Subgroups — C₃×#86948 #11906160

Order 1152.

2314 conjugacy classes of subgroups.

The subgroup lattice has 958 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×#5728	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5690	C₂	1	2	yes	maximal, complemented
5	C₃×#5689	C₂	1	2	yes	maximal, complemented
6	C₃×#5635	C₂	1	4	yes	maximal, complemented
7	C₃×#5634	C₂	1	4	yes	maximal, complemented
8	C₃×#5632	C₂	1	2	yes	maximal, complemented
9	C₃×D₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
10	C₃×#5578	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×Q₈×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5545	C₂	1	2	yes	maximal
13	C₃×C₄×D₃×D₄	C₂	1	1	yes	maximal, characteristic
14	C₃×#5543	C₂	1	2	yes	maximal, complemented
15	C₃×D₄×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5511	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×#897	C₂	1	2	yes	maximal, complemented
18	C₃×#3501	—	3	1	no	maximal
19	#86948	C₃	1	1	yes	maximal, characteristic, direct product factor
20	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	complemented
21	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₃	C₂²	1	2	yes	—
23	C₂²×C₃×Dic₆	C₂²	1	2	yes	complemented
24	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃²×#125	C₂²	1	2	yes	complemented
26	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃²×C₂²⋊Q₈	C₂²	1	4	yes	complemented
28	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
30	C₃²×C₄×D₄	C₂²	1	2	yes	—
31	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
32	C₃×#946	C₂²	1	1	yes	characteristic
33	C₃×#946	C₂²	1	2	yes	—
34	C₃×#946	C₂²	1	4	yes	complemented
35	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
36	C₃×#944	C₂²	1	1	yes	characteristic, complemented
37	C₃×D₄×Dic₃	C₂²	1	2	yes	—
38	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×C₄×#67	C₂²	1	2	yes	—
40	C₃×C₄×#67	C₂²	1	4	yes	—
41	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
42	C₂×C₃×C₄⋊Dic₃	C₂²	1	4	yes	complemented
43	C₃×#924	C₂²	1	2	yes	complemented
44	C₃×#924	C₂²	1	4	yes	complemented
45	C₃×#897	C₂²	1	1	yes	characteristic
46	C₃×#897	C₂²	1	2	yes	—
47	C₃×#897	C₂²	1	4	yes	—
48	C₃×#897	C₂²	1	2	yes	complemented
49	C₃×#897	C₂²	1	2	yes	complemented
50	C₃×#897	C₂²	1	4	yes	complemented
51	C₃×#897	C₂²	1	4	yes	complemented
52	C₃×#896	C₂²	1	2	yes	—
53	C₃×#896	C₂²	1	4	yes	—
54	C₃×#896	C₂²	1	4	yes	complemented
55	C₃×#896	C₂²	1	4	yes	complemented
56	C₃×#893	C₂²	1	1	yes	characteristic
57	C₃×#893	C₂²	1	2	yes	—
58	C₃×#892	C₂²	1	2	yes	—
59	C₃×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	complemented
66	C₃×#888	C₂²	1	1	yes	characteristic, complemented
67	C₃×#888	C₂²	1	2	yes	complemented
68	C₃×#888	C₂²	1	4	yes	complemented
69	C₃×#887	C₂²	1	2	yes	complemented
70	C₃×#67⋊C₄	C₂²	1	2	yes	—
71	C₃×#67⋊C₄	C₂²	1	4	yes	—
72	C₃×D₃×C₂²⋊C₄	C₂²	1	2	yes	—
73	C₃×D₃×C₂²⋊C₄	C₂²	1	4	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	1	yes	characteristic
78	C₃×C₄×D₁₂	C₂²	1	2	yes	—
79	C₃×#872	C₂²	1	2	yes	—
80	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
81	C₃×#869	C₂²	1	1	yes	characteristic, complemented
82	C₃×#869	C₂²	1	2	yes	complemented
83	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic, complemented
84	C₃×C₄×Dic₆	C₂²	1	2	yes	complemented
85	C₃×#554	—	2	1	no	—
86	C₃×#554	—	3	1	no	—
87	C₃×#554	—	3	2	no	—
88	C₃×#554	—	3	4	no	—
89	C₃×#554	—	3	2	no	—
90	C₃×#554	—	3	2	no	—
91	C₃×#554	D₃	1	1	yes	characteristic, complemented
92	C₃×#554	C₂×C₃	1	1	yes	characteristic, complemented
93	C₃×D₄×Q₈	—	3	2	no	—
94	C₃×D₄×Q₈	—	3	1	no	—
95	C₃×D₄×Q₈	—	3	1	no	—
96	C₃×#544	—	3	2	no	—
97	C₃×#543	—	3	4	no	—
98	C₃×#533	—	3	1	no	—
99	C₃×#533	—	3	1	no	—
100	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
101	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
102	C₃×#518	—	3	2	no	—
103	C₂×C₃×C₄×D₄	—	3	1	no	—
104	#5730	C₂×C₃	1	1	yes	characteristic, complemented
105	#5728	C₂×C₃	1	1	yes	characteristic, complemented
106	#5690	C₂×C₃	1	2	yes	complemented
107	#5689	C₂×C₃	1	2	yes	complemented
108	#5635	C₂×C₃	1	4	yes	complemented
109	#5634	C₂×C₃	1	4	yes	complemented
110	#5632	C₂×C₃	1	2	yes	complemented
111	D₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
112	#5578	C₂×C₃	1	1	yes	characteristic, complemented
113	Q₈×D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
114	#5545	C₂×C₃	1	2	yes	—
115	C₄×D₃×D₄	C₂×C₃	1	1	yes	characteristic
116	#5543	C₂×C₃	1	2	yes	complemented
117	D₄×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
118	#5511	C₂×C₃	1	2	yes	complemented
119	C₂×#897	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	—	4	4	no	—
130	C₃×D₃×D₄	Q₈	1	8	yes	complemented
131	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₄×D₃	—	4	4	no	—
133	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
134	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
136	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
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	1	yes	characteristic
141	C₂×C₃×Dic₆	—	4	4	no	—
142	C₂×C₃×Dic₆	C₂³	1	2	yes	—
143	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
144	C₂×C₃×Dic₆	C₂³	1	4	yes	—
145	C₂×C₃×Dic₆	C₂³	1	4	yes	—
146	C₂×C₃×Dic₆	C₂³	1	2	yes	—
147	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
148	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₃²×C₄⋊C₄	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	4	yes	—
153	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
154	C₃²×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
156	C₃²×C₄²	C₂³	1	2	yes	—
157	C₃²×C₄²	C₂³	1	1	yes	characteristic
158	C₃×#217	C₂³	1	2	yes	—
159	C₃×#217	C₂³	1	4	yes	—
160	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
161	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
162	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
163	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
164	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	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	1	yes	characteristic
172	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
173	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
174	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
175	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
176	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
177	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
178	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
179	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
180	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
181	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
182	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
183	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
184	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
185	C₃×C₄×Dic₃	C₂³	1	4	yes	—
186	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
187	C₃×C₄×Dic₃	C₂³	1	2	yes	—
188	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
189	#3501	—	3	1	no	Sylow
190	C₂²×C₃×Q₈	—	3	2	no	—
191	C₂²×C₃×Q₈	—	3	2	no	—
192	C₂²×C₃×D₄	—	3	1	no	—
193	C₂³×C₃×C₄	—	3	2	no	—
194	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	complemented
195	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
196	C₂²×C₄×D₃	C₂²×C₃	1	2	yes	—
197	C₂²×Dic₆	C₂²×C₃	1	2	yes	complemented
198	C₃×C₄⋊Q₈	—	2	1	no	—
199	C₃×C₄⋊Q₈	—	3	1	no	—
200	C₃×C₄⋊Q₈	—	3	1	no	—
201	C₃×C₄⋊Q₈	—	3	4	no	—
202	C₃×C₄⋊Q₈	—	3	2	no	—
203	C₃×C₄⋊Q₈	—	3	1	no	—
204	C₃×C₄⋊Q₈	—	3	2	no	—
205	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
206	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
207	C₃×#125	—	2	2	no	—
208	C₃×#125	—	3	2	no	—
209	C₃×#125	—	3	4	no	—
210	C₃×#125	—	3	2	no	—
211	C₃×#125	—	3	2	no	—
212	C₃×#125	C₂×D₃	1	2	yes	complemented
213	C₃×#125	C₂²×C₃	1	2	yes	complemented
214	C₃×C₂²⋊Q₈	—	2	2	no	—
215	C₃×C₂²⋊Q₈	—	2	4	no	—
216	C₃×C₂²⋊Q₈	—	3	1	no	—
217	C₃×C₂²⋊Q₈	—	3	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	4	no	—
222	C₃×C₂²⋊Q₈	—	3	2	no	—
223	C₃×C₂²⋊Q₈	—	3	4	no	—
224	C₃×C₂²⋊Q₈	—	3	4	no	—
225	C₃×C₂²⋊Q₈	—	3	2	no	—
226	C₃×C₂²⋊Q₈	—	3	1	no	—
227	C₃×C₂²⋊Q₈	—	3	4	no	—
228	C₃×C₂²⋊Q₈	—	3	2	no	—
229	C₃×C₂²⋊Q₈	—	3	2	no	—
230	C₃×C₂²⋊Q₈	—	3	4	no	—
231	C₃×C₂²⋊Q₈	—	3	4	no	—
232	C₃×C₂²⋊Q₈	—	3	4	no	—
233	C₃×C₂²⋊Q₈	—	3	4	no	—
234	C₃×C₂²⋊Q₈	—	3	4	no	—
235	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
236	C₃×C₂²⋊Q₈	C₂×D₃	1	4	yes	complemented
237	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
238	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
239	C₃×C₄×Q₈	—	2	1	no	—
240	C₃×C₄×Q₈	—	3	2	no	—
241	C₃×C₄×Q₈	—	3	2	no	—
242	C₃×C₄×Q₈	—	3	1	no	—
243	C₃×C₄×Q₈	—	3	2	no	—
244	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
245	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
246	C₃×C₄×D₄	—	2	1	no	—
247	C₃×C₄×D₄	—	2	2	no	—
248	C₃×C₄×D₄	—	3	1	no	—
249	C₃×C₄×D₄	—	3	2	no	—
250	C₃×C₄×D₄	—	3	2	no	—
251	C₃×C₄×D₄	—	3	4	no	—
252	C₃×C₄×D₄	—	3	1	no	—
253	C₃×C₄×D₄	—	3	2	no	—
254	C₃×C₄×D₄	—	3	2	no	—
255	C₃×C₄×D₄	—	3	4	no	—
256	C₃×C₄×D₄	—	3	1	no	—
257	C₃×C₄×D₄	—	3	2	no	—
258	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
259	C₃×C₄×D₄	C₂×D₃	1	2	yes	—
260	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
261	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
262	C₃×#117	—	3	2	no	—
263	C₃×#117	—	3	2	no	—
264	C₂×C₃×C₄⋊C₄	—	2	2	no	—
265	C₂×C₃×C₄⋊C₄	—	3	4	no	—
266	C₂×C₃×C₄⋊C₄	—	3	1	no	—
267	C₂×C₃×C₄⋊C₄	—	3	4	no	—
268	C₂×C₃×C₄⋊C₄	—	3	2	no	—
269	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
270	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
271	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
272	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
273	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
274	C₂×C₃×C₄²	—	3	1	no	—
275	#946	C₂²×C₃	1	2	yes	—
276	#946	C₂²×C₃	1	1	yes	characteristic
277	#946	C₂²×C₃	1	4	yes	complemented
278	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
279	#944	C₂²×C₃	1	1	yes	characteristic, complemented
280	D₄×Dic₃	C₂²×C₃	1	2	yes	—
281	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
282	C₄×#67	C₂²×C₃	1	2	yes	—
283	C₄×#67	C₂²×C₃	1	4	yes	—
284	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
285	C₂×C₄⋊Dic₃	C₂²×C₃	1	4	yes	complemented
286	#924	C₂²×C₃	1	4	yes	complemented
287	#924	C₂²×C₃	1	2	yes	complemented
288	#897	C₂²×C₃	1	4	yes	—
289	#897	C₂²×C₃	1	2	yes	—
290	#897	C₂²×C₃	1	1	yes	characteristic
291	#897	C₂²×C₃	1	2	yes	complemented
292	#897	C₂²×C₃	1	4	yes	complemented
293	#897	C₂²×C₃	1	4	yes	complemented
294	#897	C₂²×C₃	1	2	yes	complemented
295	#896	C₂²×C₃	1	2	yes	—
296	#896	C₂²×C₃	1	4	yes	—
297	#896	C₂²×C₃	1	4	yes	complemented
298	#896	C₂²×C₃	1	4	yes	complemented
299	#893	C₂²×C₃	1	1	yes	characteristic
300	#893	C₂²×C₃	1	2	yes	—
301	#892	C₂²×C₃	1	2	yes	—
302	D₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
303	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
304	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
305	#890	C₂²×C₃	1	2	yes	complemented
306	#890	C₂²×C₃	1	2	yes	complemented
307	#889	C₂²×C₃	1	2	yes	complemented
308	#889	C₂²×C₃	1	4	yes	complemented
309	#888	C₂²×C₃	1	4	yes	complemented
310	#888	C₂²×C₃	1	2	yes	complemented
311	#888	C₂²×C₃	1	1	yes	characteristic, complemented
312	#887	C₂²×C₃	1	2	yes	complemented
313	#67⋊C₄	C₂²×C₃	1	4	yes	—
314	#67⋊C₄	C₂²×C₃	1	2	yes	—
315	D₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
316	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
317	#878	C₂²×C₃	1	4	yes	complemented
318	#878	C₂²×C₃	1	4	yes	complemented
319	#878	C₂²×C₃	1	4	yes	complemented
320	C₄×D₁₂	C₂²×C₃	1	2	yes	—
321	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
322	#872	C₂²×C₃	1	2	yes	—
323	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
324	#869	C₂²×C₃	1	2	yes	complemented
325	#869	C₂²×C₃	1	1	yes	characteristic, complemented
326	C₄×Dic₆	C₂²×C₃	1	2	yes	complemented
327	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
328	C₂³×C₃²	C₂⁴	1	2	yes	—
329	C₂²×C₃×D₃	—	4	2	no	—
330	C₂²×C₃×D₃	—	4	2	no	—
331	C₂²×C₃×D₃	C₂×Q₈	1	8	yes	complemented
332	C₂²×C₃×D₃	C₂⁴	1	1	yes	characteristic
333	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
334	C₃²×Q₈	—	2	2	no	—
335	C₃²×Q₈	—	4	2	no	—
336	C₃²×D₄	C₂×Q₈	1	4	yes	complemented
337	C₂×C₃²×C₄	—	2	4	no	—
338	C₂×C₃²×C₄	—	4	4	no	—
339	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
340	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
341	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
342	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
343	C₂×C₃²×C₄	C₂⁴	1	2	yes	—
344	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
345	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
346	C₃×#67	C₂×Q₈	1	8	yes	complemented
347	C₂×C₃×Dic₃	—	4	4	no	—
348	C₂×C₃×Dic₃	—	4	2	no	—
349	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
352	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
353	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
354	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
355	C₂×C₃×Dic₃	C₂⁴	1	1	yes	characteristic
356	C₃×D₁₂	C₂×Q₈	1	4	yes	complemented
357	C₃×C₄×D₃	—	2	2	no	—
358	C₃×C₄×D₃	—	2	4	no	—
359	C₃×C₄×D₃	—	4	2	no	—
360	C₃×C₄×D₃	—	4	2	no	—
361	C₃×C₄×D₃	—	4	1	no	—
362	C₃×C₄×D₃	—	4	4	no	—
363	C₃×C₄×D₃	—	4	4	no	—
364	C₃×C₄×D₃	C₂×Q₈	1	4	yes	complemented
365	C₃×Dic₆	—	2	2	no	—
366	C₃×Dic₆	—	2	4	no	—
367	C₃×Dic₆	—	4	4	no	—
368	C₃×Dic₆	—	4	2	no	—
369	C₃×Dic₆	—	4	4	no	—
370	#554	—	3	1	no	—
371	#554	—	3	2	no	—
372	#554	—	3	4	no	—
373	#554	—	3	2	no	—
374	#554	—	3	2	no	—
375	#554	C₃×D₃	1	1	yes	characteristic, complemented
376	D₄×Q₈	—	3	2	no	—
377	D₄×Q₈	—	3	1	no	—
378	D₄×Q₈	—	3	1	no	—
379	#544	—	3	2	no	—
380	#543	—	3	4	no	—
381	#533	—	3	1	no	—
382	#533	—	3	1	no	—
383	C₂×C₂²⋊Q₈	—	3	2	no	—
384	C₂×C₂²⋊Q₈	—	3	2	no	—
385	#518	—	3	2	no	—
386	C₂×C₄×D₄	—	3	1	no	—
387	C₂⁴×C₃	—	3	2	no	—
388	C₂³×D₃	C₂³×C₃	1	2	yes	—
389	C₂×C₃×Q₈	—	2	1	no	—
390	C₂×C₃×Q₈	—	2	2	no	—
391	C₂×C₃×Q₈	—	3	2	no	—
392	C₂×C₃×Q₈	—	3	1	no	—
393	C₂×C₃×Q₈	—	3	2	no	—
394	C₂×C₃×Q₈	—	3	4	no	—
395	C₂×C₃×Q₈	—	3	4	no	—
396	C₂×C₃×Q₈	—	12	4	no	—
397	C₂×C₃×Q₈	—	12	4	no	—
398	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
399	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
400	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
401	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
402	C₂×C₃×D₄	—	2	1	no	—
403	C₂×C₃×D₄	—	3	2	no	—
404	C₂×C₃×D₄	—	3	8	no	—
405	C₂×C₃×D₄	—	3	1	no	—
406	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
407	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
408	C₂²×C₃×C₄	—	2	2	no	—
409	C₂²×C₃×C₄	—	2	4	no	—
410	C₂²×C₃×C₄	—	3	1	no	—
411	C₂²×C₃×C₄	—	3	4	no	—
412	C₂²×C₃×C₄	—	3	2	no	—
413	C₂²×C₃×C₄	—	3	1	no	—
414	C₂²×C₃×C₄	—	3	2	no	—
415	C₂²×C₃×C₄	—	3	1	no	—
416	C₂²×C₃×C₄	—	3	4	no	—
417	C₂²×C₃×C₄	—	3	4	no	—
418	C₂²×C₃×C₄	—	3	2	no	—
419	C₂²×C₃×C₄	—	3	2	no	—
420	C₂²×C₃×C₄	—	12	4	no	—
421	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
422	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
423	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
424	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
425	C₂×#67	C₂³×C₃	1	2	yes	—
426	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
427	C₂²×Dic₃	C₂³×C₃	1	4	yes	—
428	D₃×Q₈	—	4	4	no	—
429	D₃×D₄	C₃×Q₈	1	8	yes	complemented
430	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
431	C₂×C₄×D₃	—	4	4	no	—
432	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
433	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
434	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
436	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
437	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
438	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
439	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
440	C₂×Dic₆	—	4	4	no	—
441	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
442	C₂×Dic₆	C₂³×C₃	1	2	yes	—
443	C₂×Dic₆	C₂³×C₃	1	2	yes	—
444	C₂×Dic₆	C₂³×C₃	1	4	yes	—
445	C₂×Dic₆	C₂³×C₃	1	4	yes	—
446	C₃×C₄⋊C₄	—	2	1	no	—
447	C₃×C₄⋊C₄	—	2	4	no	—
448	C₃×C₄⋊C₄	—	2	2	no	—
449	C₃×C₄⋊C₄	—	2	1	no	—
450	C₃×C₄⋊C₄	—	2	2	no	—
451	C₃×C₄⋊C₄	—	2	2	no	—
452	C₃×C₄⋊C₄	—	2	4	no	—
453	C₃×C₄⋊C₄	—	3	2	no	—
454	C₃×C₄⋊C₄	—	3	2	no	—
455	C₃×C₄⋊C₄	—	3	4	no	—
456	C₃×C₄⋊C₄	—	3	4	no	—
457	C₃×C₄⋊C₄	—	3	2	no	—
458	C₃×C₄⋊C₄	—	3	2	no	—
459	C₃×C₄⋊C₄	—	3	4	no	—
460	C₃×C₄⋊C₄	—	3	2	no	—
461	C₃×C₄⋊C₄	—	3	2	no	—
462	C₃×C₄⋊C₄	—	3	4	no	—
463	C₃×C₄⋊C₄	—	3	2	no	—
464	C₃×C₄⋊C₄	—	3	1	no	—
465	C₃×C₄⋊C₄	—	3	1	no	—
466	C₃×C₄⋊C₄	—	3	4	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	C₂²×D₃	1	2	yes	—
471	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
472	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
473	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
474	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
475	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
476	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
477	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
478	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
479	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
480	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
481	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
483	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
484	C₃×C₂²⋊C₄	—	2	4	no	—
485	C₃×C₂²⋊C₄	—	2	2	no	—
486	C₃×C₂²⋊C₄	—	3	2	no	—
487	C₃×C₂²⋊C₄	—	3	4	no	—
488	C₃×C₂²⋊C₄	—	3	2	no	—
489	C₃×C₂²⋊C₄	—	3	4	no	—
490	C₃×C₂²⋊C₄	—	3	2	no	—
491	C₃×C₂²⋊C₄	—	3	2	no	—
492	C₃×C₂²⋊C₄	—	3	4	no	—
493	C₃×C₂²⋊C₄	—	3	4	no	—
494	C₃×C₂²⋊C₄	—	3	2	no	—
495	C₃×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
496	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
497	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
498	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
499	C₃×C₄²	—	2	2	no	—
500	C₃×C₄²	—	2	1	no	—
501	C₃×C₄²	—	3	1	no	—
502	C₃×C₄²	—	3	1	no	—
503	C₃×C₄²	—	3	1	no	—
504	C₃×C₄²	—	3	4	no	—
505	C₃×C₄²	—	3	2	no	—
506	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
507	C₃×C₄²	C₂²×D₃	1	2	yes	—
508	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
509	C₃×C₄²	C₂³×C₃	1	2	yes	—
510	#217	C₂³×C₃	1	2	yes	—
511	#217	C₂³×C₃	1	4	yes	—
512	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
513	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
514	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
515	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
516	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
517	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
518	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
519	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
520	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
521	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
522	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
523	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
524	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
525	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
526	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
527	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
528	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
529	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
530	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
531	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
532	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
533	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
534	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
535	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
536	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
537	C₄×Dic₃	C₂³×C₃	1	2	yes	—
538	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
539	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
540	C₄×Dic₃	C₂³×C₃	1	4	yes	—
541	C₂²×C₃²	—	2	2	no	—
542	C₂²×C₃²	—	2	2	no	—
543	C₂²×C₃²	C₂²×Q₈	1	4	yes	—
544	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
545	C₂×C₃×D₃	—	2	2	no	—
546	C₂×C₃×D₃	—	2	1	no	—
547	C₂×C₃×D₃	—	2	2	no	—
548	C₂×C₃×D₃	—	2	1	no	—
549	C₂×C₃×D₃	—	4	8	no	—
550	C₂×C₃×D₃	C₂²×Q₈	1	2	yes	—
551	C₂×C₃×D₃	C₂²×Q₈	1	4	yes	—
552	C₃²×C₄	—	2	2	no	—
553	C₃²×C₄	—	2	2	no	—
554	C₃²×C₄	—	2	2	no	—
555	C₃²×C₄	—	2	4	no	—
556	C₃²×C₄	—	2	1	no	—
557	C₃²×C₄	C₂²×Q₈	1	2	yes	—
558	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
559	C₃×Dic₃	—	2	4	no	—
560	C₃×Dic₃	—	2	2	no	—
561	C₃×Dic₃	—	2	2	no	—
562	C₃×Dic₃	—	2	1	no	—
563	C₃×Dic₃	—	2	1	no	—
564	C₃×Dic₃	—	2	2	no	—
565	C₃×Dic₃	C₂²×Q₈	1	2	yes	—
566	C₂²×Q₈	—	3	2	no	—
567	C₂²×Q₈	—	3	2	no	—
568	C₂²×D₄	—	3	1	no	—
569	C₂³×C₄	—	3	2	no	—
570	C₄⋊Q₈	—	3	1	no	—
571	C₄⋊Q₈	—	3	1	no	—
572	C₄⋊Q₈	—	3	4	no	—
573	C₄⋊Q₈	—	3	2	no	—
574	C₄⋊Q₈	—	3	1	no	—
575	C₄⋊Q₈	—	3	2	no	—
576	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
577	#125	—	3	2	no	—
578	#125	—	3	2	no	—
579	#125	—	3	4	no	—
580	#125	—	3	2	no	—
581	#125	C₂×C₃×D₃	1	2	yes	complemented
582	C₂²⋊Q₈	—	3	1	no	—
583	C₂²⋊Q₈	—	3	2	no	—
584	C₂²⋊Q₈	—	3	4	no	—
585	C₂²⋊Q₈	—	3	2	no	—
586	C₂²⋊Q₈	—	3	4	no	—
587	C₂²⋊Q₈	—	3	2	no	—
588	C₂²⋊Q₈	—	3	1	no	—
589	C₂²⋊Q₈	—	3	4	no	—
590	C₂²⋊Q₈	—	3	4	no	—
591	C₂²⋊Q₈	—	3	2	no	—
592	C₂²⋊Q₈	—	3	2	no	—
593	C₂²⋊Q₈	—	3	4	no	—
594	C₂²⋊Q₈	—	3	2	no	—
595	C₂²⋊Q₈	—	3	4	no	—
596	C₂²⋊Q₈	—	3	4	no	—
597	C₂²⋊Q₈	—	3	4	no	—
598	C₂²⋊Q₈	—	3	4	no	—
599	C₂²⋊Q₈	—	3	4	no	—
600	C₂²⋊Q₈	—	3	4	no	—
601	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
602	C₂²⋊Q₈	C₂×C₃×D₃	1	4	yes	complemented
603	C₄×Q₈	—	3	2	no	—
604	C₄×Q₈	—	3	2	no	—
605	C₄×Q₈	—	3	1	no	—
606	C₄×Q₈	—	3	2	no	—
607	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
608	C₄×D₄	—	3	1	no	—
609	C₄×D₄	—	3	2	no	—
610	C₄×D₄	—	3	2	no	—
611	C₄×D₄	—	3	4	no	—
612	C₄×D₄	—	3	1	no	—
613	C₄×D₄	—	3	2	no	—
614	C₄×D₄	—	3	2	no	—
615	C₄×D₄	—	3	4	no	—
616	C₄×D₄	—	3	1	no	—
617	C₄×D₄	—	3	2	no	—
618	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
619	C₄×D₄	C₂×C₃×D₃	1	2	yes	—
620	#117	—	3	2	no	—
621	#117	—	3	2	no	—
622	C₂×C₄⋊C₄	—	3	4	no	—
623	C₂×C₄⋊C₄	—	3	1	no	—
624	C₂×C₄⋊C₄	—	3	4	no	—
625	C₂×C₄⋊C₄	—	3	2	no	—
626	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
627	C₂×C₂²⋊C₄	—	3	4	no	—
628	C₂×C₂²⋊C₄	—	3	2	no	—
629	C₂×C₂²⋊C₄	—	3	4	no	—
630	C₂×C₄²	—	3	1	no	—
631	C₂³×C₃	—	2	2	no	—
632	C₂³×C₃	—	3	1	no	—
633	C₂³×C₃	—	3	2	no	—
634	C₂³×C₃	—	3	8	no	—
635	C₂³×C₃	—	12	2	no	—
636	C₂³×C₃	—	12	2	no	—
637	C₂³×C₃	C₂³×D₃	1	2	yes	—
638	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
639	C₂²×D₃	—	4	2	no	—
640	C₂²×D₃	—	4	2	no	—
641	C₂²×D₃	C₂×C₃×Q₈	1	8	yes	complemented
642	C₂²×D₃	C₂⁴×C₃	1	1	yes	characteristic
643	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
644	C₃×Q₈	—	2	2	no	—
645	C₃×Q₈	—	2	2	no	—
646	C₃×Q₈	—	4	2	no	—
647	C₃×Q₈	—	4	2	no	—
648	C₃×Q₈	—	4	2	no	—
649	C₃×Q₈	—	6	2	no	—
650	C₃×Q₈	—	6	4	no	—
651	C₃×Q₈	—	8	2	no	—
652	C₃×Q₈	—	12	2	no	—
653	C₃×Q₈	—	12	4	no	—
654	C₃×Q₈	—	12	4	no	—
655	C₃×D₄	—	2	4	no	—
656	C₃×D₄	—	3	8	no	—
657	C₃×D₄	—	3	4	no	—
658	C₃×D₄	D₃×Q₈	1	4	yes	complemented
659	C₃×D₄	C₂×C₃×Q₈	1	4	yes	complemented
660	C₂×C₃×C₄	—	2	4	no	—
661	C₂×C₃×C₄	—	2	4	no	—
662	C₂×C₃×C₄	—	2	1	no	—
663	C₂×C₃×C₄	—	2	1	no	—
664	C₂×C₃×C₄	—	2	2	no	—
665	C₂×C₃×C₄	—	2	1	no	—
666	C₂×C₃×C₄	—	2	2	no	—
667	C₂×C₃×C₄	—	2	2	no	—
668	C₂×C₃×C₄	—	2	4	no	—
669	C₂×C₃×C₄	—	3	1	no	—
670	C₂×C₃×C₄	—	3	4	no	—
671	C₂×C₃×C₄	—	3	1	no	—
672	C₂×C₃×C₄	—	3	1	no	—
673	C₂×C₃×C₄	—	3	2	no	—
674	C₂×C₃×C₄	—	3	2	no	—
675	C₂×C₃×C₄	—	3	4	no	—
676	C₂×C₃×C₄	—	3	2	no	—
677	C₂×C₃×C₄	—	4	4	no	—
678	C₂×C₃×C₄	—	4	4	no	—
679	C₂×C₃×C₄	—	4	4	no	—
680	C₂×C₃×C₄	—	6	2	no	—
681	C₂×C₃×C₄	—	6	4	no	—
682	C₂×C₃×C₄	—	8	4	no	—
683	C₂×C₃×C₄	—	12	4	no	—
684	C₂×C₃×C₄	—	12	1	no	—
685	C₂×C₃×C₄	—	12	2	no	—
686	C₂×C₃×C₄	—	12	2	no	—
687	C₂×C₃×C₄	—	12	4	no	—
688	C₂×C₃×C₄	—	12	2	no	—
689	C₂×C₃×C₄	—	12	4	no	—
690	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
691	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
692	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
693	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
694	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
695	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
696	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
697	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
698	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
699	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
700	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
701	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
702	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
703	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
704	#67	C₂×C₃×Q₈	1	8	yes	complemented
705	C₂×Dic₃	—	4	4	no	—
706	C₂×Dic₃	—	4	2	no	—
707	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
708	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
709	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
710	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
711	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
712	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
713	C₂×Dic₃	C₂⁴×C₃	1	1	yes	characteristic
714	D₁₂	C₂×C₃×Q₈	1	4	yes	complemented
715	C₄×D₃	—	2	2	no	—
716	C₄×D₃	—	2	4	no	—
717	C₄×D₃	—	4	2	no	—
718	C₄×D₃	—	4	2	no	—
719	C₄×D₃	—	4	1	no	—
720	C₄×D₃	—	4	4	no	—
721	C₄×D₃	—	4	4	no	—
722	C₄×D₃	C₂×C₃×Q₈	1	4	yes	complemented
723	Dic₆	—	2	2	no	—
724	Dic₆	—	2	4	no	—
725	Dic₆	—	4	4	no	—
726	Dic₆	—	4	2	no	—
727	Dic₆	—	4	4	no	—
728	C₂×C₃²	—	2	4	no	—
729	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
730	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
731	C₂×C₃²	#585	1	1	yes	characteristic
732	C₃×D₃	—	2	2	no	—
733	C₃×D₃	—	2	4	no	—
734	C₂⁴	—	3	2	no	—
735	C₂×Q₈	—	3	2	no	—
736	C₂×Q₈	—	3	1	no	—
737	C₂×Q₈	—	3	2	no	—
738	C₂×Q₈	—	3	4	no	—
739	C₂×Q₈	—	3	4	no	—
740	C₂×Q₈	—	12	4	no	—
741	C₂×Q₈	—	12	4	no	—
742	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
743	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
744	C₂×D₄	—	3	2	no	—
745	C₂×D₄	—	3	8	no	—
746	C₂×D₄	—	3	1	no	—
747	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
748	C₂²×C₄	—	3	1	no	—
749	C₂²×C₄	—	3	4	no	—
750	C₂²×C₄	—	3	2	no	—
751	C₂²×C₄	—	3	1	no	—
752	C₂²×C₄	—	3	2	no	—
753	C₂²×C₄	—	3	1	no	—
754	C₂²×C₄	—	3	4	no	—
755	C₂²×C₄	—	3	4	no	—
756	C₂²×C₄	—	3	2	no	—
757	C₂²×C₄	—	3	2	no	—
758	C₂²×C₄	—	12	4	no	—
759	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
760	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
761	C₄⋊C₄	—	3	2	no	—
762	C₄⋊C₄	—	3	4	no	—
763	C₄⋊C₄	—	3	2	no	—
764	C₄⋊C₄	—	3	1	no	—
765	C₄⋊C₄	—	3	2	no	—
766	C₄⋊C₄	—	3	1	no	—
767	C₄⋊C₄	—	3	4	no	—
768	C₄⋊C₄	—	3	4	no	—
769	C₄⋊C₄	—	3	4	no	—
770	C₄⋊C₄	—	3	4	no	—
771	C₄⋊C₄	—	3	2	no	—
772	C₄⋊C₄	—	3	2	no	—
773	C₄⋊C₄	—	3	2	no	—
774	C₄⋊C₄	—	3	4	no	—
775	C₄⋊C₄	—	3	2	no	—
776	C₄⋊C₄	—	3	2	no	—
777	C₄⋊C₄	—	3	2	no	—
778	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
779	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
781	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
783	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
784	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
785	C₂²⋊C₄	—	3	2	no	—
786	C₂²⋊C₄	—	3	4	no	—
787	C₂²⋊C₄	—	3	2	no	—
788	C₂²⋊C₄	—	3	4	no	—
789	C₂²⋊C₄	—	3	2	no	—
790	C₂²⋊C₄	—	3	2	no	—
791	C₂²⋊C₄	—	3	4	no	—
792	C₂²⋊C₄	—	3	4	no	—
793	C₂²⋊C₄	—	3	2	no	—
794	C₂²⋊C₄	C₂²×C₃×D₃	1	2	yes	—
795	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
796	C₄²	—	3	1	no	—
797	C₄²	—	3	1	no	—
798	C₄²	—	3	1	no	—
799	C₄²	—	3	4	no	—
800	C₄²	—	3	2	no	—
801	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
802	C₄²	C₂²×C₃×D₃	1	2	yes	—
803	C₂²×C₃	—	2	2	no	—
804	C₂²×C₃	—	2	2	no	—
805	C₂²×C₃	—	2	2	no	—
806	C₂²×C₃	—	2	2	no	—
807	C₂²×C₃	—	2	4	no	—
808	C₂²×C₃	—	2	1	no	—
809	C₂²×C₃	—	3	2	no	—
810	C₂²×C₃	—	3	4	no	—
811	C₂²×C₃	—	4	2	no	—
812	C₂²×C₃	—	4	2	no	—
813	C₂²×C₃	—	6	2	no	—
814	C₂²×C₃	—	6	1	no	—
815	C₂²×C₃	—	6	2	no	—
816	C₂²×C₃	—	6	1	no	—
817	C₂²×C₃	—	12	8	no	—
818	C₂²×C₃	C₂×D₃×Q₈	1	4	yes	—
819	C₂²×C₃	C₂²×C₃×Q₈	1	4	yes	—
820	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
821	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
822	C₂×D₃	—	2	2	no	—
823	C₂×D₃	—	2	1	no	—
824	C₂×D₃	—	2	2	no	—
825	C₂×D₃	—	2	1	no	—
826	C₂×D₃	—	4	8	no	—
827	C₂×D₃	C₂²×C₃×Q₈	1	2	yes	—
828	C₂×D₃	C₂²×C₃×Q₈	1	4	yes	—
829	C₃×C₄	—	2	2	no	—
830	C₃×C₄	—	2	2	no	—
831	C₃×C₄	—	2	2	no	—
832	C₃×C₄	—	2	4	no	—
833	C₃×C₄	—	2	1	no	—
834	C₃×C₄	—	2	2	no	—
835	C₃×C₄	—	2	2	no	—
836	C₃×C₄	—	2	2	no	—
837	C₃×C₄	—	2	4	no	—
838	C₃×C₄	—	2	1	no	—
839	C₃×C₄	—	2	2	no	—
840	C₃×C₄	—	2	2	no	—
841	C₃×C₄	—	3	2	no	—
842	C₃×C₄	—	4	2	no	—
843	C₃×C₄	—	4	2	no	—
844	C₃×C₄	—	4	4	no	—
845	C₃×C₄	—	4	2	no	—
846	C₃×C₄	—	4	1	no	—
847	C₃×C₄	—	6	1	no	—
848	C₃×C₄	—	6	2	no	—
849	C₃×C₄	—	6	4	no	—
850	C₃×C₄	—	6	2	no	—
851	C₃×C₄	—	6	2	no	—
852	C₃×C₄	—	6	1	no	—
853	C₃×C₄	C₂×D₃×Q₈	1	2	yes	—
854	C₃×C₄	#1009	1	2	yes	—
855	C₃×C₄	C₂²×C₃×Q₈	1	2	yes	—
856	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
857	Dic₃	—	2	4	no	—
858	Dic₃	—	2	2	no	—
859	Dic₃	—	2	2	no	—
860	Dic₃	—	2	1	no	—
861	Dic₃	—	2	1	no	—
862	Dic₃	—	2	2	no	—
863	Dic₃	C₂²×C₃×Q₈	1	2	yes	—
864	C₃²	#3501	1	1	yes	characteristic, complemented, Sylow
865	C₂³	—	3	1	no	—
866	C₂³	—	3	2	no	—
867	C₂³	—	3	8	no	—
868	C₂³	—	12	2	no	—
869	C₂³	—	12	2	no	—
870	C₂³	C₂³×C₃×D₃	1	2	yes	—
871	Q₈	—	2	2	no	—
872	Q₈	—	4	2	no	—
873	Q₈	—	6	2	no	—
874	Q₈	—	6	4	no	—
875	Q₈	—	12	4	no	—
876	Q₈	—	12	4	no	—
877	Q₈	—	12	2	no	—
878	D₄	—	3	8	no	—
879	D₄	—	3	4	no	—
880	D₄	C₃×D₃×Q₈	1	4	yes	complemented
881	C₂×C₄	—	2	4	no	—
882	C₂×C₄	—	3	1	no	—
883	C₂×C₄	—	3	4	no	—
884	C₂×C₄	—	3	1	no	—
885	C₂×C₄	—	3	1	no	—
886	C₂×C₄	—	3	2	no	—
887	C₂×C₄	—	3	4	no	—
888	C₂×C₄	—	3	2	no	—
889	C₂×C₄	—	3	2	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	6	2	no	—
892	C₂×C₄	—	6	4	no	—
893	C₂×C₄	—	12	2	no	—
894	C₂×C₄	—	12	2	no	—
895	C₂×C₄	—	12	4	no	—
896	C₂×C₄	—	12	4	no	—
897	C₂×C₄	—	12	1	no	—
898	C₂×C₄	—	12	2	no	—
899	C₂×C₄	—	12	4	no	—
900	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
901	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
902	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
903	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
904	C₂×C₄	C₂³×C₃×D₃	1	2	yes	—
905	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
906	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
907	C₂×C₃	—	2	4	no	—
908	C₂×C₃	—	2	4	no	—
909	C₂×C₃	—	2	1	no	—
910	C₂×C₃	—	2	1	no	—
911	C₂×C₃	—	2	1	no	—
912	C₂×C₃	—	4	4	no	—
913	C₂×C₃	—	6	2	no	—
914	C₂×C₃	—	6	4	no	—
915	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
916	C₂×C₃	C₂×#1009	1	1	yes	characteristic
917	C₂×C₃	#5966	1	1	yes	characteristic
918	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
919	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
920	C₂×C₃	C₃×#585	1	1	yes	characteristic
921	D₃	—	2	2	no	—
922	D₃	—	2	4	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	3	2	no	—
926	C₂²	—	3	4	no	—
927	C₂²	—	6	2	no	—
928	C₂²	—	6	1	no	—
929	C₂²	—	6	2	no	—
930	C₂²	—	6	1	no	—
931	C₂²	—	12	8	no	—
932	C₂²	C₂×C₃×D₃×Q₈	1	4	yes	—
933	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	1	no	—
939	C₄	—	3	2	no	—
940	C₄	—	6	1	no	—
941	C₄	—	6	2	no	—
942	C₄	—	6	4	no	—
943	C₄	—	6	2	no	—
944	C₄	—	6	2	no	—
945	C₄	—	6	1	no	—
946	C₄	C₂×C₃×D₃×Q₈	1	2	yes	—
947	C₄	C₃×#1009	1	2	yes	—
948	C₃	—	2	1	no	—
949	C₃	#86948	1	1	yes	characteristic, direct product factor
950	C₃	C₃×#3501	1	1	yes	characteristic, complemented
951	C₂	—	2	4	no	—
952	C₂	—	6	2	no	—
953	C₂	—	6	4	no	—
954	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
955	C₂	C₂×C₃×#1009	1	1	yes	characteristic
956	C₂	C₃×#5966	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	C₃×#3501
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×#5728	C₂	semidirect
4. C₃×#5690	C₂	semidirect
5. C₃×#5689	C₂	semidirect
6. C₃×#5635	C₂	semidirect
7. C₃×#5634	C₂	semidirect
8. C₃×#5632	C₂	semidirect
9. C₃×D₃×C₂²⋊Q₈	C₂	semidirect
10. C₃×#5578	C₂	semidirect
11. C₃×Q₈×D₁₂	C₂	semidirect
14. C₃×#5543	C₂	semidirect
15. C₃×D₄×Dic₆	C₂	semidirect
16. C₃×#5511	C₂	semidirect
17. C₂×C₃×#897	C₂	semidirect
19. #86948	C₃	direct (N × H)
20. C₂×C₃×D₃×Q₈	C₂²	semidirect
23. C₂²×C₃×Dic₆	C₂²	semidirect
24. C₃²×C₄⋊Q₈	C₂²	semidirect
25. C₃²×#125	C₂²	semidirect
26. C₃²×C₂²⋊Q₈	C₂²	semidirect
27. C₃²×C₂²⋊Q₈	C₂²	semidirect
28. C₃²×C₄×Q₈	C₂²	semidirect
31. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
34. C₃×#946	C₂²	semidirect
35. C₃×Q₈×Dic₃	C₂²	semidirect
36. C₃×#944	C₂²	semidirect
42. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
43. C₃×#924	C₂²	semidirect
44. C₃×#924	C₂²	semidirect
48. C₃×#897	C₂²	semidirect
49. C₃×#897	C₂²	semidirect
50. C₃×#897	C₂²	semidirect
51. C₃×#897	C₂²	semidirect
54. C₃×#896	C₂²	semidirect
55. C₃×#896	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×#888	C₂²	semidirect
69. C₃×#887	C₂²	semidirect
74. C₃×#878	C₂²	semidirect
75. C₃×#878	C₂²	semidirect
76. C₃×#878	C₂²	semidirect
81. C₃×#869	C₂²	semidirect
82. C₃×#869	C₂²	semidirect
83. C₃×C₄×Dic₆	C₂²	semidirect
84. C₃×C₄×Dic₆	C₂²	semidirect
91. C₃×#554	D₃	semidirect
92. C₃×#554	C₂×C₃	semidirect
104. #5730	C₂×C₃	semidirect
105. #5728	C₂×C₃	semidirect
106. #5690	C₂×C₃	semidirect
107. #5689	C₂×C₃	semidirect
108. #5635	C₂×C₃	semidirect
109. #5634	C₂×C₃	semidirect
110. #5632	C₂×C₃	semidirect
111. D₃×C₂²⋊Q₈	C₂×C₃	semidirect
112. #5578	C₂×C₃	semidirect
113. Q₈×D₁₂	C₂×C₃	semidirect
116. #5543	C₂×C₃	semidirect
117. D₄×Dic₆	C₂×C₃	semidirect
118. #5511	C₂×C₃	semidirect
119. C₂×#897	C₂×C₃	semidirect
130. C₃×D₃×D₄	Q₈	semidirect
194. C₂×D₃×Q₈	C₂²×C₃	semidirect
197. C₂²×Dic₆	C₂²×C₃	semidirect
205. C₃×C₄⋊Q₈	C₂×D₃	semidirect
206. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
212. C₃×#125	C₂×D₃	semidirect
213. C₃×#125	C₂²×C₃	semidirect
235. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
236. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
237. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
238. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
244. C₃×C₄×Q₈	C₂×D₃	semidirect
245. C₃×C₄×Q₈	C₂²×C₃	semidirect
269. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
270. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
277. #946	C₂²×C₃	semidirect
278. Q₈×Dic₃	C₂²×C₃	semidirect
279. #944	C₂²×C₃	semidirect
285. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
286. #924	C₂²×C₃	semidirect
287. #924	C₂²×C₃	semidirect
291. #897	C₂²×C₃	semidirect
292. #897	C₂²×C₃	semidirect
293. #897	C₂²×C₃	semidirect
294. #897	C₂²×C₃	semidirect
297. #896	C₂²×C₃	semidirect
298. #896	C₂²×C₃	semidirect
303. D₃×C₄⋊C₄	C₂²×C₃	semidirect
304. D₃×C₄⋊C₄	C₂²×C₃	semidirect
305. #890	C₂²×C₃	semidirect
306. #890	C₂²×C₃	semidirect
307. #889	C₂²×C₃	semidirect
308. #889	C₂²×C₃	semidirect
309. #888	C₂²×C₃	semidirect
310. #888	C₂²×C₃	semidirect
311. #888	C₂²×C₃	semidirect
312. #887	C₂²×C₃	semidirect
317. #878	C₂²×C₃	semidirect
318. #878	C₂²×C₃	semidirect
319. #878	C₂²×C₃	semidirect
324. #869	C₂²×C₃	semidirect
325. #869	C₂²×C₃	semidirect
326. C₄×Dic₆	C₂²×C₃	semidirect
327. C₄×Dic₆	C₂²×C₃	semidirect
331. C₂²×C₃×D₃	C₂×Q₈	semidirect
336. C₃²×D₄	C₂×Q₈	semidirect
346. C₃×#67	C₂×Q₈	semidirect
356. C₃×D₁₂	C₂×Q₈	semidirect
364. C₃×C₄×D₃	C₂×Q₈	semidirect
375. #554	C₃×D₃	semidirect
429. D₃×D₄	C₃×Q₈	semidirect
576. C₄⋊Q₈	C₂×C₃×D₃	semidirect
581. #125	C₂×C₃×D₃	semidirect
601. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
602. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
607. C₄×Q₈	C₂×C₃×D₃	semidirect
626. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
641. C₂²×D₃	C₂×C₃×Q₈	semidirect
658. C₃×D₄	D₃×Q₈	semidirect
659. C₃×D₄	C₂×C₃×Q₈	semidirect
704. #67	C₂×C₃×Q₈	semidirect
714. D₁₂	C₂×C₃×Q₈	semidirect
722. C₄×D₃	C₂×C₃×Q₈	semidirect
864. C₃²	#3501	semidirect
880. D₄	C₃×D₃×Q₈	semidirect
949. C₃	#86948	direct (N × H)
950. C₃	C₃×#3501	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×#5728	2
C₃×#5690	2
C₃×#5689	2
C₃×#5635	2
C₃×#5634	2
C₃×#5632	2
C₃×D₃×C₂²⋊Q₈	2
C₃×#5578	2
C₃×Q₈×D₁₂	2
C₃×#5545	2
C₃×C₄×D₃×D₄	2
C₃×#5543	2
C₃×D₄×Dic₆	2
C₃×#5511	2
C₂×C₃×#897	2
C₃×#3501	3
#86948	3

Subgroups — C3×#86948 #11906160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#86948 #11906160