Subgroups — C₃×#61841 #10680448

Order 768.

1744 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3388	C₂	1	4	yes	maximal, complemented
4	C₃×#3384	C₂	1	2	yes	maximal, complemented
5	C₃×#3381	C₂	1	2	yes	maximal, complemented
6	C₃×#3376	C₂	1	4	yes	maximal, complemented
7	C₃×#3372	C₂	1	2	yes	maximal, complemented
8	C₃×#3360	C₂	1	2	yes	maximal, complemented
9	C₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3236	C₂	1	2	yes	maximal, complemented
11	C₃×#3232	C₂	1	2	yes	maximal, complemented
12	C₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3114	C₂	1	2	yes	maximal
14	C₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3105	C₂	1	1	yes	maximal, characteristic
16	C₃×#3101	C₂	1	2	yes	maximal, complemented
17	C₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	#61841	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×#557	C₂²	1	1	yes	characteristic, complemented
20	C₃×#557	C₂²	1	2	yes	complemented
21	C₃×#557	C₂²	1	1	yes	characteristic, complemented
22	C₃×#556	C₂²	1	1	yes	characteristic, complemented
23	C₃×#556	C₂²	1	2	yes	complemented
24	C₃×#554	—	2	1	no	—
25	C₃×#554	—	2	1	no	—
26	C₃×#554	—	2	2	no	—
27	C₃×#554	C₂²	1	2	yes	—
28	C₃×#554	C₂²	1	4	yes	—
29	C₃×#554	C₂²	1	2	yes	—
30	C₃×#552	—	2	1	no	—
31	C₃×#552	—	2	2	no	—
32	C₃×D₄×Q₈	—	2	1	no	—
33	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#541	—	2	2	no	—
35	C₃×#541	—	2	1	no	—
36	C₃×#533	C₂²	1	1	yes	characteristic
37	C₃×#533	C₂²	1	2	yes	—
38	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₃×#529	C₂²	1	2	yes	—
40	C₃×#529	C₂²	1	1	yes	characteristic
41	C₂×C₃×#125	C₂²	1	2	yes	—
42	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₃×C₂²⋊Q₈	—	2	2	no	—
44	C₃×#519	—	2	1	no	—
45	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
47	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
48	C₂²×C₃×C₄⋊C₄	—	2	1	no	—
49	C₃×#501	C₂²	1	4	yes	complemented
50	C₃×#501	C₂²	1	2	yes	complemented
51	C₃×#499	C₂²	1	4	yes	complemented
52	C₃×#498	C₂²	1	2	yes	complemented
53	C₃×#491	C₂²	1	4	yes	complemented
54	C₃×#489	C₂²	1	2	yes	complemented
55	C₃×#488	C₂²	1	4	yes	complemented
56	C₃×#487	C₂²	1	2	yes	complemented
57	C₃×#484	C₂²	1	2	yes	—
58	C₃×#484	C₂²	1	1	yes	characteristic
59	C₃×#483	C₂²	1	2	yes	—
60	C₃×#483	C₂²	1	2	yes	—
61	C₃×#483	C₂²	1	2	yes	—
62	C₃×#481	C₂²	1	1	yes	characteristic
63	C₃×#480	C₂²	1	2	yes	—
64	C₃×#479	C₂²	1	4	yes	complemented
65	C₃×#479	C₂²	1	4	yes	complemented
66	C₃×#479	C₂²	1	4	yes	complemented
67	C₃×#478	C₂²	1	2	yes	—
68	C₃×#478	C₂²	1	4	yes	—
69	C₃×#478	C₂²	1	4	yes	complemented
70	C₃×#477	C₂²	1	2	yes	complemented
71	C₃×#476	C₂²	1	4	yes	—
72	C₃×#476	C₂²	1	2	yes	complemented
73	C₃×#475	C₂²	1	4	yes	complemented
74	C₃×#474	C₂²	1	2	yes	—
75	C₃×#463	C₂²	1	4	yes	—
76	C₃×#463	C₂²	1	2	yes	—
77	C₃×#461	C₂²	1	4	yes	—
78	C₃×#461	C₂²	1	2	yes	—
79	C₃×#450	C₂²	1	1	yes	characteristic
80	C₃×#450	C₂²	1	2	yes	—
81	C₃×#447	C₂²	1	1	yes	characteristic
82	C₃×#446	C₂²	1	2	yes	complemented
83	C₃×#446	C₂²	1	4	yes	complemented
84	C₃×C₈×Q₈	C₂²	1	2	yes	complemented
85	C₃×#442	C₂²	1	4	yes	—
86	C₃×#440	C₂²	1	4	yes	—
87	C₃×#440	C₂²	1	4	yes	—
88	C₃×C₄×SD₁₆	C₂²	1	4	yes	—
89	C₃×C₄×SD₁₆	C₂²	1	4	yes	—
90	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
91	C₃×C₄×D₈	C₂²	1	2	yes	—
92	C₃×#432	C₂²	1	2	yes	—
93	C₃×#432	C₂²	1	1	yes	characteristic
94	C₃×#431	C₂²	1	1	yes	characteristic
95	C₃×#431	C₂²	1	2	yes	—
96	#3523	C₂×C₃	1	1	yes	characteristic, complemented
97	C₂×#554	C₂×C₃	1	1	yes	characteristic, complemented
98	#3388	C₂×C₃	1	4	yes	complemented
99	#3384	C₂×C₃	1	2	yes	complemented
100	#3381	C₂×C₃	1	2	yes	complemented
101	#3376	C₂×C₃	1	4	yes	complemented
102	#3372	C₂×C₃	1	2	yes	complemented
103	#3360	C₂×C₃	1	2	yes	complemented
104	#3238	C₂×C₃	1	1	yes	characteristic, complemented
105	#3236	C₂×C₃	1	2	yes	complemented
106	#3232	C₂×C₃	1	2	yes	complemented
107	#3229	C₂×C₃	1	1	yes	characteristic, complemented
108	#3114	C₂×C₃	1	2	yes	—
109	#3110	C₂×C₃	1	1	yes	characteristic, complemented
110	#3105	C₂×C₃	1	1	yes	characteristic
111	#3101	C₂×C₃	1	2	yes	complemented
112	#2984	C₂×C₃	1	1	yes	characteristic, complemented
113	C₂²×C₃×Q₈	—	2	1	no	—
114	C₂²×C₃×Q₈	—	2	1	no	—
115	C₂²×C₃×Q₈	D₄	1	1	yes	characteristic
116	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
117	C₂³×C₃×C₄	—	2	1	no	—
118	C₂³×C₃×C₄	—	2	2	no	—
119	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
120	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₃×D₈	C₂³	1	2	yes	—
122	C₃×C₄⋊Q₈	—	2	1	no	—
123	C₃×C₄⋊Q₈	—	2	2	no	—
124	C₃×C₄⋊Q₈	—	2	1	no	—
125	C₃×C₄⋊Q₈	—	2	1	no	—
126	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₃×#126	—	2	2	no	—
133	C₃×#126	—	2	2	no	—
134	C₃×#126	—	2	2	no	—
135	C₃×#126	—	2	2	no	—
136	C₃×#126	—	2	1	no	—
137	C₃×#125	—	2	2	no	—
138	C₃×#125	—	2	2	no	—
139	C₃×#125	—	2	2	no	—
140	C₃×#125	—	2	1	no	—
141	C₃×#125	—	2	2	no	—
142	C₃×#125	—	2	2	no	—
143	C₃×#125	—	2	2	no	—
144	C₃×#125	—	2	2	no	—
145	C₃×#125	—	2	1	no	—
146	C₃×#125	C₂³	1	4	yes	—
147	C₃×#125	C₂³	1	4	yes	—
148	C₃×#125	C₂³	1	2	yes	—
149	C₃×#125	C₂³	1	1	yes	characteristic
150	C₃×#124	C₂³	1	2	yes	—
151	C₃×#124	C₂³	1	1	yes	characteristic
152	C₃×#123	—	2	1	no	—
153	C₃×#123	—	2	2	no	—
154	C₃×C₂²⋊Q₈	—	2	2	no	—
155	C₃×C₂²⋊Q₈	—	2	2	no	—
156	C₃×C₂²⋊Q₈	—	2	4	no	—
157	C₃×C₂²⋊Q₈	—	2	1	no	—
158	C₃×C₂²⋊Q₈	—	2	2	no	—
159	C₃×C₂²⋊Q₈	—	2	1	no	—
160	C₃×C₂²⋊Q₈	—	2	2	no	—
161	C₃×C₂²⋊Q₈	—	2	4	no	—
162	C₃×C₂²⋊Q₈	—	2	4	no	—
163	C₃×C₂²⋊Q₈	—	2	4	no	—
164	C₃×C₂²⋊Q₈	—	2	4	no	—
165	C₃×C₂²⋊Q₈	—	2	1	no	—
166	C₃×C₂²⋊Q₈	—	2	2	no	—
167	C₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₃×#121	C₂³	1	1	yes	characteristic
170	C₃×C₄×Q₈	—	2	1	no	—
171	C₃×C₄×Q₈	—	2	1	no	—
172	C₃×C₄×Q₈	—	2	2	no	—
173	C₃×C₄×Q₈	—	2	2	no	—
174	C₃×C₄×Q₈	—	2	1	no	—
175	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
176	C₃×C₄×Q₈	D₄	1	2	yes	—
177	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
178	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
179	C₃×C₄×Q₈	C₂³	1	2	yes	—
180	C₃×C₄×Q₈	C₂³	1	2	yes	—
181	C₃×C₄×Q₈	C₂³	1	2	yes	—
182	C₃×C₄×Q₈	C₂³	1	2	yes	—
183	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
184	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
185	C₃×C₄×Q₈	C₂³	1	2	yes	—
186	C₃×C₄×D₄	—	2	1	no	—
187	C₃×C₄×D₄	—	2	2	no	—
188	C₃×C₄×D₄	—	2	2	no	—
189	C₃×C₄×D₄	—	2	1	no	—
190	C₃×C₄×D₄	—	2	2	no	—
191	C₃×C₄×D₄	—	2	1	no	—
192	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
193	C₃×C₄×D₄	C₂³	1	2	yes	—
194	C₃×C₄×D₄	C₂³	1	4	yes	—
195	C₃×C₄×D₄	C₂³	1	2	yes	—
196	C₃×C₄×D₄	C₂³	1	4	yes	—
197	C₃×C₄×D₄	C₂³	1	2	yes	—
198	C₃×#117	—	2	1	no	—
199	C₃×#117	—	2	2	no	—
200	C₃×#117	—	2	1	no	—
201	C₃×#117	—	2	2	no	—
202	C₃×#117	—	2	2	no	—
203	C₃×#117	—	2	1	no	—
204	C₂×C₃×C₄⋊C₄	—	2	2	no	—
205	C₂×C₃×C₄⋊C₄	—	2	1	no	—
206	C₂×C₃×C₄⋊C₄	—	2	2	no	—
207	C₂×C₃×C₄⋊C₄	—	2	2	no	—
208	C₂×C₃×C₄⋊C₄	—	2	2	no	—
209	C₂×C₃×C₄⋊C₄	—	2	4	no	—
210	C₂×C₃×C₄⋊C₄	D₄	1	1	yes	characteristic
211	C₂×C₃×C₄⋊C₄	D₄	1	2	yes	—
212	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
213	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
214	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
215	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
216	C₂×C₃×C₄²	C₂³	1	2	yes	—
217	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
218	C₃×#107	C₂³	1	2	yes	—
219	C₃×#107	C₂³	1	4	yes	—
220	C₃×#107	C₂³	1	4	yes	—
221	C₃×#106	C₂³	1	4	yes	—
222	C₃×#106	C₂³	1	4	yes	—
223	C₃×#106	C₂³	1	2	yes	—
224	C₃×#106	C₂³	1	4	yes	—
225	C₃×C₄⋊C₈	C₂³	1	4	yes	—
226	C₃×C₄⋊C₈	C₂³	1	2	yes	—
227	C₃×C₄⋊C₈	C₂³	1	2	yes	—
228	C₃×C₄⋊C₈	C₂³	1	4	yes	—
229	C₃×#103	C₂³	1	4	yes	—
230	C₃×#103	C₂³	1	4	yes	—
231	C₃×#103	C₂³	1	2	yes	—
232	C₃×#103	C₂³	1	4	yes	—
233	C₃×#103	C₂³	1	4	yes	—
234	C₃×#102	C₂³	1	2	yes	—
235	C₃×#102	C₂³	1	2	yes	—
236	C₃×#102	C₂³	1	2	yes	—
237	C₃×#102	C₂³	1	4	yes	—
238	C₃×#102	C₂³	1	4	yes	—
239	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
240	C₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
241	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
242	C₃×#97	C₂³	1	2	yes	—
243	C₃×#97	C₂³	1	4	yes	—
244	C₃×C₄×C₈	C₂³	1	2	yes	—
245	C₃×C₄×C₈	C₂³	1	4	yes	—
246	#557	C₂²×C₃	1	1	yes	characteristic, complemented
247	#557	C₂²×C₃	1	1	yes	characteristic, complemented
248	#557	C₂²×C₃	1	2	yes	complemented
249	#556	C₂²×C₃	1	1	yes	characteristic, complemented
250	#556	C₂²×C₃	1	2	yes	complemented
251	#554	—	2	1	no	—
252	#554	—	2	1	no	—
253	#554	—	2	2	no	—
254	#554	C₂²×C₃	1	2	yes	—
255	#554	C₂²×C₃	1	2	yes	—
256	#554	C₂²×C₃	1	4	yes	—
257	#552	—	2	1	no	—
258	#552	—	2	2	no	—
259	D₄×Q₈	—	2	1	no	—
260	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
261	#541	—	2	2	no	—
262	#541	—	2	1	no	—
263	#533	C₂²×C₃	1	2	yes	—
264	#533	C₂²×C₃	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
266	#529	C₂²×C₃	1	1	yes	characteristic
267	#529	C₂²×C₃	1	2	yes	—
268	C₂×#125	C₂²×C₃	1	2	yes	—
269	C₂×C₂²⋊Q₈	—	2	1	no	—
270	C₂×C₂²⋊Q₈	—	2	2	no	—
271	#519	—	2	1	no	—
272	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
273	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
274	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
275	C₂²×C₄⋊C₄	—	2	1	no	—
276	#501	C₂²×C₃	1	4	yes	complemented
277	#501	C₂²×C₃	1	2	yes	complemented
278	#499	C₂²×C₃	1	4	yes	complemented
279	#498	C₂²×C₃	1	2	yes	complemented
280	#491	C₂²×C₃	1	4	yes	complemented
281	#489	C₂²×C₃	1	2	yes	complemented
282	#488	C₂²×C₃	1	4	yes	complemented
283	#487	C₂²×C₃	1	2	yes	complemented
284	#484	C₂²×C₃	1	1	yes	characteristic
285	#484	C₂²×C₃	1	2	yes	—
286	#483	C₂²×C₃	1	2	yes	—
287	#483	C₂²×C₃	1	2	yes	—
288	#483	C₂²×C₃	1	2	yes	—
289	#481	C₂²×C₃	1	1	yes	characteristic
290	#480	C₂²×C₃	1	2	yes	—
291	#479	C₂²×C₃	1	4	yes	complemented
292	#479	C₂²×C₃	1	4	yes	complemented
293	#479	C₂²×C₃	1	4	yes	complemented
294	#478	C₂²×C₃	1	2	yes	—
295	#478	C₂²×C₃	1	4	yes	—
296	#478	C₂²×C₃	1	4	yes	complemented
297	#477	C₂²×C₃	1	2	yes	complemented
298	#476	C₂²×C₃	1	4	yes	—
299	#476	C₂²×C₃	1	2	yes	complemented
300	#475	C₂²×C₃	1	4	yes	complemented
301	#474	C₂²×C₃	1	2	yes	—
302	#463	C₂²×C₃	1	4	yes	—
303	#463	C₂²×C₃	1	2	yes	—
304	#461	C₂²×C₃	1	4	yes	—
305	#461	C₂²×C₃	1	2	yes	—
306	#450	C₂²×C₃	1	1	yes	characteristic
307	#450	C₂²×C₃	1	2	yes	—
308	#447	C₂²×C₃	1	1	yes	characteristic
309	#446	C₂²×C₃	1	2	yes	complemented
310	#446	C₂²×C₃	1	4	yes	complemented
311	C₈×Q₈	C₂²×C₃	1	2	yes	complemented
312	#442	C₂²×C₃	1	4	yes	—
313	#440	C₂²×C₃	1	4	yes	—
314	#440	C₂²×C₃	1	4	yes	—
315	C₄×SD₁₆	C₂²×C₃	1	4	yes	—
316	C₄×SD₁₆	C₂²×C₃	1	4	yes	—
317	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
318	C₄×D₈	C₂²×C₃	1	2	yes	—
319	#432	C₂²×C₃	1	1	yes	characteristic
320	#432	C₂²×C₃	1	2	yes	—
321	#431	C₂²×C₃	1	2	yes	—
322	#431	C₂²×C₃	1	1	yes	characteristic
323	C₂⁴×C₃	—	2	1	no	—
324	C₂×C₃×Q₈	—	2	2	no	—
325	C₂×C₃×Q₈	—	2	1	no	—
326	C₂×C₃×Q₈	—	2	2	no	—
327	C₂×C₃×Q₈	—	2	2	no	—
328	C₂×C₃×Q₈	—	4	2	no	—
329	C₂×C₃×Q₈	—	4	4	no	—
330	C₂×C₃×Q₈	—	8	2	no	—
331	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
332	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
333	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
334	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
335	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
336	C₂×C₃×D₄	—	2	4	no	—
337	C₂×C₃×D₄	—	2	1	no	—
338	C₂×C₃×D₄	—	2	1	no	—
339	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
340	C₂×C₃×D₄	C₂⁴	1	2	yes	—
341	C₂²×C₃×C₄	—	2	1	no	—
342	C₂²×C₃×C₄	—	2	2	no	—
343	C₂²×C₃×C₄	—	2	2	no	—
344	C₂²×C₃×C₄	—	2	2	no	—
345	C₂²×C₃×C₄	—	2	2	no	—
346	C₂²×C₃×C₄	—	2	1	no	—
347	C₂²×C₃×C₄	—	2	4	no	—
348	C₂²×C₃×C₄	—	2	4	no	—
349	C₂²×C₃×C₄	—	4	4	no	—
350	C₂²×C₃×C₄	—	8	4	no	—
351	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
353	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
355	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
356	C₃×SD₁₆	—	2	4	no	—
357	C₃×SD₁₆	—	2	8	no	—
358	C₃×D₈	—	2	4	no	—
359	C₂×C₃×C₈	C₂⁴	1	2	yes	—
360	C₂×C₃×C₈	C₂⁴	1	4	yes	—
361	C₂×C₃×C₈	C₂⁴	1	2	yes	—
362	C₃×C₄⋊C₄	—	2	4	no	—
363	C₃×C₄⋊C₄	—	2	4	no	—
364	C₃×C₄⋊C₄	—	2	2	no	—
365	C₃×C₄⋊C₄	—	2	2	no	—
366	C₃×C₄⋊C₄	—	2	4	no	—
367	C₃×C₄⋊C₄	—	2	4	no	—
368	C₃×C₄⋊C₄	—	2	1	no	—
369	C₃×C₄⋊C₄	—	2	2	no	—
370	C₃×C₄⋊C₄	—	2	2	no	—
371	C₃×C₄⋊C₄	—	2	1	no	—
372	C₃×C₄⋊C₄	—	2	2	no	—
373	C₃×C₄⋊C₄	—	2	1	no	—
374	C₃×C₄⋊C₄	—	2	1	no	—
375	C₃×C₄⋊C₄	—	2	2	no	—
376	C₃×C₄⋊C₄	—	2	1	no	—
377	C₃×C₄⋊C₄	—	2	2	no	—
378	C₃×C₄⋊C₄	—	2	1	no	—
379	C₃×C₄⋊C₄	—	2	2	no	—
380	C₃×C₄⋊C₄	—	2	2	no	—
381	C₃×C₄⋊C₄	—	2	1	no	—
382	C₃×C₄⋊C₄	—	2	2	no	—
383	C₃×C₄⋊C₄	—	2	2	no	—
384	C₃×C₄⋊C₄	—	2	2	no	—
385	C₃×C₄⋊C₄	—	2	1	no	—
386	C₃×C₄⋊C₄	—	2	2	no	—
387	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
388	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
390	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
391	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
395	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
396	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
397	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
398	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
399	C₃×C₂²⋊C₄	—	2	2	no	—
400	C₃×C₂²⋊C₄	—	2	1	no	—
401	C₃×C₂²⋊C₄	—	2	2	no	—
402	C₃×C₂²⋊C₄	—	2	2	no	—
403	C₃×C₂²⋊C₄	—	2	4	no	—
404	C₃×C₂²⋊C₄	—	2	4	no	—
405	C₃×C₂²⋊C₄	—	2	1	no	—
406	C₃×C₂²⋊C₄	—	2	1	no	—
407	C₃×C₂²⋊C₄	—	2	2	no	—
408	C₃×C₂²⋊C₄	—	2	2	no	—
409	C₃×C₂²⋊C₄	—	2	1	no	—
410	C₃×C₂²⋊C₄	—	2	1	no	—
411	C₃×C₂²⋊C₄	—	2	2	no	—
412	C₃×C₄²	—	2	2	no	—
413	C₃×C₄²	—	2	2	no	—
414	C₃×C₄²	—	2	2	no	—
415	C₃×C₄²	—	2	2	no	—
416	C₃×C₄²	—	2	1	no	—
417	C₃×C₄²	C₂×D₄	1	2	yes	—
418	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
419	C₃×C₄²	C₂×D₄	1	2	yes	—
420	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
421	C₃×C₄²	C₂⁴	1	1	yes	characteristic
422	C₃×C₄²	C₂⁴	1	2	yes	—
423	C₃×C₄²	C₂⁴	1	2	yes	—
424	C₃×C₄²	C₂⁴	1	1	yes	characteristic
425	C₂²×Q₈	—	2	1	no	—
426	C₂²×Q₈	—	2	1	no	—
427	C₂²×Q₈	C₃×D₄	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
429	C₂³×C₄	—	2	1	no	—
430	C₂³×C₄	—	2	2	no	—
431	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
432	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
433	C₂×D₈	C₂³×C₃	1	2	yes	—
434	C₄⋊Q₈	—	2	1	no	—
435	C₄⋊Q₈	—	2	2	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	—	2	1	no	—
438	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
439	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
440	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
441	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
442	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
443	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
444	#126	—	2	2	no	—
445	#126	—	2	2	no	—
446	#126	—	2	2	no	—
447	#126	—	2	2	no	—
448	#126	—	2	1	no	—
449	#125	—	2	2	no	—
450	#125	—	2	2	no	—
451	#125	—	2	2	no	—
452	#125	—	2	1	no	—
453	#125	—	2	2	no	—
454	#125	—	2	2	no	—
455	#125	—	2	2	no	—
456	#125	—	2	2	no	—
457	#125	—	2	1	no	—
458	#125	C₂³×C₃	1	4	yes	—
459	#125	C₂³×C₃	1	4	yes	—
460	#125	C₂³×C₃	1	2	yes	—
461	#125	C₂³×C₃	1	1	yes	characteristic
462	#124	C₂³×C₃	1	2	yes	—
463	#124	C₂³×C₃	1	1	yes	characteristic
464	#123	—	2	1	no	—
465	#123	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	4	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	2	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	2	no	—
473	C₂²⋊Q₈	—	2	4	no	—
474	C₂²⋊Q₈	—	2	4	no	—
475	C₂²⋊Q₈	—	2	4	no	—
476	C₂²⋊Q₈	—	2	4	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	C₂³×C₃	1	1	yes	characteristic
480	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
481	#121	C₂³×C₃	1	1	yes	characteristic
482	C₄×Q₈	—	2	1	no	—
483	C₄×Q₈	—	2	1	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×Q₈	—	2	2	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
488	C₄×Q₈	C₃×D₄	1	2	yes	—
489	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
490	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
491	C₄×Q₈	C₂³×C₃	1	2	yes	—
492	C₄×Q₈	C₂³×C₃	1	2	yes	—
493	C₄×Q₈	C₂³×C₃	1	2	yes	—
494	C₄×Q₈	C₂³×C₃	1	2	yes	—
495	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
496	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
497	C₄×Q₈	C₂³×C₃	1	2	yes	—
498	C₄×D₄	—	2	1	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	C₂³×C₃	1	2	yes	—
505	C₄×D₄	C₂³×C₃	1	4	yes	—
506	C₄×D₄	C₂³×C₃	1	2	yes	—
507	C₄×D₄	C₂³×C₃	1	4	yes	—
508	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
509	C₄×D₄	C₂³×C₃	1	2	yes	—
510	#117	—	2	1	no	—
511	#117	—	2	2	no	—
512	#117	—	2	1	no	—
513	#117	—	2	2	no	—
514	#117	—	2	2	no	—
515	#117	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	2	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	2	no	—
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	4	no	—
522	C₂×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₃×D₄	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	2	no	—
528	C₂×C₄²	C₂³×C₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
530	#107	C₂³×C₃	1	2	yes	—
531	#107	C₂³×C₃	1	4	yes	—
532	#107	C₂³×C₃	1	4	yes	—
533	#106	C₂³×C₃	1	4	yes	—
534	#106	C₂³×C₃	1	4	yes	—
535	#106	C₂³×C₃	1	2	yes	—
536	#106	C₂³×C₃	1	4	yes	—
537	C₄⋊C₈	C₂³×C₃	1	4	yes	—
538	C₄⋊C₈	C₂³×C₃	1	2	yes	—
539	C₄⋊C₈	C₂³×C₃	1	2	yes	—
540	C₄⋊C₈	C₂³×C₃	1	4	yes	—
541	#103	C₂³×C₃	1	4	yes	—
542	#103	C₂³×C₃	1	4	yes	—
543	#103	C₂³×C₃	1	2	yes	—
544	#103	C₂³×C₃	1	4	yes	—
545	#103	C₂³×C₃	1	4	yes	—
546	#102	C₂³×C₃	1	2	yes	—
547	#102	C₂³×C₃	1	2	yes	—
548	#102	C₂³×C₃	1	2	yes	—
549	#102	C₂³×C₃	1	4	yes	—
550	#102	C₂³×C₃	1	4	yes	—
551	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
552	C₂²⋊C₈	C₂³×C₃	1	1	yes	characteristic
553	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
554	#97	C₂³×C₃	1	2	yes	—
555	#97	C₂³×C₃	1	4	yes	—
556	C₄×C₈	C₂³×C₃	1	2	yes	—
557	C₄×C₈	C₂³×C₃	1	4	yes	—
558	C₂³×C₃	—	2	4	no	—
559	C₂³×C₃	—	2	2	no	—
560	C₂³×C₃	—	2	1	no	—
561	C₂³×C₃	—	4	2	no	—
562	C₂³×C₃	—	4	2	no	—
563	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
564	C₃×Q₈	—	2	2	no	—
565	C₃×Q₈	—	2	2	no	—
566	C₃×Q₈	—	2	2	no	—
567	C₃×Q₈	—	2	4	no	—
568	C₃×Q₈	—	4	2	no	—
569	C₃×Q₈	—	4	4	no	—
570	C₃×Q₈	—	4	2	no	—
571	C₃×Q₈	—	8	2	no	—
572	C₃×Q₈	—	8	2	no	—
573	C₃×D₄	—	2	4	no	—
574	C₃×D₄	—	2	2	no	—
575	C₃×D₄	—	2	2	no	—
576	C₃×D₄	—	4	2	no	—
577	C₃×D₄	2₋¹⁺⁴	1	4	yes	—
578	C₂×C₃×C₄	—	2	4	no	—
579	C₂×C₃×C₄	—	2	2	no	—
580	C₂×C₃×C₄	—	2	2	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	2	no	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	—	2	1	no	—
585	C₂×C₃×C₄	—	2	2	no	—
586	C₂×C₃×C₄	—	2	1	no	—
587	C₂×C₃×C₄	—	2	2	no	—
588	C₂×C₃×C₄	—	2	4	no	—
589	C₂×C₃×C₄	—	4	2	no	—
590	C₂×C₃×C₄	—	4	4	no	—
591	C₂×C₃×C₄	—	4	4	no	—
592	C₂×C₃×C₄	—	4	2	no	—
593	C₂×C₃×C₄	—	4	4	no	—
594	C₂×C₃×C₄	—	4	4	no	—
595	C₂×C₃×C₄	—	4	2	no	—
596	C₂×C₃×C₄	—	8	4	no	—
597	C₂×C₃×C₄	—	8	4	no	—
598	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
600	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
601	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
603	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
605	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
608	C₃×C₈	—	2	2	no	—
609	C₃×C₈	—	2	2	no	—
610	C₃×C₈	—	2	4	no	—
611	C₂⁴	—	2	1	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	2	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	4	2	no	—
617	C₂×Q₈	—	4	4	no	—
618	C₂×Q₈	—	8	2	no	—
619	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
620	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
621	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
622	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
623	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
628	C₂×D₄	C₂⁴×C₃	1	2	yes	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	4	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	4	4	no	—
638	C₂²×C₄	—	8	4	no	—
639	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
640	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
641	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
642	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
644	SD₁₆	—	2	4	no	—
645	SD₁₆	—	2	8	no	—
646	D₈	—	2	4	no	—
647	C₂×C₈	C₂⁴×C₃	1	2	yes	—
648	C₂×C₈	C₂⁴×C₃	1	4	yes	—
649	C₂×C₈	C₂⁴×C₃	1	2	yes	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
676	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
677	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
678	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
679	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
680	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
681	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
683	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
685	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
686	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	1	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₄²	—	2	2	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	1	no	—
705	C₄²	C₂×C₃×D₄	1	2	yes	—
706	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
707	C₄²	C₂×C₃×D₄	1	2	yes	—
708	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
709	C₄²	C₂⁴×C₃	1	1	yes	characteristic
710	C₄²	C₂⁴×C₃	1	2	yes	—
711	C₄²	C₂⁴×C₃	1	2	yes	—
712	C₄²	C₂⁴×C₃	1	1	yes	characteristic
713	C₂²×C₃	—	2	1	no	—
714	C₂²×C₃	—	2	1	no	—
715	C₂²×C₃	—	2	4	no	—
716	C₂²×C₃	—	4	8	no	—
717	C₂²×C₃	—	4	2	no	—
718	C₂²×C₃	—	4	2	no	—
719	C₂²×C₃	—	4	1	no	—
720	C₂²×C₃	—	4	1	no	—
721	C₂²×C₃	—	4	1	no	—
722	C₂²×C₃	#577	1	2	yes	—
723	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
724	C₃×C₄	—	2	1	no	—
725	C₃×C₄	—	2	1	no	—
726	C₃×C₄	—	2	2	no	—
727	C₃×C₄	—	2	2	no	—
728	C₃×C₄	—	2	2	no	—
729	C₃×C₄	—	2	2	no	—
730	C₃×C₄	—	2	1	no	—
731	C₃×C₄	—	2	1	no	—
732	C₃×C₄	—	4	2	no	—
733	C₃×C₄	—	4	1	no	—
734	C₃×C₄	—	4	2	no	—
735	C₃×C₄	—	4	2	no	—
736	C₃×C₄	—	4	1	no	—
737	C₃×C₄	—	4	4	no	—
738	C₃×C₄	—	4	1	no	—
739	C₃×C₄	#575	1	2	yes	—
740	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
741	C₂³	—	2	4	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	4	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
747	Q₈	—	2	2	no	—
748	Q₈	—	2	2	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	2	4	no	—
751	Q₈	—	4	2	no	—
752	Q₈	—	4	4	no	—
753	Q₈	—	4	2	no	—
754	Q₈	—	8	2	no	—
755	Q₈	—	8	2	no	—
756	D₄	—	2	4	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	4	2	no	—
760	D₄	C₃×2₋¹⁺⁴	1	4	yes	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	4	2	no	—
773	C₂×C₄	—	4	4	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	2	no	—
779	C₂×C₄	—	8	4	no	—
780	C₂×C₄	—	8	4	no	—
781	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
782	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
783	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
784	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
785	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
786	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
787	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
788	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
789	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
790	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₈	—	2	4	no	—
794	C₂×C₃	—	2	2	no	—
795	C₂×C₃	—	4	4	no	—
796	C₂×C₃	—	8	1	no	—
797	C₂×C₃	#3486	1	1	yes	characteristic
798	C₂×C₃	C₂×#575	1	1	yes	characteristic
799	C₂×C₃	C₂×#577	1	1	yes	characteristic
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	4	no	—
803	C₂²	—	4	8	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	C₃×#577	1	2	yes	—
810	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	4	no	—
825	C₄	—	4	1	no	—
826	C₄	C₃×#575	1	2	yes	—
827	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
828	C₃	#61841	1	1	yes	characteristic, direct product factor, Sylow
829	C₂	—	2	2	no	—
830	C₂	—	4	4	no	—
831	C₂	—	8	1	no	—
832	C₂	C₃×#3486	1	1	yes	characteristic
833	C₂	C₂×C₃×#575	1	1	yes	characteristic
834	C₂	C₂×C₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#447	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3523	C₂	semidirect
2. C₂×C₃×#554	C₂	semidirect
3. C₃×#3388	C₂	semidirect
4. C₃×#3384	C₂	semidirect
5. C₃×#3381	C₂	semidirect
6. C₃×#3376	C₂	semidirect
7. C₃×#3372	C₂	semidirect
8. C₃×#3360	C₂	semidirect
9. C₃×#3238	C₂	semidirect
10. C₃×#3236	C₂	semidirect
11. C₃×#3232	C₂	semidirect
12. C₃×#3229	C₂	semidirect
14. C₃×#3110	C₂	semidirect
16. C₃×#3101	C₂	semidirect
17. C₃×#2984	C₂	semidirect
18. #61841	C₃	direct (N × H)
19. C₃×#557	C₂²	semidirect
20. C₃×#557	C₂²	semidirect
21. C₃×#557	C₂²	semidirect
22. C₃×#556	C₂²	semidirect
23. C₃×#556	C₂²	semidirect
33. C₃×D₄×Q₈	C₂²	semidirect
49. C₃×#501	C₂²	semidirect
50. C₃×#501	C₂²	semidirect
51. C₃×#499	C₂²	semidirect
52. C₃×#498	C₂²	semidirect
53. C₃×#491	C₂²	semidirect
54. C₃×#489	C₂²	semidirect
55. C₃×#488	C₂²	semidirect
56. C₃×#487	C₂²	semidirect
64. C₃×#479	C₂²	semidirect
65. C₃×#479	C₂²	semidirect
66. C₃×#479	C₂²	semidirect
69. C₃×#478	C₂²	semidirect
70. C₃×#477	C₂²	semidirect
72. C₃×#476	C₂²	semidirect
73. C₃×#475	C₂²	semidirect
82. C₃×#446	C₂²	semidirect
83. C₃×#446	C₂²	semidirect
84. C₃×C₈×Q₈	C₂²	semidirect
96. #3523	C₂×C₃	semidirect
97. C₂×#554	C₂×C₃	semidirect
98. #3388	C₂×C₃	semidirect
99. #3384	C₂×C₃	semidirect
100. #3381	C₂×C₃	semidirect
101. #3376	C₂×C₃	semidirect
102. #3372	C₂×C₃	semidirect
103. #3360	C₂×C₃	semidirect
104. #3238	C₂×C₃	semidirect
105. #3236	C₂×C₃	semidirect
106. #3232	C₂×C₃	semidirect
107. #3229	C₂×C₃	semidirect
109. #3110	C₂×C₃	semidirect
111. #3101	C₂×C₃	semidirect
112. #2984	C₂×C₃	semidirect
246. #557	C₂²×C₃	semidirect
247. #557	C₂²×C₃	semidirect
248. #557	C₂²×C₃	semidirect
249. #556	C₂²×C₃	semidirect
250. #556	C₂²×C₃	semidirect
260. D₄×Q₈	C₂²×C₃	semidirect
276. #501	C₂²×C₃	semidirect
277. #501	C₂²×C₃	semidirect
278. #499	C₂²×C₃	semidirect
279. #498	C₂²×C₃	semidirect
280. #491	C₂²×C₃	semidirect
281. #489	C₂²×C₃	semidirect
282. #488	C₂²×C₃	semidirect
283. #487	C₂²×C₃	semidirect
291. #479	C₂²×C₃	semidirect
292. #479	C₂²×C₃	semidirect
293. #479	C₂²×C₃	semidirect
296. #478	C₂²×C₃	semidirect
297. #477	C₂²×C₃	semidirect
299. #476	C₂²×C₃	semidirect
300. #475	C₂²×C₃	semidirect
309. #446	C₂²×C₃	semidirect
310. #446	C₂²×C₃	semidirect
311. C₈×Q₈	C₂²×C₃	semidirect
828. C₃	#61841	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×#3523	2
C₂×C₃×#554	2
C₃×#3388	2
C₃×#3384	2
C₃×#3381	2
C₃×#3376	2
C₃×#3372	2
C₃×#3360	2
C₃×#3238	2
C₃×#3236	2
C₃×#3232	2
C₃×#3229	2
C₃×#3114	2
C₃×#3110	2
C₃×#3105	2
C₃×#3101	2
C₃×#2984	2
#61841	3

Subgroups — C3×#61841 #10680448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61841 #10680448