Subgroups — C₃×D₃×#556 #11903349

Order 1152.

2330 conjugacy classes of subgroups.

The subgroup lattice has 949 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5732	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₃×#126	C₂	1	4	yes	maximal, complemented
5	C₃×#5702	C₂	1	4	yes	maximal, complemented
6	C₃×D₃×#124	C₂	1	2	yes	maximal
7	C₃×#5671	C₂	1	2	yes	maximal, complemented
8	C₃×#5641	C₂	1	2	yes	maximal, complemented
9	C₃×D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
10	C₃×#5584	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×D₃×Q₈	C₂	1	2	yes	maximal, complemented
13	C₃×#5568	C₂	1	2	yes	maximal, complemented
14	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
15	C₃×#5542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5533	C₂	1	2	yes	maximal, complemented
17	C₃×D₃×#117	C₂	1	2	yes	maximal, complemented
18	C₂×C₃×#556	—	3	1	no	maximal
19	D₃×#556	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	—
22	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
24	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃²×#126	C₂²	1	4	yes	complemented
26	C₃²×#124	C₂²	1	2	yes	—
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₃²×C₄×Q₈	C₂²	1	2	yes	complemented
29	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
31	C₃²×#117	C₂²	1	2	yes	complemented
32	C₃×#947	C₂²	1	2	yes	—
33	C₃×#946	C₂²	1	2	yes	complemented
34	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
36	C₃×#944	C₂²	1	2	yes	complemented
37	C₃×#936	C₂²	1	2	yes	—
38	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×C₄×#67	C₂²	1	2	yes	—
40	C₃×#926	C₂²	1	2	yes	complemented
41	C₃×#924	C₂²	1	2	yes	complemented
42	C₃×#898	C₂²	1	4	yes	complemented
43	C₃×#898	C₂²	1	4	yes	complemented
44	C₃×#898	C₂²	1	4	yes	complemented
45	C₃×#897	C₂²	1	2	yes	complemented
46	C₃×#896	C₂²	1	4	yes	complemented
47	C₃×#893	C₂²	1	1	yes	characteristic
48	C₃×#892	C₂²	1	2	yes	complemented
49	C₃×#892	C₂²	1	2	yes	complemented
50	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
52	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
54	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
55	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
56	C₃×#888	C₂²	1	2	yes	complemented
57	C₃×#888	C₂²	1	2	yes	complemented
58	C₃×#887	C₂²	1	1	yes	characteristic, complemented
59	C₃×#887	C₂²	1	2	yes	complemented
60	C₃×#887	C₂²	1	4	yes	complemented
61	C₃×#887	C₂²	1	2	yes	complemented
62	C₃×#885	C₂²	1	4	yes	—
63	C₃×#885	C₂²	1	4	yes	—
64	C₃×#67⋊C₄	C₂²	1	2	yes	—
65	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
66	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
67	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
68	C₃×#879	C₂²	1	4	yes	complemented
69	C₃×#879	C₂²	1	4	yes	complemented
70	C₃×#879	C₂²	1	4	yes	complemented
71	C₃×#878	C₂²	1	4	yes	complemented
72	C₃×#877	C₂²	1	4	yes	complemented
73	C₃×#876	C₂²	1	4	yes	complemented
74	C₃×#875	C₂²	1	2	yes	—
75	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
76	C₃×#872	C₂²	1	4	yes	complemented
77	C₃×C₄²×D₃	C₂²	1	4	yes	—
78	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
79	C₃×C₄²×D₃	C₂²	1	2	yes	—
80	C₃×#869	C₂²	1	1	yes	characteristic, complemented
81	C₃×C₄×Dic₆	C₂²	1	4	yes	complemented
82	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
84	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
85	C₃×#556	—	2	1	no	—
86	C₃×#556	—	3	1	no	—
87	C₃×#556	—	3	4	no	—
88	C₃×#556	—	3	2	no	—
89	C₃×#556	—	3	2	no	—
90	C₃×#556	—	3	2	no	—
91	C₃×#556	—	3	1	no	—
92	C₃×#556	—	3	1	no	—
93	C₃×#556	—	3	2	no	—
94	C₃×#556	D₃	1	1	yes	characteristic, direct product factor
95	C₃×#556	C₂×C₃	1	1	yes	characteristic, complemented
96	C₂×C₃×C₄⋊Q₈	—	3	1	no	—
97	C₂×C₃×#126	—	3	4	no	—
98	C₂×C₃×#124	—	3	2	no	—
99	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
100	C₂×C₃×C₄×Q₈	—	3	2	no	—
101	C₂×C₃×C₄×Q₈	—	3	1	no	—
102	C₂×C₃×C₄×D₄	—	3	1	no	—
103	C₂×C₃×#117	—	3	2	no	—
104	#5732	C₂×C₃	1	1	yes	characteristic, complemented
105	D₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
106	D₃×#126	C₂×C₃	1	4	yes	complemented
107	#5702	C₂×C₃	1	4	yes	complemented
108	D₃×#124	C₂×C₃	1	2	yes	—
109	#5671	C₂×C₃	1	2	yes	complemented
110	#5641	C₂×C₃	1	2	yes	complemented
111	D₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
112	#5584	C₂×C₃	1	1	yes	characteristic, complemented
113	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
114	C₄×D₃×Q₈	C₂×C₃	1	2	yes	complemented
115	#5568	C₂×C₃	1	2	yes	complemented
116	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic
117	#5542	C₂×C₃	1	1	yes	characteristic, complemented
118	#5533	C₂×C₃	1	2	yes	complemented
119	D₃×#117	C₂×C₃	1	2	yes	complemented
120	C₂³×C₃×D₃	C₂³	1	2	yes	—
121	C₂×C₃²×Q₈	C₂³	1	2	yes	—
122	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
123	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
124	C₂²×C₃²×C₄	C₂³	1	2	yes	—
125	C₂×C₃×#67	C₂³	1	2	yes	—
126	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
127	C₃×D₃×Q₈	—	2	4	no	—
128	C₃×D₃×Q₈	—	2	8	no	—
129	C₃×D₃×D₄	—	2	4	no	—
130	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
131	C₂×C₃×C₄×D₃	—	2	8	no	—
132	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
134	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
135	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
136	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
137	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
138	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
139	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
141	C₂×C₃×Dic₆	C₂³	1	2	yes	—
142	C₂×C₃×Dic₆	C₂³	1	4	yes	—
143	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
144	C₂×C₃×Dic₆	C₂³	1	2	yes	—
145	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
149	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
150	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₃²×C₄²	C₂³	1	4	yes	—
155	C₃²×C₄²	C₂³	1	1	yes	characteristic
156	C₃²×C₄²	C₂³	1	2	yes	—
157	C₃×#217	C₂³	1	4	yes	—
158	C₃×#217	C₂³	1	4	yes	—
159	C₃×#217	C₂³	1	2	yes	—
160	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
161	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
162	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
163	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
164	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
165	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
166	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
167	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
168	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
169	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
170	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
171	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
172	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
173	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
174	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
175	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
176	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
177	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
178	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
179	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
180	C₃×C₄×Dic₃	C₂³	1	4	yes	—
181	C₃×C₄×Dic₃	C₂³	1	4	yes	—
182	C₃×C₄×Dic₃	C₂³	1	4	yes	—
183	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
184	C₃×C₄×Dic₃	C₂³	1	2	yes	—
185	C₃×C₄×Dic₃	C₂³	1	2	yes	—
186	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
187	C₃×C₄×Dic₃	C₂³	1	2	yes	—
188	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
189	C₂×#556	—	3	1	no	Sylow
190	C₂²×C₃×Q₈	—	3	1	no	—
191	C₂²×C₃×Q₈	—	3	2	no	—
192	C₂²×C₃×D₄	—	3	1	no	—
193	C₂³×C₃×C₄	—	3	2	no	—
194	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	—
195	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
196	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
197	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
198	C₃×C₄⋊Q₈	—	2	1	no	—
199	C₃×C₄⋊Q₈	—	3	2	no	—
200	C₃×C₄⋊Q₈	—	3	2	no	—
201	C₃×C₄⋊Q₈	—	3	2	no	—
202	C₃×C₄⋊Q₈	—	3	1	no	—
203	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
204	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
205	C₃×#126	—	2	4	no	—
206	C₃×#126	—	3	4	no	—
207	C₃×#126	—	3	4	no	—
208	C₃×#126	—	3	4	no	—
209	C₃×#126	—	3	4	no	—
210	C₃×#126	—	3	4	no	—
211	C₃×#126	—	3	4	no	—
212	C₃×#126	—	3	4	no	—
213	C₃×#126	C₂×D₃	1	4	yes	complemented
214	C₃×#126	C₂²×C₃	1	4	yes	complemented
215	C₃×#124	—	2	2	no	—
216	C₃×#124	—	3	2	no	—
217	C₃×#124	—	3	2	no	—
218	C₃×#124	—	3	4	no	—
219	C₃×#124	—	3	4	no	—
220	C₃×#124	—	3	2	no	—
221	C₃×#124	C₂×D₃	1	2	yes	—
222	C₃×#124	C₂²×C₃	1	2	yes	—
223	C₃×C₂²⋊Q₈	—	2	2	no	—
224	C₃×C₂²⋊Q₈	—	3	2	no	—
225	C₃×C₂²⋊Q₈	—	3	2	no	—
226	C₃×C₂²⋊Q₈	—	3	4	no	—
227	C₃×C₂²⋊Q₈	—	3	2	no	—
228	C₃×C₂²⋊Q₈	—	3	4	no	—
229	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
230	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
231	C₃×C₄×Q₈	—	2	2	no	—
232	C₃×C₄×Q₈	—	2	1	no	—
233	C₃×C₄×Q₈	—	3	2	no	—
234	C₃×C₄×Q₈	—	3	1	no	—
235	C₃×C₄×Q₈	—	3	4	no	—
236	C₃×C₄×Q₈	—	3	2	no	—
237	C₃×C₄×Q₈	—	3	2	no	—
238	C₃×C₄×Q₈	—	3	1	no	—
239	C₃×C₄×Q₈	—	3	2	no	—
240	C₃×C₄×Q₈	—	3	4	no	—
241	C₃×C₄×Q₈	—	3	2	no	—
242	C₃×C₄×Q₈	—	3	1	no	—
243	C₃×C₄×Q₈	C₂×D₃	1	2	yes	complemented
244	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
245	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
246	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
247	C₃×C₄×D₄	—	2	1	no	—
248	C₃×C₄×D₄	—	3	1	no	—
249	C₃×C₄×D₄	—	3	2	no	—
250	C₃×C₄×D₄	—	3	1	no	—
251	C₃×C₄×D₄	—	3	2	no	—
252	C₃×C₄×D₄	—	3	1	no	—
253	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
254	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
255	C₃×#117	—	2	2	no	—
256	C₃×#117	—	3	2	no	—
257	C₃×#117	—	3	2	no	—
258	C₃×#117	—	3	2	no	—
259	C₃×#117	—	3	4	no	—
260	C₃×#117	—	3	4	no	—
261	C₃×#117	C₂×D₃	1	2	yes	complemented
262	C₃×#117	C₂²×C₃	1	2	yes	complemented
263	C₂×C₃×C₄⋊C₄	—	3	1	no	—
264	C₂×C₃×C₄⋊C₄	—	3	2	no	—
265	C₂×C₃×C₄⋊C₄	—	3	1	no	—
266	C₂×C₃×C₄⋊C₄	—	3	4	no	—
267	C₂×C₃×C₄⋊C₄	—	3	2	no	—
268	C₂×C₃×C₄⋊C₄	—	3	2	no	—
269	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
270	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
271	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
272	C₂×C₃×C₄²	—	3	4	no	—
273	C₂×C₃×C₄²	—	3	1	no	—
274	C₂×C₃×C₄²	—	3	2	no	—
275	#947	C₂²×C₃	1	2	yes	—
276	#946	C₂²×C₃	1	2	yes	complemented
277	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
278	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
279	#944	C₂²×C₃	1	2	yes	complemented
280	#936	C₂²×C₃	1	2	yes	—
281	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
282	C₄×#67	C₂²×C₃	1	2	yes	—
283	#926	C₂²×C₃	1	2	yes	complemented
284	#924	C₂²×C₃	1	2	yes	complemented
285	#898	C₂²×C₃	1	4	yes	complemented
286	#898	C₂²×C₃	1	4	yes	complemented
287	#898	C₂²×C₃	1	4	yes	complemented
288	#897	C₂²×C₃	1	2	yes	complemented
289	#896	C₂²×C₃	1	4	yes	complemented
290	#893	C₂²×C₃	1	1	yes	characteristic
291	#892	C₂²×C₃	1	2	yes	complemented
292	#892	C₂²×C₃	1	2	yes	complemented
293	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
294	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
295	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
296	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
297	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
298	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
299	#888	C₂²×C₃	1	2	yes	complemented
300	#888	C₂²×C₃	1	2	yes	complemented
301	#887	C₂²×C₃	1	4	yes	complemented
302	#887	C₂²×C₃	1	2	yes	complemented
303	#887	C₂²×C₃	1	1	yes	characteristic, complemented
304	#887	C₂²×C₃	1	2	yes	complemented
305	#885	C₂²×C₃	1	4	yes	—
306	#885	C₂²×C₃	1	4	yes	—
307	#67⋊C₄	C₂²×C₃	1	2	yes	—
308	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
309	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
310	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
311	#879	C₂²×C₃	1	4	yes	complemented
312	#879	C₂²×C₃	1	4	yes	complemented
313	#879	C₂²×C₃	1	4	yes	complemented
314	#878	C₂²×C₃	1	4	yes	complemented
315	#877	C₂²×C₃	1	4	yes	complemented
316	#876	C₂²×C₃	1	4	yes	complemented
317	#875	C₂²×C₃	1	2	yes	—
318	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
319	#872	C₂²×C₃	1	4	yes	complemented
320	C₄²×D₃	C₂²×C₃	1	2	yes	—
321	C₄²×D₃	C₂²×C₃	1	4	yes	—
322	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
323	#869	C₂²×C₃	1	1	yes	characteristic, complemented
324	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
325	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
326	C₄×Dic₆	C₂²×C₃	1	4	yes	complemented
327	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
328	C₂³×C₃²	C₂⁴	1	2	yes	—
329	C₂²×C₃×D₃	—	2	4	no	—
330	C₂²×C₃×D₃	—	2	4	no	—
331	C₂²×C₃×D₃	—	2	4	no	—
332	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
333	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
334	C₃²×Q₈	—	2	4	no	—
335	C₃²×Q₈	—	2	2	no	—
336	C₃²×D₄	—	2	2	no	—
337	C₂×C₃²×C₄	—	2	4	no	—
338	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
339	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
340	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
341	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
342	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
343	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
344	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
345	C₃×#67	—	2	4	no	—
346	C₂×C₃×Dic₃	—	2	4	no	—
347	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
348	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
349	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
351	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
352	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
354	C₃×D₁₂	—	2	2	no	—
355	C₃×C₄×D₃	—	2	4	no	—
356	C₃×C₄×D₃	—	2	4	no	—
357	C₃×C₄×D₃	—	2	8	no	—
358	C₃×C₄×D₃	—	2	2	no	—
359	C₃×C₄×D₃	—	2	4	no	—
360	C₃×C₄×D₃	—	2	4	no	—
361	C₃×C₄×D₃	—	2	4	no	—
362	C₃×C₄×D₃	#41	1	4	yes	—
363	C₃×C₄×D₃	#41	1	4	yes	—
364	C₃×Dic₆	—	2	4	no	—
365	C₃×Dic₆	—	2	2	no	—
366	C₃×Dic₆	—	2	8	no	—
367	C₃×Dic₆	—	2	4	no	—
368	#556	—	3	1	no	—
369	#556	—	3	4	no	—
370	#556	—	3	2	no	—
371	#556	—	3	2	no	—
372	#556	—	3	2	no	—
373	#556	—	3	1	no	—
374	#556	—	3	1	no	—
375	#556	—	3	2	no	—
376	#556	C₃×D₃	1	1	yes	characteristic, direct product factor
377	C₂×C₄⋊Q₈	—	3	1	no	—
378	C₂×#126	—	3	4	no	—
379	C₂×#124	—	3	2	no	—
380	C₂×C₂²⋊Q₈	—	3	2	no	—
381	C₂×C₄×Q₈	—	3	2	no	—
382	C₂×C₄×Q₈	—	3	1	no	—
383	C₂×C₄×D₄	—	3	1	no	—
384	C₂×#117	—	3	2	no	—
385	C₂⁴×C₃	—	3	2	no	—
386	C₂³×D₃	C₂³×C₃	1	2	yes	—
387	C₂×C₃×Q₈	—	2	1	no	—
388	C₂×C₃×Q₈	—	2	2	no	—
389	C₂×C₃×Q₈	—	3	2	no	—
390	C₂×C₃×Q₈	—	3	1	no	—
391	C₂×C₃×Q₈	—	3	4	no	—
392	C₂×C₃×Q₈	—	3	2	no	—
393	C₂×C₃×Q₈	—	6	4	no	—
394	C₂×C₃×Q₈	—	6	8	no	—
395	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
396	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
397	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
398	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
399	C₂×C₃×D₄	—	2	1	no	—
400	C₂×C₃×D₄	—	3	2	no	—
401	C₂×C₃×D₄	—	3	1	no	—
402	C₂×C₃×D₄	—	6	4	no	—
403	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
404	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
405	C₂²×C₃×C₄	—	2	2	no	—
406	C₂²×C₃×C₄	—	3	1	no	—
407	C₂²×C₃×C₄	—	3	1	no	—
408	C₂²×C₃×C₄	—	3	2	no	—
409	C₂²×C₃×C₄	—	3	2	no	—
410	C₂²×C₃×C₄	—	3	2	no	—
411	C₂²×C₃×C₄	—	3	1	no	—
412	C₂²×C₃×C₄	—	3	4	no	—
413	C₂²×C₃×C₄	—	3	2	no	—
414	C₂²×C₃×C₄	—	3	2	no	—
415	C₂²×C₃×C₄	—	3	2	no	—
416	C₂²×C₃×C₄	—	6	8	no	—
417	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
418	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
419	C₂×#67	C₂³×C₃	1	2	yes	—
420	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
421	D₃×Q₈	—	2	4	no	—
422	D₃×Q₈	—	2	8	no	—
423	D₃×D₄	—	2	4	no	—
424	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₄×D₃	—	2	8	no	—
426	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
427	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
428	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
429	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
430	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
431	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
432	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
433	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
434	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
435	C₂×Dic₆	C₂³×C₃	1	2	yes	—
436	C₂×Dic₆	C₂³×C₃	1	2	yes	—
437	C₂×Dic₆	C₂³×C₃	1	4	yes	—
438	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
439	C₃×C₄⋊C₄	—	2	1	no	—
440	C₃×C₄⋊C₄	—	2	2	no	—
441	C₃×C₄⋊C₄	—	2	1	no	—
442	C₃×C₄⋊C₄	—	2	4	no	—
443	C₃×C₄⋊C₄	—	2	2	no	—
444	C₃×C₄⋊C₄	—	2	2	no	—
445	C₃×C₄⋊C₄	—	3	2	no	—
446	C₃×C₄⋊C₄	—	3	4	no	—
447	C₃×C₄⋊C₄	—	3	2	no	—
448	C₃×C₄⋊C₄	—	3	4	no	—
449	C₃×C₄⋊C₄	—	3	4	no	—
450	C₃×C₄⋊C₄	—	3	2	no	—
451	C₃×C₄⋊C₄	—	3	2	no	—
452	C₃×C₄⋊C₄	—	3	4	no	—
453	C₃×C₄⋊C₄	—	3	1	no	—
454	C₃×C₄⋊C₄	—	3	2	no	—
455	C₃×C₄⋊C₄	—	3	1	no	—
456	C₃×C₄⋊C₄	—	3	4	no	—
457	C₃×C₄⋊C₄	—	3	2	no	—
458	C₃×C₄⋊C₄	—	3	2	no	—
459	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
460	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
461	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
462	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
463	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
464	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
465	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
466	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
467	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
468	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
469	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
470	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
471	C₃×C₂²⋊C₄	—	2	4	no	—
472	C₃×C₂²⋊C₄	—	2	2	no	—
473	C₃×C₂²⋊C₄	—	2	4	no	—
474	C₃×C₂²⋊C₄	—	3	4	no	—
475	C₃×C₂²⋊C₄	—	3	2	no	—
476	C₃×C₂²⋊C₄	—	3	4	no	—
477	C₃×C₂²⋊C₄	—	3	4	no	—
478	C₃×C₂²⋊C₄	—	3	4	no	—
479	C₃×C₂²⋊C₄	—	3	2	no	—
480	C₃×C₂²⋊C₄	—	3	2	no	—
481	C₃×C₂²⋊C₄	—	3	4	no	—
482	C₃×C₂²⋊C₄	—	3	4	no	—
483	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
484	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
485	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
486	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
487	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
488	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
489	C₃×C₄²	—	2	4	no	—
490	C₃×C₄²	—	2	1	no	—
491	C₃×C₄²	—	2	2	no	—
492	C₃×C₄²	—	3	4	no	—
493	C₃×C₄²	—	3	4	no	—
494	C₃×C₄²	—	3	4	no	—
495	C₃×C₄²	—	3	1	no	—
496	C₃×C₄²	—	3	1	no	—
497	C₃×C₄²	—	3	1	no	—
498	C₃×C₄²	—	3	2	no	—
499	C₃×C₄²	—	3	2	no	—
500	C₃×C₄²	—	3	2	no	—
501	C₃×C₄²	C₂²×D₃	1	4	yes	—
502	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
503	C₃×C₄²	C₂²×D₃	1	2	yes	—
504	C₃×C₄²	C₂³×C₃	1	2	yes	—
505	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
506	C₃×C₄²	C₂³×C₃	1	4	yes	—
507	#217	C₂³×C₃	1	4	yes	—
508	#217	C₂³×C₃	1	4	yes	—
509	#217	C₂³×C₃	1	2	yes	—
510	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
511	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
512	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
513	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
514	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
515	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
516	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
517	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
518	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
519	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
520	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
521	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
522	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
523	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
524	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
525	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
526	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
527	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
528	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
529	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
530	C₄×Dic₃	C₂³×C₃	1	4	yes	—
531	C₄×Dic₃	C₂³×C₃	1	2	yes	—
532	C₄×Dic₃	C₂³×C₃	1	2	yes	—
533	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
534	C₄×Dic₃	C₂³×C₃	1	4	yes	—
535	C₄×Dic₃	C₂³×C₃	1	4	yes	—
536	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
537	C₄×Dic₃	C₂³×C₃	1	2	yes	—
538	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
539	C₂²×C₃²	—	2	2	no	—
540	C₂²×C₃²	—	2	2	no	—
541	C₂²×C₃²	—	2	2	no	—
542	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
543	C₂×C₃×D₃	—	2	2	no	—
544	C₂×C₃×D₃	—	2	2	no	—
545	C₂×C₃×D₃	—	2	2	no	—
546	C₂×C₃×D₃	—	4	8	no	—
547	C₂×C₃×D₃	C₂×#41	1	2	yes	—
548	C₂×C₃×D₃	C₂×#41	1	2	yes	—
549	C₂×C₃×D₃	2₋¹⁺⁴	1	2	yes	—
550	C₃²×C₄	—	2	4	no	—
551	C₃²×C₄	—	2	2	no	—
552	C₃²×C₄	—	2	2	no	—
553	C₃²×C₄	—	2	2	no	—
554	C₃²×C₄	—	2	1	no	—
555	C₃²×C₄	C₂×#41	1	2	yes	—
556	C₃²×C₄	C₂×#41	1	2	yes	—
557	C₃×Dic₃	—	2	4	no	—
558	C₃×Dic₃	—	2	2	no	—
559	C₃×Dic₃	—	2	2	no	—
560	C₃×Dic₃	—	2	2	no	—
561	C₃×Dic₃	—	2	1	no	—
562	C₃×Dic₃	C₂×#41	1	2	yes	—
563	C₃×Dic₃	C₂×#41	1	2	yes	—
564	C₂²×Q₈	—	3	1	no	—
565	C₂²×Q₈	—	3	2	no	—
566	C₂²×D₄	—	3	1	no	—
567	C₂³×C₄	—	3	2	no	—
568	C₄⋊Q₈	—	3	2	no	—
569	C₄⋊Q₈	—	3	2	no	—
570	C₄⋊Q₈	—	3	2	no	—
571	C₄⋊Q₈	—	3	1	no	—
572	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
573	#126	—	3	4	no	—
574	#126	—	3	4	no	—
575	#126	—	3	4	no	—
576	#126	—	3	4	no	—
577	#126	—	3	4	no	—
578	#126	—	3	4	no	—
579	#126	—	3	4	no	—
580	#126	C₂×C₃×D₃	1	4	yes	complemented
581	#124	—	3	2	no	—
582	#124	—	3	2	no	—
583	#124	—	3	4	no	—
584	#124	—	3	4	no	—
585	#124	—	3	2	no	—
586	#124	C₂×C₃×D₃	1	2	yes	—
587	C₂²⋊Q₈	—	3	2	no	—
588	C₂²⋊Q₈	—	3	2	no	—
589	C₂²⋊Q₈	—	3	4	no	—
590	C₂²⋊Q₈	—	3	2	no	—
591	C₂²⋊Q₈	—	3	4	no	—
592	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
593	C₄×Q₈	—	3	2	no	—
594	C₄×Q₈	—	3	1	no	—
595	C₄×Q₈	—	3	4	no	—
596	C₄×Q₈	—	3	2	no	—
597	C₄×Q₈	—	3	2	no	—
598	C₄×Q₈	—	3	1	no	—
599	C₄×Q₈	—	3	2	no	—
600	C₄×Q₈	—	3	4	no	—
601	C₄×Q₈	—	3	2	no	—
602	C₄×Q₈	—	3	1	no	—
603	C₄×Q₈	C₂×C₃×D₃	1	2	yes	complemented
604	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
605	C₄×D₄	—	3	1	no	—
606	C₄×D₄	—	3	2	no	—
607	C₄×D₄	—	3	1	no	—
608	C₄×D₄	—	3	2	no	—
609	C₄×D₄	—	3	1	no	—
610	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
611	#117	—	3	2	no	—
612	#117	—	3	2	no	—
613	#117	—	3	2	no	—
614	#117	—	3	4	no	—
615	#117	—	3	4	no	—
616	#117	C₂×C₃×D₃	1	2	yes	complemented
617	C₂×C₄⋊C₄	—	3	1	no	—
618	C₂×C₄⋊C₄	—	3	2	no	—
619	C₂×C₄⋊C₄	—	3	1	no	—
620	C₂×C₄⋊C₄	—	3	4	no	—
621	C₂×C₄⋊C₄	—	3	2	no	—
622	C₂×C₄⋊C₄	—	3	2	no	—
623	C₂×C₂²⋊C₄	—	3	4	no	—
624	C₂×C₂²⋊C₄	—	3	2	no	—
625	C₂×C₂²⋊C₄	—	3	4	no	—
626	C₂×C₄²	—	3	4	no	—
627	C₂×C₄²	—	3	1	no	—
628	C₂×C₄²	—	3	2	no	—
629	C₂³×C₃	—	2	2	no	—
630	C₂³×C₃	—	3	1	no	—
631	C₂³×C₃	—	3	2	no	—
632	C₂³×C₃	—	6	4	no	—
633	C₂³×C₃	—	6	4	no	—
634	C₂³×C₃	—	6	4	no	—
635	C₂³×C₃	C₂³×D₃	1	2	yes	—
636	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
637	C₂²×D₃	—	2	4	no	—
638	C₂²×D₃	—	2	4	no	—
639	C₂²×D₃	—	2	4	no	—
640	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
641	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
642	C₃×Q₈	—	2	2	no	—
643	C₃×Q₈	—	2	4	no	—
644	C₃×Q₈	—	2	4	no	—
645	C₃×Q₈	—	2	2	no	—
646	C₃×Q₈	—	4	2	no	—
647	C₃×Q₈	—	4	4	no	—
648	C₃×Q₈	—	6	4	no	—
649	C₃×Q₈	—	6	8	no	—
650	C₃×Q₈	—	6	2	no	—
651	C₃×Q₈	—	6	4	no	—
652	C₃×D₄	—	2	2	no	—
653	C₃×D₄	—	2	2	no	—
654	C₃×D₄	—	4	2	no	—
655	C₃×D₄	—	6	4	no	—
656	C₃×D₄	—	6	2	no	—
657	C₂×C₃×C₄	—	2	4	no	—
658	C₂×C₃×C₄	—	2	4	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	1	no	—
661	C₂×C₃×C₄	—	2	2	no	—
662	C₂×C₃×C₄	—	2	2	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	4	no	—
665	C₂×C₃×C₄	—	2	2	no	—
666	C₂×C₃×C₄	—	3	1	no	—
667	C₂×C₃×C₄	—	3	1	no	—
668	C₂×C₃×C₄	—	3	4	no	—
669	C₂×C₃×C₄	—	3	4	no	—
670	C₂×C₃×C₄	—	3	2	no	—
671	C₂×C₃×C₄	—	3	2	no	—
672	C₂×C₃×C₄	—	3	1	no	—
673	C₂×C₃×C₄	—	3	4	no	—
674	C₂×C₃×C₄	—	3	2	no	—
675	C₂×C₃×C₄	—	4	4	no	—
676	C₂×C₃×C₄	—	6	4	no	—
677	C₂×C₃×C₄	—	6	4	no	—
678	C₂×C₃×C₄	—	6	2	no	—
679	C₂×C₃×C₄	—	6	4	no	—
680	C₂×C₃×C₄	—	6	4	no	—
681	C₂×C₃×C₄	—	6	8	no	—
682	C₂×C₃×C₄	—	6	4	no	—
683	C₂×C₃×C₄	—	6	4	no	—
684	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
685	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
686	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
687	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
688	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
689	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
690	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
691	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
692	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
693	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
694	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
695	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
696	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
697	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
698	#67	—	2	4	no	—
699	C₂×Dic₃	—	2	4	no	—
700	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
701	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
702	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
703	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
704	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
705	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
706	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
707	D₁₂	—	2	2	no	—
708	C₄×D₃	—	2	4	no	—
709	C₄×D₃	—	2	4	no	—
710	C₄×D₃	—	2	8	no	—
711	C₄×D₃	—	2	4	no	—
712	C₄×D₃	—	2	2	no	—
713	C₄×D₃	—	2	4	no	—
714	C₄×D₃	—	2	4	no	—
715	C₄×D₃	C₃×#41	1	4	yes	—
716	C₄×D₃	C₃×#41	1	4	yes	—
717	Dic₆	—	2	4	no	—
718	Dic₆	—	2	2	no	—
719	Dic₆	—	2	8	no	—
720	Dic₆	—	2	4	no	—
721	C₂×C₃²	—	4	2	no	—
722	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
723	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
724	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
725	C₃×D₃	—	4	2	no	—
726	C₃×D₃	#556	1	4	yes	direct product factor
727	C₂⁴	—	3	2	no	—
728	C₂×Q₈	—	3	2	no	—
729	C₂×Q₈	—	3	1	no	—
730	C₂×Q₈	—	3	4	no	—
731	C₂×Q₈	—	3	2	no	—
732	C₂×Q₈	—	6	4	no	—
733	C₂×Q₈	—	6	8	no	—
734	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
735	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
736	C₂×D₄	—	3	2	no	—
737	C₂×D₄	—	3	1	no	—
738	C₂×D₄	—	6	4	no	—
739	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
740	C₂²×C₄	—	3	1	no	—
741	C₂²×C₄	—	3	1	no	—
742	C₂²×C₄	—	3	2	no	—
743	C₂²×C₄	—	3	2	no	—
744	C₂²×C₄	—	3	2	no	—
745	C₂²×C₄	—	3	1	no	—
746	C₂²×C₄	—	3	4	no	—
747	C₂²×C₄	—	3	2	no	—
748	C₂²×C₄	—	3	2	no	—
749	C₂²×C₄	—	3	2	no	—
750	C₂²×C₄	—	6	8	no	—
751	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
752	C₄⋊C₄	—	3	2	no	—
753	C₄⋊C₄	—	3	1	no	—
754	C₄⋊C₄	—	3	4	no	—
755	C₄⋊C₄	—	3	2	no	—
756	C₄⋊C₄	—	3	2	no	—
757	C₄⋊C₄	—	3	1	no	—
758	C₄⋊C₄	—	3	4	no	—
759	C₄⋊C₄	—	3	4	no	—
760	C₄⋊C₄	—	3	4	no	—
761	C₄⋊C₄	—	3	2	no	—
762	C₄⋊C₄	—	3	2	no	—
763	C₄⋊C₄	—	3	2	no	—
764	C₄⋊C₄	—	3	4	no	—
765	C₄⋊C₄	—	3	2	no	—
766	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
768	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
770	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
771	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
772	C₂²⋊C₄	—	3	4	no	—
773	C₂²⋊C₄	—	3	2	no	—
774	C₂²⋊C₄	—	3	4	no	—
775	C₂²⋊C₄	—	3	4	no	—
776	C₂²⋊C₄	—	3	4	no	—
777	C₂²⋊C₄	—	3	2	no	—
778	C₂²⋊C₄	—	3	2	no	—
779	C₂²⋊C₄	—	3	4	no	—
780	C₂²⋊C₄	—	3	4	no	—
781	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
782	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
783	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
784	C₄²	—	3	4	no	—
785	C₄²	—	3	4	no	—
786	C₄²	—	3	4	no	—
787	C₄²	—	3	1	no	—
788	C₄²	—	3	1	no	—
789	C₄²	—	3	1	no	—
790	C₄²	—	3	2	no	—
791	C₄²	—	3	2	no	—
792	C₄²	—	3	2	no	—
793	C₄²	C₂²×C₃×D₃	1	4	yes	—
794	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
795	C₄²	C₂²×C₃×D₃	1	2	yes	—
796	C₂²×C₃	—	2	2	no	—
797	C₂²×C₃	—	2	2	no	—
798	C₂²×C₃	—	2	2	no	—
799	C₂²×C₃	—	2	2	no	—
800	C₂²×C₃	—	2	2	no	—
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	1	no	—
803	C₂²×C₃	—	3	2	no	—
804	C₂²×C₃	—	3	2	no	—
805	C₂²×C₃	—	3	2	no	—
806	C₂²×C₃	—	4	2	no	—
807	C₂²×C₃	—	4	2	no	—
808	C₂²×C₃	—	4	2	no	—
809	C₂²×C₃	—	6	2	no	—
810	C₂²×C₃	—	6	2	no	—
811	C₂²×C₃	—	6	2	no	—
812	C₂²×C₃	—	12	8	no	—
813	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
814	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
815	C₂×D₃	—	2	2	no	—
816	C₂×D₃	—	2	2	no	—
817	C₂×D₃	—	2	2	no	—
818	C₂×D₃	—	4	8	no	—
819	C₂×D₃	C₂×C₃×#41	1	2	yes	—
820	C₂×D₃	C₂×C₃×#41	1	2	yes	—
821	C₂×D₃	C₃×2₋¹⁺⁴	1	2	yes	—
822	C₃×C₄	—	2	2	no	—
823	C₃×C₄	—	2	2	no	—
824	C₃×C₄	—	2	4	no	—
825	C₃×C₄	—	2	2	no	—
826	C₃×C₄	—	2	1	no	—
827	C₃×C₄	—	2	4	no	—
828	C₃×C₄	—	2	2	no	—
829	C₃×C₄	—	2	2	no	—
830	C₃×C₄	—	2	2	no	—
831	C₃×C₄	—	2	1	no	—
832	C₃×C₄	—	2	2	no	—
833	C₃×C₄	—	2	2	no	—
834	C₃×C₄	—	3	2	no	—
835	C₃×C₄	—	3	2	no	—
836	C₃×C₄	—	4	2	no	—
837	C₃×C₄	—	4	2	no	—
838	C₃×C₄	—	4	4	no	—
839	C₃×C₄	—	4	2	no	—
840	C₃×C₄	—	4	1	no	—
841	C₃×C₄	—	6	2	no	—
842	C₃×C₄	—	6	2	no	—
843	C₃×C₄	—	6	4	no	—
844	C₃×C₄	—	6	2	no	—
845	C₃×C₄	—	6	1	no	—
846	C₃×C₄	D₃×#41	1	2	yes	—
847	C₃×C₄	D₃×#41	1	2	yes	—
848	C₃×C₄	C₂×C₃×#41	1	2	yes	—
849	C₃×C₄	C₂×C₃×#41	1	2	yes	—
850	Dic₃	—	2	4	no	—
851	Dic₃	—	2	2	no	—
852	Dic₃	—	2	2	no	—
853	Dic₃	—	2	2	no	—
854	Dic₃	—	2	1	no	—
855	Dic₃	C₂×C₃×#41	1	2	yes	—
856	Dic₃	C₂×C₃×#41	1	2	yes	—
857	C₃²	C₂×#556	1	1	yes	characteristic, complemented, Sylow
858	C₂³	—	3	1	no	—
859	C₂³	—	3	2	no	—
860	C₂³	—	6	4	no	—
861	C₂³	—	6	4	no	—
862	C₂³	—	6	4	no	—
863	C₂³	C₂³×C₃×D₃	1	2	yes	—
864	Q₈	—	2	2	no	—
865	Q₈	—	2	4	no	—
866	Q₈	—	6	4	no	—
867	Q₈	—	6	8	no	—
868	Q₈	—	6	2	no	—
869	Q₈	—	6	4	no	—
870	D₄	—	2	2	no	—
871	D₄	—	6	4	no	—
872	D₄	—	6	2	no	—
873	C₂×C₄	—	2	4	no	—
874	C₂×C₄	—	3	1	no	—
875	C₂×C₄	—	3	1	no	—
876	C₂×C₄	—	3	4	no	—
877	C₂×C₄	—	3	4	no	—
878	C₂×C₄	—	3	2	no	—
879	C₂×C₄	—	3	2	no	—
880	C₂×C₄	—	3	1	no	—
881	C₂×C₄	—	3	4	no	—
882	C₂×C₄	—	3	2	no	—
883	C₂×C₄	—	6	4	no	—
884	C₂×C₄	—	6	4	no	—
885	C₂×C₄	—	6	4	no	—
886	C₂×C₄	—	6	8	no	—
887	C₂×C₄	—	6	4	no	—
888	C₂×C₄	—	6	2	no	—
889	C₂×C₄	—	6	4	no	—
890	C₂×C₄	—	6	4	no	—
891	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
892	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
893	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
894	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
895	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
896	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
897	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
898	C₂×C₃	—	2	1	no	—
899	C₂×C₃	—	2	1	no	—
900	C₂×C₃	—	2	1	no	—
901	C₂×C₃	—	3	4	no	—
902	C₂×C₃	—	4	2	no	—
903	C₂×C₃	—	4	2	no	—
904	C₂×C₃	—	8	2	no	—
905	C₂×C₃	—	12	2	no	—
906	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
907	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
908	C₂×C₃	D₃×2₋¹⁺⁴	1	1	yes	characteristic
909	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
910	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
911	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
912	D₃	—	4	2	no	—
913	D₃	C₃×#556	1	4	yes	direct product factor
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	3	2	no	—
918	C₂²	—	3	2	no	—
919	C₂²	—	3	2	no	—
920	C₂²	—	6	2	no	—
921	C₂²	—	6	2	no	—
922	C₂²	—	6	2	no	—
923	C₂²	—	12	8	no	—
924	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	4	no	—
928	C₄	—	2	2	no	—
929	C₄	—	2	1	no	—
930	C₄	—	3	2	no	—
931	C₄	—	3	2	no	—
932	C₄	—	6	2	no	—
933	C₄	—	6	2	no	—
934	C₄	—	6	4	no	—
935	C₄	—	6	2	no	—
936	C₄	—	6	1	no	—
937	C₄	C₃×D₃×#41	1	2	yes	—
938	C₄	C₃×D₃×#41	1	2	yes	—
939	C₃	—	2	1	no	—
940	C₃	D₃×#556	1	1	yes	characteristic, direct product factor
941	C₃	C₂×C₃×#556	1	1	yes	characteristic, complemented
942	C₂	—	3	4	no	—
943	C₂	—	4	2	no	—
944	C₂	—	12	2	no	—
945	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
946	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
947	C₂	C₃×D₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#556	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂×C₃×D₃×D₄	C₂²
hypercenter	C₃×#556	D₃
hypocenter	C₃	C₂×C₃×#556
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#556

Complements

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

N	H ≅ G/N	type
1. C₃²×#556	C₂	semidirect
2. C₃×#5732	C₂	semidirect
3. C₃×D₃×C₄⋊Q₈	C₂	semidirect
4. C₃×D₃×#126	C₂	semidirect
5. C₃×#5702	C₂	semidirect
7. C₃×#5671	C₂	semidirect
8. C₃×#5641	C₂	semidirect
9. C₃×D₃×C₂²⋊Q₈	C₂	semidirect
10. C₃×#5584	C₂	semidirect
11. C₃×C₄×D₃×Q₈	C₂	semidirect
12. C₃×C₄×D₃×Q₈	C₂	semidirect
13. C₃×#5568	C₂	semidirect
15. C₃×#5542	C₂	semidirect
16. C₃×#5533	C₂	semidirect
17. C₃×D₃×#117	C₂	semidirect
19. D₃×#556	C₃	direct (N × H)
24. C₃²×C₄⋊Q₈	C₂²	semidirect
25. C₃²×#126	C₂²	semidirect
27. C₃²×C₂²⋊Q₈	C₂²	semidirect
28. C₃²×C₄×Q₈	C₂²	semidirect
29. C₃²×C₄×Q₈	C₂²	semidirect
31. C₃²×#117	C₂²	semidirect
33. C₃×#946	C₂²	semidirect
34. C₃×Q₈×Dic₃	C₂²	semidirect
35. C₃×Q₈×Dic₃	C₂²	semidirect
36. C₃×#944	C₂²	semidirect
40. C₃×#926	C₂²	semidirect
41. C₃×#924	C₂²	semidirect
42. C₃×#898	C₂²	semidirect
43. C₃×#898	C₂²	semidirect
44. C₃×#898	C₂²	semidirect
45. C₃×#897	C₂²	semidirect
46. C₃×#896	C₂²	semidirect
48. C₃×#892	C₂²	semidirect
49. C₃×#892	C₂²	semidirect
56. C₃×#888	C₂²	semidirect
57. C₃×#888	C₂²	semidirect
58. C₃×#887	C₂²	semidirect
59. C₃×#887	C₂²	semidirect
60. C₃×#887	C₂²	semidirect
61. C₃×#887	C₂²	semidirect
68. C₃×#879	C₂²	semidirect
69. C₃×#879	C₂²	semidirect
70. C₃×#879	C₂²	semidirect
71. C₃×#878	C₂²	semidirect
72. C₃×#877	C₂²	semidirect
73. C₃×#876	C₂²	semidirect
76. C₃×#872	C₂²	semidirect
80. C₃×#869	C₂²	semidirect
81. C₃×C₄×Dic₆	C₂²	semidirect
82. C₃×C₄×Dic₆	C₂²	semidirect
83. C₃×C₄×Dic₆	C₂²	semidirect
84. C₃×C₄×Dic₆	C₂²	semidirect
94. C₃×#556	D₃	direct (N × H)
95. C₃×#556	C₂×C₃	semidirect
104. #5732	C₂×C₃	semidirect
105. D₃×C₄⋊Q₈	C₂×C₃	semidirect
106. D₃×#126	C₂×C₃	semidirect
107. #5702	C₂×C₃	semidirect
109. #5671	C₂×C₃	semidirect
110. #5641	C₂×C₃	semidirect
111. D₃×C₂²⋊Q₈	C₂×C₃	semidirect
112. #5584	C₂×C₃	semidirect
113. C₄×D₃×Q₈	C₂×C₃	semidirect
114. C₄×D₃×Q₈	C₂×C₃	semidirect
115. #5568	C₂×C₃	semidirect
117. #5542	C₂×C₃	semidirect
118. #5533	C₂×C₃	semidirect
119. D₃×#117	C₂×C₃	semidirect
203. C₃×C₄⋊Q₈	C₂×D₃	semidirect
204. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
213. C₃×#126	C₂×D₃	semidirect
214. C₃×#126	C₂²×C₃	semidirect
229. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
230. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
243. C₃×C₄×Q₈	C₂×D₃	semidirect
244. C₃×C₄×Q₈	C₂×D₃	semidirect
245. C₃×C₄×Q₈	C₂²×C₃	semidirect
246. C₃×C₄×Q₈	C₂²×C₃	semidirect
261. C₃×#117	C₂×D₃	semidirect
262. C₃×#117	C₂²×C₃	semidirect
276. #946	C₂²×C₃	semidirect
277. Q₈×Dic₃	C₂²×C₃	semidirect
278. Q₈×Dic₃	C₂²×C₃	semidirect
279. #944	C₂²×C₃	semidirect
283. #926	C₂²×C₃	semidirect
284. #924	C₂²×C₃	semidirect
285. #898	C₂²×C₃	semidirect
286. #898	C₂²×C₃	semidirect
287. #898	C₂²×C₃	semidirect
288. #897	C₂²×C₃	semidirect
289. #896	C₂²×C₃	semidirect
291. #892	C₂²×C₃	semidirect
292. #892	C₂²×C₃	semidirect
299. #888	C₂²×C₃	semidirect
300. #888	C₂²×C₃	semidirect
301. #887	C₂²×C₃	semidirect
302. #887	C₂²×C₃	semidirect
303. #887	C₂²×C₃	semidirect
304. #887	C₂²×C₃	semidirect
311. #879	C₂²×C₃	semidirect
312. #879	C₂²×C₃	semidirect
313. #879	C₂²×C₃	semidirect
314. #878	C₂²×C₃	semidirect
315. #877	C₂²×C₃	semidirect
316. #876	C₂²×C₃	semidirect
319. #872	C₂²×C₃	semidirect
323. #869	C₂²×C₃	semidirect
324. C₄×Dic₆	C₂²×C₃	semidirect
325. C₄×Dic₆	C₂²×C₃	semidirect
326. C₄×Dic₆	C₂²×C₃	semidirect
327. C₄×Dic₆	C₂²×C₃	semidirect
376. #556	C₃×D₃	direct (N × H)
572. C₄⋊Q₈	C₂×C₃×D₃	semidirect
580. #126	C₂×C₃×D₃	semidirect
592. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
603. C₄×Q₈	C₂×C₃×D₃	semidirect
604. C₄×Q₈	C₂×C₃×D₃	semidirect
616. #117	C₂×C₃×D₃	semidirect
726. C₃×D₃	#556	direct (N × H)
857. C₃²	C₂×#556	semidirect
913. D₃	C₃×#556	direct (N × H)
940. C₃	D₃×#556	direct (N × H)
941. C₃	C₂×C₃×#556	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#556	2
C₃×#5732	2
C₃×D₃×C₄⋊Q₈	2
C₃×D₃×#126	2
C₃×#5702	2
C₃×D₃×#124	2
C₃×#5671	2
C₃×#5641	2
C₃×D₃×C₂²⋊Q₈	2
C₃×#5584	2
C₃×C₄×D₃×Q₈	2
C₃×#5568	2
C₃×C₄×D₃×D₄	2
C₃×#5542	2
C₃×#5533	2
C₃×D₃×#117	2
C₂×C₃×#556	3
D₃×#556	3

Subgroups — C3×D3×#556 #11903349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#556 #11903349