Subgroups — C₃×#86923 #11903740

Order 1152.

2250 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5728	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5722	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5688	C₂	1	2	yes	maximal, complemented
5	C₃×#5685	C₂	1	2	yes	maximal, complemented
6	C₃×#5636	C₂	1	4	yes	maximal, complemented
7	C₃×#5632	C₂	1	2	yes	maximal, complemented
8	C₃×#5622	C₂	1	4	yes	maximal, complemented
9	C₃×#5622	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#5567	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5539	C₂	1	2	yes	maximal, complemented
13	C₃×D₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×#237	C₂	1	2	yes	maximal
15	C₃×C₄×#237	C₂	1	1	yes	maximal, characteristic
16	C₃×#5511	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×#887	C₂	1	2	yes	maximal, complemented
18	C₃×Q₈×#41	—	3	1	no	maximal
19	#86923	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×#237	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Dic₆	C₂²	1	2	yes	—
23	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₃²×#125	C₂²	1	2	yes	—
25	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
28	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₃²×C₄×D₄	C₂²	1	2	yes	—
30	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	—
31	C₃×#946	C₂²	1	2	yes	—
32	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic
33	C₃×Q₈×Dic₃	C₂²	1	2	yes	—
34	C₃×#944	C₂²	1	2	yes	—
35	C₃×#944	C₂²	1	4	yes	—
36	C₃×D₄×Dic₃	C₂²	1	2	yes	—
37	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
38	C₃×C₄×#67	C₂²	1	2	yes	—
39	C₃×C₄×#67	C₂²	1	4	yes	—
40	C₃×#924	C₂²	1	2	yes	—
41	C₃×#924	C₂²	1	4	yes	—
42	C₂×C₃×Dic₃⋊C₄	C₂²	1	4	yes	—
43	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
44	C₂×C₃×C₄×Dic₃	C₂²	1	4	yes	—
45	C₃×#897	C₂²	1	2	yes	—
46	C₃×#896	C₂²	1	4	yes	—
47	C₃×#896	C₂²	1	4	yes	—
48	C₃×#892	C₂²	1	1	yes	characteristic
49	C₃×#892	C₂²	1	2	yes	—
50	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
52	C₃×#890	C₂²	1	2	yes	—
53	C₃×#889	C₂²	1	4	yes	—
54	C₃×#889	C₂²	1	4	yes	—
55	C₃×#889	C₂²	1	4	yes	—
56	C₃×#888	C₂²	1	2	yes	—
57	C₃×#888	C₂²	1	2	yes	—
58	C₃×#888	C₂²	1	2	yes	—
59	C₃×#888	C₂²	1	4	yes	—
60	C₃×#887	C₂²	1	1	yes	characteristic
61	C₃×#887	C₂²	1	2	yes	—
62	C₃×#887	C₂²	1	4	yes	—
63	C₃×#887	C₂²	1	2	yes	—
64	C₃×#887	C₂²	1	2	yes	—
65	C₃×#887	C₂²	1	4	yes	—
66	C₃×#887	C₂²	1	1	yes	characteristic
67	C₃×#887	C₂²	1	2	yes	—
68	C₃×#887	C₂²	1	2	yes	—
69	C₃×#887	C₂²	1	4	yes	—
70	C₃×#67⋊C₄	C₂²	1	4	yes	—
71	C₃×#67⋊C₄	C₂²	1	2	yes	—
72	C₃×#878	C₂²	1	4	yes	—
73	C₃×#878	C₂²	1	4	yes	—
74	C₃×#878	C₂²	1	4	yes	—
75	C₃×#877	C₂²	1	4	yes	—
76	C₃×#877	C₂²	1	2	yes	—
77	C₃×C₄²×D₃	C₂²	1	2	yes	—
78	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
79	C₃×#870	C₂²	1	2	yes	—
80	C₃×#869	C₂²	1	1	yes	characteristic
81	C₃×C₄×Dic₆	C₂²	1	2	yes	—
82	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
83	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
84	C₃×C₄×Dic₆	C₂²	1	2	yes	—
85	C₃×Q₈²	—	3	1	no	—
86	C₃×#557	—	3	2	no	—
87	C₃×#557	—	3	1	no	—
88	C₃×#554	—	2	1	no	—
89	C₃×#554	—	3	4	no	—
90	C₃×#554	—	3	2	no	—
91	C₃×#554	—	3	2	no	—
92	C₃×#554	D₃	1	1	yes	characteristic, complemented
93	C₃×#554	C₂×C₃	1	1	yes	characteristic, complemented
94	C₃×D₄×Q₈	—	3	2	no	—
95	C₃×D₄×Q₈	—	3	1	no	—
96	C₃×#533	—	3	1	no	—
97	C₃×#533	—	3	2	no	—
98	C₃×#533	—	3	2	no	—
99	C₃×#533	—	3	4	no	—
100	C₃×C₄×#41	—	3	2	no	—
101	C₃×C₄×#41	—	3	1	no	—
102	C₂×C₃×C₄×Q₈	—	3	1	no	—
103	C₂×C₃×C₄×Q₈	—	3	2	no	—
104	#5728	C₂×C₃	1	1	yes	characteristic, complemented
105	#5722	C₂×C₃	1	1	yes	characteristic, complemented
106	#5688	C₂×C₃	1	2	yes	complemented
107	#5685	C₂×C₃	1	2	yes	complemented
108	#5636	C₂×C₃	1	4	yes	complemented
109	#5632	C₂×C₃	1	2	yes	complemented
110	#5622	C₂×C₃	1	4	yes	complemented
111	#5622	C₂×C₃	1	2	yes	complemented
112	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
113	#5567	C₂×C₃	1	1	yes	characteristic, complemented
114	#5539	C₂×C₃	1	2	yes	complemented
115	D₄×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
116	C₄×#237	C₂×C₃	1	2	yes	—
117	C₄×#237	C₂×C₃	1	1	yes	characteristic
118	#5511	C₂×C₃	1	2	yes	complemented
119	C₂×#887	C₂×C₃	1	2	yes	complemented
120	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
121	C₂×C₃²×Q₈	C₂³	1	2	yes	—
122	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
123	C₂²×C₃²×C₄	C₂³	1	2	yes	—
124	C₂²×C₃²×C₄	C₂³	1	4	yes	—
125	C₂×C₃×#67	C₂³	1	2	yes	—
126	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
127	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
128	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
129	C₃×D₃×Q₈	—	2	4	no	—
130	C₃×#237	Q₈	1	8	yes	complemented
131	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
132	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
134	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
135	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
136	C₂×C₃×Dic₆	—	2	8	no	—
137	C₂×C₃×Dic₆	C₂³	1	2	yes	—
138	C₂×C₃×Dic₆	C₂³	1	4	yes	—
139	C₂×C₃×Dic₆	C₂³	1	2	yes	—
140	C₂×C₃×Dic₆	C₂³	1	4	yes	—
141	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
142	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
143	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
145	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
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×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₄²	C₂³	1	2	yes	—
153	C₃²×C₄²	C₂³	1	1	yes	characteristic
154	C₃×#217	C₂³	1	2	yes	—
155	C₃×#217	C₂³	1	4	yes	—
156	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
157	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
158	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
159	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
160	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
161	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
162	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
163	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
164	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
165	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
166	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
167	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
168	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
169	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
170	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
171	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
172	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
173	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
174	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
175	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
176	C₃×C₄×Dic₃	C₂³	1	2	yes	—
177	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
178	C₃×C₄×Dic₃	C₂³	1	2	yes	—
179	C₃×C₄×Dic₃	C₂³	1	4	yes	—
180	C₃×C₄×Dic₃	C₂³	1	4	yes	—
181	C₃×C₄×Dic₃	C₂³	1	2	yes	—
182	C₃×C₄×Dic₃	C₂³	1	2	yes	—
183	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
184	C₃×C₄×Dic₃	C₂³	1	2	yes	—
185	C₃×C₄×Dic₃	C₂³	1	4	yes	—
186	C₃×C₄×Dic₃	C₂³	1	2	yes	—
187	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
188	Q₈×#41	—	3	1	no	Sylow
189	C₂×C₃×#41	—	3	1	no	—
190	C₂²×C₃×Q₈	—	3	1	no	—
191	C₂²×C₃×Q₈	—	3	2	no	—
192	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
193	C₂×#237	C₂²×C₃	1	1	yes	characteristic
194	C₂²×Dic₆	C₂²×C₃	1	2	yes	—
195	C₃×C₄⋊Q₈	—	2	1	no	—
196	C₃×C₄⋊Q₈	—	3	4	no	—
197	C₃×C₄⋊Q₈	—	3	2	no	—
198	C₃×C₄⋊Q₈	—	3	2	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	C₂×D₃	1	1	yes	characteristic
204	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
205	C₃×#125	—	2	2	no	—
206	C₃×#125	—	3	4	no	—
207	C₃×#125	—	3	4	no	—
208	C₃×#125	—	3	4	no	—
209	C₃×#125	—	3	2	no	—
210	C₃×#125	—	3	2	no	—
211	C₃×#125	C₂×D₃	1	2	yes	—
212	C₃×#125	C₂²×C₃	1	2	yes	—
213	C₃×C₂²⋊Q₈	—	2	2	no	—
214	C₃×C₂²⋊Q₈	—	2	4	no	—
215	C₃×C₂²⋊Q₈	—	3	2	no	—
216	C₃×C₂²⋊Q₈	—	3	2	no	—
217	C₃×C₂²⋊Q₈	—	3	4	no	—
218	C₃×C₂²⋊Q₈	—	3	4	no	—
219	C₃×C₂²⋊Q₈	—	3	4	no	—
220	C₃×C₂²⋊Q₈	—	3	2	no	—
221	C₃×C₂²⋊Q₈	—	3	4	no	—
222	C₃×C₂²⋊Q₈	—	3	4	no	—
223	C₃×C₂²⋊Q₈	—	3	4	no	—
224	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
225	C₃×C₂²⋊Q₈	C₂×D₃	1	4	yes	—
226	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
227	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
228	C₃×C₄×Q₈	—	2	1	no	—
229	C₃×C₄×Q₈	—	3	1	no	—
230	C₃×C₄×Q₈	—	3	2	no	—
231	C₃×C₄×Q₈	—	3	2	no	—
232	C₃×C₄×Q₈	—	3	2	no	—
233	C₃×C₄×Q₈	—	3	1	no	—
234	C₃×C₄×Q₈	—	3	2	no	—
235	C₃×C₄×Q₈	—	3	2	no	—
236	C₃×C₄×Q₈	—	3	4	no	—
237	C₃×C₄×Q₈	—	3	4	no	—
238	C₃×C₄×Q₈	—	3	2	no	—
239	C₃×C₄×Q₈	—	3	1	no	—
240	C₃×C₄×Q₈	—	3	4	no	—
241	C₃×C₄×Q₈	—	3	1	no	—
242	C₃×C₄×Q₈	—	3	1	no	—
243	C₃×C₄×Q₈	—	3	2	no	—
244	C₃×C₄×Q₈	—	3	2	no	—
245	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
246	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
247	C₃×C₄×D₄	—	2	1	no	—
248	C₃×C₄×D₄	—	2	2	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	4	no	—
253	C₃×C₄×D₄	—	3	4	no	—
254	C₃×C₄×D₄	—	3	2	no	—
255	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
256	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
257	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
258	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
259	C₃×#117	—	3	2	no	—
260	C₃×#117	—	3	1	no	—
261	C₃×#117	—	3	4	no	—
262	C₃×#117	—	3	2	no	—
263	C₂×C₃×C₄⋊C₄	—	2	2	no	—
264	C₂×C₃×C₄⋊C₄	—	3	4	no	—
265	C₂×C₃×C₄⋊C₄	—	3	2	no	—
266	C₂×C₃×C₄⋊C₄	—	3	1	no	—
267	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
268	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
269	C₂×C₃×C₄²	—	3	4	no	—
270	C₂×C₃×C₄²	—	3	2	no	—
271	C₂×C₃×C₄²	—	3	1	no	—
272	C₂×C₃×C₄²	—	3	2	no	—
273	#946	C₂²×C₃	1	2	yes	—
274	Q₈×Dic₃	C₂²×C₃	1	2	yes	—
275	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
276	#944	C₂²×C₃	1	2	yes	—
277	#944	C₂²×C₃	1	4	yes	—
278	D₄×Dic₃	C₂²×C₃	1	2	yes	—
279	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
280	C₄×#67	C₂²×C₃	1	2	yes	—
281	C₄×#67	C₂²×C₃	1	4	yes	—
282	#924	C₂²×C₃	1	2	yes	—
283	#924	C₂²×C₃	1	4	yes	—
284	C₂×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
285	C₂×C₄×Dic₃	C₂²×C₃	1	2	yes	—
286	C₂×C₄×Dic₃	C₂²×C₃	1	4	yes	—
287	#897	C₂²×C₃	1	2	yes	—
288	#896	C₂²×C₃	1	4	yes	—
289	#896	C₂²×C₃	1	4	yes	—
290	#892	C₂²×C₃	1	1	yes	characteristic
291	#892	C₂²×C₃	1	2	yes	—
292	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
293	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
294	#890	C₂²×C₃	1	2	yes	—
295	#889	C₂²×C₃	1	4	yes	—
296	#889	C₂²×C₃	1	4	yes	—
297	#889	C₂²×C₃	1	4	yes	—
298	#888	C₂²×C₃	1	4	yes	—
299	#888	C₂²×C₃	1	2	yes	—
300	#888	C₂²×C₃	1	2	yes	—
301	#888	C₂²×C₃	1	2	yes	—
302	#887	C₂²×C₃	1	2	yes	—
303	#887	C₂²×C₃	1	4	yes	—
304	#887	C₂²×C₃	1	1	yes	characteristic
305	#887	C₂²×C₃	1	2	yes	—
306	#887	C₂²×C₃	1	4	yes	—
307	#887	C₂²×C₃	1	4	yes	—
308	#887	C₂²×C₃	1	2	yes	—
309	#887	C₂²×C₃	1	1	yes	characteristic
310	#887	C₂²×C₃	1	2	yes	—
311	#887	C₂²×C₃	1	2	yes	—
312	#67⋊C₄	C₂²×C₃	1	4	yes	—
313	#67⋊C₄	C₂²×C₃	1	2	yes	—
314	#878	C₂²×C₃	1	4	yes	—
315	#878	C₂²×C₃	1	4	yes	—
316	#878	C₂²×C₃	1	4	yes	—
317	#877	C₂²×C₃	1	4	yes	—
318	#877	C₂²×C₃	1	2	yes	—
319	C₄²×D₃	C₂²×C₃	1	2	yes	—
320	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
321	#870	C₂²×C₃	1	2	yes	—
322	#869	C₂²×C₃	1	1	yes	characteristic
323	C₄×Dic₆	C₂²×C₃	1	2	yes	—
324	C₄×Dic₆	C₂²×C₃	1	2	yes	—
325	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
326	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
327	C₂³×C₃²	C₂⁴	1	2	yes	—
328	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
329	C₃²×Q₈	—	2	2	no	—
330	C₃²×Q₈	—	4	2	no	—
331	C₃²×D₄	C₂×Q₈	1	4	yes	complemented
332	C₂×C₃²×C₄	—	2	4	no	—
333	C₂×C₃²×C₄	—	4	4	no	—
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	2	yes	—
339	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
340	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
341	C₃×#67	C₂×Q₈	1	8	yes	complemented
342	C₂×C₃×Dic₃	—	2	8	no	—
343	C₂×C₃×Dic₃	—	4	2	no	—
344	C₂×C₃×Dic₃	C₂×Q₈	1	8	yes	complemented
345	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
346	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
347	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
348	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
349	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
352	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
353	C₃×C₄×D₃	—	2	2	no	—
354	C₃×C₄×D₃	—	2	4	no	—
355	C₃×C₄×D₃	—	4	2	no	—
356	C₃×C₄×D₃	—	4	1	no	—
357	C₃×C₄×D₃	C₂×Q₈	1	4	yes	complemented
358	C₃×Dic₆	—	2	4	no	—
359	C₃×Dic₆	—	2	8	no	—
360	C₃×Dic₆	—	2	4	no	—
361	C₃×Dic₆	—	4	4	no	—
362	C₃×Dic₆	C₂×Q₈	1	4	yes	complemented
363	C₃×Dic₆	#41	1	4	yes	complemented
364	Q₈²	—	3	1	no	—
365	#557	—	3	2	no	—
366	#557	—	3	1	no	—
367	#554	—	3	4	no	—
368	#554	—	3	2	no	—
369	#554	—	3	2	no	—
370	#554	C₃×D₃	1	1	yes	characteristic, complemented
371	D₄×Q₈	—	3	2	no	—
372	D₄×Q₈	—	3	1	no	—
373	#533	—	3	1	no	—
374	#533	—	3	2	no	—
375	#533	—	3	2	no	—
376	#533	—	3	4	no	—
377	C₄×#41	—	3	2	no	—
378	C₄×#41	—	3	1	no	—
379	C₂×C₄×Q₈	—	3	1	no	—
380	C₂×C₄×Q₈	—	3	2	no	—
381	C₃×#41	—	3	8	no	—
382	C₂×C₃×Q₈	—	2	1	no	—
383	C₂×C₃×Q₈	—	2	2	no	—
384	C₂×C₃×Q₈	—	3	1	no	—
385	C₂×C₃×Q₈	—	3	1	no	—
386	C₂×C₃×Q₈	—	3	4	no	—
387	C₂×C₃×Q₈	—	3	2	no	—
388	C₂×C₃×Q₈	—	3	2	no	—
389	C₂×C₃×Q₈	—	3	4	no	—
390	C₂×C₃×Q₈	—	6	8	no	—
391	C₂×C₃×Q₈	—	6	4	no	—
392	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
393	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
394	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
395	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
396	C₂×C₃×D₄	—	2	1	no	—
397	C₂×C₃×D₄	—	3	2	no	—
398	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
399	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
400	C₂²×C₃×C₄	—	2	2	no	—
401	C₂²×C₃×C₄	—	2	4	no	—
402	C₂²×C₃×C₄	—	3	2	no	—
403	C₂²×C₃×C₄	—	3	1	no	—
404	C₂²×C₃×C₄	—	3	4	no	—
405	C₂²×C₃×C₄	—	3	2	no	—
406	C₂²×C₃×C₄	—	3	2	no	—
407	C₂²×C₃×C₄	—	3	1	no	—
408	C₂²×C₃×C₄	—	3	1	no	—
409	C₂²×C₃×C₄	—	3	2	no	—
410	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
411	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
412	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
413	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
414	C₂×#67	C₂³×C₃	1	2	yes	—
415	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
416	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
417	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
418	D₃×Q₈	—	2	4	no	—
419	#237	C₃×Q₈	1	8	yes	complemented
420	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
421	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
422	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
423	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
424	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
425	C₂×Dic₆	—	2	8	no	—
426	C₂×Dic₆	C₂³×C₃	1	2	yes	—
427	C₂×Dic₆	C₂³×C₃	1	2	yes	—
428	C₂×Dic₆	C₂³×C₃	1	4	yes	—
429	C₂×Dic₆	C₂³×C₃	1	4	yes	—
430	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
431	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
432	C₃×C₄⋊C₄	—	2	1	no	—
433	C₃×C₄⋊C₄	—	2	4	no	—
434	C₃×C₄⋊C₄	—	2	2	no	—
435	C₃×C₄⋊C₄	—	2	1	no	—
436	C₃×C₄⋊C₄	—	2	2	no	—
437	C₃×C₄⋊C₄	—	2	2	no	—
438	C₃×C₄⋊C₄	—	2	4	no	—
439	C₃×C₄⋊C₄	—	3	2	no	—
440	C₃×C₄⋊C₄	—	3	4	no	—
441	C₃×C₄⋊C₄	—	3	4	no	—
442	C₃×C₄⋊C₄	—	3	2	no	—
443	C₃×C₄⋊C₄	—	3	4	no	—
444	C₃×C₄⋊C₄	—	3	2	no	—
445	C₃×C₄⋊C₄	—	3	4	no	—
446	C₃×C₄⋊C₄	—	3	2	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	4	no	—
451	C₃×C₄⋊C₄	—	3	2	no	—
452	C₃×C₄⋊C₄	—	3	1	no	—
453	C₃×C₄⋊C₄	—	3	1	no	—
454	C₃×C₄⋊C₄	—	3	2	no	—
455	C₃×C₄⋊C₄	—	3	4	no	—
456	C₃×C₄⋊C₄	—	3	2	no	—
457	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
458	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
459	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
460	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
461	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
462	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
463	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
464	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
465	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
466	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
467	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
468	C₃×C₄⋊C₄	C₂³×C₃	1	4	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	—	3	4	no	—
474	C₃×C₂²⋊C₄	—	3	2	no	—
475	C₃×C₂²⋊C₄	—	3	4	no	—
476	C₃×C₂²⋊C₄	—	3	2	no	—
477	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
478	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
479	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
480	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
481	C₃×C₄²	—	2	2	no	—
482	C₃×C₄²	—	2	1	no	—
483	C₃×C₄²	—	3	2	no	—
484	C₃×C₄²	—	3	1	no	—
485	C₃×C₄²	—	3	4	no	—
486	C₃×C₄²	—	3	2	no	—
487	C₃×C₄²	—	3	1	no	—
488	C₃×C₄²	—	3	2	no	—
489	C₃×C₄²	—	3	2	no	—
490	C₃×C₄²	—	3	4	no	—
491	C₃×C₄²	—	3	1	no	—
492	C₃×C₄²	—	3	4	no	—
493	C₃×C₄²	—	3	2	no	—
494	C₃×C₄²	—	3	2	no	—
495	C₃×C₄²	C₂²×D₃	1	2	yes	—
496	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
497	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
498	C₃×C₄²	C₂³×C₃	1	2	yes	—
499	#217	C₂³×C₃	1	2	yes	—
500	#217	C₂³×C₃	1	4	yes	—
501	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
502	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
503	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
504	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
505	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
506	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
507	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
508	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
509	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
510	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
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	4	yes	—
515	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
516	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
517	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
518	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
519	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
520	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
521	C₄×Dic₃	C₂³×C₃	1	2	yes	—
522	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
523	C₄×Dic₃	C₂³×C₃	1	2	yes	—
524	C₄×Dic₃	C₂³×C₃	1	4	yes	—
525	C₄×Dic₃	C₂³×C₃	1	2	yes	—
526	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
527	C₄×Dic₃	C₂³×C₃	1	2	yes	—
528	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
529	C₄×Dic₃	C₂³×C₃	1	2	yes	—
530	C₄×Dic₃	C₂³×C₃	1	4	yes	—
531	C₄×Dic₃	C₂³×C₃	1	4	yes	—
532	C₄×Dic₃	C₂³×C₃	1	2	yes	—
533	C₂²×C₃²	—	2	2	no	—
534	C₂²×C₃²	—	2	2	no	—
535	C₂²×C₃²	C₂²×Q₈	1	4	yes	—
536	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
537	C₂×C₃×D₃	—	2	1	no	—
538	C₂×C₃×D₃	—	2	1	no	—
539	C₂×C₃×D₃	C₂²×Q₈	1	2	yes	—
540	C₃²×C₄	—	2	2	no	—
541	C₃²×C₄	—	2	2	no	—
542	C₃²×C₄	—	2	4	no	—
543	C₃²×C₄	—	2	2	no	—
544	C₃²×C₄	—	2	1	no	—
545	C₃²×C₄	C₂²×Q₈	1	2	yes	—
546	C₃²×C₄	C₂×#41	1	2	yes	—
547	C₃×Dic₃	—	2	1	no	—
548	C₃×Dic₃	—	2	4	no	—
549	C₃×Dic₃	—	2	2	no	—
550	C₃×Dic₃	—	2	2	no	—
551	C₃×Dic₃	—	2	1	no	—
552	C₃×Dic₃	C₂²×Q₈	1	4	yes	—
553	C₃×Dic₃	C₂²×Q₈	1	2	yes	—
554	C₃×Dic₃	C₂×#41	1	4	yes	—
555	C₂×#41	—	3	1	no	—
556	C₂²×Q₈	—	3	1	no	—
557	C₂²×Q₈	—	3	2	no	—
558	C₄⋊Q₈	—	3	2	no	—
559	C₄⋊Q₈	—	3	4	no	—
560	C₄⋊Q₈	—	3	4	no	—
561	C₄⋊Q₈	—	3	2	no	—
562	C₄⋊Q₈	—	3	2	no	—
563	C₄⋊Q₈	—	3	2	no	—
564	C₄⋊Q₈	—	3	1	no	—
565	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic
566	#125	—	3	4	no	—
567	#125	—	3	4	no	—
568	#125	—	3	4	no	—
569	#125	—	3	2	no	—
570	#125	—	3	2	no	—
571	#125	C₂×C₃×D₃	1	2	yes	—
572	C₂²⋊Q₈	—	3	2	no	—
573	C₂²⋊Q₈	—	3	2	no	—
574	C₂²⋊Q₈	—	3	4	no	—
575	C₂²⋊Q₈	—	3	4	no	—
576	C₂²⋊Q₈	—	3	2	no	—
577	C₂²⋊Q₈	—	3	4	no	—
578	C₂²⋊Q₈	—	3	4	no	—
579	C₂²⋊Q₈	—	3	4	no	—
580	C₂²⋊Q₈	—	3	4	no	—
581	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
582	C₂²⋊Q₈	C₂×C₃×D₃	1	4	yes	—
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	2	no	—
588	C₄×Q₈	—	3	4	no	—
589	C₄×Q₈	—	3	2	no	—
590	C₄×Q₈	—	3	4	no	—
591	C₄×Q₈	—	3	2	no	—
592	C₄×Q₈	—	3	1	no	—
593	C₄×Q₈	—	3	2	no	—
594	C₄×Q₈	—	3	4	no	—
595	C₄×Q₈	—	3	1	no	—
596	C₄×Q₈	—	3	2	no	—
597	C₄×Q₈	—	3	2	no	—
598	C₄×Q₈	—	3	1	no	—
599	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
600	C₄×D₄	—	3	2	no	—
601	C₄×D₄	—	3	1	no	—
602	C₄×D₄	—	3	2	no	—
603	C₄×D₄	—	3	4	no	—
604	C₄×D₄	—	3	4	no	—
605	C₄×D₄	—	3	2	no	—
606	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
607	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
608	#117	—	3	2	no	—
609	#117	—	3	1	no	—
610	#117	—	3	4	no	—
611	#117	—	3	2	no	—
612	C₂×C₄⋊C₄	—	3	4	no	—
613	C₂×C₄⋊C₄	—	3	2	no	—
614	C₂×C₄⋊C₄	—	3	1	no	—
615	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
616	C₂×C₄²	—	3	4	no	—
617	C₂×C₄²	—	3	2	no	—
618	C₂×C₄²	—	3	1	no	—
619	C₂×C₄²	—	3	2	no	—
620	C₂³×C₃	—	2	2	no	—
621	C₂³×C₃	—	3	1	no	—
622	C₂³×C₃	C₂³×D₃	1	2	yes	—
623	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
624	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
625	C₃×Q₈	—	2	2	no	—
626	C₃×Q₈	—	2	2	no	—
627	C₃×Q₈	—	3	4	no	—
628	C₃×Q₈	—	3	4	no	—
629	C₃×Q₈	—	4	2	no	—
630	C₃×Q₈	—	4	2	no	—
631	C₃×Q₈	—	4	2	no	—
632	C₃×Q₈	—	6	8	no	—
633	C₃×Q₈	—	6	4	no	—
634	C₃×Q₈	—	6	4	no	—
635	C₃×Q₈	—	8	2	no	—
636	C₃×Q₈	—	12	4	no	—
637	C₃×D₄	—	2	4	no	—
638	C₃×D₄	—	3	8	no	—
639	C₃×D₄	D₃×Q₈	1	4	yes	complemented
640	C₃×D₄	C₂×C₃×Q₈	1	4	yes	complemented
641	C₂×C₃×C₄	—	2	4	no	—
642	C₂×C₃×C₄	—	2	4	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	4	no	—
650	C₂×C₃×C₄	—	3	8	no	—
651	C₂×C₃×C₄	—	3	1	no	—
652	C₂×C₃×C₄	—	3	2	no	—
653	C₂×C₃×C₄	—	3	2	no	—
654	C₂×C₃×C₄	—	3	4	no	—
655	C₂×C₃×C₄	—	3	1	no	—
656	C₂×C₃×C₄	—	3	4	no	—
657	C₂×C₃×C₄	—	3	1	no	—
658	C₂×C₃×C₄	—	3	2	no	—
659	C₂×C₃×C₄	—	3	2	no	—
660	C₂×C₃×C₄	—	4	4	no	—
661	C₂×C₃×C₄	—	4	4	no	—
662	C₂×C₃×C₄	—	4	4	no	—
663	C₂×C₃×C₄	—	6	4	no	—
664	C₂×C₃×C₄	—	6	8	no	—
665	C₂×C₃×C₄	—	6	2	no	—
666	C₂×C₃×C₄	—	8	4	no	—
667	C₂×C₃×C₄	—	12	2	no	—
668	C₂×C₃×C₄	—	12	1	no	—
669	C₂×C₃×C₄	—	12	2	no	—
670	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
671	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
672	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
673	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
674	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
675	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
676	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
677	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
678	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
679	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
680	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
681	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
682	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
683	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
684	#67	C₂×C₃×Q₈	1	8	yes	complemented
685	C₂×Dic₃	—	2	8	no	—
686	C₂×Dic₃	—	4	2	no	—
687	C₂×Dic₃	C₂×C₃×Q₈	1	8	yes	complemented
688	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
689	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
690	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
691	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
692	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
693	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
694	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
695	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
696	C₄×D₃	—	2	2	no	—
697	C₄×D₃	—	2	4	no	—
698	C₄×D₃	—	4	2	no	—
699	C₄×D₃	—	4	1	no	—
700	C₄×D₃	C₂×C₃×Q₈	1	4	yes	complemented
701	Dic₆	—	2	4	no	—
702	Dic₆	—	2	8	no	—
703	Dic₆	—	2	4	no	—
704	Dic₆	—	4	4	no	—
705	Dic₆	C₂×C₃×Q₈	1	4	yes	complemented
706	Dic₆	C₃×#41	1	4	yes	complemented
707	C₂×C₃²	—	2	4	no	—
708	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
709	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
710	C₂×C₃²	#585	1	1	yes	characteristic
711	C₃×D₃	—	2	2	no	—
712	#41	—	3	8	no	—
713	C₂×Q₈	—	3	1	no	—
714	C₂×Q₈	—	3	1	no	—
715	C₂×Q₈	—	3	4	no	—
716	C₂×Q₈	—	3	2	no	—
717	C₂×Q₈	—	3	2	no	—
718	C₂×Q₈	—	3	4	no	—
719	C₂×Q₈	—	6	8	no	—
720	C₂×Q₈	—	6	4	no	—
721	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
722	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
723	C₂×D₄	—	3	2	no	—
724	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
725	C₂²×C₄	—	3	2	no	—
726	C₂²×C₄	—	3	1	no	—
727	C₂²×C₄	—	3	4	no	—
728	C₂²×C₄	—	3	2	no	—
729	C₂²×C₄	—	3	2	no	—
730	C₂²×C₄	—	3	1	no	—
731	C₂²×C₄	—	3	1	no	—
732	C₂²×C₄	—	3	2	no	—
733	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
734	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
735	C₄⋊C₄	—	3	2	no	—
736	C₄⋊C₄	—	3	4	no	—
737	C₄⋊C₄	—	3	4	no	—
738	C₄⋊C₄	—	3	2	no	—
739	C₄⋊C₄	—	3	2	no	—
740	C₄⋊C₄	—	3	4	no	—
741	C₄⋊C₄	—	3	2	no	—
742	C₄⋊C₄	—	3	1	no	—
743	C₄⋊C₄	—	3	4	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	—	3	1	no	—
749	C₄⋊C₄	—	3	4	no	—
750	C₄⋊C₄	—	3	4	no	—
751	C₄⋊C₄	—	3	4	no	—
752	C₄⋊C₄	—	3	2	no	—
753	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
755	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
756	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
757	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
758	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
760	C₂²⋊C₄	—	3	4	no	—
761	C₂²⋊C₄	—	3	2	no	—
762	C₂²⋊C₄	—	3	4	no	—
763	C₂²⋊C₄	—	3	2	no	—
764	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
765	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
766	C₄²	—	3	2	no	—
767	C₄²	—	3	1	no	—
768	C₄²	—	3	4	no	—
769	C₄²	—	3	2	no	—
770	C₄²	—	3	1	no	—
771	C₄²	—	3	2	no	—
772	C₄²	—	3	2	no	—
773	C₄²	—	3	4	no	—
774	C₄²	—	3	1	no	—
775	C₄²	—	3	4	no	—
776	C₄²	—	3	2	no	—
777	C₄²	—	3	2	no	—
778	C₄²	C₂²×C₃×D₃	1	2	yes	—
779	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
780	C₂²×C₃	—	2	2	no	—
781	C₂²×C₃	—	2	2	no	—
782	C₂²×C₃	—	2	2	no	—
783	C₂²×C₃	—	2	2	no	—
784	C₂²×C₃	—	2	4	no	—
785	C₂²×C₃	—	2	1	no	—
786	C₂²×C₃	—	3	2	no	—
787	C₂²×C₃	—	4	2	no	—
788	C₂²×C₃	—	4	2	no	—
789	C₂²×C₃	—	6	1	no	—
790	C₂²×C₃	—	6	1	no	—
791	C₂²×C₃	C₂×D₃×Q₈	1	4	yes	—
792	C₂²×C₃	C₂²×C₃×Q₈	1	4	yes	—
793	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
794	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
795	C₂×D₃	—	2	1	no	—
796	C₂×D₃	—	2	1	no	—
797	C₂×D₃	C₂²×C₃×Q₈	1	2	yes	—
798	C₃×C₄	—	2	2	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	2	no	—
801	C₃×C₄	—	2	4	no	—
802	C₃×C₄	—	2	1	no	—
803	C₃×C₄	—	2	2	no	—
804	C₃×C₄	—	2	2	no	—
805	C₃×C₄	—	2	4	no	—
806	C₃×C₄	—	2	2	no	—
807	C₃×C₄	—	2	1	no	—
808	C₃×C₄	—	2	2	no	—
809	C₃×C₄	—	2	2	no	—
810	C₃×C₄	—	3	2	no	—
811	C₃×C₄	—	3	4	no	—
812	C₃×C₄	—	3	4	no	—
813	C₃×C₄	—	4	2	no	—
814	C₃×C₄	—	4	2	no	—
815	C₃×C₄	—	4	4	no	—
816	C₃×C₄	—	4	2	no	—
817	C₃×C₄	—	4	1	no	—
818	C₃×C₄	—	6	4	no	—
819	C₃×C₄	—	6	1	no	—
820	C₃×C₄	—	6	1	no	—
821	C₃×C₄	—	6	2	no	—
822	C₃×C₄	—	6	2	no	—
823	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
824	C₃×C₄	D₃×#41	1	2	yes	—
825	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
826	C₃×C₄	C₂×C₃×#41	1	2	yes	—
827	Dic₃	—	2	1	no	—
828	Dic₃	—	2	4	no	—
829	Dic₃	—	2	2	no	—
830	Dic₃	—	2	2	no	—
831	Dic₃	—	2	1	no	—
832	Dic₃	C₂²×C₃×Q₈	1	4	yes	—
833	Dic₃	C₂²×C₃×Q₈	1	2	yes	—
834	Dic₃	C₂×C₃×#41	1	4	yes	—
835	C₃²	Q₈×#41	1	1	yes	characteristic, complemented, Sylow
836	C₂³	—	3	1	no	—
837	C₂³	C₂³×C₃×D₃	1	2	yes	—
838	Q₈	—	2	2	no	—
839	Q₈	—	3	4	no	—
840	Q₈	—	3	4	no	—
841	Q₈	—	4	2	no	—
842	Q₈	—	6	8	no	—
843	Q₈	—	6	4	no	—
844	Q₈	—	6	4	no	—
845	Q₈	—	12	4	no	—
846	D₄	—	3	8	no	—
847	D₄	C₃×D₃×Q₈	1	4	yes	complemented
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	3	8	no	—
850	C₂×C₄	—	3	1	no	—
851	C₂×C₄	—	3	2	no	—
852	C₂×C₄	—	3	2	no	—
853	C₂×C₄	—	3	4	no	—
854	C₂×C₄	—	3	1	no	—
855	C₂×C₄	—	3	1	no	—
856	C₂×C₄	—	3	4	no	—
857	C₂×C₄	—	3	2	no	—
858	C₂×C₄	—	3	2	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	6	4	no	—
861	C₂×C₄	—	6	8	no	—
862	C₂×C₄	—	6	2	no	—
863	C₂×C₄	—	12	2	no	—
864	C₂×C₄	—	12	1	no	—
865	C₂×C₄	—	12	2	no	—
866	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
867	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
868	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
869	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
870	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
871	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
872	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
873	C₂×C₃	—	2	4	no	—
874	C₂×C₃	—	2	4	no	—
875	C₂×C₃	—	2	1	no	—
876	C₂×C₃	—	2	1	no	—
877	C₂×C₃	—	2	1	no	—
878	C₂×C₃	—	4	4	no	—
879	C₂×C₃	—	6	2	no	—
880	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
881	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
882	C₂×C₃	#5966	1	1	yes	characteristic
883	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
884	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
885	C₂×C₃	C₃×#585	1	1	yes	characteristic
886	D₃	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	3	2	no	—
890	C₂²	—	6	1	no	—
891	C₂²	—	6	1	no	—
892	C₂²	C₂×C₃×D₃×Q₈	1	4	yes	—
893	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	4	no	—
898	C₄	—	2	1	no	—
899	C₄	—	3	2	no	—
900	C₄	—	3	4	no	—
901	C₄	—	3	4	no	—
902	C₄	—	6	4	no	—
903	C₄	—	6	1	no	—
904	C₄	—	6	1	no	—
905	C₄	—	6	2	no	—
906	C₄	—	6	2	no	—
907	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
908	C₄	C₃×D₃×#41	1	2	yes	—
909	C₃	—	2	1	no	—
910	C₃	#86923	1	1	yes	characteristic, direct product factor
911	C₃	C₃×Q₈×#41	1	1	yes	characteristic, complemented
912	C₂	—	2	4	no	—
913	C₂	—	6	2	no	—
914	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
915	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
916	C₂	C₃×#5966	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×#554	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂×C₃×#237	C₂²
hypercenter	C₃×#554	D₃
hypocenter	C₃	C₃×Q₈×#41
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#554

Complements

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

N	H ≅ G/N	type
1. C₃²×#554	C₂	semidirect
2. C₃×#5728	C₂	semidirect
3. C₃×#5722	C₂	semidirect
4. C₃×#5688	C₂	semidirect
5. C₃×#5685	C₂	semidirect
6. C₃×#5636	C₂	semidirect
7. C₃×#5632	C₂	semidirect
8. C₃×#5622	C₂	semidirect
9. C₃×#5622	C₂	semidirect
10. C₃×C₄×D₃×Q₈	C₂	semidirect
11. C₃×#5567	C₂	semidirect
12. C₃×#5539	C₂	semidirect
13. C₃×D₄×Dic₆	C₂	semidirect
16. C₃×#5511	C₂	semidirect
17. C₂×C₃×#887	C₂	semidirect
19. #86923	C₃	direct (N × H)
92. C₃×#554	D₃	semidirect
93. C₃×#554	C₂×C₃	semidirect
104. #5728	C₂×C₃	semidirect
105. #5722	C₂×C₃	semidirect
106. #5688	C₂×C₃	semidirect
107. #5685	C₂×C₃	semidirect
108. #5636	C₂×C₃	semidirect
109. #5632	C₂×C₃	semidirect
110. #5622	C₂×C₃	semidirect
111. #5622	C₂×C₃	semidirect
112. C₄×D₃×Q₈	C₂×C₃	semidirect
113. #5567	C₂×C₃	semidirect
114. #5539	C₂×C₃	semidirect
115. D₄×Dic₆	C₂×C₃	semidirect
118. #5511	C₂×C₃	semidirect
119. C₂×#887	C₂×C₃	semidirect
130. C₃×#237	Q₈	semidirect
331. C₃²×D₄	C₂×Q₈	semidirect
341. C₃×#67	C₂×Q₈	semidirect
344. C₂×C₃×Dic₃	C₂×Q₈	semidirect
357. C₃×C₄×D₃	C₂×Q₈	semidirect
362. C₃×Dic₆	C₂×Q₈	semidirect
363. C₃×Dic₆	#41	semidirect
370. #554	C₃×D₃	semidirect
419. #237	C₃×Q₈	semidirect
639. C₃×D₄	D₃×Q₈	semidirect
640. C₃×D₄	C₂×C₃×Q₈	semidirect
684. #67	C₂×C₃×Q₈	semidirect
687. C₂×Dic₃	C₂×C₃×Q₈	semidirect
700. C₄×D₃	C₂×C₃×Q₈	semidirect
705. Dic₆	C₂×C₃×Q₈	semidirect
706. Dic₆	C₃×#41	semidirect
835. C₃²	Q₈×#41	semidirect
847. D₄	C₃×D₃×Q₈	semidirect
910. C₃	#86923	direct (N × H)
911. C₃	C₃×Q₈×#41	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#554	2
C₃×#5728	2
C₃×#5722	2
C₃×#5688	2
C₃×#5685	2
C₃×#5636	2
C₃×#5632	2
C₃×#5622	2
C₃×C₄×D₃×Q₈	2
C₃×#5567	2
C₃×#5539	2
C₃×D₄×Dic₆	2
C₃×C₄×#237	2
C₃×#5511	2
C₂×C₃×#887	2
C₃×Q₈×#41	3
#86923	3

Subgroups — C3×#86923 #11903740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86923 #11903740