Subgroups — C₃×#37676 #10656283

Order 768.

3078 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2674	C₂	1	4	yes	maximal, complemented
7	C₃×#2672	C₂	1	4	yes	maximal, complemented
8	C₃×#2658	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2437	C₂	1	4	yes	maximal, complemented
13	C₃×#2436	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2418	C₂	1	4	yes	maximal, complemented
18	C₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
20	#37676	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
22	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic
23	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
25	C₃×D₄×Q₈	—	2	8	no	—
26	C₃×#546	—	2	8	no	—
27	C₃×#536	—	2	8	no	—
28	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#124	—	2	8	no	—
34	C₂×C₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₃×#124	C₂²	1	4	yes	—
36	C₂×C₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₃×#124	C₂²	1	1	yes	characteristic
38	C₂×C₃×#124	C₂²	1	1	yes	characteristic
39	C₂×C₃×#124	C₂²	1	1	yes	characteristic
40	C₂×C₃×#124	C₂²	1	1	yes	characteristic
41	C₂×C₃×#124	C₂²	1	1	yes	characteristic
42	C₂×C₃×#123	C₂²	1	2	yes	—
43	C₂×C₃×#123	C₂²	1	4	yes	complemented
44	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
47	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
49	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
50	C₂×C₃×#121	C₂²	1	1	yes	characteristic
51	C₂×C₃×#121	C₂²	1	2	yes	—
52	C₂×C₃×#120	C₂²	1	2	yes	—
53	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
55	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
56	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
57	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
58	C₂²×C₃×C₂²⋊C₄	C₂²	1	4	yes	—
59	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
60	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
61	C₃×#399	C₂²	1	4	yes	complemented
62	C₃×#399	C₂²	1	4	yes	complemented
63	C₃×#397	C₂²	1	4	yes	complemented
64	C₃×#396	C₂²	1	4	yes	complemented
65	C₃×#396	C₂²	1	4	yes	complemented
66	C₃×#395	C₂²	1	4	yes	complemented
67	C₃×#394	C₂²	1	4	yes	—
68	C₃×#394	C₂²	1	4	yes	complemented
69	C₃×#394	C₂²	1	4	yes	complemented
70	C₃×#393	C₂²	1	4	yes	complemented
71	C₃×#391	C₂²	1	1	yes	characteristic, complemented
72	C₃×#391	C₂²	1	1	yes	characteristic, complemented
73	C₃×#391	C₂²	1	1	yes	characteristic, complemented
74	C₃×#391	C₂²	1	1	yes	characteristic, complemented
75	C₃×#390	C₂²	1	1	yes	characteristic
76	C₃×#390	C₂²	1	1	yes	characteristic
77	C₃×#389	C₂²	1	4	yes	complemented
78	C₃×#388	C₂²	1	2	yes	complemented
79	C₃×#388	C₂²	1	4	yes	complemented
80	C₃×#388	C₂²	1	4	yes	complemented
81	C₃×#387	C₂²	1	2	yes	complemented
82	C₃×#386	C₂²	1	2	yes	—
83	C₃×#386	C₂²	1	4	yes	complemented
84	C₃×#385	C₂²	1	4	yes	—
85	C₃×#385	C₂²	1	2	yes	—
86	C₃×#385	C₂²	1	4	yes	complemented
87	C₃×#385	C₂²	1	4	yes	complemented
88	C₃×#384	C₂²	1	1	yes	characteristic, complemented
89	C₃×#380	C₂²	1	4	yes	—
90	C₃×#380	C₂²	1	4	yes	complemented
91	C₃×#379	C₂²	1	4	yes	—
92	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
93	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
94	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
95	C₃×#376	C₂²	1	1	yes	characteristic, complemented
96	C₂×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#546	C₂×C₃	1	1	yes	characteristic
98	C₂×#536	C₂×C₃	1	1	yes	characteristic, complemented
99	C₂²×#124	C₂×C₃	1	1	yes	characteristic, complemented
100	#2857	C₂×C₃	1	1	yes	characteristic, complemented
101	#2674	C₂×C₃	1	4	yes	complemented
102	#2672	C₂×C₃	1	4	yes	complemented
103	#2658	C₂×C₃	1	1	yes	characteristic, complemented
104	#2620	C₂×C₃	1	1	yes	characteristic, complemented
105	#2547	C₂×C₃	1	1	yes	characteristic, complemented
106	#2545	C₂×C₃	1	1	yes	characteristic, complemented
107	#2437	C₂×C₃	1	4	yes	complemented
108	#2436	C₂×C₃	1	1	yes	characteristic, complemented
109	#2435	C₂×C₃	1	1	yes	characteristic, complemented
110	#2434	C₂×C₃	1	1	yes	characteristic, complemented
111	#2432	C₂×C₃	1	1	yes	characteristic, complemented
112	#2418	C₂×C₃	1	4	yes	complemented
113	#2326	C₂×C₃	1	1	yes	characteristic, complemented
114	#2290	C₂×C₃	1	1	yes	characteristic, complemented
115	C₂⁵×C₃	C₂³	1	2	yes	—
116	C₂×C₃×#41	—	2	4	no	—
117	C₂×C₃×#41	—	2	4	no	—
118	C₂×C₃×#41	—	4	2	no	—
119	C₂²×C₃×Q₈	—	2	4	no	—
120	C₂²×C₃×Q₈	—	2	4	no	—
121	C₂²×C₃×Q₈	—	2	4	no	—
122	C₂²×C₃×Q₈	—	2	4	no	—
123	C₂²×C₃×Q₈	—	4	2	no	—
124	C₂²×C₃×Q₈	—	4	2	no	—
125	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
128	C₂²×C₃×Q₈	C₂³	1	2	yes	—
129	C₂²×C₃×Q₈	C₂³	1	2	yes	—
130	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
131	C₂²×C₃×D₄	—	2	4	no	—
132	C₂²×C₃×D₄	—	2	4	no	—
133	C₂²×C₃×D₄	—	4	2	no	—
134	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
135	C₂²×C₃×D₄	C₂³	1	2	yes	—
136	C₂²×C₃×D₄	C₂³	1	2	yes	—
137	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
138	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
139	C₂²×C₃×D₄	C₂³	1	2	yes	—
140	C₂³×C₃×C₄	C₂³	1	2	yes	—
141	C₂³×C₃×C₄	C₂³	1	2	yes	—
142	C₂³×C₃×C₄	C₂³	1	2	yes	—
143	C₂³×C₃×C₄	C₂³	1	2	yes	—
144	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
145	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
146	C₂³×C₃×C₄	C₂³	1	2	yes	—
147	C₃×C₄⋊Q₈	—	2	4	no	—
148	C₃×C₄⋊Q₈	—	2	8	no	—
149	C₃×C₄⋊Q₈	—	2	4	no	—
150	C₃×C₄⋊Q₈	—	2	4	no	—
151	C₃×C₄⋊Q₈	—	4	2	no	—
152	C₃×#124	—	2	4	no	—
153	C₃×#124	—	2	4	no	—
154	C₃×#124	—	2	4	no	—
155	C₃×#124	—	2	16	no	—
156	C₃×#124	—	2	4	no	—
157	C₃×#124	—	2	4	no	—
158	C₃×#124	—	4	2	no	—
159	C₃×#124	D₄	1	8	yes	complemented
160	C₃×#123	—	2	8	no	—
161	C₃×#123	—	2	16	no	—
162	C₃×C₂²⋊Q₈	—	2	4	no	—
163	C₃×C₂²⋊Q₈	—	2	4	no	—
164	C₃×C₂²⋊Q₈	—	2	4	no	—
165	C₃×C₂²⋊Q₈	—	2	8	no	—
166	C₃×C₂²⋊Q₈	—	2	16	no	—
167	C₃×C₂²⋊Q₈	—	2	8	no	—
168	C₃×#121	—	2	4	no	—
169	C₃×#121	—	2	8	no	—
170	C₃×#120	—	2	8	no	—
171	C₃×C₄×Q₈	—	2	4	no	—
172	C₃×C₄×D₄	—	2	8	no	—
173	C₃×C₄×D₄	—	2	4	no	—
174	C₃×C₄×D₄	D₄	1	8	yes	—
175	C₃×#117	—	2	4	no	—
176	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
177	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
182	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
188	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
190	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₂×C₃×C₂²⋊C₄	—	2	16	no	—
192	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
196	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
200	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
208	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
210	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄²	—	2	4	no	—
214	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
215	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
216	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄²	C₂³	1	2	yes	—
218	C₂×C₃×C₄²	C₂³	1	2	yes	—
219	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
220	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
221	C₃×#95	C₂³	1	2	yes	—
222	C₃×#95	C₂³	1	2	yes	—
223	C₃×#95	C₂³	1	2	yes	—
224	C₃×#95	C₂³	1	2	yes	—
225	C₃×#95	C₂³	1	2	yes	—
226	C₃×#95	C₂³	1	4	yes	—
227	C₃×#95	C₂³	1	4	yes	—
228	C₃×#95	C₂³	1	4	yes	—
229	C₃×#95	C₂³	1	4	yes	—
230	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
231	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic
232	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
233	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
234	D₄×Q₈	—	2	8	no	—
235	#546	—	2	8	no	—
236	#536	—	2	8	no	—
237	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
238	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
239	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
240	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
241	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
242	C₂×#124	—	2	8	no	—
243	C₂×#124	C₂²×C₃	1	1	yes	characteristic
244	C₂×#124	C₂²×C₃	1	1	yes	characteristic
245	C₂×#124	C₂²×C₃	1	4	yes	—
246	C₂×#124	C₂²×C₃	1	1	yes	characteristic
247	C₂×#124	C₂²×C₃	1	1	yes	characteristic
248	C₂×#124	C₂²×C₃	1	1	yes	characteristic
249	C₂×#124	C₂²×C₃	1	1	yes	characteristic
250	C₂×#124	C₂²×C₃	1	1	yes	characteristic
251	C₂×#123	C₂²×C₃	1	2	yes	—
252	C₂×#123	C₂²×C₃	1	4	yes	complemented
253	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
254	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
255	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
256	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
257	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
258	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
259	C₂×#121	C₂²×C₃	1	1	yes	characteristic
260	C₂×#121	C₂²×C₃	1	2	yes	—
261	C₂×#120	C₂²×C₃	1	2	yes	—
262	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
263	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
265	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
266	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
267	C₂²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
268	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
269	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
270	#399	C₂²×C₃	1	4	yes	complemented
271	#399	C₂²×C₃	1	4	yes	complemented
272	#397	C₂²×C₃	1	4	yes	complemented
273	#396	C₂²×C₃	1	4	yes	complemented
274	#396	C₂²×C₃	1	4	yes	complemented
275	#395	C₂²×C₃	1	4	yes	complemented
276	#394	C₂²×C₃	1	4	yes	—
277	#394	C₂²×C₃	1	4	yes	complemented
278	#394	C₂²×C₃	1	4	yes	complemented
279	#393	C₂²×C₃	1	4	yes	complemented
280	#391	C₂²×C₃	1	1	yes	characteristic, complemented
281	#391	C₂²×C₃	1	1	yes	characteristic, complemented
282	#391	C₂²×C₃	1	1	yes	characteristic, complemented
283	#391	C₂²×C₃	1	1	yes	characteristic, complemented
284	#390	C₂²×C₃	1	1	yes	characteristic
285	#390	C₂²×C₃	1	1	yes	characteristic
286	#389	C₂²×C₃	1	4	yes	complemented
287	#388	C₂²×C₃	1	4	yes	complemented
288	#388	C₂²×C₃	1	2	yes	complemented
289	#388	C₂²×C₃	1	4	yes	complemented
290	#387	C₂²×C₃	1	2	yes	complemented
291	#386	C₂²×C₃	1	2	yes	—
292	#386	C₂²×C₃	1	4	yes	complemented
293	#385	C₂²×C₃	1	4	yes	—
294	#385	C₂²×C₃	1	2	yes	—
295	#385	C₂²×C₃	1	4	yes	complemented
296	#385	C₂²×C₃	1	4	yes	complemented
297	#384	C₂²×C₃	1	1	yes	characteristic, complemented
298	#380	C₂²×C₃	1	4	yes	—
299	#380	C₂²×C₃	1	4	yes	complemented
300	#379	C₂²×C₃	1	4	yes	—
301	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
302	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
303	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
304	#376	C₂²×C₃	1	1	yes	characteristic, complemented
305	C₂⁴×C₃	—	2	4	no	—
306	C₂⁴×C₃	—	2	4	no	—
307	C₂⁴×C₃	—	2	8	no	—
308	C₂⁴×C₃	—	4	4	no	—
309	C₂⁴×C₃	—	4	2	no	—
310	C₂⁴×C₃	C₂⁴	1	2	yes	—
311	C₂⁴×C₃	C₂⁴	1	2	yes	—
312	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
313	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
314	C₃×#41	—	4	16	no	—
315	C₂×C₃×Q₈	—	2	2	no	—
316	C₂×C₃×Q₈	—	2	4	no	—
317	C₂×C₃×Q₈	—	2	2	no	—
318	C₂×C₃×Q₈	—	2	4	no	—
319	C₂×C₃×Q₈	—	2	4	no	—
320	C₂×C₃×Q₈	—	2	2	no	—
321	C₂×C₃×Q₈	—	2	2	no	—
322	C₂×C₃×Q₈	—	2	4	no	—
323	C₂×C₃×Q₈	—	2	2	no	—
324	C₂×C₃×Q₈	—	2	2	no	—
325	C₂×C₃×Q₈	—	2	2	no	—
326	C₂×C₃×Q₈	—	2	2	no	—
327	C₂×C₃×Q₈	—	2	2	no	—
328	C₂×C₃×Q₈	—	2	2	no	—
329	C₂×C₃×Q₈	—	2	2	no	—
330	C₂×C₃×Q₈	—	4	2	no	—
331	C₂×C₃×Q₈	—	4	2	no	—
332	C₂×C₃×Q₈	—	4	16	no	—
333	C₂×C₃×Q₈	—	4	16	no	—
334	C₂×C₃×Q₈	C₂×D₄	1	4	yes	—
335	C₂×C₃×D₄	—	2	4	no	—
336	C₂×C₃×D₄	—	2	4	no	—
337	C₂×C₃×D₄	—	2	4	no	—
338	C₂×C₃×D₄	—	2	4	no	—
339	C₂×C₃×D₄	—	2	4	no	—
340	C₂×C₃×D₄	—	2	2	no	—
341	C₂×C₃×D₄	—	2	4	no	—
342	C₂×C₃×D₄	—	2	2	no	—
343	C₂×C₃×D₄	—	2	2	no	—
344	C₂×C₃×D₄	—	2	2	no	—
345	C₂×C₃×D₄	—	2	2	no	—
346	C₂×C₃×D₄	—	4	16	no	—
347	C₂×C₃×D₄	—	4	2	no	—
348	C₂×C₃×D₄	—	4	2	no	—
349	C₂×C₃×D₄	—	4	4	no	—
350	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
351	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
352	C₂²×C₃×C₄	—	2	2	no	—
353	C₂²×C₃×C₄	—	2	2	no	—
354	C₂²×C₃×C₄	—	2	2	no	—
355	C₂²×C₃×C₄	—	2	2	no	—
356	C₂²×C₃×C₄	—	2	4	no	—
357	C₂²×C₃×C₄	—	2	4	no	—
358	C₂²×C₃×C₄	—	2	4	no	—
359	C₂²×C₃×C₄	—	2	4	no	—
360	C₂²×C₃×C₄	—	2	4	no	—
361	C₂²×C₃×C₄	—	2	4	no	—
362	C₂²×C₃×C₄	—	2	4	no	—
363	C₂²×C₃×C₄	—	2	4	no	—
364	C₂²×C₃×C₄	—	2	4	no	—
365	C₂²×C₃×C₄	—	4	2	no	—
366	C₂²×C₃×C₄	—	4	2	no	—
367	C₂²×C₃×C₄	—	4	2	no	—
368	C₂²×C₃×C₄	—	4	2	no	—
369	C₂²×C₃×C₄	—	4	4	no	—
370	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
371	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
372	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
373	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
374	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
375	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
376	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
377	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
378	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
379	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
380	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
381	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
382	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
385	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
387	C₃×C₄⋊C₄	—	2	4	no	—
388	C₃×C₄⋊C₄	—	2	2	no	—
389	C₃×C₄⋊C₄	—	2	4	no	—
390	C₃×C₄⋊C₄	—	2	4	no	—
391	C₃×C₄⋊C₄	—	2	2	no	—
392	C₃×C₄⋊C₄	—	2	4	no	—
393	C₃×C₄⋊C₄	—	2	4	no	—
394	C₃×C₄⋊C₄	—	2	4	no	—
395	C₃×C₄⋊C₄	—	2	4	no	—
396	C₃×C₄⋊C₄	—	2	8	no	—
397	C₃×C₄⋊C₄	—	2	8	no	—
398	C₃×C₄⋊C₄	—	4	4	no	—
399	C₃×C₄⋊C₄	—	4	2	no	—
400	C₃×C₄⋊C₄	—	4	4	no	—
401	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
402	C₃×C₂²⋊C₄	—	2	4	no	—
403	C₃×C₂²⋊C₄	—	2	8	no	—
404	C₃×C₂²⋊C₄	—	2	4	no	—
405	C₃×C₂²⋊C₄	—	2	4	no	—
406	C₃×C₂²⋊C₄	—	2	8	no	—
407	C₃×C₂²⋊C₄	—	2	4	no	—
408	C₃×C₂²⋊C₄	—	2	4	no	—
409	C₃×C₂²⋊C₄	—	2	4	no	—
410	C₃×C₂²⋊C₄	—	2	8	no	—
411	C₃×C₂²⋊C₄	—	2	8	no	—
412	C₃×C₂²⋊C₄	—	2	4	no	—
413	C₃×C₂²⋊C₄	—	2	4	no	—
414	C₃×C₂²⋊C₄	—	2	4	no	—
415	C₃×C₂²⋊C₄	—	4	4	no	—
416	C₃×C₂²⋊C₄	—	4	2	no	—
417	C₃×C₂²⋊C₄	—	4	4	no	—
418	C₃×C₂²⋊C₄	—	4	4	no	—
419	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
420	C₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
421	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
422	C₃×C₄²	—	2	4	no	—
423	C₃×C₄²	—	2	2	no	—
424	C₃×C₄²	—	2	2	no	—
425	C₃×C₄²	—	2	4	no	—
426	C₃×C₄²	—	2	2	no	—
427	C₃×C₄²	C₂×D₄	1	4	yes	—
428	C₃×C₄²	C₂×D₄	1	4	yes	—
429	C₂⁵	C₂³×C₃	1	2	yes	—
430	C₂×#41	—	2	4	no	—
431	C₂×#41	—	2	4	no	—
432	C₂×#41	—	4	2	no	—
433	C₂²×Q₈	—	2	4	no	—
434	C₂²×Q₈	—	2	4	no	—
435	C₂²×Q₈	—	2	4	no	—
436	C₂²×Q₈	—	2	4	no	—
437	C₂²×Q₈	—	4	2	no	—
438	C₂²×Q₈	—	4	2	no	—
439	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
441	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₃	1	2	yes	—
443	C₂²×Q₈	C₂³×C₃	1	2	yes	—
444	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
445	C₂²×D₄	—	2	4	no	—
446	C₂²×D₄	—	2	4	no	—
447	C₂²×D₄	—	4	2	no	—
448	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
449	C₂²×D₄	C₂³×C₃	1	2	yes	—
450	C₂²×D₄	C₂³×C₃	1	2	yes	—
451	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
453	C₂²×D₄	C₂³×C₃	1	2	yes	—
454	C₂³×C₄	C₂³×C₃	1	2	yes	—
455	C₂³×C₄	C₂³×C₃	1	2	yes	—
456	C₂³×C₄	C₂³×C₃	1	2	yes	—
457	C₂³×C₄	C₂³×C₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₃	1	2	yes	—
461	C₄⋊Q₈	—	2	4	no	—
462	C₄⋊Q₈	—	2	8	no	—
463	C₄⋊Q₈	—	2	4	no	—
464	C₄⋊Q₈	—	2	4	no	—
465	C₄⋊Q₈	—	4	2	no	—
466	#124	—	2	4	no	—
467	#124	—	2	4	no	—
468	#124	—	2	4	no	—
469	#124	—	2	16	no	—
470	#124	—	2	4	no	—
471	#124	—	2	4	no	—
472	#124	—	4	2	no	—
473	#124	C₃×D₄	1	8	yes	complemented
474	#123	—	2	8	no	—
475	#123	—	2	16	no	—
476	C₂²⋊Q₈	—	2	4	no	—
477	C₂²⋊Q₈	—	2	4	no	—
478	C₂²⋊Q₈	—	2	4	no	—
479	C₂²⋊Q₈	—	2	8	no	—
480	C₂²⋊Q₈	—	2	16	no	—
481	C₂²⋊Q₈	—	2	8	no	—
482	#121	—	2	4	no	—
483	#121	—	2	8	no	—
484	#120	—	2	8	no	—
485	C₄×Q₈	—	2	4	no	—
486	C₄×D₄	—	2	8	no	—
487	C₄×D₄	—	2	4	no	—
488	C₄×D₄	C₃×D₄	1	8	yes	—
489	#117	—	2	4	no	—
490	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	—	2	16	no	—
506	C₂×C₂²⋊C₄	—	2	8	no	—
507	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
527	C₂×C₄²	—	2	4	no	—
528	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₃	1	2	yes	—
532	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
533	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
535	#95	C₂³×C₃	1	2	yes	—
536	#95	C₂³×C₃	1	2	yes	—
537	#95	C₂³×C₃	1	2	yes	—
538	#95	C₂³×C₃	1	2	yes	—
539	#95	C₂³×C₃	1	2	yes	—
540	#95	C₂³×C₃	1	4	yes	—
541	#95	C₂³×C₃	1	4	yes	—
542	#95	C₂³×C₃	1	4	yes	—
543	#95	C₂³×C₃	1	4	yes	—
544	C₂³×C₃	—	2	1	no	—
545	C₂³×C₃	—	2	1	no	—
546	C₂³×C₃	—	2	2	no	—
547	C₂³×C₃	—	2	1	no	—
548	C₂³×C₃	—	2	2	no	—
549	C₂³×C₃	—	2	1	no	—
550	C₂³×C₃	—	2	2	no	—
551	C₂³×C₃	—	2	2	no	—
552	C₂³×C₃	—	2	4	no	—
553	C₂³×C₃	—	2	4	no	—
554	C₂³×C₃	—	2	2	no	—
555	C₂³×C₃	—	2	2	no	—
556	C₂³×C₃	—	2	2	no	—
557	C₂³×C₃	—	2	2	no	—
558	C₂³×C₃	—	2	4	no	—
559	C₂³×C₃	—	2	4	no	—
560	C₂³×C₃	—	4	8	no	—
561	C₂³×C₃	—	4	16	no	—
562	C₂³×C₃	—	4	8	no	—
563	C₂³×C₃	—	8	4	no	—
564	C₂³×C₃	—	8	8	no	—
565	C₂³×C₃	C₂²×D₄	1	4	yes	—
566	C₂³×C₃	C₂²×D₄	1	2	yes	—
567	C₂³×C₃	C₂²×D₄	1	2	yes	—
568	C₂³×C₃	2₋¹⁺⁴	1	4	yes	—
569	C₂³×C₃	C₂⁵	1	1	yes	characteristic
570	C₃×Q₈	—	2	8	no	—
571	C₃×Q₈	—	4	8	no	—
572	C₃×Q₈	—	4	8	no	—
573	C₃×Q₈	—	4	4	no	—
574	C₃×Q₈	—	4	4	no	—
575	C₃×Q₈	—	4	4	no	—
576	C₃×D₄	—	2	8	no	—
577	C₃×D₄	—	2	8	no	—
578	C₃×D₄	—	4	8	no	—
579	C₃×D₄	—	4	8	no	—
580	C₃×D₄	—	4	4	no	—
581	C₃×D₄	—	8	4	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	2	no	—
584	C₂×C₃×C₄	—	2	1	no	—
585	C₂×C₃×C₄	—	2	1	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	2	no	—
588	C₂×C₃×C₄	—	2	2	no	—
589	C₂×C₃×C₄	—	2	2	no	—
590	C₂×C₃×C₄	—	2	2	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	—	2	8	no	—
593	C₂×C₃×C₄	—	2	8	no	—
594	C₂×C₃×C₄	—	2	2	no	—
595	C₂×C₃×C₄	—	2	2	no	—
596	C₂×C₃×C₄	—	2	2	no	—
597	C₂×C₃×C₄	—	2	2	no	—
598	C₂×C₃×C₄	—	2	2	no	—
599	C₂×C₃×C₄	—	2	2	no	—
600	C₂×C₃×C₄	—	2	2	no	—
601	C₂×C₃×C₄	—	2	2	no	—
602	C₂×C₃×C₄	—	2	2	no	—
603	C₂×C₃×C₄	—	2	2	no	—
604	C₂×C₃×C₄	—	2	2	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	2	no	—
607	C₂×C₃×C₄	—	2	2	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	2	no	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	4	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	4	no	—
616	C₂×C₃×C₄	—	4	8	no	—
617	C₂×C₃×C₄	—	4	8	no	—
618	C₂×C₃×C₄	—	4	8	no	—
619	C₂×C₃×C₄	—	4	8	no	—
620	C₂×C₃×C₄	—	8	4	no	—
621	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
622	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
623	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
624	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
625	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
626	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
627	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
628	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
629	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
630	C₂⁴	—	2	4	no	—
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	2	8	no	—
633	C₂⁴	—	4	2	no	—
634	C₂⁴	—	4	4	no	—
635	C₂⁴	C₂⁴×C₃	1	2	yes	—
636	C₂⁴	C₂⁴×C₃	1	2	yes	—
637	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
638	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
639	#41	—	4	16	no	—
640	C₂×Q₈	—	2	2	no	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	2	4	no	—
645	C₂×Q₈	—	2	2	no	—
646	C₂×Q₈	—	2	2	no	—
647	C₂×Q₈	—	2	4	no	—
648	C₂×Q₈	—	2	2	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	4	2	no	—
656	C₂×Q₈	—	4	2	no	—
657	C₂×Q₈	—	4	16	no	—
658	C₂×Q₈	—	4	16	no	—
659	C₂×Q₈	C₂×C₃×D₄	1	4	yes	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	4	16	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
676	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	4	no	—
695	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
696	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
697	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	8	no	—
722	C₄⋊C₄	—	2	8	no	—
723	C₄⋊C₄	—	4	4	no	—
724	C₄⋊C₄	—	4	4	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	8	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	8	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	8	no	—
736	C₂²⋊C₄	—	2	8	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	4	4	no	—
741	C₂²⋊C₄	—	4	4	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	4	no	—
744	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
745	C₂²⋊C₄	C₂×C₃×D₄	1	16	yes	—
746	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	—	2	4	no	—
751	C₄²	—	2	2	no	—
752	C₄²	C₂×C₃×D₄	1	4	yes	—
753	C₄²	C₂×C₃×D₄	1	4	yes	—
754	C₂²×C₃	—	2	2	no	—
755	C₂²×C₃	—	2	4	no	—
756	C₂²×C₃	—	2	2	no	—
757	C₂²×C₃	—	2	4	no	—
758	C₂²×C₃	—	2	2	no	—
759	C₂²×C₃	—	2	2	no	—
760	C₂²×C₃	—	2	4	no	—
761	C₂²×C₃	—	2	8	no	—
762	C₂²×C₃	—	2	2	no	—
763	C₂²×C₃	—	4	2	no	—
764	C₂²×C₃	—	4	2	no	—
765	C₂²×C₃	—	4	2	no	—
766	C₂²×C₃	—	4	2	no	—
767	C₂²×C₃	—	4	4	no	—
768	C₂²×C₃	—	4	2	no	—
769	C₂²×C₃	—	4	2	no	—
770	C₂²×C₃	—	4	4	no	—
771	C₂²×C₃	—	4	2	no	—
772	C₂²×C₃	—	4	4	no	—
773	C₂²×C₃	—	8	16	no	—
774	C₂²×C₃	#536	1	4	yes	complemented
775	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
776	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
777	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
778	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
779	C₂²×C₃	#585	1	2	yes	—
780	C₃×C₄	—	2	2	no	—
781	C₃×C₄	—	2	2	no	—
782	C₃×C₄	—	2	2	no	—
783	C₃×C₄	—	2	4	no	—
784	C₃×C₄	—	2	4	no	—
785	C₃×C₄	—	2	2	no	—
786	C₃×C₄	—	4	2	no	—
787	C₃×C₄	—	4	2	no	—
788	C₃×C₄	—	4	2	no	—
789	C₃×C₄	—	4	2	no	—
790	C₃×C₄	—	4	2	no	—
791	C₃×C₄	—	4	2	no	—
792	C₃×C₄	—	4	2	no	—
793	C₃×C₄	—	4	2	no	—
794	C₃×C₄	D₄²	1	4	yes	—
795	C₂³	—	2	1	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	1	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	4	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	4	no	—
811	C₂³	—	4	8	no	—
812	C₂³	—	4	16	no	—
813	C₂³	—	4	8	no	—
814	C₂³	—	8	4	no	—
815	C₂³	—	8	8	no	—
816	C₂³	C₂²×C₃×D₄	1	4	yes	—
817	C₂³	C₂²×C₃×D₄	1	2	yes	—
818	C₂³	C₂²×C₃×D₄	1	2	yes	—
819	C₂³	C₃×2₋¹⁺⁴	1	4	yes	—
820	C₂³	C₂⁵×C₃	1	1	yes	characteristic
821	Q₈	—	2	8	no	—
822	Q₈	—	4	8	no	—
823	Q₈	—	4	8	no	—
824	Q₈	—	4	4	no	—
825	Q₈	—	4	4	no	—
826	Q₈	—	4	4	no	—
827	D₄	—	2	8	no	—
828	D₄	—	2	8	no	—
829	D₄	—	4	8	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	4	no	—
832	D₄	—	8	4	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	8	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	4	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	8	no	—
869	C₂×C₄	—	4	8	no	—
870	C₂×C₄	—	4	8	no	—
871	C₂×C₄	—	8	4	no	—
872	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
873	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
874	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
875	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
876	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
877	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
878	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
879	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
880	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
881	C₂×C₃	—	2	4	no	—
882	C₂×C₃	—	4	2	no	—
883	C₂×C₃	—	4	4	no	—
884	C₂×C₃	—	8	2	no	—
885	C₂×C₃	C₂×#536	1	1	yes	characteristic
886	C₂×C₃	C₂×D₄²	1	1	yes	characteristic
887	C₂×C₃	#3489	1	2	yes	—
888	C₂×C₃	#3500	1	1	yes	characteristic
889	C₂×C₃	#3561	1	2	yes	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	2	8	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	4	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	4	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	4	no	—
909	C₂²	—	8	16	no	—
910	C₂²	C₃×#536	1	4	yes	complemented
911	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
912	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
913	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
914	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
915	C₂²	C₃×#585	1	2	yes	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	4	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	C₃×D₄²	1	4	yes	—
931	C₃	#37676	1	1	yes	characteristic, direct product factor, Sylow
932	C₂	—	2	4	no	—
933	C₂	—	4	4	no	—
934	C₂	—	4	2	no	—
935	C₂	—	8	2	no	—
936	C₂	C₂×C₃×#536	1	1	yes	characteristic
937	C₂	C₂×C₃×D₄²	1	1	yes	characteristic
938	C₂	C₃×#3489	1	2	yes	—
939	C₂	C₃×#3500	1	1	yes	characteristic
940	C₂	C₃×#3561	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#546	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×Q₈	C₂	semidirect
3. C₂×C₃×#536	C₂	semidirect
4. C₂²×C₃×#124	C₂	semidirect
5. C₃×#2857	C₂	semidirect
6. C₃×#2674	C₂	semidirect
7. C₃×#2672	C₂	semidirect
8. C₃×#2658	C₂	semidirect
9. C₃×#2620	C₂	semidirect
10. C₃×#2547	C₂	semidirect
11. C₃×#2545	C₂	semidirect
12. C₃×#2437	C₂	semidirect
13. C₃×#2436	C₂	semidirect
14. C₃×#2435	C₂	semidirect
15. C₃×#2434	C₂	semidirect
16. C₃×#2432	C₂	semidirect
17. C₃×#2418	C₂	semidirect
18. C₃×#2326	C₂	semidirect
19. C₃×#2290	C₂	semidirect
20. #37676	C₃	direct (N × H)
23. C₂³×C₃×Q₈	C₂²	semidirect
28. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
32. C₂×C₃×C₄⋊Q₈	C₂²	semidirect
43. C₂×C₃×#123	C₂²	semidirect
47. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
48. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
49. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₃×C₄×Q₈	C₂²	semidirect
57. C₂×C₃×#117	C₂²	semidirect
61. C₃×#399	C₂²	semidirect
62. C₃×#399	C₂²	semidirect
63. C₃×#397	C₂²	semidirect
64. C₃×#396	C₂²	semidirect
65. C₃×#396	C₂²	semidirect
66. C₃×#395	C₂²	semidirect
68. C₃×#394	C₂²	semidirect
69. C₃×#394	C₂²	semidirect
70. C₃×#393	C₂²	semidirect
71. C₃×#391	C₂²	semidirect
72. C₃×#391	C₂²	semidirect
73. C₃×#391	C₂²	semidirect
74. C₃×#391	C₂²	semidirect
77. C₃×#389	C₂²	semidirect
78. C₃×#388	C₂²	semidirect
79. C₃×#388	C₂²	semidirect
80. C₃×#388	C₂²	semidirect
81. C₃×#387	C₂²	semidirect
83. C₃×#386	C₂²	semidirect
86. C₃×#385	C₂²	semidirect
87. C₃×#385	C₂²	semidirect
88. C₃×#384	C₂²	semidirect
90. C₃×#380	C₂²	semidirect
92. C₃×C₄×C₄⋊C₄	C₂²	semidirect
94. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
95. C₃×#376	C₂²	semidirect
96. C₂×D₄×Q₈	C₂×C₃	semidirect
98. C₂×#536	C₂×C₃	semidirect
99. C₂²×#124	C₂×C₃	semidirect
100. #2857	C₂×C₃	semidirect
101. #2674	C₂×C₃	semidirect
102. #2672	C₂×C₃	semidirect
103. #2658	C₂×C₃	semidirect
104. #2620	C₂×C₃	semidirect
105. #2547	C₂×C₃	semidirect
106. #2545	C₂×C₃	semidirect
107. #2437	C₂×C₃	semidirect
108. #2436	C₂×C₃	semidirect
109. #2435	C₂×C₃	semidirect
110. #2434	C₂×C₃	semidirect
111. #2432	C₂×C₃	semidirect
112. #2418	C₂×C₃	semidirect
113. #2326	C₂×C₃	semidirect
114. #2290	C₂×C₃	semidirect
159. C₃×#124	D₄	semidirect
232. C₂³×Q₈	C₂²×C₃	semidirect
237. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
238. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
239. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
240. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
241. C₂×C₄⋊Q₈	C₂²×C₃	semidirect
252. C₂×#123	C₂²×C₃	semidirect
256. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
257. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
258. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
262. C₂×C₄×Q₈	C₂²×C₃	semidirect
266. C₂×#117	C₂²×C₃	semidirect
270. #399	C₂²×C₃	semidirect
271. #399	C₂²×C₃	semidirect
272. #397	C₂²×C₃	semidirect
273. #396	C₂²×C₃	semidirect
274. #396	C₂²×C₃	semidirect
275. #395	C₂²×C₃	semidirect
277. #394	C₂²×C₃	semidirect
278. #394	C₂²×C₃	semidirect
279. #393	C₂²×C₃	semidirect
280. #391	C₂²×C₃	semidirect
281. #391	C₂²×C₃	semidirect
282. #391	C₂²×C₃	semidirect
283. #391	C₂²×C₃	semidirect
286. #389	C₂²×C₃	semidirect
287. #388	C₂²×C₃	semidirect
288. #388	C₂²×C₃	semidirect
289. #388	C₂²×C₃	semidirect
290. #387	C₂²×C₃	semidirect
292. #386	C₂²×C₃	semidirect
295. #385	C₂²×C₃	semidirect
296. #385	C₂²×C₃	semidirect
297. #384	C₂²×C₃	semidirect
299. #380	C₂²×C₃	semidirect
301. C₄×C₄⋊C₄	C₂²×C₃	semidirect
303. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
304. #376	C₂²×C₃	semidirect
473. #124	C₃×D₄	semidirect
774. C₂²×C₃	#536	semidirect
910. C₂²	C₃×#536	semidirect
931. C₃	#37676	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄×Q₈	2
C₂×C₃×#546	2
C₂×C₃×#536	2
C₂²×C₃×#124	2
C₃×#2857	2
C₃×#2674	2
C₃×#2672	2
C₃×#2658	2
C₃×#2620	2
C₃×#2547	2
C₃×#2545	2
C₃×#2437	2
C₃×#2436	2
C₃×#2435	2
C₃×#2434	2
C₃×#2432	2
C₃×#2418	2
C₃×#2326	2
C₃×#2290	2
#37676	3

Subgroups — C3×#37676 #10656283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#37676 #10656283