Subgroups — C₃×D₃×#554 #11903213

Order 1152.

2514 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5730	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5690	C₂	1	2	yes	maximal, complemented
5	C₃×D₃×#125	C₂	1	2	yes	maximal, complemented
6	C₃×#5636	C₂	1	4	yes	maximal, complemented
7	C₃×#5635	C₂	1	2	yes	maximal, complemented
8	C₃×D₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
9	C₃×D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
10	C₃×#5579	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×D₃×D₄	C₂	1	2	yes	maximal
13	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
14	C₃×#5543	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#5539	C₂	1	2	yes	maximal, complemented
16	C₃×#5511	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×D₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
18	C₂×C₃×#554	—	3	1	no	maximal
19	D₃×#554	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	—
22	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
24	C₂²×C₃×C₄×D₃	C₂²	1	4	yes	—
25	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃²×#125	C₂²	1	2	yes	complemented
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
29	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₃²×C₄×D₄	C₂²	1	2	yes	—
31	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
33	C₃×#946	C₂²	1	2	yes	complemented
34	C₃×#946	C₂²	1	4	yes	complemented
35	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
36	C₃×#944	C₂²	1	2	yes	complemented
37	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
38	C₃×D₄×Dic₃	C₂²	1	2	yes	—
39	C₃×C₄×#67	C₂²	1	2	yes	—
40	C₃×C₄×#67	C₂²	1	4	yes	—
41	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	complemented
42	C₃×#924	C₂²	1	4	yes	complemented
43	C₃×#924	C₂²	1	2	yes	complemented
44	C₂×C₃×Dic₃⋊C₄	C₂²	1	4	yes	complemented
45	C₃×#897	C₂²	1	2	yes	complemented
46	C₃×#897	C₂²	1	4	yes	complemented
47	C₃×#896	C₂²	1	4	yes	complemented
48	C₃×#896	C₂²	1	4	yes	complemented
49	C₃×#896	C₂²	1	4	yes	complemented
50	C₃×#893	C₂²	1	1	yes	characteristic
51	C₃×#893	C₂²	1	2	yes	—
52	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
54	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
55	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
56	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
57	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
58	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	—
59	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
60	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
61	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
62	C₃×#890	C₂²	1	2	yes	complemented
63	C₃×#890	C₂²	1	2	yes	complemented
64	C₃×#889	C₂²	1	4	yes	complemented
65	C₃×#889	C₂²	1	4	yes	complemented
66	C₃×#888	C₂²	1	2	yes	complemented
67	C₃×#888	C₂²	1	2	yes	complemented
68	C₃×#887	C₂²	1	1	yes	characteristic, complemented
69	C₃×#887	C₂²	1	2	yes	complemented
70	C₃×#67⋊C₄	C₂²	1	4	yes	—
71	C₃×#67⋊C₄	C₂²	1	2	yes	—
72	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
73	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
74	C₃×#878	C₂²	1	4	yes	complemented
75	C₃×#878	C₂²	1	4	yes	complemented
76	C₃×#878	C₂²	1	4	yes	complemented
77	C₃×C₄×D₁₂	C₂²	1	2	yes	—
78	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
79	C₃×C₄²×D₃	C₂²	1	2	yes	—
80	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
81	C₃×#870	C₂²	1	2	yes	complemented
82	C₃×#869	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
84	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
85	C₃×#554	—	2	1	no	—
86	C₃×#554	—	3	1	no	—
87	C₃×#554	—	3	2	no	—
88	C₃×#554	—	3	2	no	—
89	C₃×#554	—	3	4	no	—
90	C₃×#554	—	3	1	no	—
91	C₃×#554	—	3	2	no	—
92	C₃×#554	—	3	1	no	—
93	C₃×#554	—	3	2	no	—
94	C₃×#554	D₃	1	1	yes	characteristic, direct product factor
95	C₃×#554	C₂×C₃	1	1	yes	characteristic, complemented
96	C₂×C₃×C₄⋊Q₈	—	3	1	no	—
97	C₂×C₃×#125	—	3	2	no	—
98	C₂×C₃×C₂²⋊Q₈	—	3	4	no	—
99	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
100	C₂×C₃×C₄×Q₈	—	3	1	no	—
101	C₂×C₃×C₄×D₄	—	3	2	no	—
102	C₂×C₃×C₄×D₄	—	3	1	no	—
103	C₂²×C₃×C₄⋊C₄	—	3	2	no	—
104	#5730	C₂×C₃	1	1	yes	characteristic, complemented
105	D₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
106	#5690	C₂×C₃	1	2	yes	complemented
107	D₃×#125	C₂×C₃	1	2	yes	complemented
108	#5636	C₂×C₃	1	4	yes	complemented
109	#5635	C₂×C₃	1	2	yes	complemented
110	D₃×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
111	D₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
112	#5579	C₂×C₃	1	1	yes	characteristic, complemented
113	C₄×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
114	C₄×D₃×D₄	C₂×C₃	1	2	yes	—
115	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic
116	#5543	C₂×C₃	1	1	yes	characteristic, complemented
117	#5539	C₂×C₃	1	2	yes	complemented
118	#5511	C₂×C₃	1	2	yes	complemented
119	C₂×D₃×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
120	C₂³×C₃×D₃	C₂³	1	2	yes	—
121	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
122	C₂×C₃²×Q₈	C₂³	1	2	yes	—
123	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
124	C₂²×C₃²×C₄	C₂³	1	2	yes	—
125	C₂²×C₃²×C₄	C₂³	1	4	yes	—
126	C₂×C₃×#67	C₂³	1	2	yes	—
127	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
128	C₂²×C₃×Dic₃	C₂³	1	4	yes	—
129	C₃×D₃×Q₈	—	2	4	no	—
130	C₃×D₃×Q₈	—	4	4	no	—
131	C₃×D₃×D₄	Q₈	1	8	yes	complemented
132	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
133	C₂×C₃×C₄×D₃	—	2	8	no	—
134	C₂×C₃×C₄×D₃	—	4	8	no	—
135	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
136	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
137	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
138	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
139	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
140	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
141	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
142	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
143	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
144	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
145	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
146	C₂×C₃×Dic₆	C₂³	1	2	yes	—
147	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
148	C₂×C₃×Dic₆	C₂³	1	2	yes	—
149	C₂×C₃×Dic₆	C₂³	1	4	yes	—
150	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
152	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
153	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
154	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
155	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
156	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃²×C₄²	C₂³	1	2	yes	—
160	C₃²×C₄²	C₂³	1	1	yes	characteristic
161	C₃×#217	C₂³	1	4	yes	—
162	C₃×#217	C₂³	1	2	yes	—
163	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
164	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
165	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
166	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
167	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
168	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
169	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
170	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
171	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
172	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
173	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
174	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
175	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
176	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
177	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
178	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
179	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
180	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
181	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
182	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
183	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
184	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
185	C₃×C₄×Dic₃	C₂³	1	2	yes	—
186	C₃×C₄×Dic₃	C₂³	1	2	yes	—
187	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
188	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
189	C₃×C₄×Dic₃	C₂³	1	2	yes	—
190	C₂×#554	—	3	1	no	Sylow
191	C₂²×C₃×Q₈	—	3	1	no	—
192	C₂²×C₃×Q₈	—	3	2	no	—
193	C₂²×C₃×D₄	—	3	1	no	—
194	C₂³×C₃×C₄	—	3	2	no	—
195	C₂³×C₃×C₄	—	3	4	no	—
196	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
197	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	—
198	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
199	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
200	C₂²×C₄×D₃	C₂²×C₃	1	4	yes	—
201	C₃×C₄⋊Q₈	—	2	1	no	—
202	C₃×C₄⋊Q₈	—	3	2	no	—
203	C₃×C₄⋊Q₈	—	3	2	no	—
204	C₃×C₄⋊Q₈	—	3	2	no	—
205	C₃×C₄⋊Q₈	—	3	1	no	—
206	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
207	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₃×#125	—	2	2	no	—
209	C₃×#125	—	3	4	no	—
210	C₃×#125	—	3	4	no	—
211	C₃×#125	—	3	2	no	—
212	C₃×#125	—	3	2	no	—
213	C₃×#125	—	3	2	no	—
214	C₃×#125	C₂×D₃	1	2	yes	complemented
215	C₃×#125	C₂²×C₃	1	2	yes	complemented
216	C₃×C₂²⋊Q₈	—	2	4	no	—
217	C₃×C₂²⋊Q₈	—	2	2	no	—
218	C₃×C₂²⋊Q₈	—	3	4	no	—
219	C₃×C₂²⋊Q₈	—	3	2	no	—
220	C₃×C₂²⋊Q₈	—	3	4	no	—
221	C₃×C₂²⋊Q₈	—	3	2	no	—
222	C₃×C₂²⋊Q₈	—	3	4	no	—
223	C₃×C₂²⋊Q₈	—	3	4	no	—
224	C₃×C₂²⋊Q₈	—	3	4	no	—
225	C₃×C₂²⋊Q₈	—	3	4	no	—
226	C₃×C₂²⋊Q₈	—	3	2	no	—
227	C₃×C₂²⋊Q₈	—	3	4	no	—
228	C₃×C₂²⋊Q₈	—	3	4	no	—
229	C₃×C₂²⋊Q₈	—	3	4	no	—
230	C₃×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
231	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
232	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
233	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
234	C₃×C₄×Q₈	—	2	1	no	—
235	C₃×C₄×Q₈	—	3	1	no	—
236	C₃×C₄×Q₈	—	3	2	no	—
237	C₃×C₄×Q₈	—	3	1	no	—
238	C₃×C₄×Q₈	—	3	1	no	—
239	C₃×C₄×Q₈	—	3	2	no	—
240	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
241	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
242	C₃×C₄×D₄	—	2	2	no	—
243	C₃×C₄×D₄	—	2	1	no	—
244	C₃×C₄×D₄	—	3	2	no	—
245	C₃×C₄×D₄	—	3	1	no	—
246	C₃×C₄×D₄	—	3	4	no	—
247	C₃×C₄×D₄	—	3	2	no	—
248	C₃×C₄×D₄	—	3	2	no	—
249	C₃×C₄×D₄	—	3	1	no	—
250	C₃×C₄×D₄	—	3	4	no	—
251	C₃×C₄×D₄	—	3	2	no	—
252	C₃×C₄×D₄	—	3	2	no	—
253	C₃×C₄×D₄	—	3	1	no	—
254	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
255	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
256	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
257	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
258	C₂×C₃×C₄⋊C₄	—	2	2	no	—
259	C₂×C₃×C₄⋊C₄	—	3	4	no	—
260	C₂×C₃×C₄⋊C₄	—	3	2	no	—
261	C₂×C₃×C₄⋊C₄	—	3	1	no	—
262	C₂×C₃×C₄⋊C₄	—	3	4	no	—
263	C₂×C₃×C₄⋊C₄	—	3	2	no	—
264	C₂×C₃×C₄⋊C₄	—	3	1	no	—
265	C₂×C₃×C₄⋊C₄	—	3	2	no	—
266	C₂×C₃×C₄⋊C₄	—	3	2	no	—
267	C₂×C₃×C₄⋊C₄	—	3	4	no	—
268	C₂×C₃×C₄⋊C₄	—	3	4	no	—
269	C₂×C₃×C₄⋊C₄	—	3	2	no	—
270	C₂×C₃×C₄⋊C₄	—	3	2	no	—
271	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
272	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
273	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
274	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
275	C₂×C₃×C₄²	—	3	2	no	—
276	C₂×C₃×C₄²	—	3	1	no	—
277	#946	C₂²×C₃	1	2	yes	complemented
278	#946	C₂²×C₃	1	4	yes	complemented
279	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
280	#944	C₂²×C₃	1	2	yes	complemented
281	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
282	D₄×Dic₃	C₂²×C₃	1	2	yes	—
283	C₄×#67	C₂²×C₃	1	2	yes	—
284	C₄×#67	C₂²×C₃	1	4	yes	—
285	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	complemented
286	#924	C₂²×C₃	1	4	yes	complemented
287	#924	C₂²×C₃	1	2	yes	complemented
288	C₂×Dic₃⋊C₄	C₂²×C₃	1	4	yes	complemented
289	#897	C₂²×C₃	1	4	yes	complemented
290	#897	C₂²×C₃	1	2	yes	complemented
291	#896	C₂²×C₃	1	4	yes	complemented
292	#896	C₂²×C₃	1	4	yes	complemented
293	#896	C₂²×C₃	1	4	yes	complemented
294	#893	C₂²×C₃	1	1	yes	characteristic
295	#893	C₂²×C₃	1	2	yes	—
296	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
297	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
298	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
299	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
300	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
301	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
302	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
303	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
304	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
305	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
306	#890	C₂²×C₃	1	2	yes	complemented
307	#890	C₂²×C₃	1	2	yes	complemented
308	#889	C₂²×C₃	1	4	yes	complemented
309	#889	C₂²×C₃	1	4	yes	complemented
310	#888	C₂²×C₃	1	2	yes	complemented
311	#888	C₂²×C₃	1	2	yes	complemented
312	#887	C₂²×C₃	1	2	yes	complemented
313	#887	C₂²×C₃	1	1	yes	characteristic, complemented
314	#67⋊C₄	C₂²×C₃	1	4	yes	—
315	#67⋊C₄	C₂²×C₃	1	2	yes	—
316	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
317	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
318	#878	C₂²×C₃	1	4	yes	complemented
319	#878	C₂²×C₃	1	4	yes	complemented
320	#878	C₂²×C₃	1	4	yes	complemented
321	C₄×D₁₂	C₂²×C₃	1	2	yes	—
322	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
323	C₄²×D₃	C₂²×C₃	1	2	yes	—
324	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
325	#870	C₂²×C₃	1	2	yes	complemented
326	#869	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
328	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
329	C₂³×C₃²	C₂⁴	1	2	yes	—
330	C₂²×C₃×D₃	—	2	4	no	—
331	C₂²×C₃×D₃	—	2	4	no	—
332	C₂²×C₃×D₃	C₂×Q₈	1	8	yes	—
333	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
334	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
335	C₃²×Q₈	—	2	2	no	—
336	C₃²×Q₈	—	4	2	no	—
337	C₃²×D₄	C₂×Q₈	1	4	yes	complemented
338	C₂×C₃²×C₄	—	2	4	no	—
339	C₂×C₃²×C₄	—	4	4	no	—
340	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
341	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
342	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
343	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
344	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
345	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
346	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
347	C₃×#67	C₂×Q₈	1	8	yes	complemented
348	C₂×C₃×Dic₃	—	2	4	no	—
349	C₂×C₃×Dic₃	—	4	4	no	—
350	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
351	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
352	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
354	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
355	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
357	C₃×D₁₂	C₂×Q₈	1	4	yes	complemented
358	C₃×C₄×D₃	—	2	4	no	—
359	C₃×C₄×D₃	—	2	4	no	—
360	C₃×C₄×D₃	—	2	4	no	—
361	C₃×C₄×D₃	—	2	8	no	—
362	C₃×C₄×D₃	—	2	2	no	—
363	C₃×C₄×D₃	—	2	4	no	—
364	C₃×C₄×D₃	—	2	4	no	—
365	C₃×C₄×D₃	—	4	4	no	—
366	C₃×C₄×D₃	—	4	4	no	—
367	C₃×C₄×D₃	C₂×Q₈	1	4	yes	—
368	C₃×C₄×D₃	#41	1	4	yes	—
369	C₃×Dic₆	—	2	2	no	—
370	C₃×Dic₆	—	2	4	no	—
371	C₃×Dic₆	—	4	4	no	—
372	C₃×Dic₆	—	4	2	no	—
373	#554	—	3	1	no	—
374	#554	—	3	2	no	—
375	#554	—	3	2	no	—
376	#554	—	3	4	no	—
377	#554	—	3	1	no	—
378	#554	—	3	2	no	—
379	#554	—	3	1	no	—
380	#554	—	3	2	no	—
381	#554	C₃×D₃	1	1	yes	characteristic, direct product factor
382	C₂×C₄⋊Q₈	—	3	1	no	—
383	C₂×#125	—	3	2	no	—
384	C₂×C₂²⋊Q₈	—	3	4	no	—
385	C₂×C₂²⋊Q₈	—	3	2	no	—
386	C₂×C₄×Q₈	—	3	1	no	—
387	C₂×C₄×D₄	—	3	2	no	—
388	C₂×C₄×D₄	—	3	1	no	—
389	C₂²×C₄⋊C₄	—	3	2	no	—
390	C₂⁴×C₃	—	3	2	no	—
391	C₂³×D₃	C₂³×C₃	1	2	yes	—
392	C₂×C₃×Q₈	—	2	1	no	—
393	C₂×C₃×Q₈	—	2	2	no	—
394	C₂×C₃×Q₈	—	3	2	no	—
395	C₂×C₃×Q₈	—	3	1	no	—
396	C₂×C₃×Q₈	—	3	4	no	—
397	C₂×C₃×Q₈	—	3	2	no	—
398	C₂×C₃×Q₈	—	6	4	no	—
399	C₂×C₃×Q₈	—	12	4	no	—
400	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
401	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
402	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
404	C₂×C₃×D₄	—	2	1	no	—
405	C₂×C₃×D₄	—	3	2	no	—
406	C₂×C₃×D₄	—	3	8	no	—
407	C₂×C₃×D₄	—	3	1	no	—
408	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
409	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
410	C₂²×C₃×C₄	—	2	2	no	—
411	C₂²×C₃×C₄	—	2	4	no	—
412	C₂²×C₃×C₄	—	3	1	no	—
413	C₂²×C₃×C₄	—	3	1	no	—
414	C₂²×C₃×C₄	—	3	2	no	—
415	C₂²×C₃×C₄	—	3	4	no	—
416	C₂²×C₃×C₄	—	3	2	no	—
417	C₂²×C₃×C₄	—	3	1	no	—
418	C₂²×C₃×C₄	—	3	2	no	—
419	C₂²×C₃×C₄	—	3	2	no	—
420	C₂²×C₃×C₄	—	3	4	no	—
421	C₂²×C₃×C₄	—	3	2	no	—
422	C₂²×C₃×C₄	—	3	2	no	—
423	C₂²×C₃×C₄	—	3	4	no	—
424	C₂²×C₃×C₄	—	3	4	no	—
425	C₂²×C₃×C₄	—	6	8	no	—
426	C₂²×C₃×C₄	—	12	8	no	—
427	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
428	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
429	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
430	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
431	C₂×#67	C₂³×C₃	1	2	yes	—
432	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
433	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
434	D₃×Q₈	—	2	4	no	—
435	D₃×Q₈	—	4	4	no	—
436	D₃×D₄	C₃×Q₈	1	8	yes	complemented
437	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
438	C₂×C₄×D₃	—	2	8	no	—
439	C₂×C₄×D₃	—	4	8	no	—
440	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
441	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
442	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
443	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
444	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
445	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
446	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
447	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
448	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
449	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
450	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
451	C₂×Dic₆	C₂³×C₃	1	2	yes	—
452	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
453	C₂×Dic₆	C₂³×C₃	1	2	yes	—
454	C₂×Dic₆	C₂³×C₃	1	4	yes	—
455	C₃×C₄⋊C₄	—	2	1	no	—
456	C₃×C₄⋊C₄	—	2	4	no	—
457	C₃×C₄⋊C₄	—	2	2	no	—
458	C₃×C₄⋊C₄	—	2	1	no	—
459	C₃×C₄⋊C₄	—	2	2	no	—
460	C₃×C₄⋊C₄	—	2	2	no	—
461	C₃×C₄⋊C₄	—	2	4	no	—
462	C₃×C₄⋊C₄	—	3	2	no	—
463	C₃×C₄⋊C₄	—	3	4	no	—
464	C₃×C₄⋊C₄	—	3	4	no	—
465	C₃×C₄⋊C₄	—	3	4	no	—
466	C₃×C₄⋊C₄	—	3	2	no	—
467	C₃×C₄⋊C₄	—	3	4	no	—
468	C₃×C₄⋊C₄	—	3	2	no	—
469	C₃×C₄⋊C₄	—	3	2	no	—
470	C₃×C₄⋊C₄	—	3	4	no	—
471	C₃×C₄⋊C₄	—	3	4	no	—
472	C₃×C₄⋊C₄	—	3	1	no	—
473	C₃×C₄⋊C₄	—	3	4	no	—
474	C₃×C₄⋊C₄	—	3	2	no	—
475	C₃×C₄⋊C₄	—	3	1	no	—
476	C₃×C₄⋊C₄	—	3	2	no	—
477	C₃×C₄⋊C₄	—	3	2	no	—
478	C₃×C₄⋊C₄	—	3	4	no	—
479	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
480	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
481	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
482	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
483	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
484	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
485	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
486	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
487	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
489	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
490	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
491	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
492	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
493	C₃×C₂²⋊C₄	—	2	4	no	—
494	C₃×C₂²⋊C₄	—	2	2	no	—
495	C₃×C₂²⋊C₄	—	3	4	no	—
496	C₃×C₂²⋊C₄	—	3	2	no	—
497	C₃×C₂²⋊C₄	—	3	4	no	—
498	C₃×C₂²⋊C₄	—	3	2	no	—
499	C₃×C₂²⋊C₄	—	3	2	no	—
500	C₃×C₂²⋊C₄	—	3	4	no	—
501	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
502	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
503	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
504	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
505	C₃×C₄²	—	2	2	no	—
506	C₃×C₄²	—	2	1	no	—
507	C₃×C₄²	—	3	2	no	—
508	C₃×C₄²	—	3	2	no	—
509	C₃×C₄²	—	3	2	no	—
510	C₃×C₄²	—	3	1	no	—
511	C₃×C₄²	—	3	1	no	—
512	C₃×C₄²	—	3	1	no	—
513	C₃×C₄²	C₂²×D₃	1	2	yes	—
514	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
515	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
516	C₃×C₄²	C₂³×C₃	1	2	yes	—
517	#217	C₂³×C₃	1	4	yes	—
518	#217	C₂³×C₃	1	2	yes	—
519	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
520	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
521	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
522	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
523	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
524	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
525	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
526	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
527	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
528	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
529	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
530	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
531	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
532	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
533	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
534	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
535	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
536	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
537	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
538	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
539	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
540	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
541	C₄×Dic₃	C₂³×C₃	1	2	yes	—
542	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
543	C₄×Dic₃	C₂³×C₃	1	2	yes	—
544	C₄×Dic₃	C₂³×C₃	1	2	yes	—
545	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
546	C₂²×C₃²	—	2	2	no	—
547	C₂²×C₃²	—	2	2	no	—
548	C₂²×C₃²	C₂²×Q₈	1	4	yes	—
549	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
550	C₂×C₃×D₃	—	2	2	no	—
551	C₂×C₃×D₃	—	2	2	no	—
552	C₂×C₃×D₃	—	2	16	no	—
553	C₂×C₃×D₃	C₂²×Q₈	1	4	yes	—
554	C₂×C₃×D₃	C₂²×Q₈	1	2	yes	—
555	C₂×C₃×D₃	C₂×#41	1	2	yes	—
556	C₂×C₃×D₃	H(5,𝔽₂)	1	2	yes	—
557	C₃²×C₄	—	2	2	no	—
558	C₃²×C₄	—	2	2	no	—
559	C₃²×C₄	—	2	1	no	—
560	C₃²×C₄	—	2	4	no	—
561	C₃²×C₄	—	2	2	no	—
562	C₃²×C₄	C₂²×Q₈	1	2	yes	—
563	C₃²×C₄	C₂×#41	1	2	yes	—
564	C₃×Dic₃	—	2	2	no	—
565	C₃×Dic₃	—	2	2	no	—
566	C₃×Dic₃	—	2	1	no	—
567	C₃×Dic₃	—	2	4	no	—
568	C₃×Dic₃	—	2	2	no	—
569	C₃×Dic₃	C₂²×Q₈	1	2	yes	—
570	C₃×Dic₃	C₂×#41	1	2	yes	—
571	C₂²×Q₈	—	3	1	no	—
572	C₂²×Q₈	—	3	2	no	—
573	C₂²×D₄	—	3	1	no	—
574	C₂³×C₄	—	3	2	no	—
575	C₂³×C₄	—	3	4	no	—
576	C₄⋊Q₈	—	3	2	no	—
577	C₄⋊Q₈	—	3	2	no	—
578	C₄⋊Q₈	—	3	2	no	—
579	C₄⋊Q₈	—	3	1	no	—
580	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
581	#125	—	3	4	no	—
582	#125	—	3	4	no	—
583	#125	—	3	2	no	—
584	#125	—	3	2	no	—
585	#125	—	3	2	no	—
586	#125	C₂×C₃×D₃	1	2	yes	complemented
587	C₂²⋊Q₈	—	3	4	no	—
588	C₂²⋊Q₈	—	3	2	no	—
589	C₂²⋊Q₈	—	3	4	no	—
590	C₂²⋊Q₈	—	3	2	no	—
591	C₂²⋊Q₈	—	3	4	no	—
592	C₂²⋊Q₈	—	3	4	no	—
593	C₂²⋊Q₈	—	3	4	no	—
594	C₂²⋊Q₈	—	3	4	no	—
595	C₂²⋊Q₈	—	3	2	no	—
596	C₂²⋊Q₈	—	3	4	no	—
597	C₂²⋊Q₈	—	3	4	no	—
598	C₂²⋊Q₈	—	3	4	no	—
599	C₂²⋊Q₈	C₂×C₃×D₃	1	4	yes	complemented
600	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
601	C₄×Q₈	—	3	1	no	—
602	C₄×Q₈	—	3	2	no	—
603	C₄×Q₈	—	3	1	no	—
604	C₄×Q₈	—	3	1	no	—
605	C₄×Q₈	—	3	2	no	—
606	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
607	C₄×D₄	—	3	2	no	—
608	C₄×D₄	—	3	1	no	—
609	C₄×D₄	—	3	4	no	—
610	C₄×D₄	—	3	2	no	—
611	C₄×D₄	—	3	2	no	—
612	C₄×D₄	—	3	1	no	—
613	C₄×D₄	—	3	4	no	—
614	C₄×D₄	—	3	2	no	—
615	C₄×D₄	—	3	2	no	—
616	C₄×D₄	—	3	1	no	—
617	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
618	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	—	3	4	no	—
620	C₂×C₄⋊C₄	—	3	2	no	—
621	C₂×C₄⋊C₄	—	3	1	no	—
622	C₂×C₄⋊C₄	—	3	4	no	—
623	C₂×C₄⋊C₄	—	3	2	no	—
624	C₂×C₄⋊C₄	—	3	4	no	—
625	C₂×C₄⋊C₄	—	3	2	no	—
626	C₂×C₄⋊C₄	—	3	2	no	—
627	C₂×C₄⋊C₄	—	3	1	no	—
628	C₂×C₄⋊C₄	—	3	2	no	—
629	C₂×C₄⋊C₄	—	3	2	no	—
630	C₂×C₄⋊C₄	—	3	4	no	—
631	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
632	C₂×C₂²⋊C₄	—	3	4	no	—
633	C₂×C₂²⋊C₄	—	3	2	no	—
634	C₂×C₄²	—	3	2	no	—
635	C₂×C₄²	—	3	1	no	—
636	C₂³×C₃	—	2	2	no	—
637	C₂³×C₃	—	3	1	no	—
638	C₂³×C₃	—	3	8	no	—
639	C₂³×C₃	—	3	2	no	—
640	C₂³×C₃	—	6	4	no	—
641	C₂³×C₃	—	6	4	no	—
642	C₂³×C₃	C₂³×D₃	1	2	yes	—
643	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
644	C₂²×D₃	—	2	4	no	—
645	C₂²×D₃	—	2	4	no	—
646	C₂²×D₃	C₂×C₃×Q₈	1	8	yes	—
647	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
648	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
649	C₃×Q₈	—	2	2	no	—
650	C₃×Q₈	—	2	2	no	—
651	C₃×Q₈	—	4	2	no	—
652	C₃×Q₈	—	4	2	no	—
653	C₃×Q₈	—	4	2	no	—
654	C₃×Q₈	—	6	4	no	—
655	C₃×Q₈	—	6	2	no	—
656	C₃×Q₈	—	8	2	no	—
657	C₃×Q₈	—	12	4	no	—
658	C₃×Q₈	—	12	2	no	—
659	C₃×D₄	—	2	4	no	—
660	C₃×D₄	—	3	8	no	—
661	C₃×D₄	—	3	4	no	—
662	C₃×D₄	D₃×Q₈	1	4	yes	complemented
663	C₃×D₄	C₂×C₃×Q₈	1	4	yes	complemented
664	C₂×C₃×C₄	—	2	4	no	—
665	C₂×C₃×C₄	—	2	4	no	—
666	C₂×C₃×C₄	—	2	1	no	—
667	C₂×C₃×C₄	—	2	1	no	—
668	C₂×C₃×C₄	—	2	2	no	—
669	C₂×C₃×C₄	—	2	1	no	—
670	C₂×C₃×C₄	—	2	2	no	—
671	C₂×C₃×C₄	—	2	2	no	—
672	C₂×C₃×C₄	—	2	4	no	—
673	C₂×C₃×C₄	—	3	1	no	—
674	C₂×C₃×C₄	—	3	1	no	—
675	C₂×C₃×C₄	—	3	4	no	—
676	C₂×C₃×C₄	—	3	4	no	—
677	C₂×C₃×C₄	—	3	2	no	—
678	C₂×C₃×C₄	—	3	1	no	—
679	C₂×C₃×C₄	—	3	2	no	—
680	C₂×C₃×C₄	—	3	2	no	—
681	C₂×C₃×C₄	—	3	4	no	—
682	C₂×C₃×C₄	—	4	4	no	—
683	C₂×C₃×C₄	—	4	4	no	—
684	C₂×C₃×C₄	—	4	4	no	—
685	C₂×C₃×C₄	—	6	4	no	—
686	C₂×C₃×C₄	—	6	4	no	—
687	C₂×C₃×C₄	—	6	4	no	—
688	C₂×C₃×C₄	—	6	8	no	—
689	C₂×C₃×C₄	—	6	4	no	—
690	C₂×C₃×C₄	—	6	2	no	—
691	C₂×C₃×C₄	—	6	4	no	—
692	C₂×C₃×C₄	—	6	4	no	—
693	C₂×C₃×C₄	—	8	4	no	—
694	C₂×C₃×C₄	—	12	4	no	—
695	C₂×C₃×C₄	—	12	4	no	—
696	C₂×C₃×C₄	—	12	4	no	—
697	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
698	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
699	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
700	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
701	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
702	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
703	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
704	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
705	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
706	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
707	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
708	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
709	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
710	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
711	#67	C₂×C₃×Q₈	1	8	yes	complemented
712	C₂×Dic₃	—	2	4	no	—
713	C₂×Dic₃	—	4	4	no	—
714	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
715	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
716	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
717	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
718	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
719	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
720	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
721	D₁₂	C₂×C₃×Q₈	1	4	yes	complemented
722	C₄×D₃	—	2	4	no	—
723	C₄×D₃	—	2	4	no	—
724	C₄×D₃	—	2	4	no	—
725	C₄×D₃	—	2	8	no	—
726	C₄×D₃	—	2	2	no	—
727	C₄×D₃	—	2	4	no	—
728	C₄×D₃	—	2	4	no	—
729	C₄×D₃	—	4	4	no	—
730	C₄×D₃	—	4	4	no	—
731	C₄×D₃	C₂×C₃×Q₈	1	4	yes	—
732	C₄×D₃	C₃×#41	1	4	yes	—
733	Dic₆	—	2	2	no	—
734	Dic₆	—	2	4	no	—
735	Dic₆	—	4	4	no	—
736	Dic₆	—	4	2	no	—
737	C₂×C₃²	—	2	4	no	—
738	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
739	C₂×C₃²	C₂²×#41	1	1	yes	characteristic
740	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
741	C₃×D₃	—	2	4	no	—
742	C₃×D₃	#554	1	4	yes	direct product factor
743	C₂⁴	—	3	2	no	—
744	C₂×Q₈	—	3	2	no	—
745	C₂×Q₈	—	3	1	no	—
746	C₂×Q₈	—	3	4	no	—
747	C₂×Q₈	—	3	2	no	—
748	C₂×Q₈	—	6	4	no	—
749	C₂×Q₈	—	12	4	no	—
750	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
751	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
752	C₂×D₄	—	3	2	no	—
753	C₂×D₄	—	3	8	no	—
754	C₂×D₄	—	3	1	no	—
755	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
756	C₂²×C₄	—	3	1	no	—
757	C₂²×C₄	—	3	1	no	—
758	C₂²×C₄	—	3	2	no	—
759	C₂²×C₄	—	3	4	no	—
760	C₂²×C₄	—	3	2	no	—
761	C₂²×C₄	—	3	1	no	—
762	C₂²×C₄	—	3	2	no	—
763	C₂²×C₄	—	3	2	no	—
764	C₂²×C₄	—	3	4	no	—
765	C₂²×C₄	—	3	2	no	—
766	C₂²×C₄	—	3	2	no	—
767	C₂²×C₄	—	3	4	no	—
768	C₂²×C₄	—	3	4	no	—
769	C₂²×C₄	—	6	8	no	—
770	C₂²×C₄	—	12	8	no	—
771	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
772	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
773	C₄⋊C₄	—	3	2	no	—
774	C₄⋊C₄	—	3	1	no	—
775	C₄⋊C₄	—	3	4	no	—
776	C₄⋊C₄	—	3	4	no	—
777	C₄⋊C₄	—	3	4	no	—
778	C₄⋊C₄	—	3	4	no	—
779	C₄⋊C₄	—	3	2	no	—
780	C₄⋊C₄	—	3	2	no	—
781	C₄⋊C₄	—	3	1	no	—
782	C₄⋊C₄	—	3	4	no	—
783	C₄⋊C₄	—	3	2	no	—
784	C₄⋊C₄	—	3	2	no	—
785	C₄⋊C₄	—	3	2	no	—
786	C₄⋊C₄	—	3	2	no	—
787	C₄⋊C₄	—	3	4	no	—
788	C₄⋊C₄	—	3	4	no	—
789	C₄⋊C₄	—	3	4	no	—
790	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
792	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
793	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
795	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
796	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
797	C₂²⋊C₄	—	3	4	no	—
798	C₂²⋊C₄	—	3	2	no	—
799	C₂²⋊C₄	—	3	4	no	—
800	C₂²⋊C₄	—	3	2	no	—
801	C₂²⋊C₄	—	3	2	no	—
802	C₂²⋊C₄	—	3	4	no	—
803	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
804	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
805	C₄²	—	3	2	no	—
806	C₄²	—	3	2	no	—
807	C₄²	—	3	2	no	—
808	C₄²	—	3	1	no	—
809	C₄²	—	3	1	no	—
810	C₄²	—	3	1	no	—
811	C₄²	C₂²×C₃×D₃	1	2	yes	—
812	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
813	C₂²×C₃	—	2	2	no	—
814	C₂²×C₃	—	2	2	no	—
815	C₂²×C₃	—	2	2	no	—
816	C₂²×C₃	—	2	2	no	—
817	C₂²×C₃	—	2	4	no	—
818	C₂²×C₃	—	2	1	no	—
819	C₂²×C₃	—	3	2	no	—
820	C₂²×C₃	—	3	2	no	—
821	C₂²×C₃	—	3	2	no	—
822	C₂²×C₃	—	3	4	no	—
823	C₂²×C₃	—	4	2	no	—
824	C₂²×C₃	—	4	2	no	—
825	C₂²×C₃	—	6	16	no	—
826	C₂²×C₃	—	6	2	no	—
827	C₂²×C₃	—	6	2	no	—
828	C₂²×C₃	C₂×D₃×Q₈	1	4	yes	—
829	C₂²×C₃	C₂²×C₃×Q₈	1	4	yes	—
830	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
831	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
832	C₂×D₃	—	2	2	no	—
833	C₂×D₃	—	2	2	no	—
834	C₂×D₃	—	2	16	no	—
835	C₂×D₃	C₂²×C₃×Q₈	1	4	yes	—
836	C₂×D₃	C₂²×C₃×Q₈	1	2	yes	—
837	C₂×D₃	C₂×C₃×#41	1	2	yes	—
838	C₂×D₃	C₃×H(5,𝔽₂)	1	2	yes	—
839	C₃×C₄	—	2	2	no	—
840	C₃×C₄	—	2	2	no	—
841	C₃×C₄	—	2	2	no	—
842	C₃×C₄	—	2	4	no	—
843	C₃×C₄	—	2	1	no	—
844	C₃×C₄	—	2	2	no	—
845	C₃×C₄	—	2	2	no	—
846	C₃×C₄	—	2	1	no	—
847	C₃×C₄	—	2	4	no	—
848	C₃×C₄	—	2	2	no	—
849	C₃×C₄	—	2	2	no	—
850	C₃×C₄	—	2	2	no	—
851	C₃×C₄	—	3	2	no	—
852	C₃×C₄	—	3	2	no	—
853	C₃×C₄	—	4	2	no	—
854	C₃×C₄	—	4	2	no	—
855	C₃×C₄	—	4	4	no	—
856	C₃×C₄	—	4	2	no	—
857	C₃×C₄	—	4	1	no	—
858	C₃×C₄	—	6	2	no	—
859	C₃×C₄	—	6	2	no	—
860	C₃×C₄	—	6	2	no	—
861	C₃×C₄	—	6	4	no	—
862	C₃×C₄	—	6	1	no	—
863	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
864	C₃×C₄	D₃×#41	1	2	yes	—
865	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
866	C₃×C₄	C₂×C₃×#41	1	2	yes	—
867	Dic₃	—	2	2	no	—
868	Dic₃	—	2	2	no	—
869	Dic₃	—	2	1	no	—
870	Dic₃	—	2	4	no	—
871	Dic₃	—	2	2	no	—
872	Dic₃	C₂²×C₃×Q₈	1	2	yes	—
873	Dic₃	C₂×C₃×#41	1	2	yes	—
874	C₃²	C₂×#554	1	1	yes	characteristic, complemented, Sylow
875	C₂³	—	3	1	no	—
876	C₂³	—	3	8	no	—
877	C₂³	—	3	2	no	—
878	C₂³	—	6	4	no	—
879	C₂³	—	6	4	no	—
880	C₂³	C₂³×C₃×D₃	1	2	yes	—
881	Q₈	—	2	2	no	—
882	Q₈	—	4	2	no	—
883	Q₈	—	6	4	no	—
884	Q₈	—	6	2	no	—
885	Q₈	—	12	4	no	—
886	Q₈	—	12	2	no	—
887	D₄	—	3	8	no	—
888	D₄	—	3	4	no	—
889	D₄	C₃×D₃×Q₈	1	4	yes	complemented
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	3	1	no	—
892	C₂×C₄	—	3	1	no	—
893	C₂×C₄	—	3	4	no	—
894	C₂×C₄	—	3	4	no	—
895	C₂×C₄	—	3	2	no	—
896	C₂×C₄	—	3	1	no	—
897	C₂×C₄	—	3	2	no	—
898	C₂×C₄	—	3	2	no	—
899	C₂×C₄	—	3	4	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	6	4	no	—
902	C₂×C₄	—	6	4	no	—
903	C₂×C₄	—	6	4	no	—
904	C₂×C₄	—	6	8	no	—
905	C₂×C₄	—	6	4	no	—
906	C₂×C₄	—	6	2	no	—
907	C₂×C₄	—	6	4	no	—
908	C₂×C₄	—	6	4	no	—
909	C₂×C₄	—	12	4	no	—
910	C₂×C₄	—	12	4	no	—
911	C₂×C₄	—	12	4	no	—
912	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
913	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
914	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
915	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
916	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
917	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
918	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
919	C₂×C₃	—	2	4	no	—
920	C₂×C₃	—	2	4	no	—
921	C₂×C₃	—	2	1	no	—
922	C₂×C₃	—	2	1	no	—
923	C₂×C₃	—	2	1	no	—
924	C₂×C₃	—	3	4	no	—
925	C₂×C₃	—	4	4	no	—
926	C₂×C₃	—	6	4	no	—
927	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
928	C₂×C₃	C₂×D₃×#41	1	1	yes	characteristic
929	C₂×C₃	D₃×H(5,𝔽₂)	1	1	yes	characteristic
930	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
931	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
932	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
933	D₃	—	2	4	no	—
934	D₃	C₃×#554	1	4	yes	direct product factor
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	3	2	no	—
938	C₂²	—	3	2	no	—
939	C₂²	—	3	2	no	—
940	C₂²	—	3	4	no	—
941	C₂²	—	6	16	no	—
942	C₂²	—	6	2	no	—
943	C₂²	—	6	2	no	—
944	C₂²	C₂×C₃×D₃×Q₈	1	4	yes	—
945	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	4	no	—
950	C₄	—	2	1	no	—
951	C₄	—	3	2	no	—
952	C₄	—	3	2	no	—
953	C₄	—	6	2	no	—
954	C₄	—	6	2	no	—
955	C₄	—	6	2	no	—
956	C₄	—	6	4	no	—
957	C₄	—	6	1	no	—
958	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
959	C₄	C₃×D₃×#41	1	2	yes	—
960	C₃	—	2	1	no	—
961	C₃	D₃×#554	1	1	yes	characteristic, direct product factor
962	C₃	C₂×C₃×#554	1	1	yes	characteristic, complemented
963	C₂	—	2	4	no	—
964	C₂	—	3	4	no	—
965	C₂	—	6	4	no	—
966	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
967	C₂	C₂×C₃×D₃×#41	1	1	yes	characteristic
968	C₂	C₃×D₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₃²×#554	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂×C₃×D₃×D₄	C₂²
hypercenter	C₃×#554	D₃
hypocenter	C₃	C₂×C₃×#554
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#554

Complements

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

N	H ≅ G/N	type
1. C₃²×#554	C₂	semidirect
2. C₃×#5730	C₂	semidirect
3. C₃×D₃×C₄⋊Q₈	C₂	semidirect
4. C₃×#5690	C₂	semidirect
5. C₃×D₃×#125	C₂	semidirect
6. C₃×#5636	C₂	semidirect
7. C₃×#5635	C₂	semidirect
8. C₃×D₃×C₂²⋊Q₈	C₂	semidirect
9. C₃×D₃×C₂²⋊Q₈	C₂	semidirect
10. C₃×#5579	C₂	semidirect
11. C₃×C₄×D₃×Q₈	C₂	semidirect
14. C₃×#5543	C₂	semidirect
15. C₃×#5539	C₂	semidirect
16. C₃×#5511	C₂	semidirect
17. C₂×C₃×D₃×C₄⋊C₄	C₂	semidirect
19. D₃×#554	C₃	direct (N × H)
25. C₃²×C₄⋊Q₈	C₂²	semidirect
26. C₃²×#125	C₂²	semidirect
27. C₃²×C₂²⋊Q₈	C₂²	semidirect
28. C₃²×C₂²⋊Q₈	C₂²	semidirect
29. C₃²×C₄×Q₈	C₂²	semidirect
32. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
33. C₃×#946	C₂²	semidirect
34. C₃×#946	C₂²	semidirect
35. C₃×Q₈×Dic₃	C₂²	semidirect
36. C₃×#944	C₂²	semidirect
41. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
42. C₃×#924	C₂²	semidirect
43. C₃×#924	C₂²	semidirect
44. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
45. C₃×#897	C₂²	semidirect
46. C₃×#897	C₂²	semidirect
47. C₃×#896	C₂²	semidirect
48. C₃×#896	C₂²	semidirect
49. C₃×#896	C₂²	semidirect
59. C₃×D₃×C₄⋊C₄	C₂²	semidirect
60. C₃×D₃×C₄⋊C₄	C₂²	semidirect
61. C₃×D₃×C₄⋊C₄	C₂²	semidirect
62. C₃×#890	C₂²	semidirect
63. C₃×#890	C₂²	semidirect
64. C₃×#889	C₂²	semidirect
65. C₃×#889	C₂²	semidirect
66. C₃×#888	C₂²	semidirect
67. C₃×#888	C₂²	semidirect
68. C₃×#887	C₂²	semidirect
69. C₃×#887	C₂²	semidirect
74. C₃×#878	C₂²	semidirect
75. C₃×#878	C₂²	semidirect
76. C₃×#878	C₂²	semidirect
81. C₃×#870	C₂²	semidirect
82. C₃×#869	C₂²	semidirect
83. C₃×C₄×Dic₆	C₂²	semidirect
84. C₃×C₄×Dic₆	C₂²	semidirect
94. C₃×#554	D₃	direct (N × H)
95. C₃×#554	C₂×C₃	semidirect
104. #5730	C₂×C₃	semidirect
105. D₃×C₄⋊Q₈	C₂×C₃	semidirect
106. #5690	C₂×C₃	semidirect
107. D₃×#125	C₂×C₃	semidirect
108. #5636	C₂×C₃	semidirect
109. #5635	C₂×C₃	semidirect
110. D₃×C₂²⋊Q₈	C₂×C₃	semidirect
111. D₃×C₂²⋊Q₈	C₂×C₃	semidirect
112. #5579	C₂×C₃	semidirect
113. C₄×D₃×Q₈	C₂×C₃	semidirect
116. #5543	C₂×C₃	semidirect
117. #5539	C₂×C₃	semidirect
118. #5511	C₂×C₃	semidirect
119. C₂×D₃×C₄⋊C₄	C₂×C₃	semidirect
131. C₃×D₃×D₄	Q₈	semidirect
206. C₃×C₄⋊Q₈	C₂×D₃	semidirect
207. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
214. C₃×#125	C₂×D₃	semidirect
215. C₃×#125	C₂²×C₃	semidirect
230. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
231. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
232. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
233. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
240. C₃×C₄×Q₈	C₂×D₃	semidirect
241. C₃×C₄×Q₈	C₂²×C₃	semidirect
271. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
272. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
277. #946	C₂²×C₃	semidirect
278. #946	C₂²×C₃	semidirect
279. Q₈×Dic₃	C₂²×C₃	semidirect
280. #944	C₂²×C₃	semidirect
285. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
286. #924	C₂²×C₃	semidirect
287. #924	C₂²×C₃	semidirect
288. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
289. #897	C₂²×C₃	semidirect
290. #897	C₂²×C₃	semidirect
291. #896	C₂²×C₃	semidirect
292. #896	C₂²×C₃	semidirect
293. #896	C₂²×C₃	semidirect
303. D₃×C₄⋊C₄	C₂²×C₃	semidirect
304. D₃×C₄⋊C₄	C₂²×C₃	semidirect
305. D₃×C₄⋊C₄	C₂²×C₃	semidirect
306. #890	C₂²×C₃	semidirect
307. #890	C₂²×C₃	semidirect
308. #889	C₂²×C₃	semidirect
309. #889	C₂²×C₃	semidirect
310. #888	C₂²×C₃	semidirect
311. #888	C₂²×C₃	semidirect
312. #887	C₂²×C₃	semidirect
313. #887	C₂²×C₃	semidirect
318. #878	C₂²×C₃	semidirect
319. #878	C₂²×C₃	semidirect
320. #878	C₂²×C₃	semidirect
325. #870	C₂²×C₃	semidirect
326. #869	C₂²×C₃	semidirect
327. C₄×Dic₆	C₂²×C₃	semidirect
328. C₄×Dic₆	C₂²×C₃	semidirect
337. C₃²×D₄	C₂×Q₈	semidirect
347. C₃×#67	C₂×Q₈	semidirect
357. C₃×D₁₂	C₂×Q₈	semidirect
381. #554	C₃×D₃	direct (N × H)
436. D₃×D₄	C₃×Q₈	semidirect
580. C₄⋊Q₈	C₂×C₃×D₃	semidirect
586. #125	C₂×C₃×D₃	semidirect
599. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
600. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
606. C₄×Q₈	C₂×C₃×D₃	semidirect
631. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
662. C₃×D₄	D₃×Q₈	semidirect
663. C₃×D₄	C₂×C₃×Q₈	semidirect
711. #67	C₂×C₃×Q₈	semidirect
721. D₁₂	C₂×C₃×Q₈	semidirect
742. C₃×D₃	#554	direct (N × H)
874. C₃²	C₂×#554	semidirect
889. D₄	C₃×D₃×Q₈	semidirect
934. D₃	C₃×#554	direct (N × H)
961. C₃	D₃×#554	direct (N × H)
962. C₃	C₂×C₃×#554	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#554	2
C₃×#5730	2
C₃×D₃×C₄⋊Q₈	2
C₃×#5690	2
C₃×D₃×#125	2
C₃×#5636	2
C₃×#5635	2
C₃×D₃×C₂²⋊Q₈	2
C₃×#5579	2
C₃×C₄×D₃×Q₈	2
C₃×C₄×D₃×D₄	2
C₃×#5543	2
C₃×#5539	2
C₃×#5511	2
C₂×C₃×D₃×C₄⋊C₄	2
C₂×C₃×#554	3
D₃×#554	3

Subgroups — C3×D3×#554 #11903213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#554 #11903213