Subgroups — D₃×#234591 #72255503

Order 3072.

At least 7558 conjugacy classes of subgroups; only the 1403 normal subgroups are shown.

The subgroup lattice has 623 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72255493	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×#35050	C₂	1	1	yes	maximal, characteristic, complemented
3	#72255489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃×#1462	C₂	1	1	yes	maximal, characteristic, complemented
5	#72255480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#234591	C₂	1	1	yes	maximal, characteristic, complemented
7	#72255471	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×#9922	C₂	1	4	yes	maximal, complemented
9	C₂×D₃×#1504	C₂	1	1	yes	maximal, characteristic, complemented
10	#72255463	C₂	1	4	yes	maximal, complemented
11	#72255459	C₂	1	1	yes	maximal, characteristic, complemented
12	#72255458	C₂	1	4	yes	maximal, complemented
13	D₃×#9914	C₂	1	4	yes	maximal, complemented
14	D₃×#20598	C₂	1	1	yes	maximal, characteristic, complemented
15	#72247861	C₂	1	1	yes	maximal, characteristic, complemented
16	#72247804	C₂	1	1	yes	maximal, characteristic, complemented
17	D₃×#8020	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×D₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×D₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₃×D₄	C₂²	1	1	yes	characteristic
21	C₂×D₃×#525	C₂²	1	1	yes	characteristic
22	C₂³×D₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×#78637	C₂²	1	1	yes	characteristic, complemented
24	C₂×#80146	C₂²	1	2	yes	complemented
25	C₂×#84038	C₂²	1	1	yes	characteristic, complemented
26	C₂×#82927	C₂²	1	1	yes	characteristic, complemented
27	C₂×#80002	C₂²	1	2	yes	complemented
28	C₂×D₃×#450	C₂²	1	2	yes	complemented
29	C₂×D₃×#447	C₂²	1	2	yes	complemented
30	C₂×D₃×#407	C₂²	1	1	yes	characteristic
31	C₂×D₃×#407	C₂²	1	1	yes	characteristic
32	#10969055	C₂²	1	1	yes	characteristic, complemented
33	#10969053	C₂²	1	2	yes	complemented
34	#10969051	C₂²	1	1	yes	characteristic, complemented
35	#10969049	C₂²	1	1	yes	characteristic, complemented
36	#10969043	C₂²	1	2	yes	complemented
37	D₃×#2626	C₂²	1	2	yes	complemented
38	D₃×#2617	C₂²	1	2	yes	complemented
39	C₂²×#4671	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#4960	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#5223	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₃×#392	C₂²	1	4	yes	—
43	C₂×D₃×#392	C₂²	1	4	yes	complemented
44	D₃×#2280	C₂²	1	1	yes	characteristic
45	C₂²×D₃×#95	C₂²	1	1	yes	characteristic
46	#10794391	C₂²	1	1	yes	characteristic, complemented
47	#10794390	C₂²	1	1	yes	characteristic, complemented
48	#10794389	C₂²	1	1	yes	characteristic, complemented
49	#10794387	C₂²	1	4	yes	complemented
50	D₃×#1786	C₂²	1	4	yes	complemented
51	C₂×#69976	C₂²	1	1	yes	characteristic, complemented
52	C₂×#71708	C₂²	1	1	yes	characteristic, complemented
53	C₂×#68334	C₂²	1	2	yes	complemented
54	C₂×#69398	C₂²	1	1	yes	characteristic, complemented
55	C₂×#68302	C₂²	1	2	yes	complemented
56	C₂×D₃×#328	C₂²	1	2	yes	complemented
57	C₂×D₃×#327	C₂²	1	2	yes	complemented
58	C₂×#71539	C₂²	1	1	yes	characteristic, complemented
59	C₂×#69967	C₂²	1	1	yes	characteristic, complemented
60	C₂×#69967	C₂²	1	1	yes	characteristic, complemented
61	C₂×#68120	C₂²	1	4	yes	complemented
62	C₂×D₃×#323	C₂²	1	4	yes	complemented
63	#10695442	C₂²	1	4	yes	complemented
64	#10695441	C₂²	1	4	yes	complemented
65	#10695440	C₂²	1	4	yes	complemented
66	#10695439	C₂²	1	4	yes	complemented
67	#10695438	C₂²	1	4	yes	complemented
68	#10695437	C₂²	1	4	yes	complemented
69	#10695436	C₂²	1	4	yes	complemented
70	#10695386	C₂²	1	4	yes	complemented
71	#10695385	C₂²	1	4	yes	complemented
72	#10695384	C₂²	1	4	yes	complemented
73	#10695383	C₂²	1	4	yes	complemented
74	#10695382	C₂²	1	4	yes	complemented
75	#10695381	C₂²	1	4	yes	complemented
76	#10695380	C₂²	1	4	yes	complemented
77	#10685208	C₂²	1	1	yes	characteristic, complemented
78	#10685207	C₂²	1	1	yes	characteristic, complemented
79	#10685206	C₂²	1	1	yes	characteristic, complemented
80	#10685205	C₂²	1	4	yes	complemented
81	D₃×#1294	C₂²	1	4	yes	complemented
82	C₂×C₃×#3003	C₂²	1	1	yes	characteristic, complemented
83	C₃×#35050	C₂²	1	1	yes	characteristic, complemented
84	C₂²×C₃×#392	C₂²	1	1	yes	characteristic, complemented
85	C₃×#20598	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₃×#1504	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₃×#1462	C₂²	1	1	yes	characteristic, complemented
88	C₃×#9922	C₂²	1	4	yes	complemented
89	C₃×#9914	C₂²	1	4	yes	complemented
90	C₃×#8020	C₂²	1	1	yes	characteristic, complemented
91	#234591	D₃	1	1	yes	characteristic, direct product factor
92	C₂⁶×D₃	D₄	1	1	yes	characteristic
93	C₂⁴×C₃×D₄	C₂³	1	1	yes	characteristic
94	C₂²×D₃×#41	D₄	1	1	yes	characteristic, complemented
95	C₂³×D₃×D₄	D₄	1	8	yes	complemented
96	C₂³×D₃×D₄	C₂³	1	2	yes	—
97	C₂³×D₃×D₄	C₂³	1	2	yes	—
98	C₂⁴×D₁₂	C₂³	1	1	yes	characteristic
99	C₂⁴×C₄×D₃	D₄	1	1	yes	characteristic
100	C₂⁴×C₄×D₃	C₂³	1	1	yes	characteristic
101	C₂×C₃×#525	C₂³	1	1	yes	characteristic
102	C₂³×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
103	C₂³×#217	D₄	1	1	yes	characteristic
104	C₂×#5828	D₄	1	1	yes	characteristic, complemented
105	C₂×#5791	C₂³	1	1	yes	characteristic
106	C₂³×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
107	C₂³×(C₂×D₃)⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×D₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
109	C₂×D₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
110	C₂×#5627	D₄	1	1	yes	characteristic, complemented
111	C₂×#5627	C₂³	1	1	yes	characteristic
112	C₂×D₃×#121	D₄	1	1	yes	characteristic, complemented
113	C₂×D₃×#121	C₂³	1	1	yes	characteristic
114	C₂×#5606	D₄	1	1	yes	characteristic, complemented
115	C₂×#5606	C₂³	1	1	yes	characteristic
116	C₂×#5524	D₄	1	1	yes	characteristic, complemented
117	C₂×D₃×#117	D₄	1	1	yes	characteristic, complemented
118	C₂×D₃×#117	D₄	1	2	yes	complemented
119	C₂²×D₃×C₂²⋊C₄	D₄	1	2	yes	—
120	C₂²×D₃×C₂²⋊C₄	D₄	1	2	yes	—
121	C₂²×D₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂²×D₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₃×#450	C₂³	1	2	yes	complemented
124	C₂×C₃×#447	C₂³	1	2	yes	complemented
125	C₂×C₃×#407	C₂³	1	1	yes	characteristic
126	C₂×C₃×#407	C₂³	1	1	yes	characteristic
127	C₃×#2626	C₂³	1	2	yes	complemented
128	C₃×#2617	C₂³	1	2	yes	complemented
129	C₂×C₃×#392	C₂³	1	4	yes	—
130	C₃×#2280	C₂³	1	1	yes	characteristic
131	C₂²×C₃×#95	C₂³	1	1	yes	characteristic
132	C₂×#5223	C₂³	1	4	yes	—
133	C₂×#5218	C₂³	1	2	yes	complemented
134	C₂×#5217	C₂³	1	2	yes	complemented
135	#84027	C₂³	1	1	yes	characteristic
136	C₂²×C₃⋊#95	C₂³	1	1	yes	characteristic
137	C₂×#5207	C₂³	1	1	yes	characteristic
138	C₂×#5207	C₂³	1	1	yes	characteristic
139	#82822	C₂³	1	2	yes	complemented
140	C₂×#5046	C₂³	1	2	yes	complemented
141	#82710	C₂³	1	2	yes	complemented
142	C₂×#5036	C₂³	1	2	yes	complemented
143	#82267	D₄	1	2	yes	complemented
144	#82130	C₂³	1	2	yes	complemented
145	C₂×#4960	C₂³	1	4	yes	—
146	#82117	C₂³	1	2	yes	complemented
147	D₃×#407	D₄	1	8	yes	complemented
148	C₂×#4731	C₂³	1	2	yes	complemented
149	C₂×#4732	C₂³	1	2	yes	complemented
150	C₂×#4726	C₂³	1	2	yes	—
151	C₂×#4726	C₂³	1	2	yes	—
152	C₂×D₃×C₂²⋊C₈	C₂³	1	2	yes	—
153	C₂×D₃×C₂²⋊C₈	C₂³	1	2	yes	—
154	#74031	C₂³	1	2	yes	complemented
155	D₃×#380	D₄	1	2	yes	complemented
156	D₃×#380	C₂³	1	2	yes	—
157	#73952	C₂³	1	2	yes	complemented
158	#73862	D₄	1	2	yes	complemented
159	#73862	C₂³	1	2	yes	—
160	C₂×#4671	C₂³	1	4	yes	—
161	C₂×D₃×#95	D₄	1	8	yes	complemented
162	C₂×D₃×#95	C₂³	1	2	yes	—
163	C₂×D₃×#95	C₂³	1	2	yes	—
164	C₃×#1786	C₂³	1	4	yes	complemented
165	C₂×C₃×#328	C₂³	1	2	yes	complemented
166	C₂×C₃×#327	C₂³	1	2	yes	complemented
167	C₂×C₃×#323	C₂³	1	4	yes	complemented
168	#72128	C₂³	1	4	yes	complemented
169	C₂×#4538	C₂³	1	2	yes	complemented
170	C₂×#4537	C₂³	1	2	yes	complemented
171	C₂×#4525	C₂³	1	4	yes	complemented
172	#69959	C₂³	1	4	yes	complemented
173	C₂×#4467	C₂³	1	2	yes	complemented
174	C₂×#4470	C₂³	1	2	yes	complemented
175	C₂×#4468	C₂³	1	4	yes	complemented
176	C₂×#4468	C₂³	1	4	yes	complemented
177	#69521	C₂³	1	4	yes	complemented
178	C₂×#4452	C₂³	1	2	yes	complemented
179	C₂×#4451	C₂³	1	2	yes	complemented
180	C₃×#1294	C₂³	1	4	yes	complemented
181	#67675	C₂³	1	4	yes	complemented
182	#67624	C₂³	1	4	yes	complemented
183	#67612	C₂³	1	4	yes	complemented
184	C₂×#3003	C₂×D₃	1	1	yes	characteristic, complemented
185	#35050	C₂×D₃	1	1	yes	characteristic, complemented
186	C₂²×#392	C₂×D₃	1	1	yes	characteristic, complemented
187	#20598	C₂×D₃	1	1	yes	characteristic, complemented
188	C₂×#1504	C₂×D₃	1	1	yes	characteristic, complemented
189	C₂×#1462	C₂×D₃	1	1	yes	characteristic, complemented
190	#9922	C₂×D₃	1	4	yes	complemented
191	#9914	C₂×D₃	1	4	yes	complemented
192	#8020	C₂×D₃	1	1	yes	characteristic, complemented
193	C₂⁶×C₃	C₂×D₄	1	1	yes	characteristic
194	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
195	C₂⁵×D₃	C₂×D₄	1	2	yes	—
196	C₂⁵×D₃	C₂×D₄	1	1	yes	characteristic
197	C₂⁵×D₃	C₂×D₄	1	2	yes	—
198	C₂²×C₃×#41	C₂×D₄	1	1	yes	characteristic, complemented
199	C₂³×C₃×D₄	C₂×D₄	1	4	yes	complemented
200	C₂³×C₃×D₄	C₂⁴	1	2	yes	—
201	C₂⁴×C₃×C₄	C₂×D₄	1	1	yes	characteristic
202	C₂⁴×C₃×C₄	C₂⁴	1	1	yes	characteristic
203	C₂⁴×Dic₃	C₂×D₄	1	1	yes	characteristic
204	C₂⁴×Dic₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×#239	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂²×D₃×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
207	C₂²×#237	C₂×D₄	1	1	yes	characteristic, complemented
208	C₂²×D₃×D₄	C₂×D₄	1	8	yes	—
209	C₂²×D₃×D₄	C₂×D₄	1	8	yes	complemented
210	C₂²×D₃×D₄	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂²×#235	C₂×D₄	1	1	yes	characteristic, complemented
212	C₂³×D₁₂	C₂×D₄	1	4	yes	complemented
213	C₂³×D₁₂	C₂⁴	1	2	yes	—
214	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
215	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
216	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
217	C₂³×C₄×D₃	C₂×D₄	1	2	yes	—
218	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
219	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
220	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
221	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
222	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
223	C₂³×C₄×D₃	C₂×D₄	1	4	yes	—
224	C₂³×C₄×D₃	C₂×D₄	1	4	yes	—
225	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
226	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₄×D₃	C₂×D₄	1	4	yes	—
228	C₂³×C₄×D₃	C₂×D₄	1	1	yes	characteristic
229	C₂³×C₄×D₃	#41	1	4	yes	—
230	C₂³×C₄×D₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₄×D₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₃×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
233	C₂×C₃×C₂²⋊Q₈	C₂⁴	1	1	yes	characteristic
234	C₂×C₃×#121	C₂×D₄	1	1	yes	characteristic, complemented
235	C₂×C₃×#121	C₂⁴	1	1	yes	characteristic
236	C₂×C₃×#117	C₂×D₄	1	1	yes	characteristic, complemented
237	C₂×C₃×#117	C₂×D₄	1	2	yes	complemented
238	C₂²×C₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
239	C₂²×C₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
240	C₂²×#217	C₂×D₄	1	2	yes	—
241	C₂²×#217	C₂×D₄	1	2	yes	—
242	C₂×#946	C₂×D₄	1	1	yes	characteristic, complemented
243	C₂×#946	C₂×D₄	1	1	yes	characteristic, complemented
244	C₂×#938	C₂×D₄	1	1	yes	characteristic, complemented
245	C₂×#938	C₂×D₄	1	1	yes	characteristic, complemented
246	C₂×#930	C₂×D₄	1	1	yes	characteristic, complemented
247	C₂×#930	C₂⁴	1	1	yes	characteristic
248	C₂²×(C₂×D₃)⋊C₄	C₂×D₄	1	2	yes	—
249	C₂²×(C₂×D₃)⋊C₄	C₂×D₄	1	2	yes	—
250	C₂²×(C₂×D₃)⋊C₄	C₂×D₄	1	2	yes	—
251	C₂²×(C₂×D₃)⋊C₄	C₂⁴	1	2	yes	—
252	C₂×#926	C₂×D₄	1	1	yes	characteristic, complemented
253	C₂×#926	C₂×D₄	1	2	yes	complemented
254	C₂×#924	C₂×D₄	1	1	yes	characteristic, complemented
255	C₂×#924	C₂⁴	1	1	yes	characteristic
256	C₂×#897	C₂×D₄	1	1	yes	characteristic, complemented
257	C₂×#897	C₂×D₄	1	1	yes	characteristic, complemented
258	C₂×#895	C₂×D₄	1	1	yes	characteristic, complemented
259	C₂×#895	C₂×D₄	1	1	yes	characteristic, complemented
260	C₂×#892	C₂×D₄	1	1	yes	characteristic, complemented
261	C₂×#892	C₂×D₄	1	1	yes	characteristic, complemented
262	C₂×#892	C₂×D₄	1	4	yes	complemented
263	C₂×D₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
264	C₂×D₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
265	C₂×D₃×C₄⋊C₄	C₂×D₄	1	4	yes	complemented
266	C₃×#407	C₂×D₄	1	4	yes	complemented
267	C₂×C₃×C₂²⋊C₈	C₂⁴	1	2	yes	—
268	C₂×C₃×C₂²⋊C₈	C₂⁴	1	2	yes	—
269	C₃×#380	C₂×D₄	1	2	yes	complemented
270	C₃×#380	C₂⁴	1	2	yes	—
271	C₂×C₃×#95	C₂×D₄	1	4	yes	complemented
272	C₂×C₃×#95	C₂⁴	1	2	yes	—
273	#5212	C₂×D₄	1	2	yes	complemented
274	#5212	C₂⁴	1	2	yes	—
275	C₂×C₃⋊#95	C₂×D₄	1	4	yes	complemented
276	C₂×C₃⋊#95	C₂⁴	1	2	yes	—
277	#5207	C₂×D₄	1	4	yes	complemented
278	C₂×#830	C₂⁴	1	2	yes	—
279	C₂×#830	C₂⁴	1	2	yes	—
280	#4987	C₂×D₄	1	4	yes	complemented
281	#4987	C₂×D₄	1	4	yes	complemented
282	#4726	C₂×D₄	1	8	yes	complemented
283	D₃×C₂²⋊C₈	C₂×D₄	1	8	yes	complemented
284	D₃×#95	C₂×D₄	1	8	yes	—
285	D₃×#95	C₂×D₄	1	8	yes	complemented
286	C₂⁴×D₄	C₂²×D₃	1	1	yes	characteristic
287	C₂×#525	C₂²×D₃	1	1	yes	characteristic
288	C₂³×C₂²⋊C₄	C₂²×D₃	1	1	yes	characteristic
289	C₂×#450	C₂²×D₃	1	2	yes	complemented
290	C₂×#447	C₂²×D₃	1	2	yes	complemented
291	C₂×#407	C₂²×D₃	1	1	yes	characteristic
292	C₂×#407	C₂²×D₃	1	1	yes	characteristic
293	#2626	C₂²×D₃	1	2	yes	complemented
294	#2617	C₂²×D₃	1	2	yes	complemented
295	C₂×#392	C₂²×D₃	1	4	yes	—
296	#2280	C₂²×D₃	1	1	yes	characteristic
297	C₂²×#95	C₂²×D₃	1	1	yes	characteristic
298	#1786	C₂²×D₃	1	4	yes	complemented
299	C₂×#328	C₂²×D₃	1	2	yes	complemented
300	C₂×#327	C₂²×D₃	1	2	yes	complemented
301	C₂×#323	C₂²×D₃	1	4	yes	complemented
302	#1294	C₂²×D₃	1	4	yes	complemented
303	C₂⁵×C₃	C₂²×D₄	1	1	yes	characteristic
304	C₂⁵×C₃	C₂²×D₄	1	2	yes	—
305	C₂⁴×D₃	#120	1	4	yes	—
306	C₂⁴×D₃	#120	1	1	yes	characteristic
307	C₂⁴×D₃	#120	1	1	yes	characteristic
308	C₂⁴×D₃	#120	1	1	yes	characteristic
309	C₂⁴×D₃	#120	1	1	yes	characteristic
310	C₂⁴×D₃	#121	1	4	yes	—
311	C₂⁴×D₃	AGL(1,ℤ/8)	1	8	yes	complemented
312	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
313	C₂⁴×D₃	C₂²×D₄	1	1	yes	characteristic
314	C₂⁴×D₃	C₂²×D₄	1	2	yes	—
315	C₂²×C₃×Q₈	C₂²×D₄	1	1	yes	characteristic, complemented
316	C₂²×C₃×D₄	C₂²×D₄	1	4	yes	—
317	C₂²×C₃×D₄	C₂²×D₄	1	1	yes	characteristic, complemented
318	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
319	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
320	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
321	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
322	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
324	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
325	C₂³×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂³×C₃×C₄	C₂²×D₄	1	2	yes	—
327	C₂³×C₃×C₄	C₂×#41	1	2	yes	—
328	C₂³×C₃×C₄	C₂⁵	1	1	yes	characteristic
329	C₂³×Dic₃	#120	1	1	yes	characteristic
330	C₂³×Dic₃	#120	1	1	yes	characteristic
331	C₂³×Dic₃	#120	1	1	yes	characteristic
332	C₂³×Dic₃	#120	1	1	yes	characteristic
333	C₂³×Dic₃	#120	1	4	yes	—
334	C₂³×Dic₃	#121	1	4	yes	—
335	C₂³×Dic₃	C₂²×D₄	1	2	yes	—
336	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
337	C₂³×Dic₃	C₂²×D₄	1	1	yes	characteristic
338	C₂²×D₁₂	C₂²×D₄	1	4	yes	—
339	C₂²×D₁₂	C₂²×D₄	1	1	yes	characteristic, complemented
340	C₂²×C₄×D₃	#120	1	4	yes	—
341	C₂²×C₄×D₃	#120	1	1	yes	characteristic
342	C₂²×C₄×D₃	#120	1	1	yes	characteristic
343	C₂²×C₄×D₃	#120	1	1	yes	characteristic
344	C₂²×C₄×D₃	#120	1	1	yes	characteristic
345	C₂²×C₄×D₃	#120	1	4	yes	—
346	C₂²×C₄×D₃	#120	1	4	yes	—
347	C₂²×C₄×D₃	#120	1	4	yes	—
348	C₂²×C₄×D₃	#120	1	4	yes	—
349	C₂²×C₄×D₃	#120	1	4	yes	—
350	C₂²×C₄×D₃	#120	1	1	yes	characteristic
351	C₂²×C₄×D₃	#120	1	1	yes	characteristic
352	C₂²×C₄×D₃	#120	1	1	yes	characteristic
353	C₂²×C₄×D₃	#120	1	1	yes	characteristic
354	C₂²×C₄×D₃	#121	1	4	yes	—
355	C₂²×C₄×D₃	#121	1	4	yes	—
356	C₂²×C₄×D₃	#121	1	4	yes	—
357	C₂²×C₄×D₃	#121	1	4	yes	—
358	C₂²×C₄×D₃	#121	1	4	yes	—
359	C₂²×C₄×D₃	#121	1	4	yes	—
360	C₂²×C₄×D₃	#121	1	4	yes	—
361	C₂²×C₄×D₃	#121	1	4	yes	—
362	C₂²×C₄×D₃	#121	1	4	yes	—
363	C₂²×C₄×D₃	#121	1	4	yes	—
364	C₂²×C₄×D₃	#127	1	4	yes	—
365	C₂²×C₄×D₃	#127	1	4	yes	—
366	C₂²×C₄×D₃	#127	1	4	yes	—
367	C₂²×C₄×D₃	#127	1	4	yes	—
368	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
369	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
370	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
371	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
372	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
373	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
374	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
375	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
376	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
377	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
378	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
379	C₂²×C₄×D₃	C₂²×D₄	1	2	yes	—
380	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
381	C₂²×C₄×D₃	C₂²×D₄	1	1	yes	characteristic
382	C₂²×C₄×D₃	C₂×#41	1	2	yes	—
383	C₂²×C₄×D₃	C₂×#41	1	2	yes	—
384	C₂²×Dic₆	C₂²×D₄	1	1	yes	characteristic, complemented
385	C₂×C₃×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
386	C₂×C₃×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic, complemented
387	C₂×C₃×C₄⋊C₄	C₂²×D₄	1	4	yes	complemented
388	C₂×C₄⋊Dic₃	C₂²×D₄	1	1	yes	characteristic, complemented
389	C₂×C₄⋊Dic₃	C₂²×D₄	1	1	yes	characteristic, complemented
390	C₂×C₄⋊Dic₃	C₂²×D₄	1	4	yes	complemented
391	C₃×C₂²⋊C₈	C₂²×D₄	1	4	yes	complemented
392	C₃×#95	C₂²×D₄	1	4	yes	—
393	C₃⋊#95	C₂²×D₄	1	4	yes	—
394	#830	C₂²×D₄	1	4	yes	complemented
395	C₂⁶	D₃×D₄	1	1	yes	characteristic
396	C₂²×#41	D₃×D₄	1	1	yes	characteristic, complemented
397	C₂³×D₄	D₃×D₄	1	4	yes	complemented
398	C₂³×D₄	C₂³×D₃	1	2	yes	—
399	C₂⁴×C₄	D₃×D₄	1	1	yes	characteristic
400	C₂⁴×C₄	C₂³×D₃	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	D₃×D₄	1	1	yes	characteristic, complemented
402	C₂×C₂²⋊Q₈	C₂³×D₃	1	1	yes	characteristic
403	C₂×#121	D₃×D₄	1	1	yes	characteristic, complemented
404	C₂×#121	C₂³×D₃	1	1	yes	characteristic
405	C₂×#117	D₃×D₄	1	1	yes	characteristic, complemented
406	C₂×#117	D₃×D₄	1	2	yes	complemented
407	C₂²×C₂²⋊C₄	D₃×D₄	1	2	yes	—
408	C₂²×C₂²⋊C₄	C₂³×D₃	1	2	yes	—
409	#407	D₃×D₄	1	4	yes	complemented
410	C₂×C₂²⋊C₈	C₂³×D₃	1	2	yes	—
411	C₂×C₂²⋊C₈	C₂³×D₃	1	2	yes	—
412	#380	D₃×D₄	1	2	yes	complemented
413	#380	C₂³×D₃	1	2	yes	—
414	C₂×#95	D₃×D₄	1	4	yes	complemented
415	C₂×#95	C₂³×D₃	1	2	yes	—
416	C₂⁴×C₃	C₂×#120	1	2	yes	—
417	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
418	C₂⁴×C₃	C₂×#120	1	1	yes	characteristic
419	C₂⁴×C₃	C₂×#121	1	2	yes	—
420	C₂⁴×C₃	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
421	C₂⁴×C₃	C₂³×D₄	1	1	yes	characteristic
422	C₂³×D₃	#392	1	4	yes	—
423	C₂³×D₃	#392	1	4	yes	—
424	C₂³×D₃	#392	1	4	yes	—
425	C₂³×D₃	#392	1	4	yes	—
426	C₂³×D₃	#453	1	8	yes	—
427	C₂³×D₃	B(4,𝔽₂)	1	8	yes	—
428	C₂³×D₃	C₂×#120	1	2	yes	—
429	C₂³×D₃	C₂×#120	1	2	yes	—
430	C₂³×D₃	C₂×#120	1	1	yes	characteristic
431	C₂³×D₃	C₂×#120	1	1	yes	characteristic
432	C₂³×D₃	C₂×#120	1	1	yes	characteristic
433	C₂³×D₃	C₂×#120	1	1	yes	characteristic
434	C₂³×D₃	C₂×#121	1	2	yes	—
435	C₂³×D₃	C₂×#121	1	2	yes	—
436	C₂³×D₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
437	C₂³×D₃	C₂×AGL(1,ℤ/8)	1	4	yes	complemented
438	C₂³×D₃	#575	1	4	yes	—
439	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂×#120	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
442	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
443	C₂²×C₃×C₄	C₂×#120	1	2	yes	—
444	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
445	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
446	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
447	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
448	C₂²×C₃×C₄	C₂×#121	1	2	yes	—
449	C₂²×C₃×C₄	C₂×#127	1	2	yes	—
450	C₂²×C₃×C₄	C₂×#127	1	2	yes	—
451	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
452	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
453	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
454	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
455	C₂²×C₃×C₄	C₂³×D₄	1	1	yes	characteristic
456	C₂²×C₃×C₄	C₂²×#41	1	1	yes	characteristic
457	C₂²×Dic₃	#392	1	4	yes	—
458	C₂²×Dic₃	#392	1	4	yes	—
459	C₂²×Dic₃	#392	1	4	yes	—
460	C₂²×Dic₃	#392	1	4	yes	—
461	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
462	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
463	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
464	C₂²×Dic₃	C₂×#120	1	1	yes	characteristic
465	C₂²×Dic₃	C₂×#120	1	2	yes	—
466	C₂²×Dic₃	C₂×#120	1	2	yes	—
467	C₂²×Dic₃	C₂×#121	1	2	yes	—
468	C₂²×Dic₃	C₂×#121	1	2	yes	—
469	C₂×C₄×D₃	#392	1	4	yes	—
470	C₂×C₄×D₃	#392	1	4	yes	—
471	C₂×C₄×D₃	#392	1	4	yes	—
472	C₂×C₄×D₃	#392	1	4	yes	—
473	C₂×C₄×D₃	#392	1	4	yes	—
474	C₂×C₄×D₃	#392	1	4	yes	—
475	C₂×C₄×D₃	#392	1	4	yes	—
476	C₂×C₄×D₃	#392	1	4	yes	—
477	C₂×C₄×D₃	C₂×#120	1	2	yes	—
478	C₂×C₄×D₃	C₂×#120	1	2	yes	—
479	C₂×C₄×D₃	C₂×#120	1	2	yes	—
480	C₂×C₄×D₃	C₂×#120	1	2	yes	—
481	C₂×C₄×D₃	C₂×#121	1	2	yes	—
482	C₂×C₄×D₃	C₂×#121	1	2	yes	—
483	C₂×C₄×D₃	C₂×#121	1	2	yes	—
484	C₂×C₄×D₃	C₂×#121	1	2	yes	—
485	C₂×C₄×D₃	C₂×#121	1	2	yes	—
486	C₂×C₄×D₃	C₂×#121	1	2	yes	—
487	C₂×C₄×D₃	C₂×#121	1	2	yes	—
488	C₂×C₄×D₃	C₂×#121	1	2	yes	—
489	C₂×C₄×D₃	C₂×#127	1	2	yes	—
490	C₂×C₄×D₃	C₂×#127	1	2	yes	—
491	C₂×C₄×D₃	C₂×#127	1	2	yes	—
492	C₂×C₄×D₃	C₂×#127	1	2	yes	—
493	C₂⁵	C₂×D₃×D₄	1	1	yes	characteristic
494	C₂⁵	C₂×D₃×D₄	1	2	yes	—
495	C₂²×Q₈	C₂×D₃×D₄	1	1	yes	characteristic, complemented
496	C₂²×D₄	C₂×D₃×D₄	1	4	yes	—
497	C₂²×D₄	C₂×D₃×D₄	1	1	yes	characteristic, complemented
498	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
499	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
500	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
501	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
502	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
503	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
504	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
505	C₂³×C₄	C₂×D₃×D₄	1	2	yes	—
506	C₂³×C₄	C₂×D₃×D₄	1	1	yes	characteristic
507	C₂³×C₄	D₃×#41	1	2	yes	—
508	C₂³×C₄	C₂⁴×D₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂×D₃×D₄	1	1	yes	characteristic, complemented
510	C₂×C₄⋊C₄	C₂×D₃×D₄	1	1	yes	characteristic, complemented
511	C₂×C₄⋊C₄	C₂×D₃×D₄	1	4	yes	complemented
512	C₂²⋊C₈	C₂×D₃×D₄	1	4	yes	complemented
513	#95	C₂×D₃×D₄	1	4	yes	—
514	C₂³×C₃	C₂×#392	1	2	yes	—
515	C₂³×C₃	C₂×#392	1	2	yes	—
516	C₂³×C₃	C₂×#453	1	4	yes	—
517	C₂³×C₃	C₂×B(4,𝔽₂)	1	4	yes	—
518	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
519	C₂³×C₃	C₂²×#120	1	1	yes	characteristic
520	C₂³×C₃	C₂²×#121	1	1	yes	characteristic
521	C₂³×C₃	C₂²×AGL(1,ℤ/8)	1	2	yes	—
522	C₂³×C₃	C₂×#575	1	2	yes	—
523	C₂²×D₃	#2002	1	16	yes	—
524	C₂²×D₃	#2021	1	16	yes	—
525	C₂²×D₃	C₂×#392	1	2	yes	—
526	C₂²×D₃	C₂×#392	1	2	yes	—
527	C₂²×D₃	C₂×#392	1	2	yes	—
528	C₂²×D₃	C₂×#392	1	2	yes	—
529	C₂²×D₃	#3003	1	4	yes	—
530	C₂²×D₃	#3005	1	4	yes	—
531	C₂²×D₃	#3006	1	4	yes	—
532	C₂²×D₃	#3006	1	4	yes	—
533	C₂²×D₃	C₂×#453	1	4	yes	—
534	C₂²×D₃	C₂×#453	1	4	yes	—
535	C₂²×D₃	C₂×B(4,𝔽₂)	1	4	yes	—
536	C₂²×D₃	C₂×B(4,𝔽₂)	1	4	yes	—
537	C₂²×D₃	#3055	1	8	yes	—
538	C₂×C₃×C₄	C₂×#392	1	2	yes	—
539	C₂×C₃×C₄	C₂×#392	1	2	yes	—
540	C₂×C₃×C₄	C₂²×#120	1	1	yes	characteristic
541	C₂×C₃×C₄	C₂²×#121	1	1	yes	characteristic
542	C₂×C₃×C₄	C₂²×#121	1	1	yes	characteristic
543	C₂×C₃×C₄	C₂²×#127	1	1	yes	characteristic
544	C₂×Dic₃	C₂×#392	1	2	yes	—
545	C₂×Dic₃	C₂×#392	1	2	yes	—
546	C₂×Dic₃	C₂×#392	1	2	yes	—
547	C₂×Dic₃	C₂×#392	1	2	yes	—
548	C₂⁴	D₃×#120	1	2	yes	—
549	C₂⁴	D₃×#120	1	1	yes	characteristic
550	C₂⁴	D₃×#120	1	1	yes	characteristic
551	C₂⁴	D₃×#121	1	2	yes	—
552	C₂⁴	D₃×AGL(1,ℤ/8)	1	4	yes	complemented
553	C₂⁴	C₂²×D₃×D₄	1	1	yes	characteristic
554	C₂²×C₄	D₃×#120	1	2	yes	—
555	C₂²×C₄	D₃×#120	1	1	yes	characteristic
556	C₂²×C₄	D₃×#120	1	1	yes	characteristic
557	C₂²×C₄	D₃×#120	1	2	yes	—
558	C₂²×C₄	D₃×#120	1	2	yes	—
559	C₂²×C₄	D₃×#121	1	2	yes	—
560	C₂²×C₄	D₃×#121	1	2	yes	—
561	C₂²×C₄	D₃×#121	1	2	yes	—
562	C₂²×C₄	D₃×#121	1	2	yes	—
563	C₂²×C₄	D₃×#121	1	2	yes	—
564	C₂²×C₄	D₃×#127	1	2	yes	—
565	C₂²×C₄	D₃×#127	1	2	yes	—
566	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
567	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
568	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
569	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
570	C₂²×C₄	C₂²×D₃×D₄	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₃×#41	1	1	yes	characteristic
572	C₂²×C₃	C₂×#2002	1	4	yes	—
573	C₂²×C₃	C₂×#2021	1	4	yes	—
574	C₂²×C₃	C₂²×#392	1	1	yes	characteristic
575	C₂²×C₃	C₂×#3003	1	1	yes	characteristic
576	C₂²×C₃	C₂×#3005	1	1	yes	characteristic
577	C₂²×C₃	C₂×#3006	1	2	yes	—
578	C₂²×C₃	C₂²×#453	1	2	yes	—
579	C₂²×C₃	C₂²×B(4,𝔽₂)	1	2	yes	—
580	C₂²×C₃	C₂×#3055	1	2	yes	—
581	C₂×D₃	#18162	1	16	yes	—
582	C₂×D₃	#23391	1	4	yes	—
583	C₂×D₃	#23391	1	4	yes	—
584	C₂×D₃	C₂×#2002	1	4	yes	—
585	C₂×D₃	C₂×#2002	1	4	yes	—
586	C₂×D₃	C₂×#2021	1	4	yes	—
587	C₂×D₃	C₂×#2021	1	4	yes	—
588	C₂³	D₃×#392	1	2	yes	—
589	C₂³	D₃×#392	1	2	yes	—
590	C₂³	D₃×#453	1	4	yes	—
591	C₂³	D₃×B(4,𝔽₂)	1	4	yes	—
592	C₂³	C₂×D₃×#120	1	1	yes	characteristic
593	C₂³	C₂×D₃×#120	1	1	yes	characteristic
594	C₂³	C₂×D₃×#121	1	1	yes	characteristic
595	C₂³	C₂×D₃×AGL(1,ℤ/8)	1	2	yes	—
596	C₂³	D₃×#575	1	2	yes	—
597	C₂×C₄	D₃×#392	1	2	yes	—
598	C₂×C₄	D₃×#392	1	2	yes	—
599	C₂×C₄	C₂×D₃×#120	1	1	yes	characteristic
600	C₂×C₄	C₂×D₃×#121	1	1	yes	characteristic
601	C₂×C₄	C₂×D₃×#121	1	1	yes	characteristic
602	C₂×C₄	C₂×D₃×#127	1	1	yes	characteristic
603	C₂×C₃	C₂×#18162	1	4	yes	—
604	C₂×C₃	C₂×#23391	1	1	yes	characteristic
605	C₂×C₃	C₂²×#2002	1	1	yes	characteristic
606	C₂×C₃	C₂²×#2021	1	1	yes	characteristic
607	D₃	#234591	1	8	yes	direct product factor
608	C₂²	D₃×#2002	1	4	yes	—
609	C₂²	D₃×#2021	1	4	yes	—
610	C₂²	C₂×D₃×#392	1	1	yes	characteristic
611	C₂²	D₃×#3003	1	1	yes	characteristic
612	C₂²	D₃×#3005	1	1	yes	characteristic
613	C₂²	D₃×#3006	1	2	yes	—
614	C₂²	C₂×D₃×#453	1	2	yes	—
615	C₂²	C₂×D₃×B(4,𝔽₂)	1	2	yes	—
616	C₂²	D₃×#3055	1	2	yes	—
617	C₃	C₂×#234591	1	1	yes	characteristic, complemented, Sylow
618	C₂	C₂×D₃×#2021	1	1	yes	characteristic
619	C₂	D₃×#18162	1	4	yes	—
620	C₂	C₂×D₃×#2002	1	1	yes	characteristic
621	C₂	D₃×#23391	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×#120
commutator, cosocle	C₂³×C₃×C₄	C₂⁵
Frattini	C₂³×C₄	C₂⁴×D₃
Fitting	C₃×#234591	C₂
socle	C₂³×C₃	C₂²×#120
hypercenter	#234591	D₃
hypocenter	C₃	C₂×#234591
LCS	G ▷ C₂³×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ #234591

Complements

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

N	H ≅ G/N	type
1. #72255493	C₂	semidirect
2. D₃×#35050	C₂	semidirect
3. #72255489	C₂	semidirect
4. C₂×D₃×#1462	C₂	semidirect
5. #72255480	C₂	semidirect
6. C₃×#234591	C₂	semidirect
7. #72255471	C₂	semidirect
8. D₃×#9922	C₂	semidirect
9. C₂×D₃×#1504	C₂	semidirect
10. #72255463	C₂	semidirect
11. #72255459	C₂	semidirect
12. #72255458	C₂	semidirect
13. D₃×#9914	C₂	semidirect
14. D₃×#20598	C₂	semidirect
15. #72247861	C₂	semidirect
16. #72247804	C₂	semidirect
17. D₃×#8020	C₂	semidirect
18. C₂²×D₃×#392	C₂	semidirect
19. C₂×D₃×#3003	C₂	semidirect
23. C₂×#78637	C₂²	semidirect
24. C₂×#80146	C₂²	semidirect
25. C₂×#84038	C₂²	semidirect
26. C₂×#82927	C₂²	semidirect
27. C₂×#80002	C₂²	semidirect
28. C₂×D₃×#450	C₂²	semidirect
29. C₂×D₃×#447	C₂²	semidirect
32. #10969055	C₂²	semidirect
33. #10969053	C₂²	semidirect
34. #10969051	C₂²	semidirect
35. #10969049	C₂²	semidirect
36. #10969043	C₂²	semidirect
37. D₃×#2626	C₂²	semidirect
38. D₃×#2617	C₂²	semidirect
39. C₂²×#4671	C₂²	semidirect
40. C₂²×#4960	C₂²	semidirect
41. C₂²×#5223	C₂²	semidirect
43. C₂×D₃×#392	C₂²	semidirect
46. #10794391	C₂²	semidirect
47. #10794390	C₂²	semidirect
48. #10794389	C₂²	semidirect
49. #10794387	C₂²	semidirect
50. D₃×#1786	C₂²	semidirect
51. C₂×#69976	C₂²	semidirect
52. C₂×#71708	C₂²	semidirect
53. C₂×#68334	C₂²	semidirect
54. C₂×#69398	C₂²	semidirect
55. C₂×#68302	C₂²	semidirect
56. C₂×D₃×#328	C₂²	semidirect
57. C₂×D₃×#327	C₂²	semidirect
58. C₂×#71539	C₂²	semidirect
59. C₂×#69967	C₂²	semidirect
60. C₂×#69967	C₂²	semidirect
61. C₂×#68120	C₂²	semidirect
62. C₂×D₃×#323	C₂²	semidirect
63. #10695442	C₂²	semidirect
64. #10695441	C₂²	semidirect
65. #10695440	C₂²	semidirect
66. #10695439	C₂²	semidirect
67. #10695438	C₂²	semidirect
68. #10695437	C₂²	semidirect
69. #10695436	C₂²	semidirect
70. #10695386	C₂²	semidirect
71. #10695385	C₂²	semidirect
72. #10695384	C₂²	semidirect
73. #10695383	C₂²	semidirect
74. #10695382	C₂²	semidirect
75. #10695381	C₂²	semidirect
76. #10695380	C₂²	semidirect
77. #10685208	C₂²	semidirect
78. #10685207	C₂²	semidirect
79. #10685206	C₂²	semidirect
80. #10685205	C₂²	semidirect
81. D₃×#1294	C₂²	semidirect
82. C₂×C₃×#3003	C₂²	semidirect
83. C₃×#35050	C₂²	semidirect
84. C₂²×C₃×#392	C₂²	semidirect
85. C₃×#20598	C₂²	semidirect
86. C₂×C₃×#1504	C₂²	semidirect
87. C₂×C₃×#1462	C₂²	semidirect
88. C₃×#9922	C₂²	semidirect
89. C₃×#9914	C₂²	semidirect
90. C₃×#8020	C₂²	semidirect
91. #234591	D₃	direct (N × H)
94. C₂²×D₃×#41	D₄	semidirect
95. C₂³×D₃×D₄	D₄	semidirect
104. C₂×#5828	D₄	semidirect
108. C₂×D₃×C₂²⋊Q₈	D₄	semidirect
110. C₂×#5627	D₄	semidirect
112. C₂×D₃×#121	D₄	semidirect
114. C₂×#5606	D₄	semidirect
116. C₂×#5524	D₄	semidirect
117. C₂×D₃×#117	D₄	semidirect
118. C₂×D₃×#117	D₄	semidirect
123. C₂×C₃×#450	C₂³	semidirect
124. C₂×C₃×#447	C₂³	semidirect
127. C₃×#2626	C₂³	semidirect
128. C₃×#2617	C₂³	semidirect
133. C₂×#5218	C₂³	semidirect
134. C₂×#5217	C₂³	semidirect
139. #82822	C₂³	semidirect
140. C₂×#5046	C₂³	semidirect
141. #82710	C₂³	semidirect
142. C₂×#5036	C₂³	semidirect
143. #82267	D₄	semidirect
144. #82130	C₂³	semidirect
146. #82117	C₂³	semidirect
147. D₃×#407	D₄	semidirect
148. C₂×#4731	C₂³	semidirect
149. C₂×#4732	C₂³	semidirect
154. #74031	C₂³	semidirect
155. D₃×#380	D₄	semidirect
157. #73952	C₂³	semidirect
158. #73862	D₄	semidirect
161. C₂×D₃×#95	D₄	semidirect
164. C₃×#1786	C₂³	semidirect
165. C₂×C₃×#328	C₂³	semidirect
166. C₂×C₃×#327	C₂³	semidirect
167. C₂×C₃×#323	C₂³	semidirect
168. #72128	C₂³	semidirect
169. C₂×#4538	C₂³	semidirect
170. C₂×#4537	C₂³	semidirect
171. C₂×#4525	C₂³	semidirect
172. #69959	C₂³	semidirect
173. C₂×#4467	C₂³	semidirect
174. C₂×#4470	C₂³	semidirect
175. C₂×#4468	C₂³	semidirect
176. C₂×#4468	C₂³	semidirect
177. #69521	C₂³	semidirect
178. C₂×#4452	C₂³	semidirect
179. C₂×#4451	C₂³	semidirect
180. C₃×#1294	C₂³	semidirect
181. #67675	C₂³	semidirect
182. #67624	C₂³	semidirect
183. #67612	C₂³	semidirect
184. C₂×#3003	C₂×D₃	semidirect
185. #35050	C₂×D₃	semidirect
186. C₂²×#392	C₂×D₃	semidirect
187. #20598	C₂×D₃	semidirect
188. C₂×#1504	C₂×D₃	semidirect
189. C₂×#1462	C₂×D₃	semidirect
190. #9922	C₂×D₃	semidirect
191. #9914	C₂×D₃	semidirect
192. #8020	C₂×D₃	semidirect
198. C₂²×C₃×#41	C₂×D₄	semidirect
199. C₂³×C₃×D₄	C₂×D₄	semidirect
205. C₂²×#239	C₂×D₄	semidirect
206. C₂²×D₃×Q₈	C₂×D₄	semidirect
207. C₂²×#237	C₂×D₄	semidirect
209. C₂²×D₃×D₄	C₂×D₄	semidirect
210. C₂²×D₃×D₄	C₂×D₄	semidirect
211. C₂²×#235	C₂×D₄	semidirect
212. C₂³×D₁₂	C₂×D₄	semidirect
232. C₂×C₃×C₂²⋊Q₈	C₂×D₄	semidirect
234. C₂×C₃×#121	C₂×D₄	semidirect
236. C₂×C₃×#117	C₂×D₄	semidirect
237. C₂×C₃×#117	C₂×D₄	semidirect
242. C₂×#946	C₂×D₄	semidirect
243. C₂×#946	C₂×D₄	semidirect
244. C₂×#938	C₂×D₄	semidirect
245. C₂×#938	C₂×D₄	semidirect
246. C₂×#930	C₂×D₄	semidirect
252. C₂×#926	C₂×D₄	semidirect
253. C₂×#926	C₂×D₄	semidirect
254. C₂×#924	C₂×D₄	semidirect
256. C₂×#897	C₂×D₄	semidirect
257. C₂×#897	C₂×D₄	semidirect
258. C₂×#895	C₂×D₄	semidirect
259. C₂×#895	C₂×D₄	semidirect
260. C₂×#892	C₂×D₄	semidirect
261. C₂×#892	C₂×D₄	semidirect
262. C₂×#892	C₂×D₄	semidirect
263. C₂×D₃×C₄⋊C₄	C₂×D₄	semidirect
264. C₂×D₃×C₄⋊C₄	C₂×D₄	semidirect
265. C₂×D₃×C₄⋊C₄	C₂×D₄	semidirect
266. C₃×#407	C₂×D₄	semidirect
269. C₃×#380	C₂×D₄	semidirect
271. C₂×C₃×#95	C₂×D₄	semidirect
273. #5212	C₂×D₄	semidirect
275. C₂×C₃⋊#95	C₂×D₄	semidirect
277. #5207	C₂×D₄	semidirect
280. #4987	C₂×D₄	semidirect
281. #4987	C₂×D₄	semidirect
282. #4726	C₂×D₄	semidirect
283. D₃×C₂²⋊C₈	C₂×D₄	semidirect
285. D₃×#95	C₂×D₄	semidirect
289. C₂×#450	C₂²×D₃	semidirect
290. C₂×#447	C₂²×D₃	semidirect
293. #2626	C₂²×D₃	semidirect
294. #2617	C₂²×D₃	semidirect
298. #1786	C₂²×D₃	semidirect
299. C₂×#328	C₂²×D₃	semidirect
300. C₂×#327	C₂²×D₃	semidirect
301. C₂×#323	C₂²×D₃	semidirect
302. #1294	C₂²×D₃	semidirect
311. C₂⁴×D₃	AGL(1,ℤ/8)	semidirect
315. C₂²×C₃×Q₈	C₂²×D₄	semidirect
317. C₂²×C₃×D₄	C₂²×D₄	semidirect
339. C₂²×D₁₂	C₂²×D₄	semidirect
384. C₂²×Dic₆	C₂²×D₄	semidirect
385. C₂×C₃×C₄⋊C₄	C₂²×D₄	semidirect
386. C₂×C₃×C₄⋊C₄	C₂²×D₄	semidirect
387. C₂×C₃×C₄⋊C₄	C₂²×D₄	semidirect
388. C₂×C₄⋊Dic₃	C₂²×D₄	semidirect
389. C₂×C₄⋊Dic₃	C₂²×D₄	semidirect
390. C₂×C₄⋊Dic₃	C₂²×D₄	semidirect
391. C₃×C₂²⋊C₈	C₂²×D₄	semidirect
394. #830	C₂²×D₄	semidirect
396. C₂²×#41	D₃×D₄	semidirect
397. C₂³×D₄	D₃×D₄	semidirect
401. C₂×C₂²⋊Q₈	D₃×D₄	semidirect
403. C₂×#121	D₃×D₄	semidirect
405. C₂×#117	D₃×D₄	semidirect
406. C₂×#117	D₃×D₄	semidirect
409. #407	D₃×D₄	semidirect
412. #380	D₃×D₄	semidirect
414. C₂×#95	D₃×D₄	semidirect
420. C₂⁴×C₃	C₂×AGL(1,ℤ/8)	semidirect
437. C₂³×D₃	C₂×AGL(1,ℤ/8)	semidirect
495. C₂²×Q₈	C₂×D₃×D₄	semidirect
497. C₂²×D₄	C₂×D₃×D₄	semidirect
509. C₂×C₄⋊C₄	C₂×D₃×D₄	semidirect
510. C₂×C₄⋊C₄	C₂×D₃×D₄	semidirect
511. C₂×C₄⋊C₄	C₂×D₃×D₄	semidirect
512. C₂²⋊C₈	C₂×D₃×D₄	semidirect
552. C₂⁴	D₃×AGL(1,ℤ/8)	semidirect
607. D₃	#234591	direct (N × H)
617. C₃	C₂×#234591	semidirect

Maximal subgroups

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

subgroup	index
#72255493	2
D₃×#35050	2
#72255489	2
C₂×D₃×#1462	2
#72255480	2
C₃×#234591	2
#72255471	2
D₃×#9922	2
C₂×D₃×#1504	2
#72255463	2
#72255459	2
#72255458	2
D₃×#9914	2
D₃×#20598	2
#72247861	2
#72247804	2
D₃×#8020	2
C₂²×D₃×#392	2
C₂×D₃×#3003	2
C₂×#234591	3

Subgroups — D3×#234591 #72255503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#234591 #72255503