Subgroups — C₃×#34495 #10653102

Order 768.

2600 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#546	C₂	1	1	yes	maximal, characteristic
2	C₃×#2376	C₂	1	2	yes	maximal, complemented
3	C₃×#2375	C₂	1	2	yes	maximal, complemented
4	C₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2363	C₂	1	2	yes	maximal, complemented
6	C₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2342	C₂	1	2	yes	maximal, complemented
11	C₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₄×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2335	C₂	1	2	yes	maximal, complemented
14	C₃×#2333	C₂	1	2	yes	maximal, complemented
15	C₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2323	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2321	C₂	1	2	yes	maximal, complemented
18	C₃×#2312	C₂	1	2	yes	maximal, complemented
19	C₃×#2311	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃×#2309	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃×C₄×#124	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	#34495	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₃×#41	C₂²	1	1	yes	characteristic
26	C₂³×C₃×D₄	C₂²	1	1	yes	characteristic
27	C₃×#546	C₄	1	16	yes	complemented
28	C₂×C₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₃×#123	C₂²	1	2	yes	—
30	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₃×#121	C₂²	1	2	yes	—
33	C₂×C₃×#120	C₂²	1	2	yes	—
34	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₄×D₄	C₂²	1	2	yes	complemented
41	C₂×C₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃×#117	C₂²	1	1	yes	characteristic
43	C₂×C₃×#117	C₂²	1	2	yes	complemented
44	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
47	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
48	C₃×#391	C₂²	1	1	yes	characteristic, complemented
49	C₃×#391	C₂²	1	1	yes	characteristic, complemented
50	C₃×#390	C₂²	1	1	yes	characteristic
51	C₃×#390	C₂²	1	2	yes	—
52	C₃×#390	C₂²	1	1	yes	characteristic
53	C₃×#390	C₂²	1	1	yes	characteristic
54	C₃×#390	C₂²	1	1	yes	characteristic
55	C₃×#390	C₂²	1	1	yes	characteristic
56	C₃×#390	C₂²	1	1	yes	characteristic
57	C₃×#390	C₂²	1	2	yes	—
58	C₃×#390	C₂²	1	1	yes	characteristic
59	C₃×#390	C₂²	1	1	yes	characteristic
60	C₃×#390	C₂²	1	2	yes	complemented
61	C₃×#390	C₂²	1	2	yes	complemented
62	C₃×#390	C₂²	1	2	yes	complemented
63	C₃×#389	C₂²	1	1	yes	characteristic, complemented
64	C₃×#389	C₂²	1	2	yes	complemented
65	C₃×#389	C₂²	1	1	yes	characteristic, complemented
66	C₃×#389	C₂²	1	1	yes	characteristic, complemented
67	C₃×#389	C₂²	1	1	yes	characteristic, complemented
68	C₃×#388	C₂²	1	2	yes	—
69	C₃×#388	C₂²	1	2	yes	—
70	C₃×#388	C₂²	1	2	yes	—
71	C₃×#388	C₂²	1	1	yes	characteristic
72	C₃×#388	C₂²	1	1	yes	characteristic
73	C₃×#388	C₂²	1	2	yes	—
74	C₃×#388	C₂²	1	2	yes	—
75	C₃×#388	C₂²	1	2	yes	complemented
76	C₃×#388	C₂²	1	1	yes	characteristic, 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×#388	C₂²	1	2	yes	complemented
82	C₃×#388	C₂²	1	2	yes	complemented
83	C₃×#388	C₂²	1	2	yes	complemented
84	C₃×#388	C₂²	1	1	yes	characteristic, complemented
85	C₃×#388	C₂²	1	2	yes	complemented
86	C₃×#388	C₂²	1	2	yes	complemented
87	C₃×#387	C₂²	1	2	yes	complemented
88	C₃×#387	C₂²	1	2	yes	complemented
89	C₃×#387	C₂²	1	2	yes	complemented
90	C₃×#386	C₂²	1	2	yes	—
91	C₃×#386	C₂²	1	2	yes	—
92	C₃×#386	C₂²	1	2	yes	—
93	C₃×#386	C₂²	1	2	yes	complemented
94	C₃×#386	C₂²	1	2	yes	complemented
95	C₃×#386	C₂²	1	2	yes	complemented
96	C₃×#386	C₂²	1	2	yes	complemented
97	C₃×#385	C₂²	1	2	yes	complemented
98	C₃×#385	C₂²	1	2	yes	complemented
99	C₃×#385	C₂²	1	2	yes	complemented
100	C₃×#382	C₂²	1	1	yes	characteristic, complemented
101	C₃×#381	C₂²	1	2	yes	complemented
102	C₃×#380	C₂²	1	1	yes	characteristic
103	C₃×#380	C₂²	1	2	yes	complemented
104	C₃×#380	C₂²	1	2	yes	complemented
105	C₃×#380	C₂²	1	2	yes	complemented
106	C₃×#380	C₂²	1	1	yes	characteristic, complemented
107	C₃×#379	C₂²	1	2	yes	—
108	C₃×#379	C₂²	1	2	yes	—
109	C₃×#379	C₂²	1	2	yes	—
110	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
111	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	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×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
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×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
124	C₃×C₄³	C₂²	1	1	yes	characteristic, complemented
125	C₂×#546	C₂×C₃	1	1	yes	characteristic
126	#2376	C₂×C₃	1	2	yes	complemented
127	#2375	C₂×C₃	1	2	yes	complemented
128	#2367	C₂×C₃	1	1	yes	characteristic, complemented
129	#2363	C₂×C₃	1	2	yes	complemented
130	#2362	C₂×C₃	1	1	yes	characteristic, complemented
131	#2361	C₂×C₃	1	1	yes	characteristic, complemented
132	#2357	C₂×C₃	1	1	yes	characteristic, complemented
133	#2352	C₂×C₃	1	1	yes	characteristic, complemented
134	#2342	C₂×C₃	1	2	yes	complemented
135	#2341	C₂×C₃	1	1	yes	characteristic, complemented
136	D₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
137	#2335	C₂×C₃	1	2	yes	complemented
138	#2333	C₂×C₃	1	2	yes	complemented
139	#2324	C₂×C₃	1	1	yes	characteristic, complemented
140	#2323	C₂×C₃	1	1	yes	characteristic, complemented
141	#2321	C₂×C₃	1	2	yes	complemented
142	#2312	C₂×C₃	1	2	yes	complemented
143	#2311	C₂×C₃	1	1	yes	characteristic, complemented
144	#2309	C₂×C₃	1	1	yes	characteristic, complemented
145	C₄×#124	C₂×C₃	1	1	yes	characteristic, complemented
146	#2293	C₂×C₃	1	1	yes	characteristic, complemented
147	#2293	C₂×C₃	1	1	yes	characteristic, complemented
148	C₂⁵×C₃	C₂³	1	2	yes	—
149	C₂×C₃×#41	—	4	2	no	—
150	C₂×C₃×#41	—	4	2	no	—
151	C₂×C₃×#41	C₂×C₄	1	8	yes	complemented
152	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
153	C₂²×C₃×D₄	—	4	2	no	—
154	C₂²×C₃×D₄	—	4	2	no	—
155	C₂²×C₃×D₄	C₂×C₄	1	8	yes	complemented
156	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
157	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₃×D₄	C₂³	1	2	yes	—
159	C₂²×C₃×D₄	C₂³	1	2	yes	—
160	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
161	C₂²×C₃×D₄	C₂³	1	2	yes	—
162	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
163	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
164	C₂³×C₃×C₄	C₂³	1	2	yes	—
165	C₂³×C₃×C₄	C₂³	1	2	yes	—
166	C₂³×C₃×C₄	C₂³	1	2	yes	—
167	C₂³×C₃×C₄	C₂³	1	2	yes	—
168	C₂³×C₃×C₄	C₂³	1	2	yes	—
169	C₃×#124	C₂×C₄	1	8	yes	complemented
170	C₃×#123	C₂×C₄	1	16	yes	complemented
171	C₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
172	C₃×#121	C₂×C₄	1	8	yes	—
173	C₃×#121	C₂×C₄	1	16	yes	complemented
174	C₃×#120	C₂×C₄	1	16	yes	complemented
175	C₃×C₄×Q₈	—	4	2	no	—
176	C₃×C₄×Q₈	—	4	2	no	—
177	C₃×C₄×D₄	—	4	2	no	—
178	C₃×C₄×D₄	—	4	2	no	—
179	C₃×C₄×D₄	—	4	4	no	—
180	C₃×C₄×D₄	C₂×C₄	1	8	yes	complemented
181	C₃×C₄×D₄	C₂×C₄	1	8	yes	complemented
182	C₃×#117	—	4	2	no	—
183	C₃×#117	—	4	2	no	—
184	C₃×#117	—	4	4	no	—
185	C₃×#117	—	4	2	no	—
186	C₂×C₃×C₄⋊C₄	—	4	2	no	—
187	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
191	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
193	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
194	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
206	C₂×C₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
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	1	yes	characteristic
210	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
222	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
223	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
226	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
227	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
228	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
229	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
230	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
231	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
236	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
238	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
239	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
240	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
241	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
242	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
243	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
244	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
245	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
246	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
247	C₂×C₃×C₄²	C₂³	1	2	yes	—
248	C₂×C₃×C₄²	C₂³	1	2	yes	—
249	C₂×C₃×C₄²	C₂³	1	2	yes	—
250	C₂×C₃×C₄²	C₂³	1	2	yes	—
251	C₂×C₃×C₄²	C₂³	1	2	yes	—
252	C₂×C₃×C₄²	C₂³	1	2	yes	—
253	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
254	C₃×#95	C₂³	1	1	yes	characteristic
255	C₃×#95	C₂³	1	1	yes	characteristic
256	C₃×#95	C₂³	1	2	yes	—
257	C₃×#95	C₂³	1	1	yes	characteristic
258	C₃×#95	C₂³	1	1	yes	characteristic
259	C₃×#95	C₂³	1	1	yes	characteristic
260	C₃×#95	C₂³	1	2	yes	—
261	C₃×#95	C₂³	1	2	yes	—
262	C₃×#95	C₂³	1	1	yes	characteristic
263	C₃×#95	C₂³	1	2	yes	—
264	C₃×#95	C₂³	1	2	yes	—
265	C₃×#95	C₂³	1	2	yes	—
266	C₃×#95	C₂³	1	2	yes	—
267	C₃×#95	C₂³	1	2	yes	—
268	C₃×#95	C₂³	1	2	yes	—
269	C₃×#95	C₂³	1	2	yes	—
270	C₃×#95	C₂³	1	2	yes	—
271	C₃×#95	C₂³	1	2	yes	—
272	C₃×#95	C₂³	1	2	yes	—
273	C₂²×#41	C₂²×C₃	1	1	yes	characteristic
274	C₂³×D₄	C₂²×C₃	1	1	yes	characteristic
275	#546	C₃×C₄	1	16	yes	complemented
276	C₂×#124	C₂²×C₃	1	1	yes	characteristic
277	C₂×#123	C₂²×C₃	1	2	yes	—
278	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
279	C₂×#121	C₂²×C₃	1	1	yes	characteristic
280	C₂×#121	C₂²×C₃	1	2	yes	—
281	C₂×#120	C₂²×C₃	1	2	yes	—
282	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
283	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
284	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
285	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₃	1	2	yes	complemented
289	C₂×#117	C₂²×C₃	1	1	yes	characteristic
290	C₂×#117	C₂²×C₃	1	1	yes	characteristic
291	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
292	C₂×#117	C₂²×C₃	1	2	yes	complemented
293	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
294	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
295	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
296	#391	C₂²×C₃	1	1	yes	characteristic, complemented
297	#391	C₂²×C₃	1	1	yes	characteristic, complemented
298	#390	C₂²×C₃	1	1	yes	characteristic
299	#390	C₂²×C₃	1	1	yes	characteristic
300	#390	C₂²×C₃	1	2	yes	—
301	#390	C₂²×C₃	1	1	yes	characteristic
302	#390	C₂²×C₃	1	1	yes	characteristic
303	#390	C₂²×C₃	1	2	yes	—
304	#390	C₂²×C₃	1	1	yes	characteristic
305	#390	C₂²×C₃	1	1	yes	characteristic
306	#390	C₂²×C₃	1	1	yes	characteristic
307	#390	C₂²×C₃	1	1	yes	characteristic
308	#390	C₂²×C₃	1	2	yes	complemented
309	#390	C₂²×C₃	1	2	yes	complemented
310	#390	C₂²×C₃	1	2	yes	complemented
311	#389	C₂²×C₃	1	1	yes	characteristic, complemented
312	#389	C₂²×C₃	1	2	yes	complemented
313	#389	C₂²×C₃	1	1	yes	characteristic, complemented
314	#389	C₂²×C₃	1	1	yes	characteristic, complemented
315	#389	C₂²×C₃	1	1	yes	characteristic, complemented
316	#388	C₂²×C₃	1	1	yes	characteristic
317	#388	C₂²×C₃	1	2	yes	—
318	#388	C₂²×C₃	1	2	yes	—
319	#388	C₂²×C₃	1	2	yes	—
320	#388	C₂²×C₃	1	2	yes	—
321	#388	C₂²×C₃	1	2	yes	—
322	#388	C₂²×C₃	1	1	yes	characteristic
323	#388	C₂²×C₃	1	2	yes	complemented
324	#388	C₂²×C₃	1	2	yes	complemented
325	#388	C₂²×C₃	1	2	yes	complemented
326	#388	C₂²×C₃	1	2	yes	complemented
327	#388	C₂²×C₃	1	2	yes	complemented
328	#388	C₂²×C₃	1	2	yes	complemented
329	#388	C₂²×C₃	1	1	yes	characteristic, complemented
330	#388	C₂²×C₃	1	2	yes	complemented
331	#388	C₂²×C₃	1	2	yes	complemented
332	#388	C₂²×C₃	1	1	yes	characteristic, complemented
333	#388	C₂²×C₃	1	2	yes	complemented
334	#388	C₂²×C₃	1	2	yes	complemented
335	#387	C₂²×C₃	1	2	yes	complemented
336	#387	C₂²×C₃	1	2	yes	complemented
337	#387	C₂²×C₃	1	2	yes	complemented
338	#386	C₂²×C₃	1	2	yes	—
339	#386	C₂²×C₃	1	2	yes	—
340	#386	C₂²×C₃	1	2	yes	—
341	#386	C₂²×C₃	1	2	yes	complemented
342	#386	C₂²×C₃	1	2	yes	complemented
343	#386	C₂²×C₃	1	2	yes	complemented
344	#386	C₂²×C₃	1	2	yes	complemented
345	#385	C₂²×C₃	1	2	yes	complemented
346	#385	C₂²×C₃	1	2	yes	complemented
347	#385	C₂²×C₃	1	2	yes	complemented
348	#382	C₂²×C₃	1	1	yes	characteristic, complemented
349	#381	C₂²×C₃	1	2	yes	complemented
350	#380	C₂²×C₃	1	1	yes	characteristic
351	#380	C₂²×C₃	1	2	yes	complemented
352	#380	C₂²×C₃	1	2	yes	complemented
353	#380	C₂²×C₃	1	2	yes	complemented
354	#380	C₂²×C₃	1	1	yes	characteristic, complemented
355	#379	C₂²×C₃	1	2	yes	—
356	#379	C₂²×C₃	1	2	yes	—
357	#379	C₂²×C₃	1	2	yes	—
358	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
359	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
360	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
361	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
362	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
363	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
364	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
365	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
366	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
367	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
368	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
369	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
370	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
371	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
372	C₄³	C₂²×C₃	1	1	yes	characteristic, complemented
373	C₂⁴×C₃	—	4	2	no	—
374	C₂⁴×C₃	—	4	2	no	—
375	C₂⁴×C₃	—	4	2	no	—
376	C₂⁴×C₃	—	4	2	no	—
377	C₂⁴×C₃	—	4	2	no	—
378	C₂⁴×C₃	—	4	2	no	—
379	C₂⁴×C₃	C₂²×C₄	1	8	yes	—
380	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
381	C₂⁴×C₃	C₂⁴	1	2	yes	—
382	C₂⁴×C₃	C₂⁴	1	2	yes	—
383	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
384	C₃×#41	—	4	16	no	—
385	C₂×C₃×Q₈	—	2	2	no	—
386	C₂×C₃×Q₈	—	2	2	no	—
387	C₂×C₃×Q₈	C₂²×C₄	1	4	yes	—
388	C₂×C₃×D₄	—	2	2	no	—
389	C₂×C₃×D₄	—	2	2	no	—
390	C₂×C₃×D₄	—	2	2	no	—
391	C₂×C₃×D₄	—	2	2	no	—
392	C₂×C₃×D₄	—	4	16	no	—
393	C₂×C₃×D₄	—	4	2	no	—
394	C₂×C₃×D₄	—	4	2	no	—
395	C₂×C₃×D₄	—	4	2	no	—
396	C₂×C₃×D₄	—	4	1	no	—
397	C₂×C₃×D₄	—	4	1	no	—
398	C₂×C₃×D₄	—	4	2	no	—
399	C₂×C₃×D₄	—	4	2	no	—
400	C₂×C₃×D₄	—	4	2	no	—
401	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
402	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
403	C₂×C₃×D₄	C₂²×C₄	1	4	yes	—
404	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
405	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
406	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
407	C₂²×C₃×C₄	—	2	2	no	—
408	C₂²×C₃×C₄	—	2	2	no	—
409	C₂²×C₃×C₄	—	2	2	no	—
410	C₂²×C₃×C₄	—	2	2	no	—
411	C₂²×C₃×C₄	—	2	4	no	—
412	C₂²×C₃×C₄	—	4	2	no	—
413	C₂²×C₃×C₄	—	4	2	no	—
414	C₂²×C₃×C₄	—	4	2	no	—
415	C₂²×C₃×C₄	—	4	2	no	—
416	C₂²×C₃×C₄	—	4	2	no	—
417	C₂²×C₃×C₄	—	4	2	no	—
418	C₂²×C₃×C₄	—	4	2	no	—
419	C₂²×C₃×C₄	—	4	2	no	—
420	C₂²×C₃×C₄	—	4	2	no	—
421	C₂²×C₃×C₄	—	4	2	no	—
422	C₂²×C₃×C₄	—	4	2	no	—
423	C₂²×C₃×C₄	—	4	2	no	—
424	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
425	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
426	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
427	C₂²×C₃×C₄	C₂²×C₄	1	8	yes	—
428	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
430	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
431	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
434	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
435	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
436	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
437	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
442	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
443	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
444	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
445	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
446	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
447	C₃×C₄⋊C₄	—	2	2	no	—
448	C₃×C₄⋊C₄	—	2	2	no	—
449	C₃×C₄⋊C₄	—	2	4	no	—
450	C₃×C₄⋊C₄	—	2	2	no	—
451	C₃×C₄⋊C₄	—	2	2	no	—
452	C₃×C₄⋊C₄	—	4	2	no	—
453	C₃×C₄⋊C₄	—	4	1	no	—
454	C₃×C₄⋊C₄	—	4	1	no	—
455	C₃×C₄⋊C₄	—	4	2	no	—
456	C₃×C₄⋊C₄	—	4	1	no	—
457	C₃×C₄⋊C₄	—	4	1	no	—
458	C₃×C₄⋊C₄	—	4	1	no	—
459	C₃×C₄⋊C₄	—	4	1	no	—
460	C₃×C₄⋊C₄	—	4	2	no	—
461	C₃×C₄⋊C₄	—	4	2	no	—
462	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
463	C₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
464	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
465	C₃×C₂²⋊C₄	—	2	2	no	—
466	C₃×C₂²⋊C₄	—	2	4	no	—
467	C₃×C₂²⋊C₄	—	2	2	no	—
468	C₃×C₂²⋊C₄	—	4	2	no	—
469	C₃×C₂²⋊C₄	—	4	2	no	—
470	C₃×C₂²⋊C₄	—	4	1	no	—
471	C₃×C₂²⋊C₄	—	4	2	no	—
472	C₃×C₂²⋊C₄	—	4	2	no	—
473	C₃×C₂²⋊C₄	—	4	2	no	—
474	C₃×C₂²⋊C₄	—	4	1	no	—
475	C₃×C₂²⋊C₄	—	4	2	no	—
476	C₃×C₂²⋊C₄	—	4	2	no	—
477	C₃×C₂²⋊C₄	—	4	2	no	—
478	C₃×C₂²⋊C₄	—	4	2	no	—
479	C₃×C₂²⋊C₄	—	4	2	no	—
480	C₃×C₂²⋊C₄	—	4	2	no	—
481	C₃×C₂²⋊C₄	—	4	1	no	—
482	C₃×C₂²⋊C₄	—	4	1	no	—
483	C₃×C₂²⋊C₄	—	4	1	no	—
484	C₃×C₂²⋊C₄	—	4	1	no	—
485	C₃×C₂²⋊C₄	—	4	2	no	—
486	C₃×C₂²⋊C₄	—	4	2	no	—
487	C₃×C₂²⋊C₄	—	4	2	no	—
488	C₃×C₂²⋊C₄	—	4	2	no	—
489	C₃×C₂²⋊C₄	—	4	2	no	—
490	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
491	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
492	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
493	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
494	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
495	C₃×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
496	C₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
497	C₃×C₄²	—	2	2	no	—
498	C₃×C₄²	—	2	2	no	—
499	C₃×C₄²	—	2	2	no	—
500	C₃×C₄²	—	2	2	no	—
501	C₃×C₄²	—	2	2	no	—
502	C₃×C₄²	—	4	1	no	—
503	C₃×C₄²	—	4	1	no	—
504	C₃×C₄²	—	4	1	no	—
505	C₃×C₄²	—	4	2	no	—
506	C₃×C₄²	—	4	2	no	—
507	C₃×C₄²	—	4	2	no	—
508	C₃×C₄²	—	4	2	no	—
509	C₃×C₄²	—	4	2	no	—
510	C₃×C₄²	—	4	2	no	—
511	C₃×C₄²	C₂²×C₄	1	4	yes	—
512	C₂⁵	C₂³×C₃	1	2	yes	—
513	C₂×#41	—	4	2	no	—
514	C₂×#41	—	4	2	no	—
515	C₂×#41	C₂×C₃×C₄	1	8	yes	complemented
516	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
517	C₂²×D₄	—	4	2	no	—
518	C₂²×D₄	—	4	2	no	—
519	C₂²×D₄	C₂×C₃×C₄	1	8	yes	complemented
520	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
522	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
523	C₂²×D₄	C₂³×C₃	1	2	yes	—
524	C₂²×D₄	C₂³×C₃	1	2	yes	—
525	C₂²×D₄	C₂³×C₃	1	2	yes	—
526	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₃	1	2	yes	—
529	C₂³×C₄	C₂³×C₃	1	2	yes	—
530	C₂³×C₄	C₂³×C₃	1	2	yes	—
531	C₂³×C₄	C₂³×C₃	1	2	yes	—
532	C₂³×C₄	C₂³×C₃	1	2	yes	—
533	#124	C₂×C₃×C₄	1	8	yes	complemented
534	#123	C₂×C₃×C₄	1	16	yes	complemented
535	C₂²⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
536	#121	C₂×C₃×C₄	1	8	yes	—
537	#121	C₂×C₃×C₄	1	16	yes	complemented
538	#120	C₂×C₃×C₄	1	16	yes	complemented
539	C₄×Q₈	—	4	2	no	—
540	C₄×Q₈	—	4	2	no	—
541	C₄×D₄	—	4	2	no	—
542	C₄×D₄	—	4	2	no	—
543	C₄×D₄	—	4	4	no	—
544	C₄×D₄	C₂×C₃×C₄	1	8	yes	complemented
545	C₄×D₄	C₂×C₃×C₄	1	8	yes	complemented
546	#117	—	4	2	no	—
547	#117	—	4	2	no	—
548	#117	—	4	4	no	—
549	#117	—	4	2	no	—
550	C₂×C₄⋊C₄	—	4	2	no	—
551	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
569	C₂×C₂²⋊C₄	—	4	4	no	—
570	C₂×C₂²⋊C₄	C₂×C₃×C₄	1	16	yes	complemented
571	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
572	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
578	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
603	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₃	1	2	yes	—
609	C₂×C₄²	C₂³×C₃	1	2	yes	—
610	C₂×C₄²	C₂³×C₃	1	2	yes	—
611	C₂×C₄²	C₂³×C₃	1	2	yes	—
612	C₂×C₄²	C₂³×C₃	1	2	yes	—
613	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₃	1	2	yes	—
617	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
618	#95	C₂³×C₃	1	1	yes	characteristic
619	#95	C₂³×C₃	1	1	yes	characteristic
620	#95	C₂³×C₃	1	2	yes	—
621	#95	C₂³×C₃	1	1	yes	characteristic
622	#95	C₂³×C₃	1	1	yes	characteristic
623	#95	C₂³×C₃	1	1	yes	characteristic
624	#95	C₂³×C₃	1	2	yes	—
625	#95	C₂³×C₃	1	2	yes	—
626	#95	C₂³×C₃	1	1	yes	characteristic
627	#95	C₂³×C₃	1	2	yes	—
628	#95	C₂³×C₃	1	2	yes	—
629	#95	C₂³×C₃	1	2	yes	—
630	#95	C₂³×C₃	1	2	yes	—
631	#95	C₂³×C₃	1	2	yes	—
632	#95	C₂³×C₃	1	2	yes	—
633	#95	C₂³×C₃	1	2	yes	—
634	#95	C₂³×C₃	1	2	yes	—
635	#95	C₂³×C₃	1	2	yes	—
636	#95	C₂³×C₃	1	2	yes	—
637	C₂³×C₃	—	2	2	no	—
638	C₂³×C₃	—	2	1	no	—
639	C₂³×C₃	—	2	1	no	—
640	C₂³×C₃	—	2	1	no	—
641	C₂³×C₃	—	2	1	no	—
642	C₂³×C₃	—	2	1	no	—
643	C₂³×C₃	—	2	2	no	—
644	C₂³×C₃	—	2	2	no	—
645	C₂³×C₃	—	2	2	no	—
646	C₂³×C₃	—	2	1	no	—
647	C₂³×C₃	—	2	2	no	—
648	C₂³×C₃	—	2	2	no	—
649	C₂³×C₃	—	2	1	no	—
650	C₂³×C₃	—	2	2	no	—
651	C₂³×C₃	—	2	2	no	—
652	C₂³×C₃	—	2	2	no	—
653	C₂³×C₃	—	2	2	no	—
654	C₂³×C₃	—	2	2	no	—
655	C₂³×C₃	—	2	1	no	—
656	C₂³×C₃	—	2	2	no	—
657	C₂³×C₃	—	2	1	no	—
658	C₂³×C₃	—	2	1	no	—
659	C₂³×C₃	—	2	1	no	—
660	C₂³×C₃	—	2	1	no	—
661	C₂³×C₃	—	4	8	no	—
662	C₂³×C₃	—	4	8	no	—
663	C₂³×C₃	—	4	8	no	—
664	C₂³×C₃	—	8	4	no	—
665	C₂³×C₃	—	8	4	no	—
666	C₂³×C₃	—	8	4	no	—
667	C₂³×C₃	—	8	4	no	—
668	C₂³×C₃	C₂³×C₄	1	2	yes	—
669	C₂³×C₃	C₂³×C₄	1	4	yes	—
670	C₂³×C₃	C₂³×C₄	1	4	yes	—
671	C₂³×C₃	C₂³×C₄	1	2	yes	—
672	C₂³×C₃	C₂⁵	1	1	yes	characteristic
673	C₃×Q₈	—	2	8	no	—
674	C₃×D₄	—	2	8	no	—
675	C₃×D₄	—	2	8	no	—
676	C₃×D₄	—	4	8	no	—
677	C₃×D₄	—	4	4	no	—
678	C₃×D₄	—	4	8	no	—
679	C₃×D₄	—	4	8	no	—
680	C₂×C₃×C₄	—	2	1	no	—
681	C₂×C₃×C₄	—	2	1	no	—
682	C₂×C₃×C₄	—	2	1	no	—
683	C₂×C₃×C₄	—	2	2	no	—
684	C₂×C₃×C₄	—	2	2	no	—
685	C₂×C₃×C₄	—	2	2	no	—
686	C₂×C₃×C₄	—	2	1	no	—
687	C₂×C₃×C₄	—	2	1	no	—
688	C₂×C₃×C₄	—	2	1	no	—
689	C₂×C₃×C₄	—	2	1	no	—
690	C₂×C₃×C₄	—	2	1	no	—
691	C₂×C₃×C₄	—	2	1	no	—
692	C₂×C₃×C₄	—	2	1	no	—
693	C₂×C₃×C₄	—	2	2	no	—
694	C₂×C₃×C₄	—	2	8	no	—
695	C₂×C₃×C₄	—	2	8	no	—
696	C₂×C₃×C₄	—	2	1	no	—
697	C₂×C₃×C₄	—	2	1	no	—
698	C₂×C₃×C₄	—	2	1	no	—
699	C₂×C₃×C₄	—	2	1	no	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	2	1	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	1	no	—
704	C₂×C₃×C₄	—	2	1	no	—
705	C₂×C₃×C₄	—	2	2	no	—
706	C₂×C₃×C₄	—	2	2	no	—
707	C₂×C₃×C₄	—	2	2	no	—
708	C₂×C₃×C₄	—	2	2	no	—
709	C₂×C₃×C₄	—	2	2	no	—
710	C₂×C₃×C₄	—	2	2	no	—
711	C₂×C₃×C₄	—	2	1	no	—
712	C₂×C₃×C₄	—	2	2	no	—
713	C₂×C₃×C₄	—	2	1	no	—
714	C₂×C₃×C₄	—	2	1	no	—
715	C₂×C₃×C₄	—	2	1	no	—
716	C₂×C₃×C₄	—	2	1	no	—
717	C₂×C₃×C₄	—	2	1	no	—
718	C₂×C₃×C₄	—	2	1	no	—
719	C₂×C₃×C₄	—	2	2	no	—
720	C₂×C₃×C₄	—	2	1	no	—
721	C₂×C₃×C₄	—	2	2	no	—
722	C₂×C₃×C₄	—	2	1	no	—
723	C₂×C₃×C₄	—	2	1	no	—
724	C₂×C₃×C₄	—	2	1	no	—
725	C₂×C₃×C₄	—	2	2	no	—
726	C₂×C₃×C₄	—	2	2	no	—
727	C₂×C₃×C₄	—	2	2	no	—
728	C₂×C₃×C₄	—	2	1	no	—
729	C₂×C₃×C₄	—	4	8	no	—
730	C₂×C₃×C₄	—	4	8	no	—
731	C₂×C₃×C₄	—	8	4	no	—
732	C₂×C₃×C₄	—	8	4	no	—
733	C₂×C₃×C₄	—	8	4	no	—
734	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
735	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
736	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
737	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
738	C₂×C₃×C₄	C₂³×C₄	1	4	yes	—
739	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
740	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
741	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
742	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
743	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
744	C₂⁴	—	4	2	no	—
745	C₂⁴	—	4	2	no	—
746	C₂⁴	—	4	2	no	—
747	C₂⁴	—	4	2	no	—
748	C₂⁴	—	4	2	no	—
749	C₂⁴	—	4	2	no	—
750	C₂⁴	C₂²×C₃×C₄	1	8	yes	—
751	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
752	C₂⁴	C₂⁴×C₃	1	2	yes	—
753	C₂⁴	C₂⁴×C₃	1	2	yes	—
754	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
755	#41	—	4	16	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	2	2	no	—
758	C₂×Q₈	C₂²×C₃×C₄	1	4	yes	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	4	16	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	2	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	1	no	—
770	C₂×D₄	—	4	1	no	—
771	C₂×D₄	—	4	2	no	—
772	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
773	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
774	C₂×D₄	C₂²×C₃×C₄	1	4	yes	—
775	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
776	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
777	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	4	2	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	2	no	—
793	C₂²×C₄	—	4	2	no	—
794	C₂²×C₄	—	4	2	no	—
795	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
796	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
797	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
798	C₂²×C₄	C₂²×C₃×C₄	1	8	yes	—
799	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	4	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	4	2	no	—
824	C₄⋊C₄	—	4	2	no	—
825	C₄⋊C₄	—	4	1	no	—
826	C₄⋊C₄	—	4	1	no	—
827	C₄⋊C₄	—	4	1	no	—
828	C₄⋊C₄	—	4	1	no	—
829	C₄⋊C₄	—	4	2	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	1	no	—
832	C₄⋊C₄	—	4	1	no	—
833	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
834	C₄⋊C₄	C₂²×C₃×C₄	1	4	yes	—
835	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	4	2	no	—
840	C₂²⋊C₄	—	4	2	no	—
841	C₂²⋊C₄	—	4	1	no	—
842	C₂²⋊C₄	—	4	1	no	—
843	C₂²⋊C₄	—	4	1	no	—
844	C₂²⋊C₄	—	4	1	no	—
845	C₂²⋊C₄	—	4	2	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	—	4	1	no	—
851	C₂²⋊C₄	—	4	2	no	—
852	C₂²⋊C₄	—	4	2	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₂²⋊C₄	—	4	1	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
862	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
863	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
864	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
865	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
866	C₂²⋊C₄	C₂²×C₃×C₄	1	4	yes	—
867	C₂²⋊C₄	C₂²×C₃×C₄	1	8	yes	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	4	2	no	—
874	C₄²	—	4	2	no	—
875	C₄²	—	4	2	no	—
876	C₄²	—	4	2	no	—
877	C₄²	—	4	2	no	—
878	C₄²	—	4	1	no	—
879	C₄²	—	4	1	no	—
880	C₄²	—	4	1	no	—
881	C₄²	—	4	2	no	—
882	C₄²	C₂²×C₃×C₄	1	4	yes	—
883	C₂²×C₃	—	2	2	no	—
884	C₂²×C₃	—	2	2	no	—
885	C₂²×C₃	—	2	4	no	—
886	C₂²×C₃	—	2	4	no	—
887	C₂²×C₃	—	2	2	no	—
888	C₂²×C₃	—	2	2	no	—
889	C₂²×C₃	—	2	4	no	—
890	C₂²×C₃	—	2	4	no	—
891	C₂²×C₃	—	2	4	no	—
892	C₂²×C₃	—	2	2	no	—
893	C₂²×C₃	—	2	4	no	—
894	C₂²×C₃	—	2	2	no	—
895	C₂²×C₃	—	4	2	no	—
896	C₂²×C₃	—	4	1	no	—
897	C₂²×C₃	—	4	2	no	—
898	C₂²×C₃	—	4	1	no	—
899	C₂²×C₃	—	4	1	no	—
900	C₂²×C₃	—	4	2	no	—
901	C₂²×C₃	—	4	2	no	—
902	C₂²×C₃	—	4	1	no	—
903	C₂²×C₃	—	4	1	no	—
904	C₂²×C₃	—	4	2	no	—
905	C₂²×C₃	—	4	2	no	—
906	C₂²×C₃	—	4	1	no	—
907	C₂²×C₃	—	4	1	no	—
908	C₂²×C₃	—	4	2	no	—
909	C₂²×C₃	—	4	2	no	—
910	C₂²×C₃	—	4	1	no	—
911	C₂²×C₃	—	8	16	no	—
912	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
913	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
914	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
915	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
916	C₂²×C₃	#585	1	1	yes	characteristic
917	C₂²×C₃	#585	1	1	yes	characteristic
918	C₂²×C₃	#585	1	1	yes	characteristic
919	C₃×C₄	—	2	2	no	—
920	C₃×C₄	—	2	2	no	—
921	C₃×C₄	—	2	4	no	—
922	C₃×C₄	—	2	2	no	—
923	C₃×C₄	—	2	2	no	—
924	C₃×C₄	—	2	4	no	—
925	C₃×C₄	—	2	2	no	—
926	C₃×C₄	—	4	1	no	—
927	C₃×C₄	—	4	1	no	—
928	C₃×C₄	—	4	2	no	—
929	C₃×C₄	—	4	1	no	—
930	C₃×C₄	—	4	1	no	—
931	C₃×C₄	—	4	1	no	—
932	C₃×C₄	—	4	1	no	—
933	C₃×C₄	—	4	2	no	—
934	C₃×C₄	—	4	2	no	—
935	C₃×C₄	—	4	1	no	—
936	C₃×C₄	—	4	2	no	—
937	C₃×C₄	#518	1	4	yes	—
938	C₂³	—	2	2	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	2	no	—
945	C₂³	—	2	2	no	—
946	C₂³	—	2	2	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	1	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	1	no	—
959	C₂³	—	2	1	no	—
960	C₂³	—	2	1	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	4	8	no	—
963	C₂³	—	4	8	no	—
964	C₂³	—	4	8	no	—
965	C₂³	—	8	4	no	—
966	C₂³	—	8	4	no	—
967	C₂³	—	8	4	no	—
968	C₂³	—	8	4	no	—
969	C₂³	C₂³×C₃×C₄	1	2	yes	—
970	C₂³	C₂³×C₃×C₄	1	4	yes	—
971	C₂³	C₂³×C₃×C₄	1	4	yes	—
972	C₂³	C₂³×C₃×C₄	1	2	yes	—
973	C₂³	C₂⁵×C₃	1	1	yes	characteristic
974	Q₈	—	2	8	no	—
975	D₄	—	2	8	no	—
976	D₄	—	2	8	no	—
977	D₄	—	4	8	no	—
978	D₄	—	4	8	no	—
979	D₄	—	4	4	no	—
980	D₄	—	4	8	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	8	no	—
996	C₂×C₄	—	2	8	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	4	8	no	—
1031	C₂×C₄	—	4	8	no	—
1032	C₂×C₄	—	8	4	no	—
1033	C₂×C₄	—	8	4	no	—
1034	C₂×C₄	—	8	4	no	—
1035	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1036	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1037	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
1038	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1039	C₂×C₄	C₂³×C₃×C₄	1	4	yes	—
1040	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1041	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
1042	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1043	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1044	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
1045	C₂×C₃	—	4	2	no	—
1046	C₂×C₃	—	4	4	no	—
1047	C₂×C₃	—	4	4	no	—
1048	C₂×C₃	—	4	2	no	—
1049	C₂×C₃	C₂×#518	1	1	yes	characteristic
1050	C₂×C₃	#3428	1	1	yes	characteristic
1051	C₂×C₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
1052	C₂×C₃	#3546	1	1	yes	characteristic
1053	C₂×C₃	#3551	1	1	yes	characteristic
1054	C₂×C₃	#3558	1	1	yes	characteristic
1055	C₂×C₃	#3562	1	1	yes	characteristic
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	4	no	—
1059	C₂²	—	2	4	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	4	no	—
1063	C₂²	—	2	4	no	—
1064	C₂²	—	2	4	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	4	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	8	16	no	—
1085	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
1086	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1087	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1088	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1089	C₂²	C₃×#585	1	1	yes	characteristic
1090	C₂²	C₃×#585	1	1	yes	characteristic
1091	C₂²	C₃×#585	1	1	yes	characteristic
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	4	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	4	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	C₃×#518	1	4	yes	—
1111	C₃	#34495	1	1	yes	characteristic, direct product factor, Sylow
1112	C₂	—	4	2	no	—
1113	C₂	—	4	4	no	—
1114	C₂	—	4	4	no	—
1115	C₂	—	4	2	no	—
1116	C₂	C₂×C₃×#518	1	1	yes	characteristic
1117	C₂	C₃×#3428	1	1	yes	characteristic
1118	C₂	C₃×C₄×H(5,𝔽₂)	1	1	yes	characteristic
1119	C₂	C₃×#3546	1	1	yes	characteristic
1120	C₂	C₃×#3551	1	1	yes	characteristic
1121	C₂	C₃×#3558	1	1	yes	characteristic
1122	C₂	C₃×#3562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#546	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2376	C₂	semidirect
3. C₃×#2375	C₂	semidirect
4. C₃×#2367	C₂	semidirect
5. C₃×#2363	C₂	semidirect
6. C₃×#2362	C₂	semidirect
7. C₃×#2361	C₂	semidirect
8. C₃×#2357	C₂	semidirect
9. C₃×#2352	C₂	semidirect
10. C₃×#2342	C₂	semidirect
11. C₃×#2341	C₂	semidirect
12. C₃×D₄×C₂²⋊C₄	C₂	semidirect
13. C₃×#2335	C₂	semidirect
14. C₃×#2333	C₂	semidirect
15. C₃×#2324	C₂	semidirect
16. C₃×#2323	C₂	semidirect
17. C₃×#2321	C₂	semidirect
18. C₃×#2312	C₂	semidirect
19. C₃×#2311	C₂	semidirect
20. C₃×#2309	C₂	semidirect
21. C₃×C₄×#124	C₂	semidirect
22. C₃×#2293	C₂	semidirect
23. C₃×#2293	C₂	semidirect
24. #34495	C₃	direct (N × H)
27. C₃×#546	C₄	semidirect
34. C₂×C₃×C₄×Q₈	C₂²	semidirect
35. C₂×C₃×C₄×Q₈	C₂²	semidirect
40. C₂×C₃×C₄×D₄	C₂²	semidirect
43. C₂×C₃×#117	C₂²	semidirect
44. C₂×C₃×#117	C₂²	semidirect
45. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
48. C₃×#391	C₂²	semidirect
49. C₃×#391	C₂²	semidirect
60. C₃×#390	C₂²	semidirect
61. C₃×#390	C₂²	semidirect
62. C₃×#390	C₂²	semidirect
63. C₃×#389	C₂²	semidirect
64. C₃×#389	C₂²	semidirect
65. C₃×#389	C₂²	semidirect
66. C₃×#389	C₂²	semidirect
67. C₃×#389	C₂²	semidirect
75. C₃×#388	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×#388	C₂²	semidirect
82. C₃×#388	C₂²	semidirect
83. C₃×#388	C₂²	semidirect
84. C₃×#388	C₂²	semidirect
85. C₃×#388	C₂²	semidirect
86. C₃×#388	C₂²	semidirect
87. C₃×#387	C₂²	semidirect
88. C₃×#387	C₂²	semidirect
89. C₃×#387	C₂²	semidirect
93. C₃×#386	C₂²	semidirect
94. C₃×#386	C₂²	semidirect
95. C₃×#386	C₂²	semidirect
96. C₃×#386	C₂²	semidirect
97. C₃×#385	C₂²	semidirect
98. C₃×#385	C₂²	semidirect
99. C₃×#385	C₂²	semidirect
100. C₃×#382	C₂²	semidirect
101. C₃×#381	C₂²	semidirect
103. C₃×#380	C₂²	semidirect
104. C₃×#380	C₂²	semidirect
105. C₃×#380	C₂²	semidirect
106. C₃×#380	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
114. C₃×C₄×C₄⋊C₄	C₂²	semidirect
116. C₃×C₄×C₂²⋊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×C₄×C₂²⋊C₄	C₂²	semidirect
121. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
122. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
123. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
124. C₃×C₄³	C₂²	semidirect
126. #2376	C₂×C₃	semidirect
127. #2375	C₂×C₃	semidirect
128. #2367	C₂×C₃	semidirect
129. #2363	C₂×C₃	semidirect
130. #2362	C₂×C₃	semidirect
131. #2361	C₂×C₃	semidirect
132. #2357	C₂×C₃	semidirect
133. #2352	C₂×C₃	semidirect
134. #2342	C₂×C₃	semidirect
135. #2341	C₂×C₃	semidirect
136. D₄×C₂²⋊C₄	C₂×C₃	semidirect
137. #2335	C₂×C₃	semidirect
138. #2333	C₂×C₃	semidirect
139. #2324	C₂×C₃	semidirect
140. #2323	C₂×C₃	semidirect
141. #2321	C₂×C₃	semidirect
142. #2312	C₂×C₃	semidirect
143. #2311	C₂×C₃	semidirect
144. #2309	C₂×C₃	semidirect
145. C₄×#124	C₂×C₃	semidirect
146. #2293	C₂×C₃	semidirect
147. #2293	C₂×C₃	semidirect
151. C₂×C₃×#41	C₂×C₄	semidirect
155. C₂²×C₃×D₄	C₂×C₄	semidirect
169. C₃×#124	C₂×C₄	semidirect
170. C₃×#123	C₂×C₄	semidirect
171. C₃×C₂²⋊Q₈	C₂×C₄	semidirect
173. C₃×#121	C₂×C₄	semidirect
174. C₃×#120	C₂×C₄	semidirect
180. C₃×C₄×D₄	C₂×C₄	semidirect
181. C₃×C₄×D₄	C₂×C₄	semidirect
206. C₂×C₃×C₂²⋊C₄	C₂×C₄	semidirect
275. #546	C₃×C₄	semidirect
282. C₂×C₄×Q₈	C₂²×C₃	semidirect
283. C₂×C₄×Q₈	C₂²×C₃	semidirect
288. C₂×C₄×D₄	C₂²×C₃	semidirect
291. C₂×#117	C₂²×C₃	semidirect
292. C₂×#117	C₂²×C₃	semidirect
293. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
296. #391	C₂²×C₃	semidirect
297. #391	C₂²×C₃	semidirect
308. #390	C₂²×C₃	semidirect
309. #390	C₂²×C₃	semidirect
310. #390	C₂²×C₃	semidirect
311. #389	C₂²×C₃	semidirect
312. #389	C₂²×C₃	semidirect
313. #389	C₂²×C₃	semidirect
314. #389	C₂²×C₃	semidirect
315. #389	C₂²×C₃	semidirect
323. #388	C₂²×C₃	semidirect
324. #388	C₂²×C₃	semidirect
325. #388	C₂²×C₃	semidirect
326. #388	C₂²×C₃	semidirect
327. #388	C₂²×C₃	semidirect
328. #388	C₂²×C₃	semidirect
329. #388	C₂²×C₃	semidirect
330. #388	C₂²×C₃	semidirect
331. #388	C₂²×C₃	semidirect
332. #388	C₂²×C₃	semidirect
333. #388	C₂²×C₃	semidirect
334. #388	C₂²×C₃	semidirect
335. #387	C₂²×C₃	semidirect
336. #387	C₂²×C₃	semidirect
337. #387	C₂²×C₃	semidirect
341. #386	C₂²×C₃	semidirect
342. #386	C₂²×C₃	semidirect
343. #386	C₂²×C₃	semidirect
344. #386	C₂²×C₃	semidirect
345. #385	C₂²×C₃	semidirect
346. #385	C₂²×C₃	semidirect
347. #385	C₂²×C₃	semidirect
348. #382	C₂²×C₃	semidirect
349. #381	C₂²×C₃	semidirect
351. #380	C₂²×C₃	semidirect
352. #380	C₂²×C₃	semidirect
353. #380	C₂²×C₃	semidirect
354. #380	C₂²×C₃	semidirect
358. C₄×C₄⋊C₄	C₂²×C₃	semidirect
359. C₄×C₄⋊C₄	C₂²×C₃	semidirect
360. C₄×C₄⋊C₄	C₂²×C₃	semidirect
361. C₄×C₄⋊C₄	C₂²×C₃	semidirect
362. C₄×C₄⋊C₄	C₂²×C₃	semidirect
364. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
365. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
366. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
367. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
368. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
369. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
370. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
371. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
372. C₄³	C₂²×C₃	semidirect
515. C₂×#41	C₂×C₃×C₄	semidirect
519. C₂²×D₄	C₂×C₃×C₄	semidirect
533. #124	C₂×C₃×C₄	semidirect
534. #123	C₂×C₃×C₄	semidirect
535. C₂²⋊Q₈	C₂×C₃×C₄	semidirect
537. #121	C₂×C₃×C₄	semidirect
538. #120	C₂×C₃×C₄	semidirect
544. C₄×D₄	C₂×C₃×C₄	semidirect
545. C₄×D₄	C₂×C₃×C₄	semidirect
570. C₂×C₂²⋊C₄	C₂×C₃×C₄	semidirect
1111. C₃	#34495	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×#546	2
C₃×#2376	2
C₃×#2375	2
C₃×#2367	2
C₃×#2363	2
C₃×#2362	2
C₃×#2361	2
C₃×#2357	2
C₃×#2352	2
C₃×#2342	2
C₃×#2341	2
C₃×D₄×C₂²⋊C₄	2
C₃×#2335	2
C₃×#2333	2
C₃×#2324	2
C₃×#2323	2
C₃×#2321	2
C₃×#2312	2
C₃×#2311	2
C₃×#2309	2
C₃×C₄×#124	2
C₃×#2293	2
#34495	3

Subgroups — C3×#34495 #10653102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34495 #10653102