Subgroups — #72265946

Order 2048.

At least 13725 conjugacy classes of subgroups; only the 1088 normal subgroups are shown.

The subgroup lattice has 588 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72265945	C₂	1	2	yes	maximal, complemented
2	#72265944	C₂	1	1	yes	maximal, characteristic, complemented
3	#72265943	C₂	1	2	yes	maximal, complemented
4	#72265924	C₂	1	1	yes	maximal, characteristic, complemented
5	#72265917	C₂	1	1	yes	maximal, characteristic, complemented
6	#72265850	C₂	1	1	yes	maximal, characteristic, complemented
7	#72265239	C₂	1	2	yes	maximal, complemented
8	#72261568	C₂	1	4	yes	maximal, complemented
9	#72252238	C₂	1	1	yes	maximal, characteristic, complemented
10	#72251608	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#251827	C₂	1	1	yes	maximal, characteristic, complemented
12	#72240111	C₂	1	2	yes	maximal, complemented
13	#72237496	C₂	1	2	yes	maximal, complemented
14	#72234956	C₂	1	4	yes	maximal, complemented
15	#72234587	C₂	1	2	yes	maximal, complemented
16	#72233127	C₂	1	2	yes	maximal, complemented
17	#72232805	C₂	1	2	yes	maximal, complemented
18	C₂²×#2883	C₂²	1	1	yes	characteristic, complemented
19	#7806599	C₂²	1	1	yes	characteristic, complemented
20	#7804409	C₂²	1	1	yes	characteristic, complemented
21	#7721731	C₂²	1	2	yes	complemented
22	#7721725	C₂²	1	2	yes	—
23	#7712875	C₂²	1	1	yes	characteristic
24	C₂×#46996	C₂²	1	1	yes	characteristic
25	#7658231	C₂²	1	1	yes	characteristic, complemented
26	#7652796	C₂²	1	1	yes	characteristic, complemented
27	#7631294	C₂²	1	2	yes	—
28	#7630442	C₂²	1	1	yes	characteristic
29	#7626663	C₂²	1	2	yes	complemented
30	#7625704	C₂²	1	1	yes	characteristic
31	#6628892	C₂²	1	2	yes	complemented
32	C₂×#32898	C₂²	1	2	yes	complemented
33	#6470225	C₂²	1	4	yes	—
34	C₂×#20984	C₂²	1	1	yes	characteristic
35	C₂×#20585	C₂²	1	1	yes	characteristic, complemented
36	#394470	C₂²	1	4	yes	complemented
37	#394267	C₂²	1	4	yes	complemented
38	#392699	C₂²	1	2	yes	complemented
39	#392658	C₂²	1	2	yes	complemented
40	#392231	C₂²	1	2	yes	complemented
41	#364471	C₂²	1	4	yes	complemented
42	#364440	C₂²	1	2	yes	—
43	#364440	C₂²	1	2	yes	—
44	#364440	C₂²	1	4	yes	complemented
45	#364440	C₂²	1	2	yes	complemented
46	#364440	C₂²	1	2	yes	complemented
47	#353408	C₂²	1	1	yes	characteristic, complemented
48	#353314	C₂²	1	1	yes	characteristic, complemented
49	#238082	C₂²	1	2	yes	complemented
50	C₂×#10390	C₂²	1	2	yes	complemented
51	#233549	C₂²	1	2	yes	complemented
52	#233549	C₂²	1	4	yes	complemented
53	#233541	C₂²	1	4	yes	complemented
54	C₂×#10336	C₂²	1	2	yes	complemented
55	#201687	C₂²	1	2	yes	complemented
56	#201687	C₂²	1	2	yes	complemented
57	#201678	C₂²	1	4	yes	—
58	#201678	C₂²	1	4	yes	complemented
59	C₂×#9495	C₂²	1	2	yes	complemented
60	C₂×#9495	C₂²	1	4	yes	complemented
61	C₂×#9495	C₂²	1	2	yes	complemented
62	C₂×#8746	C₂²	1	1	yes	characteristic, complemented
63	C₂×#8746	C₂²	1	1	yes	characteristic, complemented
64	#188049	C₂²	1	2	yes	—
65	#187928	C₂²	1	4	yes	complemented
66	#122191	C₂²	1	2	yes	complemented
67	#122187	C₂²	1	4	yes	complemented
68	#122038	C₂²	1	2	yes	complemented
69	#115204	C₂²	1	4	yes	complemented
70	#115163	C₂²	1	4	yes	complemented
71	#111467	C₂²	1	2	yes	complemented
72	#111467	C₂²	1	4	yes	complemented
73	#111458	C₂²	1	2	yes	complemented
74	#107194	C₂²	1	4	yes	complemented
75	#107194	C₂²	1	4	yes	complemented
76	#106654	C₂²	1	4	yes	complemented
77	#106542	C₂²	1	4	yes	complemented
78	#105752	C₂²	1	4	yes	complemented
79	#105752	C₂²	1	2	yes	complemented
80	#105752	C₂²	1	2	yes	complemented
81	#105752	C₂²	1	2	yes	complemented
82	#105752	C₂²	1	2	yes	complemented
83	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
84	C₂×#3490	D₄	1	2	yes	complemented
85	C₂×#3484	C₂³	1	2	yes	—
86	C₂²×#534	C₂³	1	1	yes	characteristic
87	C₂²×#518	D₄	1	1	yes	characteristic, complemented
88	C₂²×#518	C₂³	1	1	yes	characteristic
89	C₂²×#518	C₂³	1	1	yes	characteristic
90	C₂³×#99	C₂³	1	2	yes	—
91	C₂³×#99	C₂³	1	2	yes	—
92	#46999	D₄	1	1	yes	characteristic, complemented
93	#46997	D₄	1	2	yes	complemented
94	#46996	D₄	1	1	yes	characteristic, complemented
95	#46996	D₄	1	1	yes	characteristic, complemented
96	#46996	D₄	1	2	yes	complemented
97	#46996	D₄	1	2	yes	complemented
98	#46996	D₄	1	1	yes	characteristic, complemented
99	#46996	D₄	1	1	yes	characteristic, complemented
100	#46996	D₄	1	1	yes	characteristic, complemented
101	#46837	D₄	1	1	yes	characteristic, complemented
102	#46387	D₄	1	1	yes	characteristic, complemented
103	#46386	D₄	1	2	yes	complemented
104	#37475	C₂³	1	1	yes	characteristic
105	#37436	C₂³	1	2	yes	—
106	#37436	C₂³	1	1	yes	characteristic
107	#37117	D₄	1	2	yes	complemented
108	#36721	D₄	1	2	yes	complemented
109	#36717	D₄	1	2	yes	complemented
110	#36714	D₄	1	2	yes	complemented
111	C₂×#2840	C₂³	1	1	yes	characteristic
112	#35512	D₄	1	2	yes	complemented
113	#35360	D₄	1	2	yes	complemented
114	#35359	D₄	1	2	yes	complemented
115	#35355	D₄	1	2	yes	complemented
116	#35354	D₄	1	2	yes	complemented
117	#35350	D₄	1	2	yes	complemented
118	#35348	D₄	1	2	yes	complemented
119	#35346	D₄	1	2	yes	complemented
120	#34982	C₂³	1	2	yes	—
121	#34980	C₂³	1	2	yes	—
122	#34980	C₂³	1	2	yes	—
123	#34980	C₂³	1	4	yes	—
124	#34980	C₂³	1	2	yes	—
125	#34980	C₂³	1	2	yes	—
126	C₂×#2410	C₂³	1	2	yes	—
127	C₂×#2403	C₂³	1	1	yes	characteristic
128	C₂×#2403	C₂³	1	2	yes	—
129	C₂×#2403	C₂³	1	4	yes	—
130	#34356	C₂³	1	2	yes	—
131	#34356	C₂³	1	2	yes	—
132	#34273	D₄	1	2	yes	complemented
133	#34251	D₄	1	2	yes	complemented
134	#34199	D₄	1	1	yes	characteristic, complemented
135	#34199	D₄	1	1	yes	characteristic, complemented
136	#34199	D₄	1	1	yes	characteristic, complemented
137	#34199	D₄	1	1	yes	characteristic, complemented
138	#34198	D₄	1	2	yes	complemented
139	#34198	C₂³	1	1	yes	characteristic
140	#34198	C₂³	1	1	yes	characteristic
141	#34198	C₂³	1	1	yes	characteristic
142	#34198	C₂³	1	1	yes	characteristic
143	#34198	C₂³	1	2	yes	—
144	C₂×D₄×C₂²⋊C₄	C₂³	1	2	yes	—
145	C₂×#2315	D₄	1	1	yes	characteristic, complemented
146	C₂×#2308	D₄	1	1	yes	characteristic, complemented
147	C₂×#2308	C₂³	1	1	yes	characteristic
148	C₂×#2308	C₂³	1	2	yes	—
149	C₂×#2308	C₂³	1	1	yes	characteristic
150	C₂×#2308	C₂³	1	1	yes	characteristic
151	C₂×#2273	D₄	1	1	yes	characteristic, complemented
152	#21746	C₂³	1	4	yes	—
153	#21746	C₂³	1	4	yes	—
154	#21746	C₂³	1	4	yes	—
155	#21746	C₂³	1	4	yes	—
156	C₂×#1898	C₂³	1	2	yes	—
157	C₂×#1898	C₂³	1	2	yes	—
158	C₂×#1898	C₂³	1	4	yes	—
159	C₂×#1781	C₂³	1	4	yes	—
160	C₂×#1781	C₂³	1	2	yes	—
161	C₂×#1781	C₂³	1	2	yes	—
162	C₂×#1781	C₂³	1	4	yes	—
163	C₂×#1781	C₂³	1	2	yes	—
164	C₂×#1781	C₂³	1	2	yes	—
165	C₂×#1781	C₂³	1	4	yes	—
166	C₂×#1781	C₂³	1	4	yes	—
167	#13867	C₂³	1	4	yes	—
168	#10735	C₂³	1	4	yes	—
169	#10735	C₂³	1	4	yes	—
170	#10735	C₂³	1	4	yes	—
171	#10735	C₂³	1	2	yes	—
172	#10735	C₂³	1	2	yes	—
173	#10725	C₂³	1	2	yes	—
174	#10725	C₂³	1	2	yes	—
175	#10725	C₂³	1	4	yes	—
176	#8101	C₂³	1	4	yes	—
177	#8101	C₂³	1	4	yes	—
178	C₂×#1304	C₂³	1	2	yes	—
179	C₂×#1304	C₂³	1	2	yes	—
180	C₂×#1304	C₂³	1	2	yes	—
181	C₂×#1304	C₂³	1	2	yes	—
182	C₂×#1304	C₂³	1	4	yes	—
183	C₂×#1304	C₂³	1	4	yes	—
184	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
185	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×D₄	C₂⁴	1	2	yes	—
187	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
188	C₂⁴×D₄	C₂⁴	1	2	yes	—
189	C₂×#543	C₂×D₄	1	2	yes	complemented
190	C₂×#534	C₂×D₄	1	2	yes	—
191	C₂×#534	C₂×D₄	1	2	yes	—
192	C₂×#534	C₂×D₄	1	2	yes	—
193	C₂×#534	C₂×D₄	1	2	yes	—
194	C₂²×#123	C₂×D₄	1	1	yes	characteristic
195	C₂²×#123	C₂×D₄	1	1	yes	characteristic
196	C₂²×#123	C₂×D₄	1	2	yes	—
197	C₂²×#121	C₂×D₄	1	2	yes	—
198	C₂²×#121	C₂×D₄	1	2	yes	—
199	C₂²×#120	C₂×D₄	1	2	yes	—
200	C₂²×#120	C₂×D₄	1	2	yes	—
201	C₂²×#120	C₂×D₄	1	2	yes	—
202	C₂²×#120	C₂×D₄	1	2	yes	complemented
203	C₂²×#120	C₂⁴	1	2	yes	—
204	C₂²×#120	C₂⁴	1	1	yes	characteristic
205	C₂²×#120	C₂⁴	1	1	yes	characteristic
206	C₂×#518	C₂×D₄	1	2	yes	—
207	C₂×#518	C₂×D₄	1	1	yes	characteristic
208	C₂×#518	C₂×D₄	1	1	yes	characteristic
209	C₂×#518	C₂×D₄	1	1	yes	characteristic
210	C₂×#518	C₂×D₄	1	1	yes	characteristic
211	C₂×#518	C₂×D₄	1	2	yes	—
212	C₂×#518	C₂×D₄	1	2	yes	—
213	C₂×#518	C₂×D₄	1	2	yes	—
214	C₂×#518	C₂×D₄	1	2	yes	—
215	C₂×#518	C₂×D₄	1	2	yes	complemented
216	C₂²×#117	C₂×D₄	1	1	yes	characteristic
217	C₂²×#117	C₂×D₄	1	1	yes	characteristic
218	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
223	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
224	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
225	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
226	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
227	#2849	#41	1	4	yes	complemented
228	#2846	#41	1	4	yes	complemented
229	#2842	C₂×D₄	1	2	yes	complemented
230	#2842	C₂×D₄	1	1	yes	characteristic, complemented
231	#2840	C₂×D₄	1	1	yes	characteristic, complemented
232	#2840	C₂×D₄	1	2	yes	complemented
233	#2840	C₂×D₄	1	1	yes	characteristic, complemented
234	#2840	C₂×D₄	1	1	yes	characteristic, complemented
235	#2483	C₂×D₄	1	2	yes	—
236	#2483	C₂×D₄	1	1	yes	characteristic, complemented
237	#2405	C₂×D₄	1	2	yes	—
238	#2405	C₂×D₄	1	2	yes	—
239	#2405	C₂×D₄	1	2	yes	—
240	#2405	C₂×D₄	1	2	yes	—
241	#2405	C₂×D₄	1	2	yes	—
242	#2405	C₂×D₄	1	2	yes	—
243	#2405	C₂×D₄	1	2	yes	—
244	#2405	C₂×D₄	1	2	yes	—
245	#2405	C₂×D₄	1	2	yes	complemented
246	#2403	C₂×D₄	1	2	yes	—
247	#2403	C₂×D₄	1	2	yes	—
248	#2403	C₂×D₄	1	2	yes	—
249	#2403	C₂×D₄	1	2	yes	—
250	#2403	C₂×D₄	1	2	yes	—
251	#2403	C₂×D₄	1	2	yes	—
252	#2403	C₂×D₄	1	2	yes	—
253	#2403	C₂×D₄	1	2	yes	—
254	#2403	C₂×D₄	1	2	yes	—
255	#2403	C₂×D₄	1	2	yes	—
256	#2403	C₂×D₄	1	2	yes	—
257	#2403	C₂×D₄	1	2	yes	—
258	#2403	C₂×D₄	1	2	yes	—
259	#2403	C₂×D₄	1	2	yes	—
260	#2403	C₂×D₄	1	2	yes	—
261	#2403	C₂×D₄	1	1	yes	characteristic, complemented
262	#2403	C₂×D₄	1	2	yes	complemented
263	#2403	C₂×D₄	1	1	yes	characteristic, complemented
264	#2403	C₂×D₄	1	1	yes	characteristic, complemented
265	#2315	C₂×D₄	1	1	yes	characteristic
266	#2315	C₂×D₄	1	1	yes	characteristic
267	#2315	C₂×D₄	1	1	yes	characteristic
268	#2315	C₂×D₄	1	1	yes	characteristic
269	#2315	C₂×D₄	1	2	yes	complemented
270	#2315	C₂×D₄	1	2	yes	complemented
271	#2315	C₂×D₄	1	2	yes	complemented
272	#2315	C₂×D₄	1	2	yes	complemented
273	#2312	C₂×D₄	1	2	yes	—
274	#2312	C₂×D₄	1	2	yes	—
275	#2312	C₂×D₄	1	2	yes	complemented
276	#2312	C₂×D₄	1	2	yes	complemented
277	#2309	C₂×D₄	1	2	yes	—
278	#2309	C₂×D₄	1	2	yes	complemented
279	#2308	C₂×D₄	1	2	yes	—
280	#2308	C₂×D₄	1	1	yes	characteristic
281	#2308	C₂×D₄	1	1	yes	characteristic
282	#2308	C₂×D₄	1	1	yes	characteristic
283	#2308	C₂×D₄	1	1	yes	characteristic
284	#2308	C₂×D₄	1	1	yes	characteristic
285	#2308	C₂×D₄	1	1	yes	characteristic
286	#2308	C₂×D₄	1	1	yes	characteristic
287	#2308	C₂×D₄	1	1	yes	characteristic
288	#2308	C₂×D₄	1	1	yes	characteristic
289	#2308	C₂×D₄	1	1	yes	characteristic
290	#2308	C₂×D₄	1	1	yes	characteristic
291	#2308	C₂×D₄	1	1	yes	characteristic
292	#2308	C₂×D₄	1	2	yes	—
293	#2308	C₂×D₄	1	2	yes	—
294	#2308	C₂×D₄	1	2	yes	complemented
295	#2308	C₂×D₄	1	2	yes	complemented
296	#2308	C₂×D₄	1	2	yes	complemented
297	#2308	C₂×D₄	1	2	yes	complemented
298	#2308	C₂×D₄	1	2	yes	complemented
299	#2308	C₂×D₄	1	2	yes	complemented
300	C₂×#386	C₂×D₄	1	2	yes	—
301	C₂×#386	C₂×D₄	1	2	yes	—
302	C₂×#386	C₂×D₄	1	2	yes	complemented
303	C₂×#385	C₂×D₄	1	2	yes	complemented
304	C₂×#381	C₂×D₄	1	1	yes	characteristic
305	C₂×#381	C₂×D₄	1	1	yes	characteristic
306	C₂×#380	C₂×D₄	1	2	yes	complemented
307	C₂×#379	C₂×D₄	1	2	yes	complemented
308	C₂×#379	C₂×D₄	1	2	yes	complemented
309	C₂×#379	C₂⁴	1	4	yes	—
310	C₂×#379	C₂⁴	1	4	yes	—
311	C₂×#379	C₂⁴	1	2	yes	—
312	C₂×#379	C₂⁴	1	2	yes	—
313	C₂×#379	C₂⁴	1	2	yes	—
314	C₂×#379	C₂⁴	1	1	yes	characteristic
315	C₂×#379	C₂⁴	1	2	yes	—
316	C₂×#379	C₂⁴	1	1	yes	characteristic
317	#2273	C₂×D₄	1	1	yes	characteristic
318	#2273	C₂×D₄	1	1	yes	characteristic
319	#2273	C₂×D₄	1	1	yes	characteristic
320	#2273	C₂×D₄	1	1	yes	characteristic
321	#2273	C₂×D₄	1	2	yes	complemented
322	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
323	C₂⁶	#120	1	1	yes	characteristic
324	C₂⁶	C₂²×D₄	1	1	yes	characteristic
325	C₂⁶	C₂²×D₄	1	2	yes	—
326	C₂⁶	C₂×#41	1	2	yes	complemented
327	C₂⁶	C₂⁵	1	1	yes	characteristic
328	C₂³×D₄	#120	1	1	yes	characteristic
329	C₂³×D₄	#120	1	1	yes	characteristic
330	C₂³×D₄	C₂²×D₄	1	2	yes	—
331	C₂³×D₄	C₂²×D₄	1	2	yes	—
332	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
333	C₂³×D₄	C₂²×D₄	1	2	yes	—
334	C₂³×D₄	C₂²×D₄	1	2	yes	—
335	C₂³×D₄	C₂²×D₄	1	2	yes	—
336	C₂³×D₄	C₂²×D₄	1	2	yes	—
337	C₂³×D₄	C₂²×D₄	1	2	yes	—
338	C₂³×D₄	C₂²×D₄	1	2	yes	—
339	C₂³×D₄	C₂²×D₄	1	2	yes	—
340	C₂³×D₄	C₂²×D₄	1	2	yes	—
341	C₂³×D₄	C₂²×D₄	1	2	yes	—
342	C₂³×D₄	C₂²×D₄	1	2	yes	—
343	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
345	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
346	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
347	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
348	C₂³×D₄	C₂²×D₄	1	2	yes	—
349	C₂⁴×C₄	#120	1	1	yes	characteristic
350	C₂⁴×C₄	#120	1	2	yes	—
351	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
352	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
353	C₂⁴×C₄	C₂×#41	1	2	yes	complemented
354	C₂×#123	#120	1	2	yes	—
355	C₂×#123	#120	1	2	yes	—
356	C₂×#123	#120	1	2	yes	—
357	C₂×#123	#120	1	2	yes	—
358	C₂×#120	#120	1	2	yes	—
359	C₂×#120	#120	1	2	yes	—
360	C₂×#120	#120	1	2	yes	—
361	C₂×#120	#120	1	2	yes	—
362	C₂×#120	#120	1	2	yes	—
363	C₂×#120	#120	1	2	yes	—
364	C₂×#120	#120	1	2	yes	—
365	C₂×#120	#120	1	2	yes	—
366	C₂×#120	#120	1	2	yes	—
367	C₂×#120	#120	1	2	yes	—
368	C₂×#120	#120	1	2	yes	—
369	C₂×#120	#120	1	2	yes	—
370	C₂×#120	C₂×#41	1	4	yes	—
371	C₂×#120	H(5,𝔽₂)	1	4	yes	—
372	C₂×#117	#120	1	2	yes	—
373	C₂×#117	#120	1	2	yes	—
374	C₂×#117	#120	1	2	yes	—
375	C₂×#117	#120	1	2	yes	—
376	C₂²×C₄⋊C₄	#120	1	2	yes	—
377	C₂²×C₄⋊C₄	#120	1	2	yes	—
378	C₂²×C₂²⋊C₄	#120	1	2	yes	—
379	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
380	C₂²×C₂²⋊C₄	#120	1	2	yes	—
381	C₂²×C₂²⋊C₄	#120	1	2	yes	—
382	C₂²×C₂²⋊C₄	#120	1	2	yes	—
383	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
384	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
385	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
386	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
387	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
388	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
389	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
390	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
391	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	#120	1	2	yes	—
395	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
396	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
397	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
398	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
399	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
400	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
402	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
403	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
405	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
406	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
411	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
412	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
413	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
414	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
417	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
418	#386	#120	1	2	yes	—
419	#386	#120	1	2	yes	—
420	#386	#120	1	2	yes	—
421	#386	#120	1	2	yes	—
422	#386	#120	1	2	yes	—
423	#386	#120	1	2	yes	—
424	#386	#120	1	2	yes	—
425	#386	#120	1	2	yes	—
426	#386	#120	1	2	yes	—
427	#386	#120	1	2	yes	—
428	#386	#120	1	2	yes	—
429	#386	#120	1	2	yes	—
430	#386	#120	1	2	yes	—
431	#386	#120	1	2	yes	—
432	#386	#120	1	2	yes	—
433	#386	#120	1	2	yes	—
434	#381	#120	1	1	yes	characteristic
435	#381	#120	1	1	yes	characteristic
436	#381	#120	1	1	yes	characteristic
437	#381	#120	1	1	yes	characteristic
438	#381	#120	1	1	yes	characteristic
439	#381	#120	1	1	yes	characteristic
440	#381	#120	1	1	yes	characteristic
441	#381	#120	1	1	yes	characteristic
442	#379	C₂²×D₄	1	1	yes	characteristic
443	#379	C₂²×D₄	1	1	yes	characteristic
444	#379	C₂²×D₄	1	2	yes	—
445	#379	C₂²×D₄	1	2	yes	—
446	#379	C₂²×D₄	1	1	yes	characteristic
447	#379	C₂²×D₄	1	1	yes	characteristic
448	#379	C₂²×D₄	1	1	yes	characteristic
449	#379	C₂²×D₄	1	1	yes	characteristic
450	#379	C₂²×D₄	1	1	yes	characteristic
451	#379	C₂²×D₄	1	1	yes	characteristic
452	#379	C₂²×D₄	1	2	yes	—
453	#379	C₂²×D₄	1	2	yes	—
454	#379	C₂²×D₄	1	2	yes	—
455	#379	C₂²×D₄	1	2	yes	—
456	#379	C₂²×D₄	1	2	yes	—
457	#379	C₂²×D₄	1	2	yes	—
458	#379	C₂×#41	1	4	yes	complemented
459	C₂⁵	C₂×#120	1	1	yes	characteristic
460	C₂⁵	C₂×#120	1	1	yes	characteristic
461	C₂⁵	C₂×#120	1	1	yes	characteristic
462	C₂⁵	C₂×#120	1	1	yes	characteristic
463	C₂⁵	C₂×#120	1	1	yes	characteristic
464	C₂⁵	C₂×#120	1	1	yes	characteristic
465	C₂⁵	C₂×#120	1	2	yes	—
466	C₂⁵	C₂×#120	1	2	yes	—
467	C₂⁵	C₂×#120	1	2	yes	—
468	C₂⁵	C₂×#120	1	1	yes	characteristic
469	C₂⁵	C₂×#120	1	1	yes	characteristic
470	C₂⁵	C₂³×D₄	1	1	yes	characteristic
471	C₂⁵	C₂³×D₄	1	2	yes	—
472	C₂⁵	C₂³×D₄	1	2	yes	—
473	C₂⁵	C₂³×D₄	1	1	yes	characteristic
474	C₂⁵	C₂³×D₄	1	1	yes	characteristic
475	C₂⁵	C₂²×#41	1	2	yes	—
476	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
477	C₂⁵	#585	1	2	yes	—
478	C₂⁵	#585	1	2	yes	—
479	C₂²×D₄	C₂×#120	1	2	yes	—
480	C₂²×D₄	C₂×#120	1	2	yes	—
481	C₂²×D₄	C₂×#120	1	2	yes	—
482	C₂²×D₄	C₂×#120	1	2	yes	—
483	C₂²×D₄	C₂×#120	1	2	yes	—
484	C₂²×D₄	C₂×#120	1	2	yes	—
485	C₂²×D₄	C₂×#120	1	2	yes	—
486	C₂²×D₄	C₂×#120	1	2	yes	—
487	C₂²×D₄	#525	1	2	yes	—
488	C₂²×D₄	#535	1	2	yes	—
489	C₂²×D₄	#546	1	8	yes	—
490	C₂³×C₄	C₂×#120	1	2	yes	—
491	C₂³×C₄	C₂×#120	1	2	yes	—
492	C₂³×C₄	C₂×#120	1	1	yes	characteristic
493	C₂³×C₄	C₂×#120	1	2	yes	—
494	C₂³×C₄	C₂×#120	1	2	yes	—
495	C₂³×C₄	C₂×#120	1	2	yes	—
496	C₂³×C₄	C₂×#120	1	2	yes	—
497	C₂³×C₄	C₂×#120	1	2	yes	—
498	C₂³×C₄	C₂×#120	1	2	yes	—
499	C₂³×C₄	C₂×#120	1	1	yes	characteristic
500	C₂³×C₄	C₂×#120	1	1	yes	characteristic
501	C₂³×C₄	C₂×#120	1	1	yes	characteristic
502	C₂³×C₄	C₂×#120	1	2	yes	—
503	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	complemented
504	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
506	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
510	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
526	C₂×C₂²⋊C₄	#525	1	2	yes	—
527	C₂×C₂²⋊C₄	#535	1	2	yes	—
528	C₂×C₂²⋊C₄	#546	1	8	yes	—
529	C₂⁴	#2404	1	2	yes	—
530	C₂⁴	#2846	1	1	yes	characteristic
531	C₂⁴	#2846	1	1	yes	characteristic
532	C₂⁴	#2846	1	1	yes	characteristic
533	C₂⁴	#2846	1	1	yes	characteristic
534	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
535	C₂⁴	#3025	1	2	yes	—
536	C₂⁴	#3026	1	2	yes	—
537	C₂⁴	#3027	1	2	yes	—
538	C₂⁴	C₂²×#120	1	1	yes	characteristic
539	C₂⁴	C₂²×#120	1	2	yes	—
540	C₂⁴	C₂²×#120	1	2	yes	—
541	C₂⁴	C₂²×#120	1	1	yes	characteristic
542	C₂⁴	C₂²×#120	1	1	yes	characteristic
543	C₂⁴	C₂×#525	1	1	yes	characteristic
544	C₂⁴	C₂×#535	1	1	yes	characteristic
545	C₂⁴	#3449	1	1	yes	characteristic
546	C₂⁴	#3449	1	1	yes	characteristic
547	C₂⁴	C₂×#546	1	4	yes	—
548	C₂⁴	D₄×#41	1	4	yes	—
549	C₂⁴	D₄×#41	1	2	yes	—
550	C₂⁴	D₄×#41	1	2	yes	—
551	C₂⁴	#3485	1	4	yes	—
552	C₂⁴	#3488	1	4	yes	—
553	C₂⁴	#3488	1	2	yes	—
554	C₂⁴	#3488	1	2	yes	—
555	C₂²×C₄	#2404	1	4	yes	—
556	C₂²×C₄	#2404	1	2	yes	—
557	C₂²×C₄	#2846	1	2	yes	—
558	C₂²×C₄	#2846	1	2	yes	—
559	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
560	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
561	C₂³	#32898	1	2	yes	—
562	C₂³	#32898	1	2	yes	—
563	C₂³	#32899	1	2	yes	—
564	C₂³	#32899	1	2	yes	—
565	C₂³	C₂×#2404	1	1	yes	characteristic
566	C₂³	#34736	1	1	yes	characteristic
567	C₂³	#34736	1	1	yes	characteristic
568	C₂³	#35088	1	1	yes	characteristic
569	C₂³	#35250	1	1	yes	characteristic
570	C₂³	#35250	1	1	yes	characteristic
571	C₂³	#36212	1	4	yes	—
572	C₂³	#36212	1	4	yes	—
573	C₂³	C₂×#2846	1	1	yes	characteristic
574	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
575	C₂³	C₂×#3025	1	1	yes	characteristic
576	C₂³	C₂×#3026	1	1	yes	characteristic
577	C₂³	C₂×#3027	1	1	yes	characteristic
578	C₂²	#613188	1	1	yes	characteristic
579	C₂²	#6454041	1	1	yes	characteristic
580	C₂²	#6454047	1	1	yes	characteristic
581	C₂²	#6491100	1	1	yes	characteristic
582	C₂²	#6491103	1	1	yes	characteristic
583	C₂²	C₂×#32898	1	1	yes	characteristic
584	C₂²	C₂×#32899	1	1	yes	characteristic
585	C₂	#72237919	1	2	yes	—
586	C₂	#72262146	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#613188
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72265945	C₂	semidirect
2. #72265944	C₂	semidirect
3. #72265943	C₂	semidirect
4. #72265924	C₂	semidirect
5. #72265917	C₂	semidirect
6. #72265850	C₂	semidirect
7. #72265239	C₂	semidirect
8. #72261568	C₂	semidirect
9. #72252238	C₂	semidirect
10. #72251608	C₂	semidirect
11. C₂×#251827	C₂	semidirect
12. #72240111	C₂	semidirect
13. #72237496	C₂	semidirect
14. #72234956	C₂	semidirect
15. #72234587	C₂	semidirect
16. #72233127	C₂	semidirect
17. #72232805	C₂	semidirect
18. C₂²×#2883	C₂²	semidirect
19. #7806599	C₂²	semidirect
20. #7804409	C₂²	semidirect
21. #7721731	C₂²	semidirect
25. #7658231	C₂²	semidirect
26. #7652796	C₂²	semidirect
29. #7626663	C₂²	semidirect
31. #6628892	C₂²	semidirect
32. C₂×#32898	C₂²	semidirect
35. C₂×#20585	C₂²	semidirect
36. #394470	C₂²	semidirect
37. #394267	C₂²	semidirect
38. #392699	C₂²	semidirect
39. #392658	C₂²	semidirect
40. #392231	C₂²	semidirect
41. #364471	C₂²	semidirect
44. #364440	C₂²	semidirect
45. #364440	C₂²	semidirect
46. #364440	C₂²	semidirect
47. #353408	C₂²	semidirect
48. #353314	C₂²	semidirect
49. #238082	C₂²	semidirect
50. C₂×#10390	C₂²	semidirect
51. #233549	C₂²	semidirect
52. #233549	C₂²	semidirect
53. #233541	C₂²	semidirect
54. C₂×#10336	C₂²	semidirect
55. #201687	C₂²	semidirect
56. #201687	C₂²	semidirect
58. #201678	C₂²	semidirect
59. C₂×#9495	C₂²	semidirect
60. C₂×#9495	C₂²	semidirect
61. C₂×#9495	C₂²	semidirect
62. C₂×#8746	C₂²	semidirect
63. C₂×#8746	C₂²	semidirect
65. #187928	C₂²	semidirect
66. #122191	C₂²	semidirect
67. #122187	C₂²	semidirect
68. #122038	C₂²	semidirect
69. #115204	C₂²	semidirect
70. #115163	C₂²	semidirect
71. #111467	C₂²	semidirect
72. #111467	C₂²	semidirect
73. #111458	C₂²	semidirect
74. #107194	C₂²	semidirect
75. #107194	C₂²	semidirect
76. #106654	C₂²	semidirect
77. #106542	C₂²	semidirect
78. #105752	C₂²	semidirect
79. #105752	C₂²	semidirect
80. #105752	C₂²	semidirect
81. #105752	C₂²	semidirect
82. #105752	C₂²	semidirect
84. C₂×#3490	D₄	semidirect
87. C₂²×#518	D₄	semidirect
92. #46999	D₄	semidirect
93. #46997	D₄	semidirect
94. #46996	D₄	semidirect
95. #46996	D₄	semidirect
96. #46996	D₄	semidirect
97. #46996	D₄	semidirect
98. #46996	D₄	semidirect
99. #46996	D₄	semidirect
100. #46996	D₄	semidirect
101. #46837	D₄	semidirect
102. #46387	D₄	semidirect
103. #46386	D₄	semidirect
107. #37117	D₄	semidirect
108. #36721	D₄	semidirect
109. #36717	D₄	semidirect
110. #36714	D₄	semidirect
112. #35512	D₄	semidirect
113. #35360	D₄	semidirect
114. #35359	D₄	semidirect
115. #35355	D₄	semidirect
116. #35354	D₄	semidirect
117. #35350	D₄	semidirect
118. #35348	D₄	semidirect
119. #35346	D₄	semidirect
132. #34273	D₄	semidirect
133. #34251	D₄	semidirect
134. #34199	D₄	semidirect
135. #34199	D₄	semidirect
136. #34199	D₄	semidirect
137. #34199	D₄	semidirect
138. #34198	D₄	semidirect
145. C₂×#2315	D₄	semidirect
146. C₂×#2308	D₄	semidirect
151. C₂×#2273	D₄	semidirect
189. C₂×#543	C₂×D₄	semidirect
202. C₂²×#120	C₂×D₄	semidirect
215. C₂×#518	C₂×D₄	semidirect
223. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
227. #2849	#41	semidirect
228. #2846	#41	semidirect
229. #2842	C₂×D₄	semidirect
230. #2842	C₂×D₄	semidirect
231. #2840	C₂×D₄	semidirect
232. #2840	C₂×D₄	semidirect
233. #2840	C₂×D₄	semidirect
234. #2840	C₂×D₄	semidirect
236. #2483	C₂×D₄	semidirect
245. #2405	C₂×D₄	semidirect
261. #2403	C₂×D₄	semidirect
262. #2403	C₂×D₄	semidirect
263. #2403	C₂×D₄	semidirect
264. #2403	C₂×D₄	semidirect
269. #2315	C₂×D₄	semidirect
270. #2315	C₂×D₄	semidirect
271. #2315	C₂×D₄	semidirect
272. #2315	C₂×D₄	semidirect
275. #2312	C₂×D₄	semidirect
276. #2312	C₂×D₄	semidirect
278. #2309	C₂×D₄	semidirect
294. #2308	C₂×D₄	semidirect
295. #2308	C₂×D₄	semidirect
296. #2308	C₂×D₄	semidirect
297. #2308	C₂×D₄	semidirect
298. #2308	C₂×D₄	semidirect
299. #2308	C₂×D₄	semidirect
302. C₂×#386	C₂×D₄	semidirect
303. C₂×#385	C₂×D₄	semidirect
306. C₂×#380	C₂×D₄	semidirect
307. C₂×#379	C₂×D₄	semidirect
308. C₂×#379	C₂×D₄	semidirect
321. #2273	C₂×D₄	semidirect
322. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
326. C₂⁶	C₂×#41	semidirect
353. C₂⁴×C₄	C₂×#41	semidirect
458. #379	C₂×#41	semidirect
503. C₂×C₂²⋊C₄	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72265945	2
#72265944	2
#72265943	2
#72265924	2
#72265917	2
#72265850	2
#72265239	2
#72261568	2
#72252238	2
#72251608	2
C₂×#251827	2
#72240111	2
#72237496	2
#72234956	2
#72234587	2
#72233127	2
#72232805	2