Subgroups — C₃×#86586 #11906324

Order 1152.

2223 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5729	C₂	1	2	yes	maximal, complemented
3	C₃×#5727	C₂	1	2	yes	maximal, complemented
4	C₃×D₃×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
5	C₃×#5722	C₂	1	2	yes	maximal, complemented
6	C₃×#5690	C₂	1	2	yes	maximal, complemented
7	C₃×#5689	C₂	1	2	yes	maximal, complemented
8	C₃×#5688	C₂	1	2	yes	maximal, complemented
9	C₃×#5685	C₂	1	2	yes	maximal, complemented
10	C₃×#5636	C₂	1	4	yes	maximal, complemented
11	C₃×#5632	C₂	1	4	yes	maximal, complemented
12	C₃×#5523	C₂	1	1	yes	maximal, characteristic
13	C₃×#5522	C₂	1	1	yes	maximal, characteristic
14	C₃×#5519	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#5517	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5504	C₂	1	1	yes	maximal, characteristic
17	C₂×C₃×#888	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3503	—	3	1	no	maximal
19	#86586	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃×D₃×Q₈	C₂²	1	4	yes	—
21	C₂×C₃×#235	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
23	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₃²×C₄⋊Q₈	C₂²	1	2	yes	—
25	C₃²×#125	C₂²	1	2	yes	—
26	C₃²×#125	C₂²	1	2	yes	—
27	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
28	C₃²×#117	C₂²	1	1	yes	characteristic
29	C₃²×#117	C₂²	1	1	yes	characteristic
30	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×#946	C₂²	1	4	yes	—
32	C₃×#944	C₂²	1	4	yes	—
33	C₃×#944	C₂²	1	4	yes	—
34	C₃×C₄×#67	C₂²	1	4	yes	—
35	C₃×#926	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
38	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×#897	C₂²	1	4	yes	—
40	C₃×#896	C₂²	1	4	yes	—
41	C₃×#896	C₂²	1	4	yes	—
42	C₃×#896	C₂²	1	4	yes	—
43	C₃×#896	C₂²	1	4	yes	—
44	C₃×#893	C₂²	1	2	yes	—
45	C₃×#893	C₂²	1	1	yes	characteristic
46	C₃×#893	C₂²	1	1	yes	characteristic
47	C₃×#892	C₂²	1	2	yes	—
48	C₃×#892	C₂²	1	2	yes	—
49	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
50	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
51	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
52	C₃×#890	C₂²	1	1	yes	characteristic
53	C₃×#890	C₂²	1	1	yes	characteristic
54	C₃×#890	C₂²	1	2	yes	—
55	C₃×#889	C₂²	1	4	yes	—
56	C₃×#889	C₂²	1	4	yes	—
57	C₃×#888	C₂²	1	2	yes	—
58	C₃×#888	C₂²	1	2	yes	—
59	C₃×#888	C₂²	1	2	yes	—
60	C₃×#888	C₂²	1	2	yes	—
61	C₃×#888	C₂²	1	1	yes	characteristic
62	C₃×#888	C₂²	1	1	yes	characteristic
63	C₃×#888	C₂²	1	2	yes	—
64	C₃×#888	C₂²	1	4	yes	—
65	C₃×#888	C₂²	1	4	yes	—
66	C₃×#887	C₂²	1	2	yes	—
67	C₃×#887	C₂²	1	1	yes	characteristic
68	C₃×#887	C₂²	1	1	yes	characteristic
69	C₃×#887	C₂²	1	4	yes	—
70	C₃×#887	C₂²	1	4	yes	—
71	C₃×#67⋊C₄	C₂²	1	2	yes	—
72	C₃×#67⋊C₄	C₂²	1	2	yes	—
73	C₃×#67⋊C₄	C₂²	1	4	yes	—
74	C₃×#878	C₂²	1	2	yes	—
75	C₃×#878	C₂²	1	2	yes	—
76	C₃×#878	C₂²	1	4	yes	—
77	C₃×C₄×D₁₂	C₂²	1	2	yes	—
78	C₃×#872	C₂²	1	2	yes	—
79	C₃×C₄²×D₃	C₂²	1	2	yes	—
80	C₃×#870	C₂²	1	2	yes	—
81	C₃×#869	C₂²	1	2	yes	—
82	C₃×C₄×Dic₆	C₂²	1	2	yes	—
83	C₃×C₄×Dic₆	C₂²	1	2	yes	—
84	C₃×C₄×Dic₆	C₂²	1	2	yes	—
85	C₃×Q₈²	—	3	2	no	—
86	C₃×#557	—	3	2	no	—
87	C₃×#554	—	3	2	no	—
88	C₃×#554	—	3	4	no	—
89	C₃×D₄×Q₈	—	3	2	no	—
90	C₃×D₄×Q₈	—	3	4	no	—
91	C₃×#544	—	2	1	no	—
92	C₃×#544	—	3	2	no	—
93	C₃×#544	—	3	2	no	—
94	C₃×#544	—	3	1	no	—
95	C₃×#544	D₃	1	1	yes	characteristic, complemented
96	C₃×#544	C₂×C₃	1	1	yes	characteristic, complemented
97	C₃×#533	—	3	2	no	—
98	C₃×#533	—	3	1	no	—
99	C₂×C₃×C₄⋊Q₈	—	3	2	no	—
100	C₂×C₃×C₄⋊Q₈	—	3	1	no	—
101	C₃×#520	—	3	1	no	—
102	C₃×#520	—	3	1	no	—
103	C₃×C₄×#41	—	3	1	no	—
104	#5729	C₂×C₃	1	2	yes	complemented
105	#5727	C₂×C₃	1	2	yes	complemented
106	D₃×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
107	#5722	C₂×C₃	1	2	yes	complemented
108	#5690	C₂×C₃	1	2	yes	complemented
109	#5689	C₂×C₃	1	2	yes	complemented
110	#5688	C₂×C₃	1	2	yes	complemented
111	#5685	C₂×C₃	1	2	yes	complemented
112	#5636	C₂×C₃	1	4	yes	complemented
113	#5632	C₂×C₃	1	4	yes	complemented
114	#5523	C₂×C₃	1	1	yes	characteristic
115	#5522	C₂×C₃	1	1	yes	characteristic
116	#5519	C₂×C₃	1	1	yes	characteristic, complemented
117	#5517	C₂×C₃	1	1	yes	characteristic, complemented
118	#5504	C₂×C₃	1	1	yes	characteristic
119	C₂×#888	C₂×C₃	1	1	yes	characteristic, complemented
120	C₂×C₃²×Q₈	C₂³	1	4	yes	—
121	C₂²×C₃²×C₄	C₂³	1	2	yes	—
122	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
123	C₂×C₃×#67	C₂³	1	2	yes	—
124	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
125	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
126	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
127	C₃×D₃×Q₈	—	4	8	no	—
128	C₃×#235	Q₈	1	8	yes	complemented
129	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
131	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
132	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
133	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
134	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
135	C₂×C₃×Dic₆	—	4	4	no	—
136	C₂×C₃×Dic₆	C₂³	1	2	yes	—
137	C₂×C₃×Dic₆	C₂³	1	2	yes	—
138	C₂×C₃×Dic₆	C₂³	1	4	yes	—
139	C₂×C₃×Dic₆	C₂³	1	4	yes	—
140	C₂×C₃×Dic₆	C₂³	1	4	yes	—
141	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
142	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
145	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
146	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
149	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃²×C₄²	C₂³	1	2	yes	—
154	C₃²×C₄²	C₂³	1	2	yes	—
155	C₃×#217	C₂³	1	2	yes	—
156	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	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	4	yes	—
160	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
161	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
162	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
163	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
164	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
165	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
166	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
167	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
168	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
169	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
170	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
171	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
172	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
173	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
174	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
175	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
176	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
177	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
178	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
179	C₃×C₄×Dic₃	C₂³	1	2	yes	—
180	C₃×C₄×Dic₃	C₂³	1	2	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	1	yes	characteristic
185	C₃×C₄×Dic₃	C₂³	1	2	yes	—
186	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
187	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
188	#3503	—	3	1	no	Sylow
189	C₂×C₃×#41	—	3	1	no	—
190	C₂²×C₃×Q₈	—	3	4	no	—
191	C₂²×C₃×Q₈	—	3	2	no	—
192	C₂×D₃×Q₈	C₂²×C₃	1	4	yes	—
193	C₂×#235	C₂²×C₃	1	1	yes	characteristic
194	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
195	C₃×C₄⋊Q₈	—	2	2	no	—
196	C₃×C₄⋊Q₈	—	2	2	no	—
197	C₃×C₄⋊Q₈	—	3	4	no	—
198	C₃×C₄⋊Q₈	—	3	4	no	—
199	C₃×C₄⋊Q₈	—	3	2	no	—
200	C₃×C₄⋊Q₈	—	3	4	no	—
201	C₃×C₄⋊Q₈	—	3	2	no	—
202	C₃×C₄⋊Q₈	—	3	1	no	—
203	C₃×C₄⋊Q₈	—	3	2	no	—
204	C₃×C₄⋊Q₈	—	3	2	no	—
205	C₃×C₄⋊Q₈	—	3	4	no	—
206	C₃×C₄⋊Q₈	—	3	2	no	—
207	C₃×C₄⋊Q₈	—	3	1	no	—
208	C₃×C₄⋊Q₈	—	3	2	no	—
209	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	—
210	C₃×C₄⋊Q₈	C₂×D₃	1	2	yes	—
211	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
212	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
213	C₃×#125	—	2	2	no	—
214	C₃×#125	—	2	2	no	—
215	C₃×#125	—	3	4	no	—
216	C₃×#125	—	3	4	no	—
217	C₃×#125	—	3	1	no	—
218	C₃×#125	—	3	1	no	—
219	C₃×#125	—	3	2	no	—
220	C₃×#125	—	3	2	no	—
221	C₃×#125	C₂×D₃	1	2	yes	—
222	C₃×#125	C₂×D₃	1	2	yes	—
223	C₃×#125	C₂²×C₃	1	2	yes	—
224	C₃×#125	C₂²×C₃	1	2	yes	—
225	C₃×C₂²⋊Q₈	—	2	4	no	—
226	C₃×C₂²⋊Q₈	—	3	4	no	—
227	C₃×C₂²⋊Q₈	—	3	4	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	4	no	—
232	C₃×C₂²⋊Q₈	—	3	2	no	—
233	C₃×C₂²⋊Q₈	—	3	2	no	—
234	C₃×C₂²⋊Q₈	—	3	4	no	—
235	C₃×C₂²⋊Q₈	C₂×D₃	1	4	yes	—
236	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
237	C₃×C₄×Q₈	—	3	1	no	—
238	C₃×C₄×Q₈	—	3	2	no	—
239	C₃×C₄×Q₈	—	3	4	no	—
240	C₃×C₄×Q₈	—	3	1	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	2	no	—
245	C₃×C₄×D₄	—	3	4	no	—
246	C₃×C₄×D₄	—	3	1	no	—
247	C₃×C₄×D₄	—	3	1	no	—
248	C₃×C₄×D₄	—	3	2	no	—
249	C₃×C₄×D₄	—	3	2	no	—
250	C₃×C₄×D₄	—	3	2	no	—
251	C₃×C₄×D₄	—	3	4	no	—
252	C₃×C₄×D₄	—	3	2	no	—
253	C₃×#117	—	2	1	no	—
254	C₃×#117	—	2	1	no	—
255	C₃×#117	—	3	1	no	—
256	C₃×#117	—	3	2	no	—
257	C₃×#117	—	3	2	no	—
258	C₃×#117	—	3	2	no	—
259	C₃×#117	C₂×D₃	1	1	yes	characteristic
260	C₃×#117	C₂×D₃	1	1	yes	characteristic
261	C₃×#117	C₂²×C₃	1	1	yes	characteristic
262	C₃×#117	C₂²×C₃	1	1	yes	characteristic
263	C₂×C₃×C₄⋊C₄	—	2	1	no	—
264	C₂×C₃×C₄⋊C₄	—	3	2	no	—
265	C₂×C₃×C₄⋊C₄	—	3	1	no	—
266	C₂×C₃×C₄⋊C₄	—	3	2	no	—
267	C₂×C₃×C₄⋊C₄	—	3	2	no	—
268	C₂×C₃×C₄⋊C₄	—	3	4	no	—
269	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
270	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
271	C₂×C₃×C₄²	—	3	1	no	—
272	C₂×C₃×C₄²	—	3	2	no	—
273	#946	C₂²×C₃	1	4	yes	—
274	#944	C₂²×C₃	1	4	yes	—
275	#944	C₂²×C₃	1	4	yes	—
276	C₄×#67	C₂²×C₃	1	4	yes	—
277	#926	C₂²×C₃	1	1	yes	characteristic
278	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
279	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
280	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
281	#897	C₂²×C₃	1	4	yes	—
282	#896	C₂²×C₃	1	4	yes	—
283	#896	C₂²×C₃	1	4	yes	—
284	#896	C₂²×C₃	1	4	yes	—
285	#896	C₂²×C₃	1	4	yes	—
286	#893	C₂²×C₃	1	1	yes	characteristic
287	#893	C₂²×C₃	1	2	yes	—
288	#893	C₂²×C₃	1	1	yes	characteristic
289	#892	C₂²×C₃	1	2	yes	—
290	#892	C₂²×C₃	1	2	yes	—
291	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
292	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
293	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
294	#890	C₂²×C₃	1	2	yes	—
295	#890	C₂²×C₃	1	1	yes	characteristic
296	#890	C₂²×C₃	1	1	yes	characteristic
297	#889	C₂²×C₃	1	4	yes	—
298	#889	C₂²×C₃	1	4	yes	—
299	#888	C₂²×C₃	1	4	yes	—
300	#888	C₂²×C₃	1	4	yes	—
301	#888	C₂²×C₃	1	2	yes	—
302	#888	C₂²×C₃	1	1	yes	characteristic
303	#888	C₂²×C₃	1	2	yes	—
304	#888	C₂²×C₃	1	2	yes	—
305	#888	C₂²×C₃	1	2	yes	—
306	#888	C₂²×C₃	1	2	yes	—
307	#888	C₂²×C₃	1	1	yes	characteristic
308	#887	C₂²×C₃	1	4	yes	—
309	#887	C₂²×C₃	1	4	yes	—
310	#887	C₂²×C₃	1	1	yes	characteristic
311	#887	C₂²×C₃	1	2	yes	—
312	#887	C₂²×C₃	1	1	yes	characteristic
313	#67⋊C₄	C₂²×C₃	1	2	yes	—
314	#67⋊C₄	C₂²×C₃	1	4	yes	—
315	#67⋊C₄	C₂²×C₃	1	2	yes	—
316	#878	C₂²×C₃	1	2	yes	—
317	#878	C₂²×C₃	1	4	yes	—
318	#878	C₂²×C₃	1	2	yes	—
319	C₄×D₁₂	C₂²×C₃	1	2	yes	—
320	#872	C₂²×C₃	1	2	yes	—
321	C₄²×D₃	C₂²×C₃	1	2	yes	—
322	#870	C₂²×C₃	1	2	yes	—
323	#869	C₂²×C₃	1	2	yes	—
324	C₄×Dic₆	C₂²×C₃	1	2	yes	—
325	C₄×Dic₆	C₂²×C₃	1	2	yes	—
326	C₄×Dic₆	C₂²×C₃	1	2	yes	—
327	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
328	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
329	C₃²×Q₈	—	4	4	no	—
330	C₂×C₃²×C₄	—	4	2	no	—
331	C₂×C₃²×C₄	C₂×Q₈	1	4	yes	complemented
332	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
333	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
334	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
335	C₂×C₃²×C₄	C₂⁴	1	4	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	C₃×#67	C₂×Q₈	1	8	yes	complemented
340	C₂×C₃×Dic₃	—	2	2	no	—
341	C₂×C₃×Dic₃	—	2	2	no	—
342	C₂×C₃×Dic₃	—	4	2	no	—
343	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
344	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
346	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
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	1	yes	characteristic
351	C₃×D₁₂	C₂×Q₈	1	4	yes	complemented
352	C₃×C₄×D₃	—	2	4	no	—
353	C₃×C₄×D₃	—	2	4	no	—
354	C₃×C₄×D₃	—	4	4	no	—
355	C₃×C₄×D₃	—	4	4	no	—
356	C₃×C₄×D₃	C₂×Q₈	1	8	yes	complemented
357	C₃×Dic₆	—	2	8	no	—
358	C₃×Dic₆	—	2	4	no	—
359	C₃×Dic₆	—	2	4	no	—
360	C₃×Dic₆	—	4	4	no	—
361	C₃×Dic₆	—	4	4	no	—
362	C₃×Dic₆	C₂×Q₈	1	4	yes	complemented
363	Q₈²	—	3	2	no	—
364	#557	—	3	2	no	—
365	#554	—	3	2	no	—
366	#554	—	3	4	no	—
367	D₄×Q₈	—	3	2	no	—
368	D₄×Q₈	—	3	4	no	—
369	#544	—	3	2	no	—
370	#544	—	3	2	no	—
371	#544	—	3	1	no	—
372	#544	C₃×D₃	1	1	yes	characteristic, complemented
373	#533	—	3	2	no	—
374	#533	—	3	1	no	—
375	C₂×C₄⋊Q₈	—	3	2	no	—
376	C₂×C₄⋊Q₈	—	3	1	no	—
377	#520	—	3	1	no	—
378	#520	—	3	1	no	—
379	C₄×#41	—	3	1	no	—
380	C₃×#41	—	3	8	no	—
381	C₂×C₃×Q₈	—	2	4	no	—
382	C₂×C₃×Q₈	—	3	1	no	—
383	C₂×C₃×Q₈	—	3	2	no	—
384	C₂×C₃×Q₈	—	3	4	no	—
385	C₂×C₃×Q₈	—	3	2	no	—
386	C₂×C₃×Q₈	—	3	4	no	—
387	C₂×C₃×Q₈	—	3	4	no	—
388	C₂×C₃×Q₈	—	12	4	no	—
389	C₂×C₃×Q₈	—	12	8	no	—
390	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
391	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
392	C₂×C₃×D₄	—	3	2	no	—
393	C₂×C₃×D₄	—	3	1	no	—
394	C₂²×C₃×C₄	—	2	1	no	—
395	C₂²×C₃×C₄	—	2	2	no	—
396	C₂²×C₃×C₄	—	3	2	no	—
397	C₂²×C₃×C₄	—	3	1	no	—
398	C₂²×C₃×C₄	—	3	1	no	—
399	C₂²×C₃×C₄	—	3	2	no	—
400	C₂²×C₃×C₄	—	3	2	no	—
401	C₂²×C₃×C₄	—	3	2	no	—
402	C₂²×C₃×C₄	—	3	4	no	—
403	C₂²×C₃×C₄	—	3	4	no	—
404	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
405	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
406	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
407	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
408	C₂×#67	C₂³×C₃	1	2	yes	—
409	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
410	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
411	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
412	D₃×Q₈	—	4	8	no	—
413	#235	C₃×Q₈	1	8	yes	complemented
414	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
415	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
416	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
417	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
418	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
419	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
420	C₂×Dic₆	—	4	4	no	—
421	C₂×Dic₆	C₂³×C₃	1	2	yes	—
422	C₂×Dic₆	C₂³×C₃	1	2	yes	—
423	C₂×Dic₆	C₂³×C₃	1	4	yes	—
424	C₂×Dic₆	C₂³×C₃	1	4	yes	—
425	C₂×Dic₆	C₂³×C₃	1	4	yes	—
426	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
427	C₃×C₄⋊C₄	—	2	2	no	—
428	C₃×C₄⋊C₄	—	2	2	no	—
429	C₃×C₄⋊C₄	—	2	1	no	—
430	C₃×C₄⋊C₄	—	2	1	no	—
431	C₃×C₄⋊C₄	—	2	1	no	—
432	C₃×C₄⋊C₄	—	2	1	no	—
433	C₃×C₄⋊C₄	—	2	4	no	—
434	C₃×C₄⋊C₄	—	2	4	no	—
435	C₃×C₄⋊C₄	—	2	4	no	—
436	C₃×C₄⋊C₄	—	3	4	no	—
437	C₃×C₄⋊C₄	—	3	2	no	—
438	C₃×C₄⋊C₄	—	3	4	no	—
439	C₃×C₄⋊C₄	—	3	4	no	—
440	C₃×C₄⋊C₄	—	3	4	no	—
441	C₃×C₄⋊C₄	—	3	2	no	—
442	C₃×C₄⋊C₄	—	3	2	no	—
443	C₃×C₄⋊C₄	—	3	2	no	—
444	C₃×C₄⋊C₄	—	3	4	no	—
445	C₃×C₄⋊C₄	—	3	2	no	—
446	C₃×C₄⋊C₄	—	3	2	no	—
447	C₃×C₄⋊C₄	—	3	4	no	—
448	C₃×C₄⋊C₄	—	3	2	no	—
449	C₃×C₄⋊C₄	—	3	1	no	—
450	C₃×C₄⋊C₄	—	3	2	no	—
451	C₃×C₄⋊C₄	—	3	4	no	—
452	C₃×C₄⋊C₄	—	3	1	no	—
453	C₃×C₄⋊C₄	—	3	2	no	—
454	C₃×C₄⋊C₄	—	3	2	no	—
455	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
456	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
457	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
458	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
459	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
460	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
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	4	yes	—
464	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
465	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
466	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
467	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
468	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
469	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
470	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
471	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
472	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
473	C₃×C₂²⋊C₄	—	2	2	no	—
474	C₃×C₂²⋊C₄	—	2	2	no	—
475	C₃×C₂²⋊C₄	—	3	2	no	—
476	C₃×C₂²⋊C₄	—	3	4	no	—
477	C₃×C₂²⋊C₄	—	3	2	no	—
478	C₃×C₂²⋊C₄	—	3	2	no	—
479	C₃×C₂²⋊C₄	—	3	4	no	—
480	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
481	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
482	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
483	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
484	C₃×C₄²	—	2	2	no	—
485	C₃×C₄²	—	2	2	no	—
486	C₃×C₄²	—	3	1	no	—
487	C₃×C₄²	—	3	1	no	—
488	C₃×C₄²	—	3	2	no	—
489	C₃×C₄²	—	3	2	no	—
490	C₃×C₄²	—	3	1	no	—
491	C₃×C₄²	—	3	1	no	—
492	C₃×C₄²	—	3	4	no	—
493	C₃×C₄²	—	3	4	no	—
494	C₃×C₄²	—	3	2	no	—
495	C₃×C₄²	C₂²×D₃	1	2	yes	—
496	C₃×C₄²	C₂²×D₃	1	2	yes	—
497	C₃×C₄²	C₂³×C₃	1	2	yes	—
498	C₃×C₄²	C₂³×C₃	1	2	yes	—
499	#217	C₂³×C₃	1	2	yes	—
500	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
501	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
502	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
503	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
504	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
505	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
506	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
507	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
508	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
509	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
510	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
511	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
512	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
513	Dic₃⋊C₄	C₂³×C₃	1	2	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	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
518	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
519	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
520	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
521	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
522	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
523	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
524	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
525	C₄×Dic₃	C₂³×C₃	1	2	yes	—
526	C₄×Dic₃	C₂³×C₃	1	4	yes	—
527	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
528	C₄×Dic₃	C₂³×C₃	1	2	yes	—
529	C₄×Dic₃	C₂³×C₃	1	2	yes	—
530	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
531	C₄×Dic₃	C₂³×C₃	1	4	yes	—
532	C₂²×C₃²	—	2	1	no	—
533	C₂²×C₃²	—	2	1	no	—
534	C₂²×C₃²	C₂²×Q₈	1	2	yes	—
535	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
536	C₂×C₃×D₃	—	2	2	no	—
537	C₂×C₃×D₃	—	2	2	no	—
538	C₂×C₃×D₃	C₂²×Q₈	1	4	yes	—
539	C₃²×C₄	—	2	4	no	—
540	C₃²×C₄	—	2	2	no	—
541	C₃²×C₄	—	2	2	no	—
542	C₃²×C₄	—	2	2	no	—
543	C₃²×C₄	—	2	2	no	—
544	C₃²×C₄	C₂²×Q₈	1	2	yes	—
545	C₃²×C₄	C₂²×Q₈	1	2	yes	—
546	C₃×Dic₃	—	2	2	no	—
547	C₃×Dic₃	—	2	4	no	—
548	C₃×Dic₃	—	2	1	no	—
549	C₃×Dic₃	—	2	2	no	—
550	C₃×Dic₃	—	2	1	no	—
551	C₃×Dic₃	C₂²×Q₈	1	4	yes	—
552	C₃×Dic₃	H(5,𝔽₂)	1	2	yes	—
553	C₃×Dic₃	2₋¹⁺⁴	1	2	yes	—
554	C₂×#41	—	3	1	no	—
555	C₂²×Q₈	—	3	4	no	—
556	C₂²×Q₈	—	3	2	no	—
557	C₄⋊Q₈	—	3	4	no	—
558	C₄⋊Q₈	—	3	4	no	—
559	C₄⋊Q₈	—	3	1	no	—
560	C₄⋊Q₈	—	3	2	no	—
561	C₄⋊Q₈	—	3	2	no	—
562	C₄⋊Q₈	—	3	4	no	—
563	C₄⋊Q₈	—	3	2	no	—
564	C₄⋊Q₈	—	3	2	no	—
565	C₄⋊Q₈	—	3	1	no	—
566	C₄⋊Q₈	—	3	4	no	—
567	C₄⋊Q₈	—	3	2	no	—
568	C₄⋊Q₈	—	3	2	no	—
569	C₄⋊Q₈	C₂×C₃×D₃	1	2	yes	—
570	C₄⋊Q₈	C₂×C₃×D₃	1	2	yes	—
571	#125	—	3	1	no	—
572	#125	—	3	1	no	—
573	#125	—	3	4	no	—
574	#125	—	3	4	no	—
575	#125	—	3	2	no	—
576	#125	—	3	2	no	—
577	#125	C₂×C₃×D₃	1	2	yes	—
578	#125	C₂×C₃×D₃	1	2	yes	—
579	C₂²⋊Q₈	—	3	4	no	—
580	C₂²⋊Q₈	—	3	4	no	—
581	C₂²⋊Q₈	—	3	4	no	—
582	C₂²⋊Q₈	—	3	4	no	—
583	C₂²⋊Q₈	—	3	4	no	—
584	C₂²⋊Q₈	—	3	4	no	—
585	C₂²⋊Q₈	—	3	2	no	—
586	C₂²⋊Q₈	—	3	2	no	—
587	C₂²⋊Q₈	—	3	4	no	—
588	C₂²⋊Q₈	C₂×C₃×D₃	1	4	yes	—
589	C₄×Q₈	—	3	1	no	—
590	C₄×Q₈	—	3	1	no	—
591	C₄×Q₈	—	3	2	no	—
592	C₄×Q₈	—	3	4	no	—
593	C₄×Q₈	—	3	4	no	—
594	C₄×Q₈	—	3	2	no	—
595	C₄×Q₈	—	3	2	no	—
596	C₄×Q₈	—	3	2	no	—
597	C₄×D₄	—	3	4	no	—
598	C₄×D₄	—	3	1	no	—
599	C₄×D₄	—	3	1	no	—
600	C₄×D₄	—	3	2	no	—
601	C₄×D₄	—	3	2	no	—
602	C₄×D₄	—	3	2	no	—
603	C₄×D₄	—	3	4	no	—
604	C₄×D₄	—	3	2	no	—
605	#117	—	3	1	no	—
606	#117	—	3	2	no	—
607	#117	—	3	2	no	—
608	#117	—	3	2	no	—
609	#117	C₂×C₃×D₃	1	1	yes	characteristic
610	#117	C₂×C₃×D₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	—	3	1	no	—
612	C₂×C₄⋊C₄	—	3	2	no	—
613	C₂×C₄⋊C₄	—	3	2	no	—
614	C₂×C₄⋊C₄	—	3	2	no	—
615	C₂×C₄⋊C₄	—	3	4	no	—
616	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
617	C₂×C₄²	—	3	1	no	—
618	C₂×C₄²	—	3	2	no	—
619	C₂³×C₃	—	2	1	no	—
620	C₂³×C₃	—	3	2	no	—
621	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
622	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
623	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
624	C₃×Q₈	—	3	4	no	—
625	C₃×Q₈	—	4	4	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×Q₈	—	8	4	no	—
631	C₃×Q₈	—	12	4	no	—
632	C₃×Q₈	—	12	4	no	—
633	C₃×D₄	—	3	8	no	—
634	C₃×D₄	—	3	4	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	2	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	4	no	—
642	C₂×C₃×C₄	—	2	4	no	—
643	C₂×C₃×C₄	—	3	2	no	—
644	C₂×C₃×C₄	—	3	1	no	—
645	C₂×C₃×C₄	—	3	1	no	—
646	C₂×C₃×C₄	—	3	8	no	—
647	C₂×C₃×C₄	—	3	2	no	—
648	C₂×C₃×C₄	—	3	1	no	—
649	C₂×C₃×C₄	—	3	1	no	—
650	C₂×C₃×C₄	—	3	4	no	—
651	C₂×C₃×C₄	—	3	2	no	—
652	C₂×C₃×C₄	—	4	2	no	—
653	C₂×C₃×C₄	—	4	2	no	—
654	C₂×C₃×C₄	—	6	4	no	—
655	C₂×C₃×C₄	—	6	4	no	—
656	C₂×C₃×C₄	—	6	2	no	—
657	C₂×C₃×C₄	—	6	2	no	—
658	C₂×C₃×C₄	—	8	2	no	—
659	C₂×C₃×C₄	—	12	4	no	—
660	C₂×C₃×C₄	—	12	4	no	—
661	C₂×C₃×C₄	—	12	2	no	—
662	C₂×C₃×C₄	D₃×Q₈	1	4	yes	complemented
663	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	complemented
664	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
665	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
666	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
667	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
668	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
669	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
670	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
671	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
672	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
673	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
674	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
675	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
676	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
677	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
678	#67	C₂×C₃×Q₈	1	8	yes	complemented
679	C₂×Dic₃	—	2	2	no	—
680	C₂×Dic₃	—	2	2	no	—
681	C₂×Dic₃	—	4	2	no	—
682	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
683	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
684	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
685	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
686	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
687	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
688	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
689	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
690	D₁₂	C₂×C₃×Q₈	1	4	yes	complemented
691	C₄×D₃	—	2	4	no	—
692	C₄×D₃	—	2	4	no	—
693	C₄×D₃	—	4	4	no	—
694	C₄×D₃	—	4	4	no	—
695	C₄×D₃	C₂×C₃×Q₈	1	8	yes	complemented
696	Dic₆	—	2	8	no	—
697	Dic₆	—	2	4	no	—
698	Dic₆	—	2	4	no	—
699	Dic₆	—	4	4	no	—
700	Dic₆	—	4	4	no	—
701	Dic₆	C₂×C₃×Q₈	1	4	yes	complemented
702	C₂×C₃²	—	2	2	no	—
703	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
704	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂×C₃²	C₂×2₋¹⁺⁴	1	1	yes	characteristic
706	C₃×D₃	—	2	4	no	—
707	#41	—	3	8	no	—
708	C₂×Q₈	—	3	1	no	—
709	C₂×Q₈	—	3	2	no	—
710	C₂×Q₈	—	3	4	no	—
711	C₂×Q₈	—	3	2	no	—
712	C₂×Q₈	—	3	4	no	—
713	C₂×Q₈	—	3	4	no	—
714	C₂×Q₈	—	12	4	no	—
715	C₂×Q₈	—	12	8	no	—
716	C₂×Q₈	C₂²×C₃×D₃	1	4	yes	—
717	C₂×D₄	—	3	2	no	—
718	C₂×D₄	—	3	1	no	—
719	C₂²×C₄	—	3	2	no	—
720	C₂²×C₄	—	3	1	no	—
721	C₂²×C₄	—	3	1	no	—
722	C₂²×C₄	—	3	2	no	—
723	C₂²×C₄	—	3	2	no	—
724	C₂²×C₄	—	3	2	no	—
725	C₂²×C₄	—	3	4	no	—
726	C₂²×C₄	—	3	4	no	—
727	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
728	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
729	C₄⋊C₄	—	3	2	no	—
730	C₄⋊C₄	—	3	1	no	—
731	C₄⋊C₄	—	3	4	no	—
732	C₄⋊C₄	—	3	2	no	—
733	C₄⋊C₄	—	3	4	no	—
734	C₄⋊C₄	—	3	4	no	—
735	C₄⋊C₄	—	3	2	no	—
736	C₄⋊C₄	—	3	4	no	—
737	C₄⋊C₄	—	3	4	no	—
738	C₄⋊C₄	—	3	1	no	—
739	C₄⋊C₄	—	3	2	no	—
740	C₄⋊C₄	—	3	2	no	—
741	C₄⋊C₄	—	3	2	no	—
742	C₄⋊C₄	—	3	4	no	—
743	C₄⋊C₄	—	3	2	no	—
744	C₄⋊C₄	—	3	2	no	—
745	C₄⋊C₄	—	3	2	no	—
746	C₄⋊C₄	—	3	4	no	—
747	C₄⋊C₄	—	3	2	no	—
748	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
750	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
751	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
752	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
756	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
757	C₂²⋊C₄	—	3	2	no	—
758	C₂²⋊C₄	—	3	4	no	—
759	C₂²⋊C₄	—	3	2	no	—
760	C₂²⋊C₄	—	3	2	no	—
761	C₂²⋊C₄	—	3	4	no	—
762	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
763	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
764	C₄²	—	3	1	no	—
765	C₄²	—	3	1	no	—
766	C₄²	—	3	2	no	—
767	C₄²	—	3	2	no	—
768	C₄²	—	3	1	no	—
769	C₄²	—	3	1	no	—
770	C₄²	—	3	4	no	—
771	C₄²	—	3	4	no	—
772	C₄²	—	3	2	no	—
773	C₄²	C₂²×C₃×D₃	1	2	yes	—
774	C₄²	C₂²×C₃×D₃	1	2	yes	—
775	C₂²×C₃	—	2	1	no	—
776	C₂²×C₃	—	2	1	no	—
777	C₂²×C₃	—	2	1	no	—
778	C₂²×C₃	—	2	1	no	—
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	2	1	no	—
781	C₂²×C₃	—	3	4	no	—
782	C₂²×C₃	—	4	1	no	—
783	C₂²×C₃	—	4	1	no	—
784	C₂²×C₃	—	6	2	no	—
785	C₂²×C₃	—	6	2	no	—
786	C₂²×C₃	C₂×D₃×Q₈	1	2	yes	—
787	C₂²×C₃	C₂²×C₃×Q₈	1	2	yes	—
788	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
789	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
790	C₂×D₃	—	2	2	no	—
791	C₂×D₃	—	2	2	no	—
792	C₂×D₃	C₂²×C₃×Q₈	1	4	yes	—
793	C₃×C₄	—	2	4	no	—
794	C₃×C₄	—	2	2	no	—
795	C₃×C₄	—	2	2	no	—
796	C₃×C₄	—	2	2	no	—
797	C₃×C₄	—	2	2	no	—
798	C₃×C₄	—	2	4	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	2	no	—
801	C₃×C₄	—	2	2	no	—
802	C₃×C₄	—	2	2	no	—
803	C₃×C₄	—	2	2	no	—
804	C₃×C₄	—	2	2	no	—
805	C₃×C₄	—	3	4	no	—
806	C₃×C₄	—	3	2	no	—
807	C₃×C₄	—	3	2	no	—
808	C₃×C₄	—	4	4	no	—
809	C₃×C₄	—	4	2	no	—
810	C₃×C₄	—	4	2	no	—
811	C₃×C₄	—	4	2	no	—
812	C₃×C₄	—	4	2	no	—
813	C₃×C₄	—	6	1	no	—
814	C₃×C₄	—	6	2	no	—
815	C₃×C₄	—	6	4	no	—
816	C₃×C₄	—	6	1	no	—
817	C₃×C₄	—	6	2	no	—
818	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
819	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
820	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
821	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
822	Dic₃	—	2	2	no	—
823	Dic₃	—	2	4	no	—
824	Dic₃	—	2	1	no	—
825	Dic₃	—	2	2	no	—
826	Dic₃	—	2	1	no	—
827	Dic₃	C₂²×C₃×Q₈	1	4	yes	—
828	Dic₃	C₃×H(5,𝔽₂)	1	2	yes	—
829	Dic₃	C₃×2₋¹⁺⁴	1	2	yes	—
830	C₃²	#3503	1	1	yes	characteristic, complemented, Sylow
831	C₂³	—	3	2	no	—
832	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
833	Q₈	—	3	4	no	—
834	Q₈	—	4	4	no	—
835	Q₈	—	6	8	no	—
836	Q₈	—	6	4	no	—
837	Q₈	—	6	4	no	—
838	Q₈	—	12	4	no	—
839	Q₈	—	12	4	no	—
840	D₄	—	3	8	no	—
841	D₄	—	3	4	no	—
842	C₂×C₄	—	3	2	no	—
843	C₂×C₄	—	3	1	no	—
844	C₂×C₄	—	3	1	no	—
845	C₂×C₄	—	3	8	no	—
846	C₂×C₄	—	3	2	no	—
847	C₂×C₄	—	3	1	no	—
848	C₂×C₄	—	3	1	no	—
849	C₂×C₄	—	3	2	no	—
850	C₂×C₄	—	3	4	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	6	4	no	—
853	C₂×C₄	—	6	4	no	—
854	C₂×C₄	—	6	2	no	—
855	C₂×C₄	—	6	2	no	—
856	C₂×C₄	—	12	4	no	—
857	C₂×C₄	—	12	4	no	—
858	C₂×C₄	—	12	2	no	—
859	C₂×C₄	C₃×D₃×Q₈	1	4	yes	complemented
860	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
861	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
862	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
863	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
864	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
865	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
866	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
867	C₂×C₃	—	2	2	no	—
868	C₂×C₃	—	2	2	no	—
869	C₂×C₃	—	2	1	no	—
870	C₂×C₃	—	2	1	no	—
871	C₂×C₃	—	2	1	no	—
872	C₂×C₃	—	4	2	no	—
873	C₂×C₃	—	6	4	no	—
874	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
875	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
876	C₂×C₃	D₃×2₋¹⁺⁴	1	1	yes	characteristic
877	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
878	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
879	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
880	D₃	—	2	4	no	—
881	C₂²	—	2	1	no	—
882	C₂²	—	2	1	no	—
883	C₂²	—	3	4	no	—
884	C₂²	—	6	2	no	—
885	C₂²	—	6	2	no	—
886	C₂²	C₂×C₃×D₃×Q₈	1	2	yes	—
887	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
888	C₄	—	2	4	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	3	4	no	—
894	C₄	—	3	2	no	—
895	C₄	—	3	2	no	—
896	C₄	—	6	1	no	—
897	C₄	—	6	2	no	—
898	C₄	—	6	4	no	—
899	C₄	—	6	1	no	—
900	C₄	—	6	2	no	—
901	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
902	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
903	C₃	—	2	1	no	—
904	C₃	#86586	1	1	yes	characteristic, direct product factor
905	C₃	C₃×#3503	1	1	yes	characteristic, complemented
906	C₂	—	2	2	no	—
907	C₂	—	6	4	no	—
908	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
909	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic
910	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×#544	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂×C₃×#235	C₂²
hypercenter	C₃×#544	D₃
hypocenter	C₃	C₃×#3503
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#544

Complements

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

N	H ≅ G/N	type
1. C₃²×#544	C₂	semidirect
2. C₃×#5729	C₂	semidirect
3. C₃×#5727	C₂	semidirect
4. C₃×D₃×C₄⋊Q₈	C₂	semidirect
5. C₃×#5722	C₂	semidirect
6. C₃×#5690	C₂	semidirect
7. C₃×#5689	C₂	semidirect
8. C₃×#5688	C₂	semidirect
9. C₃×#5685	C₂	semidirect
10. C₃×#5636	C₂	semidirect
11. C₃×#5632	C₂	semidirect
14. C₃×#5519	C₂	semidirect
15. C₃×#5517	C₂	semidirect
17. C₂×C₃×#888	C₂	semidirect
19. #86586	C₃	direct (N × H)
95. C₃×#544	D₃	semidirect
96. C₃×#544	C₂×C₃	semidirect
104. #5729	C₂×C₃	semidirect
105. #5727	C₂×C₃	semidirect
106. D₃×C₄⋊Q₈	C₂×C₃	semidirect
107. #5722	C₂×C₃	semidirect
108. #5690	C₂×C₃	semidirect
109. #5689	C₂×C₃	semidirect
110. #5688	C₂×C₃	semidirect
111. #5685	C₂×C₃	semidirect
112. #5636	C₂×C₃	semidirect
113. #5632	C₂×C₃	semidirect
116. #5519	C₂×C₃	semidirect
117. #5517	C₂×C₃	semidirect
119. C₂×#888	C₂×C₃	semidirect
128. C₃×#235	Q₈	semidirect
331. C₂×C₃²×C₄	C₂×Q₈	semidirect
339. C₃×#67	C₂×Q₈	semidirect
351. C₃×D₁₂	C₂×Q₈	semidirect
356. C₃×C₄×D₃	C₂×Q₈	semidirect
362. C₃×Dic₆	C₂×Q₈	semidirect
372. #544	C₃×D₃	semidirect
413. #235	C₃×Q₈	semidirect
662. C₂×C₃×C₄	D₃×Q₈	semidirect
663. C₂×C₃×C₄	C₂×C₃×Q₈	semidirect
678. #67	C₂×C₃×Q₈	semidirect
690. D₁₂	C₂×C₃×Q₈	semidirect
695. C₄×D₃	C₂×C₃×Q₈	semidirect
701. Dic₆	C₂×C₃×Q₈	semidirect
830. C₃²	#3503	semidirect
859. C₂×C₄	C₃×D₃×Q₈	semidirect
904. C₃	#86586	direct (N × H)
905. C₃	C₃×#3503	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#544	2
C₃×#5729	2
C₃×#5727	2
C₃×D₃×C₄⋊Q₈	2
C₃×#5722	2
C₃×#5690	2
C₃×#5689	2
C₃×#5688	2
C₃×#5685	2
C₃×#5636	2
C₃×#5632	2
C₃×#5523	2
C₃×#5522	2
C₃×#5519	2
C₃×#5517	2
C₃×#5504	2
C₂×C₃×#888	2
C₃×#3503	3
#86586	3

Subgroups — C3×#86586 #11906324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86586 #11906324