Subgroups — C₃×D₃×#464 #11865664

Order 1152.

1056 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×D₃×#124	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#464	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5185	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5166	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5028	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4845	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4798	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×D₃×#102	C₂	1	1	yes	maximal, characteristic
15	C₃×#4767	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#464	—	3	1	no	maximal
17	D₃×#464	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
21	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
23	C₃²×#124	C₂²	1	1	yes	characteristic
24	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×#947	C₂²	1	1	yes	characteristic
26	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×#216	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#216	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×#215	C₂²	1	1	yes	characteristic
30	C₃×#936	C₂²	1	1	yes	characteristic
31	C₂×C₃×#214	C₂²	1	1	yes	characteristic
32	C₃×D₃×Q₁₆	—	2	4	no	—
33	C₃×D₃×SD₁₆	—	2	4	no	—
34	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×#204	C₂²	1	1	yes	characteristic
36	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
37	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
38	C₃×D₃×C₄⋊C₄	—	2	1	no	—
39	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×#887	—	2	1	no	—
41	C₃×#887	C₂²	1	1	yes	characteristic, complemented
42	C₃×#885	—	2	1	no	—
43	C₃×#885	—	2	1	no	—
44	C₃×D₃×C₂²⋊C₄	—	2	1	no	—
45	C₃×D₃×C₂²⋊C₄	—	2	1	no	—
46	C₃×#875	C₂²	1	1	yes	characteristic
47	C₃×C₄²×D₃	—	2	1	no	—
48	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
49	C₃×C₄×Dic₆	—	2	1	no	—
50	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
51	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₃²×#103	C₂²	1	1	yes	characteristic, complemented
53	C₃²×#102	C₂²	1	1	yes	characteristic
54	C₃×#835	C₂²	1	1	yes	characteristic, complemented
55	C₃×#832	C₂²	1	1	yes	characteristic
56	C₃×#821	C₂²	1	1	yes	characteristic
57	C₃×#816	C₂²	1	1	yes	characteristic, complemented
58	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₃×#810	C₂²	1	1	yes	characteristic, complemented
61	C₃×#809	C₂²	1	1	yes	characteristic
62	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₃×Q₁₆	—	3	1	no	—
64	C₂²×C₃×SD₁₆	—	3	1	no	—
65	C₂×C₃×#124	—	3	1	no	—
66	C₂×C₃×C₄×Q₈	—	3	1	no	—
67	C₂×D₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
68	C₂×D₃×SD₁₆	C₂×C₃	1	1	yes	characteristic
69	D₃×#124	C₂×C₃	1	1	yes	characteristic
70	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
71	C₃×#464	—	2	1	no	—
72	C₃×#464	—	3	1	no	—
73	C₃×#464	—	3	1	no	—
74	C₃×#464	—	3	1	no	—
75	C₃×#464	—	3	1	no	—
76	C₃×#464	—	3	1	no	—
77	C₃×#464	—	3	1	no	—
78	C₃×#464	—	3	1	no	—
79	C₃×#464	D₃	1	1	yes	characteristic, direct product factor
80	C₃×#464	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂×C₃×C₄⋊C₈	—	3	1	no	—
82	C₂×C₃×#103	—	3	1	no	—
83	C₂×C₃×#102	—	3	1	no	—
84	#5185	C₂×C₃	1	1	yes	characteristic, complemented
85	#5166	C₂×C₃	1	1	yes	characteristic, complemented
86	#5054	C₂×C₃	1	1	yes	characteristic, complemented
87	#5028	C₂×C₃	1	1	yes	characteristic, complemented
88	#4845	C₂×C₃	1	1	yes	characteristic, complemented
89	D₃×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
90	D₃×#103	C₂×C₃	1	1	yes	characteristic, complemented
91	#4798	C₂×C₃	1	1	yes	characteristic, complemented
92	D₃×#102	C₂×C₃	1	1	yes	characteristic
93	#4767	C₂×C₃	1	1	yes	characteristic, complemented
94	C₂³×C₃×D₃	—	2	1	no	—
95	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
96	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
97	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
98	C₂×C₃×#67	—	2	1	no	—
99	C₃×D₃×Q₈	—	2	2	no	—
100	C₃×D₃×Q₈	—	2	2	no	—
101	C₃×D₃×Q₈	—	2	2	no	—
102	C₃×D₃×Q₈	D₄	1	4	yes	—
103	C₃×D₃×D₄	—	2	2	no	—
104	C₃×D₃×D₄	—	2	2	no	—
105	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₄×D₃	—	2	1	no	—
107	C₂×C₃×C₄×D₃	—	2	1	no	—
108	C₂×C₃×C₄×D₃	—	2	1	no	—
109	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
112	C₂×C₃×Dic₆	—	2	1	no	—
113	C₂×C₃×Dic₆	—	2	1	no	—
114	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
115	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
116	C₃²×Q₁₆	—	2	2	no	—
117	C₃²×SD₁₆	—	2	2	no	—
118	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
119	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
120	C₃²×C₄⋊C₄	—	2	1	no	—
121	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₃²×C₂²⋊C₄	—	2	1	no	—
123	C₃²×C₂²⋊C₄	—	2	1	no	—
124	C₃²×C₄²	—	2	1	no	—
125	C₃²×C₄²	C₂³	1	1	yes	characteristic
126	C₃×#217	—	2	1	no	—
127	C₃×#217	—	2	1	no	—
128	C₃×#216	—	2	2	no	—
129	C₃×#216	—	2	2	no	—
130	C₃×#215	—	2	2	no	—
131	C₃×#214	—	2	2	no	—
132	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
133	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
134	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
135	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
136	C₃×C₄⋊Dic₃	—	2	1	no	—
137	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
138	C₃×Dic₃⋊C₄	—	2	1	no	—
139	C₃×Dic₃⋊C₄	—	2	1	no	—
140	C₃×Dic₃⋊C₄	—	2	1	no	—
141	C₃×C₄×Dic₃	—	2	1	no	—
142	C₃×C₄×Dic₃	—	2	1	no	—
143	C₃×C₄×Dic₃	—	2	1	no	—
144	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
145	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
146	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
147	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
148	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
149	C₃×Dic₁₂	—	2	2	no	—
150	C₃×#204	—	2	2	no	—
151	C₃×D₃×C₈	—	2	2	no	—
152	C₃×D₃×C₈	—	2	2	no	—
153	C₂×#464	—	3	1	no	Sylow
154	C₂²×C₃×Q₈	—	3	1	no	—
155	C₂²×C₃×Q₈	—	3	1	no	—
156	C₂²×C₃×D₄	—	3	1	no	—
157	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₃×Q₁₆	—	2	1	no	—
161	C₂×C₃×Q₁₆	—	3	1	no	—
162	C₂×C₃×Q₁₆	—	3	1	no	—
163	C₂×C₃×Q₁₆	—	3	1	no	—
164	C₂×C₃×Q₁₆	—	6	4	no	—
165	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
166	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂×C₃×SD₁₆	—	2	1	no	—
168	C₂×C₃×SD₁₆	—	3	1	no	—
169	C₂×C₃×SD₁₆	—	3	1	no	—
170	C₂×C₃×SD₁₆	—	3	1	no	—
171	C₂×C₃×SD₁₆	—	6	4	no	—
172	C₂×C₃×SD₁₆	C₂×D₃	1	1	yes	characteristic
173	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
174	C₂²×C₃×C₈	—	3	1	no	—
175	C₂²×C₃×C₈	—	3	1	no	—
176	C₃×#124	—	2	1	no	—
177	C₃×#124	—	3	1	no	—
178	C₃×#124	—	3	1	no	—
179	C₃×#124	—	3	1	no	—
180	C₃×#124	—	6	1	no	—
181	C₃×#124	—	6	1	no	—
182	C₃×#124	C₂×D₃	1	1	yes	characteristic
183	C₃×#124	C₂²×C₃	1	1	yes	characteristic
184	C₃×C₄×Q₈	—	2	1	no	—
185	C₃×C₄×Q₈	—	3	1	no	—
186	C₃×C₄×Q₈	—	3	1	no	—
187	C₃×C₄×Q₈	—	3	1	no	—
188	C₃×C₄×Q₈	—	6	1	no	—
189	C₃×C₄×Q₈	—	6	1	no	—
190	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
191	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₂×C₃×C₄⋊C₄	—	3	1	no	—
193	C₂×C₃×C₄⋊C₄	—	6	1	no	—
194	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
195	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
196	C₂×C₃×C₄²	—	3	1	no	—
197	C₂×C₃×C₄²	—	6	1	no	—
198	#947	C₂²×C₃	1	1	yes	characteristic
199	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
200	C₂×#216	C₂²×C₃	1	1	yes	characteristic, complemented
201	C₂×#216	C₂²×C₃	1	1	yes	characteristic, complemented
202	C₂×#215	C₂²×C₃	1	1	yes	characteristic
203	#936	C₂²×C₃	1	1	yes	characteristic
204	C₂×#214	C₂²×C₃	1	1	yes	characteristic
205	D₃×Q₁₆	—	2	4	no	—
206	D₃×SD₁₆	—	2	4	no	—
207	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₂×#204	C₂²×C₃	1	1	yes	characteristic
209	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
210	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
211	D₃×C₄⋊C₄	—	2	1	no	—
212	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
213	#887	—	2	1	no	—
214	#887	C₂²×C₃	1	1	yes	characteristic, complemented
215	#885	—	2	1	no	—
216	#885	—	2	1	no	—
217	D₃×C₂²⋊C₄	—	2	1	no	—
218	D₃×C₂²⋊C₄	—	2	1	no	—
219	#875	C₂²×C₃	1	1	yes	characteristic
220	C₄²×D₃	—	2	1	no	—
221	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
222	C₄×Dic₆	—	2	1	no	—
223	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
224	C₃×C₄⋊C₈	—	2	1	no	—
225	C₃×C₄⋊C₈	—	3	1	no	—
226	C₃×C₄⋊C₈	—	3	1	no	—
227	C₃×C₄⋊C₈	—	3	1	no	—
228	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
229	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
230	C₃×#103	—	2	1	no	—
231	C₃×#103	—	3	1	no	—
232	C₃×#103	—	3	1	no	—
233	C₃×#103	—	3	1	no	—
234	C₃×#103	C₂×D₃	1	1	yes	characteristic, complemented
235	C₃×#103	C₂²×C₃	1	1	yes	characteristic, complemented
236	C₃×#102	—	2	1	no	—
237	C₃×#102	—	3	1	no	—
238	C₃×#102	—	3	1	no	—
239	C₃×#102	—	3	1	no	—
240	C₃×#102	C₂×D₃	1	1	yes	characteristic
241	C₃×#102	C₂²×C₃	1	1	yes	characteristic
242	#835	C₂²×C₃	1	1	yes	characteristic, complemented
243	#832	C₂²×C₃	1	1	yes	characteristic
244	#821	C₂²×C₃	1	1	yes	characteristic
245	#816	C₂²×C₃	1	1	yes	characteristic, complemented
246	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
247	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
248	#810	C₂²×C₃	1	1	yes	characteristic, complemented
249	#809	C₂²×C₃	1	1	yes	characteristic
250	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
251	C₂³×C₃²	—	2	1	no	—
252	C₂²×C₃×D₃	—	2	1	no	—
253	C₂²×C₃×D₃	—	4	2	no	—
254	C₂²×C₃×D₃	—	4	2	no	—
255	C₂²×C₃×D₃	—	4	2	no	—
256	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
257	C₃²×Q₈	—	2	1	no	—
258	C₃²×Q₈	—	2	1	no	—
259	C₃²×Q₈	—	2	1	no	—
260	C₃²×Q₈	C₂×D₄	1	2	yes	—
261	C₃²×D₄	—	2	1	no	—
262	C₃²×D₄	—	2	1	no	—
263	C₂×C₃²×C₄	—	2	1	no	—
264	C₂×C₃²×C₄	—	2	1	no	—
265	C₂×C₃²×C₄	—	2	1	no	—
266	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
267	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
268	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
269	C₃×#67	—	4	2	no	—
270	C₂×C₃×Dic₃	—	2	1	no	—
271	C₂×C₃×Dic₃	—	2	1	no	—
272	C₂×C₃×Dic₃	—	2	1	no	—
273	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
274	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
275	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
276	C₃×D₁₂	—	2	1	no	—
277	C₃×D₁₂	—	2	1	no	—
278	C₃×C₄×D₃	—	2	4	no	—
279	C₃×C₄×D₃	—	2	2	no	—
280	C₃×C₄×D₃	—	2	2	no	—
281	C₃×C₄×D₃	—	4	2	no	—
282	C₃×C₄×D₃	—	4	2	no	—
283	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
284	C₃×C₄×D₃	#41	1	2	yes	—
285	C₃×Dic₆	—	2	1	no	—
286	C₃×Dic₆	—	2	4	no	—
287	C₃×Dic₆	—	2	1	no	—
288	C₃×Dic₆	—	2	1	no	—
289	C₃×Dic₆	—	4	2	no	—
290	C₃×Dic₆	C₂×D₄	1	2	yes	—
291	C₃²×C₈	—	2	1	no	—
292	C₃²×C₈	—	2	1	no	—
293	C₃×C₃⋊C₈	—	2	1	no	—
294	C₃×C₃⋊C₈	—	2	1	no	—
295	C₂²×Q₁₆	—	3	1	no	—
296	C₂²×SD₁₆	—	3	1	no	—
297	C₂×#124	—	3	1	no	—
298	C₂×C₄×Q₈	—	3	1	no	—
299	#464	—	3	1	no	—
300	#464	—	3	1	no	—
301	#464	—	3	1	no	—
302	#464	—	3	1	no	—
303	#464	—	3	1	no	—
304	#464	—	3	1	no	—
305	#464	—	3	1	no	—
306	#464	C₃×D₃	1	1	yes	characteristic, direct product factor
307	C₂×C₄⋊C₈	—	3	1	no	—
308	C₂×#103	—	3	1	no	—
309	C₂×#102	—	3	1	no	—
310	C₂⁴×C₃	—	6	1	no	—
311	C₂³×D₃	—	2	1	no	—
312	C₂×C₃×Q₈	—	2	1	no	—
313	C₂×C₃×Q₈	—	2	1	no	—
314	C₂×C₃×Q₈	—	3	4	no	—
315	C₂×C₃×Q₈	—	3	1	no	—
316	C₂×C₃×Q₈	—	3	1	no	—
317	C₂×C₃×Q₈	—	6	1	no	—
318	C₂×C₃×Q₈	—	6	1	no	—
319	C₂×C₃×Q₈	—	6	2	no	—
320	C₂×C₃×Q₈	—	6	2	no	—
321	C₂×C₃×Q₈	—	6	2	no	—
322	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
323	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
324	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
325	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
326	C₂×C₃×D₄	—	2	1	no	—
327	C₂×C₃×D₄	—	3	1	no	—
328	C₂×C₃×D₄	—	6	2	no	—
329	C₂×C₃×D₄	—	6	2	no	—
330	C₂×C₃×D₄	—	6	1	no	—
331	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
332	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
333	C₂²×C₃×C₄	—	3	1	no	—
334	C₂²×C₃×C₄	—	3	1	no	—
335	C₂²×C₃×C₄	—	3	1	no	—
336	C₂²×C₃×C₄	—	6	1	no	—
337	C₂²×C₃×C₄	—	6	1	no	—
338	C₂²×C₃×C₄	—	6	1	no	—
339	C₂×#67	—	2	1	no	—
340	D₃×Q₈	—	2	2	no	—
341	D₃×Q₈	—	2	2	no	—
342	D₃×Q₈	—	2	2	no	—
343	D₃×Q₈	C₃×D₄	1	4	yes	—
344	D₃×D₄	—	2	2	no	—
345	D₃×D₄	—	2	2	no	—
346	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
347	C₂×C₄×D₃	—	2	1	no	—
348	C₂×C₄×D₃	—	2	1	no	—
349	C₂×C₄×D₃	—	2	1	no	—
350	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
351	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
352	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
353	C₂×Dic₆	—	2	1	no	—
354	C₂×Dic₆	—	2	1	no	—
355	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
356	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
357	C₃×Q₁₆	—	2	2	no	—
358	C₃×Q₁₆	—	2	2	no	—
359	C₃×Q₁₆	—	4	2	no	—
360	C₃×Q₁₆	—	6	2	no	—
361	C₃×Q₁₆	—	6	2	no	—
362	C₃×Q₁₆	—	6	2	no	—
363	C₃×SD₁₆	—	2	2	no	—
364	C₃×SD₁₆	—	2	2	no	—
365	C₃×SD₁₆	—	4	2	no	—
366	C₃×SD₁₆	—	6	2	no	—
367	C₃×SD₁₆	—	6	2	no	—
368	C₃×SD₁₆	—	6	2	no	—
369	C₂×C₃×C₈	—	2	1	no	—
370	C₂×C₃×C₈	—	2	1	no	—
371	C₂×C₃×C₈	—	3	1	no	—
372	C₂×C₃×C₈	—	3	1	no	—
373	C₂×C₃×C₈	—	6	2	no	—
374	C₂×C₃×C₈	—	6	2	no	—
375	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
376	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
377	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
378	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
379	C₃×C₄⋊C₄	—	2	1	no	—
380	C₃×C₄⋊C₄	—	2	1	no	—
381	C₃×C₄⋊C₄	—	2	1	no	—
382	C₃×C₄⋊C₄	—	3	1	no	—
383	C₃×C₄⋊C₄	—	4	1	no	—
384	C₃×C₄⋊C₄	—	6	1	no	—
385	C₃×C₄⋊C₄	—	6	1	no	—
386	C₃×C₄⋊C₄	—	6	1	no	—
387	C₃×C₄⋊C₄	—	6	1	no	—
388	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
389	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
390	C₃×C₂²⋊C₄	—	2	1	no	—
391	C₃×C₂²⋊C₄	—	2	1	no	—
392	C₃×C₂²⋊C₄	—	2	1	no	—
393	C₃×C₂²⋊C₄	—	2	1	no	—
394	C₃×C₂²⋊C₄	—	4	1	no	—
395	C₃×C₂²⋊C₄	—	4	1	no	—
396	C₃×C₂²⋊C₄	—	6	1	no	—
397	C₃×C₂²⋊C₄	—	6	1	no	—
398	C₃×C₂²⋊C₄	—	6	1	no	—
399	C₃×C₂²⋊C₄	—	6	1	no	—
400	C₃×C₂²⋊C₄	—	6	1	no	—
401	C₃×C₂²⋊C₄	—	6	1	no	—
402	C₃×C₄²	—	2	1	no	—
403	C₃×C₄²	—	2	1	no	—
404	C₃×C₄²	—	2	1	no	—
405	C₃×C₄²	—	3	1	no	—
406	C₃×C₄²	—	3	1	no	—
407	C₃×C₄²	—	3	1	no	—
408	C₃×C₄²	—	4	1	no	—
409	C₃×C₄²	—	6	1	no	—
410	C₃×C₄²	—	6	1	no	—
411	C₃×C₄²	—	6	1	no	—
412	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
413	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
414	#217	—	2	1	no	—
415	#217	—	2	1	no	—
416	#216	—	2	2	no	—
417	#216	—	2	2	no	—
418	#215	—	2	2	no	—
419	#214	—	2	2	no	—
420	(C₂×D₃)⋊C₄	—	2	1	no	—
421	(C₂×D₃)⋊C₄	—	2	1	no	—
422	(C₂×D₃)⋊C₄	—	2	1	no	—
423	(C₂×D₃)⋊C₄	—	2	1	no	—
424	C₄⋊Dic₃	—	2	1	no	—
425	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
426	Dic₃⋊C₄	—	2	1	no	—
427	Dic₃⋊C₄	—	2	1	no	—
428	Dic₃⋊C₄	—	2	1	no	—
429	C₄×Dic₃	—	2	1	no	—
430	C₄×Dic₃	—	2	1	no	—
431	C₄×Dic₃	—	2	1	no	—
432	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
433	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
434	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
436	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
437	Dic₁₂	—	2	2	no	—
438	#204	—	2	2	no	—
439	D₃×C₈	—	2	2	no	—
440	D₃×C₈	—	2	2	no	—
441	C₂²×C₃²	—	4	1	no	—
442	C₂²×C₃²	—	4	1	no	—
443	C₂²×C₃²	—	4	1	no	—
444	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₃×D₃	—	4	1	no	—
446	C₂×C₃×D₃	—	4	1	no	—
447	C₂×C₃×D₃	—	4	1	no	—
448	C₂×C₃×D₃	—	8	4	no	—
449	C₂×C₃×D₃	#121	1	2	yes	—
450	C₂×C₃×D₃	#135	1	2	yes	—
451	C₂×C₃×D₃	#137	1	2	yes	—
452	C₃²×C₄	—	2	2	no	—
453	C₃²×C₄	—	2	1	no	—
454	C₃²×C₄	—	2	1	no	—
455	C₃²×C₄	—	4	1	no	—
456	C₃²×C₄	—	4	1	no	—
457	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
458	C₃²×C₄	C₂×#41	1	1	yes	characteristic
459	C₃×Dic₃	—	2	2	no	—
460	C₃×Dic₃	—	2	1	no	—
461	C₃×Dic₃	—	2	1	no	—
462	C₃×Dic₃	—	4	1	no	—
463	C₃×Dic₃	—	4	1	no	—
464	C₃×Dic₃	#121	1	2	yes	—
465	C₂²×Q₈	—	3	1	no	—
466	C₂²×Q₈	—	3	1	no	—
467	C₂²×D₄	—	3	1	no	—
468	C₂×Q₁₆	—	3	1	no	—
469	C₂×Q₁₆	—	3	1	no	—
470	C₂×Q₁₆	—	3	1	no	—
471	C₂×Q₁₆	—	6	4	no	—
472	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic, complemented
473	C₂×SD₁₆	—	3	1	no	—
474	C₂×SD₁₆	—	3	1	no	—
475	C₂×SD₁₆	—	3	1	no	—
476	C₂×SD₁₆	—	6	4	no	—
477	C₂×SD₁₆	C₂×C₃×D₃	1	1	yes	characteristic
478	C₂²×C₈	—	3	1	no	—
479	C₂²×C₈	—	3	1	no	—
480	#124	—	3	1	no	—
481	#124	—	3	1	no	—
482	#124	—	3	1	no	—
483	#124	—	6	1	no	—
484	#124	—	6	1	no	—
485	#124	C₂×C₃×D₃	1	1	yes	characteristic
486	C₄×Q₈	—	3	1	no	—
487	C₄×Q₈	—	3	1	no	—
488	C₄×Q₈	—	3	1	no	—
489	C₄×Q₈	—	6	1	no	—
490	C₄×Q₈	—	6	1	no	—
491	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
492	C₂×C₄⋊C₄	—	3	1	no	—
493	C₂×C₄⋊C₄	—	6	1	no	—
494	C₂×C₂²⋊C₄	—	6	1	no	—
495	C₂×C₂²⋊C₄	—	6	1	no	—
496	C₂×C₄²	—	3	1	no	—
497	C₂×C₄²	—	6	1	no	—
498	C₄⋊C₈	—	3	1	no	—
499	C₄⋊C₈	—	3	1	no	—
500	C₄⋊C₈	—	3	1	no	—
501	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
502	#103	—	3	1	no	—
503	#103	—	3	1	no	—
504	#103	—	3	1	no	—
505	#103	C₂×C₃×D₃	1	1	yes	characteristic, complemented
506	#102	—	3	1	no	—
507	#102	—	3	1	no	—
508	#102	—	3	1	no	—
509	#102	C₂×C₃×D₃	1	1	yes	characteristic
510	C₂³×C₃	—	2	1	no	—
511	C₂³×C₃	—	2	1	no	—
512	C₂³×C₃	—	3	1	no	—
513	C₂³×C₃	—	4	1	no	—
514	C₂³×C₃	—	6	1	no	—
515	C₂³×C₃	—	12	2	no	—
516	C₂³×C₃	—	12	2	no	—
517	C₂³×C₃	—	12	2	no	—
518	C₂²×D₃	—	2	1	no	—
519	C₂²×D₃	—	4	2	no	—
520	C₂²×D₃	—	4	2	no	—
521	C₂²×D₃	—	4	2	no	—
522	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
523	C₃×Q₈	—	2	1	no	—
524	C₃×Q₈	—	2	1	no	—
525	C₃×Q₈	—	2	1	no	—
526	C₃×Q₈	—	2	1	no	—
527	C₃×Q₈	—	2	1	no	—
528	C₃×Q₈	—	2	1	no	—
529	C₃×Q₈	—	2	2	no	—
530	C₃×Q₈	—	3	2	no	—
531	C₃×Q₈	—	4	1	no	—
532	C₃×Q₈	—	4	1	no	—
533	C₃×Q₈	—	4	1	no	—
534	C₃×Q₈	—	6	4	no	—
535	C₃×Q₈	—	6	1	no	—
536	C₃×Q₈	—	6	1	no	—
537	C₃×Q₈	—	6	1	no	—
538	C₃×Q₈	—	12	2	no	—
539	C₃×Q₈	D₃×D₄	1	2	yes	—
540	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
541	C₃×D₄	—	2	1	no	—
542	C₃×D₄	—	2	1	no	—
543	C₃×D₄	—	2	1	no	—
544	C₃×D₄	—	2	1	no	—
545	C₃×D₄	—	4	1	no	—
546	C₃×D₄	—	4	1	no	—
547	C₃×D₄	—	6	1	no	—
548	C₃×D₄	—	6	1	no	—
549	C₃×D₄	—	12	2	no	—
550	C₂×C₃×C₄	—	2	1	no	—
551	C₂×C₃×C₄	—	2	1	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	1	no	—
555	C₂×C₃×C₄	—	2	1	no	—
556	C₂×C₃×C₄	—	2	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	3	1	no	—
560	C₂×C₃×C₄	—	3	2	no	—
561	C₂×C₃×C₄	—	3	2	no	—
562	C₂×C₃×C₄	—	3	1	no	—
563	C₂×C₃×C₄	—	3	1	no	—
564	C₂×C₃×C₄	—	4	1	no	—
565	C₂×C₃×C₄	—	4	1	no	—
566	C₂×C₃×C₄	—	4	1	no	—
567	C₂×C₃×C₄	—	6	2	no	—
568	C₂×C₃×C₄	—	6	2	no	—
569	C₂×C₃×C₄	—	6	4	no	—
570	C₂×C₃×C₄	—	6	1	no	—
571	C₂×C₃×C₄	—	6	1	no	—
572	C₂×C₃×C₄	—	6	1	no	—
573	C₂×C₃×C₄	—	12	2	no	—
574	C₂×C₃×C₄	—	12	2	no	—
575	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
576	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
577	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
579	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
580	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
581	#67	—	4	2	no	—
582	C₂×Dic₃	—	2	1	no	—
583	C₂×Dic₃	—	2	1	no	—
584	C₂×Dic₃	—	2	1	no	—
585	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
586	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
587	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
588	D₁₂	—	2	1	no	—
589	D₁₂	—	2	1	no	—
590	C₄×D₃	—	2	4	no	—
591	C₄×D₃	—	2	2	no	—
592	C₄×D₃	—	2	2	no	—
593	C₄×D₃	—	4	2	no	—
594	C₄×D₃	—	4	2	no	—
595	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
596	C₄×D₃	C₃×#41	1	2	yes	—
597	Dic₆	—	2	1	no	—
598	Dic₆	—	2	4	no	—
599	Dic₆	—	2	1	no	—
600	Dic₆	—	2	1	no	—
601	Dic₆	—	4	2	no	—
602	Dic₆	C₂×C₃×D₄	1	2	yes	—
603	C₃×C₈	—	2	1	no	—
604	C₃×C₈	—	2	1	no	—
605	C₃×C₈	—	2	1	no	—
606	C₃×C₈	—	2	1	no	—
607	C₃×C₈	—	4	1	no	—
608	C₃×C₈	—	4	1	no	—
609	C₃×C₈	—	6	1	no	—
610	C₃×C₈	—	6	1	no	—
611	C₃⋊C₈	—	2	1	no	—
612	C₃⋊C₈	—	2	1	no	—
613	C₂×C₃²	—	8	1	no	—
614	C₂×C₃²	C₂×#121	1	1	yes	characteristic
615	C₂×C₃²	C₂×#135	1	1	yes	characteristic
616	C₂×C₃²	C₂×#137	1	1	yes	characteristic
617	C₃×D₃	—	8	1	no	—
618	C₃×D₃	#464	1	4	yes	direct product factor
619	C₂⁴	—	6	1	no	—
620	C₂×Q₈	—	3	4	no	—
621	C₂×Q₈	—	3	1	no	—
622	C₂×Q₈	—	3	1	no	—
623	C₂×Q₈	—	6	1	no	—
624	C₂×Q₈	—	6	1	no	—
625	C₂×Q₈	—	6	2	no	—
626	C₂×Q₈	—	6	2	no	—
627	C₂×Q₈	—	6	2	no	—
628	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
629	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
630	C₂×D₄	—	3	1	no	—
631	C₂×D₄	—	6	2	no	—
632	C₂×D₄	—	6	2	no	—
633	C₂×D₄	—	6	1	no	—
634	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
635	C₂²×C₄	—	3	1	no	—
636	C₂²×C₄	—	3	1	no	—
637	C₂²×C₄	—	3	1	no	—
638	C₂²×C₄	—	6	1	no	—
639	C₂²×C₄	—	6	1	no	—
640	C₂²×C₄	—	6	1	no	—
641	Q₁₆	—	2	2	no	—
642	Q₁₆	—	6	2	no	—
643	Q₁₆	—	6	2	no	—
644	Q₁₆	—	6	2	no	—
645	SD₁₆	—	2	2	no	—
646	SD₁₆	—	6	2	no	—
647	SD₁₆	—	6	2	no	—
648	SD₁₆	—	6	2	no	—
649	C₂×C₈	—	3	1	no	—
650	C₂×C₈	—	3	1	no	—
651	C₂×C₈	—	6	2	no	—
652	C₂×C₈	—	6	2	no	—
653	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
654	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	3	1	no	—
657	C₄⋊C₄	—	6	1	no	—
658	C₄⋊C₄	—	6	1	no	—
659	C₄⋊C₄	—	6	1	no	—
660	C₄⋊C₄	—	6	1	no	—
661	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
662	C₂²⋊C₄	—	2	1	no	—
663	C₂²⋊C₄	—	2	1	no	—
664	C₂²⋊C₄	—	6	1	no	—
665	C₂²⋊C₄	—	6	1	no	—
666	C₂²⋊C₄	—	6	1	no	—
667	C₂²⋊C₄	—	6	1	no	—
668	C₂²⋊C₄	—	6	1	no	—
669	C₂²⋊C₄	—	6	1	no	—
670	C₄²	—	2	1	no	—
671	C₄²	—	3	1	no	—
672	C₄²	—	3	1	no	—
673	C₄²	—	3	1	no	—
674	C₄²	—	6	1	no	—
675	C₄²	—	6	1	no	—
676	C₄²	—	6	1	no	—
677	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
678	C₂²×C₃	—	2	1	no	—
679	C₂²×C₃	—	3	2	no	—
680	C₂²×C₃	—	3	2	no	—
681	C₂²×C₃	—	3	2	no	—
682	C₂²×C₃	—	4	1	no	—
683	C₂²×C₃	—	4	1	no	—
684	C₂²×C₃	—	4	1	no	—
685	C₂²×C₃	—	4	1	no	—
686	C₂²×C₃	—	4	1	no	—
687	C₂²×C₃	—	4	1	no	—
688	C₂²×C₃	—	8	1	no	—
689	C₂²×C₃	—	8	1	no	—
690	C₂²×C₃	—	8	1	no	—
691	C₂²×C₃	—	12	1	no	—
692	C₂²×C₃	—	12	1	no	—
693	C₂²×C₃	—	12	1	no	—
694	C₂²×C₃	—	24	4	no	—
695	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
696	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
697	C₂×D₃	—	4	1	no	—
698	C₂×D₃	—	4	1	no	—
699	C₂×D₃	—	4	1	no	—
700	C₂×D₃	—	8	4	no	—
701	C₂×D₃	C₃×#121	1	2	yes	—
702	C₂×D₃	C₃×#135	1	2	yes	—
703	C₂×D₃	C₃×#137	1	2	yes	—
704	C₃×C₄	—	2	1	no	—
705	C₃×C₄	—	2	1	no	—
706	C₃×C₄	—	2	1	no	—
707	C₃×C₄	—	2	1	no	—
708	C₃×C₄	—	2	2	no	—
709	C₃×C₄	—	2	2	no	—
710	C₃×C₄	—	2	1	no	—
711	C₃×C₄	—	2	1	no	—
712	C₃×C₄	—	3	2	no	—
713	C₃×C₄	—	4	1	no	—
714	C₃×C₄	—	4	1	no	—
715	C₃×C₄	—	4	2	no	—
716	C₃×C₄	—	4	1	no	—
717	C₃×C₄	—	4	1	no	—
718	C₃×C₄	—	4	1	no	—
719	C₃×C₄	—	4	1	no	—
720	C₃×C₄	—	6	1	no	—
721	C₃×C₄	—	6	1	no	—
722	C₃×C₄	—	6	2	no	—
723	C₃×C₄	—	8	1	no	—
724	C₃×C₄	—	8	1	no	—
725	C₃×C₄	—	12	1	no	—
726	C₃×C₄	—	12	1	no	—
727	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
728	C₃×C₄	D₃×#41	1	1	yes	characteristic
729	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
730	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
731	Dic₃	—	2	1	no	—
732	Dic₃	—	2	1	no	—
733	Dic₃	—	2	2	no	—
734	Dic₃	—	4	1	no	—
735	Dic₃	—	4	1	no	—
736	Dic₃	C₃×#121	1	2	yes	—
737	C₃²	C₂×#464	1	1	yes	characteristic, complemented, Sylow
738	C₂³	—	2	1	no	—
739	C₂³	—	3	1	no	—
740	C₂³	—	6	1	no	—
741	C₂³	—	12	2	no	—
742	C₂³	—	12	2	no	—
743	C₂³	—	12	2	no	—
744	Q₈	—	2	1	no	—
745	Q₈	—	2	1	no	—
746	Q₈	—	2	1	no	—
747	Q₈	—	3	2	no	—
748	Q₈	—	6	4	no	—
749	Q₈	—	6	1	no	—
750	Q₈	—	6	1	no	—
751	Q₈	—	6	1	no	—
752	Q₈	—	12	2	no	—
753	Q₈	C₃×D₃×D₄	1	2	yes	—
754	D₄	—	2	1	no	—
755	D₄	—	2	1	no	—
756	D₄	—	6	1	no	—
757	D₄	—	6	1	no	—
758	D₄	—	12	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	3	1	no	—
763	C₂×C₄	—	3	2	no	—
764	C₂×C₄	—	3	2	no	—
765	C₂×C₄	—	3	1	no	—
766	C₂×C₄	—	3	1	no	—
767	C₂×C₄	—	6	2	no	—
768	C₂×C₄	—	6	2	no	—
769	C₂×C₄	—	6	4	no	—
770	C₂×C₄	—	6	1	no	—
771	C₂×C₄	—	6	1	no	—
772	C₂×C₄	—	6	1	no	—
773	C₂×C₄	—	12	2	no	—
774	C₂×C₄	—	12	2	no	—
775	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
776	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
777	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
778	C₈	—	2	1	no	—
779	C₈	—	2	1	no	—
780	C₈	—	6	1	no	—
781	C₈	—	6	1	no	—
782	C₂×C₃	—	2	1	no	—
783	C₂×C₃	—	2	1	no	—
784	C₂×C₃	—	2	1	no	—
785	C₂×C₃	—	3	4	no	—
786	C₂×C₃	—	8	1	no	—
787	C₂×C₃	—	8	1	no	—
788	C₂×C₃	—	16	1	no	—
789	C₂×C₃	—	24	1	no	—
790	C₂×C₃	D₃×#121	1	1	yes	characteristic
791	C₂×C₃	D₃×#135	1	1	yes	characteristic
792	C₂×C₃	D₃×#137	1	1	yes	characteristic
793	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
794	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
795	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
796	D₃	—	8	1	no	—
797	D₃	C₃×#464	1	4	yes	direct product factor
798	C₂²	—	3	2	no	—
799	C₂²	—	3	2	no	—
800	C₂²	—	3	2	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	12	1	no	—
805	C₂²	—	12	1	no	—
806	C₂²	—	12	1	no	—
807	C₂²	—	24	4	no	—
808	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	2	no	—
812	C₄	—	3	2	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	1	no	—
815	C₄	—	6	1	no	—
816	C₄	—	6	1	no	—
817	C₄	—	6	2	no	—
818	C₄	—	12	1	no	—
819	C₄	—	12	1	no	—
820	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
821	C₄	C₃×D₃×#41	1	1	yes	characteristic
822	C₃	—	2	1	no	—
823	C₃	D₃×#464	1	1	yes	characteristic, direct product factor
824	C₃	C₂×C₃×#464	1	1	yes	characteristic, complemented
825	C₂	—	3	4	no	—
826	C₂	—	8	1	no	—
827	C₂	—	24	1	no	—
828	C₂	C₃×D₃×#121	1	1	yes	characteristic
829	C₂	C₃×D₃×#135	1	1	yes	characteristic
830	C₂	C₃×D₃×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#464	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×D₃×D₄	C₂²
hypercenter	C₃×#464	D₃
hypocenter	C₃	C₂×C₃×#464
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#464

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×Q₁₆	C₂	semidirect
4. C₃×C₄×D₃×Q₈	C₂	semidirect
5. C₃²×#464	C₂	semidirect
6. C₃×#5185	C₂	semidirect
7. C₃×#5166	C₂	semidirect
8. C₃×#5054	C₂	semidirect
9. C₃×#5028	C₂	semidirect
10. C₃×#4845	C₂	semidirect
11. C₃×D₃×C₄⋊C₈	C₂	semidirect
12. C₃×D₃×#103	C₂	semidirect
13. C₃×#4798	C₂	semidirect
15. C₃×#4767	C₂	semidirect
17. D₃×#464	C₃	direct (N × H)
21. C₂×C₃²×Q₁₆	C₂²	semidirect
24. C₃²×C₄×Q₈	C₂²	semidirect
26. C₃×Q₈×Dic₃	C₂²	semidirect
27. C₂×C₃×#216	C₂²	semidirect
28. C₂×C₃×#216	C₂²	semidirect
34. C₂×C₃×Dic₁₂	C₂²	semidirect
41. C₃×#887	C₂²	semidirect
50. C₃×C₄×Dic₆	C₂²	semidirect
51. C₃²×C₄⋊C₈	C₂²	semidirect
52. C₃²×#103	C₂²	semidirect
54. C₃×#835	C₂²	semidirect
57. C₃×#816	C₂²	semidirect
58. C₃×Dic₃⋊C₈	C₂²	semidirect
59. C₃×Dic₃⋊C₈	C₂²	semidirect
60. C₃×#810	C₂²	semidirect
62. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
67. C₂×D₃×Q₁₆	C₂×C₃	semidirect
70. C₄×D₃×Q₈	C₂×C₃	semidirect
79. C₃×#464	D₃	direct (N × H)
80. C₃×#464	C₂×C₃	semidirect
84. #5185	C₂×C₃	semidirect
85. #5166	C₂×C₃	semidirect
86. #5054	C₂×C₃	semidirect
87. #5028	C₂×C₃	semidirect
88. #4845	C₂×C₃	semidirect
89. D₃×C₄⋊C₈	C₂×C₃	semidirect
90. D₃×#103	C₂×C₃	semidirect
91. #4798	C₂×C₃	semidirect
93. #4767	C₂×C₃	semidirect
165. C₂×C₃×Q₁₆	C₂×D₃	semidirect
166. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
190. C₃×C₄×Q₈	C₂×D₃	semidirect
191. C₃×C₄×Q₈	C₂²×C₃	semidirect
199. Q₈×Dic₃	C₂²×C₃	semidirect
200. C₂×#216	C₂²×C₃	semidirect
201. C₂×#216	C₂²×C₃	semidirect
207. C₂×Dic₁₂	C₂²×C₃	semidirect
214. #887	C₂²×C₃	semidirect
223. C₄×Dic₆	C₂²×C₃	semidirect
228. C₃×C₄⋊C₈	C₂×D₃	semidirect
229. C₃×C₄⋊C₈	C₂²×C₃	semidirect
234. C₃×#103	C₂×D₃	semidirect
235. C₃×#103	C₂²×C₃	semidirect
242. #835	C₂²×C₃	semidirect
245. #816	C₂²×C₃	semidirect
246. Dic₃⋊C₈	C₂²×C₃	semidirect
247. Dic₃⋊C₈	C₂²×C₃	semidirect
248. #810	C₂²×C₃	semidirect
250. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
306. #464	C₃×D₃	direct (N × H)
472. C₂×Q₁₆	C₂×C₃×D₃	semidirect
491. C₄×Q₈	C₂×C₃×D₃	semidirect
501. C₄⋊C₈	C₂×C₃×D₃	semidirect
505. #103	C₂×C₃×D₃	semidirect
618. C₃×D₃	#464	direct (N × H)
737. C₃²	C₂×#464	semidirect
797. D₃	C₃×#464	direct (N × H)
823. C₃	D₃×#464	direct (N × H)
824. C₃	C₂×C₃×#464	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×Q₁₆	2
C₂×C₃×D₃×SD₁₆	2
C₃×D₃×#124	2
C₃×C₄×D₃×Q₈	2
C₃²×#464	2
C₃×#5185	2
C₃×#5166	2
C₃×#5054	2
C₃×#5028	2
C₃×#4845	2
C₃×D₃×C₄⋊C₈	2
C₃×D₃×#103	2
C₃×#4798	2
C₃×D₃×#102	2
C₃×#4767	2
C₂×C₃×#464	3
D₃×#464	3

Subgroups — C3×D3×#464 #11865664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#464 #11865664