Subgroups — C₃×#62819 #10681426

Order 768.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3541	C₂	1	8	yes	maximal, complemented
2	C₃×#3538	C₂	1	4	yes	maximal, complemented
3	C₃×#3536	C₂	1	4	yes	maximal, complemented
4	C₃×#3535	C₂	1	8	yes	maximal, complemented
5	C₃×#3520	C₂	1	8	yes	maximal, complemented
6	C₃×#3505	C₂	1	4	yes	maximal, complemented
7	C₃×#3501	C₂	1	4	yes	maximal, complemented
8	C₃×#3495	C₂	1	4	yes	maximal, complemented
9	C₃×#3492	C₂	1	2	yes	maximal, complemented
10	C₃×#3492	C₂	1	4	yes	maximal, complemented
11	C₃×#3490	C₂	1	4	yes	maximal, complemented
12	C₃×#3489	C₂	1	4	yes	maximal, complemented
13	C₃×#3486	C₂	1	2	yes	maximal, complemented
14	C₂×C₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×C₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	#62819	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂×C₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
18	C₂²×C₃×#41	C₂²	1	2	yes	complemented
19	C₂³×C₃×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
21	C₃×#563	C₂²	1	16	yes	complemented
22	C₃×#562	C₂²	1	16	yes	complemented
23	C₃×#556	C₂²	1	8	yes	complemented
24	C₃×#554	C₂²	1	8	yes	complemented
25	C₃×#554	C₂²	1	16	yes	complemented
26	C₃×#554	C₂²	1	8	yes	complemented
27	C₃×#554	C₂²	1	16	yes	complemented
28	C₃×#553	C₂²	1	8	yes	complemented
29	C₃×#553	C₂²	1	16	yes	complemented
30	C₃×#552	C₂²	1	16	yes	complemented
31	C₃×#552	C₂²	1	8	yes	complemented
32	C₃×#552	C₂²	1	8	yes	complemented
33	C₃×#552	C₂²	1	8	yes	complemented
34	C₃×#551	C₂²	1	16	yes	complemented
35	C₃×#551	C₂²	1	16	yes	complemented
36	C₃×#551	C₂²	1	16	yes	complemented
37	C₃×D₄×Q₈	C₂²	1	8	yes	complemented
38	C₃×D₄×Q₈	C₂²	1	8	yes	complemented
39	C₃×D₄×Q₈	C₂²	1	8	yes	complemented
40	C₃×#548	C₂²	1	8	yes	complemented
41	C₃×#548	C₂²	1	8	yes	complemented
42	C₃×#548	C₂²	1	8	yes	complemented
43	C₃×#547	C₂²	1	16	yes	complemented
44	C₃×#547	C₂²	1	8	yes	complemented
45	C₃×#547	C₂²	1	8	yes	complemented
46	C₃×#546	C₂²	1	16	yes	complemented
47	C₃×#546	C₂²	1	16	yes	complemented
48	C₃×#546	C₂²	1	8	yes	complemented
49	C₃×#544	C₂²	1	2	yes	complemented
50	C₃×#544	C₂²	1	4	yes	complemented
51	C₃×#544	C₂²	1	8	yes	complemented
52	C₃×#543	C₂²	1	4	yes	—
53	C₃×#543	C₂²	1	8	yes	complemented
54	C₃×#542	C₂²	1	8	yes	complemented
55	C₃×#542	C₂²	1	16	yes	complemented
56	C₃×#541	C₂²	1	8	yes	complemented
57	C₃×#539	C₂²	1	8	yes	complemented
58	C₃×#539	C₂²	1	8	yes	complemented
59	C₃×#539	C₂²	1	8	yes	complemented
60	C₃×#539	C₂²	1	8	yes	complemented
61	C₃×#539	C₂²	1	16	yes	complemented
62	C₃×#538	C₂²	1	8	yes	complemented
63	C₃×#538	C₂²	1	8	yes	complemented
64	C₃×#538	C₂²	1	8	yes	complemented
65	C₃×#537	C₂²	1	2	yes	complemented
66	C₃×#537	C₂²	1	4	yes	complemented
67	C₃×#537	C₂²	1	8	yes	complemented
68	C₃×#536	C₂²	1	4	yes	complemented
69	C₃×#536	C₂²	1	8	yes	complemented
70	C₃×#536	C₂²	1	8	yes	complemented
71	C₃×#534	C₂²	1	4	yes	—
72	C₃×#533	C₂²	1	8	yes	complemented
73	C₃×#529	C₂²	1	8	yes	complemented
74	C₃×#525	C₂²	1	4	yes	—
75	C₃×#525	C₂²	1	4	yes	—
76	C₃×#525	C₂²	1	4	yes	—
77	C₃×#525	C₂²	1	4	yes	—
78	C₃×#525	C₂²	1	4	yes	complemented
79	C₃×#525	C₂²	1	4	yes	complemented
80	C₃×#525	C₂²	1	4	yes	complemented
81	C₃×#525	C₂²	1	4	yes	complemented
82	C₃×#525	C₂²	1	8	yes	complemented
83	C₃×#525	C₂²	1	8	yes	complemented
84	C₃×#525	C₂²	1	8	yes	complemented
85	C₂×C₃×#123	C₂²	1	4	yes	complemented
86	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
87	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
88	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
89	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
90	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
91	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
92	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
93	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
94	C₂×C₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
95	C₂×C₃×#121	C₂²	1	2	yes	—
96	C₂×C₃×#121	C₂²	1	2	yes	complemented
97	C₂×C₃×#120	C₂²	1	4	yes	—
98	C₃×#520	C₂²	1	4	yes	complemented
99	C₃×#520	C₂²	1	8	yes	complemented
100	C₃×#519	C₂²	1	2	yes	complemented
101	C₃×#518	C₂²	1	8	yes	—
102	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
103	C₂×C₃×C₄×D₄	C₂²	1	4	yes	complemented
104	C₂×C₃×#117	C₂²	1	2	yes	complemented
105	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
107	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
108	#3541	C₂×C₃	1	8	yes	complemented
109	#3538	C₂×C₃	1	4	yes	complemented
110	#3536	C₂×C₃	1	4	yes	complemented
111	#3535	C₂×C₃	1	8	yes	complemented
112	#3520	C₂×C₃	1	8	yes	complemented
113	#3505	C₂×C₃	1	4	yes	complemented
114	#3501	C₂×C₃	1	4	yes	complemented
115	#3495	C₂×C₃	1	4	yes	complemented
116	#3492	C₂×C₃	1	2	yes	complemented
117	#3492	C₂×C₃	1	4	yes	complemented
118	#3490	C₂×C₃	1	4	yes	complemented
119	#3489	C₂×C₃	1	4	yes	complemented
120	#3486	C₂×C₃	1	2	yes	complemented
121	C₂×#525	C₂×C₃	1	2	yes	complemented
122	C₂²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
123	C₂⁵×C₃	C₂³	1	1	yes	characteristic
124	C₃×2₋¹⁺⁴	—	4	8	no	—
125	C₂×C₃×#41	—	4	8	no	—
126	C₂×C₃×#41	C₂³	1	4	yes	—
127	C₂×C₃×#41	C₂³	1	4	yes	—
128	C₂×C₃×#41	C₂³	1	4	yes	—
129	C₂×C₃×#41	C₂³	1	4	yes	—
130	C₂×C₃×#41	C₂³	1	8	yes	—
131	C₂×C₃×#41	C₂³	1	8	yes	—
132	C₂×C₃×#41	C₂³	1	8	yes	complemented
133	C₂²×C₃×Q₈	—	4	4	no	—
134	C₂²×C₃×Q₈	C₂³	1	2	yes	—
135	C₂²×C₃×Q₈	C₂³	1	4	yes	—
136	C₂²×C₃×Q₈	C₂³	1	2	yes	—
137	C₂²×C₃×Q₈	C₂³	1	4	yes	—
138	C₂²×C₃×Q₈	C₂³	1	2	yes	—
139	C₂²×C₃×Q₈	C₂³	1	8	yes	complemented
140	C₂²×C₃×D₄	C₂³	1	4	yes	—
141	C₂²×C₃×D₄	C₂³	1	4	yes	—
142	C₂²×C₃×D₄	C₂³	1	2	yes	—
143	C₂²×C₃×D₄	C₂³	1	4	yes	—
144	C₂³×C₃×C₄	—	4	4	no	—
145	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
146	C₂³×C₃×C₄	C₂³	1	2	yes	—
147	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
148	C₂³×C₃×C₄	C₂³	1	2	yes	—
149	C₂³×C₃×C₄	C₂³	1	2	yes	—
150	C₂³×C₃×C₄	C₂³	1	2	yes	—
151	C₂³×C₃×C₄	C₂³	1	2	yes	—
152	C₂³×C₃×C₄	C₂³	1	2	yes	—
153	C₂³×C₃×C₄	C₂³	1	2	yes	—
154	C₂³×C₃×C₄	C₂³	1	4	yes	—
155	C₂³×C₃×C₄	C₂³	1	2	yes	—
156	C₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
157	C₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
158	C₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
159	C₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
160	C₃×#126	C₂³	1	16	yes	—
161	C₃×#126	C₂³	1	16	yes	—
162	C₃×#126	C₂³	1	16	yes	complemented
163	C₃×#126	C₂³	1	16	yes	complemented
164	C₃×#126	C₂³	1	16	yes	complemented
165	C₃×#125	C₂³	1	16	yes	complemented
166	C₃×#125	C₂³	1	16	yes	complemented
167	C₃×#125	C₂³	1	16	yes	complemented
168	C₃×#125	C₂³	1	8	yes	complemented
169	C₃×#125	C₂³	1	16	yes	complemented
170	C₃×#124	C₂³	1	16	yes	—
171	C₃×#124	C₂³	1	16	yes	—
172	C₃×#124	C₂³	1	16	yes	complemented
173	C₃×#124	C₂³	1	8	yes	complemented
174	C₃×#123	C₂³	1	8	yes	—
175	C₃×#123	C₂³	1	16	yes	—
176	C₃×#123	C₂³	1	16	yes	—
177	C₃×#123	C₂³	1	8	yes	—
178	C₃×#123	C₂³	1	8	yes	—
179	C₃×#123	C₂³	1	8	yes	—
180	C₃×#123	C₂³	1	16	yes	—
181	C₃×#123	C₂³	1	16	yes	—
182	C₃×#123	C₂³	1	16	yes	—
183	C₃×#123	C₂³	1	16	yes	complemented
184	C₃×#123	C₂³	1	16	yes	complemented
185	C₃×#123	C₂³	1	16	yes	complemented
186	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
187	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
188	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
189	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
190	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
193	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
194	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
195	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
196	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
197	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
198	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
199	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
200	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
201	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
202	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
203	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
204	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
205	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
206	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
207	C₃×C₂²⋊Q₈	C₂³	1	16	yes	—
208	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
209	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
210	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
211	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
212	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
213	C₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
214	C₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
215	C₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
216	C₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
217	C₃×#121	C₂³	1	4	yes	—
218	C₃×#121	C₂³	1	16	yes	—
219	C₃×#121	C₂³	1	16	yes	—
220	C₃×#121	C₂³	1	4	yes	—
221	C₃×#121	C₂³	1	4	yes	—
222	C₃×#121	C₂³	1	4	yes	—
223	C₃×#121	C₂³	1	4	yes	—
224	C₃×#121	C₂³	1	4	yes	—
225	C₃×#121	C₂³	1	4	yes	—
226	C₃×#121	C₂³	1	4	yes	—
227	C₃×#121	C₂³	1	8	yes	—
228	C₃×#121	C₂³	1	8	yes	—
229	C₃×#121	C₂³	1	8	yes	—
230	C₃×#121	C₂³	1	8	yes	—
231	C₃×#121	C₂³	1	16	yes	complemented
232	C₃×#121	C₂³	1	8	yes	complemented
233	C₃×#120	C₂³	1	8	yes	—
234	C₃×#120	C₂³	1	8	yes	—
235	C₃×#120	C₂³	1	8	yes	—
236	C₃×#120	C₂³	1	8	yes	—
237	C₃×#120	C₂³	1	16	yes	—
238	C₃×C₄×Q₈	C₂³	1	8	yes	complemented
239	C₃×C₄×Q₈	C₂³	1	8	yes	complemented
240	C₃×C₄×Q₈	C₂³	1	8	yes	complemented
241	C₃×C₄×Q₈	C₂³	1	16	yes	complemented
242	C₃×C₄×D₄	C₂³	1	8	yes	—
243	C₃×C₄×D₄	C₂³	1	8	yes	—
244	C₃×C₄×D₄	C₂³	1	8	yes	—
245	C₃×C₄×D₄	C₂³	1	8	yes	—
246	C₃×C₄×D₄	C₂³	1	8	yes	—
247	C₃×C₄×D₄	C₂³	1	8	yes	—
248	C₃×C₄×D₄	C₂³	1	8	yes	—
249	C₃×C₄×D₄	C₂³	1	8	yes	—
250	C₃×C₄×D₄	C₂³	1	16	yes	—
251	C₃×C₄×D₄	C₂³	1	16	yes	—
252	C₃×C₄×D₄	C₂³	1	16	yes	—
253	C₃×C₄×D₄	C₂³	1	16	yes	—
254	C₃×C₄×D₄	C₂³	1	16	yes	—
255	C₃×C₄×D₄	C₂³	1	16	yes	—
256	C₃×C₄×D₄	C₂³	1	16	yes	complemented
257	C₃×C₄×D₄	C₂³	1	8	yes	complemented
258	C₃×#117	C₂³	1	4	yes	—
259	C₃×#117	C₂³	1	4	yes	—
260	C₃×#117	C₂³	1	4	yes	—
261	C₃×#117	C₂³	1	4	yes	—
262	C₃×#117	C₂³	1	16	yes	—
263	C₃×#117	C₂³	1	8	yes	—
264	C₃×#117	C₂³	1	8	yes	—
265	C₃×#117	C₂³	1	8	yes	complemented
266	C₃×#117	C₂³	1	16	yes	complemented
267	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
268	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
269	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
270	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
271	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
272	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
274	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
275	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
276	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
277	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
278	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
279	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	complemented
280	C₂×C₃×C₄⋊C₄	C₂³	1	16	yes	complemented
281	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
282	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
283	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
284	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
285	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
286	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
287	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
288	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
289	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
290	C₂×C₃×C₂²⋊C₄	C₂³	1	16	yes	—
291	C₂×C₃×C₄²	C₂³	1	4	yes	—
292	C₂×2₋¹⁺⁴	C₂²×C₃	1	2	yes	complemented
293	C₂²×#41	C₂²×C₃	1	2	yes	complemented
294	C₂³×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
295	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
296	#563	C₂²×C₃	1	16	yes	complemented
297	#562	C₂²×C₃	1	16	yes	complemented
298	#556	C₂²×C₃	1	8	yes	complemented
299	#554	C₂²×C₃	1	8	yes	complemented
300	#554	C₂²×C₃	1	16	yes	complemented
301	#554	C₂²×C₃	1	8	yes	complemented
302	#554	C₂²×C₃	1	16	yes	complemented
303	#553	C₂²×C₃	1	8	yes	complemented
304	#553	C₂²×C₃	1	16	yes	complemented
305	#552	C₂²×C₃	1	16	yes	complemented
306	#552	C₂²×C₃	1	8	yes	complemented
307	#552	C₂²×C₃	1	8	yes	complemented
308	#552	C₂²×C₃	1	8	yes	complemented
309	#551	C₂²×C₃	1	16	yes	complemented
310	#551	C₂²×C₃	1	16	yes	complemented
311	#551	C₂²×C₃	1	16	yes	complemented
312	D₄×Q₈	C₂²×C₃	1	8	yes	complemented
313	D₄×Q₈	C₂²×C₃	1	8	yes	complemented
314	D₄×Q₈	C₂²×C₃	1	8	yes	complemented
315	#548	C₂²×C₃	1	8	yes	complemented
316	#548	C₂²×C₃	1	8	yes	complemented
317	#548	C₂²×C₃	1	8	yes	complemented
318	#547	C₂²×C₃	1	16	yes	complemented
319	#547	C₂²×C₃	1	8	yes	complemented
320	#547	C₂²×C₃	1	8	yes	complemented
321	#546	C₂²×C₃	1	16	yes	complemented
322	#546	C₂²×C₃	1	16	yes	complemented
323	#546	C₂²×C₃	1	8	yes	complemented
324	#544	C₂²×C₃	1	2	yes	complemented
325	#544	C₂²×C₃	1	4	yes	complemented
326	#544	C₂²×C₃	1	8	yes	complemented
327	#543	C₂²×C₃	1	4	yes	—
328	#543	C₂²×C₃	1	8	yes	complemented
329	#542	C₂²×C₃	1	8	yes	complemented
330	#542	C₂²×C₃	1	16	yes	complemented
331	#541	C₂²×C₃	1	8	yes	complemented
332	#539	C₂²×C₃	1	8	yes	complemented
333	#539	C₂²×C₃	1	8	yes	complemented
334	#539	C₂²×C₃	1	8	yes	complemented
335	#539	C₂²×C₃	1	8	yes	complemented
336	#539	C₂²×C₃	1	16	yes	complemented
337	#538	C₂²×C₃	1	8	yes	complemented
338	#538	C₂²×C₃	1	8	yes	complemented
339	#538	C₂²×C₃	1	8	yes	complemented
340	#537	C₂²×C₃	1	2	yes	complemented
341	#537	C₂²×C₃	1	4	yes	complemented
342	#537	C₂²×C₃	1	8	yes	complemented
343	#536	C₂²×C₃	1	4	yes	complemented
344	#536	C₂²×C₃	1	8	yes	complemented
345	#536	C₂²×C₃	1	8	yes	complemented
346	#534	C₂²×C₃	1	4	yes	—
347	#533	C₂²×C₃	1	8	yes	complemented
348	#529	C₂²×C₃	1	8	yes	complemented
349	#525	C₂²×C₃	1	4	yes	—
350	#525	C₂²×C₃	1	4	yes	—
351	#525	C₂²×C₃	1	4	yes	—
352	#525	C₂²×C₃	1	4	yes	—
353	#525	C₂²×C₃	1	4	yes	complemented
354	#525	C₂²×C₃	1	4	yes	complemented
355	#525	C₂²×C₃	1	4	yes	complemented
356	#525	C₂²×C₃	1	4	yes	complemented
357	#525	C₂²×C₃	1	8	yes	complemented
358	#525	C₂²×C₃	1	8	yes	complemented
359	#525	C₂²×C₃	1	8	yes	complemented
360	C₂×#123	C₂²×C₃	1	4	yes	complemented
361	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
362	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
363	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
364	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
365	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
366	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
367	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
368	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
369	C₂×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
370	C₂×#121	C₂²×C₃	1	2	yes	—
371	C₂×#121	C₂²×C₃	1	2	yes	complemented
372	C₂×#120	C₂²×C₃	1	4	yes	—
373	#520	C₂²×C₃	1	4	yes	complemented
374	#520	C₂²×C₃	1	8	yes	complemented
375	#519	C₂²×C₃	1	2	yes	complemented
376	#518	C₂²×C₃	1	8	yes	—
377	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
378	C₂×C₄×D₄	C₂²×C₃	1	4	yes	complemented
379	C₂×#117	C₂²×C₃	1	2	yes	complemented
380	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
381	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
382	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
383	C₂⁴×C₃	—	2	4	no	—
384	C₂⁴×C₃	—	4	2	no	—
385	C₂⁴×C₃	—	4	2	no	—
386	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
387	C₂⁴×C₃	C₂⁴	1	2	yes	—
388	C₂⁴×C₃	C₂⁴	1	2	yes	—
389	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
390	C₂⁴×C₃	C₂⁴	1	4	yes	—
391	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
392	C₃×#41	—	2	16	no	—
393	C₃×#41	—	4	8	no	—
394	C₃×#41	—	4	8	no	—
395	C₃×#41	—	4	16	no	—
396	C₃×#41	—	4	16	no	—
397	C₃×#41	—	4	8	no	—
398	C₃×#41	—	4	16	no	—
399	C₂×C₃×Q₈	—	2	8	no	—
400	C₂×C₃×Q₈	—	4	4	no	—
401	C₂×C₃×Q₈	—	4	8	no	—
402	C₂×C₃×Q₈	—	4	8	no	—
403	C₂×C₃×Q₈	—	4	4	no	—
404	C₂×C₃×Q₈	—	4	16	no	—
405	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
406	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
407	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
408	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
409	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
410	C₂×C₃×Q₈	C₂⁴	1	8	yes	—
411	C₂×C₃×D₄	—	2	16	no	—
412	C₂×C₃×D₄	—	4	4	no	—
413	C₂×C₃×D₄	—	4	8	no	—
414	C₂×C₃×D₄	—	4	8	no	—
415	C₂×C₃×D₄	C₂⁴	1	8	yes	—
416	C₂×C₃×D₄	C₂⁴	1	8	yes	—
417	C₂×C₃×D₄	C₂⁴	1	8	yes	—
418	C₂×C₃×D₄	C₂⁴	1	8	yes	—
419	C₂×C₃×D₄	C₂⁴	1	4	yes	—
420	C₂×C₃×D₄	C₂⁴	1	8	yes	—
421	C₂×C₃×D₄	C₂⁴	1	8	yes	—
422	C₂×C₃×D₄	C₂⁴	1	8	yes	—
423	C₂×C₃×D₄	C₂⁴	1	8	yes	—
424	C₂×C₃×D₄	C₂⁴	1	4	yes	—
425	C₂²×C₃×C₄	—	2	4	no	—
426	C₂²×C₃×C₄	—	2	8	no	—
427	C₂²×C₃×C₄	—	4	4	no	—
428	C₂²×C₃×C₄	—	4	4	no	—
429	C₂²×C₃×C₄	—	4	4	no	—
430	C₂²×C₃×C₄	—	4	4	no	—
431	C₂²×C₃×C₄	—	4	8	no	—
432	C₂²×C₃×C₄	—	4	4	no	—
433	C₂²×C₃×C₄	—	4	2	no	—
434	C₂²×C₃×C₄	—	4	4	no	—
435	C₂²×C₃×C₄	—	4	4	no	—
436	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
437	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
438	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
439	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
440	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
441	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
442	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
443	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
444	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
445	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
446	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
447	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
448	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
449	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
450	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
451	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
452	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
453	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
454	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
455	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
456	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
457	C₂²×C₃×C₄	C₂⁴	1	16	yes	—
458	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
459	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
460	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
461	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
462	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
463	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
464	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
465	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
466	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
467	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
468	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
469	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
470	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
471	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
472	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
473	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
474	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
475	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
476	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
477	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
478	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
479	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
480	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
481	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
482	C₃×C₄⋊C₄	C₂⁴	1	16	yes	—
483	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
484	C₃×C₄⋊C₄	C₂⁴	1	8	yes	—
485	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
486	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
487	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
488	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
489	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
490	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
491	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
492	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
493	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
494	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
495	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
496	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
497	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
498	C₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
499	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
500	C₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
501	C₃×C₄²	C₂⁴	1	8	yes	—
502	C₃×C₄²	C₂⁴	1	8	yes	—
503	C₃×C₄²	C₂⁴	1	16	yes	—
504	C₃×C₄²	C₂⁴	1	16	yes	—
505	C₂⁵	C₂³×C₃	1	1	yes	characteristic
506	2₋¹⁺⁴	—	4	8	no	—
507	C₂×#41	—	4	8	no	—
508	C₂×#41	C₂³×C₃	1	4	yes	—
509	C₂×#41	C₂³×C₃	1	8	yes	—
510	C₂×#41	C₂³×C₃	1	4	yes	—
511	C₂×#41	C₂³×C₃	1	4	yes	—
512	C₂×#41	C₂³×C₃	1	4	yes	—
513	C₂×#41	C₂³×C₃	1	8	yes	—
514	C₂×#41	C₂³×C₃	1	8	yes	complemented
515	C₂²×Q₈	—	4	4	no	—
516	C₂²×Q₈	C₂³×C₃	1	2	yes	—
517	C₂²×Q₈	C₂³×C₃	1	4	yes	—
518	C₂²×Q₈	C₂³×C₃	1	2	yes	—
519	C₂²×Q₈	C₂³×C₃	1	2	yes	—
520	C₂²×Q₈	C₂³×C₃	1	4	yes	—
521	C₂²×Q₈	C₂³×C₃	1	8	yes	complemented
522	C₂²×D₄	C₂³×C₃	1	4	yes	—
523	C₂²×D₄	C₂³×C₃	1	4	yes	—
524	C₂²×D₄	C₂³×C₃	1	4	yes	—
525	C₂²×D₄	C₂³×C₃	1	2	yes	—
526	C₂³×C₄	—	4	4	no	—
527	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₃	1	2	yes	—
529	C₂³×C₄	C₂³×C₃	1	2	yes	—
530	C₂³×C₄	C₂³×C₃	1	2	yes	—
531	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₃	1	2	yes	—
533	C₂³×C₄	C₂³×C₃	1	4	yes	—
534	C₂³×C₄	C₂³×C₃	1	2	yes	—
535	C₂³×C₄	C₂³×C₃	1	2	yes	—
536	C₂³×C₄	C₂³×C₃	1	2	yes	—
537	C₂³×C₄	C₂³×C₃	1	2	yes	—
538	C₄⋊Q₈	C₂³×C₃	1	8	yes	complemented
539	C₄⋊Q₈	C₂³×C₃	1	8	yes	complemented
540	C₄⋊Q₈	C₂³×C₃	1	16	yes	complemented
541	C₄⋊Q₈	C₂³×C₃	1	16	yes	complemented
542	#126	C₂³×C₃	1	16	yes	—
543	#126	C₂³×C₃	1	16	yes	—
544	#126	C₂³×C₃	1	16	yes	complemented
545	#126	C₂³×C₃	1	16	yes	complemented
546	#126	C₂³×C₃	1	16	yes	complemented
547	#125	C₂³×C₃	1	8	yes	complemented
548	#125	C₂³×C₃	1	16	yes	complemented
549	#125	C₂³×C₃	1	16	yes	complemented
550	#125	C₂³×C₃	1	16	yes	complemented
551	#125	C₂³×C₃	1	16	yes	complemented
552	#124	C₂³×C₃	1	16	yes	—
553	#124	C₂³×C₃	1	16	yes	—
554	#124	C₂³×C₃	1	8	yes	complemented
555	#124	C₂³×C₃	1	16	yes	complemented
556	#123	C₂³×C₃	1	8	yes	—
557	#123	C₂³×C₃	1	8	yes	—
558	#123	C₂³×C₃	1	8	yes	—
559	#123	C₂³×C₃	1	8	yes	—
560	#123	C₂³×C₃	1	16	yes	—
561	#123	C₂³×C₃	1	16	yes	—
562	#123	C₂³×C₃	1	16	yes	—
563	#123	C₂³×C₃	1	16	yes	—
564	#123	C₂³×C₃	1	16	yes	—
565	#123	C₂³×C₃	1	16	yes	complemented
566	#123	C₂³×C₃	1	16	yes	complemented
567	#123	C₂³×C₃	1	16	yes	complemented
568	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
569	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
570	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
571	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
572	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
573	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
574	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
575	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
576	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
577	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
578	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
579	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
580	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
581	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
582	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
583	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
584	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
585	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
586	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
587	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
588	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
589	C₂²⋊Q₈	C₂³×C₃	1	16	yes	—
590	C₂²⋊Q₈	C₂³×C₃	1	8	yes	complemented
591	C₂²⋊Q₈	C₂³×C₃	1	8	yes	complemented
592	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
593	C₂²⋊Q₈	C₂³×C₃	1	8	yes	complemented
594	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
595	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
596	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
597	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
598	C₂²⋊Q₈	C₂³×C₃	1	16	yes	complemented
599	#121	C₂³×C₃	1	4	yes	—
600	#121	C₂³×C₃	1	4	yes	—
601	#121	C₂³×C₃	1	4	yes	—
602	#121	C₂³×C₃	1	4	yes	—
603	#121	C₂³×C₃	1	4	yes	—
604	#121	C₂³×C₃	1	4	yes	—
605	#121	C₂³×C₃	1	4	yes	—
606	#121	C₂³×C₃	1	4	yes	—
607	#121	C₂³×C₃	1	8	yes	—
608	#121	C₂³×C₃	1	8	yes	—
609	#121	C₂³×C₃	1	8	yes	—
610	#121	C₂³×C₃	1	8	yes	—
611	#121	C₂³×C₃	1	16	yes	—
612	#121	C₂³×C₃	1	16	yes	—
613	#121	C₂³×C₃	1	8	yes	complemented
614	#121	C₂³×C₃	1	16	yes	complemented
615	#120	C₂³×C₃	1	8	yes	—
616	#120	C₂³×C₃	1	8	yes	—
617	#120	C₂³×C₃	1	8	yes	—
618	#120	C₂³×C₃	1	8	yes	—
619	#120	C₂³×C₃	1	16	yes	—
620	C₄×Q₈	C₂³×C₃	1	8	yes	complemented
621	C₄×Q₈	C₂³×C₃	1	8	yes	complemented
622	C₄×Q₈	C₂³×C₃	1	8	yes	complemented
623	C₄×Q₈	C₂³×C₃	1	16	yes	complemented
624	C₄×D₄	C₂³×C₃	1	8	yes	—
625	C₄×D₄	C₂³×C₃	1	8	yes	—
626	C₄×D₄	C₂³×C₃	1	8	yes	—
627	C₄×D₄	C₂³×C₃	1	8	yes	—
628	C₄×D₄	C₂³×C₃	1	8	yes	—
629	C₄×D₄	C₂³×C₃	1	8	yes	—
630	C₄×D₄	C₂³×C₃	1	8	yes	—
631	C₄×D₄	C₂³×C₃	1	8	yes	—
632	C₄×D₄	C₂³×C₃	1	16	yes	—
633	C₄×D₄	C₂³×C₃	1	16	yes	—
634	C₄×D₄	C₂³×C₃	1	16	yes	—
635	C₄×D₄	C₂³×C₃	1	16	yes	—
636	C₄×D₄	C₂³×C₃	1	16	yes	—
637	C₄×D₄	C₂³×C₃	1	16	yes	—
638	C₄×D₄	C₂³×C₃	1	16	yes	complemented
639	C₄×D₄	C₂³×C₃	1	8	yes	complemented
640	#117	C₂³×C₃	1	4	yes	—
641	#117	C₂³×C₃	1	4	yes	—
642	#117	C₂³×C₃	1	4	yes	—
643	#117	C₂³×C₃	1	4	yes	—
644	#117	C₂³×C₃	1	16	yes	—
645	#117	C₂³×C₃	1	8	yes	—
646	#117	C₂³×C₃	1	8	yes	—
647	#117	C₂³×C₃	1	8	yes	complemented
648	#117	C₂³×C₃	1	16	yes	complemented
649	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
651	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
652	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
653	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
654	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
656	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
657	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
661	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
662	C₂×C₄⋊C₄	C₂³×C₃	1	16	yes	complemented
663	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
673	C₂×C₄²	C₂³×C₃	1	4	yes	—
674	C₂³×C₃	—	2	2	no	—
675	C₂³×C₃	—	2	2	no	—
676	C₂³×C₃	—	2	2	no	—
677	C₂³×C₃	—	2	4	no	—
678	C₂³×C₃	—	2	4	no	—
679	C₂³×C₃	—	2	4	no	—
680	C₂³×C₃	—	2	2	no	—
681	C₂³×C₃	—	2	4	no	—
682	C₂³×C₃	—	2	8	no	—
683	C₂³×C₃	—	4	1	no	—
684	C₂³×C₃	—	4	2	no	—
685	C₂³×C₃	—	4	1	no	—
686	C₂³×C₃	—	4	1	no	—
687	C₂³×C₃	—	4	2	no	—
688	C₂³×C₃	—	4	1	no	—
689	C₂³×C₃	—	4	4	no	—
690	C₂³×C₃	—	4	4	no	—
691	C₂³×C₃	—	4	16	no	—
692	C₂³×C₃	2₋¹⁺⁴	1	4	yes	complemented
693	C₂³×C₃	C₂⁵	1	2	yes	—
694	C₂³×C₃	C₂⁵	1	8	yes	—
695	C₂³×C₃	C₂⁵	1	1	yes	characteristic
696	C₂³×C₃	C₂⁵	1	2	yes	—
697	C₂³×C₃	C₂⁵	1	1	yes	characteristic
698	C₂³×C₃	C₂⁵	1	1	yes	characteristic
699	C₃×Q₈	—	2	16	no	—
700	C₃×Q₈	—	2	8	no	—
701	C₃×Q₈	—	4	8	no	—
702	C₃×Q₈	—	4	8	no	—
703	C₃×Q₈	—	4	4	no	—
704	C₃×Q₈	—	4	8	no	—
705	C₃×D₄	—	2	16	no	—
706	C₃×D₄	—	2	16	no	—
707	C₃×D₄	—	2	16	no	—
708	C₃×D₄	—	2	16	no	—
709	C₃×D₄	—	2	8	no	—
710	C₃×D₄	—	4	8	no	—
711	C₃×D₄	—	4	4	no	—
712	C₃×D₄	—	4	8	no	—
713	C₃×D₄	—	4	8	no	—
714	C₃×D₄	—	4	8	no	—
715	C₂×C₃×C₄	—	2	2	no	—
716	C₂×C₃×C₄	—	2	4	no	—
717	C₂×C₃×C₄	—	2	8	no	—
718	C₂×C₃×C₄	—	2	8	no	—
719	C₂×C₃×C₄	—	2	8	no	—
720	C₂×C₃×C₄	—	2	4	no	—
721	C₂×C₃×C₄	—	2	4	no	—
722	C₂×C₃×C₄	—	2	4	no	—
723	C₂×C₃×C₄	—	2	4	no	—
724	C₂×C₃×C₄	—	2	4	no	—
725	C₂×C₃×C₄	—	2	4	no	—
726	C₂×C₃×C₄	—	2	16	no	—
727	C₂×C₃×C₄	—	4	1	no	—
728	C₂×C₃×C₄	—	4	2	no	—
729	C₂×C₃×C₄	—	4	2	no	—
730	C₂×C₃×C₄	—	4	2	no	—
731	C₂×C₃×C₄	—	4	1	no	—
732	C₂×C₃×C₄	—	4	2	no	—
733	C₂×C₃×C₄	—	4	2	no	—
734	C₂×C₃×C₄	—	4	4	no	—
735	C₂×C₃×C₄	—	4	4	no	—
736	C₂×C₃×C₄	—	4	4	no	—
737	C₂×C₃×C₄	—	4	4	no	—
738	C₂×C₃×C₄	—	4	4	no	—
739	C₂×C₃×C₄	—	4	8	no	—
740	C₂×C₃×C₄	—	4	4	no	—
741	C₂×C₃×C₄	—	4	16	no	—
742	C₂×C₃×C₄	—	4	16	no	—
743	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
744	C₂×C₃×C₄	C₂⁵	1	8	yes	—
745	C₂×C₃×C₄	C₂⁵	1	8	yes	—
746	C₂×C₃×C₄	C₂⁵	1	2	yes	—
747	C₂×C₃×C₄	C₂⁵	1	8	yes	—
748	C₂×C₃×C₄	C₂⁵	1	8	yes	—
749	C₂×C₃×C₄	C₂⁵	1	8	yes	—
750	C₂×C₃×C₄	C₂⁵	1	2	yes	—
751	C₂×C₃×C₄	C₂⁵	1	2	yes	—
752	C₂×C₃×C₄	C₂⁵	1	2	yes	—
753	C₂⁴	—	2	4	no	—
754	C₂⁴	—	4	2	no	—
755	C₂⁴	—	4	2	no	—
756	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
757	C₂⁴	C₂⁴×C₃	1	2	yes	—
758	C₂⁴	C₂⁴×C₃	1	2	yes	—
759	C₂⁴	C₂⁴×C₃	1	4	yes	—
760	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
761	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
762	#41	—	2	16	no	—
763	#41	—	4	8	no	—
764	#41	—	4	8	no	—
765	#41	—	4	16	no	—
766	#41	—	4	16	no	—
767	#41	—	4	8	no	—
768	#41	—	4	16	no	—
769	C₂×Q₈	—	2	8	no	—
770	C₂×Q₈	—	4	4	no	—
771	C₂×Q₈	—	4	8	no	—
772	C₂×Q₈	—	4	8	no	—
773	C₂×Q₈	—	4	4	no	—
774	C₂×Q₈	—	4	16	no	—
775	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
776	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
777	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
778	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
779	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
780	C₂×Q₈	C₂⁴×C₃	1	8	yes	—
781	C₂×D₄	—	2	16	no	—
782	C₂×D₄	—	4	4	no	—
783	C₂×D₄	—	4	8	no	—
784	C₂×D₄	—	4	8	no	—
785	C₂×D₄	C₂⁴×C₃	1	8	yes	—
786	C₂×D₄	C₂⁴×C₃	1	8	yes	—
787	C₂×D₄	C₂⁴×C₃	1	8	yes	—
788	C₂×D₄	C₂⁴×C₃	1	8	yes	—
789	C₂×D₄	C₂⁴×C₃	1	4	yes	—
790	C₂×D₄	C₂⁴×C₃	1	8	yes	—
791	C₂×D₄	C₂⁴×C₃	1	8	yes	—
792	C₂×D₄	C₂⁴×C₃	1	8	yes	—
793	C₂×D₄	C₂⁴×C₃	1	8	yes	—
794	C₂×D₄	C₂⁴×C₃	1	4	yes	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	8	no	—
797	C₂²×C₄	—	4	4	no	—
798	C₂²×C₄	—	4	4	no	—
799	C₂²×C₄	—	4	4	no	—
800	C₂²×C₄	—	4	4	no	—
801	C₂²×C₄	—	4	8	no	—
802	C₂²×C₄	—	4	4	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	4	no	—
805	C₂²×C₄	—	4	4	no	—
806	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
808	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
809	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
810	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
811	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
812	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
815	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
816	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
819	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
820	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
821	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
822	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
823	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
825	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
827	C₂²×C₄	C₂⁴×C₃	1	16	yes	—
828	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
831	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
832	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
835	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
836	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
837	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
838	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
839	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
840	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
841	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
842	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
843	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
844	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
845	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
846	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
847	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
848	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
849	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
850	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
851	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
852	C₄⋊C₄	C₂⁴×C₃	1	16	yes	—
853	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
854	C₄⋊C₄	C₂⁴×C₃	1	8	yes	—
855	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
856	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
857	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
858	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
859	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
860	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
861	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
862	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
863	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
864	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
865	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
866	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
867	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
868	C₂²⋊C₄	C₂⁴×C₃	1	8	yes	—
869	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
870	C₂²⋊C₄	C₂⁴×C₃	1	16	yes	—
871	C₄²	C₂⁴×C₃	1	8	yes	—
872	C₄²	C₂⁴×C₃	1	8	yes	—
873	C₄²	C₂⁴×C₃	1	16	yes	—
874	C₄²	C₂⁴×C₃	1	16	yes	—
875	C₂²×C₃	—	2	8	no	—
876	C₂²×C₃	—	2	1	no	—
877	C₂²×C₃	—	2	1	no	—
878	C₂²×C₃	—	2	2	no	—
879	C₂²×C₃	—	2	1	no	—
880	C₂²×C₃	—	2	1	no	—
881	C₂²×C₃	—	2	1	no	—
882	C₂²×C₃	—	2	1	no	—
883	C₂²×C₃	—	2	2	no	—
884	C₂²×C₃	—	2	2	no	—
885	C₂²×C₃	—	2	8	no	—
886	C₂²×C₃	—	2	8	no	—
887	C₂²×C₃	—	2	2	no	—
888	C₂²×C₃	—	2	8	no	—
889	C₂²×C₃	—	2	2	no	—
890	C₂²×C₃	—	4	4	no	—
891	C₂²×C₃	—	4	8	no	—
892	C₂²×C₃	—	4	8	no	—
893	C₂²×C₃	—	4	4	no	—
894	C₂²×C₃	—	8	8	no	—
895	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
896	C₂²×C₃	C₂×2₋¹⁺⁴	1	4	yes	—
897	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
898	C₂²×C₃	#585	1	2	yes	—
899	C₂²×C₃	C₂⁶	1	1	yes	characteristic
900	C₃×C₄	—	2	2	no	—
901	C₃×C₄	—	2	2	no	—
902	C₃×C₄	—	2	2	no	—
903	C₃×C₄	—	2	8	no	—
904	C₃×C₄	—	2	8	no	—
905	C₃×C₄	—	2	8	no	—
906	C₃×C₄	—	2	8	no	—
907	C₃×C₄	—	2	8	no	—
908	C₃×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	4	no	—
913	C₂³	—	2	4	no	—
914	C₂³	—	2	4	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	4	no	—
917	C₂³	—	2	8	no	—
918	C₂³	—	4	1	no	—
919	C₂³	—	4	2	no	—
920	C₂³	—	4	1	no	—
921	C₂³	—	4	1	no	—
922	C₂³	—	4	2	no	—
923	C₂³	—	4	1	no	—
924	C₂³	—	4	4	no	—
925	C₂³	—	4	4	no	—
926	C₂³	—	4	16	no	—
927	C₂³	C₃×2₋¹⁺⁴	1	4	yes	complemented
928	C₂³	C₂⁵×C₃	1	2	yes	—
929	C₂³	C₂⁵×C₃	1	8	yes	—
930	C₂³	C₂⁵×C₃	1	1	yes	characteristic
931	C₂³	C₂⁵×C₃	1	2	yes	—
932	C₂³	C₂⁵×C₃	1	1	yes	characteristic
933	C₂³	C₂⁵×C₃	1	1	yes	characteristic
934	Q₈	—	2	16	no	—
935	Q₈	—	2	8	no	—
936	Q₈	—	4	8	no	—
937	Q₈	—	4	8	no	—
938	Q₈	—	4	4	no	—
939	Q₈	—	4	8	no	—
940	D₄	—	2	16	no	—
941	D₄	—	2	16	no	—
942	D₄	—	2	16	no	—
943	D₄	—	2	16	no	—
944	D₄	—	2	8	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	8	no	—
947	D₄	—	4	8	no	—
948	D₄	—	4	8	no	—
949	D₄	—	4	8	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	4	no	—
952	C₂×C₄	—	2	8	no	—
953	C₂×C₄	—	2	8	no	—
954	C₂×C₄	—	2	8	no	—
955	C₂×C₄	—	2	4	no	—
956	C₂×C₄	—	2	4	no	—
957	C₂×C₄	—	2	4	no	—
958	C₂×C₄	—	2	4	no	—
959	C₂×C₄	—	2	4	no	—
960	C₂×C₄	—	2	4	no	—
961	C₂×C₄	—	2	16	no	—
962	C₂×C₄	—	4	1	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	4	2	no	—
969	C₂×C₄	—	4	4	no	—
970	C₂×C₄	—	4	4	no	—
971	C₂×C₄	—	4	4	no	—
972	C₂×C₄	—	4	8	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	16	no	—
977	C₂×C₄	—	4	16	no	—
978	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
979	C₂×C₄	C₂⁵×C₃	1	8	yes	—
980	C₂×C₄	C₂⁵×C₃	1	8	yes	—
981	C₂×C₄	C₂⁵×C₃	1	2	yes	—
982	C₂×C₄	C₂⁵×C₃	1	8	yes	—
983	C₂×C₄	C₂⁵×C₃	1	8	yes	—
984	C₂×C₄	C₂⁵×C₃	1	8	yes	—
985	C₂×C₄	C₂⁵×C₃	1	2	yes	—
986	C₂×C₄	C₂⁵×C₃	1	2	yes	—
987	C₂×C₄	C₂⁵×C₃	1	2	yes	—
988	C₂×C₃	—	2	2	no	—
989	C₂×C₃	—	2	2	no	—
990	C₂×C₃	—	2	2	no	—
991	C₂×C₃	—	2	4	no	—
992	C₂×C₃	—	4	2	no	—
993	C₂×C₃	—	4	8	no	—
994	C₂×C₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
995	C₂×C₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
996	C₂×C₃	C₂×#585	1	1	yes	characteristic
997	C₂²	—	2	8	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	8	no	—
1008	C₂²	—	2	8	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	8	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	4	4	no	—
1013	C₂²	—	4	8	no	—
1014	C₂²	—	4	8	no	—
1015	C₂²	—	4	4	no	—
1016	C₂²	—	8	8	no	—
1017	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
1018	C₂²	C₂×C₃×2₋¹⁺⁴	1	4	yes	—
1019	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
1020	C₂²	C₃×#585	1	2	yes	—
1021	C₂²	C₂⁶×C₃	1	1	yes	characteristic
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	8	no	—
1026	C₄	—	2	8	no	—
1027	C₄	—	2	8	no	—
1028	C₄	—	2	8	no	—
1029	C₄	—	2	8	no	—
1030	C₄	C₂×C₃×H(5,𝔽₂)	1	4	yes	—
1031	C₃	#62819	1	1	yes	characteristic, direct product factor, Sylow
1032	C₂	—	2	2	no	—
1033	C₂	—	2	2	no	—
1034	C₂	—	2	2	no	—
1035	C₂	—	2	4	no	—
1036	C₂	—	4	2	no	—
1037	C₂	—	4	8	no	—
1038	C₂	C₂²×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1039	C₂	C₂²×C₃×2₋¹⁺⁴	1	1	yes	characteristic
1040	C₂	C₂×C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3541	C₂	semidirect
2. C₃×#3538	C₂	semidirect
3. C₃×#3536	C₂	semidirect
4. C₃×#3535	C₂	semidirect
5. C₃×#3520	C₂	semidirect
6. C₃×#3505	C₂	semidirect
7. C₃×#3501	C₂	semidirect
8. C₃×#3495	C₂	semidirect
9. C₃×#3492	C₂	semidirect
10. C₃×#3492	C₂	semidirect
11. C₃×#3490	C₂	semidirect
12. C₃×#3489	C₂	semidirect
13. C₃×#3486	C₂	semidirect
14. C₂×C₃×#525	C₂	semidirect
15. C₂²×C₃×C₂²⋊Q₈	C₂	semidirect
16. #62819	C₃	direct (N × H)
17. C₂×C₃×2₋¹⁺⁴	C₂²	semidirect
18. C₂²×C₃×#41	C₂²	semidirect
19. C₂³×C₃×Q₈	C₂²	semidirect
21. C₃×#563	C₂²	semidirect
22. C₃×#562	C₂²	semidirect
23. C₃×#556	C₂²	semidirect
24. C₃×#554	C₂²	semidirect
25. C₃×#554	C₂²	semidirect
26. C₃×#554	C₂²	semidirect
27. C₃×#554	C₂²	semidirect
28. C₃×#553	C₂²	semidirect
29. C₃×#553	C₂²	semidirect
30. C₃×#552	C₂²	semidirect
31. C₃×#552	C₂²	semidirect
32. C₃×#552	C₂²	semidirect
33. C₃×#552	C₂²	semidirect
34. C₃×#551	C₂²	semidirect
35. C₃×#551	C₂²	semidirect
36. C₃×#551	C₂²	semidirect
37. C₃×D₄×Q₈	C₂²	semidirect
38. C₃×D₄×Q₈	C₂²	semidirect
39. C₃×D₄×Q₈	C₂²	semidirect
40. C₃×#548	C₂²	semidirect
41. C₃×#548	C₂²	semidirect
42. C₃×#548	C₂²	semidirect
43. C₃×#547	C₂²	semidirect
44. C₃×#547	C₂²	semidirect
45. C₃×#547	C₂²	semidirect
46. C₃×#546	C₂²	semidirect
47. C₃×#546	C₂²	semidirect
48. C₃×#546	C₂²	semidirect
49. C₃×#544	C₂²	semidirect
50. C₃×#544	C₂²	semidirect
51. C₃×#544	C₂²	semidirect
53. C₃×#543	C₂²	semidirect
54. C₃×#542	C₂²	semidirect
55. C₃×#542	C₂²	semidirect
56. C₃×#541	C₂²	semidirect
57. C₃×#539	C₂²	semidirect
58. C₃×#539	C₂²	semidirect
59. C₃×#539	C₂²	semidirect
60. C₃×#539	C₂²	semidirect
61. C₃×#539	C₂²	semidirect
62. C₃×#538	C₂²	semidirect
63. C₃×#538	C₂²	semidirect
64. C₃×#538	C₂²	semidirect
65. C₃×#537	C₂²	semidirect
66. C₃×#537	C₂²	semidirect
67. C₃×#537	C₂²	semidirect
68. C₃×#536	C₂²	semidirect
69. C₃×#536	C₂²	semidirect
70. C₃×#536	C₂²	semidirect
72. C₃×#533	C₂²	semidirect
73. C₃×#529	C₂²	semidirect
78. C₃×#525	C₂²	semidirect
79. C₃×#525	C₂²	semidirect
80. C₃×#525	C₂²	semidirect
81. C₃×#525	C₂²	semidirect
82. C₃×#525	C₂²	semidirect
83. C₃×#525	C₂²	semidirect
84. C₃×#525	C₂²	semidirect
85. C₂×C₃×#123	C₂²	semidirect
88. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
89. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
90. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
91. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
92. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
94. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
96. C₂×C₃×#121	C₂²	semidirect
98. C₃×#520	C₂²	semidirect
99. C₃×#520	C₂²	semidirect
100. C₃×#519	C₂²	semidirect
103. C₂×C₃×C₄×D₄	C₂²	semidirect
104. C₂×C₃×#117	C₂²	semidirect
105. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
106. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
108. #3541	C₂×C₃	semidirect
109. #3538	C₂×C₃	semidirect
110. #3536	C₂×C₃	semidirect
111. #3535	C₂×C₃	semidirect
112. #3520	C₂×C₃	semidirect
113. #3505	C₂×C₃	semidirect
114. #3501	C₂×C₃	semidirect
115. #3495	C₂×C₃	semidirect
116. #3492	C₂×C₃	semidirect
117. #3492	C₂×C₃	semidirect
118. #3490	C₂×C₃	semidirect
119. #3489	C₂×C₃	semidirect
120. #3486	C₂×C₃	semidirect
121. C₂×#525	C₂×C₃	semidirect
122. C₂²×C₂²⋊Q₈	C₂×C₃	semidirect
132. C₂×C₃×#41	C₂³	semidirect
139. C₂²×C₃×Q₈	C₂³	semidirect
156. C₃×C₄⋊Q₈	C₂³	semidirect
157. C₃×C₄⋊Q₈	C₂³	semidirect
158. C₃×C₄⋊Q₈	C₂³	semidirect
159. C₃×C₄⋊Q₈	C₂³	semidirect
162. C₃×#126	C₂³	semidirect
163. C₃×#126	C₂³	semidirect
164. C₃×#126	C₂³	semidirect
165. C₃×#125	C₂³	semidirect
166. C₃×#125	C₂³	semidirect
167. C₃×#125	C₂³	semidirect
168. C₃×#125	C₂³	semidirect
169. C₃×#125	C₂³	semidirect
172. C₃×#124	C₂³	semidirect
173. C₃×#124	C₂³	semidirect
183. C₃×#123	C₂³	semidirect
184. C₃×#123	C₂³	semidirect
185. C₃×#123	C₂³	semidirect
208. C₃×C₂²⋊Q₈	C₂³	semidirect
209. C₃×C₂²⋊Q₈	C₂³	semidirect
210. C₃×C₂²⋊Q₈	C₂³	semidirect
211. C₃×C₂²⋊Q₈	C₂³	semidirect
212. C₃×C₂²⋊Q₈	C₂³	semidirect
213. C₃×C₂²⋊Q₈	C₂³	semidirect
214. C₃×C₂²⋊Q₈	C₂³	semidirect
215. C₃×C₂²⋊Q₈	C₂³	semidirect
216. C₃×C₂²⋊Q₈	C₂³	semidirect
231. C₃×#121	C₂³	semidirect
232. C₃×#121	C₂³	semidirect
238. C₃×C₄×Q₈	C₂³	semidirect
239. C₃×C₄×Q₈	C₂³	semidirect
240. C₃×C₄×Q₈	C₂³	semidirect
241. C₃×C₄×Q₈	C₂³	semidirect
256. C₃×C₄×D₄	C₂³	semidirect
257. C₃×C₄×D₄	C₂³	semidirect
265. C₃×#117	C₂³	semidirect
266. C₃×#117	C₂³	semidirect
279. C₂×C₃×C₄⋊C₄	C₂³	semidirect
280. C₂×C₃×C₄⋊C₄	C₂³	semidirect
292. C₂×2₋¹⁺⁴	C₂²×C₃	semidirect
293. C₂²×#41	C₂²×C₃	semidirect
294. C₂³×Q₈	C₂²×C₃	semidirect
296. #563	C₂²×C₃	semidirect
297. #562	C₂²×C₃	semidirect
298. #556	C₂²×C₃	semidirect
299. #554	C₂²×C₃	semidirect
300. #554	C₂²×C₃	semidirect
301. #554	C₂²×C₃	semidirect
302. #554	C₂²×C₃	semidirect
303. #553	C₂²×C₃	semidirect
304. #553	C₂²×C₃	semidirect
305. #552	C₂²×C₃	semidirect
306. #552	C₂²×C₃	semidirect
307. #552	C₂²×C₃	semidirect
308. #552	C₂²×C₃	semidirect
309. #551	C₂²×C₃	semidirect
310. #551	C₂²×C₃	semidirect
311. #551	C₂²×C₃	semidirect
312. D₄×Q₈	C₂²×C₃	semidirect
313. D₄×Q₈	C₂²×C₃	semidirect
314. D₄×Q₈	C₂²×C₃	semidirect
315. #548	C₂²×C₃	semidirect
316. #548	C₂²×C₃	semidirect
317. #548	C₂²×C₃	semidirect
318. #547	C₂²×C₃	semidirect
319. #547	C₂²×C₃	semidirect
320. #547	C₂²×C₃	semidirect
321. #546	C₂²×C₃	semidirect
322. #546	C₂²×C₃	semidirect
323. #546	C₂²×C₃	semidirect
324. #544	C₂²×C₃	semidirect
325. #544	C₂²×C₃	semidirect
326. #544	C₂²×C₃	semidirect
328. #543	C₂²×C₃	semidirect
329. #542	C₂²×C₃	semidirect
330. #542	C₂²×C₃	semidirect
331. #541	C₂²×C₃	semidirect
332. #539	C₂²×C₃	semidirect
333. #539	C₂²×C₃	semidirect
334. #539	C₂²×C₃	semidirect
335. #539	C₂²×C₃	semidirect
336. #539	C₂²×C₃	semidirect
337. #538	C₂²×C₃	semidirect
338. #538	C₂²×C₃	semidirect
339. #538	C₂²×C₃	semidirect
340. #537	C₂²×C₃	semidirect
341. #537	C₂²×C₃	semidirect
342. #537	C₂²×C₃	semidirect
343. #536	C₂²×C₃	semidirect
344. #536	C₂²×C₃	semidirect
345. #536	C₂²×C₃	semidirect
347. #533	C₂²×C₃	semidirect
348. #529	C₂²×C₃	semidirect
353. #525	C₂²×C₃	semidirect
354. #525	C₂²×C₃	semidirect
355. #525	C₂²×C₃	semidirect
356. #525	C₂²×C₃	semidirect
357. #525	C₂²×C₃	semidirect
358. #525	C₂²×C₃	semidirect
359. #525	C₂²×C₃	semidirect
360. C₂×#123	C₂²×C₃	semidirect
363. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
364. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
365. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
366. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
367. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
368. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
369. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
371. C₂×#121	C₂²×C₃	semidirect
373. #520	C₂²×C₃	semidirect
374. #520	C₂²×C₃	semidirect
375. #519	C₂²×C₃	semidirect
378. C₂×C₄×D₄	C₂²×C₃	semidirect
379. C₂×#117	C₂²×C₃	semidirect
380. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
381. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
514. C₂×#41	C₂³×C₃	semidirect
521. C₂²×Q₈	C₂³×C₃	semidirect
538. C₄⋊Q₈	C₂³×C₃	semidirect
539. C₄⋊Q₈	C₂³×C₃	semidirect
540. C₄⋊Q₈	C₂³×C₃	semidirect
541. C₄⋊Q₈	C₂³×C₃	semidirect
544. #126	C₂³×C₃	semidirect
545. #126	C₂³×C₃	semidirect
546. #126	C₂³×C₃	semidirect
547. #125	C₂³×C₃	semidirect
548. #125	C₂³×C₃	semidirect
549. #125	C₂³×C₃	semidirect
550. #125	C₂³×C₃	semidirect
551. #125	C₂³×C₃	semidirect
554. #124	C₂³×C₃	semidirect
555. #124	C₂³×C₃	semidirect
565. #123	C₂³×C₃	semidirect
566. #123	C₂³×C₃	semidirect
567. #123	C₂³×C₃	semidirect
590. C₂²⋊Q₈	C₂³×C₃	semidirect
591. C₂²⋊Q₈	C₂³×C₃	semidirect
592. C₂²⋊Q₈	C₂³×C₃	semidirect
593. C₂²⋊Q₈	C₂³×C₃	semidirect
594. C₂²⋊Q₈	C₂³×C₃	semidirect
595. C₂²⋊Q₈	C₂³×C₃	semidirect
596. C₂²⋊Q₈	C₂³×C₃	semidirect
597. C₂²⋊Q₈	C₂³×C₃	semidirect
598. C₂²⋊Q₈	C₂³×C₃	semidirect
613. #121	C₂³×C₃	semidirect
614. #121	C₂³×C₃	semidirect
620. C₄×Q₈	C₂³×C₃	semidirect
621. C₄×Q₈	C₂³×C₃	semidirect
622. C₄×Q₈	C₂³×C₃	semidirect
623. C₄×Q₈	C₂³×C₃	semidirect
638. C₄×D₄	C₂³×C₃	semidirect
639. C₄×D₄	C₂³×C₃	semidirect
647. #117	C₂³×C₃	semidirect
648. #117	C₂³×C₃	semidirect
661. C₂×C₄⋊C₄	C₂³×C₃	semidirect
662. C₂×C₄⋊C₄	C₂³×C₃	semidirect
692. C₂³×C₃	2₋¹⁺⁴	semidirect
927. C₂³	C₃×2₋¹⁺⁴	semidirect
1031. C₃	#62819	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3541	2
C₃×#3538	2
C₃×#3536	2
C₃×#3535	2
C₃×#3520	2
C₃×#3505	2
C₃×#3501	2
C₃×#3495	2
C₃×#3492	2
C₃×#3490	2
C₃×#3489	2
C₃×#3486	2
C₂×C₃×#525	2
C₂²×C₃×C₂²⋊Q₈	2
#62819	3

Subgroups — C3×#62819 #10681426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#62819 #10681426