Subgroups — C₃×#87025 #11909862

Order 1152.

2084 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5731	C₂	1	2	yes	maximal, complemented
3	C₃×#5728	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5727	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5727	C₂	1	2	yes	maximal, complemented
6	C₃×#5696	C₂	1	4	yes	maximal, complemented
7	C₃×#5693	C₂	1	4	yes	maximal, complemented
8	C₃×#5691	C₂	1	2	yes	maximal
9	C₃×#5685	C₂	1	2	yes	maximal, complemented
10	C₃×#5584	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5581	C₂	1	2	yes	maximal, complemented
12	C₃×#5580	C₂	1	1	yes	maximal, characteristic
13	C₃×#5578	C₂	1	2	yes	maximal, complemented
14	C₃×#5572	C₂	1	2	yes	maximal, complemented
15	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5568	C₂	1	2	yes	maximal, complemented
17	C₃×#5567	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3523	—	3	1	no	maximal
19	#87025	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	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₃²×#125	C₂²	1	2	yes	—
25	C₃²×#125	C₂²	1	4	yes	—
26	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
27	C₃²×C₄×Q₈	C₂²	1	2	yes	—
28	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
29	C₃²×C₄×Q₈	C₂²	1	2	yes	—
30	C₃×#947	C₂²	1	1	yes	characteristic
31	C₃×#946	C₂²	1	1	yes	characteristic
32	C₃×#946	C₂²	1	2	yes	—
33	C₃×#946	C₂²	1	2	yes	—
34	C₃×#946	C₂²	1	2	yes	—
35	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic
36	C₃×Q₈×Dic₃	C₂²	1	2	yes	—
37	C₃×#944	C₂²	1	2	yes	—
38	C₃×#898	C₂²	1	4	yes	—
39	C₃×#898	C₂²	1	2	yes	—
40	C₃×#898	C₂²	1	4	yes	—
41	C₃×#898	C₂²	1	4	yes	—
42	C₃×#897	C₂²	1	2	yes	—
43	C₃×#896	C₂²	1	4	yes	—
44	C₃×#896	C₂²	1	4	yes	—
45	C₃×#896	C₂²	1	4	yes	—
46	C₃×#895	C₂²	1	1	yes	characteristic
47	C₃×#894	C₂²	1	2	yes	—
48	C₃×#894	C₂²	1	4	yes	—
49	C₃×#893	C₂²	1	2	yes	—
50	C₃×#893	C₂²	1	4	yes	—
51	C₃×#892	C₂²	1	2	yes	—
52	C₃×#892	C₂²	1	4	yes	—
53	C₃×#892	C₂²	1	2	yes	—
54	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
56	C₃×#890	C₂²	1	1	yes	characteristic
57	C₃×#890	C₂²	1	2	yes	—
58	C₃×#889	C₂²	1	4	yes	—
59	C₃×#889	C₂²	1	4	yes	—
60	C₃×#889	C₂²	1	4	yes	—
61	C₃×#889	C₂²	1	4	yes	—
62	C₃×#888	C₂²	1	2	yes	—
63	C₃×#888	C₂²	1	4	yes	—
64	C₃×#887	C₂²	1	2	yes	—
65	C₃×#887	C₂²	1	2	yes	—
66	C₃×#887	C₂²	1	1	yes	characteristic
67	C₃×#887	C₂²	1	2	yes	—
68	C₃×#887	C₂²	1	4	yes	—
69	C₃×#876	C₂²	1	4	yes	—
70	C₃×#875	C₂²	1	2	yes	—
71	C₃×C₄×D₁₂	C₂²	1	2	yes	—
72	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
73	C₃×#872	C₂²	1	4	yes	—
74	C₃×#872	C₂²	1	2	yes	—
75	C₃×#872	C₂²	1	4	yes	—
76	C₃×C₄²×D₃	C₂²	1	2	yes	—
77	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
78	C₃×#870	C₂²	1	2	yes	—
79	C₃×#869	C₂²	1	1	yes	characteristic
80	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
81	C₃×C₄×Dic₆	C₂²	1	2	yes	—
82	C₃×C₄×Dic₆	C₂²	1	2	yes	—
83	C₃×C₄×Dic₆	C₂²	1	4	yes	—
84	C₃×C₄×Dic₆	C₂²	1	2	yes	—
85	C₃×#557	—	2	1	no	—
86	C₃×#557	—	3	2	no	—
87	C₃×#557	—	3	1	no	—
88	C₃×#557	D₃	1	1	yes	characteristic, complemented
89	C₃×#557	C₂×C₃	1	1	yes	characteristic, complemented
90	C₃×#556	—	3	2	no	—
91	C₃×#556	—	3	1	no	—
92	C₃×#552	—	3	4	no	—
93	C₃×#552	—	3	2	no	—
94	C₃×D₄×Q₈	—	3	2	no	—
95	C₃×D₄×Q₈	—	3	1	no	—
96	C₃×#541	—	3	2	no	—
97	C₃×#541	—	3	4	no	—
98	C₃×#533	—	3	1	no	—
99	C₃×#533	—	3	2	no	—
100	C₃×#529	—	3	2	no	—
101	C₃×#529	—	3	1	no	—
102	C₃×#519	—	3	2	no	—
103	C₂×C₃×C₄×Q₈	—	3	1	no	—
104	#5731	C₂×C₃	1	2	yes	complemented
105	#5728	C₂×C₃	1	1	yes	characteristic, complemented
106	#5727	C₂×C₃	1	1	yes	characteristic, complemented
107	#5727	C₂×C₃	1	2	yes	complemented
108	#5696	C₂×C₃	1	4	yes	complemented
109	#5693	C₂×C₃	1	4	yes	complemented
110	#5691	C₂×C₃	1	2	yes	—
111	#5685	C₂×C₃	1	2	yes	complemented
112	#5584	C₂×C₃	1	1	yes	characteristic, complemented
113	#5581	C₂×C₃	1	2	yes	complemented
114	#5580	C₂×C₃	1	1	yes	characteristic
115	#5578	C₂×C₃	1	2	yes	complemented
116	#5572	C₂×C₃	1	2	yes	complemented
117	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
118	#5568	C₂×C₃	1	2	yes	complemented
119	#5567	C₂×C₃	1	1	yes	characteristic, complemented
120	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
121	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
122	C₂×C₃²×Q₈	C₂³	1	2	yes	—
123	C₃×D₃×Q₈	—	2	4	no	—
124	C₃×D₃×Q₈	—	2	8	no	—
125	C₂×C₃×D₁₂	C₂³	1	2	yes	—
126	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
128	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
129	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
130	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
131	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
132	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
133	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
134	C₂×C₃×Dic₆	C₂³	1	2	yes	—
135	C₂×C₃×Dic₆	C₂³	1	2	yes	—
136	C₂×C₃×Dic₆	C₂³	1	4	yes	—
137	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
138	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
141	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
144	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
145	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
146	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
147	C₃²×C₄²	C₂³	1	2	yes	—
148	C₃²×C₄²	C₂³	1	4	yes	—
149	C₃²×C₄²	C₂³	1	1	yes	characteristic
150	C₃²×C₄²	C₂³	1	2	yes	—
151	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
152	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
153	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
154	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
155	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
156	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
157	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
158	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
159	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
160	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
161	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
162	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
163	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
164	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
165	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
166	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
167	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
168	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
169	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
170	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
171	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
176	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
177	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
178	C₃×C₄×Dic₃	C₂³	1	4	yes	—
179	C₃×C₄×Dic₃	C₂³	1	4	yes	—
180	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
181	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
182	C₃×C₄×Dic₃	C₂³	1	2	yes	—
183	C₃×C₄×Dic₃	C₂³	1	2	yes	—
184	C₃×C₄×Dic₃	C₂³	1	2	yes	—
185	C₃×C₄×Dic₃	C₂³	1	4	yes	—
186	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
187	#3523	—	3	1	no	Sylow
188	C₂²×C₃×Q₈	—	3	1	no	—
189	C₂²×C₃×Q₈	—	3	2	no	—
190	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
191	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	—
192	C₃×C₄⋊Q₈	—	2	1	no	—
193	C₃×C₄⋊Q₈	—	2	2	no	—
194	C₃×C₄⋊Q₈	—	3	2	no	—
195	C₃×C₄⋊Q₈	—	3	2	no	—
196	C₃×C₄⋊Q₈	—	3	4	no	—
197	C₃×C₄⋊Q₈	—	3	1	no	—
198	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
199	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	—
200	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
201	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
202	C₃×#126	—	3	2	no	—
203	C₃×#126	—	3	4	no	—
204	C₃×#126	—	3	4	no	—
205	C₃×#126	—	3	4	no	—
206	C₃×#126	—	3	4	no	—
207	C₃×#125	—	2	2	no	—
208	C₃×#125	—	2	4	no	—
209	C₃×#125	—	3	4	no	—
210	C₃×#125	—	3	4	no	—
211	C₃×#125	—	3	4	no	—
212	C₃×#125	—	3	4	no	—
213	C₃×#125	—	3	1	no	—
214	C₃×#125	—	3	2	no	—
215	C₃×#125	—	3	2	no	—
216	C₃×#125	C₂×D₃	1	2	yes	—
217	C₃×#125	C₂×D₃	1	4	yes	—
218	C₃×#125	C₂²×C₃	1	2	yes	—
219	C₃×#125	C₂²×C₃	1	4	yes	—
220	C₃×#124	—	3	1	no	—
221	C₃×#124	—	3	2	no	—
222	C₃×#123	—	3	2	no	—
223	C₃×#123	—	3	4	no	—
224	C₃×C₂²⋊Q₈	—	3	1	no	—
225	C₃×C₂²⋊Q₈	—	3	2	no	—
226	C₃×C₂²⋊Q₈	—	3	2	no	—
227	C₃×C₂²⋊Q₈	—	3	2	no	—
228	C₃×C₂²⋊Q₈	—	3	4	no	—
229	C₃×C₂²⋊Q₈	—	3	4	no	—
230	C₃×C₂²⋊Q₈	—	3	4	no	—
231	C₃×C₂²⋊Q₈	—	3	2	no	—
232	C₃×#121	—	3	1	no	—
233	C₃×C₄×Q₈	—	2	1	no	—
234	C₃×C₄×Q₈	—	2	2	no	—
235	C₃×C₄×Q₈	—	2	1	no	—
236	C₃×C₄×Q₈	—	2	2	no	—
237	C₃×C₄×Q₈	—	3	1	no	—
238	C₃×C₄×Q₈	—	3	2	no	—
239	C₃×C₄×Q₈	—	3	1	no	—
240	C₃×C₄×Q₈	—	3	2	no	—
241	C₃×C₄×Q₈	—	3	4	no	—
242	C₃×C₄×Q₈	—	3	2	no	—
243	C₃×C₄×Q₈	—	3	2	no	—
244	C₃×C₄×Q₈	—	3	1	no	—
245	C₃×C₄×Q₈	—	3	2	no	—
246	C₃×C₄×Q₈	—	3	4	no	—
247	C₃×C₄×Q₈	—	3	2	no	—
248	C₃×C₄×Q₈	—	3	2	no	—
249	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
250	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
251	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
252	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
253	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
254	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
255	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
256	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
257	C₃×C₄×D₄	—	3	4	no	—
258	C₃×C₄×D₄	—	3	2	no	—
259	C₃×C₄×D₄	—	3	2	no	—
260	C₃×C₄×D₄	—	3	1	no	—
261	C₃×#117	—	3	4	no	—
262	C₃×#117	—	3	2	no	—
263	C₃×#117	—	3	2	no	—
264	C₃×#117	—	3	2	no	—
265	C₃×#117	—	3	4	no	—
266	C₃×#117	—	3	4	no	—
267	C₂×C₃×C₄⋊C₄	—	3	2	no	—
268	C₂×C₃×C₄⋊C₄	—	3	1	no	—
269	C₂×C₃×C₄²	—	3	2	no	—
270	C₂×C₃×C₄²	—	3	1	no	—
271	#947	C₂²×C₃	1	1	yes	characteristic
272	#946	C₂²×C₃	1	2	yes	—
273	#946	C₂²×C₃	1	2	yes	—
274	#946	C₂²×C₃	1	2	yes	—
275	#946	C₂²×C₃	1	1	yes	characteristic
276	Q₈×Dic₃	C₂²×C₃	1	2	yes	—
277	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
278	#944	C₂²×C₃	1	2	yes	—
279	#898	C₂²×C₃	1	4	yes	—
280	#898	C₂²×C₃	1	4	yes	—
281	#898	C₂²×C₃	1	4	yes	—
282	#898	C₂²×C₃	1	2	yes	—
283	#897	C₂²×C₃	1	2	yes	—
284	#896	C₂²×C₃	1	4	yes	—
285	#896	C₂²×C₃	1	4	yes	—
286	#896	C₂²×C₃	1	4	yes	—
287	#895	C₂²×C₃	1	1	yes	characteristic
288	#894	C₂²×C₃	1	4	yes	—
289	#894	C₂²×C₃	1	2	yes	—
290	#893	C₂²×C₃	1	4	yes	—
291	#893	C₂²×C₃	1	2	yes	—
292	#892	C₂²×C₃	1	4	yes	—
293	#892	C₂²×C₃	1	2	yes	—
294	#892	C₂²×C₃	1	2	yes	—
295	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
296	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
297	#890	C₂²×C₃	1	1	yes	characteristic
298	#890	C₂²×C₃	1	2	yes	—
299	#889	C₂²×C₃	1	4	yes	—
300	#889	C₂²×C₃	1	4	yes	—
301	#889	C₂²×C₃	1	4	yes	—
302	#889	C₂²×C₃	1	4	yes	—
303	#888	C₂²×C₃	1	4	yes	—
304	#888	C₂²×C₃	1	2	yes	—
305	#887	C₂²×C₃	1	2	yes	—
306	#887	C₂²×C₃	1	4	yes	—
307	#887	C₂²×C₃	1	2	yes	—
308	#887	C₂²×C₃	1	2	yes	—
309	#887	C₂²×C₃	1	1	yes	characteristic
310	#876	C₂²×C₃	1	4	yes	—
311	#875	C₂²×C₃	1	2	yes	—
312	C₄×D₁₂	C₂²×C₃	1	2	yes	—
313	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
314	#872	C₂²×C₃	1	4	yes	—
315	#872	C₂²×C₃	1	4	yes	—
316	#872	C₂²×C₃	1	2	yes	—
317	C₄²×D₃	C₂²×C₃	1	2	yes	—
318	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
319	#870	C₂²×C₃	1	2	yes	—
320	#869	C₂²×C₃	1	1	yes	characteristic
321	C₄×Dic₆	C₂²×C₃	1	2	yes	—
322	C₄×Dic₆	C₂²×C₃	1	2	yes	—
323	C₄×Dic₆	C₂²×C₃	1	4	yes	—
324	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
325	C₄×Dic₆	C₂²×C₃	1	2	yes	—
326	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
327	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
328	C₃²×Q₈	—	2	2	no	—
329	C₃²×Q₈	—	2	2	no	—
330	C₃²×Q₈	—	2	4	no	—
331	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
332	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
333	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
334	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
335	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
336	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
337	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
338	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
339	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
341	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
342	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
343	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
345	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
346	C₃×D₁₂	—	2	4	no	—
347	C₃×D₁₂	—	2	2	no	—
348	C₃×C₄×D₃	—	2	2	no	—
349	C₃×C₄×D₃	—	2	4	no	—
350	C₃×C₄×D₃	—	2	2	no	—
351	C₃×C₄×D₃	—	2	4	no	—
352	C₃×C₄×D₃	—	2	2	no	—
353	C₃×C₄×D₃	—	2	4	no	—
354	C₃×C₄×D₃	—	2	8	no	—
355	C₃×Dic₆	—	2	4	no	—
356	C₃×Dic₆	—	2	4	no	—
357	C₃×Dic₆	—	2	8	no	—
358	C₃×Dic₆	#41	1	4	yes	—
359	#557	—	3	2	no	—
360	#557	—	3	1	no	—
361	#557	C₃×D₃	1	1	yes	characteristic, complemented
362	#556	—	3	2	no	—
363	#556	—	3	1	no	—
364	#552	—	3	4	no	—
365	#552	—	3	2	no	—
366	D₄×Q₈	—	3	2	no	—
367	D₄×Q₈	—	3	1	no	—
368	#541	—	3	2	no	—
369	#541	—	3	4	no	—
370	#533	—	3	1	no	—
371	#533	—	3	2	no	—
372	#529	—	3	2	no	—
373	#529	—	3	1	no	—
374	#519	—	3	2	no	—
375	C₂×C₄×Q₈	—	3	1	no	—
376	C₂×C₃×Q₈	—	2	1	no	—
377	C₂×C₃×Q₈	—	2	1	no	—
378	C₂×C₃×Q₈	—	2	2	no	—
379	C₂×C₃×Q₈	—	3	1	no	—
380	C₂×C₃×Q₈	—	3	2	no	—
381	C₂×C₃×Q₈	—	3	2	no	—
382	C₂×C₃×Q₈	—	3	4	no	—
383	C₂×C₃×Q₈	—	6	4	no	—
384	C₂×C₃×Q₈	—	6	8	no	—
385	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
386	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
387	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
388	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
389	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
390	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
391	C₂×C₃×D₄	—	3	2	no	—
392	C₂×C₃×D₄	—	3	1	no	—
393	C₂²×C₃×C₄	—	3	1	no	—
394	C₂²×C₃×C₄	—	3	1	no	—
395	C₂²×C₃×C₄	—	3	2	no	—
396	C₂²×C₃×C₄	—	3	2	no	—
397	C₂²×C₃×C₄	—	3	1	no	—
398	C₂²×C₃×C₄	—	3	4	no	—
399	C₂²×C₃×C₄	—	3	2	no	—
400	D₃×Q₈	—	2	4	no	—
401	D₃×Q₈	—	2	8	no	—
402	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
403	C₂×D₁₂	C₂³×C₃	1	2	yes	—
404	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
405	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
406	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
407	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
408	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
409	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
410	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
411	C₂×Dic₆	C₂³×C₃	1	2	yes	—
412	C₂×Dic₆	C₂³×C₃	1	2	yes	—
413	C₂×Dic₆	C₂³×C₃	1	4	yes	—
414	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
415	C₃×C₄⋊C₄	—	2	1	no	—
416	C₃×C₄⋊C₄	—	2	2	no	—
417	C₃×C₄⋊C₄	—	2	4	no	—
418	C₃×C₄⋊C₄	—	2	1	no	—
419	C₃×C₄⋊C₄	—	2	2	no	—
420	C₃×C₄⋊C₄	—	2	2	no	—
421	C₃×C₄⋊C₄	—	2	4	no	—
422	C₃×C₄⋊C₄	—	2	2	no	—
423	C₃×C₄⋊C₄	—	2	4	no	—
424	C₃×C₄⋊C₄	—	3	2	no	—
425	C₃×C₄⋊C₄	—	3	2	no	—
426	C₃×C₄⋊C₄	—	3	2	no	—
427	C₃×C₄⋊C₄	—	3	4	no	—
428	C₃×C₄⋊C₄	—	3	2	no	—
429	C₃×C₄⋊C₄	—	3	2	no	—
430	C₃×C₄⋊C₄	—	3	4	no	—
431	C₃×C₄⋊C₄	—	3	4	no	—
432	C₃×C₄⋊C₄	—	3	4	no	—
433	C₃×C₄⋊C₄	—	3	4	no	—
434	C₃×C₄⋊C₄	—	3	4	no	—
435	C₃×C₄⋊C₄	—	3	1	no	—
436	C₃×C₄⋊C₄	—	3	2	no	—
437	C₃×C₄⋊C₄	—	3	2	no	—
438	C₃×C₄⋊C₄	—	3	4	no	—
439	C₃×C₄⋊C₄	—	3	2	no	—
440	C₃×C₄⋊C₄	—	3	1	no	—
441	C₃×C₄⋊C₄	—	3	2	no	—
442	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
443	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
444	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
445	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
446	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
447	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
448	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
449	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
450	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
451	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
452	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
453	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
454	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
455	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
456	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
457	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
458	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
459	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
460	C₃×C₂²⋊C₄	—	3	2	no	—
461	C₃×C₂²⋊C₄	—	3	2	no	—
462	C₃×C₂²⋊C₄	—	3	4	no	—
463	C₃×C₂²⋊C₄	—	3	4	no	—
464	C₃×C₂²⋊C₄	—	3	2	no	—
465	C₃×C₂²⋊C₄	—	3	4	no	—
466	C₃×C₂²⋊C₄	—	3	2	no	—
467	C₃×C₂²⋊C₄	—	3	4	no	—
468	C₃×C₂²⋊C₄	—	3	2	no	—
469	C₃×C₄²	—	2	2	no	—
470	C₃×C₄²	—	2	4	no	—
471	C₃×C₄²	—	2	1	no	—
472	C₃×C₄²	—	2	2	no	—
473	C₃×C₄²	—	3	2	no	—
474	C₃×C₄²	—	3	1	no	—
475	C₃×C₄²	—	3	2	no	—
476	C₃×C₄²	—	3	1	no	—
477	C₃×C₄²	—	3	2	no	—
478	C₃×C₄²	—	3	1	no	—
479	C₃×C₄²	—	3	4	no	—
480	C₃×C₄²	—	3	4	no	—
481	C₃×C₄²	—	3	4	no	—
482	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
483	C₃×C₄²	C₂²×D₃	1	2	yes	—
484	C₃×C₄²	C₂²×D₃	1	4	yes	—
485	C₃×C₄²	C₂²×D₃	1	2	yes	—
486	C₃×C₄²	C₂³×C₃	1	2	yes	—
487	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
488	C₃×C₄²	C₂³×C₃	1	2	yes	—
489	C₃×C₄²	C₂³×C₃	1	4	yes	—
490	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
491	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
492	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
493	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
494	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
495	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
496	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
497	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
498	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
499	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
500	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
501	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
502	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
503	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
504	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
505	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
506	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
507	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
508	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
509	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
510	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
511	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
512	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
513	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
514	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
515	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
516	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
517	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
518	C₄×Dic₃	C₂³×C₃	1	2	yes	—
519	C₄×Dic₃	C₂³×C₃	1	2	yes	—
520	C₄×Dic₃	C₂³×C₃	1	4	yes	—
521	C₄×Dic₃	C₂³×C₃	1	4	yes	—
522	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
523	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
524	C₄×Dic₃	C₂³×C₃	1	2	yes	—
525	C₄×Dic₃	C₂³×C₃	1	4	yes	—
526	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
527	C₂×C₃×D₃	—	2	1	no	—
528	C₂×C₃×D₃	—	2	1	no	—
529	C₂×C₃×D₃	—	2	2	no	—
530	C₂×C₃×D₃	—	2	2	no	—
531	C₂×C₃×D₃	—	2	2	no	—
532	C₂×C₃×D₃	2₋¹⁺⁴	1	2	yes	—
533	C₃²×C₄	—	2	2	no	—
534	C₃²×C₄	—	2	2	no	—
535	C₃²×C₄	—	2	4	no	—
536	C₃²×C₄	—	2	2	no	—
537	C₃²×C₄	—	2	1	no	—
538	C₃²×C₄	—	2	2	no	—
539	C₃²×C₄	C₂×#41	1	2	yes	—
540	C₃²×C₄	2₋¹⁺⁴	1	2	yes	—
541	C₃×Dic₃	—	2	1	no	—
542	C₃×Dic₃	—	2	2	no	—
543	C₃×Dic₃	—	2	4	no	—
544	C₃×Dic₃	—	2	1	no	—
545	C₃×Dic₃	—	2	1	no	—
546	C₃×Dic₃	—	2	2	no	—
547	C₃×Dic₃	C₂×#41	1	4	yes	—
548	C₂²×Q₈	—	3	1	no	—
549	C₂²×Q₈	—	3	2	no	—
550	C₄⋊Q₈	—	3	2	no	—
551	C₄⋊Q₈	—	3	2	no	—
552	C₄⋊Q₈	—	3	4	no	—
553	C₄⋊Q₈	—	3	1	no	—
554	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
555	C₄⋊Q₈	C₂×C₃×D₃	1	2	yes	—
556	#126	—	3	2	no	—
557	#126	—	3	4	no	—
558	#126	—	3	4	no	—
559	#126	—	3	4	no	—
560	#126	—	3	4	no	—
561	#125	—	3	1	no	—
562	#125	—	3	4	no	—
563	#125	—	3	2	no	—
564	#125	—	3	4	no	—
565	#125	—	3	4	no	—
566	#125	—	3	4	no	—
567	#125	—	3	2	no	—
568	#125	C₂×C₃×D₃	1	2	yes	—
569	#125	C₂×C₃×D₃	1	4	yes	—
570	#124	—	3	1	no	—
571	#124	—	3	2	no	—
572	#123	—	3	2	no	—
573	#123	—	3	4	no	—
574	C₂²⋊Q₈	—	3	1	no	—
575	C₂²⋊Q₈	—	3	2	no	—
576	C₂²⋊Q₈	—	3	2	no	—
577	C₂²⋊Q₈	—	3	2	no	—
578	C₂²⋊Q₈	—	3	2	no	—
579	C₂²⋊Q₈	—	3	4	no	—
580	C₂²⋊Q₈	—	3	4	no	—
581	C₂²⋊Q₈	—	3	4	no	—
582	#121	—	3	1	no	—
583	C₄×Q₈	—	3	1	no	—
584	C₄×Q₈	—	3	2	no	—
585	C₄×Q₈	—	3	1	no	—
586	C₄×Q₈	—	3	2	no	—
587	C₄×Q₈	—	3	4	no	—
588	C₄×Q₈	—	3	2	no	—
589	C₄×Q₈	—	3	2	no	—
590	C₄×Q₈	—	3	1	no	—
591	C₄×Q₈	—	3	2	no	—
592	C₄×Q₈	—	3	4	no	—
593	C₄×Q₈	—	3	2	no	—
594	C₄×Q₈	—	3	2	no	—
595	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
596	C₄×Q₈	C₂×C₃×D₃	1	2	yes	—
597	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
598	C₄×Q₈	C₂×C₃×D₃	1	2	yes	—
599	C₄×D₄	—	3	4	no	—
600	C₄×D₄	—	3	2	no	—
601	C₄×D₄	—	3	2	no	—
602	C₄×D₄	—	3	1	no	—
603	#117	—	3	4	no	—
604	#117	—	3	2	no	—
605	#117	—	3	2	no	—
606	#117	—	3	2	no	—
607	#117	—	3	4	no	—
608	#117	—	3	4	no	—
609	C₂×C₄⋊C₄	—	3	2	no	—
610	C₂×C₄⋊C₄	—	3	1	no	—
611	C₂×C₄²	—	3	2	no	—
612	C₂×C₄²	—	3	1	no	—
613	C₂³×C₃	—	3	1	no	—
614	C₂³×C₃	—	3	2	no	—
615	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
616	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
617	C₃×Q₈	—	2	4	no	—
618	C₃×Q₈	—	2	2	no	—
619	C₃×Q₈	—	2	2	no	—
620	C₃×Q₈	—	2	4	no	—
621	C₃×Q₈	—	2	2	no	—
622	C₃×Q₈	—	2	4	no	—
623	C₃×Q₈	—	2	2	no	—
624	C₃×Q₈	—	3	4	no	—
625	C₃×Q₈	—	4	2	no	—
626	C₃×Q₈	—	4	4	no	—
627	C₃×Q₈	—	6	4	no	—
628	C₃×Q₈	—	6	8	no	—
629	C₃×Q₈	—	6	4	no	—
630	C₃×D₄	—	6	4	no	—
631	C₃×D₄	—	6	2	no	—
632	C₂×C₃×C₄	—	2	2	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	2	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	4	no	—
640	C₂×C₃×C₄	—	3	2	no	—
641	C₂×C₃×C₄	—	3	1	no	—
642	C₂×C₃×C₄	—	3	1	no	—
643	C₂×C₃×C₄	—	3	4	no	—
644	C₂×C₃×C₄	—	3	2	no	—
645	C₂×C₃×C₄	—	3	1	no	—
646	C₂×C₃×C₄	—	3	2	no	—
647	C₂×C₃×C₄	—	6	4	no	—
648	C₂×C₃×C₄	—	6	8	no	—
649	C₂×C₃×C₄	—	6	4	no	—
650	C₂×C₃×C₄	—	6	2	no	—
651	C₂×C₃×C₄	—	6	2	no	—
652	C₂×C₃×C₄	—	6	2	no	—
653	C₂×C₃×C₄	—	6	4	no	—
654	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
655	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
656	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
657	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
658	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
659	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
660	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
661	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
662	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
663	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
664	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
665	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
666	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
667	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
668	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
669	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
670	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
671	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
672	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
673	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
674	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
675	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
676	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
677	D₁₂	—	2	4	no	—
678	D₁₂	—	2	2	no	—
679	C₄×D₃	—	2	4	no	—
680	C₄×D₃	—	2	2	no	—
681	C₄×D₃	—	2	2	no	—
682	C₄×D₃	—	2	4	no	—
683	C₄×D₃	—	2	2	no	—
684	C₄×D₃	—	2	4	no	—
685	C₄×D₃	—	2	8	no	—
686	Dic₆	—	2	4	no	—
687	Dic₆	—	2	4	no	—
688	Dic₆	—	2	8	no	—
689	Dic₆	C₃×#41	1	4	yes	—
690	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
691	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
692	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
693	C₃×D₃	—	2	2	no	—
694	C₃×D₃	—	4	2	no	—
695	C₂×Q₈	—	3	1	no	—
696	C₂×Q₈	—	3	2	no	—
697	C₂×Q₈	—	3	2	no	—
698	C₂×Q₈	—	3	4	no	—
699	C₂×Q₈	—	6	4	no	—
700	C₂×Q₈	—	6	8	no	—
701	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
702	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
703	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
704	C₂×D₄	—	3	2	no	—
705	C₂×D₄	—	3	1	no	—
706	C₂²×C₄	—	3	1	no	—
707	C₂²×C₄	—	3	1	no	—
708	C₂²×C₄	—	3	2	no	—
709	C₂²×C₄	—	3	2	no	—
710	C₂²×C₄	—	3	1	no	—
711	C₂²×C₄	—	3	4	no	—
712	C₂²×C₄	—	3	2	no	—
713	C₄⋊C₄	—	3	2	no	—
714	C₄⋊C₄	—	3	2	no	—
715	C₄⋊C₄	—	3	1	no	—
716	C₄⋊C₄	—	3	2	no	—
717	C₄⋊C₄	—	3	2	no	—
718	C₄⋊C₄	—	3	4	no	—
719	C₄⋊C₄	—	3	2	no	—
720	C₄⋊C₄	—	3	2	no	—
721	C₄⋊C₄	—	3	4	no	—
722	C₄⋊C₄	—	3	2	no	—
723	C₄⋊C₄	—	3	4	no	—
724	C₄⋊C₄	—	3	4	no	—
725	C₄⋊C₄	—	3	2	no	—
726	C₄⋊C₄	—	3	1	no	—
727	C₄⋊C₄	—	3	2	no	—
728	C₄⋊C₄	—	3	4	no	—
729	C₄⋊C₄	—	3	4	no	—
730	C₄⋊C₄	—	3	4	no	—
731	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
733	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
734	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
735	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
736	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
737	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
739	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
740	C₂²⋊C₄	—	3	2	no	—
741	C₂²⋊C₄	—	3	2	no	—
742	C₂²⋊C₄	—	3	4	no	—
743	C₂²⋊C₄	—	3	4	no	—
744	C₂²⋊C₄	—	3	2	no	—
745	C₂²⋊C₄	—	3	4	no	—
746	C₂²⋊C₄	—	3	2	no	—
747	C₂²⋊C₄	—	3	4	no	—
748	C₂²⋊C₄	—	3	2	no	—
749	C₄²	—	3	2	no	—
750	C₄²	—	3	1	no	—
751	C₄²	—	3	2	no	—
752	C₄²	—	3	1	no	—
753	C₄²	—	3	2	no	—
754	C₄²	—	3	1	no	—
755	C₄²	—	3	4	no	—
756	C₄²	—	3	4	no	—
757	C₄²	—	3	4	no	—
758	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
759	C₄²	C₂²×C₃×D₃	1	2	yes	—
760	C₄²	C₂²×C₃×D₃	1	4	yes	—
761	C₄²	C₂²×C₃×D₃	1	2	yes	—
762	C₂²×C₃	—	2	1	no	—
763	C₂²×C₃	—	3	2	no	—
764	C₂²×C₃	—	6	1	no	—
765	C₂²×C₃	—	6	1	no	—
766	C₂²×C₃	—	6	2	no	—
767	C₂²×C₃	—	6	2	no	—
768	C₂²×C₃	—	6	2	no	—
769	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
770	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
771	C₂×D₃	—	2	1	no	—
772	C₂×D₃	—	2	1	no	—
773	C₂×D₃	—	2	2	no	—
774	C₂×D₃	—	2	2	no	—
775	C₂×D₃	—	2	2	no	—
776	C₂×D₃	C₃×2₋¹⁺⁴	1	2	yes	—
777	C₃×C₄	—	2	4	no	—
778	C₃×C₄	—	2	2	no	—
779	C₃×C₄	—	2	2	no	—
780	C₃×C₄	—	2	4	no	—
781	C₃×C₄	—	2	2	no	—
782	C₃×C₄	—	2	1	no	—
783	C₃×C₄	—	2	2	no	—
784	C₃×C₄	—	2	2	no	—
785	C₃×C₄	—	2	4	no	—
786	C₃×C₄	—	2	2	no	—
787	C₃×C₄	—	2	1	no	—
788	C₃×C₄	—	2	2	no	—
789	C₃×C₄	—	2	2	no	—
790	C₃×C₄	—	2	2	no	—
791	C₃×C₄	—	2	2	no	—
792	C₃×C₄	—	3	4	no	—
793	C₃×C₄	—	4	2	no	—
794	C₃×C₄	—	4	4	no	—
795	C₃×C₄	—	4	2	no	—
796	C₃×C₄	—	4	1	no	—
797	C₃×C₄	—	4	2	no	—
798	C₃×C₄	—	6	1	no	—
799	C₃×C₄	—	6	4	no	—
800	C₃×C₄	—	6	1	no	—
801	C₃×C₄	—	6	2	no	—
802	C₃×C₄	—	6	1	no	—
803	C₃×C₄	—	6	2	no	—
804	C₃×C₄	#1007	1	2	yes	—
805	C₃×C₄	D₃×#41	1	2	yes	—
806	C₃×C₄	C₂×C₃×#41	1	2	yes	—
807	C₃×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
808	Dic₃	—	2	1	no	—
809	Dic₃	—	2	2	no	—
810	Dic₃	—	2	4	no	—
811	Dic₃	—	2	1	no	—
812	Dic₃	—	2	1	no	—
813	Dic₃	—	2	2	no	—
814	Dic₃	C₂×C₃×#41	1	4	yes	—
815	C₃²	#3523	1	1	yes	characteristic, complemented, Sylow
816	C₂³	—	3	1	no	—
817	C₂³	—	3	2	no	—
818	Q₈	—	2	2	no	—
819	Q₈	—	2	2	no	—
820	Q₈	—	2	4	no	—
821	Q₈	—	3	4	no	—
822	Q₈	—	6	4	no	—
823	Q₈	—	6	8	no	—
824	Q₈	—	6	4	no	—
825	D₄	—	6	4	no	—
826	D₄	—	6	2	no	—
827	C₂×C₄	—	3	2	no	—
828	C₂×C₄	—	3	1	no	—
829	C₂×C₄	—	3	1	no	—
830	C₂×C₄	—	3	4	no	—
831	C₂×C₄	—	3	2	no	—
832	C₂×C₄	—	3	1	no	—
833	C₂×C₄	—	3	2	no	—
834	C₂×C₄	—	6	4	no	—
835	C₂×C₄	—	6	8	no	—
836	C₂×C₄	—	6	4	no	—
837	C₂×C₄	—	6	2	no	—
838	C₂×C₄	—	6	2	no	—
839	C₂×C₄	—	6	2	no	—
840	C₂×C₄	—	6	4	no	—
841	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
842	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
843	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
844	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
845	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
846	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
847	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
848	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
849	C₂×C₃	—	2	1	no	—
850	C₂×C₃	—	2	1	no	—
851	C₂×C₃	—	2	1	no	—
852	C₂×C₃	—	6	2	no	—
853	C₂×C₃	—	12	2	no	—
854	C₂×C₃	C₂×#1007	1	1	yes	characteristic
855	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
856	C₂×C₃	D₃×2₋¹⁺⁴	1	1	yes	characteristic
857	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
858	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
859	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
860	D₃	—	2	2	no	—
861	D₃	—	4	2	no	—
862	C₂²	—	3	2	no	—
863	C₂²	—	6	1	no	—
864	C₂²	—	6	1	no	—
865	C₂²	—	6	2	no	—
866	C₂²	—	6	2	no	—
867	C₂²	—	6	2	no	—
868	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	4	no	—
872	C₄	—	2	2	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	2	no	—
875	C₄	—	3	4	no	—
876	C₄	—	6	1	no	—
877	C₄	—	6	4	no	—
878	C₄	—	6	1	no	—
879	C₄	—	6	2	no	—
880	C₄	—	6	1	no	—
881	C₄	—	6	2	no	—
882	C₄	C₃×#1007	1	2	yes	—
883	C₄	C₃×D₃×#41	1	2	yes	—
884	C₃	—	2	1	no	—
885	C₃	#87025	1	1	yes	characteristic, direct product factor
886	C₃	C₃×#3523	1	1	yes	characteristic, complemented
887	C₂	—	6	2	no	—
888	C₂	—	12	2	no	—
889	C₂	C₂×C₃×#1007	1	1	yes	characteristic
890	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
891	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×#557	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₃×#895	C₂²
hypercenter	C₃×#557	D₃
hypocenter	C₃	C₃×#3523
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#557

Complements

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

N	H ≅ G/N	type
1. C₃²×#557	C₂	semidirect
2. C₃×#5731	C₂	semidirect
3. C₃×#5728	C₂	semidirect
4. C₃×#5727	C₂	semidirect
5. C₃×#5727	C₂	semidirect
6. C₃×#5696	C₂	semidirect
7. C₃×#5693	C₂	semidirect
9. C₃×#5685	C₂	semidirect
10. C₃×#5584	C₂	semidirect
11. C₃×#5581	C₂	semidirect
13. C₃×#5578	C₂	semidirect
14. C₃×#5572	C₂	semidirect
15. C₃×C₄×D₃×Q₈	C₂	semidirect
16. C₃×#5568	C₂	semidirect
17. C₃×#5567	C₂	semidirect
19. #87025	C₃	direct (N × H)
88. C₃×#557	D₃	semidirect
89. C₃×#557	C₂×C₃	semidirect
104. #5731	C₂×C₃	semidirect
105. #5728	C₂×C₃	semidirect
106. #5727	C₂×C₃	semidirect
107. #5727	C₂×C₃	semidirect
108. #5696	C₂×C₃	semidirect
109. #5693	C₂×C₃	semidirect
111. #5685	C₂×C₃	semidirect
112. #5584	C₂×C₃	semidirect
113. #5581	C₂×C₃	semidirect
115. #5578	C₂×C₃	semidirect
116. #5572	C₂×C₃	semidirect
117. C₄×D₃×Q₈	C₂×C₃	semidirect
118. #5568	C₂×C₃	semidirect
119. #5567	C₂×C₃	semidirect
361. #557	C₃×D₃	semidirect
815. C₃²	#3523	semidirect
885. C₃	#87025	direct (N × H)
886. C₃	C₃×#3523	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#557	2
C₃×#5731	2
C₃×#5728	2
C₃×#5727	2
C₃×#5696	2
C₃×#5693	2
C₃×#5691	2
C₃×#5685	2
C₃×#5584	2
C₃×#5581	2
C₃×#5580	2
C₃×#5578	2
C₃×#5572	2
C₃×C₄×D₃×Q₈	2
C₃×#5568	2
C₃×#5567	2
C₃×#3523	3
#87025	3

Subgroups — C3×#87025 #11909862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87025 #11909862