Subgroups — #72262921

Order 4096.

At least 19236 conjugacy classes of subgroups; only the 721 normal subgroups are shown.

The subgroup lattice has 464 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262918	C₂	1	2	yes	maximal, complemented
2	#72262911	C₂	1	2	yes	maximal, complemented
3	#72262905	C₂	1	2	yes	maximal, complemented
4	#72262900	C₂	1	2	yes	maximal, complemented
5	#72262832	C₂	1	1	yes	maximal, characteristic
6	#72262830	C₄	1	2	yes	complemented
7	#72262829	C₄	1	2	yes	complemented
8	#72262828	C₂²	1	2	yes	—
9	#72262827	C₂²	1	2	yes	—
10	#72262799	C₄	1	1	yes	characteristic, complemented
11	#72262796	C₄	1	1	yes	characteristic, complemented
12	#72262796	C₄	1	1	yes	characteristic, complemented
13	#72262608	C₂	1	1	yes	maximal, characteristic, complemented
14	#72256119	C₂²	1	1	yes	characteristic, complemented
15	#72256111	C₂²	1	1	yes	characteristic, complemented
16	#72238361	C₂	1	1	yes	maximal, characteristic, complemented
17	#72237996	C₂	1	1	yes	maximal, characteristic, complemented
18	#72237995	C₂²	1	2	yes	complemented
19	#72237994	C₂²	1	2	yes	complemented
20	#72237886	C₂	1	1	yes	maximal, characteristic, complemented
21	#72237884	C₂²	1	2	yes	complemented
22	#72237585	C₂	1	1	yes	maximal, characteristic, complemented
23	#72237583	C₂²	1	2	yes	complemented
24	#72237582	C₂²	1	2	yes	complemented
25	#72237489	C₂²	1	2	yes	complemented
26	#72237486	C₂²	1	2	yes	complemented
27	#72237471	C₂	1	1	yes	maximal, characteristic, complemented
28	#72237459	C₂²	1	2	yes	complemented
29	#72235246	C₂²	1	1	yes	characteristic, complemented
30	#72235242	C₂²	1	1	yes	characteristic, complemented
31	#72234724	C₂²	1	2	yes	complemented
32	#72234636	C₂²	1	1	yes	characteristic
33	#72234636	C₂²	1	1	yes	characteristic
34	#72225985	C₂²	1	2	yes	complemented
35	#72225870	C₂²	1	1	yes	characteristic, complemented
36	#72225713	C₂²	1	1	yes	characteristic, complemented
37	#72225665	C₂²	1	1	yes	characteristic
38	#72219499	C₄	1	1	yes	characteristic, complemented
39	#72219314	C₂²	1	1	yes	characteristic, complemented
40	#72219310	C₂²	1	1	yes	characteristic, complemented
41	C₂³×D₄²	D₄	1	1	yes	characteristic
42	C₂×#46996	D₄	1	1	yes	characteristic
43	C₂×#46996	D₄	1	1	yes	characteristic
44	C₂×#34980	C₂³	1	1	yes	characteristic
45	#6374251	C₂³	1	1	yes	characteristic
46	#6374128	C₂³	1	1	yes	characteristic
47	#5519715	C₂×C₄	1	2	yes	—
48	#5519571	C₂×C₄	1	2	yes	—
49	#5486623	C₂×C₄	1	2	yes	—
50	#5486602	D₄	1	2	yes	—
51	#5236713	C₂×C₄	1	2	yes	—
52	#5236421	D₄	1	2	yes	—
53	#5084903	D₄	1	2	yes	—
54	#5083335	D₄	1	2	yes	—
55	#5069375	D₄	1	2	yes	—
56	#5065220	D₄	1	2	yes	—
57	#5024691	D₄	1	1	yes	characteristic
58	#5024691	D₄	1	1	yes	characteristic
59	#5020751	C₂×C₄	1	1	yes	characteristic
60	#5020751	C₂×C₄	1	1	yes	characteristic
61	#4607564	C₂×C₄	1	2	yes	—
62	#4607171	D₄	1	2	yes	—
63	#4466055	C₂×C₄	1	2	yes	—
64	#4447413	D₄	1	2	yes	—
65	#4439977	D₄	1	2	yes	—
66	#4430405	D₄	1	1	yes	characteristic
67	#4430405	D₄	1	1	yes	characteristic
68	#4420586	C₂×C₄	1	1	yes	characteristic
69	#4420586	C₂×C₄	1	1	yes	characteristic
70	#4420586	D₄	1	1	yes	characteristic
71	#4420586	D₄	1	1	yes	characteristic
72	#4380237	C₂³	1	2	yes	—
73	#4379766	C₂×C₄	1	2	yes	—
74	#4379716	C₂³	1	2	yes	—
75	#2081109	D₄	1	2	yes	—
76	#2081074	D₄	1	2	yes	—
77	#2039918	D₄	1	2	yes	—
78	#2032505	D₄	1	2	yes	—
79	#1494104	C₂×C₄	1	2	yes	—
80	#1460307	C₂×C₄	1	2	yes	—
81	#1419371	D₄	1	2	yes	—
82	#1418393	C₂×C₄	1	2	yes	—
83	#845298	D₄	1	2	yes	—
84	#663621	D₄	1	1	yes	characteristic
85	#663621	D₄	1	1	yes	characteristic
86	#659380	D₄	1	2	yes	—
87	#650612	D₄	1	2	yes	—
88	#648360	C₂×C₄	1	1	yes	characteristic
89	#648360	C₂×C₄	1	1	yes	characteristic
90	#647656	C₂×C₄	1	1	yes	characteristic
91	#647656	C₂×C₄	1	1	yes	characteristic
92	#647656	D₄	1	2	yes	—
93	#617710	D₄	1	1	yes	characteristic
94	#617710	C₂³	1	1	yes	characteristic
95	#616969	D₄	1	2	yes	—
96	#616960	D₄	1	1	yes	characteristic
97	#616960	C₂³	1	1	yes	characteristic
98	#612424	D₄	1	2	yes	—
99	#576160	D₄	1	1	yes	characteristic
100	#576160	D₄	1	1	yes	characteristic
101	#556752	D₄	1	1	yes	characteristic
102	#188122	C₂³	1	2	yes	—
103	#188109	C₂³	1	1	yes	characteristic
104	#188109	C₂³	1	2	yes	—
105	#188049	C₂³	1	1	yes	characteristic
106	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
107	C₂²×D₄²	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×D₄²	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×D₄²	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×D₄²	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×D₄²	C₂²⋊C₄	1	2	yes	complemented
112	C₂²×#534	C₂×D₄	1	1	yes	characteristic
113	C₂²×#534	C₂⁴	1	1	yes	characteristic
114	C₂³×#127	C₂×D₄	1	1	yes	characteristic
115	C₂³×#120	C₂²⋊C₄	1	2	yes	complemented
116	C₂³×#120	C₂×D₄	1	1	yes	characteristic
117	C₂³×#120	C₂×D₄	1	1	yes	characteristic
118	C₂×#2760	C₂²⋊C₄	1	2	yes	complemented
119	C₂×#2684	C₂²⋊C₄	1	2	yes	complemented
120	C₂×#2675	C₂²⋊C₄	1	2	yes	complemented
121	C₂×#2670	C₂²⋊C₄	1	2	yes	complemented
122	C₂×#2840	C₂²⋊C₄	1	1	yes	characteristic, complemented
123	C₂×#2840	C₂²⋊C₄	1	1	yes	characteristic, complemented
124	C₂×#2849	C₂×D₄	1	1	yes	characteristic
125	C₂×#2849	C₂×D₄	1	1	yes	characteristic
126	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
127	C₂×#2846	C₂×D₄	1	1	yes	characteristic
128	C₂×#2846	C₂×D₄	1	2	yes	—
129	C₂×#2404	C₂×D₄	1	2	yes	—
130	C₂×#2431	C₂×D₄	1	2	yes	—
131	C₂×#2410	C₂²×C₄	1	2	yes	—
132	C₂×#2403	C₂²⋊C₄	1	1	yes	characteristic, complemented
133	C₂×#2403	C₂²⋊C₄	1	1	yes	characteristic, complemented
134	C₂×#2403	C₂²⋊C₄	1	2	yes	complemented
135	C₂×#2403	C₂×D₄	1	2	yes	—
136	C₂×#2615	C₂×D₄	1	2	yes	—
137	C₂×#2613	C₂²×C₄	1	1	yes	characteristic
138	C₂×#2613	C₂×D₄	1	1	yes	characteristic
139	C₂×#2613	C₂×D₄	1	2	yes	—
140	C₂×#2613	C₂×D₄	1	1	yes	characteristic
141	C₂×#2613	C₂×D₄	1	1	yes	characteristic
142	C₂×#2613	C₂×D₄	1	2	yes	—
143	C₂×#2308	C₂²⋊C₄	1	2	yes	complemented
144	C₂×#2308	C₂×D₄	1	1	yes	characteristic
145	C₂×#2308	C₂×D₄	1	1	yes	characteristic
146	C₂²×#379	C₂×D₄	1	1	yes	characteristic
147	#17273	C₂²⋊C₄	1	2	yes	complemented
148	#17272	C₂²⋊C₄	1	2	yes	complemented
149	#17105	C₂²⋊C₄	1	2	yes	complemented
150	#17102	C₂²⋊C₄	1	2	yes	complemented
151	#16214	C₂²⋊C₄	1	2	yes	complemented
152	#15984	C₂×D₄	1	2	yes	—
153	#15982	C₂×D₄	1	2	yes	—
154	#15950	C₂×D₄	1	2	yes	—
155	#15948	C₂²⋊C₄	1	1	yes	characteristic
156	#15948	C₂²⋊C₄	1	1	yes	characteristic
157	#15948	C₂×D₄	1	1	yes	characteristic
158	#15948	C₂×D₄	1	1	yes	characteristic
159	#15948	C₂×D₄	1	2	yes	—
160	#15948	C₂×D₄	1	2	yes	—
161	#15947	C₂²⋊C₄	1	1	yes	characteristic
162	#15947	C₂²⋊C₄	1	1	yes	characteristic
163	#15947	C₂²⋊C₄	1	2	yes	complemented
164	#15947	C₂²×C₄	1	1	yes	characteristic
165	#15947	C₂²×C₄	1	1	yes	characteristic
166	#15947	C₂×D₄	1	2	yes	—
167	#15668	C₂×D₄	1	2	yes	—
168	#15668	C₂×D₄	1	2	yes	—
169	#15636	C₂²⋊C₄	1	2	yes	complemented
170	#15622	C₂²⋊C₄	1	2	yes	complemented
171	#15467	C₂²⋊C₄	1	2	yes	complemented
172	#15467	C₂²⋊C₄	1	2	yes	complemented
173	#15420	C₂²⋊C₄	1	2	yes	complemented
174	#15412	C₂×D₄	1	2	yes	—
175	#15412	C₂×D₄	1	2	yes	—
176	#15313	C₂²⋊C₄	1	2	yes	complemented
177	#15310	C₂×D₄	1	2	yes	—
178	#15310	C₂×D₄	1	2	yes	—
179	#15267	C₂²⋊C₄	1	2	yes	complemented
180	#15267	C₂²⋊C₄	1	2	yes	complemented
181	#15267	C₂²⋊C₄	1	2	yes	complemented
182	#15267	C₂²⋊C₄	1	2	yes	complemented
183	#15266	C₂²⋊C₄	1	2	yes	complemented
184	#15261	C₂²⋊C₄	1	1	yes	characteristic
185	#15261	C₂²⋊C₄	1	1	yes	characteristic
186	#15261	C₂×D₄	1	1	yes	characteristic
187	#15261	C₂×D₄	1	1	yes	characteristic
188	#15259	C₂²⋊C₄	1	2	yes	complemented
189	#15259	C₂²⋊C₄	1	2	yes	complemented
190	#15259	C₂²×C₄	1	2	yes	—
191	#15259	C₂×D₄	1	2	yes	—
192	#15258	C₂²⋊C₄	1	1	yes	characteristic
193	#15258	C₂²⋊C₄	1	1	yes	characteristic
194	#15258	C₂²⋊C₄	1	2	yes	complemented
195	#15258	C₂²×C₄	1	2	yes	—
196	#15258	C₂²×C₄	1	1	yes	characteristic
197	#15258	C₂²×C₄	1	1	yes	characteristic
198	#15258	C₂×D₄	1	2	yes	—
199	#15257	C₂×D₄	1	2	yes	—
200	#15257	C₂×D₄	1	2	yes	—
201	#15257	C₂×D₄	1	2	yes	—
202	#15257	C₂×D₄	1	2	yes	—
203	#14706	C₂×D₄	1	2	yes	—
204	#14679	C₂²⋊C₄	1	2	yes	complemented
205	#14666	C₂²⋊C₄	1	2	yes	complemented
206	#14662	C₂²⋊C₄	1	2	yes	complemented
207	#14659	C₂×D₄	1	2	yes	—
208	#14657	C₂²⋊C₄	1	1	yes	characteristic
209	#14657	C₂²⋊C₄	1	1	yes	characteristic
210	#14657	C₂²×C₄	1	2	yes	—
211	#14651	C₂²⋊C₄	1	2	yes	complemented
212	#14651	C₂²⋊C₄	1	2	yes	complemented
213	#14507	C₂²⋊C₄	1	2	yes	complemented
214	#14419	C₂²⋊C₄	1	2	yes	complemented
215	#14358	C₂²⋊C₄	1	2	yes	complemented
216	#14358	C₂²⋊C₄	1	2	yes	complemented
217	#14335	C₂×D₄	1	1	yes	characteristic
218	#14335	C₂×D₄	1	1	yes	characteristic
219	#14290	C₂×D₄	1	2	yes	—
220	#14262	C₂²⋊C₄	1	2	yes	complemented
221	#14255	C₂×D₄	1	2	yes	—
222	#14255	C₂×D₄	1	2	yes	—
223	#14232	C₂²⋊C₄	1	2	yes	complemented
224	#14207	C₂²⋊C₄	1	2	yes	complemented
225	#14134	C₂²⋊C₄	1	1	yes	characteristic
226	#14134	C₂²⋊C₄	1	1	yes	characteristic
227	#14134	C₂²⋊C₄	1	2	yes	complemented
228	#13903	C₂×D₄	1	2	yes	—
229	#13867	C₂²⋊C₄	1	2	yes	complemented
230	#13867	C₂×D₄	1	2	yes	—
231	#13827	C₂²⋊C₄	1	1	yes	characteristic, complemented
232	#13827	C₂²⋊C₄	1	1	yes	characteristic, complemented
233	#13823	C₂²⋊C₄	1	2	yes	complemented
234	C₂²⋊C₄²	C₂²⋊C₄	1	2	yes	complemented
235	C₂²⋊C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
236	C₂²⋊C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
237	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂⁷	#120	1	1	yes	characteristic
239	C₂⁷	#120	1	1	yes	characteristic
240	C₂³×#41	#120	1	2	yes	—
241	C₂⁴×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂⁴×D₄	C₂×C₂²⋊C₄	1	2	yes	—
243	C₂⁴×D₄	#120	1	1	yes	characteristic
244	C₂⁴×D₄	#120	1	1	yes	characteristic
245	C₂⁴×D₄	#120	1	1	yes	characteristic
246	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
247	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
248	C₂⁵×C₄	#120	1	1	yes	characteristic
249	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂²×#127	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂²×#127	C₂×C₂²⋊C₄	1	2	yes	—
252	C₂²×#127	#120	1	1	yes	characteristic
253	C₂²×#127	#120	1	1	yes	characteristic
254	C₂²×#124	C₂×C₂²⋊C₄	1	2	yes	—
255	C₂²×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×#123	#120	1	1	yes	characteristic
257	C₂²×#123	#120	1	2	yes	—
258	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
259	C₂²×#123	C₂²×D₄	1	2	yes	—
260	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
261	C₂²×#121	C₂²×D₄	1	2	yes	—
262	C₂²×#121	C₂²×D₄	1	2	yes	—
263	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×#120	C₂×C₂²⋊C₄	1	2	yes	—
269	C₂²×#120	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂²×#120	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂²×#120	#120	1	1	yes	characteristic
272	C₂²×#120	#120	1	1	yes	characteristic
273	C₂²×#120	#120	1	1	yes	characteristic
274	C₂²×#120	#120	1	2	yes	—
275	C₂²×#120	#120	1	1	yes	characteristic
276	C₂²×#120	#120	1	1	yes	characteristic
277	C₂²×#120	#120	1	2	yes	—
278	C₂²×#120	#120	1	2	yes	—
279	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
280	C₂²×#120	C₂²×D₄	1	2	yes	—
281	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
282	C₂³×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
283	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
284	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
285	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
286	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
287	C₂³×C₄²	#120	1	1	yes	characteristic
288	C₂×#394	#120	1	2	yes	—
289	C₂×#394	#120	1	2	yes	—
290	C₂×#393	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂×#393	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×#393	#120	1	2	yes	—
293	C₂×#393	#120	1	2	yes	—
294	C₂×#392	C₂×C₂²⋊C₄	1	2	yes	—
295	C₂×#392	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂×#392	C₂×C₂²⋊C₄	1	2	yes	—
297	C₂×#392	C₂×C₂²⋊C₄	1	2	yes	—
298	C₂×#392	#120	1	2	yes	—
299	C₂×#392	#120	1	2	yes	—
300	C₂×#391	#120	1	2	yes	—
301	C₂×#390	#120	1	2	yes	—
302	C₂×#386	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂×#386	#120	1	2	yes	—
304	C₂×#386	#120	1	2	yes	—
305	C₂×#385	C₂×C₂²⋊C₄	1	2	yes	—
306	C₂×#381	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×#381	#120	1	2	yes	—
308	C₂×#381	#120	1	2	yes	—
309	C₂×#381	#120	1	1	yes	characteristic
310	C₂×#381	#120	1	2	yes	—
311	C₂×#381	#120	1	1	yes	characteristic
312	C₂×#381	#120	1	1	yes	characteristic
313	C₂×#380	#120	1	2	yes	—
314	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
318	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
319	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
321	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
322	C₂×#379	#120	1	1	yes	characteristic
323	C₂×#379	#120	1	1	yes	characteristic
324	C₂×#379	#120	1	1	yes	characteristic
325	C₂×#379	#120	1	2	yes	—
326	C₂×#379	#120	1	2	yes	—
327	C₂×#379	#120	1	2	yes	—
328	C₂×#379	#120	1	2	yes	—
329	C₂×C₄×C₂²⋊C₄	#120	1	2	yes	—
330	#1445	#120	1	2	yes	—
331	#1445	#120	1	2	yes	—
332	#1440	C₂×C₂²⋊C₄	1	2	yes	—
333	#1440	C₂×C₂²⋊C₄	1	2	yes	—
334	#1440	#120	1	2	yes	—
335	#1440	#120	1	2	yes	—
336	#1440	#120	1	2	yes	—
337	#1440	#120	1	2	yes	—
338	#1438	C₂×C₂²⋊C₄	1	2	yes	—
339	#1438	C₂×C₂²⋊C₄	1	2	yes	—
340	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
341	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
342	#1438	C₂×C₂²⋊C₄	1	2	yes	—
343	#1438	C₂×C₂²⋊C₄	1	2	yes	—
344	#1438	C₂×C₂²⋊C₄	1	2	yes	—
345	#1438	C₂×C₂²⋊C₄	1	2	yes	—
346	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
347	#1438	C₂×C₂²⋊C₄	1	1	yes	characteristic
348	#1438	#120	1	2	yes	—
349	#1438	#120	1	2	yes	—
350	#1438	#120	1	2	yes	—
351	#1438	#120	1	2	yes	—
352	#1438	#120	1	2	yes	—
353	#1438	#120	1	2	yes	—
354	#1438	#120	1	2	yes	—
355	#1438	#120	1	2	yes	—
356	#1437	C₂×C₂²⋊C₄	1	2	yes	—
357	#1437	C₂×C₂²⋊C₄	1	2	yes	—
358	#1437	C₂×C₂²⋊C₄	1	2	yes	—
359	#1437	C₂×C₂²⋊C₄	1	2	yes	—
360	#1437	C₂×C₂²⋊C₄	1	2	yes	—
361	#1437	C₂×C₂²⋊C₄	1	2	yes	—
362	#1437	#120	1	2	yes	—
363	#1437	#120	1	2	yes	—
364	#1437	#120	1	2	yes	—
365	#1437	#120	1	2	yes	—
366	#1436	#120	1	2	yes	—
367	#1436	#120	1	2	yes	—
368	C₂⁶	#379	1	1	yes	characteristic
369	C₂⁶	#379	1	1	yes	characteristic
370	C₂⁶	#379	1	1	yes	characteristic
371	C₂⁶	#379	1	1	yes	characteristic
372	C₂⁶	#379	1	2	yes	—
373	C₂⁶	#379	1	1	yes	characteristic
374	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
375	C₂⁶	C₂×#120	1	1	yes	characteristic
376	C₂⁶	C₂×#120	1	1	yes	characteristic
377	C₂³×Q₈	#379	1	2	yes	—
378	C₂³×D₄	#379	1	2	yes	—
379	C₂³×D₄	#379	1	1	yes	characteristic
380	C₂³×D₄	#379	1	1	yes	characteristic
381	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
382	C₂³×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
383	C₂³×D₄	C₂×#120	1	2	yes	—
384	C₂³×D₄	C₂×#120	1	2	yes	—
385	C₂³×D₄	C₂×#120	1	1	yes	characteristic
386	C₂³×D₄	C₂×#120	1	1	yes	characteristic
387	C₂³×D₄	C₂×#120	1	2	yes	—
388	C₂³×D₄	C₂×#120	1	1	yes	characteristic
389	C₂⁴×C₄	#379	1	1	yes	characteristic
390	C₂⁴×C₄	#379	1	2	yes	—
391	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
392	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
393	C₂⁴×C₄	C₂×#120	1	2	yes	—
394	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
395	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
396	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
397	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
398	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
399	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
400	C₂²×C₂²⋊C₄	#379	1	2	yes	—
401	C₂²×C₂²⋊C₄	#379	1	2	yes	—
402	C₂²×C₂²⋊C₄	#379	1	2	yes	—
403	C₂²×C₂²⋊C₄	#379	1	2	yes	—
404	C₂²×C₂²⋊C₄	#379	1	2	yes	—
405	C₂²×C₂²⋊C₄	#379	1	2	yes	—
406	C₂²×C₂²⋊C₄	#379	1	2	yes	—
407	C₂²×C₂²⋊C₄	#379	1	2	yes	—
408	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	#379	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
411	C₂²×C₂²⋊C₄	#458	1	2	yes	—
412	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
414	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
416	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
417	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
418	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
419	C₂²×C₄²	#379	1	1	yes	characteristic
420	C₂²×C₄²	#379	1	1	yes	characteristic
421	C₂²×C₄²	#379	1	2	yes	—
422	C₂²×C₄²	#379	1	2	yes	—
423	C₂×#95	#379	1	2	yes	—
424	C₂×#95	#379	1	2	yes	—
425	C₂×#95	#379	1	2	yes	—
426	C₂×#95	#379	1	2	yes	—
427	C₂×#95	#379	1	2	yes	—
428	C₂×#95	#379	1	2	yes	—
429	C₂⁵	C₂×#379	1	1	yes	characteristic
430	C₂⁵	C₂×#379	1	2	yes	—
431	C₂⁵	C₂×#379	1	1	yes	characteristic
432	C₂⁵	#2846	1	1	yes	characteristic
433	C₂⁵	#2846	1	1	yes	characteristic
434	C₂⁵	#2846	1	1	yes	characteristic
435	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
436	C₂⁵	C₂×#458	1	1	yes	characteristic
437	C₂⁵	#3026	1	1	yes	characteristic
438	C₂⁵	#3026	1	1	yes	characteristic
439	C₂³×C₄	C₂×#379	1	2	yes	—
440	C₂³×C₄	C₂×#379	1	1	yes	characteristic
441	C₂³×C₄	#2846	1	2	yes	—
442	C₂³×C₄	#2846	1	1	yes	characteristic
443	C₂³×C₄	#2846	1	2	yes	—
444	C₂×C₂²⋊C₄	#1790	1	2	yes	—
445	C₂×C₂²⋊C₄	#1790	1	2	yes	—
446	C₂⁴	#14679	1	1	yes	characteristic
447	C₂⁴	C₂×#1790	1	1	yes	characteristic
448	C₂⁴	#20609	1	1	yes	characteristic
449	C₂⁴	#32898	1	1	yes	characteristic
450	C₂⁴	#32898	1	1	yes	characteristic
451	C₂⁴	#32900	1	1	yes	characteristic
452	C₂⁴	#32900	1	1	yes	characteristic
453	C₂³	#392125	1	1	yes	characteristic
454	C₂³	#392135	1	2	yes	—
455	C₂³	#511790	1	2	yes	—
456	C₂²	#72218475	1	1	yes	characteristic
457	C₂²	#72225822	1	2	yes	—
458	C₂²	#72238343	1	1	yes	characteristic
459	C₂²	#72251662	1	1	yes	characteristic
460	C₂²	#72260564	1	2	yes	—
461	C₂	#72262333	1	1	yes	characteristic
462	C₂	#72262891	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#72251662
commutator	C₂²×#120	C₂³×C₄
Frattini, cosocle	C₂²×#534	C₂⁴
prime radical	#72262832	C₂
LCS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×#534 ◁ G
LECS	G ▷ C₂²×#534 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262918	C₂	semidirect
2. #72262911	C₂	semidirect
3. #72262905	C₂	semidirect
4. #72262900	C₂	semidirect
6. #72262830	C₄	semidirect
7. #72262829	C₄	semidirect
10. #72262799	C₄	semidirect
11. #72262796	C₄	semidirect
12. #72262796	C₄	semidirect
13. #72262608	C₂	semidirect
14. #72256119	C₂²	semidirect
15. #72256111	C₂²	semidirect
16. #72238361	C₂	semidirect
17. #72237996	C₂	semidirect
18. #72237995	C₂²	semidirect
19. #72237994	C₂²	semidirect
20. #72237886	C₂	semidirect
21. #72237884	C₂²	semidirect
22. #72237585	C₂	semidirect
23. #72237583	C₂²	semidirect
24. #72237582	C₂²	semidirect
25. #72237489	C₂²	semidirect
26. #72237486	C₂²	semidirect
27. #72237471	C₂	semidirect
28. #72237459	C₂²	semidirect
29. #72235246	C₂²	semidirect
30. #72235242	C₂²	semidirect
31. #72234724	C₂²	semidirect
34. #72225985	C₂²	semidirect
35. #72225870	C₂²	semidirect
36. #72225713	C₂²	semidirect
38. #72219499	C₄	semidirect
39. #72219314	C₂²	semidirect
40. #72219310	C₂²	semidirect
111. C₂²×D₄²	C₂²⋊C₄	semidirect
115. C₂³×#120	C₂²⋊C₄	semidirect
118. C₂×#2760	C₂²⋊C₄	semidirect
119. C₂×#2684	C₂²⋊C₄	semidirect
120. C₂×#2675	C₂²⋊C₄	semidirect
121. C₂×#2670	C₂²⋊C₄	semidirect
122. C₂×#2840	C₂²⋊C₄	semidirect
123. C₂×#2840	C₂²⋊C₄	semidirect
132. C₂×#2403	C₂²⋊C₄	semidirect
133. C₂×#2403	C₂²⋊C₄	semidirect
134. C₂×#2403	C₂²⋊C₄	semidirect
143. C₂×#2308	C₂²⋊C₄	semidirect
147. #17273	C₂²⋊C₄	semidirect
148. #17272	C₂²⋊C₄	semidirect
149. #17105	C₂²⋊C₄	semidirect
150. #17102	C₂²⋊C₄	semidirect
151. #16214	C₂²⋊C₄	semidirect
163. #15947	C₂²⋊C₄	semidirect
169. #15636	C₂²⋊C₄	semidirect
170. #15622	C₂²⋊C₄	semidirect
171. #15467	C₂²⋊C₄	semidirect
172. #15467	C₂²⋊C₄	semidirect
173. #15420	C₂²⋊C₄	semidirect
176. #15313	C₂²⋊C₄	semidirect
179. #15267	C₂²⋊C₄	semidirect
180. #15267	C₂²⋊C₄	semidirect
181. #15267	C₂²⋊C₄	semidirect
182. #15267	C₂²⋊C₄	semidirect
183. #15266	C₂²⋊C₄	semidirect
188. #15259	C₂²⋊C₄	semidirect
189. #15259	C₂²⋊C₄	semidirect
194. #15258	C₂²⋊C₄	semidirect
204. #14679	C₂²⋊C₄	semidirect
205. #14666	C₂²⋊C₄	semidirect
206. #14662	C₂²⋊C₄	semidirect
211. #14651	C₂²⋊C₄	semidirect
212. #14651	C₂²⋊C₄	semidirect
213. #14507	C₂²⋊C₄	semidirect
214. #14419	C₂²⋊C₄	semidirect
215. #14358	C₂²⋊C₄	semidirect
216. #14358	C₂²⋊C₄	semidirect
220. #14262	C₂²⋊C₄	semidirect
223. #14232	C₂²⋊C₄	semidirect
224. #14207	C₂²⋊C₄	semidirect
227. #14134	C₂²⋊C₄	semidirect
229. #13867	C₂²⋊C₄	semidirect
231. #13827	C₂²⋊C₄	semidirect
232. #13827	C₂²⋊C₄	semidirect
233. #13823	C₂²⋊C₄	semidirect
234. C₂²⋊C₄²	C₂²⋊C₄	semidirect
235. C₂²⋊C₄²	C₂²⋊C₄	semidirect
236. C₂²⋊C₄²	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72262918	2
#72262911	2
#72262905	2
#72262900	2
#72262832	2
#72262608	2
#72238361	2
#72237996	2
#72237886	2
#72237585	2
#72237471	2