Subgroups — #72315618

Order 4096.

Only the 953 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 529 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72315407	C₂	1	2	yes	maximal, complemented
2	#72315351	C₂	1	2	yes	maximal, complemented
3	#72315275	C₂	1	2	yes	maximal, complemented
4	#72315242	C₂	1	2	yes	maximal, complemented
5	#72315149	C₂	1	1	yes	maximal, characteristic, complemented
6	#72315113	C₂	1	1	yes	maximal, characteristic, complemented
7	#72314953	C₂	1	2	yes	maximal, complemented
8	#72314855	C₂²	1	2	yes	complemented
9	#72314808	C₂	1	2	yes	maximal, complemented
10	#72314779	C₂	1	2	yes	maximal, complemented
11	#72314739	C₂²	1	2	yes	complemented
12	#72314729	C₂²	1	2	yes	complemented
13	#72312226	C₂	1	1	yes	maximal, characteristic, complemented
14	#72312218	C₂²	1	2	yes	complemented
15	#72312216	C₂²	1	2	yes	complemented
16	#72312214	C₂²	1	2	yes	complemented
17	#72310377	C₂	1	1	yes	maximal, characteristic, complemented
18	#72310366	C₂²	1	2	yes	complemented
19	#72310358	C₂²	1	2	yes	complemented
20	#72310327	C₂	1	1	yes	maximal, characteristic, complemented
21	#72310322	C₂²	1	2	yes	complemented
22	#72310319	C₂²	1	2	yes	complemented
23	#72264854	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#72216344	C₂	1	2	yes	maximal, complemented
25	#72258368	C₂²	1	2	yes	complemented
26	C₂×#135516	C₂²	1	2	yes	complemented
27	#72258334	C₂²	1	2	yes	complemented
28	C₂×#144639	C₂²	1	2	yes	complemented
29	C₂×#139739	C₂²	1	2	yes	complemented
30	C₂×#139742	C₂²	1	2	yes	complemented
31	#72255867	C₂²	1	2	yes	complemented
32	#72246299	C₂²	1	2	yes	complemented
33	#72238976	C₂²	1	2	yes	complemented
34	#72238976	C₂²	1	2	yes	complemented
35	#72238974	C₂²	1	2	yes	complemented
36	C₂×#144631	C₂²	1	2	yes	complemented
37	#72225784	C₂	1	1	yes	maximal, characteristic, complemented
38	#72225747	C₂	1	1	yes	maximal, characteristic, complemented
39	#72225745	C₂²	1	1	yes	characteristic, complemented
40	#72225744	C₂²	1	1	yes	characteristic, complemented
41	#72225743	C₂²	1	1	yes	characteristic, complemented
42	#72225742	C₂²	1	1	yes	characteristic, complemented
43	#72225742	C₂²	1	1	yes	characteristic, complemented
44	#72225741	C₂²	1	1	yes	characteristic, complemented
45	#72225740	C₂²	1	1	yes	characteristic, complemented
46	C₂×#7266798	C₂²	1	1	yes	characteristic, complemented
47	#72225667	C₂²	1	1	yes	characteristic, complemented
48	#72225617	C₂²	1	1	yes	characteristic, complemented
49	#72219440	C₂	1	1	yes	maximal, characteristic, complemented
50	C₂×#139748	C₂²	1	2	yes	complemented
51	C₂×#139748	C₂²	1	2	yes	complemented
52	#72219438	C₂²	1	2	yes	complemented
53	#72219438	C₂²	1	2	yes	complemented
54	#72219415	C₂²	1	1	yes	characteristic, complemented
55	#72219414	C₂²	1	1	yes	characteristic, complemented
56	#72219393	C₂²	1	2	yes	complemented
57	#72219393	C₂²	1	2	yes	complemented
58	C₂×#493474	C₂²	1	2	yes	complemented
59	C₂×#493474	C₂²	1	2	yes	complemented
60	#72219301	C₂²	1	1	yes	characteristic
61	#72219299	C₂²	1	1	yes	characteristic
62	#72219295	C₂	1	1	yes	maximal, characteristic, complemented
63	#72219293	C₂²	1	2	yes	complemented
64	#72219293	C₂²	1	2	yes	complemented
65	C₂×#139716	C₂²	1	2	yes	complemented
66	C₂×#139716	C₂²	1	2	yes	complemented
67	#72219251	C₂²	1	1	yes	characteristic, complemented
68	#72219251	C₂²	1	1	yes	characteristic, complemented
69	#72219250	C₂	1	1	yes	maximal, characteristic, complemented
70	#72219248	C₂²	1	1	yes	characteristic, complemented
71	#72219243	C₂²	1	1	yes	characteristic, complemented
72	C₂²×#347042	C₂	1	1	yes	maximal, characteristic, complemented
73	C₂²×#8541	C₂²	1	1	yes	characteristic
74	C₂²×#15947	C₂²	1	1	yes	characteristic
75	C₂²×#8534	C₂²	1	1	yes	characteristic
76	C₂²×#8534	C₂²	1	1	yes	characteristic
77	#72219162	C₂²	1	2	yes	complemented
78	#72219162	C₂²	1	2	yes	complemented
79	#72219158	C₂²	1	2	yes	complemented
80	#72219120	C₂	1	1	yes	maximal, characteristic, complemented
81	C₂²×#62817	C₂²	1	1	yes	characteristic
82	#72218847	C₂	1	1	yes	maximal, characteristic, complemented
83	#72218475	C₂²	1	2	yes	complemented
84	#72218475	C₂²	1	2	yes	complemented
85	#72218391	C₂²	1	2	yes	complemented
86	#72218391	C₂²	1	2	yes	complemented
87	#72218381	C₂²	1	1	yes	characteristic, complemented
88	#72218321	C₂	1	1	yes	maximal, characteristic, complemented
89	#72218317	C₂²	1	2	yes	complemented
90	#72218317	C₂²	1	2	yes	complemented
91	#72218313	C₂²	1	1	yes	characteristic, complemented
92	#72218313	C₂²	1	1	yes	characteristic, complemented
93	#72218306	C₂²	1	1	yes	characteristic
94	#72218306	C₂²	1	1	yes	characteristic
95	#72218306	C₂²	1	1	yes	characteristic
96	#72218291	C₂²	1	1	yes	characteristic, complemented
97	C₂×#144366	C₂²	1	2	yes	complemented
98	C₂×#144366	C₂²	1	2	yes	complemented
99	C₂×#139750	C₂²	1	2	yes	complemented
100	#72218069	C₂²	1	1	yes	characteristic, complemented
101	C₂²×#23900	C₂²	1	1	yes	characteristic
102	C₂²×#23900	C₂²	1	1	yes	characteristic
103	C₂×#144382	C₂²	1	2	yes	complemented
104	C₂×#144382	C₂²	1	2	yes	complemented
105	C₂×#139731	C₂²	1	2	yes	complemented
106	C₂×#139731	C₂²	1	2	yes	complemented
107	#72217789	C₂²	1	1	yes	characteristic, complemented
108	#72215858	C₂²	1	1	yes	characteristic
109	#72215858	C₂²	1	1	yes	characteristic, complemented
110	#72215179	C₂²	1	1	yes	characteristic
111	#72215179	C₂²	1	1	yes	characteristic
112	#72215179	C₂²	1	1	yes	characteristic
113	#72215179	C₂²	1	1	yes	characteristic, complemented
114	C₂×#347042	C₂²	1	2	yes	—
115	C₂×#347042	C₂²	1	2	yes	—
116	C₂×#347042	C₂²	1	2	yes	—
117	C₂×#347042	C₂²	1	2	yes	—
118	C₂×#511790	C₂²	1	2	yes	complemented
119	C₂×#511790	C₂²	1	2	yes	complemented
120	#72213862	C₂²	1	1	yes	characteristic
121	#72210555	C₂²	1	1	yes	characteristic
122	#72210511	C₂²	1	1	yes	characteristic
123	C₂×#62817	C₂³	1	2	yes	—
124	C₂×#62817	C₂³	1	2	yes	—
125	C₂²×#3484	C₂³	1	1	yes	characteristic
126	C₂²×#3484	C₂³	1	1	yes	characteristic
127	C₂⁴×#120	C₂³	1	1	yes	characteristic
128	C₂⁴×#120	C₂³	1	1	yes	characteristic
129	C₂²×#2846	D₄	1	2	yes	complemented
130	#7630939	C₂³	1	1	yes	characteristic
131	C₂×#32873	C₂³	1	1	yes	characteristic, complemented
132	C₂×#23895	D₄	1	2	yes	complemented
133	C₂×#23895	C₂³	1	1	yes	characteristic
134	C₂×#23895	C₂³	1	1	yes	characteristic
135	#6437621	D₄	1	2	yes	complemented
136	C₂×#23900	D₄	1	2	yes	complemented
137	C₂×#23900	D₄	1	2	yes	complemented
138	C₂×#23900	C₂³	1	1	yes	characteristic
139	C₂×#23900	C₂³	1	1	yes	characteristic
140	C₂×#23900	C₂³	1	1	yes	characteristic
141	C₂×#23900	C₂³	1	1	yes	characteristic
142	C₂×#23900	C₂³	1	2	yes	—
143	C₂×#23900	C₂³	1	2	yes	—
144	C₂×#23900	C₂³	1	2	yes	—
145	C₂×#23900	C₂³	1	1	yes	characteristic, complemented
146	C₂×#23900	C₂³	1	1	yes	characteristic, complemented
147	C₂×#23897	C₂³	1	2	yes	—
148	C₂×#21778	C₂³	1	2	yes	—
149	C₂×#21776	D₄	1	2	yes	complemented
150	C₂×#21776	C₂³	1	1	yes	characteristic
151	C₂×#21776	C₂³	1	1	yes	characteristic
152	C₂×#21776	C₂³	1	1	yes	characteristic, complemented
153	C₂×#21746	C₂³	1	1	yes	characteristic, complemented
154	C₂×#21746	C₂³	1	1	yes	characteristic, complemented
155	C₂²×#1898	D₄	1	2	yes	complemented
156	#6370693	D₄	1	2	yes	complemented
157	C₂²×#1781	C₂³	1	1	yes	characteristic
158	C₂²×#1781	C₂³	1	1	yes	characteristic
159	C₂×#15947	C₂³	1	2	yes	—
160	C₂×#15947	C₂³	1	2	yes	—
161	C₂²×#1438	C₂³	1	1	yes	characteristic
162	C₂×#12707	C₂³	1	2	yes	—
163	C₂×#12707	C₂³	1	2	yes	—
164	C₂×#12705	C₂³	1	2	yes	—
165	C₂×#12705	C₂³	1	2	yes	—
166	C₂×#12705	C₂³	1	2	yes	—
167	C₂×#12705	C₂³	1	2	yes	—
168	C₂×#12705	C₂³	1	2	yes	—
169	C₂×#12705	C₂³	1	2	yes	—
170	C₂×#12705	C₂³	1	2	yes	complemented
171	C₂×#12687	C₂³	1	2	yes	—
172	C₂×#12687	C₂³	1	2	yes	—
173	C₂×#12687	C₂³	1	2	yes	—
174	C₂×#12687	C₂³	1	2	yes	—
175	C₂×#12687	C₂³	1	2	yes	—
176	C₂×#12687	C₂³	1	2	yes	—
177	C₂×#12687	C₂³	1	2	yes	complemented
178	C₂×#12687	C₂³	1	2	yes	complemented
179	#392231	D₄	1	2	yes	complemented
180	#392113	C₂³	1	1	yes	characteristic
181	#392113	C₂³	1	1	yes	characteristic
182	#392113	C₂³	1	1	yes	characteristic
183	#392109	C₂³	1	1	yes	characteristic
184	#392109	C₂³	1	1	yes	characteristic
185	#392109	C₂³	1	1	yes	characteristic
186	#392109	C₂³	1	1	yes	characteristic
187	#392030	C₂³	1	1	yes	characteristic, complemented
188	#392030	C₂³	1	1	yes	characteristic, complemented
189	#392030	C₂³	1	1	yes	characteristic, complemented
190	#382544	C₂³	1	1	yes	characteristic, complemented
191	#382436	C₂³	1	2	yes	—
192	#382434	D₄	1	2	yes	complemented
193	#382434	C₂³	1	1	yes	characteristic
194	#382434	C₂³	1	1	yes	characteristic
195	#382434	C₂³	1	1	yes	characteristic, complemented
196	#382422	C₂³	1	1	yes	characteristic, complemented
197	#382422	C₂³	1	1	yes	characteristic, complemented
198	#359558	C₂³	1	2	yes	—
199	#359549	D₄	1	2	yes	complemented
200	#359549	C₂³	1	1	yes	characteristic
201	#359549	C₂³	1	1	yes	characteristic
202	#359501	C₂³	1	2	yes	—
203	#359501	C₂³	1	1	yes	characteristic, complemented
204	#359501	C₂³	1	1	yes	characteristic, complemented
205	#359442	D₄	1	2	yes	complemented
206	#355096	C₂³	1	1	yes	characteristic, complemented
207	#347042	D₄	1	16	yes	complemented
208	C₂×#8547	C₂³	1	2	yes	complemented
209	C₂×#8547	C₂³	1	2	yes	complemented
210	C₂×#8541	C₂³	1	2	yes	—
211	C₂×#8541	C₂³	1	2	yes	—
212	C₂×#8534	C₂³	1	2	yes	—
213	C₂×#8534	C₂³	1	2	yes	—
214	C₂×#8534	C₂³	1	2	yes	—
215	C₂×#8534	C₂³	1	2	yes	—
216	C₂×#8453	C₂³	1	2	yes	complemented
217	#146475	C₂³	1	2	yes	complemented
218	C₂×#7304	C₂³	1	2	yes	complemented
219	C₂×#7304	C₂³	1	2	yes	complemented
220	C₂×#7304	C₂³	1	2	yes	complemented
221	C₂×#7304	C₂³	1	2	yes	complemented
222	C₂×#7316	C₂³	1	2	yes	complemented
223	C₂×#7316	C₂³	1	2	yes	complemented
224	C₂×#7314	C₂³	1	2	yes	complemented
225	C₂×#7314	C₂³	1	2	yes	complemented
226	C₂×#7314	C₂³	1	2	yes	complemented
227	C₂×#7314	C₂³	1	2	yes	complemented
228	C₂×#7311	C₂³	1	2	yes	complemented
229	C₂×#7311	C₂³	1	2	yes	complemented
230	C₂×#7310	C₂³	1	2	yes	complemented
231	C₂×#7310	C₂³	1	2	yes	complemented
232	C₂×#7307	C₂³	1	2	yes	complemented
233	C₂×#7307	C₂³	1	2	yes	complemented
234	#107130	C₂³	1	2	yes	complemented
235	C₂⁸	C₂×D₄	1	1	yes	characteristic
236	C₂⁸	#41	1	1	yes	characteristic, complemented
237	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
238	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
239	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
240	#62817	C₂×D₄	1	8	yes	—
241	C₂×#3484	C₂×D₄	1	2	yes	—
242	C₂×#3484	C₂×D₄	1	2	yes	—
243	C₂×#3484	C₂×D₄	1	1	yes	characteristic
244	C₂×#3484	C₂×D₄	1	1	yes	characteristic
245	C₂×#3484	C₂×D₄	1	1	yes	characteristic
246	C₂×#3484	C₂×D₄	1	1	yes	characteristic
247	C₂×#3484	#41	1	2	yes	complemented
248	C₂×#3484	C₂⁴	1	1	yes	characteristic
249	C₂×#3484	C₂⁴	1	1	yes	characteristic
250	C₂×#3484	C₂⁴	1	1	yes	characteristic
251	C₂×#3484	C₂⁴	1	2	yes	—
252	C₂²×#534	C₂×D₄	1	2	yes	—
253	C₂³×#120	C₂×D₄	1	2	yes	—
254	C₂³×#120	C₂×D₄	1	1	yes	characteristic
255	C₂³×#120	C₂×D₄	1	1	yes	characteristic
256	C₂³×#120	#41	1	2	yes	complemented
257	C₂³×#120	C₂⁴	1	1	yes	characteristic
258	C₂³×#120	C₂⁴	1	1	yes	characteristic
259	C₂³×#120	C₂⁴	1	2	yes	—
260	C₂²×#518	C₂×D₄	1	1	yes	characteristic
261	C₂²×#518	#41	1	1	yes	characteristic, complemented
262	C₂⁴×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
263	C₂⁴×C₂²⋊C₄	#41	1	1	yes	characteristic, complemented
264	C₂×#3026	C₂×D₄	1	2	yes	complemented
265	C₂×#3026	C₂×D₄	1	2	yes	complemented
266	C₂×#2883	C₂×D₄	1	2	yes	complemented
267	C₂×#2883	C₂×D₄	1	2	yes	complemented
268	C₂×#2846	C₂×D₄	1	2	yes	—
269	C₂×#2846	C₂×D₄	1	2	yes	—
270	C₂×#2846	C₂×D₄	1	2	yes	—
271	C₂×#2846	C₂×D₄	1	2	yes	—
272	#34171	C₂×D₄	1	1	yes	characteristic
273	#34171	C₂×D₄	1	1	yes	characteristic
274	#34171	C₂⁴	1	1	yes	characteristic
275	C₂²×#379	C₂×D₄	1	2	yes	—
276	#23900	C₂×D₄	1	8	yes	—
277	#23900	C₂×D₄	1	8	yes	—
278	C₂×#1913	C₂×D₄	1	2	yes	complemented
279	C₂×#1913	C₂×D₄	1	2	yes	complemented
280	C₂×#1913	C₂×D₄	1	2	yes	complemented
281	C₂×#1913	C₂×D₄	1	2	yes	complemented
282	C₂×#1898	C₂×D₄	1	2	yes	—
283	C₂×#1898	C₂×D₄	1	2	yes	—
284	C₂×#1898	C₂×D₄	1	2	yes	—
285	C₂×#1898	C₂×D₄	1	2	yes	—
286	#20960	C₂×D₄	1	2	yes	complemented
287	#20960	C₂×D₄	1	2	yes	complemented
288	C₂×#1828	C₂×D₄	1	2	yes	complemented
289	C₂×#1828	C₂×D₄	1	2	yes	complemented
290	C₂×#1828	C₂×D₄	1	2	yes	complemented
291	C₂×#1828	C₂×D₄	1	2	yes	complemented
292	C₂×#1783	C₂⁴	1	2	yes	—
293	C₂×#1783	C₂⁴	1	2	yes	—
294	C₂×#1783	C₂⁴	1	2	yes	—
295	#20585	C₂×D₄	1	2	yes	complemented
296	#20585	C₂×D₄	1	2	yes	complemented
297	C₂×#1781	C₂×D₄	1	2	yes	—
298	C₂×#1781	C₂×D₄	1	2	yes	—
299	C₂×#1781	C₂×D₄	1	2	yes	—
300	C₂×#1781	C₂×D₄	1	2	yes	—
301	C₂×#1781	C₂×D₄	1	2	yes	—
302	C₂×#1781	C₂×D₄	1	2	yes	—
303	C₂×#1781	C₂×D₄	1	2	yes	—
304	C₂×#1781	C₂⁴	1	2	yes	—
305	C₂×#1781	C₂⁴	1	1	yes	characteristic
306	C₂×#1781	C₂⁴	1	1	yes	characteristic
307	C₂×#1781	C₂⁴	1	1	yes	characteristic
308	C₂×#1781	C₂⁴	1	1	yes	characteristic
309	C₂×#1781	C₂⁴	1	1	yes	characteristic
310	C₂×#1781	C₂⁴	1	1	yes	characteristic
311	C₂×#1781	C₂⁴	1	1	yes	characteristic
312	C₂×#1781	C₂⁴	1	1	yes	characteristic
313	C₂×#1781	C₂⁴	1	2	yes	—
314	#15947	C₂×D₄	1	8	yes	—
315	C₂×#1438	C₂⁴	1	2	yes	—
316	#8541	C₂×D₄	1	8	yes	—
317	#8534	C₂×D₄	1	8	yes	—
318	#8534	C₂×D₄	1	8	yes	—
319	C₂⁷	C₂²×D₄	1	1	yes	characteristic
320	C₂⁷	C₂²×D₄	1	1	yes	characteristic
321	C₂⁷	C₂²×D₄	1	1	yes	characteristic
322	C₂⁷	C₂×#41	1	1	yes	characteristic
323	C₂⁷	C₂×#41	1	2	yes	—
324	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
325	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
326	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
327	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
328	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
329	C₂⁴×D₄	#120	1	2	yes	—
330	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
331	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
332	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
333	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
334	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
335	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
336	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
337	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
338	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
340	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
341	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
342	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
343	#3484	C₂²×D₄	1	4	yes	—
344	#3484	C₂²×D₄	1	4	yes	—
345	#3484	H(5,𝔽₂)	1	4	yes	—
346	#3484	H(5,𝔽₂)	1	4	yes	—
347	C₂×#534	#120	1	2	yes	—
348	C₂×#534	#120	1	2	yes	—
349	C₂×#534	C₂²×D₄	1	2	yes	—
350	C₂×#534	C₂²×D₄	1	2	yes	—
351	C₂²×#120	#120	1	2	yes	—
352	C₂²×#120	#120	1	2	yes	—
353	C₂²×#120	C₂²×D₄	1	2	yes	—
354	C₂²×#120	C₂²×D₄	1	2	yes	—
355	C₂²×#120	C₂²×D₄	1	4	yes	—
356	C₂²×#120	C₂²×D₄	1	4	yes	—
357	C₂²×#120	H(5,𝔽₂)	1	4	yes	—
358	C₂×#518	#120	1	2	yes	—
359	C₂×#518	C₂²×D₄	1	1	yes	characteristic
360	C₂×#518	C₂²×D₄	1	1	yes	characteristic
361	C₂×#518	C₂²×D₄	1	1	yes	characteristic
362	C₂×#518	C₂²×D₄	1	1	yes	characteristic
363	C₂×#518	C₂²×D₄	1	1	yes	characteristic
364	C₂×#518	C₂×#41	1	2	yes	—
365	C₂³×C₂²⋊C₄	#120	1	2	yes	—
366	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
367	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
368	C₂³×C₂²⋊C₄	C₂×#41	1	2	yes	—
369	C₂²×#99	C₂²×D₄	1	2	yes	—
370	C₂²×#99	C₂²×D₄	1	2	yes	—
371	C₂²×#99	C₂²×D₄	1	2	yes	—
372	C₂²×#99	C₂²×D₄	1	2	yes	—
373	C₂²×#99	C₂²×D₄	1	2	yes	—
374	C₂²×#99	C₂²×D₄	1	2	yes	—
375	#2846	#120	1	8	yes	complemented
376	C₂×#379	C₂²×D₄	1	2	yes	—
377	C₂×#379	C₂²×D₄	1	2	yes	—
378	#1898	#120	1	8	yes	complemented
379	#1781	C₂²×D₄	1	4	yes	—
380	#1781	C₂²×D₄	1	4	yes	—
381	#1438	C₂²×D₄	1	4	yes	—
382	C₂⁶	B(4,𝔽₂)	1	2	yes	—
383	C₂⁶	C₂×#120	1	1	yes	characteristic
384	C₂⁶	C₂×#120	1	1	yes	characteristic
385	C₂⁶	C₂×#120	1	2	yes	—
386	C₂⁶	#525	1	1	yes	characteristic
387	C₂⁶	#525	1	1	yes	characteristic
388	C₂⁶	#546	1	1	yes	characteristic
389	C₂⁶	#546	1	1	yes	characteristic
390	C₂⁶	#546	1	1	yes	characteristic
391	C₂⁶	#546	1	1	yes	characteristic
392	C₂⁶	#546	1	1	yes	characteristic
393	C₂⁶	#546	1	1	yes	characteristic
394	C₂⁶	#546	1	1	yes	characteristic
395	C₂⁶	#546	1	4	yes	complemented
396	C₂⁶	C₂³×D₄	1	1	yes	characteristic
397	C₂⁶	C₂²×#41	1	1	yes	characteristic
398	C₂×H(5,𝔽₂)	D₄²	1	4	yes	—
399	C₂×H(5,𝔽₂)	#546	1	4	yes	complemented
400	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
401	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
402	C₂³×D₄	C₂×#120	1	1	yes	characteristic
403	C₂³×D₄	C₂×#120	1	1	yes	characteristic
404	C₂³×D₄	C₂×#120	1	2	yes	—
405	C₂³×D₄	C₂×#120	1	2	yes	—
406	C₂³×D₄	#525	1	1	yes	characteristic
407	C₂³×D₄	#525	1	1	yes	characteristic
408	C₂³×D₄	#535	1	1	yes	characteristic
409	C₂³×D₄	#535	1	1	yes	characteristic
410	C₂³×D₄	#546	1	1	yes	characteristic
411	C₂³×D₄	#546	1	1	yes	characteristic
412	C₂³×D₄	#546	1	1	yes	characteristic
413	C₂³×D₄	#546	1	1	yes	characteristic
414	C₂³×D₄	#546	1	1	yes	characteristic
415	C₂³×D₄	#546	1	1	yes	characteristic
416	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
417	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
418	C₂³×D₄	C₂³×D₄	1	2	yes	—
419	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
420	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
422	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
423	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
424	C₂⁴×C₄	B(4,𝔽₂)	1	2	yes	—
425	C₂⁴×C₄	#535	1	1	yes	characteristic
426	C₂⁴×C₄	#535	1	1	yes	characteristic
427	C₂⁴×C₄	#546	1	1	yes	characteristic
428	C₂⁴×C₄	#546	1	1	yes	characteristic
429	C₂⁴×C₄	#546	1	1	yes	characteristic
430	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	#534	D₄²	1	8	yes	—
432	C₂×#120	B(4,𝔽₂)	1	8	yes	—
433	C₂×#120	C₂×#120	1	4	yes	—
434	C₂×#120	#534	1	4	yes	—
435	#518	D₄²	1	4	yes	—
436	#518	#546	1	4	yes	complemented
437	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
438	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
439	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
440	C₂²×C₂²⋊C₄	#546	1	4	yes	complemented
441	#379	C₂×#120	1	4	yes	—
442	C₂⁵	#2404	1	1	yes	characteristic
443	C₂⁵	#2404	1	1	yes	characteristic
444	C₂⁵	#2404	1	1	yes	characteristic
445	C₂⁵	#2404	1	1	yes	characteristic
446	C₂⁵	#2404	1	1	yes	characteristic
447	C₂⁵	#2404	1	1	yes	characteristic
448	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
449	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
450	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
451	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
452	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
453	C₂⁵	C₂²×#120	1	1	yes	characteristic
454	C₂⁵	C₂²×#120	1	1	yes	characteristic
455	C₂⁵	C₂×#525	1	1	yes	characteristic
456	C₂⁵	C₂×#534	1	1	yes	characteristic
457	C₂⁵	C₂×#546	1	2	yes	—
458	C₂⁵	C₂×#546	1	1	yes	characteristic
459	C₂⁵	C₂×#546	1	1	yes	characteristic
460	C₂⁵	C₂×#546	1	1	yes	characteristic
461	C₂⁵	#3484	1	1	yes	characteristic
462	C₂⁵	#3484	1	1	yes	characteristic
463	C₂⁵	#3490	1	2	yes	—
464	C₂²×D₄	#2403	1	4	yes	—
465	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
466	C₂²×D₄	C₂×D₄²	1	2	yes	—
467	C₂²×D₄	C₂×D₄²	1	2	yes	—
468	C₂²×D₄	C₂×#546	1	2	yes	—
469	C₂²×D₄	#3484	1	2	yes	—
470	C₂²×D₄	#3484	1	2	yes	—
471	C₂²×D₄	#3484	1	2	yes	—
472	C₂²×D₄	#3490	1	2	yes	—
473	C₂²×D₄	#3532	1	2	yes	—
474	C₂³×C₄	#2404	1	1	yes	characteristic
475	C₂³×C₄	#2404	1	1	yes	characteristic
476	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
477	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
478	C₂³×C₄	C₂×#535	1	1	yes	characteristic
479	C₂³×C₄	C₂×#546	1	1	yes	characteristic
480	C₂³×C₄	#3484	1	2	yes	—
481	C₂³×C₄	#3532	1	2	yes	—
482	C₂×C₂²⋊C₄	#2403	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
484	C₂⁴	#23900	1	4	yes	—
485	C₂⁴	#23984	1	2	yes	—
486	C₂⁴	#23984	1	2	yes	—
487	C₂⁴	#23984	1	2	yes	—
488	C₂⁴	#23984	1	1	yes	characteristic
489	C₂⁴	#23984	1	1	yes	characteristic
490	C₂⁴	#23996	1	2	yes	—
491	C₂⁴	#23996	1	2	yes	—
492	C₂⁴	#23996	1	2	yes	—
493	C₂⁴	C₂×#2403	1	1	yes	characteristic
494	C₂⁴	C₂×#2404	1	1	yes	characteristic
495	C₂⁴	#35346	1	1	yes	characteristic
496	C₂⁴	#36098	1	2	yes	—
497	C₂⁴	#36152	1	1	yes	characteristic
498	C₂⁴	#36152	1	1	yes	characteristic
499	C₂⁴	#37832	1	1	yes	characteristic
500	C₂⁴	#37832	1	1	yes	characteristic
501	C₂⁴	#58991	1	2	yes	—
502	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
503	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
504	C₂²×C₄	#23900	1	4	yes	—
505	C₂²×C₄	#37645	1	2	yes	—
506	C₂²×C₄	#58991	1	2	yes	—
507	C₂³	#251827	1	2	yes	—
508	C₂³	#251827	1	2	yes	—
509	C₂³	#647657	1	1	yes	characteristic
510	C₂³	C₂×#23900	1	2	yes	—
511	C₂³	C₂×#23996	1	1	yes	characteristic
512	C₂³	C₂×#23996	1	1	yes	characteristic
513	C₂³	C₂×#23996	1	1	yes	characteristic
514	C₂³	#6451863	1	1	yes	characteristic
515	C₂³	C₂×#23984	1	1	yes	characteristic
516	C₂³	C₂×#23984	1	1	yes	characteristic
517	C₂³	#6499867	1	2	yes	—
518	C₂²	#72216344	1	4	yes	complemented
519	C₂²	#72217617	1	1	yes	characteristic
520	C₂²	#72225632	1	1	yes	characteristic
521	C₂²	#72233156	1	1	yes	characteristic
522	C₂²	#72234644	1	1	yes	characteristic
523	C₂²	#72234955	1	1	yes	characteristic
524	C₂²	#72240110	1	1	yes	characteristic
525	C₂²	C₂×#251827	1	1	yes	characteristic
526	C₂	#72255637	1	1	yes	characteristic
527	C₂	C₂×#72216344	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×#251827
commutator, Frattini, cosocle	C₂⁴×D₄	C₂⁵
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72315407	C₂	semidirect
2. #72315351	C₂	semidirect
3. #72315275	C₂	semidirect
4. #72315242	C₂	semidirect
5. #72315149	C₂	semidirect
6. #72315113	C₂	semidirect
7. #72314953	C₂	semidirect
8. #72314855	C₂²	semidirect
9. #72314808	C₂	semidirect
10. #72314779	C₂	semidirect
11. #72314739	C₂²	semidirect
12. #72314729	C₂²	semidirect
13. #72312226	C₂	semidirect
14. #72312218	C₂²	semidirect
15. #72312216	C₂²	semidirect
16. #72312214	C₂²	semidirect
17. #72310377	C₂	semidirect
18. #72310366	C₂²	semidirect
19. #72310358	C₂²	semidirect
20. #72310327	C₂	semidirect
21. #72310322	C₂²	semidirect
22. #72310319	C₂²	semidirect
23. #72264854	C₂	semidirect
24. C₂×#72216344	C₂	semidirect
25. #72258368	C₂²	semidirect
26. C₂×#135516	C₂²	semidirect
27. #72258334	C₂²	semidirect
28. C₂×#144639	C₂²	semidirect
29. C₂×#139739	C₂²	semidirect
30. C₂×#139742	C₂²	semidirect
31. #72255867	C₂²	semidirect
32. #72246299	C₂²	semidirect
33. #72238976	C₂²	semidirect
34. #72238976	C₂²	semidirect
35. #72238974	C₂²	semidirect
36. C₂×#144631	C₂²	semidirect
37. #72225784	C₂	semidirect
38. #72225747	C₂	semidirect
39. #72225745	C₂²	semidirect
40. #72225744	C₂²	semidirect
41. #72225743	C₂²	semidirect
42. #72225742	C₂²	semidirect
43. #72225742	C₂²	semidirect
44. #72225741	C₂²	semidirect
45. #72225740	C₂²	semidirect
46. C₂×#7266798	C₂²	semidirect
47. #72225667	C₂²	semidirect
48. #72225617	C₂²	semidirect
49. #72219440	C₂	semidirect
50. C₂×#139748	C₂²	semidirect
51. C₂×#139748	C₂²	semidirect
52. #72219438	C₂²	semidirect
53. #72219438	C₂²	semidirect
54. #72219415	C₂²	semidirect
55. #72219414	C₂²	semidirect
56. #72219393	C₂²	semidirect
57. #72219393	C₂²	semidirect
58. C₂×#493474	C₂²	semidirect
59. C₂×#493474	C₂²	semidirect
62. #72219295	C₂	semidirect
63. #72219293	C₂²	semidirect
64. #72219293	C₂²	semidirect
65. C₂×#139716	C₂²	semidirect
66. C₂×#139716	C₂²	semidirect
67. #72219251	C₂²	semidirect
68. #72219251	C₂²	semidirect
69. #72219250	C₂	semidirect
70. #72219248	C₂²	semidirect
71. #72219243	C₂²	semidirect
72. C₂²×#347042	C₂	semidirect
77. #72219162	C₂²	semidirect
78. #72219162	C₂²	semidirect
79. #72219158	C₂²	semidirect
80. #72219120	C₂	semidirect
82. #72218847	C₂	semidirect
83. #72218475	C₂²	semidirect
84. #72218475	C₂²	semidirect
85. #72218391	C₂²	semidirect
86. #72218391	C₂²	semidirect
87. #72218381	C₂²	semidirect
88. #72218321	C₂	semidirect
89. #72218317	C₂²	semidirect
90. #72218317	C₂²	semidirect
91. #72218313	C₂²	semidirect
92. #72218313	C₂²	semidirect
96. #72218291	C₂²	semidirect
97. C₂×#144366	C₂²	semidirect
98. C₂×#144366	C₂²	semidirect
99. C₂×#139750	C₂²	semidirect
100. #72218069	C₂²	semidirect
103. C₂×#144382	C₂²	semidirect
104. C₂×#144382	C₂²	semidirect
105. C₂×#139731	C₂²	semidirect
106. C₂×#139731	C₂²	semidirect
107. #72217789	C₂²	semidirect
109. #72215858	C₂²	semidirect
113. #72215179	C₂²	semidirect
118. C₂×#511790	C₂²	semidirect
119. C₂×#511790	C₂²	semidirect
129. C₂²×#2846	D₄	semidirect
131. C₂×#32873	C₂³	semidirect
132. C₂×#23895	D₄	semidirect
135. #6437621	D₄	semidirect
136. C₂×#23900	D₄	semidirect
137. C₂×#23900	D₄	semidirect
145. C₂×#23900	C₂³	semidirect
146. C₂×#23900	C₂³	semidirect
149. C₂×#21776	D₄	semidirect
152. C₂×#21776	C₂³	semidirect
153. C₂×#21746	C₂³	semidirect
154. C₂×#21746	C₂³	semidirect
155. C₂²×#1898	D₄	semidirect
156. #6370693	D₄	semidirect
170. C₂×#12705	C₂³	semidirect
177. C₂×#12687	C₂³	semidirect
178. C₂×#12687	C₂³	semidirect
179. #392231	D₄	semidirect
187. #392030	C₂³	semidirect
188. #392030	C₂³	semidirect
189. #392030	C₂³	semidirect
190. #382544	C₂³	semidirect
192. #382434	D₄	semidirect
195. #382434	C₂³	semidirect
196. #382422	C₂³	semidirect
197. #382422	C₂³	semidirect
199. #359549	D₄	semidirect
203. #359501	C₂³	semidirect
204. #359501	C₂³	semidirect
205. #359442	D₄	semidirect
206. #355096	C₂³	semidirect
207. #347042	D₄	semidirect
208. C₂×#8547	C₂³	semidirect
209. C₂×#8547	C₂³	semidirect
216. C₂×#8453	C₂³	semidirect
217. #146475	C₂³	semidirect
218. C₂×#7304	C₂³	semidirect
219. C₂×#7304	C₂³	semidirect
220. C₂×#7304	C₂³	semidirect
221. C₂×#7304	C₂³	semidirect
222. C₂×#7316	C₂³	semidirect
223. C₂×#7316	C₂³	semidirect
224. C₂×#7314	C₂³	semidirect
225. C₂×#7314	C₂³	semidirect
226. C₂×#7314	C₂³	semidirect
227. C₂×#7314	C₂³	semidirect
228. C₂×#7311	C₂³	semidirect
229. C₂×#7311	C₂³	semidirect
230. C₂×#7310	C₂³	semidirect
231. C₂×#7310	C₂³	semidirect
232. C₂×#7307	C₂³	semidirect
233. C₂×#7307	C₂³	semidirect
234. #107130	C₂³	semidirect
236. C₂⁸	#41	semidirect
238. C₂³×H(5,𝔽₂)	#41	semidirect
247. C₂×#3484	#41	semidirect
256. C₂³×#120	#41	semidirect
261. C₂²×#518	#41	semidirect
263. C₂⁴×C₂²⋊C₄	#41	semidirect
264. C₂×#3026	C₂×D₄	semidirect
265. C₂×#3026	C₂×D₄	semidirect
266. C₂×#2883	C₂×D₄	semidirect
267. C₂×#2883	C₂×D₄	semidirect
278. C₂×#1913	C₂×D₄	semidirect
279. C₂×#1913	C₂×D₄	semidirect
280. C₂×#1913	C₂×D₄	semidirect
281. C₂×#1913	C₂×D₄	semidirect
286. #20960	C₂×D₄	semidirect
287. #20960	C₂×D₄	semidirect
288. C₂×#1828	C₂×D₄	semidirect
289. C₂×#1828	C₂×D₄	semidirect
290. C₂×#1828	C₂×D₄	semidirect
291. C₂×#1828	C₂×D₄	semidirect
295. #20585	C₂×D₄	semidirect
296. #20585	C₂×D₄	semidirect
375. #2846	#120	semidirect
378. #1898	#120	semidirect
395. C₂⁶	#546	semidirect
399. C₂×H(5,𝔽₂)	#546	semidirect
436. #518	#546	semidirect
440. C₂²×C₂²⋊C₄	#546	semidirect
518. C₂²	#72216344	semidirect

Maximal subgroups

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

subgroup	index
#72315407	2
#72315351	2
#72315275	2
#72315242	2
#72315149	2
#72315113	2
#72314953	2
#72314808	2
#72314779	2
#72312226	2
#72310377	2
#72310327	2
#72264854	2
C₂×#72216344	2
#72225784	2
#72225747	2
#72219440	2
#72219295	2
#72219250	2
C₂²×#347042	2
#72219120	2
#72218847	2
#72218321	2