Subgroups — #72303992

Order 2048.

At least 6939 conjugacy classes of subgroups; only the 386 normal subgroups are shown.

The subgroup lattice has 345 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72303989	C₂	1	2	yes	maximal, complemented
2	#72303988	C₂	1	2	yes	maximal, complemented
3	#72303986	C₂	1	2	yes	maximal, complemented
4	#72303982	C₂	1	1	yes	maximal, characteristic, complemented
5	#72303970	C₂	1	1	yes	maximal, characteristic, complemented
6	#72303926	C₂	1	1	yes	maximal, characteristic, complemented
7	#72303922	C₂	1	1	yes	maximal, characteristic
8	#72303900	C₂	1	1	yes	maximal, characteristic, complemented
9	#72303897	C₂	1	1	yes	maximal, characteristic, complemented
10	#72303879	C₂	1	1	yes	maximal, characteristic, complemented
11	#72233617	C₂	1	2	yes	maximal, complemented
12	C₂×#34738	C₂²	1	1	yes	characteristic
13	C₂×C₄×#560	C₄	1	1	yes	characteristic, complemented
14	#6374136	C₂²	1	1	yes	characteristic
15	#6342640	C₂²	1	1	yes	characteristic
16	#4941405	C₂²	1	1	yes	characteristic
17	#4941386	C₂²	1	1	yes	characteristic
18	#4941297	C₂²	1	1	yes	characteristic
19	#4941278	C₂²	1	1	yes	characteristic
20	#4941255	C₄	1	1	yes	characteristic, complemented
21	#4941236	C₄	1	1	yes	characteristic, complemented
22	#4941179	C₄	1	1	yes	characteristic, complemented
23	#4941160	C₄	1	1	yes	characteristic, complemented
24	#610024	C₄	1	1	yes	characteristic, complemented
25	#609932	C₂²	1	1	yes	characteristic
26	#609021	C₄	1	1	yes	characteristic, complemented
27	#609006	C₂²	1	1	yes	characteristic
28	#520948	C₄	1	1	yes	characteristic, complemented
29	#188081	C₂²	1	1	yes	characteristic
30	#188029	C₂²	1	1	yes	characteristic
31	#139938	C₂²	1	2	yes	—
32	#139906	C₂²	1	2	yes	—
33	#139827	C₂²	1	2	yes	—
34	#139826	C₂²	1	2	yes	—
35	#139511	C₂²	1	2	yes	—
36	#139509	C₂²	1	2	yes	—
37	#139472	C₂²	1	2	yes	—
38	#139432	C₂²	1	2	yes	—
39	#134020	C₂²	1	2	yes	—
40	#133972	C₂²	1	2	yes	—
41	#115167	C₂²	1	2	yes	—
42	#115165	C₂²	1	2	yes	—
43	C₂⁴×#41	D₄	1	1	yes	characteristic
44	C₂²×#560	C₂×C₄	1	1	yes	characteristic
45	C₂²×#525	C₂³	1	1	yes	characteristic
46	C₂×#2436	C₂³	1	1	yes	characteristic
47	C₂×#2435	D₄	1	1	yes	characteristic
48	C₂×#2434	D₄	1	1	yes	characteristic
49	C₂×#2433	C₂³	1	1	yes	characteristic
50	C₂×#2410	C₂×C₄	1	1	yes	characteristic
51	C₂×#2410	C₂×C₄	1	1	yes	characteristic
52	C₂×#2410	D₄	1	1	yes	characteristic
53	C₂×#2410	D₄	1	1	yes	characteristic
54	C₂×#2397	D₄	1	1	yes	characteristic
55	C₂×#2392	D₄	1	1	yes	characteristic
56	C₂×#2380	C₂×C₄	1	1	yes	characteristic
57	C₂×#2376	C₂×C₄	1	1	yes	characteristic
58	C₂×#2375	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×#127	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×#123	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×#123	D₄	1	1	yes	characteristic
62	C₂×C₄×#120	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×#120	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×#120	D₄	1	1	yes	characteristic
65	C₂×C₄×#120	D₄	1	1	yes	characteristic
66	C₂×#2297	D₄	1	1	yes	characteristic
67	C₂²×C₄×C₂²⋊C₄	D₄	1	1	yes	characteristic
68	#21752	C₂³	1	2	yes	—
69	#17396	C₂³	1	2	yes	—
70	#16014	C₂×C₄	1	1	yes	characteristic
71	#15984	D₄	1	1	yes	characteristic
72	#15984	C₂³	1	1	yes	characteristic
73	#15982	D₄	1	1	yes	characteristic
74	#15982	D₄	1	1	yes	characteristic
75	#15948	C₂×C₄	1	1	yes	characteristic
76	#15948	C₂×C₄	1	1	yes	characteristic
77	#15948	C₂×C₄	1	1	yes	characteristic
78	#15463	C₂×C₄	1	1	yes	characteristic
79	#15453	D₄	1	1	yes	characteristic
80	#15430	D₄	1	1	yes	characteristic
81	#15412	D₄	1	1	yes	characteristic
82	#15384	D₄	1	1	yes	characteristic
83	#15342	C₂×C₄	1	1	yes	characteristic
84	#15340	C₂³	1	1	yes	characteristic
85	#15313	C₂×C₄	1	1	yes	characteristic
86	#15310	C₂³	1	1	yes	characteristic
87	#15283	C₂×C₄	1	1	yes	characteristic
88	#15281	C₂×C₄	1	1	yes	characteristic
89	#15266	C₂×C₄	1	1	yes	characteristic
90	#15260	D₄	1	1	yes	characteristic
91	#15260	C₂³	1	1	yes	characteristic
92	#15258	C₂×C₄	1	1	yes	characteristic
93	#15258	C₂×C₄	1	1	yes	characteristic
94	#14516	C₂×C₄	1	1	yes	characteristic
95	#14516	C₂×C₄	1	1	yes	characteristic
96	#14358	C₂×C₄	1	1	yes	characteristic
97	#14358	C₂×C₄	1	1	yes	characteristic
98	#13851	D₄	1	1	yes	characteristic
99	#13847	C₂×C₄	1	1	yes	characteristic
100	#13839	C₂×C₄	1	1	yes	characteristic
101	#13839	D₄	1	1	yes	characteristic
102	C₄×#390	D₄	1	1	yes	characteristic
103	#13761	D₄	1	1	yes	characteristic
104	#8549	C₂³	1	2	yes	—
105	#8542	C₂³	1	2	yes	—
106	C₂³×#41	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
112	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
113	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
114	C₂²×#127	C₂²×C₄	1	1	yes	characteristic
115	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
117	C₂²×#123	C₂×D₄	1	1	yes	characteristic
118	C₂²×#123	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
121	C₂²×#121	C₂×D₄	1	1	yes	characteristic
122	C₂²×#121	C₂⁴	1	1	yes	characteristic
123	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
124	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
125	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
126	C₂²×#120	C₂×D₄	1	1	yes	characteristic
127	C₂²×#120	C₂×D₄	1	1	yes	characteristic
128	C₂²×#120	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×D₄	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄×D₄	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
134	C₂²×#117	C₂²⋊C₄	1	1	yes	characteristic
135	C₂²×#117	C₂×D₄	1	1	yes	characteristic
136	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
137	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic
139	C₂×#399	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×#399	C₂×D₄	1	1	yes	characteristic
141	C₂×#398	C₂×D₄	1	1	yes	characteristic
142	C₂×#397	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×#394	C₂×D₄	1	1	yes	characteristic
144	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
145	C₂×#392	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×#392	C₂×D₄	1	1	yes	characteristic
147	C₂×#390	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×#390	C₂²×C₄	1	1	yes	characteristic
149	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×#386	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×#386	C₂²×C₄	1	1	yes	characteristic
153	C₂×#386	C₂²×C₄	1	1	yes	characteristic
154	C₂×#386	C₂²×C₄	1	1	yes	characteristic
155	C₂×#386	C₂×D₄	1	1	yes	characteristic
156	C₂×#386	C₂×D₄	1	1	yes	characteristic
157	C₂×#386	C₂×D₄	1	1	yes	characteristic
158	C₂×#386	C₂×D₄	1	1	yes	characteristic
159	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×#385	C₂×D₄	1	1	yes	characteristic
165	C₂×#384	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×#381	C₂²⋊C₄	1	1	yes	characteristic
167	C₂×#381	C₂×D₄	1	1	yes	characteristic
168	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
169	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
178	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
179	C₂×#376	C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄³	C₂²⋊C₄	1	1	yes	characteristic
181	#1445	C₂²⋊C₄	1	1	yes	characteristic
182	#1445	C₂²⋊C₄	1	1	yes	characteristic
183	#1440	C₂²⋊C₄	1	1	yes	characteristic
184	#1440	C₂²⋊C₄	1	1	yes	characteristic
185	#1440	C₂×D₄	1	1	yes	characteristic
186	#1440	C₂×D₄	1	1	yes	characteristic
187	#1438	C₂²⋊C₄	1	1	yes	characteristic
188	#1438	C₂²⋊C₄	1	1	yes	characteristic
189	#1438	C₂²⋊C₄	1	1	yes	characteristic
190	#1438	C₂²⋊C₄	1	1	yes	characteristic
191	#1438	C₂²×C₄	1	1	yes	characteristic
192	#1438	C₂²×C₄	1	1	yes	characteristic
193	#1438	C₂²×C₄	1	1	yes	characteristic
194	#1438	C₂²×C₄	1	1	yes	characteristic
195	#1438	C₂×D₄	1	1	yes	characteristic
196	#1438	C₂×D₄	1	1	yes	characteristic
197	#1437	C₂²⋊C₄	1	1	yes	characteristic
198	#1437	C₂²⋊C₄	1	1	yes	characteristic
199	#1437	C₂²⋊C₄	1	1	yes	characteristic
200	#1437	C₂²⋊C₄	1	1	yes	characteristic
201	#1437	C₂×D₄	1	1	yes	characteristic
202	#1437	C₂×D₄	1	1	yes	characteristic
203	#1436	C₂×D₄	1	1	yes	characteristic
204	#1436	C₂×D₄	1	1	yes	characteristic
205	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×Q₈	#120	1	1	yes	characteristic
209	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂³×D₄	#120	1	1	yes	characteristic
213	C₂³×D₄	#120	1	1	yes	characteristic
214	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
215	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
216	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
217	C₂⁴×C₄	#99	1	2	yes	—
218	C₂⁴×C₄	#99	1	2	yes	—
219	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂⁴×C₄	#120	1	1	yes	characteristic
226	C₂⁴×C₄	#120	1	1	yes	characteristic
227	C₂⁴×C₄	#120	1	1	yes	characteristic
228	C₂⁴×C₄	#120	1	1	yes	characteristic
229	C₂⁴×C₄	#120	1	1	yes	characteristic
230	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
254	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
258	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₄²	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄²	#120	1	1	yes	characteristic
262	C₄×C₂²⋊C₄	#99	1	2	yes	—
263	C₄×C₂²⋊C₄	#99	1	2	yes	—
264	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×#95	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂⁵	#379	1	1	yes	characteristic
269	C₂⁵	#379	1	1	yes	characteristic
270	C₂⁵	C₂×#99	1	2	yes	—
271	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
273	C₂⁵	C₂×#120	1	1	yes	characteristic
274	C₂³×C₄	#379	1	1	yes	characteristic
275	C₂³×C₄	#379	1	1	yes	characteristic
276	C₂³×C₄	#379	1	1	yes	characteristic
277	C₂³×C₄	#379	1	1	yes	characteristic
278	C₂³×C₄	#379	1	1	yes	characteristic
279	C₂³×C₄	#379	1	1	yes	characteristic
280	C₂³×C₄	C₂×#99	1	1	yes	characteristic
281	C₂³×C₄	C₂×#99	1	1	yes	characteristic
282	C₂³×C₄	C₂×#99	1	1	yes	characteristic
283	C₂³×C₄	C₂×#99	1	1	yes	characteristic
284	C₂³×C₄	C₂×#99	1	2	yes	—
285	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
286	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
287	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
288	C₂³×C₄	B(4,𝔽₂)	1	1	yes	characteristic
289	C₂³×C₄	#458	1	1	yes	characteristic
290	C₂³×C₄	#458	1	1	yes	characteristic
291	C₂³×C₄	#458	1	1	yes	characteristic
292	C₂³×C₄	#458	1	1	yes	characteristic
293	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₂³×C₄	C₂×#120	1	1	yes	characteristic
295	C₂³×C₄	C₂×#120	1	1	yes	characteristic
296	C₂³×C₄	C₂×#120	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×#99	1	2	yes	—
299	C₂⁴	#1790	1	1	yes	characteristic
300	C₂⁴	#1790	1	1	yes	characteristic
301	C₂⁴	#1790	1	1	yes	characteristic
302	C₂⁴	#1790	1	1	yes	characteristic
303	C₂⁴	C₂×#379	1	1	yes	characteristic
304	C₂⁴	C₂²×#99	1	1	yes	characteristic
305	C₂⁴	C₂²×#99	1	1	yes	characteristic
306	C₂²×C₄	#1781	1	1	yes	characteristic
307	C₂²×C₄	#1781	1	1	yes	characteristic
308	C₂²×C₄	#1781	1	1	yes	characteristic
309	C₂²×C₄	#1781	1	1	yes	characteristic
310	C₂²×C₄	#1790	1	1	yes	characteristic
311	C₂²×C₄	#1790	1	1	yes	characteristic
312	C₂²×C₄	#1790	1	1	yes	characteristic
313	C₂²×C₄	#1790	1	1	yes	characteristic
314	C₂²×C₄	#2200	1	4	yes	—
315	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
316	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
317	C₂²×C₄	C₂×#458	1	1	yes	characteristic
318	C₂²×C₄	C₂×#458	1	1	yes	characteristic
319	C₂²⋊C₄	#2120	1	4	yes	—
320	C₂³	#12762	1	2	yes	—
321	C₂³	C₂×#1781	1	1	yes	characteristic
322	C₂³	C₂×#1790	1	1	yes	characteristic
323	C₂³	C₂×#1790	1	1	yes	characteristic
324	C₂³	C₂×#2120	1	2	yes	—
325	C₂×C₄	#8534	1	1	yes	characteristic
326	C₂×C₄	#8534	1	1	yes	characteristic
327	C₂×C₄	#8534	1	1	yes	characteristic
328	C₂×C₄	#8534	1	1	yes	characteristic
329	C₂×C₄	#12753	1	2	yes	—
330	C₂×C₄	#12762	1	2	yes	—
331	C₂×C₄	C₂×#2200	1	2	yes	—
332	C₂²	C₂×#8534	1	1	yes	characteristic
333	C₂²	#493352	1	1	yes	characteristic
334	C₂²	#493390	1	1	yes	characteristic
335	C₂²	C₂×#12753	1	1	yes	characteristic
336	C₂²	#493569	1	1	yes	characteristic
337	C₂²	C₂×#12762	1	1	yes	characteristic
338	C₂²	#493600	1	1	yes	characteristic
339	C₄	#133396	1	2	yes	—
340	C₄	#133396	1	2	yes	—
341	C₂	C₂×#133396	1	1	yes	characteristic
342	C₂	#72303814	1	1	yes	characteristic
343	C₂	#72303871	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#8534
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂²×#121	C₂⁴
socle	C₂²	C₂×#8534
prime radical	#72303922	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#525 ◁ G
LECS	G ▷ C₂²×#121 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72303989	C₂	semidirect
2. #72303988	C₂	semidirect
3. #72303986	C₂	semidirect
4. #72303982	C₂	semidirect
5. #72303970	C₂	semidirect
6. #72303926	C₂	semidirect
8. #72303900	C₂	semidirect
9. #72303897	C₂	semidirect
10. #72303879	C₂	semidirect
11. #72233617	C₂	semidirect
13. C₂×C₄×#560	C₄	semidirect
20. #4941255	C₄	semidirect
21. #4941236	C₄	semidirect
22. #4941179	C₄	semidirect
23. #4941160	C₄	semidirect
24. #610024	C₄	semidirect
26. #609021	C₄	semidirect
28. #520948	C₄	semidirect

Maximal subgroups

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

subgroup	index
#72303989	2
#72303988	2
#72303986	2
#72303982	2
#72303970	2
#72303926	2
#72303922	2
#72303900	2
#72303897	2
#72303879	2
#72233617	2