Subgroups — C₃×#86244 #11906066

Order 1152.

3235 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1010	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#1009	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#532	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5825	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5724	C₂	1	2	yes	maximal, complemented
7	C₃×#5715	C₂	1	2	yes	maximal, complemented
8	C₃×D₃×#124	C₂	1	2	yes	maximal, complemented
9	C₃×#5668	C₂	1	2	yes	maximal, complemented
10	C₃×#5610	C₂	1	8	yes	maximal, complemented
11	C₃×#5552	C₂	1	4	yes	maximal, complemented
12	C₃×#5550	C₂	1	4	yes	maximal, complemented
13	C₂×C₃×#875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3500	—	3	1	no	maximal
16	#86244	C₃	1	1	yes	maximal, characteristic, direct product factor
17	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃²×#41	C₂²	1	1	yes	characteristic, complemented
19	C₃×#1010	—	2	8	no	—
20	C₃×#1009	—	2	8	no	—
21	C₂×C₃×#239	C₂²	1	2	yes	—
22	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	complemented
23	C₂×C₃×#237	C₂²	1	4	yes	complemented
24	C₂×C₃×#237	C₂²	1	2	yes	complemented
25	C₂×C₃×D₃×D₄	C₂²	1	4	yes	—
26	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
27	C₂×C₃×#235	C₂²	1	2	yes	—
28	C₂×C₃×#235	C₂²	1	1	yes	characteristic
29	C₂×C₃×#235	C₂²	1	2	yes	complemented
30	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
31	C₂²×C₃×D₁₂	C₂²	1	1	yes	characteristic
32	C₂²×C₃×Dic₆	C₂²	1	2	yes	complemented
33	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
34	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃²×#127	C₂²	1	1	yes	characteristic, complemented
36	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
37	C₃²×#124	C₂²	1	1	yes	characteristic, complemented
38	C₃²×#121	C₂²	1	4	yes	complemented
39	C₃²×C₄×D₄	C₂²	1	4	yes	complemented
40	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic, complemented
41	C₃×#947	C₂²	1	2	yes	complemented
42	C₃×#944	C₂²	1	2	yes	complemented
43	C₃×#940	C₂²	1	2	yes	complemented
44	C₃×#939	C₂²	1	8	yes	complemented
45	C₃×#937	C₂²	1	8	yes	complemented
46	C₃×#937	C₂²	1	4	yes	complemented
47	C₃×#936	C₂²	1	2	yes	complemented
48	C₃×#935	C₂²	1	4	yes	complemented
49	C₃×#930	C₂²	1	4	yes	complemented
50	C₃×C₄×#67	C₂²	1	4	yes	complemented
51	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
52	C₃×#926	C₂²	1	1	yes	characteristic, complemented
53	C₃×#924	C₂²	1	4	yes	complemented
54	C₃×#896	C₂²	1	8	yes	complemented
55	C₃×#894	C₂²	1	8	yes	complemented
56	C₃×#885	C₂²	1	8	yes	complemented
57	C₃×#884	C₂²	1	8	yes	complemented
58	C₃×#67⋊C₄	C₂²	1	8	yes	complemented
59	C₃×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
60	C₃×#875	C₂²	1	4	yes	complemented
61	C₃×#875	C₂²	1	2	yes	complemented
62	C₃×#875	C₂²	1	2	yes	complemented
63	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
64	C₃×#872	C₂²	1	2	yes	complemented
65	C₃×C₄²×D₃	C₂²	1	2	yes	complemented
66	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
67	C₂×C₃×2₋¹⁺⁴	—	3	1	no	—
68	C₂×C₃×H(5,𝔽₂)	—	3	1	no	—
69	C₂×#1010	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂×#1009	C₂×C₃	1	1	yes	characteristic, complemented
71	C₃×#548	—	3	4	no	—
72	C₃×#546	—	3	8	no	—
73	C₃×#546	—	3	4	no	—
74	C₃×#536	—	3	1	no	—
75	C₃×#536	—	3	2	no	—
76	C₃×#535	—	3	1	no	—
77	C₃×#535	—	3	2	no	—
78	C₃×#532	—	2	1	no	—
79	C₃×#532	—	3	2	no	—
80	C₃×#532	D₃	1	1	yes	characteristic, complemented
81	C₃×#532	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×C₃×#124	—	3	2	no	—
83	C₂×C₃×#124	—	3	1	no	—
84	C₃×C₄×#41	—	3	1	no	—
85	#5830	C₂×C₃	1	1	yes	characteristic, complemented
86	#5825	C₂×C₃	1	1	yes	characteristic, complemented
87	#5724	C₂×C₃	1	2	yes	complemented
88	#5715	C₂×C₃	1	2	yes	complemented
89	D₃×#124	C₂×C₃	1	2	yes	complemented
90	#5668	C₂×C₃	1	2	yes	complemented
91	#5610	C₂×C₃	1	8	yes	complemented
92	#5552	C₂×C₃	1	4	yes	complemented
93	#5550	C₂×C₃	1	4	yes	complemented
94	C₂×#875	C₂×C₃	1	1	yes	characteristic, complemented
95	C₄×#235	C₂×C₃	1	1	yes	characteristic, complemented
96	C₂³×C₃×D₃	C₂³	1	4	yes	—
97	C₂³×C₃×D₃	C₂³	1	2	yes	—
98	C₃²×#41	—	2	4	no	—
99	C₃²×#41	—	2	4	no	—
100	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
101	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
102	C₂×C₃²×D₄	C₂³	1	2	yes	—
103	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
104	C₂×C₃²×D₄	C₂³	1	2	yes	—
105	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
106	C₂×C₃²×D₄	C₂³	1	4	yes	—
107	C₂²×C₃²×C₄	C₂³	1	2	yes	—
108	C₂²×C₃²×C₄	C₂³	1	2	yes	—
109	C₂²×C₃²×C₄	C₂³	1	2	yes	—
110	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
111	C₂×C₃×#67	C₂³	1	4	yes	—
112	C₂×C₃×#67	C₂³	1	4	yes	—
113	C₂×C₃×#67	C₂³	1	8	yes	—
114	C₂×C₃×#67	C₂³	1	2	yes	—
115	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
116	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
117	C₃×#239	—	2	8	no	—
118	C₃×D₃×Q₈	—	2	8	no	—
119	C₃×#237	—	2	16	no	—
120	C₃×#237	—	2	8	no	—
121	C₃×D₃×D₄	—	2	16	no	—
122	C₃×D₃×D₄	—	2	8	no	—
123	C₃×#235	—	2	8	no	—
124	C₃×#235	—	2	8	no	—
125	C₃×#235	D₄	1	8	yes	complemented
126	C₂×C₃×D₁₂	—	2	4	no	—
127	C₂×C₃×D₁₂	—	2	8	no	—
128	C₂×C₃×D₁₂	C₂³	1	4	yes	—
129	C₂×C₃×D₁₂	C₂³	1	2	yes	—
130	C₂×C₃×D₁₂	C₂³	1	2	yes	—
131	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
133	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
134	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
135	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
136	C₂×C₃×Dic₆	—	2	4	no	—
137	C₂×C₃×Dic₆	—	2	8	no	—
138	C₂×C₃×Dic₆	C₂³	1	4	yes	—
139	C₂×C₃×Dic₆	C₂³	1	2	yes	—
140	C₂×C₃×Dic₆	C₂³	1	2	yes	—
141	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
142	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
143	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
144	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₃²×C₄²	C₂³	1	2	yes	—
146	C₃²×C₄²	C₂³	1	1	yes	characteristic
147	C₃²×C₄²	C₂³	1	1	yes	characteristic
148	C₃×#217	C₂³	1	8	yes	—
149	C₃×#217	C₂³	1	2	yes	—
150	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
151	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
152	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
153	C₃×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
154	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
155	C₃×Dic₃⋊C₄	C₂³	1	8	yes	—
156	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
157	C₃×C₄×Dic₃	C₂³	1	4	yes	—
158	C₃×C₄×Dic₃	C₂³	1	2	yes	—
159	#3500	—	3	1	no	Sylow
160	C₃×2₋¹⁺⁴	—	6	8	no	—
161	C₃×H(5,𝔽₂)	—	6	8	no	—
162	C₂×C₃×#41	—	2	1	no	—
163	C₂×C₃×#41	—	2	1	no	—
164	C₂×C₃×#41	—	3	2	no	—
165	C₂×C₃×#41	—	3	2	no	—
166	C₂×C₃×#41	—	3	4	no	—
167	C₂×C₃×#41	—	3	1	no	—
168	C₂×C₃×#41	—	3	2	no	—
169	C₂×C₃×#41	—	3	2	no	—
170	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
171	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic, complemented
172	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₂²×C₃×Q₈	—	3	2	no	—
175	C₂²×C₃×Q₈	—	3	1	no	—
176	C₂²×C₃×Q₈	—	3	2	no	—
177	C₂²×C₃×D₄	—	3	2	no	—
178	C₂²×C₃×D₄	—	3	4	no	—
179	C₂²×C₃×D₄	—	3	1	no	—
180	C₂²×C₃×D₄	—	3	2	no	—
181	#1010	—	2	8	no	—
182	#1009	—	2	8	no	—
183	C₂×#239	C₂²×C₃	1	2	yes	—
184	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	complemented
185	C₂×#237	C₂²×C₃	1	2	yes	complemented
186	C₂×#237	C₂²×C₃	1	4	yes	complemented
187	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
188	C₂×D₃×D₄	C₂²×C₃	1	4	yes	—
189	C₂×#235	C₂²×C₃	1	2	yes	—
190	C₂×#235	C₂²×C₃	1	1	yes	characteristic
191	C₂×#235	C₂²×C₃	1	2	yes	complemented
192	C₂²×D₁₂	C₂²×C₃	1	1	yes	characteristic
193	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
194	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₂²×Dic₆	C₂²×C₃	1	2	yes	complemented
196	C₃×C₄⋊Q₈	—	2	1	no	—
197	C₃×C₄⋊Q₈	—	3	2	no	—
198	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
199	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
200	C₃×#127	—	2	1	no	—
201	C₃×#127	—	3	2	no	—
202	C₃×#127	C₂×D₃	1	1	yes	characteristic, complemented
203	C₃×#127	C₂²×C₃	1	1	yes	characteristic, complemented
204	C₃×#124	—	2	1	no	—
205	C₃×#124	—	2	1	no	—
206	C₃×#124	—	3	2	no	—
207	C₃×#124	—	3	2	no	—
208	C₃×#124	—	3	8	no	—
209	C₃×#124	—	3	2	no	—
210	C₃×#124	—	3	2	no	—
211	C₃×#124	—	3	4	no	—
212	C₃×#124	C₂×D₃	1	1	yes	characteristic, complemented
213	C₃×#124	C₂×D₃	1	1	yes	characteristic, complemented
214	C₃×#124	C₂²×C₃	1	1	yes	characteristic, complemented
215	C₃×#124	C₂²×C₃	1	1	yes	characteristic, complemented
216	C₃×#123	—	3	4	no	—
217	C₃×#123	—	3	8	no	—
218	C₃×C₂²⋊Q₈	—	3	4	no	—
219	C₃×C₂²⋊Q₈	—	3	8	no	—
220	C₃×#121	—	2	4	no	—
221	C₃×#121	—	3	8	no	—
222	C₃×#121	—	3	4	no	—
223	C₃×#121	—	3	8	no	—
224	C₃×#121	C₂×D₃	1	4	yes	complemented
225	C₃×#121	C₂²×C₃	1	4	yes	complemented
226	C₃×#120	—	3	8	no	—
227	C₃×#120	—	3	4	no	—
228	C₃×C₄×Q₈	—	3	2	no	—
229	C₃×C₄×D₄	—	2	4	no	—
230	C₃×C₄×D₄	—	3	4	no	—
231	C₃×C₄×D₄	—	3	8	no	—
232	C₃×C₄×D₄	—	3	2	no	—
233	C₃×C₄×D₄	C₂×D₃	1	4	yes	complemented
234	C₃×C₄×D₄	C₂²×C₃	1	4	yes	complemented
235	C₃×#117	—	3	1	no	—
236	C₃×#117	—	3	2	no	—
237	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
238	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
239	C₂×C₃×C₄²	—	2	1	no	—
240	C₂×C₃×C₄²	—	3	2	no	—
241	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
242	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
243	#947	C₂²×C₃	1	2	yes	complemented
244	#944	C₂²×C₃	1	2	yes	complemented
245	#940	C₂²×C₃	1	2	yes	complemented
246	#939	C₂²×C₃	1	8	yes	complemented
247	#937	C₂²×C₃	1	8	yes	complemented
248	#937	C₂²×C₃	1	4	yes	complemented
249	#936	C₂²×C₃	1	2	yes	complemented
250	#935	C₂²×C₃	1	4	yes	complemented
251	#930	C₂²×C₃	1	4	yes	complemented
252	C₄×#67	C₂²×C₃	1	4	yes	complemented
253	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	complemented
254	#926	C₂²×C₃	1	1	yes	characteristic, complemented
255	#924	C₂²×C₃	1	4	yes	complemented
256	#896	C₂²×C₃	1	8	yes	complemented
257	#894	C₂²×C₃	1	8	yes	complemented
258	#885	C₂²×C₃	1	8	yes	complemented
259	#884	C₂²×C₃	1	8	yes	complemented
260	#67⋊C₄	C₂²×C₃	1	8	yes	complemented
261	D₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
262	#875	C₂²×C₃	1	2	yes	complemented
263	#875	C₂²×C₃	1	2	yes	complemented
264	#875	C₂²×C₃	1	4	yes	complemented
265	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
266	#872	C₂²×C₃	1	2	yes	complemented
267	C₄²×D₃	C₂²×C₃	1	2	yes	complemented
268	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
269	C₂³×C₃²	C₂⁴	1	2	yes	—
270	C₂³×C₃²	C₂⁴	1	2	yes	—
271	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
272	C₂²×C₃×D₃	—	2	4	no	—
273	C₂²×C₃×D₃	—	2	8	no	—
274	C₂²×C₃×D₃	—	4	8	no	—
275	C₂²×C₃×D₃	—	4	4	no	—
276	C₂²×C₃×D₃	C₂⁴	1	4	yes	—
277	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
278	C₃²×Q₈	—	2	2	no	—
279	C₃²×Q₈	—	2	2	no	—
280	C₃²×D₄	—	2	4	no	—
281	C₃²×D₄	—	2	4	no	—
282	C₃²×D₄	—	2	2	no	—
283	C₃²×D₄	—	2	2	no	—
284	C₃²×D₄	—	4	4	no	—
285	C₂×C₃²×C₄	—	2	4	no	—
286	C₂×C₃²×C₄	—	2	4	no	—
287	C₂×C₃²×C₄	—	4	2	no	—
288	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
289	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
290	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
291	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
292	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
293	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
294	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
295	C₃×#67	—	2	8	no	—
296	C₃×#67	—	2	8	no	—
297	C₃×#67	—	4	8	no	—
298	C₃×#67	C₂×D₄	1	8	yes	—
299	C₂×C₃×Dic₃	—	2	4	no	—
300	C₂×C₃×Dic₃	—	2	8	no	—
301	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
302	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
303	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
304	C₃×D₁₂	—	2	8	no	—
305	C₃×D₁₂	—	2	4	no	—
306	C₃×D₁₂	—	2	4	no	—
307	C₃×D₁₂	C₂×D₄	1	4	yes	—
308	C₃×C₄×D₃	—	2	8	no	—
309	C₃×C₄×D₃	—	2	8	no	—
310	C₃×C₄×D₃	—	4	4	no	—
311	C₃×C₄×D₃	C₂×D₄	1	8	yes	—
312	C₃×Dic₆	—	2	4	no	—
313	C₃×Dic₆	—	2	4	no	—
314	C₃×Dic₆	—	2	8	no	—
315	C₃×Dic₆	C₂×D₄	1	4	yes	—
316	C₂×2₋¹⁺⁴	—	3	1	no	—
317	C₂×H(5,𝔽₂)	—	3	1	no	—
318	#548	—	3	4	no	—
319	#546	—	3	8	no	—
320	#546	—	3	4	no	—
321	#536	—	3	1	no	—
322	#536	—	3	2	no	—
323	#535	—	3	1	no	—
324	#535	—	3	2	no	—
325	#532	—	3	2	no	—
326	#532	C₃×D₃	1	1	yes	characteristic, complemented
327	C₂×#124	—	3	2	no	—
328	C₂×#124	—	3	1	no	—
329	C₄×#41	—	3	1	no	—
330	C₂⁴×C₃	—	3	4	no	—
331	C₂⁴×C₃	—	3	2	no	—
332	C₂³×D₃	C₂³×C₃	1	4	yes	—
333	C₂³×D₃	C₂³×C₃	1	2	yes	—
334	C₃×#41	—	2	4	no	—
335	C₃×#41	—	2	4	no	—
336	C₃×#41	—	2	4	no	—
337	C₃×#41	—	2	4	no	—
338	C₃×#41	—	3	8	no	—
339	C₃×#41	—	4	4	no	—
340	C₃×#41	—	4	4	no	—
341	C₃×#41	—	6	8	no	—
342	C₃×#41	—	6	8	no	—
343	C₃×#41	—	6	8	no	—
344	C₃×#41	—	6	8	no	—
345	C₃×#41	—	6	16	no	—
346	C₂×C₃×Q₈	—	2	1	no	—
347	C₂×C₃×Q₈	—	2	1	no	—
348	C₂×C₃×Q₈	—	3	1	no	—
349	C₂×C₃×Q₈	—	3	4	no	—
350	C₂×C₃×Q₈	—	3	2	no	—
351	C₂×C₃×Q₈	—	3	2	no	—
352	C₂×C₃×Q₈	—	6	8	no	—
353	C₂×C₃×Q₈	—	6	8	no	—
354	C₂×C₃×Q₈	—	6	4	no	—
355	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
356	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
357	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
358	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
359	C₂×C₃×D₄	—	2	4	no	—
360	C₂×C₃×D₄	—	2	2	no	—
361	C₂×C₃×D₄	—	2	2	no	—
362	C₂×C₃×D₄	—	2	1	no	—
363	C₂×C₃×D₄	—	2	1	no	—
364	C₂×C₃×D₄	—	3	2	no	—
365	C₂×C₃×D₄	—	3	4	no	—
366	C₂×C₃×D₄	—	3	4	no	—
367	C₂×C₃×D₄	—	3	8	no	—
368	C₂×C₃×D₄	—	3	1	no	—
369	C₂×C₃×D₄	—	3	4	no	—
370	C₂×C₃×D₄	—	3	2	no	—
371	C₂×C₃×D₄	—	3	2	no	—
372	C₂×C₃×D₄	—	6	8	no	—
373	C₂×C₃×D₄	—	6	8	no	—
374	C₂×C₃×D₄	—	6	16	no	—
375	C₂×C₃×D₄	—	6	4	no	—
376	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
377	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
378	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
379	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
380	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
381	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
382	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
383	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
384	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
385	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
386	C₂²×C₃×C₄	—	2	1	no	—
387	C₂²×C₃×C₄	—	2	2	no	—
388	C₂²×C₃×C₄	—	2	2	no	—
389	C₂²×C₃×C₄	—	2	2	no	—
390	C₂²×C₃×C₄	—	3	2	no	—
391	C₂²×C₃×C₄	—	3	2	no	—
392	C₂²×C₃×C₄	—	3	4	no	—
393	C₂²×C₃×C₄	—	3	4	no	—
394	C₂²×C₃×C₄	—	3	4	no	—
395	C₂²×C₃×C₄	—	3	4	no	—
396	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
397	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
398	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
399	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
400	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
401	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
402	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
403	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
404	C₂×#67	C₂³×C₃	1	4	yes	—
405	C₂×#67	C₂³×C₃	1	4	yes	—
406	C₂×#67	C₂³×C₃	1	8	yes	—
407	C₂×#67	C₂³×C₃	1	2	yes	—
408	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
409	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
410	#239	—	2	8	no	—
411	D₃×Q₈	—	2	8	no	—
412	#237	—	2	16	no	—
413	#237	—	2	8	no	—
414	D₃×D₄	—	2	16	no	—
415	D₃×D₄	—	2	8	no	—
416	#235	—	2	8	no	—
417	#235	—	2	8	no	—
418	#235	C₃×D₄	1	8	yes	complemented
419	C₂×D₁₂	—	2	4	no	—
420	C₂×D₁₂	—	2	8	no	—
421	C₂×D₁₂	C₂³×C₃	1	2	yes	—
422	C₂×D₁₂	C₂³×C₃	1	2	yes	—
423	C₂×D₁₂	C₂³×C₃	1	4	yes	—
424	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
425	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
426	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
427	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
428	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
429	C₂×Dic₆	—	2	4	no	—
430	C₂×Dic₆	—	2	8	no	—
431	C₂×Dic₆	C₂³×C₃	1	2	yes	—
432	C₂×Dic₆	C₂³×C₃	1	2	yes	—
433	C₂×Dic₆	C₂³×C₃	1	4	yes	—
434	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
435	C₃×C₄⋊C₄	—	2	4	no	—
436	C₃×C₄⋊C₄	—	3	4	no	—
437	C₃×C₄⋊C₄	—	3	8	no	—
438	C₃×C₄⋊C₄	—	3	2	no	—
439	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
440	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
441	C₃×C₂²⋊C₄	—	2	4	no	—
442	C₃×C₂²⋊C₄	—	2	4	no	—
443	C₃×C₂²⋊C₄	—	3	8	no	—
444	C₃×C₂²⋊C₄	—	3	2	no	—
445	C₃×C₂²⋊C₄	—	3	8	no	—
446	C₃×C₂²⋊C₄	—	3	8	no	—
447	C₃×C₂²⋊C₄	—	3	8	no	—
448	C₃×C₂²⋊C₄	—	3	4	no	—
449	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
450	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
451	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
452	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
453	C₃×C₄²	—	2	2	no	—
454	C₃×C₄²	—	2	1	no	—
455	C₃×C₄²	—	2	1	no	—
456	C₃×C₄²	—	3	2	no	—
457	C₃×C₄²	—	3	4	no	—
458	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
459	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
460	C₃×C₄²	C₂²×D₃	1	2	yes	—
461	C₃×C₄²	C₂³×C₃	1	2	yes	—
462	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
463	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
464	#217	C₂³×C₃	1	8	yes	—
465	#217	C₂³×C₃	1	2	yes	—
466	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
467	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
468	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
469	(C₂×D₃)⋊C₄	C₂³×C₃	1	8	yes	—
470	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
471	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
472	Dic₃⋊C₄	C₂³×C₃	1	8	yes	—
473	C₄×Dic₃	C₂³×C₃	1	4	yes	—
474	C₄×Dic₃	C₂³×C₃	1	2	yes	—
475	C₂²×C₃²	—	2	2	no	—
476	C₂²×C₃²	—	2	2	no	—
477	C₂²×C₃²	—	2	2	no	—
478	C₂²×C₃²	—	2	4	no	—
479	C₂²×C₃²	—	2	4	no	—
480	C₂²×C₃²	C₂²×D₄	1	2	yes	—
481	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
482	C₂×C₃×D₃	—	2	4	no	—
483	C₂×C₃×D₃	—	2	4	no	—
484	C₂×C₃×D₃	—	2	8	no	—
485	C₂×C₃×D₃	—	8	8	no	—
486	C₂×C₃×D₃	—	8	4	no	—
487	C₂×C₃×D₃	C₂²×D₄	1	4	yes	—
488	C₃²×C₄	—	2	2	no	—
489	C₃²×C₄	—	2	2	no	—
490	C₃²×C₄	—	2	2	no	—
491	C₃²×C₄	—	2	2	no	—
492	C₃²×C₄	C₂²×D₄	1	2	yes	—
493	C₃²×C₄	C₂²×D₄	1	2	yes	—
494	C₃×Dic₃	—	2	4	no	—
495	C₃×Dic₃	—	2	4	no	—
496	C₃×Dic₃	C₂²×D₄	1	4	yes	—
497	2₋¹⁺⁴	—	6	8	no	—
498	H(5,𝔽₂)	—	6	8	no	—
499	C₂×#41	—	3	2	no	—
500	C₂×#41	—	3	2	no	—
501	C₂×#41	—	3	4	no	—
502	C₂×#41	—	3	1	no	—
503	C₂×#41	—	3	2	no	—
504	C₂×#41	—	3	2	no	—
505	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
506	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic, complemented
507	C₂²×Q₈	—	3	2	no	—
508	C₂²×Q₈	—	3	1	no	—
509	C₂²×Q₈	—	3	2	no	—
510	C₂²×D₄	—	3	2	no	—
511	C₂²×D₄	—	3	4	no	—
512	C₂²×D₄	—	3	1	no	—
513	C₂²×D₄	—	3	2	no	—
514	C₄⋊Q₈	—	3	2	no	—
515	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
516	#127	—	3	2	no	—
517	#127	C₂×C₃×D₃	1	1	yes	characteristic, complemented
518	#124	—	3	2	no	—
519	#124	—	3	2	no	—
520	#124	—	3	8	no	—
521	#124	—	3	2	no	—
522	#124	—	3	2	no	—
523	#124	—	3	4	no	—
524	#124	C₂×C₃×D₃	1	1	yes	characteristic, complemented
525	#124	C₂×C₃×D₃	1	1	yes	characteristic, complemented
526	#123	—	3	4	no	—
527	#123	—	3	8	no	—
528	C₂²⋊Q₈	—	3	4	no	—
529	C₂²⋊Q₈	—	3	8	no	—
530	#121	—	3	8	no	—
531	#121	—	3	4	no	—
532	#121	—	3	8	no	—
533	#121	C₂×C₃×D₃	1	4	yes	complemented
534	#120	—	3	8	no	—
535	#120	—	3	4	no	—
536	C₄×Q₈	—	3	2	no	—
537	C₄×D₄	—	3	4	no	—
538	C₄×D₄	—	3	8	no	—
539	C₄×D₄	—	3	2	no	—
540	C₄×D₄	C₂×C₃×D₃	1	4	yes	complemented
541	#117	—	3	1	no	—
542	#117	—	3	2	no	—
543	C₂×C₂²⋊C₄	—	3	4	no	—
544	C₂×C₂²⋊C₄	—	3	8	no	—
545	C₂×C₄²	—	3	2	no	—
546	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
547	C₂³×C₃	—	2	1	no	—
548	C₂³×C₃	—	2	2	no	—
549	C₂³×C₃	—	2	2	no	—
550	C₂³×C₃	—	3	2	no	—
551	C₂³×C₃	—	3	4	no	—
552	C₂³×C₃	—	6	8	no	—
553	C₂³×C₃	—	6	4	no	—
554	C₂³×C₃	—	12	4	no	—
555	C₂³×C₃	—	12	8	no	—
556	C₂³×C₃	C₂³×D₃	1	2	yes	—
557	C₂³×C₃	C₂³×D₃	1	2	yes	—
558	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
559	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
560	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
561	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
562	C₂²×D₃	—	2	4	no	—
563	C₂²×D₃	—	2	8	no	—
564	C₂²×D₃	—	4	8	no	—
565	C₂²×D₃	—	4	4	no	—
566	C₂²×D₃	C₂⁴×C₃	1	4	yes	—
567	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
568	C₃×Q₈	—	2	2	no	—
569	C₃×Q₈	—	2	2	no	—
570	C₃×Q₈	—	2	2	no	—
571	C₃×Q₈	—	2	2	no	—
572	C₃×Q₈	—	3	4	no	—
573	C₃×Q₈	—	4	2	no	—
574	C₃×Q₈	—	4	2	no	—
575	C₃×Q₈	—	6	8	no	—
576	C₃×Q₈	—	6	4	no	—
577	C₃×Q₈	—	6	4	no	—
578	C₃×D₄	—	2	4	no	—
579	C₃×D₄	—	2	4	no	—
580	C₃×D₄	—	2	4	no	—
581	C₃×D₄	—	2	4	no	—
582	C₃×D₄	—	2	2	no	—
583	C₃×D₄	—	2	2	no	—
584	C₃×D₄	—	2	2	no	—
585	C₃×D₄	—	2	2	no	—
586	C₃×D₄	—	3	8	no	—
587	C₃×D₄	—	3	4	no	—
588	C₃×D₄	—	4	2	no	—
589	C₃×D₄	—	4	2	no	—
590	C₃×D₄	—	4	4	no	—
591	C₃×D₄	—	4	4	no	—
592	C₃×D₄	—	4	4	no	—
593	C₃×D₄	—	4	4	no	—
594	C₃×D₄	—	4	8	no	—
595	C₃×D₄	—	6	8	no	—
596	C₃×D₄	—	6	8	no	—
597	C₃×D₄	—	6	8	no	—
598	C₃×D₄	—	6	4	no	—
599	C₃×D₄	—	6	4	no	—
600	C₃×D₄	—	12	8	no	—
601	C₂×C₃×C₄	—	2	4	no	—
602	C₂×C₃×C₄	—	2	4	no	—
603	C₂×C₃×C₄	—	2	4	no	—
604	C₂×C₃×C₄	—	2	4	no	—
605	C₂×C₃×C₄	—	2	2	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	2	no	—
609	C₂×C₃×C₄	—	2	2	no	—
610	C₂×C₃×C₄	—	2	2	no	—
611	C₂×C₃×C₄	—	2	4	no	—
612	C₂×C₃×C₄	—	3	2	no	—
613	C₂×C₃×C₄	—	3	8	no	—
614	C₂×C₃×C₄	—	3	4	no	—
615	C₂×C₃×C₄	—	3	4	no	—
616	C₂×C₃×C₄	—	4	4	no	—
617	C₂×C₃×C₄	—	4	4	no	—
618	C₂×C₃×C₄	—	4	2	no	—
619	C₂×C₃×C₄	—	4	2	no	—
620	C₂×C₃×C₄	—	4	4	no	—
621	C₂×C₃×C₄	—	6	8	no	—
622	C₂×C₃×C₄	—	6	8	no	—
623	C₂×C₃×C₄	—	6	8	no	—
624	C₂×C₃×C₄	—	6	4	no	—
625	C₂×C₃×C₄	—	12	4	no	—
626	C₂×C₃×C₄	D₃×D₄	1	4	yes	—
627	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
628	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
629	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
630	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
631	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
632	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
633	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
634	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
635	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
636	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
637	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
638	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
639	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
640	#67	—	2	8	no	—
641	#67	—	2	8	no	—
642	#67	—	4	8	no	—
643	#67	C₂×C₃×D₄	1	8	yes	—
644	C₂×Dic₃	—	2	4	no	—
645	C₂×Dic₃	—	2	8	no	—
646	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
647	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
648	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
649	D₁₂	—	2	8	no	—
650	D₁₂	—	2	4	no	—
651	D₁₂	—	2	4	no	—
652	D₁₂	C₂×C₃×D₄	1	4	yes	—
653	C₄×D₃	—	2	8	no	—
654	C₄×D₃	—	2	8	no	—
655	C₄×D₃	—	4	4	no	—
656	C₄×D₃	C₂×C₃×D₄	1	8	yes	—
657	Dic₆	—	2	4	no	—
658	Dic₆	—	2	4	no	—
659	Dic₆	—	2	8	no	—
660	Dic₆	C₂×C₃×D₄	1	4	yes	—
661	C₂×C₃²	—	2	2	no	—
662	C₂×C₃²	—	4	2	no	—
663	C₂×C₃²	—	4	2	no	—
664	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
665	C₂×C₃²	#585	1	2	yes	—
666	C₃×D₃	—	2	4	no	—
667	C₃×D₃	—	4	4	no	—
668	C₂⁴	—	3	4	no	—
669	C₂⁴	—	3	2	no	—
670	#41	—	2	4	no	—
671	#41	—	2	4	no	—
672	#41	—	3	8	no	—
673	#41	—	6	8	no	—
674	#41	—	6	8	no	—
675	#41	—	6	8	no	—
676	#41	—	6	8	no	—
677	#41	—	6	16	no	—
678	C₂×Q₈	—	3	1	no	—
679	C₂×Q₈	—	3	4	no	—
680	C₂×Q₈	—	3	2	no	—
681	C₂×Q₈	—	3	2	no	—
682	C₂×Q₈	—	6	8	no	—
683	C₂×Q₈	—	6	8	no	—
684	C₂×Q₈	—	6	4	no	—
685	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
686	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
687	C₂×D₄	—	3	2	no	—
688	C₂×D₄	—	3	4	no	—
689	C₂×D₄	—	3	4	no	—
690	C₂×D₄	—	3	8	no	—
691	C₂×D₄	—	3	1	no	—
692	C₂×D₄	—	3	4	no	—
693	C₂×D₄	—	3	2	no	—
694	C₂×D₄	—	3	2	no	—
695	C₂×D₄	—	6	8	no	—
696	C₂×D₄	—	6	8	no	—
697	C₂×D₄	—	6	16	no	—
698	C₂×D₄	—	6	4	no	—
699	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
700	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
701	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
702	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
703	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
704	C₂²×C₄	—	3	2	no	—
705	C₂²×C₄	—	3	2	no	—
706	C₂²×C₄	—	3	4	no	—
707	C₂²×C₄	—	3	4	no	—
708	C₂²×C₄	—	3	4	no	—
709	C₂²×C₄	—	3	4	no	—
710	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
711	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
712	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
713	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
714	C₄⋊C₄	—	3	4	no	—
715	C₄⋊C₄	—	3	2	no	—
716	C₄⋊C₄	—	3	8	no	—
717	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
718	C₂²⋊C₄	—	3	8	no	—
719	C₂²⋊C₄	—	3	2	no	—
720	C₂²⋊C₄	—	3	8	no	—
721	C₂²⋊C₄	—	3	8	no	—
722	C₂²⋊C₄	—	3	8	no	—
723	C₂²⋊C₄	—	3	4	no	—
724	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
725	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
726	C₄²	—	3	2	no	—
727	C₄²	—	3	4	no	—
728	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
729	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
730	C₄²	C₂²×C₃×D₃	1	2	yes	—
731	C₂²×C₃	—	2	2	no	—
732	C₂²×C₃	—	2	2	no	—
733	C₂²×C₃	—	2	2	no	—
734	C₂²×C₃	—	2	2	no	—
735	C₂²×C₃	—	2	4	no	—
736	C₂²×C₃	—	2	4	no	—
737	C₂²×C₃	—	2	2	no	—
738	C₂²×C₃	—	2	2	no	—
739	C₂²×C₃	—	2	4	no	—
740	C₂²×C₃	—	2	4	no	—
741	C₂²×C₃	—	2	2	no	—
742	C₂²×C₃	—	2	1	no	—
743	C₂²×C₃	—	3	4	no	—
744	C₂²×C₃	—	4	2	no	—
745	C₂²×C₃	—	4	2	no	—
746	C₂²×C₃	—	4	2	no	—
747	C₂²×C₃	—	4	4	no	—
748	C₂²×C₃	—	4	4	no	—
749	C₂²×C₃	—	6	4	no	—
750	C₂²×C₃	—	6	4	no	—
751	C₂²×C₃	—	6	8	no	—
752	C₂²×C₃	—	24	4	no	—
753	C₂²×C₃	—	24	8	no	—
754	C₂²×C₃	C₂×D₃×D₄	1	2	yes	—
755	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
756	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
757	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
758	C₂×D₃	—	2	4	no	—
759	C₂×D₃	—	2	4	no	—
760	C₂×D₃	—	2	8	no	—
761	C₂×D₃	—	8	8	no	—
762	C₂×D₃	—	8	4	no	—
763	C₂×D₃	C₂²×C₃×D₄	1	4	yes	—
764	C₃×C₄	—	2	4	no	—
765	C₃×C₄	—	2	2	no	—
766	C₃×C₄	—	2	2	no	—
767	C₃×C₄	—	2	2	no	—
768	C₃×C₄	—	2	2	no	—
769	C₃×C₄	—	2	2	no	—
770	C₃×C₄	—	2	2	no	—
771	C₃×C₄	—	2	2	no	—
772	C₃×C₄	—	2	2	no	—
773	C₃×C₄	—	2	2	no	—
774	C₃×C₄	—	2	2	no	—
775	C₃×C₄	—	3	4	no	—
776	C₃×C₄	—	4	2	no	—
777	C₃×C₄	—	4	2	no	—
778	C₃×C₄	—	4	2	no	—
779	C₃×C₄	—	6	4	no	—
780	C₃×C₄	—	6	4	no	—
781	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
782	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
783	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
784	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
785	Dic₃	—	2	4	no	—
786	Dic₃	—	2	4	no	—
787	Dic₃	C₂²×C₃×D₄	1	4	yes	—
788	C₃²	#3500	1	1	yes	characteristic, complemented, Sylow
789	C₂³	—	3	2	no	—
790	C₂³	—	3	4	no	—
791	C₂³	—	6	8	no	—
792	C₂³	—	6	4	no	—
793	C₂³	—	12	4	no	—
794	C₂³	—	12	8	no	—
795	C₂³	C₂³×C₃×D₃	1	2	yes	—
796	C₂³	C₂³×C₃×D₃	1	2	yes	—
797	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
798	Q₈	—	2	2	no	—
799	Q₈	—	2	2	no	—
800	Q₈	—	3	4	no	—
801	Q₈	—	6	8	no	—
802	Q₈	—	6	4	no	—
803	Q₈	—	6	4	no	—
804	D₄	—	2	4	no	—
805	D₄	—	2	4	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	3	8	no	—
809	D₄	—	3	4	no	—
810	D₄	—	4	4	no	—
811	D₄	—	6	8	no	—
812	D₄	—	6	8	no	—
813	D₄	—	6	8	no	—
814	D₄	—	6	4	no	—
815	D₄	—	6	4	no	—
816	D₄	—	12	8	no	—
817	C₂×C₄	—	2	4	no	—
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	3	2	no	—
820	C₂×C₄	—	3	8	no	—
821	C₂×C₄	—	3	4	no	—
822	C₂×C₄	—	3	4	no	—
823	C₂×C₄	—	4	2	no	—
824	C₂×C₄	—	6	8	no	—
825	C₂×C₄	—	6	8	no	—
826	C₂×C₄	—	6	8	no	—
827	C₂×C₄	—	6	4	no	—
828	C₂×C₄	—	12	4	no	—
829	C₂×C₄	C₃×D₃×D₄	1	4	yes	—
830	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
831	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
832	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
833	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
834	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
835	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
836	C₂×C₃	—	2	2	no	—
837	C₂×C₃	—	2	2	no	—
838	C₂×C₃	—	2	1	no	—
839	C₂×C₃	—	2	2	no	—
840	C₂×C₃	—	4	2	no	—
841	C₂×C₃	—	4	2	no	—
842	C₂×C₃	—	4	2	no	—
843	C₂×C₃	—	4	2	no	—
844	C₂×C₃	—	4	2	no	—
845	C₂×C₃	—	6	4	no	—
846	C₂×C₃	—	8	2	no	—
847	C₂×C₃	—	8	2	no	—
848	C₂×C₃	—	12	4	no	—
849	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
850	C₂×C₃	#5964	1	2	yes	—
851	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
852	C₂×C₃	C₃×#585	1	2	yes	—
853	D₃	—	2	4	no	—
854	D₃	—	4	4	no	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	4	no	—
859	C₂²	—	2	4	no	—
860	C₂²	—	3	4	no	—
861	C₂²	—	6	4	no	—
862	C₂²	—	6	4	no	—
863	C₂²	—	6	8	no	—
864	C₂²	—	24	4	no	—
865	C₂²	—	24	8	no	—
866	C₂²	C₂×C₃×D₃×D₄	1	2	yes	—
867	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	3	4	no	—
873	C₄	—	6	4	no	—
874	C₄	—	6	4	no	—
875	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
876	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
877	C₃	—	2	1	no	—
878	C₃	#86244	1	1	yes	characteristic, direct product factor
879	C₃	C₃×#3500	1	1	yes	characteristic, complemented
880	C₂	—	2	2	no	—
881	C₂	—	4	2	no	—
882	C₂	—	4	2	no	—
883	C₂	—	6	4	no	—
884	C₂	—	12	4	no	—
885	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic
886	C₂	C₃×#5964	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#532	C₂
socle	C₂²×C₃²	C₂⁵
hypercenter	C₃×#532	D₃
hypocenter	C₃	C₃×#3500
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#1010	C₂	semidirect
2. C₂×C₃×#1009	C₂	semidirect
3. C₃²×#532	C₂	semidirect
4. C₃×#5830	C₂	semidirect
5. C₃×#5825	C₂	semidirect
6. C₃×#5724	C₂	semidirect
7. C₃×#5715	C₂	semidirect
8. C₃×D₃×#124	C₂	semidirect
9. C₃×#5668	C₂	semidirect
10. C₃×#5610	C₂	semidirect
11. C₃×#5552	C₂	semidirect
12. C₃×#5550	C₂	semidirect
13. C₂×C₃×#875	C₂	semidirect
14. C₃×C₄×#235	C₂	semidirect
16. #86244	C₃	direct (N × H)
18. C₂×C₃²×#41	C₂²	semidirect
22. C₂×C₃×D₃×Q₈	C₂²	semidirect
23. C₂×C₃×#237	C₂²	semidirect
24. C₂×C₃×#237	C₂²	semidirect
29. C₂×C₃×#235	C₂²	semidirect
32. C₂²×C₃×Dic₆	C₂²	semidirect
33. C₂²×C₃×Dic₆	C₂²	semidirect
34. C₃²×C₄⋊Q₈	C₂²	semidirect
35. C₃²×#127	C₂²	semidirect
36. C₃²×#124	C₂²	semidirect
37. C₃²×#124	C₂²	semidirect
38. C₃²×#121	C₂²	semidirect
39. C₃²×C₄×D₄	C₂²	semidirect
40. C₂×C₃²×C₄²	C₂²	semidirect
41. C₃×#947	C₂²	semidirect
42. C₃×#944	C₂²	semidirect
43. C₃×#940	C₂²	semidirect
44. C₃×#939	C₂²	semidirect
45. C₃×#937	C₂²	semidirect
46. C₃×#937	C₂²	semidirect
47. C₃×#936	C₂²	semidirect
48. C₃×#935	C₂²	semidirect
49. C₃×#930	C₂²	semidirect
50. C₃×C₄×#67	C₂²	semidirect
51. C₂×C₃×(C₂×D₃)⋊C₄	C₂²	semidirect
52. C₃×#926	C₂²	semidirect
53. C₃×#924	C₂²	semidirect
54. C₃×#896	C₂²	semidirect
55. C₃×#894	C₂²	semidirect
56. C₃×#885	C₂²	semidirect
57. C₃×#884	C₂²	semidirect
58. C₃×#67⋊C₄	C₂²	semidirect
59. C₃×D₃×C₂²⋊C₄	C₂²	semidirect
60. C₃×#875	C₂²	semidirect
61. C₃×#875	C₂²	semidirect
62. C₃×#875	C₂²	semidirect
63. C₃×C₄×D₁₂	C₂²	semidirect
64. C₃×#872	C₂²	semidirect
65. C₃×C₄²×D₃	C₂²	semidirect
66. C₃×C₄×Dic₆	C₂²	semidirect
69. C₂×#1010	C₂×C₃	semidirect
70. C₂×#1009	C₂×C₃	semidirect
80. C₃×#532	D₃	semidirect
81. C₃×#532	C₂×C₃	semidirect
85. #5830	C₂×C₃	semidirect
86. #5825	C₂×C₃	semidirect
87. #5724	C₂×C₃	semidirect
88. #5715	C₂×C₃	semidirect
89. D₃×#124	C₂×C₃	semidirect
90. #5668	C₂×C₃	semidirect
91. #5610	C₂×C₃	semidirect
92. #5552	C₂×C₃	semidirect
93. #5550	C₂×C₃	semidirect
94. C₂×#875	C₂×C₃	semidirect
95. C₄×#235	C₂×C₃	semidirect
125. C₃×#235	D₄	semidirect
171. C₂×C₃×#41	C₂×D₃	semidirect
173. C₂×C₃×#41	C₂²×C₃	semidirect
184. C₂×D₃×Q₈	C₂²×C₃	semidirect
185. C₂×#237	C₂²×C₃	semidirect
186. C₂×#237	C₂²×C₃	semidirect
191. C₂×#235	C₂²×C₃	semidirect
194. C₂²×Dic₆	C₂²×C₃	semidirect
195. C₂²×Dic₆	C₂²×C₃	semidirect
198. C₃×C₄⋊Q₈	C₂×D₃	semidirect
199. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
202. C₃×#127	C₂×D₃	semidirect
203. C₃×#127	C₂²×C₃	semidirect
212. C₃×#124	C₂×D₃	semidirect
213. C₃×#124	C₂×D₃	semidirect
214. C₃×#124	C₂²×C₃	semidirect
215. C₃×#124	C₂²×C₃	semidirect
224. C₃×#121	C₂×D₃	semidirect
225. C₃×#121	C₂²×C₃	semidirect
233. C₃×C₄×D₄	C₂×D₃	semidirect
234. C₃×C₄×D₄	C₂²×C₃	semidirect
241. C₂×C₃×C₄²	C₂×D₃	semidirect
242. C₂×C₃×C₄²	C₂²×C₃	semidirect
243. #947	C₂²×C₃	semidirect
244. #944	C₂²×C₃	semidirect
245. #940	C₂²×C₃	semidirect
246. #939	C₂²×C₃	semidirect
247. #937	C₂²×C₃	semidirect
248. #937	C₂²×C₃	semidirect
249. #936	C₂²×C₃	semidirect
250. #935	C₂²×C₃	semidirect
251. #930	C₂²×C₃	semidirect
252. C₄×#67	C₂²×C₃	semidirect
253. C₂×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
254. #926	C₂²×C₃	semidirect
255. #924	C₂²×C₃	semidirect
256. #896	C₂²×C₃	semidirect
257. #894	C₂²×C₃	semidirect
258. #885	C₂²×C₃	semidirect
259. #884	C₂²×C₃	semidirect
260. #67⋊C₄	C₂²×C₃	semidirect
261. D₃×C₂²⋊C₄	C₂²×C₃	semidirect
262. #875	C₂²×C₃	semidirect
263. #875	C₂²×C₃	semidirect
264. #875	C₂²×C₃	semidirect
265. C₄×D₁₂	C₂²×C₃	semidirect
266. #872	C₂²×C₃	semidirect
267. C₄²×D₃	C₂²×C₃	semidirect
268. C₄×Dic₆	C₂²×C₃	semidirect
326. #532	C₃×D₃	semidirect
418. #235	C₃×D₄	semidirect
506. C₂×#41	C₂×C₃×D₃	semidirect
515. C₄⋊Q₈	C₂×C₃×D₃	semidirect
517. #127	C₂×C₃×D₃	semidirect
524. #124	C₂×C₃×D₃	semidirect
525. #124	C₂×C₃×D₃	semidirect
533. #121	C₂×C₃×D₃	semidirect
540. C₄×D₄	C₂×C₃×D₃	semidirect
546. C₂×C₄²	C₂×C₃×D₃	semidirect
788. C₃²	#3500	semidirect
878. C₃	#86244	direct (N × H)
879. C₃	C₃×#3500	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#1010	2
C₂×C₃×#1009	2
C₃²×#532	2
C₃×#5830	2
C₃×#5825	2
C₃×#5724	2
C₃×#5715	2
C₃×D₃×#124	2
C₃×#5668	2
C₃×#5610	2
C₃×#5552	2
C₃×#5550	2
C₂×C₃×#875	2
C₃×C₄×#235	2
C₃×#3500	3
#86244	3

Subgroups — C3×#86244 #11906066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86244 #11906066