	no	—
534	C₃×D₄	—	12	1	no	—
535	C₃×D₄	—	12	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	—	2	4	no	—
538	C₂×C₃×C₄	—	2	2	no	—
539	C₂×C₃×C₄	—	2	1	no	—
540	C₂×C₃×C₄	—	2	4	no	—
541	C₂×C₃×C₄	—	3	2	no	—
542	C₂×C₃×C₄	—	3	4	no	—
543	C₂×C₃×C₄	—	3	2	no	—
544	C₂×C₃×C₄	—	3	1	no	—
545	C₂×C₃×C₄	—	3	4	no	—
546	C₂×C₃×C₄	—	4	2	no	—
547	C₂×C₃×C₄	—	4	2	no	—
548	C₂×C₃×C₄	—	6	4	no	—
549	C₂×C₃×C₄	—	6	8	no	—
550	C₂×C₃×C₄	—	6	8	no	—
551	C₂×C₃×C₄	—	6	2	no	—
552	C₂×C₃×C₄	—	6	4	no	—
553	C₂×C₃×C₄	—	8	2	no	—
554	C₂×C₃×C₄	—	12	4	no	—
555	C₂×C₃×C₄	—	12	2	no	—
556	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
557	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
558	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
559	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
560	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
561	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
562	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
563	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
564	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
565	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
566	#67	—	4	2	no	—
567	C₂×Dic₃	—	4	2	no	—
568	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
569	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
570	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
571	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
572	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
573	D₁₂	—	4	1	no	—
574	C₄×D₃	—	2	8	no	—
575	C₄×D₃	—	2	2	no	—
576	C₄×D₃	—	2	4	no	—
577	C₄×D₃	—	2	4	no	—
578	C₄×D₃	—	2	8	no	—
579	C₄×D₃	—	4	4	no	—
580	Dic₆	—	4	1	no	—
581	Dic₆	—	4	4	no	—
582	Dic₆	—	4	2	no	—
583	Dic₆	—	4	2	no	—
584	C₂×C₃²	—	4	2	no	—
585	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
586	C₂×C₃²	C₂×2₋¹⁺⁴	1	2	yes	—
587	C₃×D₃	—	4	2	no	—
588	C₃×D₃	#563	1	4	yes	direct product factor
589	C₂⁴	—	3	2	no	—
590	C₂×Q₈	—	3	4	no	—
591	C₂×Q₈	—	3	2	no	—
592	C₂×Q₈	—	3	1	no	—
593	C₂×Q₈	—	3	2	no	—
594	C₂×Q₈	—	12	4	no	—
595	C₂×Q₈	—	12	2	no	—
596	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
597	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
598	C₂×D₄	—	3	2	no	—
599	C₂×D₄	—	3	1	no	—
600	C₂×D₄	—	12	2	no	—
601	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
602	C₂²×C₄	—	3	2	no	—
603	C₂²×C₄	—	3	2	no	—
604	C₂²×C₄	—	3	4	no	—
605	C₂²×C₄	—	3	2	no	—
606	C₂²×C₄	—	3	1	no	—
607	C₂²×C₄	—	3	4	no	—
608	C₂²×C₄	—	3	4	no	—
609	C₂²×C₄	—	12	4	no	—
610	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
611	C₄⋊C₄	—	3	4	no	—
612	C₄⋊C₄	—	3	2	no	—
613	C₄⋊C₄	—	3	4	no	—
614	C₄⋊C₄	—	3	4	no	—
615	C₄⋊C₄	—	3	4	no	—
616	C₄⋊C₄	—	3	4	no	—
617	C₄⋊C₄	—	3	4	no	—
618	C₄⋊C₄	—	3	4	no	—
619	C₄⋊C₄	—	3	4	no	—
620	C₄⋊C₄	—	3	4	no	—
621	C₄⋊C₄	—	3	4	no	—
622	C₄⋊C₄	—	3	4	no	—
623	C₄⋊C₄	—	3	2	no	—
624	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
625	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
626	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
627	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
628	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
629	C₂²⋊C₄	—	3	4	no	—
630	C₂²⋊C₄	—	3	4	no	—
631	C₂²⋊C₄	—	3	2	no	—
632	C₂²⋊C₄	—	3	4	no	—
633	C₂²⋊C₄	—	3	4	no	—
634	C₂²⋊C₄	—	3	4	no	—
635	C₂²⋊C₄	—	3	4	no	—
636	C₂²⋊C₄	—	3	4	no	—
637	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
638	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
639	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
640	C₄²	—	3	1	no	—
641	C₄²	—	3	2	no	—
642	C₄²	—	3	2	no	—
643	C₄²	—	3	4	no	—
644	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
645	C₄²	C₂²×C₃×D₃	1	2	yes	—
646	C₂²×C₃	—	2	2	no	—
647	C₂²×C₃	—	2	4	no	—
648	C₂²×C₃	—	2	2	no	—
649	C₂²×C₃	—	2	4	no	—
650	C₂²×C₃	—	2	1	no	—
651	C₂²×C₃	—	3	2	no	—
652	C₂²×C₃	—	3	4	no	—
653	C₂²×C₃	—	4	2	no	—
654	C₂²×C₃	—	4	4	no	—
655	C₂²×C₃	—	6	2	no	—
656	C₂²×C₃	—	6	4	no	—
657	C₂²×C₃	—	12	8	no	—
658	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
659	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
660	C₂×D₃	—	2	2	no	—
661	C₂×D₃	—	2	4	no	—
662	C₂×D₃	—	4	8	no	—
663	C₂×D₃	C₃×H(5,𝔽₂)	1	2	yes	—
664	C₂×D₃	C₃×2₋¹⁺⁴	1	4	yes	—
665	C₃×C₄	—	2	4	no	—
666	C₃×C₄	—	2	1	no	—
667	C₃×C₄	—	2	2	no	—
668	C₃×C₄	—	2	2	no	—
669	C₃×C₄	—	2	4	no	—
670	C₃×C₄	—	2	2	no	—
671	C₃×C₄	—	2	4	no	—
672	C₃×C₄	—	2	1	no	—
673	C₃×C₄	—	2	4	no	—
674	C₃×C₄	—	2	2	no	—
675	C₃×C₄	—	4	4	no	—
676	C₃×C₄	—	4	1	no	—
677	C₃×C₄	—	4	2	no	—
678	C₃×C₄	—	4	2	no	—
679	C₃×C₄	—	4	4	no	—
680	C₃×C₄	—	6	4	no	—
681	C₃×C₄	—	6	1	no	—
682	C₃×C₄	—	6	2	no	—
683	C₃×C₄	—	6	2	no	—
684	C₃×C₄	—	6	4	no	—
685	Dic₃	—	2	2	no	—
686	Dic₃	—	2	4	no	—
687	Dic₃	—	2	1	no	—
688	Dic₃	—	2	4	no	—
689	Dic₃	—	2	2	no	—
690	C₃²	C₂×#563	1	1	yes	characteristic, complemented, Sylow
691	C₂³	—	3	1	no	—
692	C₂³	—	3	2	no	—
693	C₂³	—	6	4	no	—
694	C₂³	—	6	8	no	—
695	C₂³	C₂³×C₃×D₃	1	2	yes	—
696	Q₈	—	4	2	no	—
697	Q₈	—	4	1	no	—
698	Q₈	—	12	4	no	—
699	Q₈	—	12	1	no	—
700	Q₈	—	12	2	no	—
701	Q₈	—	12	2	no	—
702	D₄	—	4	1	no	—
703	D₄	—	12	1	no	—
704	D₄	—	12	2	no	—
705	C₂×C₄	—	3	2	no	—
706	C₂×C₄	—	3	4	no	—
707	C₂×C₄	—	3	2	no	—
708	C₂×C₄	—	3	1	no	—
709	C₂×C₄	—	3	4	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	6	8	no	—
712	C₂×C₄	—	6	2	no	—
713	C₂×C₄	—	6	4	no	—
714	C₂×C₄	—	6	4	no	—
715	C₂×C₄	—	6	8	no	—
716	C₂×C₄	—	12	4	no	—
717	C₂×C₄	—	12	2	no	—
718	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
719	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
720	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
721	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
722	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
723	C₂×C₃	—	2	1	no	—
724	C₂×C₃	—	2	2	no	—
725	C₂×C₃	—	3	4	no	—
726	C₂×C₃	—	4	2	no	—
727	C₂×C₃	—	4	2	no	—
728	C₂×C₃	—	8	2	no	—
729	C₂×C₃	—	12	2	no	—
730	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
731	C₂×C₃	D₃×2₋¹⁺⁴	1	2	yes	—
732	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
733	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
734	D₃	—	4	2	no	—
735	D₃	C₃×#563	1	4	yes	direct product factor
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	3	2	no	—
739	C₂²	—	3	4	no	—
740	C₂²	—	6	2	no	—
741	C₂²	—	6	4	no	—
742	C₂²	—	12	8	no	—
743	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
744	C₄	—	2	4	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	4	no	—
749	C₄	—	6	4	no	—
750	C₄	—	6	1	no	—
751	C₄	—	6	2	no	—
752	C₄	—	6	2	no	—
753	C₄	—	6	4	no	—
754	C₃	—	2	1	no	—
755	C₃	D₃×#563	1	1	yes	characteristic, direct product factor
756	C₃	C₂×C₃×#563	1	1	yes	characteristic, complemented
757	C₂	—	3	4	no	—
758	C₂	—	4	2	no	—
759	C₂	—	12	2	no	—
760	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂	C₃×D₃×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#563	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂×C₃×D₃×D₄	C₂²
hypercenter	C₃×#563	D₃
hypocenter	C₃	C₂×C₃×#563
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#563

Complements

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

N	H ≅ G/N	type
1. C₃²×#563	C₂	semidirect
2. C₃×#5735	C₂	semidirect
3. C₃×D₃×C₄⋊Q₈	C₂	semidirect
4. C₃×#5712	C₂	semidirect
5. C₃×D₃×#126	C₂	semidirect
6. C₃×#5699	C₂	semidirect
7. C₃×D₃×#125	C₂	semidirect
9. C₃×#5672	C₂	semidirect
11. C₃×#5651	C₂	semidirect
12. C₃×#5646	C₂	semidirect
13. C₃×D₃×C₂²⋊Q₈	C₂	semidirect
15. D₃×#563	C₃	direct (N × H)
20. C₃²×C₄⋊Q₈	C₂²	semidirect
21. C₃²×#126	C₂²	semidirect
22. C₃²×#125	C₂²	semidirect
25. C₃²×C₂²⋊Q₈	C₂²	semidirect
27. C₃×#946	C₂²	semidirect
28. C₃×#944	C₂²	semidirect
29. C₃×#944	C₂²	semidirect
33. C₃×#924	C₂²	semidirect
34. C₃×#898	C₂²	semidirect
35. C₃×#898	C₂²	semidirect
36. C₃×#898	C₂²	semidirect
37. C₃×#897	C₂²	semidirect
38. C₃×#896	C₂²	semidirect
39. C₃×#896	C₂²	semidirect
46. C₃×#890	C₂²	semidirect
47. C₃×#890	C₂²	semidirect
48. C₃×#889	C₂²	semidirect
49. C₃×#889	C₂²	semidirect
50. C₃×#888	C₂²	semidirect
51. C₃×#888	C₂²	semidirect
58. C₃×#879	C₂²	semidirect
59. C₃×#879	C₂²	semidirect
60. C₃×#879	C₂²	semidirect
61. C₃×#878	C₂²	semidirect
62. C₃×#878	C₂²	semidirect
63. C₃×#876	C₂²	semidirect
67. C₃×#870	C₂²	semidirect
68. C₃×#869	C₂²	semidirect
76. C₃×#563	D₃	direct (N × H)
77. C₃×#563	C₂×C₃	semidirect
84. #5735	C₂×C₃	semidirect
85. D₃×C₄⋊Q₈	C₂×C₃	semidirect
86. #5712	C₂×C₃	semidirect
87. D₃×#126	C₂×C₃	semidirect
88. #5699	C₂×C₃	semidirect
89. D₃×#125	C₂×C₃	semidirect
91. #5672	C₂×C₃	semidirect
93. #5651	C₂×C₃	semidirect
94. #5646	C₂×C₃	semidirect
95. D₃×C₂²⋊Q₈	C₂×C₃	semidirect
168. C₃×C₄⋊Q₈	C₂×D₃	semidirect
169. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
178. C₃×#126	C₂×D₃	semidirect
179. C₃×#126	C₂²×C₃	semidirect
186. C₃×#125	C₂×D₃	semidirect
187. C₃×#125	C₂²×C₃	semidirect
211. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
212. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
224. #946	C₂²×C₃	semidirect
225. #944	C₂²×C₃	semidirect
226. #944	C₂²×C₃	semidirect
230. #924	C₂²×C₃	semidirect
231. #898	C₂²×C₃	semidirect
232. #898	C₂²×C₃	semidirect
233. #898	C₂²×C₃	semidirect
234. #897	C₂²×C₃	semidirect
235. #896	C₂²×C₃	semidirect
236. #896	C₂²×C₃	semidirect
243. #890	C₂²×C₃	semidirect
244. #890	C₂²×C₃	semidirect
245. #889	C₂²×C₃	semidirect
246. #889	C₂²×C₃	semidirect
247. #888	C₂²×C₃	semidirect
248. #888	C₂²×C₃	semidirect
255. #879	C₂²×C₃	semidirect
256. #879	C₂²×C₃	semidirect
257. #879	C₂²×C₃	semidirect
258. #878	C₂²×C₃	semidirect
259. #878	C₂²×C₃	semidirect
260. #876	C₂²×C₃	semidirect
264. #870	C₂²×C₃	semidirect
265. #869	C₂²×C₃	semidirect
304. #563	C₃×D₃	direct (N × H)
466. C₄⋊Q₈	C₂×C₃×D₃	semidirect
474. #126	C₂×C₃×D₃	semidirect
480. #125	C₂×C₃×D₃	semidirect
499. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
588. C₃×D₃	#563	direct (N × H)
690. C₃²	C₂×#563	semidirect
735. D₃	C₃×#563	direct (N × H)
755. C₃	D₃×#563	direct (N × H)
756. C₃	C₂×C₃×#563	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#563	2
C₃×#5735	2
C₃×D₃×C₄⋊Q₈	2
C₃×#5712	2
C₃×D₃×#126	2
C₃×#5699	2
C₃×D₃×#125	2
C₃×D₃×#124	2
C₃×#5672	2
C₃×D₃×#123	2
C₃×#5651	2
C₃×#5646	2
C₃×D₃×C₂²⋊Q₈	2
C₂×C₃×#563	3
D₃×#563	3

Subgroups — C3×D3×#563 #11910280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#563 #11910280