Subgroups — C₃×#60593 #10679200

Order 768.

2110 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3126	C₂	1	4	yes	maximal, complemented
4	C₃×#3119	C₂	1	4	yes	maximal, complemented
5	C₃×#3115	C₂	1	2	yes	maximal, complemented
6	C₃×#3112	C₂	1	2	yes	maximal, complemented
7	C₃×#3106	C₂	1	2	yes	maximal, complemented
8	C₃×#3103	C₂	1	2	yes	maximal, complemented
9	C₃×#3096	C₂	1	2	yes	maximal, complemented
10	C₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3010	C₂	1	2	yes	maximal, complemented
15	C₃×#2949	C₂	1	2	yes	maximal, complemented
16	C₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	#60593	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
20	C₂×C₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂²×C₃×SD₁₆	C₂²	1	2	yes	—
22	C₃×#559	—	2	1	no	—
23	C₃×#559	—	2	1	no	—
24	C₃×#550	—	2	1	no	—
25	C₃×#550	—	2	1	no	—
26	C₃×#546	—	2	2	no	—
27	C₃×#546	—	2	2	no	—
28	C₃×#540	C₂²	1	4	yes	—
29	C₃×#535	C₂²	1	2	yes	—
30	C₃×#533	C₂²	1	1	yes	characteristic
31	C₃×#532	C₂²	1	2	yes	—
32	C₃×#532	C₂²	1	2	yes	—
33	C₂×C₃×#127	C₂²	1	1	yes	characteristic
34	C₃×#520	—	2	2	no	—
35	C₃×#520	—	2	1	no	—
36	C₃×#520	C₂²	1	1	yes	characteristic
37	C₃×#520	C₂²	1	1	yes	characteristic
38	C₃×#520	C₂²	1	2	yes	complemented
39	C₃×#519	—	2	1	no	—
40	C₃×#519	C₂²	1	1	yes	characteristic
41	C₃×#519	C₂²	1	2	yes	complemented
42	C₃×#518	C₂²	1	2	yes	—
43	C₃×C₄×#41	—	2	2	no	—
44	C₃×C₄×#41	—	2	1	no	—
45	C₃×C₄×#41	C₂²	1	1	yes	characteristic
46	C₃×C₄×#41	C₂²	1	1	yes	characteristic
47	C₃×C₄×#41	C₂²	1	2	yes	complemented
48	C₂×C₃×C₄×Q₈	—	2	1	no	—
49	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	complemented
51	C₃×#482	C₂²	1	4	yes	complemented
52	C₃×#482	C₂²	1	4	yes	complemented
53	C₃×#481	C₂²	1	4	yes	complemented
54	C₃×#480	C₂²	1	4	yes	complemented
55	C₃×#479	C₂²	1	2	yes	complemented
56	C₃×#479	C₂²	1	4	yes	complemented
57	C₃×#478	C₂²	1	2	yes	complemented
58	C₃×#477	C₂²	1	1	yes	characteristic, complemented
59	C₃×#477	C₂²	1	2	yes	complemented
60	C₃×#476	C₂²	1	1	yes	characteristic, complemented
61	C₃×#475	C₂²	1	1	yes	characteristic, complemented
62	C₃×#475	C₂²	1	2	yes	complemented
63	C₃×#474	C₂²	1	1	yes	characteristic, complemented
64	C₃×#460	C₂²	1	2	yes	—
65	C₃×#460	C₂²	1	2	yes	—
66	C₃×#460	C₂²	1	4	yes	—
67	C₃×#460	C₂²	1	2	yes	—
68	C₃×#460	C₂²	1	2	yes	—
69	C₃×#459	C₂²	1	2	yes	—
70	C₃×#459	C₂²	1	2	yes	—
71	C₃×#449	C₂²	1	4	yes	complemented
72	C₃×#449	C₂²	1	4	yes	complemented
73	C₃×#448	C₂²	1	4	yes	complemented
74	C₃×#448	C₂²	1	4	yes	complemented
75	C₃×#442	C₂²	1	4	yes	complemented
76	C₃×#440	C₂²	1	4	yes	complemented
77	C₃×#440	C₂²	1	4	yes	complemented
78	C₃×#440	C₂²	1	4	yes	complemented
79	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
80	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
81	C₃×C₄×SD₁₆	C₂²	1	4	yes	complemented
82	C₃×C₄×D₈	C₂²	1	4	yes	complemented
83	C₃×#433	C₂²	1	4	yes	complemented
84	C₃×#432	C₂²	1	2	yes	complemented
85	C₃×#431	C₂²	1	2	yes	complemented
86	C₃×#428	C₂²	1	2	yes	—
87	C₃×#427	C₂²	1	2	yes	—
88	C₃×#423	C₂²	1	1	yes	characteristic
89	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₃×#419	C₂²	1	2	yes	—
91	C₃×#418	C₂²	1	2	yes	—
92	C₃×#416	C₂²	1	2	yes	—
93	C₂×C₃×#102	C₂²	1	2	yes	—
94	C₃×#408	C₂²	1	2	yes	—
95	C₃×#405	C₂²	1	2	yes	—
96	#3508	C₂×C₃	1	1	yes	characteristic, complemented
97	C₄×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
98	#3126	C₂×C₃	1	4	yes	complemented
99	#3119	C₂×C₃	1	4	yes	complemented
100	#3115	C₂×C₃	1	2	yes	complemented
101	#3112	C₂×C₃	1	2	yes	complemented
102	#3106	C₂×C₃	1	2	yes	complemented
103	#3103	C₂×C₃	1	2	yes	complemented
104	#3096	C₂×C₃	1	2	yes	complemented
105	#3078	C₂×C₃	1	1	yes	characteristic, complemented
106	#3076	C₂×C₃	1	1	yes	characteristic, complemented
107	#3038	C₂×C₃	1	1	yes	characteristic, complemented
108	C₂×#460	C₂×C₃	1	1	yes	characteristic, complemented
109	#3010	C₂×C₃	1	2	yes	complemented
110	#2949	C₂×C₃	1	2	yes	complemented
111	#2946	C₂×C₃	1	2	yes	complemented
112	#2925	C₂×C₃	1	1	yes	characteristic, complemented
113	C₃×2₋¹⁺⁴	—	2	4	no	—
114	C₃×2₋¹⁺⁴	—	2	4	no	—
115	C₂×C₃×#41	—	2	2	no	—
116	C₂×C₃×#41	—	2	1	no	—
117	C₂×C₃×#41	—	2	2	no	—
118	C₂×C₃×#41	—	2	2	no	—
119	C₂×C₃×#41	C₂³	1	2	yes	—
120	C₂×C₃×#41	C₂³	1	1	yes	characteristic
121	C₂×C₃×#41	C₂³	1	1	yes	characteristic
122	C₂²×C₃×Q₈	—	2	1	no	—
123	C₂²×C₃×Q₈	C₂³	1	2	yes	—
124	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₃×D₄	—	2	1	no	—
126	C₂²×C₃×D₄	—	2	1	no	—
127	C₂²×C₃×D₄	C₂³	1	2	yes	—
128	C₃×AGL(1,ℤ/8)	—	2	8	no	—
129	C₂×C₃×SD₁₆	—	2	8	no	—
130	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
132	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
133	C₂×C₃×D₈	C₂³	1	4	yes	—
134	C₂×C₃×M₁₆	C₂³	1	2	yes	—
135	C₂²×C₃×C₈	C₂³	1	2	yes	—
136	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃×#127	—	2	2	no	—
139	C₃×#127	—	2	1	no	—
140	C₃×#127	—	2	1	no	—
141	C₃×#127	C₂³	1	2	yes	—
142	C₃×#127	C₂³	1	2	yes	—
143	C₃×#125	C₂³	1	2	yes	—
144	C₃×#124	—	2	2	no	—
145	C₃×#124	—	2	2	no	—
146	C₃×#124	—	2	2	no	—
147	C₃×#123	—	2	4	no	—
148	C₃×#123	—	2	4	no	—
149	C₃×C₂²⋊Q₈	—	2	1	no	—
150	C₃×C₂²⋊Q₈	—	2	1	no	—
151	C₃×#121	—	2	2	no	—
152	C₃×#121	—	2	2	no	—
153	C₃×#121	—	2	4	no	—
154	C₃×#121	—	2	4	no	—
155	C₃×#121	C₂³	1	4	yes	—
156	C₃×#121	C₂³	1	4	yes	—
157	C₃×#120	—	2	4	no	—
158	C₃×C₄×Q₈	—	2	1	no	—
159	C₃×C₄×Q₈	—	2	1	no	—
160	C₃×C₄×Q₈	—	2	2	no	—
161	C₃×C₄×Q₈	—	2	1	no	—
162	C₃×C₄×Q₈	—	2	2	no	—
163	C₃×C₄×Q₈	—	2	1	no	—
164	C₃×C₄×Q₈	—	2	1	no	—
165	C₃×C₄×Q₈	—	2	1	no	—
166	C₃×C₄×Q₈	—	2	2	no	—
167	C₃×C₄×Q₈	—	2	1	no	—
168	C₃×C₄×Q₈	—	2	2	no	—
169	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
170	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
171	C₃×C₄×Q₈	C₂³	1	2	yes	—
172	C₃×C₄×Q₈	C₂³	1	2	yes	—
173	C₃×C₄×Q₈	C₂³	1	2	yes	—
174	C₃×C₄×Q₈	C₂³	1	2	yes	—
175	C₃×C₄×Q₈	C₂³	1	2	yes	—
176	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
177	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
178	C₃×C₄×D₄	—	2	2	no	—
179	C₃×C₄×D₄	—	2	1	no	—
180	C₃×C₄×D₄	—	2	1	no	—
181	C₃×C₄×D₄	—	2	2	no	—
182	C₃×C₄×D₄	—	2	1	no	—
183	C₃×C₄×D₄	—	2	2	no	—
184	C₃×C₄×D₄	—	2	2	no	—
185	C₃×C₄×D₄	—	2	2	no	—
186	C₃×C₄×D₄	—	2	2	no	—
187	C₃×C₄×D₄	—	2	2	no	—
188	C₃×C₄×D₄	—	2	2	no	—
189	C₃×C₄×D₄	—	2	2	no	—
190	C₃×C₄×D₄	—	2	2	no	—
191	C₃×C₄×D₄	D₄	1	2	yes	—
192	C₃×C₄×D₄	D₄	1	1	yes	characteristic
193	C₃×C₄×D₄	D₄	1	2	yes	—
194	C₃×C₄×D₄	D₄	1	1	yes	characteristic
195	C₃×C₄×D₄	C₂³	1	2	yes	—
196	C₃×C₄×D₄	C₂³	1	4	yes	—
197	C₃×C₄×D₄	C₂³	1	4	yes	—
198	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
199	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
200	C₃×#117	—	2	1	no	—
201	C₃×#117	—	2	2	no	—
202	C₃×#117	—	2	2	no	—
203	C₃×#117	—	2	2	no	—
204	C₃×#117	—	2	2	no	—
205	C₃×#117	—	2	1	no	—
206	C₃×#117	—	2	2	no	—
207	C₃×#117	C₂³	1	2	yes	—
208	C₃×#117	C₂³	1	1	yes	characteristic
209	C₃×#117	C₂³	1	2	yes	—
210	C₃×#117	C₂³	1	1	yes	characteristic
211	C₃×#117	C₂³	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	—	2	1	no	—
213	C₂×C₃×C₄⋊C₄	—	2	2	no	—
214	C₂×C₃×C₄⋊C₄	—	2	1	no	—
215	C₂×C₃×C₄⋊C₄	—	2	2	no	—
216	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
218	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
219	C₂×C₃×C₄²	—	2	1	no	—
220	C₂×C₃×C₄²	—	2	2	no	—
221	C₂×C₃×C₄²	—	2	1	no	—
222	C₂×C₃×C₄²	—	2	2	no	—
223	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
224	C₂×C₃×C₄²	C₂³	1	2	yes	—
225	C₃×#107	C₂³	1	2	yes	—
226	C₃×#107	C₂³	1	2	yes	—
227	C₃×#107	C₂³	1	4	yes	—
228	C₃×#106	C₂³	1	2	yes	—
229	C₃×#106	C₂³	1	2	yes	—
230	C₃×#106	C₂³	1	4	yes	—
231	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
232	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
233	C₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₃×#103	C₂³	1	2	yes	—
237	C₃×#103	C₂³	1	2	yes	—
238	C₃×#103	C₂³	1	4	yes	—
239	C₃×#103	C₂³	1	4	yes	—
240	C₃×#102	C₂³	1	4	yes	—
241	C₃×#102	C₂³	1	4	yes	—
242	C₃×#102	C₂³	1	2	yes	—
243	C₃×#102	C₂³	1	2	yes	—
244	C₃×#102	C₂³	1	4	yes	—
245	C₃×#102	C₂³	1	4	yes	—
246	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
247	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
248	C₃×#97	C₂³	1	4	yes	—
249	C₃×C₄×C₈	C₂³	1	4	yes	—
250	C₂×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic
251	C₂×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
252	C₂²×SD₁₆	C₂²×C₃	1	2	yes	—
253	#559	—	2	1	no	—
254	#559	—	2	1	no	—
255	#550	—	2	1	no	—
256	#550	—	2	1	no	—
257	#546	—	2	2	no	—
258	#546	—	2	2	no	—
259	#540	C₂²×C₃	1	4	yes	—
260	#535	C₂²×C₃	1	2	yes	—
261	#533	C₂²×C₃	1	1	yes	characteristic
262	#532	C₂²×C₃	1	2	yes	—
263	#532	C₂²×C₃	1	2	yes	—
264	C₂×#127	C₂²×C₃	1	1	yes	characteristic
265	#520	—	2	2	no	—
266	#520	—	2	1	no	—
267	#520	C₂²×C₃	1	1	yes	characteristic
268	#520	C₂²×C₃	1	1	yes	characteristic
269	#520	C₂²×C₃	1	2	yes	complemented
270	#519	—	2	1	no	—
271	#519	C₂²×C₃	1	1	yes	characteristic
272	#519	C₂²×C₃	1	2	yes	complemented
273	#518	C₂²×C₃	1	2	yes	—
274	C₄×#41	—	2	2	no	—
275	C₄×#41	—	2	1	no	—
276	C₄×#41	C₂²×C₃	1	1	yes	characteristic
277	C₄×#41	C₂²×C₃	1	1	yes	characteristic
278	C₄×#41	C₂²×C₃	1	2	yes	complemented
279	C₂×C₄×Q₈	—	2	1	no	—
280	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
281	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	complemented
282	#482	C₂²×C₃	1	4	yes	complemented
283	#482	C₂²×C₃	1	4	yes	complemented
284	#481	C₂²×C₃	1	4	yes	complemented
285	#480	C₂²×C₃	1	4	yes	complemented
286	#479	C₂²×C₃	1	2	yes	complemented
287	#479	C₂²×C₃	1	4	yes	complemented
288	#478	C₂²×C₃	1	2	yes	complemented
289	#477	C₂²×C₃	1	1	yes	characteristic, complemented
290	#477	C₂²×C₃	1	2	yes	complemented
291	#476	C₂²×C₃	1	1	yes	characteristic, complemented
292	#475	C₂²×C₃	1	1	yes	characteristic, complemented
293	#475	C₂²×C₃	1	2	yes	complemented
294	#474	C₂²×C₃	1	1	yes	characteristic, complemented
295	#460	C₂²×C₃	1	2	yes	—
296	#460	C₂²×C₃	1	2	yes	—
297	#460	C₂²×C₃	1	2	yes	—
298	#460	C₂²×C₃	1	4	yes	—
299	#460	C₂²×C₃	1	2	yes	—
300	#459	C₂²×C₃	1	2	yes	—
301	#459	C₂²×C₃	1	2	yes	—
302	#449	C₂²×C₃	1	4	yes	complemented
303	#449	C₂²×C₃	1	4	yes	complemented
304	#448	C₂²×C₃	1	4	yes	complemented
305	#448	C₂²×C₃	1	4	yes	complemented
306	#442	C₂²×C₃	1	4	yes	complemented
307	#440	C₂²×C₃	1	4	yes	complemented
308	#440	C₂²×C₃	1	4	yes	complemented
309	#440	C₂²×C₃	1	4	yes	complemented
310	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
311	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
312	C₄×SD₁₆	C₂²×C₃	1	4	yes	complemented
313	C₄×D₈	C₂²×C₃	1	4	yes	complemented
314	#433	C₂²×C₃	1	4	yes	complemented
315	#432	C₂²×C₃	1	2	yes	complemented
316	#431	C₂²×C₃	1	2	yes	complemented
317	#428	C₂²×C₃	1	2	yes	—
318	#427	C₂²×C₃	1	2	yes	—
319	#423	C₂²×C₃	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
321	#419	C₂²×C₃	1	2	yes	—
322	#418	C₂²×C₃	1	2	yes	—
323	#416	C₂²×C₃	1	2	yes	—
324	C₂×#102	C₂²×C₃	1	2	yes	—
325	#408	C₂²×C₃	1	2	yes	—
326	#405	C₂²×C₃	1	2	yes	—
327	C₂⁴×C₃	—	2	2	no	—
328	C₃×#41	—	2	16	no	—
329	C₃×#41	—	2	8	no	—
330	C₃×#41	—	2	4	no	—
331	C₃×#41	—	2	4	no	—
332	C₃×#41	—	2	2	no	—
333	C₃×#41	—	2	2	no	—
334	C₃×#41	—	2	2	no	—
335	C₃×#41	—	8	4	no	—
336	C₃×#41	—	8	4	no	—
337	C₃×#41	#41	1	4	yes	complemented
338	C₂×C₃×Q₈	—	2	8	no	—
339	C₂×C₃×Q₈	—	2	4	no	—
340	C₂×C₃×Q₈	—	2	4	no	—
341	C₂×C₃×Q₈	—	2	2	no	—
342	C₂×C₃×Q₈	—	2	1	no	—
343	C₂×C₃×Q₈	—	2	1	no	—
344	C₂×C₃×Q₈	—	2	1	no	—
345	C₂×C₃×Q₈	—	2	2	no	—
346	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
347	C₂×C₃×Q₈	#41	1	4	yes	complemented
348	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
350	C₂×C₃×D₄	—	2	2	no	—
351	C₂×C₃×D₄	—	2	1	no	—
352	C₂×C₃×D₄	—	2	4	no	—
353	C₂×C₃×D₄	—	2	4	no	—
354	C₂×C₃×D₄	—	2	2	no	—
355	C₂×C₃×D₄	—	2	2	no	—
356	C₂×C₃×D₄	—	2	2	no	—
357	C₂×C₃×D₄	—	2	2	no	—
358	C₂×C₃×D₄	—	2	2	no	—
359	C₂×C₃×D₄	—	2	4	no	—
360	C₂×C₃×D₄	—	2	4	no	—
361	C₂×C₃×D₄	—	8	2	no	—
362	C₂×C₃×D₄	—	8	2	no	—
363	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
364	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
365	C₂×C₃×D₄	C₂⁴	1	4	yes	—
366	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
367	C₂²×C₃×C₄	—	2	2	no	—
368	C₂²×C₃×C₄	—	2	1	no	—
369	C₂²×C₃×C₄	—	2	2	no	—
370	C₂²×C₃×C₄	—	2	1	no	—
371	C₂²×C₃×C₄	—	2	2	no	—
372	C₂²×C₃×C₄	—	2	1	no	—
373	C₂²×C₃×C₄	—	2	1	no	—
374	C₂²×C₃×C₄	—	2	2	no	—
375	C₂²×C₃×C₄	—	2	1	no	—
376	C₂²×C₃×C₄	—	2	4	no	—
377	C₂²×C₃×C₄	—	2	4	no	—
378	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
379	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
380	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
381	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
383	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
384	C₃×SD₁₆	—	2	8	no	—
385	C₃×SD₁₆	—	2	8	no	—
386	C₃×SD₁₆	—	2	8	no	—
387	C₃×D₈	—	2	8	no	—
388	C₃×M₁₆	—	2	4	no	—
389	C₂×C₃×C₈	—	2	4	no	—
390	C₂×C₃×C₈	C₂⁴	1	2	yes	—
391	C₂×C₃×C₈	C₂⁴	1	4	yes	—
392	C₂×C₃×C₈	C₂⁴	1	2	yes	—
393	C₃×C₄⋊C₄	—	2	2	no	—
394	C₃×C₄⋊C₄	—	2	2	no	—
395	C₃×C₄⋊C₄	—	2	2	no	—
396	C₃×C₄⋊C₄	—	2	2	no	—
397	C₃×C₄⋊C₄	—	2	1	no	—
398	C₃×C₄⋊C₄	—	2	2	no	—
399	C₃×C₄⋊C₄	—	2	1	no	—
400	C₃×C₄⋊C₄	—	2	2	no	—
401	C₃×C₄⋊C₄	—	2	1	no	—
402	C₃×C₄⋊C₄	—	2	1	no	—
403	C₃×C₄⋊C₄	—	2	1	no	—
404	C₃×C₄⋊C₄	—	2	2	no	—
405	C₃×C₄⋊C₄	—	2	2	no	—
406	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
407	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
408	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
409	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
410	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
411	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
412	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
414	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
415	C₃×C₂²⋊C₄	—	2	2	no	—
416	C₃×C₂²⋊C₄	—	2	2	no	—
417	C₃×C₂²⋊C₄	—	2	1	no	—
418	C₃×C₂²⋊C₄	—	2	4	no	—
419	C₃×C₂²⋊C₄	—	2	4	no	—
420	C₃×C₂²⋊C₄	—	2	1	no	—
421	C₃×C₂²⋊C₄	—	2	2	no	—
422	C₃×C₂²⋊C₄	—	2	1	no	—
423	C₃×C₂²⋊C₄	—	2	4	no	—
424	C₃×C₂²⋊C₄	—	2	4	no	—
425	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
426	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₃×C₄²	—	2	2	no	—
429	C₃×C₄²	—	2	1	no	—
430	C₃×C₄²	—	2	2	no	—
431	C₃×C₄²	—	2	1	no	—
432	C₃×C₄²	—	2	2	no	—
433	C₃×C₄²	—	2	2	no	—
434	C₃×C₄²	—	2	2	no	—
435	C₃×C₄²	—	2	2	no	—
436	C₃×C₄²	—	2	1	no	—
437	C₃×C₄²	—	2	2	no	—
438	C₃×C₄²	C₂×D₄	1	2	yes	—
439	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
440	C₃×C₄²	C₂×D₄	1	2	yes	—
441	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
442	C₃×C₄²	C₂⁴	1	2	yes	—
443	C₃×C₄²	C₂⁴	1	1	yes	characteristic
444	C₃×C₄²	C₂⁴	1	1	yes	characteristic
445	2₋¹⁺⁴	—	2	4	no	—
446	2₋¹⁺⁴	—	2	4	no	—
447	C₂×#41	—	2	2	no	—
448	C₂×#41	—	2	1	no	—
449	C₂×#41	—	2	2	no	—
450	C₂×#41	—	2	2	no	—
451	C₂×#41	C₂³×C₃	1	2	yes	—
452	C₂×#41	C₂³×C₃	1	1	yes	characteristic
453	C₂×#41	C₂³×C₃	1	1	yes	characteristic
454	C₂²×Q₈	—	2	1	no	—
455	C₂²×Q₈	C₂³×C₃	1	2	yes	—
456	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	C₂³×C₃	1	2	yes	—
460	AGL(1,ℤ/8)	—	2	8	no	—
461	C₂×SD₁₆	—	2	8	no	—
462	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
463	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
464	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
465	C₂×D₈	C₂³×C₃	1	4	yes	—
466	C₂×M₁₆	C₂³×C₃	1	2	yes	—
467	C₂²×C₈	C₂³×C₃	1	2	yes	—
468	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
469	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
470	#127	—	2	2	no	—
471	#127	—	2	1	no	—
472	#127	—	2	1	no	—
473	#127	C₂³×C₃	1	2	yes	—
474	#127	C₂³×C₃	1	2	yes	—
475	#125	C₂³×C₃	1	2	yes	—
476	#124	—	2	2	no	—
477	#124	—	2	2	no	—
478	#124	—	2	2	no	—
479	#123	—	2	4	no	—
480	#123	—	2	4	no	—
481	C₂²⋊Q₈	—	2	1	no	—
482	C₂²⋊Q₈	—	2	1	no	—
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	4	no	—
486	#121	—	2	4	no	—
487	#121	C₂³×C₃	1	4	yes	—
488	#121	C₂³×C₃	1	4	yes	—
489	#120	—	2	4	no	—
490	C₄×Q₈	—	2	1	no	—
491	C₄×Q₈	—	2	1	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	1	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	1	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	1	no	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
502	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
503	C₄×Q₈	C₂³×C₃	1	2	yes	—
504	C₄×Q₈	C₂³×C₃	1	2	yes	—
505	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
506	C₄×Q₈	C₂³×C₃	1	2	yes	—
507	C₄×Q₈	C₂³×C₃	1	2	yes	—
508	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
509	C₄×Q₈	C₂³×C₃	1	2	yes	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	C₃×D₄	1	2	yes	—
524	C₄×D₄	C₃×D₄	1	1	yes	characteristic
525	C₄×D₄	C₃×D₄	1	2	yes	—
526	C₄×D₄	C₃×D₄	1	1	yes	characteristic
527	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
528	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
529	C₄×D₄	C₂³×C₃	1	2	yes	—
530	C₄×D₄	C₂³×C₃	1	4	yes	—
531	C₄×D₄	C₂³×C₃	1	4	yes	—
532	#117	—	2	1	no	—
533	#117	—	2	2	no	—
534	#117	—	2	2	no	—
535	#117	—	2	2	no	—
536	#117	—	2	2	no	—
537	#117	—	2	1	no	—
538	#117	—	2	2	no	—
539	#117	C₂³×C₃	1	1	yes	characteristic
540	#117	C₂³×C₃	1	2	yes	—
541	#117	C₂³×C₃	1	2	yes	—
542	#117	C₂³×C₃	1	1	yes	characteristic
543	#117	C₂³×C₃	1	2	yes	—
544	C₂×C₄⋊C₄	—	2	1	no	—
545	C₂×C₄⋊C₄	—	2	2	no	—
546	C₂×C₄⋊C₄	—	2	1	no	—
547	C₂×C₄⋊C₄	—	2	2	no	—
548	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
550	C₂×C₂²⋊C₄	—	2	4	no	—
551	C₂×C₄²	—	2	1	no	—
552	C₂×C₄²	—	2	2	no	—
553	C₂×C₄²	—	2	1	no	—
554	C₂×C₄²	—	2	2	no	—
555	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₃	1	2	yes	—
557	#107	C₂³×C₃	1	2	yes	—
558	#107	C₂³×C₃	1	2	yes	—
559	#107	C₂³×C₃	1	4	yes	—
560	#106	C₂³×C₃	1	2	yes	—
561	#106	C₂³×C₃	1	2	yes	—
562	#106	C₂³×C₃	1	4	yes	—
563	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
564	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
565	C₄⋊C₈	C₂³×C₃	1	2	yes	—
566	C₄⋊C₈	C₂³×C₃	1	2	yes	—
567	C₄⋊C₈	C₂³×C₃	1	2	yes	—
568	#103	C₂³×C₃	1	2	yes	—
569	#103	C₂³×C₃	1	2	yes	—
570	#103	C₂³×C₃	1	4	yes	—
571	#103	C₂³×C₃	1	4	yes	—
572	#102	C₂³×C₃	1	4	yes	—
573	#102	C₂³×C₃	1	4	yes	—
574	#102	C₂³×C₃	1	2	yes	—
575	#102	C₂³×C₃	1	2	yes	—
576	#102	C₂³×C₃	1	4	yes	—
577	#102	C₂³×C₃	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
579	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
580	#97	C₂³×C₃	1	4	yes	—
581	C₄×C₈	C₂³×C₃	1	4	yes	—
582	C₂³×C₃	—	2	1	no	—
583	C₂³×C₃	—	2	4	no	—
584	C₂³×C₃	—	4	4	no	—
585	C₂³×C₃	—	8	2	no	—
586	C₂³×C₃	—	8	2	no	—
587	C₂³×C₃	C₂²×D₄	1	2	yes	—
588	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
589	C₃×Q₈	—	2	8	no	—
590	C₃×Q₈	—	2	2	no	—
591	C₃×Q₈	—	2	4	no	—
592	C₃×Q₈	—	2	1	no	—
593	C₃×Q₈	—	2	2	no	—
594	C₃×Q₈	—	4	2	no	—
595	C₃×Q₈	—	4	2	no	—
596	C₃×Q₈	C₂×#41	1	2	yes	—
597	C₃×Q₈	C₂×#41	1	4	yes	—
598	C₃×D₄	—	2	8	no	—
599	C₃×D₄	—	2	4	no	—
600	C₃×D₄	—	2	4	no	—
601	C₃×D₄	—	2	2	no	—
602	C₃×D₄	—	2	1	no	—
603	C₃×D₄	—	2	4	no	—
604	C₃×D₄	—	2	4	no	—
605	C₃×D₄	—	4	4	no	—
606	C₃×D₄	—	4	4	no	—
607	C₃×D₄	—	4	4	no	—
608	C₃×D₄	—	8	2	no	—
609	C₃×D₄	—	8	2	no	—
610	C₃×D₄	—	8	4	no	—
611	C₃×D₄	—	8	4	no	—
612	C₃×D₄	C₂×#41	1	2	yes	—
613	C₂×C₃×C₄	—	2	8	no	—
614	C₂×C₃×C₄	—	2	8	no	—
615	C₂×C₃×C₄	—	2	4	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	4	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	4	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	no	—
623	C₂×C₃×C₄	—	2	1	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	1	no	—
626	C₂×C₃×C₄	—	2	2	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	4	1	no	—
629	C₂×C₃×C₄	—	4	2	no	—
630	C₂×C₃×C₄	—	4	2	no	—
631	C₂×C₃×C₄	—	8	2	no	—
632	C₂×C₃×C₄	—	8	1	no	—
633	C₂×C₃×C₄	—	8	4	no	—
634	C₂×C₃×C₄	—	8	4	no	—
635	C₂×C₃×C₄	—	8	1	no	—
636	C₂×C₃×C₄	—	8	2	no	—
637	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
638	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
639	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
640	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
641	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
642	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
643	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
645	C₂×C₃×C₄	C₂×#41	1	2	yes	—
646	C₂×C₃×C₄	C₂×#41	1	2	yes	—
647	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
648	C₃×C₈	—	2	2	no	—
649	C₃×C₈	—	2	2	no	—
650	C₃×C₈	—	2	4	no	—
651	C₂⁴	—	2	2	no	—
652	#41	—	2	16	no	—
653	#41	—	2	8	no	—
654	#41	—	2	4	no	—
655	#41	—	2	4	no	—
656	#41	—	2	2	no	—
657	#41	—	2	2	no	—
658	#41	—	2	2	no	—
659	#41	—	8	4	no	—
660	#41	—	8	4	no	—
661	#41	C₃×#41	1	4	yes	complemented
662	C₂×Q₈	—	2	8	no	—
663	C₂×Q₈	—	2	4	no	—
664	C₂×Q₈	—	2	4	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
671	C₂×Q₈	C₃×#41	1	4	yes	complemented
672	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
673	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	8	2	no	—
686	C₂×D₄	—	8	2	no	—
687	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
688	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
689	C₂×D₄	C₂⁴×C₃	1	4	yes	—
690	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	1	no	—
698	C₂²×C₄	—	2	2	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	4	no	—
702	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
703	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
704	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
705	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
708	SD₁₆	—	2	8	no	—
709	SD₁₆	—	2	8	no	—
710	SD₁₆	—	2	8	no	—
711	D₈	—	2	8	no	—
712	M₁₆	—	2	4	no	—
713	C₂×C₈	—	2	4	no	—
714	C₂×C₈	C₂⁴×C₃	1	2	yes	—
715	C₂×C₈	C₂⁴×C₃	1	4	yes	—
716	C₂×C₈	C₂⁴×C₃	1	2	yes	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
731	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
732	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
733	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	1	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
750	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
751	C₂²⋊C₄	C₂×C₃×D₄	1	2	yes	—
752	C₄²	—	2	2	no	—
753	C₄²	—	2	1	no	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	2	no	—
762	C₄²	C₂×C₃×D₄	1	2	yes	—
763	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
764	C₄²	C₂×C₃×D₄	1	2	yes	—
765	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
766	C₄²	C₂⁴×C₃	1	2	yes	—
767	C₄²	C₂⁴×C₃	1	1	yes	characteristic
768	C₄²	C₂⁴×C₃	1	1	yes	characteristic
769	C₂²×C₃	—	2	1	no	—
770	C₂²×C₃	—	2	1	no	—
771	C₂²×C₃	—	2	2	no	—
772	C₂²×C₃	—	2	2	no	—
773	C₂²×C₃	—	2	2	no	—
774	C₂²×C₃	—	2	2	no	—
775	C₂²×C₃	—	4	1	no	—
776	C₂²×C₃	—	4	1	no	—
777	C₂²×C₃	—	4	4	no	—
778	C₂²×C₃	—	4	4	no	—
779	C₂²×C₃	—	4	4	no	—
780	C₂²×C₃	—	16	4	no	—
781	C₂²×C₃	#525	1	2	yes	—
782	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
783	C₃×C₄	—	2	1	no	—
784	C₃×C₄	—	2	2	no	—
785	C₃×C₄	—	2	1	no	—
786	C₃×C₄	—	2	4	no	—
787	C₃×C₄	—	2	2	no	—
788	C₃×C₄	—	2	2	no	—
789	C₃×C₄	—	2	2	no	—
790	C₃×C₄	—	2	1	no	—
791	C₃×C₄	—	4	2	no	—
792	C₃×C₄	—	4	1	no	—
793	C₃×C₄	—	4	2	no	—
794	C₃×C₄	—	4	1	no	—
795	C₃×C₄	—	4	2	no	—
796	C₃×C₄	#525	1	2	yes	—
797	C₃×C₄	#577	1	2	yes	—
798	C₃×C₄	C₂²×#41	1	1	yes	characteristic
799	C₃×C₄	C₂²×#41	1	1	yes	characteristic
800	C₂³	—	2	1	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	4	4	no	—
803	C₂³	—	8	2	no	—
804	C₂³	—	8	2	no	—
805	C₂³	C₂²×C₃×D₄	1	2	yes	—
806	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
807	Q₈	—	2	8	no	—
808	Q₈	—	2	1	no	—
809	Q₈	—	2	2	no	—
810	Q₈	—	2	2	no	—
811	Q₈	—	2	4	no	—
812	Q₈	—	4	2	no	—
813	Q₈	—	4	2	no	—
814	Q₈	C₂×C₃×#41	1	2	yes	—
815	Q₈	C₂×C₃×#41	1	4	yes	—
816	D₄	—	2	8	no	—
817	D₄	—	2	4	no	—
818	D₄	—	2	4	no	—
819	D₄	—	2	1	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	4	no	—
822	D₄	—	2	2	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	4	no	—
825	D₄	—	4	4	no	—
826	D₄	—	8	2	no	—
827	D₄	—	8	2	no	—
828	D₄	—	8	4	no	—
829	D₄	—	8	4	no	—
830	D₄	C₂×C₃×#41	1	2	yes	—
831	C₂×C₄	—	2	8	no	—
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	8	4	no	—
850	C₂×C₄	—	8	4	no	—
851	C₂×C₄	—	8	2	no	—
852	C₂×C₄	—	8	1	no	—
853	C₂×C₄	—	8	1	no	—
854	C₂×C₄	—	8	2	no	—
855	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
856	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
857	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
858	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
859	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
860	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
861	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
862	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
863	C₂×C₄	C₂×C₃×#41	1	2	yes	—
864	C₂×C₄	C₂×C₃×#41	1	2	yes	—
865	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
866	C₈	—	2	2	no	—
867	C₈	—	2	2	no	—
868	C₈	—	2	4	no	—
869	C₂×C₃	—	2	2	no	—
870	C₂×C₃	—	4	2	no	—
871	C₂×C₃	—	4	2	no	—
872	C₂×C₃	—	8	4	no	—
873	C₂×C₃	C₂×#525	1	1	yes	characteristic
874	C₂×C₃	C₂×#577	1	1	yes	characteristic
875	C₂×C₃	#3585	1	1	yes	characteristic
876	C₂²	—	2	1	no	—
877	C₂²	—	2	1	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	4	no	—
885	C₂²	—	4	4	no	—
886	C₂²	—	4	4	no	—
887	C₂²	—	16	4	no	—
888	C₂²	C₃×#525	1	2	yes	—
889	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
890	C₄	—	2	4	no	—
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	2	no	—
897	C₄	—	2	1	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	C₃×#525	1	2	yes	—
904	C₄	C₃×#577	1	2	yes	—
905	C₄	C₂²×C₃×#41	1	1	yes	characteristic
906	C₄	C₂²×C₃×#41	1	1	yes	characteristic
907	C₃	#60593	1	1	yes	characteristic, direct product factor, Sylow
908	C₂	—	2	2	no	—
909	C₂	—	4	2	no	—
910	C₂	—	4	2	no	—
911	C₂	—	8	4	no	—
912	C₂	C₂×C₃×#525	1	1	yes	characteristic
913	C₂	C₂×C₃×#577	1	1	yes	characteristic
914	C₂	C₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3508	C₂	semidirect
2. C₃×C₄×2₋¹⁺⁴	C₂	semidirect
3. C₃×#3126	C₂	semidirect
4. C₃×#3119	C₂	semidirect
5. C₃×#3115	C₂	semidirect
6. C₃×#3112	C₂	semidirect
7. C₃×#3106	C₂	semidirect
8. C₃×#3103	C₂	semidirect
9. C₃×#3096	C₂	semidirect
10. C₃×#3078	C₂	semidirect
11. C₃×#3076	C₂	semidirect
12. C₃×#3038	C₂	semidirect
13. C₂×C₃×#460	C₂	semidirect
14. C₃×#3010	C₂	semidirect
15. C₃×#2949	C₂	semidirect
16. C₃×#2946	C₂	semidirect
17. C₃×#2925	C₂	semidirect
18. #60593	C₃	direct (N × H)
38. C₃×#520	C₂²	semidirect
41. C₃×#519	C₂²	semidirect
47. C₃×C₄×#41	C₂²	semidirect
50. C₂×C₃×C₄×Q₈	C₂²	semidirect
51. C₃×#482	C₂²	semidirect
52. C₃×#482	C₂²	semidirect
53. C₃×#481	C₂²	semidirect
54. C₃×#480	C₂²	semidirect
55. C₃×#479	C₂²	semidirect
56. C₃×#479	C₂²	semidirect
57. C₃×#478	C₂²	semidirect
58. C₃×#477	C₂²	semidirect
59. C₃×#477	C₂²	semidirect
60. C₃×#476	C₂²	semidirect
61. C₃×#475	C₂²	semidirect
62. C₃×#475	C₂²	semidirect
63. C₃×#474	C₂²	semidirect
71. C₃×#449	C₂²	semidirect
72. C₃×#449	C₂²	semidirect
73. C₃×#448	C₂²	semidirect
74. C₃×#448	C₂²	semidirect
75. C₃×#442	C₂²	semidirect
76. C₃×#440	C₂²	semidirect
77. C₃×#440	C₂²	semidirect
78. C₃×#440	C₂²	semidirect
79. C₃×C₄×SD₁₆	C₂²	semidirect
80. C₃×C₄×SD₁₆	C₂²	semidirect
81. C₃×C₄×SD₁₆	C₂²	semidirect
82. C₃×C₄×D₈	C₂²	semidirect
83. C₃×#433	C₂²	semidirect
84. C₃×#432	C₂²	semidirect
85. C₃×#431	C₂²	semidirect
96. #3508	C₂×C₃	semidirect
97. C₄×2₋¹⁺⁴	C₂×C₃	semidirect
98. #3126	C₂×C₃	semidirect
99. #3119	C₂×C₃	semidirect
100. #3115	C₂×C₃	semidirect
101. #3112	C₂×C₃	semidirect
102. #3106	C₂×C₃	semidirect
103. #3103	C₂×C₃	semidirect
104. #3096	C₂×C₃	semidirect
105. #3078	C₂×C₃	semidirect
106. #3076	C₂×C₃	semidirect
107. #3038	C₂×C₃	semidirect
108. C₂×#460	C₂×C₃	semidirect
109. #3010	C₂×C₃	semidirect
110. #2949	C₂×C₃	semidirect
111. #2946	C₂×C₃	semidirect
112. #2925	C₂×C₃	semidirect
269. #520	C₂²×C₃	semidirect
272. #519	C₂²×C₃	semidirect
278. C₄×#41	C₂²×C₃	semidirect
281. C₂×C₄×Q₈	C₂²×C₃	semidirect
282. #482	C₂²×C₃	semidirect
283. #482	C₂²×C₃	semidirect
284. #481	C₂²×C₃	semidirect
285. #480	C₂²×C₃	semidirect
286. #479	C₂²×C₃	semidirect
287. #479	C₂²×C₃	semidirect
288. #478	C₂²×C₃	semidirect
289. #477	C₂²×C₃	semidirect
290. #477	C₂²×C₃	semidirect
291. #476	C₂²×C₃	semidirect
292. #475	C₂²×C₃	semidirect
293. #475	C₂²×C₃	semidirect
294. #474	C₂²×C₃	semidirect
302. #449	C₂²×C₃	semidirect
303. #449	C₂²×C₃	semidirect
304. #448	C₂²×C₃	semidirect
305. #448	C₂²×C₃	semidirect
306. #442	C₂²×C₃	semidirect
307. #440	C₂²×C₃	semidirect
308. #440	C₂²×C₃	semidirect
309. #440	C₂²×C₃	semidirect
310. C₄×SD₁₆	C₂²×C₃	semidirect
311. C₄×SD₁₆	C₂²×C₃	semidirect
312. C₄×SD₁₆	C₂²×C₃	semidirect
313. C₄×D₈	C₂²×C₃	semidirect
314. #433	C₂²×C₃	semidirect
315. #432	C₂²×C₃	semidirect
316. #431	C₂²×C₃	semidirect
337. C₃×#41	#41	semidirect
347. C₂×C₃×Q₈	#41	semidirect
661. #41	C₃×#41	semidirect
671. C₂×Q₈	C₃×#41	semidirect
907. C₃	#60593	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×#3508	2
C₃×C₄×2₋¹⁺⁴	2
C₃×#3126	2
C₃×#3119	2
C₃×#3115	2
C₃×#3112	2
C₃×#3106	2
C₃×#3103	2
C₃×#3096	2
C₃×#3078	2
C₃×#3076	2
C₃×#3038	2
C₂×C₃×#460	2
C₃×#3010	2
C₃×#2949	2
C₃×#2946	2
C₃×#2925	2
#60593	3

Subgroups — C3×#60593 #10679200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#60593 #10679200