Subgroups — C₃×#85986 #11906157

Order 1152.

2361 conjugacy classes of subgroups.

The subgroup lattice has 955 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×Q₈×#67	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₄×#67	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#924	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5636	C₂	1	4	yes	maximal, complemented
6	C₃×#5635	C₂	1	2	yes	maximal, complemented
7	C₃×#5634	C₂	1	2	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×#5623	C₂	1	2	yes	maximal, complemented
11	C₃×#5622	C₂	1	2	yes	maximal, complemented
12	C₃×#5511	C₂	1	2	yes	maximal, complemented
13	C₃×#5511	C₂	1	4	yes	maximal, complemented
14	C₃×#5486	C₂	1	2	yes	maximal
15	C₃×#5483	C₂	1	2	yes	maximal, complemented
16	C₃×#3501	—	3	1	no	maximal
17	#85986	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂²×C₃²×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×#67	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	complemented
22	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
23	C₂²×C₃×Dic₆	C₂²	1	1	yes	characteristic, complemented
24	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₃²×C₂²⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃²×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₂×C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×#217	C₂²	1	2	yes	—
32	C₂×C₃×#217	C₂²	1	1	yes	characteristic
33	C₃×#946	C₂²	1	2	yes	complemented
34	C₃×#946	C₂²	1	4	yes	complemented
35	C₃×Q₈×Dic₃	C₂²	1	2	yes	complemented
36	C₃×#944	C₂²	1	2	yes	complemented
37	C₃×#944	C₂²	1	4	yes	complemented
38	C₃×C₄×#67	C₂²	1	2	yes	—
39	C₃×C₄×#67	C₂²	1	4	yes	—
40	C₃×C₄×#67	C₂²	1	2	yes	—
41	C₃×C₄×#67	C₂²	1	4	yes	—
42	C₃×C₄×#67	C₂²	1	2	yes	—
43	C₃×C₄×#67	C₂²	1	2	yes	—
44	C₂×C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
46	C₃×#924	C₂²	1	2	yes	—
47	C₃×#924	C₂²	1	2	yes	—
48	C₃×#924	C₂²	1	2	yes	complemented
49	C₃×#924	C₂²	1	4	yes	complemented
50	C₃×#924	C₂²	1	2	yes	complemented
51	C₃×#924	C₂²	1	4	yes	complemented
52	C₂×C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×C₃×Dic₃⋊C₄	C₂²	1	2	yes	complemented
54	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
55	C₃×#897	C₂²	1	2	yes	complemented
56	C₃×#897	C₂²	1	4	yes	complemented
57	C₃×#896	C₂²	1	4	yes	complemented
58	C₃×#896	C₂²	1	4	yes	complemented
59	C₃×#896	C₂²	1	4	yes	complemented
60	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	complemented
61	C₃×D₃×C₄⋊C₄	C₂²	1	4	yes	complemented
62	C₃×#889	C₂²	1	4	yes	complemented
63	C₃×#889	C₂²	1	4	yes	complemented
64	C₃×#889	C₂²	1	4	yes	complemented
65	C₃×#888	C₂²	1	2	yes	complemented
66	C₃×#888	C₂²	1	4	yes	complemented
67	C₃×#887	C₂²	1	2	yes	complemented
68	C₃×#887	C₂²	1	4	yes	complemented
69	C₃×#67⋊C₄	C₂²	1	4	yes	—
70	C₃×#67⋊C₄	C₂²	1	4	yes	—
71	C₃×D₃×C₂²⋊C₄	C₂²	1	4	yes	—
72	C₃×#878	C₂²	1	4	yes	—
73	C₃×#878	C₂²	1	4	yes	—
74	C₃×#878	C₂²	1	4	yes	complemented
75	C₃×#878	C₂²	1	4	yes	complemented
76	C₃×#877	C₂²	1	4	yes	—
77	C₃×#554	—	3	2	no	—
78	C₃×#554	—	3	4	no	—
79	C₃×#554	—	3	2	no	—
80	C₃×#554	—	3	4	no	—
81	C₃×D₄×Q₈	—	3	2	no	—
82	C₃×D₄×Q₈	—	3	2	no	—
83	C₃×#544	—	3	2	no	—
84	C₃×#543	—	3	2	no	—
85	C₃×#543	—	3	2	no	—
86	C₃×#533	—	3	2	no	—
87	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
88	C₂×C₃×C₂²⋊Q₈	—	3	1	no	—
89	C₂×C₃×C₂²⋊Q₈	—	3	2	no	—
90	C₂×C₃×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
91	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
92	C₃×#518	—	3	2	no	—
93	C₂×C₃×C₄×D₄	—	3	1	no	—
94	Q₈×#67	C₂×C₃	1	2	yes	complemented
95	C₂×C₄×#67	C₂×C₃	1	1	yes	characteristic
96	C₂×#924	C₂×C₃	1	1	yes	characteristic, complemented
97	#5636	C₂×C₃	1	4	yes	complemented
98	#5635	C₂×C₃	1	2	yes	complemented
99	#5634	C₂×C₃	1	2	yes	complemented
100	#5632	C₂×C₃	1	2	yes	complemented
101	D₃×C₂²⋊Q₈	C₂×C₃	1	2	yes	complemented
102	#5623	C₂×C₃	1	2	yes	complemented
103	#5622	C₂×C₃	1	2	yes	complemented
104	#5511	C₂×C₃	1	2	yes	complemented
105	#5511	C₂×C₃	1	4	yes	complemented
106	#5486	C₂×C₃	1	2	yes	—
107	#5483	C₂×C₃	1	2	yes	complemented
108	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
109	C₂³×C₃×D₃	C₂³	1	1	yes	characteristic
110	C₂×C₃²×Q₈	—	4	2	no	—
111	C₂×C₃²×Q₈	C₂³	1	2	yes	—
112	C₂×C₃²×Q₈	C₂³	1	2	yes	—
113	C₂²×C₃²×C₄	—	4	2	no	—
114	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
115	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
116	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
117	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
118	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
119	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
120	C₂²×C₃²×C₄	C₂³	1	2	yes	—
121	C₂²×C₃²×C₄	C₂³	1	2	yes	—
122	C₂×C₃×#67	Q₈	1	8	yes	complemented
123	C₂×C₃×#67	C₂³	1	2	yes	—
124	C₂×C₃×#67	C₂³	1	2	yes	—
125	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
126	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
127	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
128	C₂²×C₃×Dic₃	C₂³	1	2	yes	—
129	C₂²×C₃×Dic₃	C₂³	1	1	yes	characteristic
130	C₃×D₃×Q₈	—	4	4	no	—
131	C₂×C₃×C₄×D₃	—	4	2	no	—
132	C₂×C₃×C₄×D₃	C₂³	1	2	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	—	4	2	no	—
137	C₂×C₃×Dic₆	C₂³	1	2	yes	—
138	C₂×C₃×Dic₆	C₂³	1	4	yes	—
139	C₂×C₃×Dic₆	C₂³	1	4	yes	—
140	C₂×C₃×Dic₆	C₂³	1	2	yes	—
141	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
142	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
143	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
144	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
145	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
146	C₃²×C₂²⋊C₄	C₂³	1	4	yes	—
147	C₃×#217	C₂³	1	4	yes	—
148	C₃×#217	C₂³	1	2	yes	—
149	C₃×#217	C₂³	1	2	yes	—
150	C₃×#217	C₂³	1	4	yes	—
151	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
152	C₃×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
153	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
154	C₃×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
155	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
156	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
157	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
158	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
159	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
160	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
161	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
162	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
163	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
164	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
165	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
166	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
167	C₃×Dic₃⋊C₄	C₂³	1	2	yes	—
168	C₃×Dic₃⋊C₄	C₂³	1	4	yes	—
169	C₃×C₄×Dic₃	C₂³	1	4	yes	—
170	C₃×C₄×Dic₃	C₂³	1	4	yes	—
171	C₃×C₄×Dic₃	C₂³	1	2	yes	—
172	C₃×C₄×Dic₃	C₂³	1	2	yes	—
173	#3501	—	3	1	no	Sylow
174	C₂²×C₃×Q₈	—	2	1	no	—
175	C₂²×C₃×Q₈	—	3	2	no	—
176	C₂²×C₃×Q₈	—	3	1	no	—
177	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
178	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₂²×C₃×D₄	—	3	1	no	—
180	C₂³×C₃×C₄	—	2	1	no	—
181	C₂³×C₃×C₄	—	3	1	no	—
182	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
183	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
184	C₂²×#67	C₂²×C₃	1	1	yes	characteristic
185	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	complemented
186	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
187	C₂²×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₃×C₄⋊Q₈	—	3	2	no	—
189	C₃×C₄⋊Q₈	—	3	4	no	—
190	C₃×C₄⋊Q₈	—	3	2	no	—
191	C₃×C₄⋊Q₈	—	3	4	no	—
192	C₃×#125	—	3	4	no	—
193	C₃×#125	—	3	4	no	—
194	C₃×#125	—	3	4	no	—
195	C₃×C₂²⋊Q₈	—	2	2	no	—
196	C₃×C₂²⋊Q₈	—	2	2	no	—
197	C₃×C₂²⋊Q₈	—	2	2	no	—
198	C₃×C₂²⋊Q₈	—	2	2	no	—
199	C₃×C₂²⋊Q₈	—	3	2	no	—
200	C₃×C₂²⋊Q₈	—	3	4	no	—
201	C₃×C₂²⋊Q₈	—	3	2	no	—
202	C₃×C₂²⋊Q₈	—	3	2	no	—
203	C₃×C₂²⋊Q₈	—	3	2	no	—
204	C₃×C₂²⋊Q₈	—	3	2	no	—
205	C₃×C₂²⋊Q₈	—	3	4	no	—
206	C₃×C₂²⋊Q₈	—	3	4	no	—
207	C₃×C₂²⋊Q₈	—	3	4	no	—
208	C₃×C₂²⋊Q₈	—	3	4	no	—
209	C₃×C₂²⋊Q₈	—	3	4	no	—
210	C₃×C₂²⋊Q₈	—	3	2	no	—
211	C₃×C₂²⋊Q₈	—	3	4	no	—
212	C₃×C₂²⋊Q₈	—	3	4	no	—
213	C₃×C₂²⋊Q₈	—	3	4	no	—
214	C₃×C₂²⋊Q₈	—	3	4	no	—
215	C₃×C₂²⋊Q₈	—	3	4	no	—
216	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
217	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
218	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
219	C₃×C₂²⋊Q₈	C₂×D₃	1	2	yes	complemented
220	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
221	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
222	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
223	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
224	C₃×C₄×Q₈	—	3	2	no	—
225	C₃×C₄×Q₈	—	3	2	no	—
226	C₃×C₄×Q₈	—	3	4	no	—
227	C₃×C₄×D₄	—	3	2	no	—
228	C₃×C₄×D₄	—	3	2	no	—
229	C₃×C₄×D₄	—	3	2	no	—
230	C₃×C₄×D₄	—	3	2	no	—
231	C₃×C₄×D₄	—	3	4	no	—
232	C₃×C₄×D₄	—	3	4	no	—
233	C₃×C₄×D₄	—	3	4	no	—
234	C₃×C₄×D₄	—	3	4	no	—
235	C₃×#117	—	3	4	no	—
236	C₂×C₃×C₄⋊C₄	—	2	1	no	—
237	C₂×C₃×C₄⋊C₄	—	2	2	no	—
238	C₂×C₃×C₄⋊C₄	—	3	1	no	—
239	C₂×C₃×C₄⋊C₄	—	3	2	no	—
240	C₂×C₃×C₄⋊C₄	—	3	1	no	—
241	C₂×C₃×C₄⋊C₄	—	3	4	no	—
242	C₂×C₃×C₄⋊C₄	—	3	2	no	—
243	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
244	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
245	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
246	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
247	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
249	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
250	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
251	C₂×C₃×C₂²⋊C₄	—	3	4	no	—
252	C₂×C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
253	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
254	C₂×C₃×C₄²	—	3	1	no	—
255	C₂×#217	C₂²×C₃	1	1	yes	characteristic
256	C₂×#217	C₂²×C₃	1	2	yes	—
257	#946	C₂²×C₃	1	4	yes	complemented
258	#946	C₂²×C₃	1	2	yes	complemented
259	Q₈×Dic₃	C₂²×C₃	1	2	yes	complemented
260	#944	C₂²×C₃	1	2	yes	complemented
261	#944	C₂²×C₃	1	4	yes	complemented
262	C₄×#67	C₂²×C₃	1	2	yes	—
263	C₄×#67	C₂²×C₃	1	2	yes	—
264	C₄×#67	C₂²×C₃	1	4	yes	—
265	C₄×#67	C₂²×C₃	1	4	yes	—
266	C₄×#67	C₂²×C₃	1	2	yes	—
267	C₄×#67	C₂²×C₃	1	2	yes	—
268	C₂×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
269	C₂×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
270	#924	C₂²×C₃	1	2	yes	—
271	#924	C₂²×C₃	1	2	yes	—
272	#924	C₂²×C₃	1	4	yes	complemented
273	#924	C₂²×C₃	1	4	yes	complemented
274	#924	C₂²×C₃	1	2	yes	complemented
275	#924	C₂²×C₃	1	2	yes	complemented
276	C₂×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
277	C₂×Dic₃⋊C₄	C₂²×C₃	1	2	yes	complemented
278	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
279	#897	C₂²×C₃	1	2	yes	complemented
280	#897	C₂²×C₃	1	4	yes	complemented
281	#896	C₂²×C₃	1	4	yes	complemented
282	#896	C₂²×C₃	1	4	yes	complemented
283	#896	C₂²×C₃	1	4	yes	complemented
284	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
285	D₃×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
286	#889	C₂²×C₃	1	4	yes	complemented
287	#889	C₂²×C₃	1	4	yes	complemented
288	#889	C₂²×C₃	1	4	yes	complemented
289	#888	C₂²×C₃	1	4	yes	complemented
290	#888	C₂²×C₃	1	2	yes	complemented
291	#887	C₂²×C₃	1	2	yes	complemented
292	#887	C₂²×C₃	1	4	yes	complemented
293	#67⋊C₄	C₂²×C₃	1	4	yes	—
294	#67⋊C₄	C₂²×C₃	1	4	yes	—
295	D₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
296	#878	C₂²×C₃	1	4	yes	—
297	#878	C₂²×C₃	1	4	yes	—
298	#878	C₂²×C₃	1	4	yes	complemented
299	#878	C₂²×C₃	1	4	yes	complemented
300	#877	C₂²×C₃	1	4	yes	—
301	C₂³×C₃²	—	4	1	no	—
302	C₂³×C₃²	—	4	1	no	—
303	C₂³×C₃²	C₂×Q₈	1	4	yes	complemented
304	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
305	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
306	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
307	C₂²×C₃×D₃	—	4	1	no	—
308	C₂²×C₃×D₃	—	4	1	no	—
309	C₂²×C₃×D₃	C₂×Q₈	1	4	yes	complemented
310	C₂²×C₃×D₃	C₂⁴	1	2	yes	—
311	C₃²×Q₈	—	2	4	no	—
312	C₃²×Q₈	—	4	2	no	—
313	C₂×C₃²×C₄	—	2	2	no	—
314	C₂×C₃²×C₄	—	2	2	no	—
315	C₂×C₃²×C₄	—	2	2	no	—
316	C₂×C₃²×C₄	—	4	1	no	—
317	C₂×C₃²×C₄	—	4	1	no	—
318	C₂×C₃²×C₄	—	4	1	no	—
319	C₂×C₃²×C₄	—	4	2	no	—
320	C₂×C₃²×C₄	—	4	2	no	—
321	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
322	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
323	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
324	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
325	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
326	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
327	C₃×#67	C₂×Q₈	1	8	yes	complemented
328	C₃×#67	C₂×Q₈	1	8	yes	complemented
329	C₂×C₃×Dic₃	—	4	2	no	—
330	C₂×C₃×Dic₃	—	4	1	no	—
331	C₂×C₃×Dic₃	—	4	1	no	—
332	C₂×C₃×Dic₃	—	4	2	no	—
333	C₂×C₃×Dic₃	C₂×Q₈	1	4	yes	complemented
334	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
335	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
336	C₂×C₃×Dic₃	C₂⁴	1	4	yes	—
337	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
338	C₂×C₃×Dic₃	C₂⁴	1	2	yes	—
339	C₃×C₄×D₃	—	2	4	no	—
340	C₃×C₄×D₃	—	4	2	no	—
341	C₃×C₄×D₃	—	4	4	no	—
342	C₃×C₄×D₃	—	4	4	no	—
343	C₃×Dic₆	—	2	4	no	—
344	C₃×Dic₆	—	4	2	no	—
345	C₃×Dic₆	—	4	4	no	—
346	C₃×Dic₆	—	4	4	no	—
347	#554	—	3	2	no	—
348	#554	—	3	4	no	—
349	#554	—	3	2	no	—
350	#554	—	3	4	no	—
351	D₄×Q₈	—	3	2	no	—
352	D₄×Q₈	—	3	2	no	—
353	#544	—	3	2	no	—
354	#543	—	3	2	no	—
355	#543	—	3	2	no	—
356	#533	—	3	2	no	—
357	C₂×C₂²⋊Q₈	—	3	1	no	—
358	C₂×C₂²⋊Q₈	—	3	2	no	—
359	C₂×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic, complemented
360	#518	—	3	2	no	—
361	C₂×C₄×D₄	—	3	1	no	—
362	C₂⁴×C₃	—	2	1	no	—
363	C₂⁴×C₃	—	3	1	no	—
364	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
365	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
366	C₂³×D₃	C₂³×C₃	1	1	yes	characteristic
367	C₂×C₃×Q₈	—	2	2	no	—
368	C₂×C₃×Q₈	—	2	2	no	—
369	C₂×C₃×Q₈	—	3	2	no	—
370	C₂×C₃×Q₈	—	3	4	no	—
371	C₂×C₃×Q₈	—	3	2	no	—
372	C₂×C₃×Q₈	—	3	4	no	—
373	C₂×C₃×Q₈	—	4	2	no	—
374	C₂×C₃×Q₈	—	4	2	no	—
375	C₂×C₃×Q₈	—	4	4	no	—
376	C₂×C₃×Q₈	—	12	2	no	—
377	C₂×C₃×Q₈	—	12	4	no	—
378	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
379	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
380	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
381	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
382	C₂×C₃×D₄	—	3	8	no	—
383	C₂×C₃×D₄	—	3	2	no	—
384	C₂×C₃×D₄	—	3	2	no	—
385	C₂²×C₃×C₄	—	2	1	no	—
386	C₂²×C₃×C₄	—	2	2	no	—
387	C₂²×C₃×C₄	—	2	2	no	—
388	C₂²×C₃×C₄	—	2	1	no	—
389	C₂²×C₃×C₄	—	2	1	no	—
390	C₂²×C₃×C₄	—	2	1	no	—
391	C₂²×C₃×C₄	—	2	1	no	—
392	C₂²×C₃×C₄	—	2	1	no	—
393	C₂²×C₃×C₄	—	3	1	no	—
394	C₂²×C₃×C₄	—	3	1	no	—
395	C₂²×C₃×C₄	—	3	2	no	—
396	C₂²×C₃×C₄	—	3	2	no	—
397	C₂²×C₃×C₄	—	3	1	no	—
398	C₂²×C₃×C₄	—	3	2	no	—
399	C₂²×C₃×C₄	—	3	4	no	—
400	C₂²×C₃×C₄	—	3	4	no	—
401	C₂²×C₃×C₄	—	3	2	no	—
402	C₂²×C₃×C₄	—	4	2	no	—
403	C₂²×C₃×C₄	—	4	2	no	—
404	C₂²×C₃×C₄	—	4	4	no	—
405	C₂²×C₃×C₄	—	12	2	no	—
406	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
407	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
408	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
411	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
412	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
413	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
420	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
421	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
422	C₂×#67	C₃×Q₈	1	8	yes	complemented
423	C₂×#67	C₂³×C₃	1	2	yes	—
424	C₂×#67	C₂³×C₃	1	2	yes	—
425	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
426	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
427	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
428	C₂²×Dic₃	C₂³×C₃	1	2	yes	—
429	C₂²×Dic₃	C₂³×C₃	1	1	yes	characteristic
430	D₃×Q₈	—	4	4	no	—
431	C₂×C₄×D₃	—	4	2	no	—
432	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
433	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
434	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
435	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
436	C₂×Dic₆	—	4	2	no	—
437	C₂×Dic₆	C₂³×C₃	1	2	yes	—
438	C₂×Dic₆	C₂³×C₃	1	4	yes	—
439	C₂×Dic₆	C₂³×C₃	1	4	yes	—
440	C₂×Dic₆	C₂³×C₃	1	2	yes	—
441	C₃×C₄⋊C₄	—	2	4	no	—
442	C₃×C₄⋊C₄	—	2	2	no	—
443	C₃×C₄⋊C₄	—	2	2	no	—
444	C₃×C₄⋊C₄	—	2	4	no	—
445	C₃×C₄⋊C₄	—	3	4	no	—
446	C₃×C₄⋊C₄	—	3	2	no	—
447	C₃×C₄⋊C₄	—	3	2	no	—
448	C₃×C₄⋊C₄	—	3	4	no	—
449	C₃×C₄⋊C₄	—	3	4	no	—
450	C₃×C₄⋊C₄	—	3	4	no	—
451	C₃×C₄⋊C₄	—	3	4	no	—
452	C₃×C₄⋊C₄	—	3	4	no	—
453	C₃×C₄⋊C₄	—	3	4	no	—
454	C₃×C₄⋊C₄	—	3	4	no	—
455	C₃×C₄⋊C₄	—	3	2	no	—
456	C₃×C₄⋊C₄	—	3	2	no	—
457	C₃×C₄⋊C₄	—	3	4	no	—
458	C₃×C₄⋊C₄	—	3	4	no	—
459	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
460	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
461	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
462	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
463	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
464	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
465	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
466	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
467	C₃×C₂²⋊C₄	—	2	4	no	—
468	C₃×C₂²⋊C₄	—	2	4	no	—
469	C₃×C₂²⋊C₄	—	3	4	no	—
470	C₃×C₂²⋊C₄	—	3	2	no	—
471	C₃×C₂²⋊C₄	—	3	2	no	—
472	C₃×C₂²⋊C₄	—	3	4	no	—
473	C₃×C₂²⋊C₄	—	3	2	no	—
474	C₃×C₂²⋊C₄	—	3	2	no	—
475	C₃×C₂²⋊C₄	—	3	4	no	—
476	C₃×C₂²⋊C₄	—	3	4	no	—
477	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
478	C₃×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
479	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
480	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
481	C₃×C₄²	—	3	2	no	—
482	C₃×C₄²	—	3	2	no	—
483	C₃×C₄²	—	3	4	no	—
484	C₃×C₄²	—	3	4	no	—
485	#217	C₂³×C₃	1	4	yes	—
486	#217	C₂³×C₃	1	2	yes	—
487	#217	C₂³×C₃	1	2	yes	—
488	#217	C₂³×C₃	1	4	yes	—
489	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
490	(C₂×D₃)⋊C₄	C₂³×C₃	1	4	yes	—
491	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
492	(C₂×D₃)⋊C₄	C₂³×C₃	1	2	yes	—
493	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
494	C₄⋊Dic₃	C₂³×C₃	1	4	yes	—
495	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
496	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
497	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
498	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
499	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
500	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
501	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
502	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
503	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
504	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
505	Dic₃⋊C₄	C₂³×C₃	1	2	yes	—
506	Dic₃⋊C₄	C₂³×C₃	1	4	yes	—
507	C₄×Dic₃	C₂³×C₃	1	4	yes	—
508	C₄×Dic₃	C₂³×C₃	1	4	yes	—
509	C₄×Dic₃	C₂³×C₃	1	2	yes	—
510	C₄×Dic₃	C₂³×C₃	1	2	yes	—
511	C₂²×C₃²	—	2	1	no	—
512	C₂²×C₃²	—	2	1	no	—
513	C₂²×C₃²	—	2	1	no	—
514	C₂²×C₃²	—	2	1	no	—
515	C₂²×C₃²	—	2	1	no	—
516	C₂²×C₃²	—	2	1	no	—
517	C₂²×C₃²	—	4	4	no	—
518	C₂²×C₃²	C₂²×Q₈	1	2	yes	—
519	C₂²×C₃²	C₂²×Q₈	1	2	yes	—
520	C₂²×C₃²	C₂²×Q₈	1	2	yes	—
521	C₂²×C₃²	C₂⁵	1	1	yes	characteristic
522	C₂×C₃×D₃	—	2	2	no	—
523	C₂×C₃×D₃	—	2	2	no	—
524	C₂×C₃×D₃	—	4	4	no	—
525	C₂×C₃×D₃	C₂²×Q₈	1	4	yes	—
526	C₃²×C₄	—	2	1	no	—
527	C₃²×C₄	—	2	1	no	—
528	C₃²×C₄	—	2	4	no	—
529	C₃²×C₄	—	2	1	no	—
530	C₃²×C₄	—	2	4	no	—
531	C₃²×C₄	H(5,𝔽₂)	1	2	yes	—
532	C₃×Dic₃	—	2	4	no	—
533	C₃×Dic₃	—	2	2	no	—
534	C₃×Dic₃	—	2	2	no	—
535	C₃×Dic₃	—	2	4	no	—
536	C₃×Dic₃	C₂²×Q₈	1	4	yes	—
537	C₂²×Q₈	—	3	2	no	—
538	C₂²×Q₈	—	3	1	no	—
539	C₂²×Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
540	C₂²×D₄	—	3	1	no	—
541	C₂³×C₄	—	3	1	no	—
542	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
543	C₄⋊Q₈	—	3	2	no	—
544	C₄⋊Q₈	—	3	4	no	—
545	C₄⋊Q₈	—	3	2	no	—
546	C₄⋊Q₈	—	3	4	no	—
547	#125	—	3	4	no	—
548	#125	—	3	4	no	—
549	#125	—	3	4	no	—
550	C₂²⋊Q₈	—	3	2	no	—
551	C₂²⋊Q₈	—	3	4	no	—
552	C₂²⋊Q₈	—	3	2	no	—
553	C₂²⋊Q₈	—	3	2	no	—
554	C₂²⋊Q₈	—	3	2	no	—
555	C₂²⋊Q₈	—	3	2	no	—
556	C₂²⋊Q₈	—	3	4	no	—
557	C₂²⋊Q₈	—	3	4	no	—
558	C₂²⋊Q₈	—	3	2	no	—
559	C₂²⋊Q₈	—	3	4	no	—
560	C₂²⋊Q₈	—	3	4	no	—
561	C₂²⋊Q₈	—	3	4	no	—
562	C₂²⋊Q₈	—	3	4	no	—
563	C₂²⋊Q₈	—	3	4	no	—
564	C₂²⋊Q₈	—	3	4	no	—
565	C₂²⋊Q₈	—	3	4	no	—
566	C₂²⋊Q₈	—	3	4	no	—
567	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
568	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	—
569	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
570	C₂²⋊Q₈	C₂×C₃×D₃	1	2	yes	complemented
571	C₄×Q₈	—	3	2	no	—
572	C₄×Q₈	—	3	2	no	—
573	C₄×Q₈	—	3	4	no	—
574	C₄×D₄	—	3	2	no	—
575	C₄×D₄	—	3	2	no	—
576	C₄×D₄	—	3	2	no	—
577	C₄×D₄	—	3	2	no	—
578	C₄×D₄	—	3	4	no	—
579	C₄×D₄	—	3	4	no	—
580	C₄×D₄	—	3	4	no	—
581	C₄×D₄	—	3	4	no	—
582	#117	—	3	4	no	—
583	C₂×C₄⋊C₄	—	3	1	no	—
584	C₂×C₄⋊C₄	—	3	2	no	—
585	C₂×C₄⋊C₄	—	3	1	no	—
586	C₂×C₄⋊C₄	—	3	4	no	—
587	C₂×C₄⋊C₄	—	3	2	no	—
588	C₂×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	complemented
589	C₂×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
590	C₂×C₂²⋊C₄	—	3	1	no	—
591	C₂×C₂²⋊C₄	—	3	2	no	—
592	C₂×C₂²⋊C₄	—	3	1	no	—
593	C₂×C₂²⋊C₄	—	3	4	no	—
594	C₂×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
595	C₂×C₄²	—	3	1	no	—
596	C₂³×C₃	—	2	1	no	—
597	C₂³×C₃	—	2	1	no	—
598	C₂³×C₃	—	2	1	no	—
599	C₂³×C₃	—	2	4	no	—
600	C₂³×C₃	—	3	2	no	—
601	C₂³×C₃	—	3	4	no	—
602	C₂³×C₃	—	4	1	no	—
603	C₂³×C₃	—	4	1	no	—
604	C₂³×C₃	—	4	1	no	—
605	C₂³×C₃	—	4	1	no	—
606	C₂³×C₃	—	4	2	no	—
607	C₂³×C₃	—	4	2	no	—
608	C₂³×C₃	—	12	1	no	—
609	C₂³×C₃	—	12	1	no	—
610	C₂³×C₃	D₃×Q₈	1	4	yes	complemented
611	C₂³×C₃	C₂×C₃×Q₈	1	4	yes	complemented
612	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
613	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
614	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
615	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
616	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
617	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
618	C₂²×D₃	—	4	1	no	—
619	C₂²×D₃	—	4	1	no	—
620	C₂²×D₃	C₂×C₃×Q₈	1	4	yes	complemented
621	C₂²×D₃	C₂⁴×C₃	1	2	yes	—
622	C₃×Q₈	—	2	4	no	—
623	C₃×Q₈	—	2	4	no	—
624	C₃×Q₈	—	4	4	no	—
625	C₃×Q₈	—	4	2	no	—
626	C₃×Q₈	—	4	2	no	—
627	C₃×Q₈	—	4	4	no	—
628	C₃×Q₈	—	6	4	no	—
629	C₃×Q₈	—	12	4	no	—
630	C₃×Q₈	—	12	2	no	—
631	C₃×Q₈	—	12	4	no	—
632	C₃×D₄	—	3	8	no	—
633	C₃×D₄	—	3	8	no	—
634	C₂×C₃×C₄	—	2	4	no	—
635	C₂×C₃×C₄	—	2	2	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	2	2	no	—
638	C₂×C₃×C₄	—	2	2	no	—
639	C₂×C₃×C₄	—	2	2	no	—
640	C₂×C₃×C₄	—	2	2	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	4	no	—
644	C₂×C₃×C₄	—	2	4	no	—
645	C₂×C₃×C₄	—	2	1	no	—
646	C₂×C₃×C₄	—	2	1	no	—
647	C₂×C₃×C₄	—	3	4	no	—
648	C₂×C₃×C₄	—	3	2	no	—
649	C₂×C₃×C₄	—	3	2	no	—
650	C₂×C₃×C₄	—	3	4	no	—
651	C₂×C₃×C₄	—	3	4	no	—
652	C₂×C₃×C₄	—	3	2	no	—
653	C₂×C₃×C₄	—	4	2	no	—
654	C₂×C₃×C₄	—	4	2	no	—
655	C₂×C₃×C₄	—	4	1	no	—
656	C₂×C₃×C₄	—	4	1	no	—
657	C₂×C₃×C₄	—	4	1	no	—
658	C₂×C₃×C₄	—	4	1	no	—
659	C₂×C₃×C₄	—	4	1	no	—
660	C₂×C₃×C₄	—	4	1	no	—
661	C₂×C₃×C₄	—	4	2	no	—
662	C₂×C₃×C₄	—	4	2	no	—
663	C₂×C₃×C₄	—	4	2	no	—
664	C₂×C₃×C₄	—	4	2	no	—
665	C₂×C₃×C₄	—	4	2	no	—
666	C₂×C₃×C₄	—	4	2	no	—
667	C₂×C₃×C₄	—	4	4	no	—
668	C₂×C₃×C₄	—	4	2	no	—
669	C₂×C₃×C₄	—	4	4	no	—
670	C₂×C₃×C₄	—	6	4	no	—
671	C₂×C₃×C₄	—	12	4	no	—
672	C₂×C₃×C₄	—	12	2	no	—
673	C₂×C₃×C₄	—	12	4	no	—
674	C₂×C₃×C₄	—	12	2	no	—
675	C₂×C₃×C₄	—	12	1	no	—
676	C₂×C₃×C₄	—	12	1	no	—
677	C₂×C₃×C₄	—	12	2	no	—
678	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
679	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
680	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
681	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
682	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
683	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
684	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
685	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
686	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
687	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
688	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
689	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
690	#67	C₂×C₃×Q₈	1	8	yes	complemented
691	#67	C₂×C₃×Q₈	1	8	yes	complemented
692	C₂×Dic₃	—	4	2	no	—
693	C₂×Dic₃	—	4	1	no	—
694	C₂×Dic₃	—	4	1	no	—
695	C₂×Dic₃	—	4	2	no	—
696	C₂×Dic₃	C₂×C₃×Q₈	1	4	yes	complemented
697	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
698	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
699	C₂×Dic₃	C₂⁴×C₃	1	4	yes	—
700	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
701	C₂×Dic₃	C₂⁴×C₃	1	2	yes	—
702	C₄×D₃	—	2	4	no	—
703	C₄×D₃	—	4	2	no	—
704	C₄×D₃	—	4	4	no	—
705	C₄×D₃	—	4	4	no	—
706	Dic₆	—	2	4	no	—
707	Dic₆	—	4	2	no	—
708	Dic₆	—	4	4	no	—
709	Dic₆	—	4	4	no	—
710	C₂×C₃²	—	2	2	no	—
711	C₂×C₃²	—	2	2	no	—
712	C₂×C₃²	—	2	2	no	—
713	C₂×C₃²	C₂³×Q₈	1	1	yes	characteristic
714	C₂×C₃²	C₂×H(5,𝔽₂)	1	1	yes	characteristic
715	C₂×C₃²	#585	1	1	yes	characteristic
716	C₃×D₃	—	2	4	no	—
717	C₂⁴	—	3	1	no	—
718	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
719	C₂×Q₈	—	3	2	no	—
720	C₂×Q₈	—	3	4	no	—
721	C₂×Q₈	—	3	2	no	—
722	C₂×Q₈	—	3	4	no	—
723	C₂×Q₈	—	4	2	no	—
724	C₂×Q₈	—	12	2	no	—
725	C₂×Q₈	—	12	4	no	—
726	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
727	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
728	C₂×D₄	—	3	2	no	—
729	C₂×D₄	—	3	2	no	—
730	C₂×D₄	—	3	8	no	—
731	C₂²×C₄	—	3	1	no	—
732	C₂²×C₄	—	3	1	no	—
733	C₂²×C₄	—	3	2	no	—
734	C₂²×C₄	—	3	2	no	—
735	C₂²×C₄	—	3	1	no	—
736	C₂²×C₄	—	3	2	no	—
737	C₂²×C₄	—	3	4	no	—
738	C₂²×C₄	—	3	4	no	—
739	C₂²×C₄	—	3	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	12	2	no	—
742	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
743	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
744	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
745	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
746	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
747	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
748	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
749	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
750	C₄⋊C₄	—	3	4	no	—
751	C₄⋊C₄	—	3	2	no	—
752	C₄⋊C₄	—	3	2	no	—
753	C₄⋊C₄	—	3	2	no	—
754	C₄⋊C₄	—	3	4	no	—
755	C₄⋊C₄	—	3	2	no	—
756	C₄⋊C₄	—	3	4	no	—
757	C₄⋊C₄	—	3	4	no	—
758	C₄⋊C₄	—	3	4	no	—
759	C₄⋊C₄	—	3	4	no	—
760	C₄⋊C₄	—	3	4	no	—
761	C₄⋊C₄	—	3	4	no	—
762	C₄⋊C₄	—	3	4	no	—
763	C₄⋊C₄	—	3	4	no	—
764	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
765	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
766	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
767	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
768	C₂²⋊C₄	—	3	4	no	—
769	C₂²⋊C₄	—	3	2	no	—
770	C₂²⋊C₄	—	3	2	no	—
771	C₂²⋊C₄	—	3	4	no	—
772	C₂²⋊C₄	—	3	2	no	—
773	C₂²⋊C₄	—	3	2	no	—
774	C₂²⋊C₄	—	3	4	no	—
775	C₂²⋊C₄	—	3	4	no	—
776	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
777	C₂²⋊C₄	C₂²×C₃×D₃	1	4	yes	—
778	C₄²	—	3	2	no	—
779	C₄²	—	3	2	no	—
780	C₄²	—	3	4	no	—
781	C₄²	—	3	4	no	—
782	C₂²×C₃	—	2	2	no	—
783	C₂²×C₃	—	2	2	no	—
784	C₂²×C₃	—	2	1	no	—
785	C₂²×C₃	—	2	1	no	—
786	C₂²×C₃	—	2	1	no	—
787	C₂²×C₃	—	2	1	no	—
788	C₂²×C₃	—	2	1	no	—
789	C₂²×C₃	—	2	1	no	—
790	C₂²×C₃	—	2	1	no	—
791	C₂²×C₃	—	2	1	no	—
792	C₂²×C₃	—	2	1	no	—
793	C₂²×C₃	—	2	1	no	—
794	C₂²×C₃	—	2	1	no	—
795	C₂²×C₃	—	2	1	no	—
796	C₂²×C₃	—	2	2	no	—
797	C₂²×C₃	—	2	2	no	—
798	C₂²×C₃	—	2	2	no	—
799	C₂²×C₃	—	2	1	no	—
800	C₂²×C₃	—	3	4	no	—
801	C₂²×C₃	—	4	1	no	—
802	C₂²×C₃	—	4	1	no	—
803	C₂²×C₃	—	4	1	no	—
804	C₂²×C₃	—	4	1	no	—
805	C₂²×C₃	—	4	4	no	—
806	C₂²×C₃	—	4	4	no	—
807	C₂²×C₃	—	4	8	no	—
808	C₂²×C₃	—	6	2	no	—
809	C₂²×C₃	—	6	2	no	—
810	C₂²×C₃	—	12	4	no	—
811	C₂²×C₃	C₂×D₃×Q₈	1	2	yes	—
812	C₂²×C₃	C₂×D₃×Q₈	1	2	yes	—
813	C₂²×C₃	C₂×D₃×Q₈	1	2	yes	—
814	C₂²×C₃	C₂²×C₃×Q₈	1	2	yes	—
815	C₂²×C₃	C₂²×C₃×Q₈	1	2	yes	—
816	C₂²×C₃	C₂²×C₃×Q₈	1	2	yes	—
817	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
818	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
819	C₂×D₃	—	2	2	no	—
820	C₂×D₃	—	2	2	no	—
821	C₂×D₃	—	4	4	no	—
822	C₂×D₃	C₂²×C₃×Q₈	1	4	yes	—
823	C₃×C₄	—	2	2	no	—
824	C₃×C₄	—	2	1	no	—
825	C₃×C₄	—	2	1	no	—
826	C₃×C₄	—	2	1	no	—
827	C₃×C₄	—	2	4	no	—
828	C₃×C₄	—	2	4	no	—
829	C₃×C₄	—	2	1	no	—
830	C₃×C₄	—	2	4	no	—
831	C₃×C₄	—	2	1	no	—
832	C₃×C₄	—	2	1	no	—
833	C₃×C₄	—	2	4	no	—
834	C₃×C₄	—	2	2	no	—
835	C₃×C₄	—	3	4	no	—
836	C₃×C₄	—	4	1	no	—
837	C₃×C₄	—	4	1	no	—
838	C₃×C₄	—	4	4	no	—
839	C₃×C₄	—	4	4	no	—
840	C₃×C₄	—	6	2	no	—
841	C₃×C₄	—	6	4	no	—
842	C₃×C₄	—	6	4	no	—
843	C₃×C₄	—	6	2	no	—
844	C₃×C₄	#1004	1	2	yes	—
845	C₃×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
846	Dic₃	—	2	4	no	—
847	Dic₃	—	2	2	no	—
848	Dic₃	—	2	2	no	—
849	Dic₃	—	2	4	no	—
850	Dic₃	C₂²×C₃×Q₈	1	4	yes	—
851	C₃²	#3501	1	1	yes	characteristic, complemented, Sylow
852	C₂³	—	3	2	no	—
853	C₂³	—	3	4	no	—
854	C₂³	—	4	1	no	—
855	C₂³	—	4	1	no	—
856	C₂³	—	12	1	no	—
857	C₂³	—	12	1	no	—
858	C₂³	C₃×D₃×Q₈	1	4	yes	complemented
859	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
860	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
861	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
862	Q₈	—	2	4	no	—
863	Q₈	—	4	2	no	—
864	Q₈	—	6	4	no	—
865	Q₈	—	12	2	no	—
866	Q₈	—	12	4	no	—
867	Q₈	—	12	4	no	—
868	D₄	—	3	8	no	—
869	D₄	—	3	8	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	3	4	no	—
874	C₂×C₄	—	3	2	no	—
875	C₂×C₄	—	3	2	no	—
876	C₂×C₄	—	3	4	no	—
877	C₂×C₄	—	3	4	no	—
878	C₂×C₄	—	3	2	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	—	4	2	no	—
884	C₂×C₄	—	6	4	no	—
885	C₂×C₄	—	12	2	no	—
886	C₂×C₄	—	12	4	no	—
887	C₂×C₄	—	12	4	no	—
888	C₂×C₄	—	12	1	no	—
889	C₂×C₄	—	12	2	no	—
890	C₂×C₄	—	12	2	no	—
891	C₂×C₄	—	12	1	no	—
892	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
893	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
894	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
895	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
896	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
897	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
898	C₂×C₃	—	2	4	no	—
899	C₂×C₃	—	2	2	no	—
900	C₂×C₃	—	2	2	no	—
901	C₂×C₃	—	2	2	no	—
902	C₂×C₃	—	2	2	no	—
903	C₂×C₃	—	2	2	no	—
904	C₂×C₃	—	2	2	no	—
905	C₂×C₃	—	2	1	no	—
906	C₂×C₃	—	2	1	no	—
907	C₂×C₃	—	2	1	no	—
908	C₂×C₃	—	4	2	no	—
909	C₂×C₃	—	4	2	no	—
910	C₂×C₃	—	6	4	no	—
911	C₂×C₃	C₂×#1004	1	1	yes	characteristic
912	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
913	C₂×C₃	#5964	1	1	yes	characteristic
914	C₂×C₃	C₂³×C₃×Q₈	1	1	yes	characteristic
915	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
916	C₂×C₃	C₃×#585	1	1	yes	characteristic
917	D₃	—	2	4	no	—
918	C₂²	—	2	1	no	—
919	C₂²	—	2	1	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	3	4	no	—
925	C₂²	—	4	4	no	—
926	C₂²	—	6	2	no	—
927	C₂²	—	6	2	no	—
928	C₂²	—	12	4	no	—
929	C₂²	C₂×C₃×D₃×Q₈	1	2	yes	—
930	C₂²	C₂×C₃×D₃×Q₈	1	2	yes	—
931	C₂²	C₂×C₃×D₃×Q₈	1	2	yes	—
932	C₂²	C₂⁴×C₃×D₃	1	1	yes	characteristic
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	4	no	—
937	C₄	—	2	4	no	—
938	C₄	—	3	4	no	—
939	C₄	—	6	2	no	—
940	C₄	—	6	4	no	—
941	C₄	—	6	4	no	—
942	C₄	—	6	2	no	—
943	C₄	C₃×#1004	1	2	yes	—
944	C₃	—	2	1	no	—
945	C₃	#85986	1	1	yes	characteristic, direct product factor
946	C₃	C₃×#3501	1	1	yes	characteristic, complemented
947	C₂	—	2	2	no	—
948	C₂	—	2	2	no	—
949	C₂	—	2	2	no	—
950	C₂	—	6	4	no	—
951	C₂	C₂×C₃×#1004	1	1	yes	characteristic
952	C₂	C₂²×C₃×D₃×Q₈	1	1	yes	characteristic
953	C₂	C₃×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₃
Fitting	C₂×C₃²×C₂²⋊Q₈	C₂
socle	C₂²×C₃²	C₂⁵
prime radical	C₂²×C₃×#67	C₂²
hypercenter	C₂×C₃×C₂²⋊Q₈	D₃
hypocenter	C₃	C₃×#3501
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₂²⋊Q₈	C₂	semidirect
2. C₃×Q₈×#67	C₂	semidirect
4. C₂×C₃×#924	C₂	semidirect
5. C₃×#5636	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×#5623	C₂	semidirect
11. C₃×#5622	C₂	semidirect
12. C₃×#5511	C₂	semidirect
13. C₃×#5511	C₂	semidirect
15. C₃×#5483	C₂	semidirect
17. #85986	C₃	direct (N × H)
18. C₂²×C₃²×Q₈	C₂²	semidirect
21. C₂×C₃×D₃×Q₈	C₂²	semidirect
23. C₂²×C₃×Dic₆	C₂²	semidirect
26. C₃²×C₂²⋊Q₈	C₂²	semidirect
27. C₃²×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₃²×C₄⋊C₄	C₂²	semidirect
29. 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
37. C₃×#944	C₂²	semidirect
45. C₂×C₃×C₄⋊Dic₃	C₂²	semidirect
48. C₃×#924	C₂²	semidirect
49. C₃×#924	C₂²	semidirect
50. C₃×#924	C₂²	semidirect
51. C₃×#924	C₂²	semidirect
53. C₂×C₃×Dic₃⋊C₄	C₂²	semidirect
55. C₃×#897	C₂²	semidirect
56. C₃×#897	C₂²	semidirect
57. C₃×#896	C₂²	semidirect
58. C₃×#896	C₂²	semidirect
59. C₃×#896	C₂²	semidirect
60. C₃×D₃×C₄⋊C₄	C₂²	semidirect
61. C₃×D₃×C₄⋊C₄	C₂²	semidirect
62. C₃×#889	C₂²	semidirect
63. C₃×#889	C₂²	semidirect
64. C₃×#889	C₂²	semidirect
65. C₃×#888	C₂²	semidirect
66. C₃×#888	C₂²	semidirect
67. C₃×#887	C₂²	semidirect
68. C₃×#887	C₂²	semidirect
74. C₃×#878	C₂²	semidirect
75. C₃×#878	C₂²	semidirect
90. C₂×C₃×C₂²⋊Q₈	D₃	semidirect
91. C₂×C₃×C₂²⋊Q₈	C₂×C₃	semidirect
94. Q₈×#67	C₂×C₃	semidirect
96. C₂×#924	C₂×C₃	semidirect
97. #5636	C₂×C₃	semidirect
98. #5635	C₂×C₃	semidirect
99. #5634	C₂×C₃	semidirect
100. #5632	C₂×C₃	semidirect
101. D₃×C₂²⋊Q₈	C₂×C₃	semidirect
102. #5623	C₂×C₃	semidirect
103. #5622	C₂×C₃	semidirect
104. #5511	C₂×C₃	semidirect
105. #5511	C₂×C₃	semidirect
107. #5483	C₂×C₃	semidirect
122. C₂×C₃×#67	Q₈	semidirect
177. C₂²×C₃×Q₈	C₂×D₃	semidirect
178. C₂²×C₃×Q₈	C₂²×C₃	semidirect
185. C₂×D₃×Q₈	C₂²×C₃	semidirect
187. C₂²×Dic₆	C₂²×C₃	semidirect
218. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
219. C₃×C₂²⋊Q₈	C₂×D₃	semidirect
222. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
223. C₃×C₂²⋊Q₈	C₂²×C₃	semidirect
243. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
244. C₂×C₃×C₄⋊C₄	C₂×D₃	semidirect
245. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
246. C₂×C₃×C₄⋊C₄	C₂²×C₃	semidirect
257. #946	C₂²×C₃	semidirect
258. #946	C₂²×C₃	semidirect
259. Q₈×Dic₃	C₂²×C₃	semidirect
260. #944	C₂²×C₃	semidirect
261. #944	C₂²×C₃	semidirect
269. C₂×C₄⋊Dic₃	C₂²×C₃	semidirect
272. #924	C₂²×C₃	semidirect
273. #924	C₂²×C₃	semidirect
274. #924	C₂²×C₃	semidirect
275. #924	C₂²×C₃	semidirect
277. C₂×Dic₃⋊C₄	C₂²×C₃	semidirect
279. #897	C₂²×C₃	semidirect
280. #897	C₂²×C₃	semidirect
281. #896	C₂²×C₃	semidirect
282. #896	C₂²×C₃	semidirect
283. #896	C₂²×C₃	semidirect
284. D₃×C₄⋊C₄	C₂²×C₃	semidirect
285. D₃×C₄⋊C₄	C₂²×C₃	semidirect
286. #889	C₂²×C₃	semidirect
287. #889	C₂²×C₃	semidirect
288. #889	C₂²×C₃	semidirect
289. #888	C₂²×C₃	semidirect
290. #888	C₂²×C₃	semidirect
291. #887	C₂²×C₃	semidirect
292. #887	C₂²×C₃	semidirect
298. #878	C₂²×C₃	semidirect
299. #878	C₂²×C₃	semidirect
303. C₂³×C₃²	C₂×Q₈	semidirect
309. C₂²×C₃×D₃	C₂×Q₈	semidirect
327. C₃×#67	C₂×Q₈	semidirect
328. C₃×#67	C₂×Q₈	semidirect
333. C₂×C₃×Dic₃	C₂×Q₈	semidirect
359. C₂×C₂²⋊Q₈	C₃×D₃	semidirect
422. C₂×#67	C₃×Q₈	semidirect
539. C₂²×Q₈	C₂×C₃×D₃	semidirect
569. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
570. C₂²⋊Q₈	C₂×C₃×D₃	semidirect
588. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
589. C₂×C₄⋊C₄	C₂×C₃×D₃	semidirect
610. C₂³×C₃	D₃×Q₈	semidirect
611. C₂³×C₃	C₂×C₃×Q₈	semidirect
620. C₂²×D₃	C₂×C₃×Q₈	semidirect
690. #67	C₂×C₃×Q₈	semidirect
691. #67	C₂×C₃×Q₈	semidirect
696. C₂×Dic₃	C₂×C₃×Q₈	semidirect
851. C₃²	#3501	semidirect
858. C₂³	C₃×D₃×Q₈	semidirect
945. C₃	#85986	direct (N × H)
946. 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
C₂×C₃²×C₂²⋊Q₈	2
C₃×Q₈×#67	2
C₂×C₃×C₄×#67	2
C₂×C₃×#924	2
C₃×#5636	2
C₃×#5635	2
C₃×#5634	2
C₃×#5632	2
C₃×D₃×C₂²⋊Q₈	2
C₃×#5623	2
C₃×#5622	2
C₃×#5511	2
C₃×#5486	2
C₃×#5483	2
C₃×#3501	3
#85986	3

Subgroups — C3×#85986 #11906157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#85986 #11906157