Subgroups — C₃×#35873 #10654480

Order 768.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2644	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2643	C₂	1	2	yes	maximal, complemented
3	C₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2512	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2510	C₂	1	2	yes	maximal, complemented
7	C₃×#2510	C₂	1	2	yes	maximal, complemented
8	C₃×#2496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2495	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#2481	C₂	1	2	yes	maximal, complemented
12	C₃×#2480	C₂	1	2	yes	maximal, complemented
13	C₃×#2480	C₂	1	2	yes	maximal, complemented
14	C₃×#2480	C₂	1	2	yes	maximal, complemented
15	C₃×#2401	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#397	C₂	1	2	yes	maximal, complemented
17	C₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
21	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
22	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
23	C₃×#2275	C₂	1	1	yes	maximal, characteristic, complemented
24	#35873	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×#126	C₂²	1	2	yes	—
27	C₂×C₃×#126	C₂²	1	2	yes	complemented
28	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
35	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₃×#401	C₂²	1	2	yes	complemented
39	C₃×#401	C₂²	1	1	yes	characteristic, complemented
40	C₃×#400	C₂²	1	1	yes	characteristic, complemented
41	C₃×#400	C₂²	1	2	yes	complemented
42	C₃×#400	C₂²	1	2	yes	complemented
43	C₃×#400	C₂²	1	1	yes	characteristic, complemented
44	C₃×#400	C₂²	1	1	yes	characteristic, complemented
45	C₃×#397	C₂²	1	1	yes	characteristic
46	C₃×#397	C₂²	1	2	yes	—
47	C₃×#397	C₂²	1	2	yes	—
48	C₃×#397	C₂²	1	2	yes	—
49	C₃×#397	C₂²	1	1	yes	characteristic
50	C₃×#397	C₂²	1	1	yes	characteristic
51	C₃×#397	C₂²	1	2	yes	complemented
52	C₃×#397	C₂²	1	2	yes	complemented
53	C₃×#397	C₂²	1	2	yes	complemented
54	C₃×#397	C₂²	1	2	yes	complemented
55	C₃×#397	C₂²	1	2	yes	complemented
56	C₃×#397	C₂²	1	2	yes	complemented
57	C₃×#397	C₂²	1	2	yes	complemented
58	C₃×#397	C₂²	1	2	yes	complemented
59	C₃×#396	C₂²	1	1	yes	characteristic
60	C₃×#396	C₂²	1	2	yes	complemented
61	C₃×#396	C₂²	1	2	yes	complemented
62	C₃×#390	C₂²	1	1	yes	characteristic
63	C₃×#390	C₂²	1	1	yes	characteristic
64	C₃×#390	C₂²	1	1	yes	characteristic
65	C₃×#390	C₂²	1	1	yes	characteristic
66	C₃×#390	C₂²	1	1	yes	characteristic
67	C₃×#390	C₂²	1	1	yes	characteristic
68	C₃×#389	C₂²	1	1	yes	characteristic, complemented
69	C₃×#389	C₂²	1	1	yes	characteristic, complemented
70	C₃×#389	C₂²	1	1	yes	characteristic, complemented
71	C₃×#389	C₂²	1	1	yes	characteristic, complemented
72	C₃×#389	C₂²	1	1	yes	characteristic, complemented
73	C₃×#389	C₂²	1	1	yes	characteristic, complemented
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	—
76	C₃×#388	C₂²	1	2	yes	complemented
77	C₃×#388	C₂²	1	2	yes	complemented
78	C₃×#388	C₂²	1	2	yes	complemented
79	C₃×#388	C₂²	1	2	yes	complemented
80	C₃×#388	C₂²	1	2	yes	complemented
81	C₃×#387	C₂²	1	2	yes	complemented
82	C₃×#387	C₂²	1	2	yes	complemented
83	C₃×#386	C₂²	1	2	yes	—
84	C₃×#386	C₂²	1	2	yes	—
85	C₃×#386	C₂²	1	2	yes	—
86	C₃×#386	C₂²	1	2	yes	—
87	C₃×#386	C₂²	1	2	yes	—
88	C₃×#386	C₂²	1	2	yes	—
89	C₃×#385	C₂²	1	2	yes	complemented
90	C₃×#385	C₂²	1	2	yes	complemented
91	C₃×#385	C₂²	1	2	yes	complemented
92	C₃×#385	C₂²	1	2	yes	complemented
93	C₃×#385	C₂²	1	2	yes	complemented
94	C₃×#385	C₂²	1	2	yes	complemented
95	C₃×#384	C₂²	1	1	yes	characteristic, complemented
96	C₃×#383	C₂²	1	2	yes	complemented
97	C₃×#382	C₂²	1	1	yes	characteristic, complemented
98	C₃×#382	C₂²	1	1	yes	characteristic, complemented
99	C₃×#380	C₂²	1	1	yes	characteristic
100	C₃×#380	C₂²	1	1	yes	characteristic
101	C₃×#380	C₂²	1	1	yes	characteristic
102	C₃×#380	C₂²	1	2	yes	complemented
103	C₃×#380	C₂²	1	2	yes	complemented
104	C₃×#380	C₂²	1	2	yes	complemented
105	C₃×#379	C₂²	1	2	yes	—
106	C₃×#379	C₂²	1	2	yes	—
107	C₃×#379	C₂²	1	2	yes	—
108	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
109	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
110	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
112	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₃×#376	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₃×#95	C₂²	1	2	yes	complemented
122	C₂×C₃×#95	C₂²	1	2	yes	complemented
123	C₂×C₃×#95	C₂²	1	2	yes	complemented
124	#2644	C₂×C₃	1	1	yes	characteristic, complemented
125	#2643	C₂×C₃	1	2	yes	complemented
126	#2513	C₂×C₃	1	1	yes	characteristic, complemented
127	#2513	C₂×C₃	1	1	yes	characteristic, complemented
128	#2512	C₂×C₃	1	1	yes	characteristic, complemented
129	#2510	C₂×C₃	1	2	yes	complemented
130	#2510	C₂×C₃	1	2	yes	complemented
131	#2496	C₂×C₃	1	1	yes	characteristic, complemented
132	#2495	C₂×C₃	1	1	yes	characteristic, complemented
133	#2494	C₂×C₃	1	1	yes	characteristic, complemented
134	#2481	C₂×C₃	1	2	yes	complemented
135	#2480	C₂×C₃	1	2	yes	complemented
136	#2480	C₂×C₃	1	2	yes	complemented
137	#2480	C₂×C₃	1	2	yes	complemented
138	#2401	C₂×C₃	1	1	yes	characteristic, complemented
139	C₂×#397	C₂×C₃	1	2	yes	complemented
140	#2349	C₂×C₃	1	1	yes	characteristic, complemented
141	#2349	C₂×C₃	1	1	yes	characteristic, complemented
142	D₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
143	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
144	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
145	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
146	#2275	C₂×C₃	1	1	yes	characteristic, complemented
147	C₂⁵×C₃	C₂³	1	2	yes	—
148	C₂²×C₃×D₄	—	2	4	no	—
149	C₂²×C₃×D₄	—	2	4	no	—
150	C₂²×C₃×D₄	—	2	4	no	—
151	C₂²×C₃×D₄	C₂³	1	2	yes	—
152	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
154	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂³×C₃×C₄	C₂³	1	2	yes	—
156	C₂³×C₃×C₄	C₂³	1	2	yes	—
157	C₂³×C₃×C₄	C₂³	1	2	yes	—
158	C₂³×C₃×C₄	C₂³	1	2	yes	—
159	C₂³×C₃×C₄	C₂³	1	2	yes	—
160	C₂³×C₃×C₄	C₂³	1	2	yes	—
161	C₃×#126	—	4	4	no	—
162	C₃×#126	—	4	4	no	—
163	C₃×C₄×D₄	—	2	4	no	—
164	C₃×C₄×D₄	—	2	4	no	—
165	C₃×C₄×D₄	—	2	4	no	—
166	C₃×C₄×D₄	—	2	4	no	—
167	C₃×C₄×D₄	—	2	4	no	—
168	C₃×C₄×D₄	—	2	4	no	—
169	C₂×C₃×C₄⋊C₄	—	4	4	no	—
170	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
189	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
191	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
192	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
193	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₂²⋊C₄	C₂³	1	2	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	2	yes	—
205	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
207	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
222	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
225	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
226	C₂×C₃×C₄²	C₂³	1	2	yes	—
227	C₂×C₃×C₄²	C₂³	1	2	yes	—
228	C₂×C₃×C₄²	C₂³	1	2	yes	—
229	C₃×#95	C₂³	1	1	yes	characteristic
230	C₃×#95	C₂³	1	1	yes	characteristic
231	C₃×#95	C₂³	1	1	yes	characteristic
232	C₃×#95	C₂³	1	2	yes	—
233	C₃×#95	C₂³	1	2	yes	—
234	C₃×#95	C₂³	1	2	yes	—
235	C₃×#95	C₂³	1	2	yes	—
236	C₃×#95	C₂³	1	2	yes	—
237	C₃×#95	C₂³	1	2	yes	—
238	C₃×#95	C₂³	1	2	yes	—
239	C₃×#95	C₂³	1	2	yes	—
240	C₃×#95	C₂³	1	2	yes	—
241	C₃×#95	C₂³	1	1	yes	characteristic
242	C₃×#95	C₂³	1	1	yes	characteristic
243	C₃×#95	C₂³	1	1	yes	characteristic
244	C₃×#95	C₂³	1	1	yes	characteristic
245	C₃×#95	C₂³	1	1	yes	characteristic
246	C₃×#95	C₂³	1	1	yes	characteristic
247	C₃×#95	C₂³	1	1	yes	characteristic
248	C₃×#95	C₂³	1	1	yes	characteristic
249	C₃×#95	C₂³	1	1	yes	characteristic
250	C₃×#95	C₂³	1	1	yes	characteristic
251	C₃×#95	C₂³	1	1	yes	characteristic
252	C₃×#95	C₂³	1	1	yes	characteristic
253	C₃×#95	C₂³	1	1	yes	characteristic
254	C₃×#95	C₂³	1	2	yes	—
255	C₃×#95	C₂³	1	2	yes	—
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	2	yes	—
258	C₃×#95	C₂³	1	2	yes	—
259	C₃×#95	C₂³	1	2	yes	—
260	C₃×#95	C₂³	1	2	yes	—
261	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
262	C₂×#126	C₂²×C₃	1	2	yes	—
263	C₂×#126	C₂²×C₃	1	2	yes	complemented
264	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
268	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
269	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
271	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
272	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
273	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
274	#401	C₂²×C₃	1	2	yes	complemented
275	#401	C₂²×C₃	1	1	yes	characteristic, complemented
276	#400	C₂²×C₃	1	1	yes	characteristic, complemented
277	#400	C₂²×C₃	1	2	yes	complemented
278	#400	C₂²×C₃	1	2	yes	complemented
279	#400	C₂²×C₃	1	1	yes	characteristic, complemented
280	#400	C₂²×C₃	1	1	yes	characteristic, complemented
281	#397	C₂²×C₃	1	1	yes	characteristic
282	#397	C₂²×C₃	1	2	yes	—
283	#397	C₂²×C₃	1	2	yes	—
284	#397	C₂²×C₃	1	2	yes	—
285	#397	C₂²×C₃	1	1	yes	characteristic
286	#397	C₂²×C₃	1	1	yes	characteristic
287	#397	C₂²×C₃	1	2	yes	complemented
288	#397	C₂²×C₃	1	2	yes	complemented
289	#397	C₂²×C₃	1	2	yes	complemented
290	#397	C₂²×C₃	1	2	yes	complemented
291	#397	C₂²×C₃	1	2	yes	complemented
292	#397	C₂²×C₃	1	2	yes	complemented
293	#397	C₂²×C₃	1	2	yes	complemented
294	#397	C₂²×C₃	1	2	yes	complemented
295	#396	C₂²×C₃	1	1	yes	characteristic
296	#396	C₂²×C₃	1	2	yes	complemented
297	#396	C₂²×C₃	1	2	yes	complemented
298	#390	C₂²×C₃	1	1	yes	characteristic
299	#390	C₂²×C₃	1	1	yes	characteristic
300	#390	C₂²×C₃	1	1	yes	characteristic
301	#390	C₂²×C₃	1	1	yes	characteristic
302	#390	C₂²×C₃	1	1	yes	characteristic
303	#390	C₂²×C₃	1	1	yes	characteristic
304	#389	C₂²×C₃	1	1	yes	characteristic, complemented
305	#389	C₂²×C₃	1	1	yes	characteristic, complemented
306	#389	C₂²×C₃	1	1	yes	characteristic, complemented
307	#389	C₂²×C₃	1	1	yes	characteristic, complemented
308	#389	C₂²×C₃	1	1	yes	characteristic, complemented
309	#389	C₂²×C₃	1	1	yes	characteristic, complemented
310	#388	C₂²×C₃	1	2	yes	—
311	#388	C₂²×C₃	1	2	yes	—
312	#388	C₂²×C₃	1	2	yes	complemented
313	#388	C₂²×C₃	1	2	yes	complemented
314	#388	C₂²×C₃	1	2	yes	complemented
315	#388	C₂²×C₃	1	2	yes	complemented
316	#388	C₂²×C₃	1	2	yes	complemented
317	#387	C₂²×C₃	1	2	yes	complemented
318	#387	C₂²×C₃	1	2	yes	complemented
319	#386	C₂²×C₃	1	2	yes	—
320	#386	C₂²×C₃	1	2	yes	—
321	#386	C₂²×C₃	1	2	yes	—
322	#386	C₂²×C₃	1	2	yes	—
323	#386	C₂²×C₃	1	2	yes	—
324	#386	C₂²×C₃	1	2	yes	—
325	#385	C₂²×C₃	1	2	yes	complemented
326	#385	C₂²×C₃	1	2	yes	complemented
327	#385	C₂²×C₃	1	2	yes	complemented
328	#385	C₂²×C₃	1	2	yes	complemented
329	#385	C₂²×C₃	1	2	yes	complemented
330	#385	C₂²×C₃	1	2	yes	complemented
331	#384	C₂²×C₃	1	1	yes	characteristic, complemented
332	#383	C₂²×C₃	1	2	yes	complemented
333	#382	C₂²×C₃	1	1	yes	characteristic, complemented
334	#382	C₂²×C₃	1	1	yes	characteristic, complemented
335	#380	C₂²×C₃	1	1	yes	characteristic
336	#380	C₂²×C₃	1	1	yes	characteristic
337	#380	C₂²×C₃	1	1	yes	characteristic
338	#380	C₂²×C₃	1	2	yes	complemented
339	#380	C₂²×C₃	1	2	yes	complemented
340	#380	C₂²×C₃	1	2	yes	complemented
341	#379	C₂²×C₃	1	2	yes	—
342	#379	C₂²×C₃	1	2	yes	—
343	#379	C₂²×C₃	1	2	yes	—
344	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
345	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
346	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
347	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
348	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
349	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
350	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
351	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
353	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
354	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
355	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
356	#376	C₂²×C₃	1	1	yes	characteristic, complemented
357	C₂×#95	C₂²×C₃	1	2	yes	complemented
358	C₂×#95	C₂²×C₃	1	2	yes	complemented
359	C₂×#95	C₂²×C₃	1	2	yes	complemented
360	C₂⁴×C₃	—	2	4	no	—
361	C₂⁴×C₃	—	2	4	no	—
362	C₂⁴×C₃	—	2	4	no	—
363	C₂⁴×C₃	—	2	4	no	—
364	C₂⁴×C₃	—	4	2	no	—
365	C₂⁴×C₃	—	4	2	no	—
366	C₂⁴×C₃	—	4	2	no	—
367	C₂⁴×C₃	C₂⁴	1	2	yes	—
368	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
369	C₂⁴×C₃	C₂⁴	1	2	yes	—
370	C₂×C₃×D₄	—	2	4	no	—
371	C₂×C₃×D₄	—	2	4	no	—
372	C₂×C₃×D₄	—	2	4	no	—
373	C₂×C₃×D₄	—	2	2	no	—
374	C₂×C₃×D₄	—	2	2	no	—
375	C₂×C₃×D₄	—	2	2	no	—
376	C₂×C₃×D₄	—	4	16	no	—
377	C₂×C₃×D₄	#41	1	4	yes	—
378	C₂×C₃×D₄	#41	1	4	yes	—
379	C₂×C₃×D₄	#41	1	4	yes	—
380	C₂²×C₃×C₄	—	2	4	no	—
381	C₂²×C₃×C₄	—	2	4	no	—
382	C₂²×C₃×C₄	—	2	4	no	—
383	C₂²×C₃×C₄	—	2	4	no	—
384	C₂²×C₃×C₄	—	2	4	no	—
385	C₂²×C₃×C₄	—	2	4	no	—
386	C₂²×C₃×C₄	—	2	2	no	—
387	C₂²×C₃×C₄	—	2	2	no	—
388	C₂²×C₃×C₄	—	2	2	no	—
389	C₂²×C₃×C₄	—	2	4	no	—
390	C₂²×C₃×C₄	—	4	2	no	—
391	C₂²×C₃×C₄	—	4	2	no	—
392	C₂²×C₃×C₄	—	4	2	no	—
393	C₂²×C₃×C₄	—	4	2	no	—
394	C₂²×C₃×C₄	—	4	2	no	—
395	C₂²×C₃×C₄	—	4	2	no	—
396	C₂²×C₃×C₄	—	4	2	no	—
397	C₂²×C₃×C₄	—	4	2	no	—
398	C₂²×C₃×C₄	—	4	2	no	—
399	C₂²×C₃×C₄	—	4	2	no	—
400	C₂²×C₃×C₄	—	4	2	no	—
401	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
402	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
403	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
405	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
406	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
407	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
408	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
411	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
412	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
413	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
416	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
419	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
420	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
421	C₃×C₄⋊C₄	—	2	2	no	—
422	C₃×C₄⋊C₄	—	2	2	no	—
423	C₃×C₄⋊C₄	—	2	2	no	—
424	C₃×C₄⋊C₄	—	2	2	no	—
425	C₃×C₄⋊C₄	—	2	2	no	—
426	C₃×C₄⋊C₄	—	2	2	no	—
427	C₃×C₄⋊C₄	—	2	2	no	—
428	C₃×C₄⋊C₄	—	2	4	no	—
429	C₃×C₄⋊C₄	—	2	2	no	—
430	C₃×C₄⋊C₄	—	4	2	no	—
431	C₃×C₄⋊C₄	—	4	2	no	—
432	C₃×C₄⋊C₄	—	4	1	no	—
433	C₃×C₄⋊C₄	—	4	1	no	—
434	C₃×C₄⋊C₄	—	4	1	no	—
435	C₃×C₄⋊C₄	—	4	1	no	—
436	C₃×C₄⋊C₄	—	4	2	no	—
437	C₃×C₄⋊C₄	—	4	2	no	—
438	C₃×C₄⋊C₄	—	4	2	no	—
439	C₃×C₄⋊C₄	—	4	2	no	—
440	C₃×C₄⋊C₄	—	4	2	no	—
441	C₃×C₂²⋊C₄	—	2	4	no	—
442	C₃×C₂²⋊C₄	—	2	4	no	—
443	C₃×C₂²⋊C₄	—	2	4	no	—
444	C₃×C₂²⋊C₄	—	2	4	no	—
445	C₃×C₂²⋊C₄	—	2	4	no	—
446	C₃×C₂²⋊C₄	—	2	4	no	—
447	C₃×C₂²⋊C₄	—	2	2	no	—
448	C₃×C₂²⋊C₄	—	2	2	no	—
449	C₃×C₂²⋊C₄	—	2	4	no	—
450	C₃×C₂²⋊C₄	—	2	4	no	—
451	C₃×C₂²⋊C₄	—	2	2	no	—
452	C₃×C₂²⋊C₄	—	2	2	no	—
453	C₃×C₂²⋊C₄	—	2	4	no	—
454	C₃×C₂²⋊C₄	—	4	2	no	—
455	C₃×C₂²⋊C₄	—	4	2	no	—
456	C₃×C₂²⋊C₄	—	4	2	no	—
457	C₃×C₂²⋊C₄	—	4	2	no	—
458	C₃×C₂²⋊C₄	—	4	2	no	—
459	C₃×C₂²⋊C₄	—	4	2	no	—
460	C₃×C₂²⋊C₄	—	4	1	no	—
461	C₃×C₂²⋊C₄	—	4	2	no	—
462	C₃×C₂²⋊C₄	—	4	2	no	—
463	C₃×C₂²⋊C₄	—	4	2	no	—
464	C₃×C₂²⋊C₄	—	4	2	no	—
465	C₃×C₂²⋊C₄	—	4	1	no	—
466	C₃×C₂²⋊C₄	—	4	2	no	—
467	C₃×C₂²⋊C₄	—	4	2	no	—
468	C₃×C₄²	—	2	2	no	—
469	C₃×C₄²	—	2	2	no	—
470	C₃×C₄²	—	2	2	no	—
471	C₃×C₄²	—	2	2	no	—
472	C₃×C₄²	—	2	2	no	—
473	C₃×C₄²	—	2	2	no	—
474	C₃×C₄²	—	4	2	no	—
475	C₃×C₄²	—	4	2	no	—
476	C₃×C₄²	—	4	2	no	—
477	C₂⁵	C₂³×C₃	1	2	yes	—
478	C₂²×D₄	—	2	4	no	—
479	C₂²×D₄	—	2	4	no	—
480	C₂²×D₄	—	2	4	no	—
481	C₂²×D₄	C₂³×C₃	1	2	yes	—
482	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₃	1	2	yes	—
486	C₂³×C₄	C₂³×C₃	1	2	yes	—
487	C₂³×C₄	C₂³×C₃	1	2	yes	—
488	C₂³×C₄	C₂³×C₃	1	2	yes	—
489	C₂³×C₄	C₂³×C₃	1	2	yes	—
490	C₂³×C₄	C₂³×C₃	1	2	yes	—
491	#126	—	4	4	no	—
492	#126	—	4	4	no	—
493	C₄×D₄	—	2	4	no	—
494	C₄×D₄	—	2	4	no	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	—	2	4	no	—
497	C₄×D₄	—	2	4	no	—
498	C₄×D₄	—	2	4	no	—
499	C₂×C₄⋊C₄	—	4	4	no	—
500	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
520	C₂×C₂²⋊C₄	—	4	4	no	—
521	C₂×C₂²⋊C₄	—	4	4	no	—
522	C₂×C₂²⋊C₄	—	4	4	no	—
523	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₃	1	2	yes	—
557	C₂×C₄²	C₂³×C₃	1	2	yes	—
558	C₂×C₄²	C₂³×C₃	1	2	yes	—
559	#95	C₂³×C₃	1	1	yes	characteristic
560	#95	C₂³×C₃	1	1	yes	characteristic
561	#95	C₂³×C₃	1	1	yes	characteristic
562	#95	C₂³×C₃	1	2	yes	—
563	#95	C₂³×C₃	1	2	yes	—
564	#95	C₂³×C₃	1	2	yes	—
565	#95	C₂³×C₃	1	2	yes	—
566	#95	C₂³×C₃	1	2	yes	—
567	#95	C₂³×C₃	1	2	yes	—
568	#95	C₂³×C₃	1	2	yes	—
569	#95	C₂³×C₃	1	2	yes	—
570	#95	C₂³×C₃	1	2	yes	—
571	#95	C₂³×C₃	1	1	yes	characteristic
572	#95	C₂³×C₃	1	1	yes	characteristic
573	#95	C₂³×C₃	1	1	yes	characteristic
574	#95	C₂³×C₃	1	1	yes	characteristic
575	#95	C₂³×C₃	1	1	yes	characteristic
576	#95	C₂³×C₃	1	1	yes	characteristic
577	#95	C₂³×C₃	1	1	yes	characteristic
578	#95	C₂³×C₃	1	1	yes	characteristic
579	#95	C₂³×C₃	1	1	yes	characteristic
580	#95	C₂³×C₃	1	1	yes	characteristic
581	#95	C₂³×C₃	1	1	yes	characteristic
582	#95	C₂³×C₃	1	1	yes	characteristic
583	#95	C₂³×C₃	1	1	yes	characteristic
584	#95	C₂³×C₃	1	2	yes	—
585	#95	C₂³×C₃	1	2	yes	—
586	#95	C₂³×C₃	1	2	yes	—
587	#95	C₂³×C₃	1	2	yes	—
588	#95	C₂³×C₃	1	2	yes	—
589	#95	C₂³×C₃	1	2	yes	—
590	#95	C₂³×C₃	1	2	yes	—
591	C₂³×C₃	—	2	2	no	—
592	C₂³×C₃	—	2	2	no	—
593	C₂³×C₃	—	2	2	no	—
594	C₂³×C₃	—	2	2	no	—
595	C₂³×C₃	—	2	1	no	—
596	C₂³×C₃	—	2	1	no	—
597	C₂³×C₃	—	2	1	no	—
598	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	—	2	1	no	—
600	C₂³×C₃	—	2	1	no	—
601	C₂³×C₃	—	2	2	no	—
602	C₂³×C₃	—	2	2	no	—
603	C₂³×C₃	—	2	2	no	—
604	C₂³×C₃	—	2	2	no	—
605	C₂³×C₃	—	2	2	no	—
606	C₂³×C₃	—	2	2	no	—
607	C₂³×C₃	—	2	2	no	—
608	C₂³×C₃	—	4	8	no	—
609	C₂³×C₃	—	4	8	no	—
610	C₂³×C₃	—	4	8	no	—
611	C₂³×C₃	—	4	8	no	—
612	C₂³×C₃	—	8	4	no	—
613	C₂³×C₃	—	8	4	no	—
614	C₂³×C₃	—	8	4	no	—
615	C₂³×C₃	C₂×#41	1	4	yes	—
616	C₂³×C₃	C₂×#41	1	4	yes	—
617	C₂³×C₃	C₂×#41	1	4	yes	—
618	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
619	C₂³×C₃	C₂⁵	1	1	yes	characteristic
620	C₃×D₄	—	4	8	no	—
621	C₃×D₄	—	4	4	no	—
622	C₃×D₄	#126	1	16	yes	complemented
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	1	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	1	no	—
627	C₂×C₃×C₄	—	2	1	no	—
628	C₂×C₃×C₄	—	2	1	no	—
629	C₂×C₃×C₄	—	2	1	no	—
630	C₂×C₃×C₄	—	2	1	no	—
631	C₂×C₃×C₄	—	2	1	no	—
632	C₂×C₃×C₄	—	2	1	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	2	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	2	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	1	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	2	no	—
650	C₂×C₃×C₄	—	2	2	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	—	2	2	no	—
661	C₂×C₃×C₄	—	2	2	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	1	no	—
665	C₂×C₃×C₄	—	2	2	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	1	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	1	no	—
671	C₂×C₃×C₄	—	2	1	no	—
672	C₂×C₃×C₄	—	2	1	no	—
673	C₂×C₃×C₄	—	2	1	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	2	2	no	—
676	C₂×C₃×C₄	—	2	1	no	—
677	C₂×C₃×C₄	—	2	1	no	—
678	C₂×C₃×C₄	—	2	1	no	—
679	C₂×C₃×C₄	—	4	8	no	—
680	C₂×C₃×C₄	—	4	4	no	—
681	C₂×C₃×C₄	—	8	4	no	—
682	C₂×C₃×C₄	—	8	4	no	—
683	C₂×C₃×C₄	—	8	4	no	—
684	C₂×C₃×C₄	—	8	4	no	—
685	C₂×C₃×C₄	—	8	4	no	—
686	C₂×C₃×C₄	C₂×#41	1	2	yes	—
687	C₂×C₃×C₄	C₂×#41	1	2	yes	—
688	C₂×C₃×C₄	C₂×#41	1	2	yes	—
689	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
690	C₂⁴	—	2	4	no	—
691	C₂⁴	—	2	4	no	—
692	C₂⁴	—	2	4	no	—
693	C₂⁴	—	2	4	no	—
694	C₂⁴	—	4	2	no	—
695	C₂⁴	—	4	2	no	—
696	C₂⁴	—	4	2	no	—
697	C₂⁴	C₂⁴×C₃	1	2	yes	—
698	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
699	C₂⁴	C₂⁴×C₃	1	2	yes	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	4	16	no	—
707	C₂×D₄	C₃×#41	1	4	yes	—
708	C₂×D₄	C₃×#41	1	4	yes	—
709	C₂×D₄	C₃×#41	1	4	yes	—
710	C₂²×C₄	—	2	4	no	—
711	C₂²×C₄	—	2	4	no	—
712	C₂²×C₄	—	2	4	no	—
713	C₂²×C₄	—	2	4	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	4	2	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	4	2	no	—
728	C₂²×C₄	—	4	2	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	1	no	—
767	C₄⋊C₄	—	4	1	no	—
768	C₄⋊C₄	—	4	1	no	—
769	C₄⋊C₄	—	4	1	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₂²⋊C₄	—	4	1	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	2	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	1	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	2	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	4	2	no	—
805	C₄²	—	4	2	no	—
806	C₄²	—	4	2	no	—
807	C₂²×C₃	—	2	4	no	—
808	C₂²×C₃	—	2	4	no	—
809	C₂²×C₃	—	2	4	no	—
810	C₂²×C₃	—	2	4	no	—
811	C₂²×C₃	—	2	4	no	—
812	C₂²×C₃	—	2	4	no	—
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	2	no	—
815	C₂²×C₃	—	2	2	no	—
816	C₂²×C₃	—	4	1	no	—
817	C₂²×C₃	—	4	1	no	—
818	C₂²×C₃	—	4	1	no	—
819	C₂²×C₃	—	4	1	no	—
820	C₂²×C₃	—	4	2	no	—
821	C₂²×C₃	—	4	2	no	—
822	C₂²×C₃	—	4	2	no	—
823	C₂²×C₃	—	4	2	no	—
824	C₂²×C₃	—	4	2	no	—
825	C₂²×C₃	—	4	2	no	—
826	C₂²×C₃	—	4	2	no	—
827	C₂²×C₃	—	8	16	no	—
828	C₂²×C₃	C₂×#126	1	8	yes	—
829	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
830	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
831	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
832	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
833	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
834	C₂²×C₃	#585	1	1	yes	characteristic
835	C₂²×C₃	#585	1	1	yes	characteristic
836	C₃×C₄	—	2	2	no	—
837	C₃×C₄	—	4	1	no	—
838	C₃×C₄	—	4	1	no	—
839	C₃×C₄	—	4	1	no	—
840	C₃×C₄	—	4	1	no	—
841	C₃×C₄	—	4	2	no	—
842	C₃×C₄	—	4	2	no	—
843	C₃×C₄	—	4	2	no	—
844	C₃×C₄	—	4	1	no	—
845	C₃×C₄	—	4	1	no	—
846	C₃×C₄	—	4	1	no	—
847	C₃×C₄	—	4	2	no	—
848	C₃×C₄	—	4	1	no	—
849	C₃×C₄	—	4	2	no	—
850	C₃×C₄	—	4	2	no	—
851	C₃×C₄	—	4	1	no	—
852	C₃×C₄	—	4	1	no	—
853	C₃×C₄	—	4	1	no	—
854	C₃×C₄	—	4	1	no	—
855	C₃×C₄	C₂×#126	1	4	yes	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	2	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	4	8	no	—
874	C₂³	—	4	8	no	—
875	C₂³	—	4	8	no	—
876	C₂³	—	4	8	no	—
877	C₂³	—	8	4	no	—
878	C₂³	—	8	4	no	—
879	C₂³	—	8	4	no	—
880	C₂³	C₂×C₃×#41	1	4	yes	—
881	C₂³	C₂×C₃×#41	1	4	yes	—
882	C₂³	C₂×C₃×#41	1	4	yes	—
883	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
884	C₂³	C₂⁵×C₃	1	1	yes	characteristic
885	D₄	—	4	8	no	—
886	D₄	—	4	4	no	—
887	D₄	C₃×#126	1	16	yes	complemented
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	4	8	no	—
945	C₂×C₄	—	4	4	no	—
946	C₂×C₄	—	8	4	no	—
947	C₂×C₄	—	8	4	no	—
948	C₂×C₄	—	8	4	no	—
949	C₂×C₄	—	8	4	no	—
950	C₂×C₄	—	8	4	no	—
951	C₂×C₄	C₂×C₃×#41	1	2	yes	—
952	C₂×C₄	C₂×C₃×#41	1	2	yes	—
953	C₂×C₄	C₂×C₃×#41	1	2	yes	—
954	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
955	C₂×C₃	—	2	8	no	—
956	C₂×C₃	—	4	2	no	—
957	C₂×C₃	—	8	2	no	—
958	C₂×C₃	C₂²×#126	1	1	yes	characteristic
959	C₂×C₃	#3513	1	1	yes	characteristic
960	C₂×C₃	#3513	1	1	yes	characteristic
961	C₂×C₃	#3513	1	1	yes	characteristic
962	C₂×C₃	#3514	1	1	yes	characteristic
963	C₂×C₃	#3519	1	1	yes	characteristic
964	C₂×C₃	#3521	1	1	yes	characteristic
965	C₂²	—	2	4	no	—
966	C₂²	—	2	4	no	—
967	C₂²	—	2	4	no	—
968	C₂²	—	2	4	no	—
969	C₂²	—	2	4	no	—
970	C₂²	—	2	4	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	4	1	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	1	no	—
977	C₂²	—	4	1	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	4	2	no	—
981	C₂²	—	4	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	8	16	no	—
986	C₂²	C₂×C₃×#126	1	8	yes	—
987	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
988	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
989	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
990	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
991	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
992	C₂²	C₃×#585	1	1	yes	characteristic
993	C₂²	C₃×#585	1	1	yes	characteristic
994	C₄	—	2	2	no	—
995	C₄	—	4	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	1	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	1	no	—
1002	C₄	—	4	1	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	1	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	1	no	—
1007	C₄	—	4	1	no	—
1008	C₄	—	4	1	no	—
1009	C₄	—	4	2	no	—
1010	C₄	—	4	2	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	1	no	—
1013	C₄	C₂×C₃×#126	1	4	yes	—
1014	C₃	#35873	1	1	yes	characteristic, direct product factor, Sylow
1015	C₂	—	2	8	no	—
1016	C₂	—	4	2	no	—
1017	C₂	—	8	2	no	—
1018	C₂	C₂²×C₃×#126	1	1	yes	characteristic
1019	C₂	C₃×#3513	1	1	yes	characteristic
1020	C₂	C₃×#3513	1	1	yes	characteristic
1021	C₂	C₃×#3513	1	1	yes	characteristic
1022	C₂	C₃×#3514	1	1	yes	characteristic
1023	C₂	C₃×#3519	1	1	yes	characteristic
1024	C₂	C₃×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂³×C₃×D₄	C₂²
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. C₃×#2644	C₂	semidirect
2. C₃×#2643	C₂	semidirect
3. C₃×#2513	C₂	semidirect
4. C₃×#2513	C₂	semidirect
5. C₃×#2512	C₂	semidirect
6. C₃×#2510	C₂	semidirect
7. C₃×#2510	C₂	semidirect
8. C₃×#2496	C₂	semidirect
9. C₃×#2495	C₂	semidirect
10. C₃×#2494	C₂	semidirect
11. C₃×#2481	C₂	semidirect
12. C₃×#2480	C₂	semidirect
13. C₃×#2480	C₂	semidirect
14. C₃×#2480	C₂	semidirect
15. C₃×#2401	C₂	semidirect
16. C₂×C₃×#397	C₂	semidirect
17. C₃×#2349	C₂	semidirect
18. C₃×#2349	C₂	semidirect
19. C₃×D₄×C₄⋊C₄	C₂	semidirect
23. C₃×#2275	C₂	semidirect
24. #35873	C₃	direct (N × H)
27. C₂×C₃×#126	C₂²	semidirect
34. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
38. C₃×#401	C₂²	semidirect
39. C₃×#401	C₂²	semidirect
40. C₃×#400	C₂²	semidirect
41. C₃×#400	C₂²	semidirect
42. C₃×#400	C₂²	semidirect
43. C₃×#400	C₂²	semidirect
44. C₃×#400	C₂²	semidirect
51. C₃×#397	C₂²	semidirect
52. C₃×#397	C₂²	semidirect
53. C₃×#397	C₂²	semidirect
54. C₃×#397	C₂²	semidirect
55. C₃×#397	C₂²	semidirect
56. C₃×#397	C₂²	semidirect
57. C₃×#397	C₂²	semidirect
58. C₃×#397	C₂²	semidirect
60. C₃×#396	C₂²	semidirect
61. C₃×#396	C₂²	semidirect
68. C₃×#389	C₂²	semidirect
69. C₃×#389	C₂²	semidirect
70. C₃×#389	C₂²	semidirect
71. C₃×#389	C₂²	semidirect
72. C₃×#389	C₂²	semidirect
73. C₃×#389	C₂²	semidirect
76. C₃×#388	C₂²	semidirect
77. C₃×#388	C₂²	semidirect
78. C₃×#388	C₂²	semidirect
79. C₃×#388	C₂²	semidirect
80. C₃×#388	C₂²	semidirect
81. C₃×#387	C₂²	semidirect
82. C₃×#387	C₂²	semidirect
89. C₃×#385	C₂²	semidirect
90. C₃×#385	C₂²	semidirect
91. C₃×#385	C₂²	semidirect
92. C₃×#385	C₂²	semidirect
93. C₃×#385	C₂²	semidirect
94. C₃×#385	C₂²	semidirect
95. C₃×#384	C₂²	semidirect
96. C₃×#383	C₂²	semidirect
97. C₃×#382	C₂²	semidirect
98. C₃×#382	C₂²	semidirect
102. C₃×#380	C₂²	semidirect
103. C₃×#380	C₂²	semidirect
104. C₃×#380	C₂²	semidirect
108. C₃×C₄×C₄⋊C₄	C₂²	semidirect
109. C₃×C₄×C₄⋊C₄	C₂²	semidirect
110. C₃×C₄×C₄⋊C₄	C₂²	semidirect
111. C₃×C₄×C₄⋊C₄	C₂²	semidirect
112. C₃×C₄×C₄⋊C₄	C₂²	semidirect
113. C₃×C₄×C₄⋊C₄	C₂²	semidirect
117. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
118. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
119. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
120. C₃×#376	C₂²	semidirect
121. C₂×C₃×#95	C₂²	semidirect
122. C₂×C₃×#95	C₂²	semidirect
123. C₂×C₃×#95	C₂²	semidirect
124. #2644	C₂×C₃	semidirect
125. #2643	C₂×C₃	semidirect
126. #2513	C₂×C₃	semidirect
127. #2513	C₂×C₃	semidirect
128. #2512	C₂×C₃	semidirect
129. #2510	C₂×C₃	semidirect
130. #2510	C₂×C₃	semidirect
131. #2496	C₂×C₃	semidirect
132. #2495	C₂×C₃	semidirect
133. #2494	C₂×C₃	semidirect
134. #2481	C₂×C₃	semidirect
135. #2480	C₂×C₃	semidirect
136. #2480	C₂×C₃	semidirect
137. #2480	C₂×C₃	semidirect
138. #2401	C₂×C₃	semidirect
139. C₂×#397	C₂×C₃	semidirect
140. #2349	C₂×C₃	semidirect
141. #2349	C₂×C₃	semidirect
142. D₄×C₄⋊C₄	C₂×C₃	semidirect
146. #2275	C₂×C₃	semidirect
263. C₂×#126	C₂²×C₃	semidirect
270. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
274. #401	C₂²×C₃	semidirect
275. #401	C₂²×C₃	semidirect
276. #400	C₂²×C₃	semidirect
277. #400	C₂²×C₃	semidirect
278. #400	C₂²×C₃	semidirect
279. #400	C₂²×C₃	semidirect
280. #400	C₂²×C₃	semidirect
287. #397	C₂²×C₃	semidirect
288. #397	C₂²×C₃	semidirect
289. #397	C₂²×C₃	semidirect
290. #397	C₂²×C₃	semidirect
291. #397	C₂²×C₃	semidirect
292. #397	C₂²×C₃	semidirect
293. #397	C₂²×C₃	semidirect
294. #397	C₂²×C₃	semidirect
296. #396	C₂²×C₃	semidirect
297. #396	C₂²×C₃	semidirect
304. #389	C₂²×C₃	semidirect
305. #389	C₂²×C₃	semidirect
306. #389	C₂²×C₃	semidirect
307. #389	C₂²×C₃	semidirect
308. #389	C₂²×C₃	semidirect
309. #389	C₂²×C₃	semidirect
312. #388	C₂²×C₃	semidirect
313. #388	C₂²×C₃	semidirect
314. #388	C₂²×C₃	semidirect
315. #388	C₂²×C₃	semidirect
316. #388	C₂²×C₃	semidirect
317. #387	C₂²×C₃	semidirect
318. #387	C₂²×C₃	semidirect
325. #385	C₂²×C₃	semidirect
326. #385	C₂²×C₃	semidirect
327. #385	C₂²×C₃	semidirect
328. #385	C₂²×C₃	semidirect
329. #385	C₂²×C₃	semidirect
330. #385	C₂²×C₃	semidirect
331. #384	C₂²×C₃	semidirect
332. #383	C₂²×C₃	semidirect
333. #382	C₂²×C₃	semidirect
334. #382	C₂²×C₃	semidirect
338. #380	C₂²×C₃	semidirect
339. #380	C₂²×C₃	semidirect
340. #380	C₂²×C₃	semidirect
344. C₄×C₄⋊C₄	C₂²×C₃	semidirect
345. C₄×C₄⋊C₄	C₂²×C₃	semidirect
346. C₄×C₄⋊C₄	C₂²×C₃	semidirect
347. C₄×C₄⋊C₄	C₂²×C₃	semidirect
348. C₄×C₄⋊C₄	C₂²×C₃	semidirect
349. C₄×C₄⋊C₄	C₂²×C₃	semidirect
353. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
354. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
355. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
356. #376	C₂²×C₃	semidirect
357. C₂×#95	C₂²×C₃	semidirect
358. C₂×#95	C₂²×C₃	semidirect
359. C₂×#95	C₂²×C₃	semidirect
622. C₃×D₄	#126	semidirect
887. D₄	C₃×#126	semidirect
1014. C₃	#35873	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#2644	2
C₃×#2643	2
C₃×#2513	2
C₃×#2512	2
C₃×#2510	2
C₃×#2496	2
C₃×#2495	2
C₃×#2494	2
C₃×#2481	2
C₃×#2480	2
C₃×#2401	2
C₂×C₃×#397	2
C₃×#2349	2
C₃×D₄×C₄⋊C₄	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2275	2
#35873	3

Subgroups — C3×#35873 #10654480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#35873 #10654480