Subgroups — #72256183

Order 4096.

At least 19156 conjugacy classes of subgroups; only the 757 normal subgroups are shown.

The subgroup lattice has 622 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72256177	C₂	1	1	yes	maximal, characteristic, complemented
2	#72256175	C₂	1	1	yes	maximal, characteristic, complemented
3	#72256173	C₂	1	1	yes	maximal, characteristic, complemented
4	#72256172	C₂	1	1	yes	maximal, characteristic, complemented
5	#72256169	C₂	1	1	yes	maximal, characteristic, complemented
6	#72256166	C₂	1	1	yes	maximal, characteristic, complemented
7	#72256163	C₂	1	1	yes	maximal, characteristic, complemented
8	#72256158	C₂	1	1	yes	maximal, characteristic, complemented
9	#72256156	C₂²	1	1	yes	characteristic, complemented
10	#72256156	C₂²	1	1	yes	characteristic, complemented
11	#72256147	C₂	1	1	yes	maximal, characteristic, complemented
12	#72256142	C₂	1	1	yes	maximal, characteristic, complemented
13	#72256138	C₂	1	1	yes	maximal, characteristic, complemented
14	#72256137	C₂²	1	1	yes	characteristic, complemented
15	#72256135	C₂	1	1	yes	maximal, characteristic, complemented
16	#72256132	C₂²	1	1	yes	characteristic, complemented
17	#72256129	C₂	1	1	yes	maximal, characteristic, complemented
18	#72256126	C₂²	1	1	yes	characteristic, complemented
19	#72256121	C₂	1	1	yes	maximal, characteristic, complemented
20	#72256119	C₂²	1	1	yes	characteristic, complemented
21	#72256116	C₂	1	1	yes	maximal, characteristic, complemented
22	#72256113	C₂²	1	1	yes	characteristic, complemented
23	#72256111	C₂²	1	1	yes	characteristic, complemented
24	#72256106	C₂	1	1	yes	maximal, characteristic, complemented
25	#72256103	C₂²	1	1	yes	characteristic, complemented
26	#72256103	C₂²	1	1	yes	characteristic, complemented
27	#72256078	C₂	1	1	yes	maximal, characteristic, complemented
28	#72256070	C₂	1	1	yes	maximal, characteristic, complemented
29	#72256060	C₂	1	1	yes	maximal, characteristic, complemented
30	#72256048	C₂²	1	1	yes	characteristic, complemented
31	#72256043	C₂²	1	1	yes	characteristic, complemented
32	#72256017	C₂	1	1	yes	maximal, characteristic, complemented
33	#72256005	C₂²	1	1	yes	characteristic, complemented
34	#72256004	C₂²	1	1	yes	characteristic, complemented
35	#72255990	C₂²	1	1	yes	characteristic, complemented
36	#72255986	C₂²	1	1	yes	characteristic, complemented
37	#72255977	C₂²	1	1	yes	characteristic, complemented
38	#72255974	C₂	1	1	yes	maximal, characteristic, complemented
39	#72255971	C₂²	1	1	yes	characteristic, complemented
40	#72255971	C₂²	1	1	yes	characteristic, complemented
41	#72255947	C₂²	1	1	yes	characteristic, complemented
42	#72255947	C₂²	1	1	yes	characteristic, complemented
43	#72255942	C₂	1	1	yes	maximal, characteristic, complemented
44	#72255939	C₂²	1	1	yes	characteristic, complemented
45	#72255939	C₂²	1	1	yes	characteristic, complemented
46	#72255900	C₂	1	1	yes	maximal, characteristic, complemented
47	#72255897	C₂²	1	1	yes	characteristic
48	#72255897	C₂²	1	1	yes	characteristic
49	#72255894	C₂	1	1	yes	maximal, characteristic, complemented
50	#72255893	C₂²	1	1	yes	characteristic
51	#72255891	C₂²	1	1	yes	characteristic
52	#72255891	C₂²	1	1	yes	characteristic, complemented
53	#72255878	C₂²	1	1	yes	characteristic, complemented
54	#72255871	C₂²	1	1	yes	characteristic, complemented
55	#72255867	C₂²	1	1	yes	characteristic, complemented
56	#72255860	C₂²	1	1	yes	characteristic, complemented
57	#72255857	C₂	1	1	yes	maximal, characteristic, complemented
58	#72255853	C₂²	1	1	yes	characteristic, complemented
59	#72255853	C₂²	1	1	yes	characteristic, complemented
60	#72255849	C₂²	1	1	yes	characteristic, complemented
61	#72255846	C₂	1	1	yes	maximal, characteristic, complemented
62	#72255841	C₂²	1	1	yes	characteristic, complemented
63	#72255841	C₂²	1	1	yes	characteristic, complemented
64	#72255838	C₂²	1	1	yes	characteristic, complemented
65	#72255838	C₂²	1	1	yes	characteristic, complemented
66	#72255829	C₂²	1	1	yes	characteristic, complemented
67	#72255826	C₂²	1	1	yes	characteristic, complemented
68	#72255819	C₂²	1	1	yes	characteristic, complemented
69	#72255803	C₂²	1	1	yes	characteristic, complemented
70	#72255793	C₂²	1	1	yes	characteristic, complemented
71	#72255785	C₂²	1	1	yes	characteristic, complemented
72	#72255777	C₂²	1	1	yes	characteristic, complemented
73	#72255776	C₂²	1	1	yes	characteristic
74	#72255776	C₂²	1	1	yes	characteristic
75	#72255774	C₂²	1	1	yes	characteristic, complemented
76	#72255771	C₂²	1	1	yes	characteristic, complemented
77	C₂×#139759	C₂²	1	1	yes	characteristic
78	#72255754	C₂²	1	1	yes	characteristic
79	#72255754	C₂²	1	1	yes	characteristic, complemented
80	#72252596	C₂	1	1	yes	maximal, characteristic, complemented
81	#72252595	C₂	1	1	yes	maximal, characteristic, complemented
82	#72251552	C₂²	1	1	yes	characteristic, complemented
83	#72251550	C₂²	1	1	yes	characteristic, complemented
84	#72251501	C₂²	1	1	yes	characteristic, complemented
85	#72251499	C₂²	1	1	yes	characteristic, complemented
86	#72251476	C₂²	1	1	yes	characteristic, complemented
87	#72251475	C₂²	1	1	yes	characteristic, complemented
88	#72251463	C₂²	1	1	yes	characteristic, complemented
89	#72251185	C₂	1	1	yes	maximal, characteristic, complemented
90	#72251171	C₂²	1	1	yes	characteristic, complemented
91	#72251028	C₂²	1	1	yes	characteristic, complemented
92	#72251028	C₂²	1	1	yes	characteristic, complemented
93	#72249647	C₂²	1	1	yes	characteristic, complemented
94	#72249638	C₂²	1	1	yes	characteristic, complemented
95	#72249638	C₂²	1	1	yes	characteristic, complemented
96	#72249626	C₂²	1	1	yes	characteristic, complemented
97	#72249626	C₂²	1	1	yes	characteristic, complemented
98	#72249623	C₂²	1	1	yes	characteristic, complemented
99	#72249623	C₂²	1	1	yes	characteristic, complemented
100	#72249606	C₂²	1	1	yes	characteristic, complemented
101	#72249606	C₂²	1	1	yes	characteristic, complemented
102	#72249591	C₂²	1	1	yes	characteristic, complemented
103	#72249587	C₂²	1	1	yes	characteristic
104	#72249584	C₂²	1	1	yes	characteristic, complemented
105	#72246299	C₂²	1	1	yes	characteristic, complemented
106	C₂×#493480	C₂²	1	1	yes	characteristic, complemented
107	C₂×#511811	C₂²	1	1	yes	characteristic
108	#72240083	C₂²	1	1	yes	characteristic, complemented
109	C₂×#144633	C₂²	1	1	yes	characteristic, complemented
110	#72238974	C₂²	1	1	yes	characteristic, complemented
111	C₂×#144631	C₂²	1	1	yes	characteristic, complemented
112	#72238613	C₂²	1	1	yes	characteristic, complemented
113	#72238611	C₂²	1	1	yes	characteristic, complemented
114	#72238609	C₂²	1	1	yes	characteristic, complemented
115	#72238443	C₂²	1	1	yes	characteristic, complemented
116	#72238349	C₂²	1	1	yes	characteristic, complemented
117	#72238349	C₂²	1	1	yes	characteristic, complemented
118	#72237903	C₂²	1	1	yes	characteristic, complemented
119	#72237900	C₂²	1	1	yes	characteristic, complemented
120	#72237829	C₂²	1	1	yes	characteristic, complemented
121	#72237639	C₂	1	1	yes	maximal, characteristic, complemented
122	#72237638	C₂²	1	1	yes	characteristic, complemented
123	#72237637	C₂²	1	1	yes	characteristic, complemented
124	#72237476	C₂²	1	1	yes	characteristic, complemented
125	#72237473	C₂²	1	1	yes	characteristic, complemented
126	#72237473	C₂²	1	1	yes	characteristic, complemented
127	#72237472	C₂²	1	1	yes	characteristic, complemented
128	#72237467	C₂²	1	1	yes	characteristic, complemented
129	#72237467	C₂²	1	1	yes	characteristic, complemented
130	#72237374	C₂²	1	1	yes	characteristic, complemented
131	#72237034	C₂²	1	1	yes	characteristic, complemented
132	#72237033	C₂²	1	1	yes	characteristic, complemented
133	#72236948	C₂²	1	1	yes	characteristic, complemented
134	#72236636	C₂²	1	1	yes	characteristic, complemented
135	#72236521	C₂²	1	1	yes	characteristic, complemented
136	#72236508	C₂²	1	1	yes	characteristic, complemented
137	#72236233	C₂²	1	1	yes	characteristic, complemented
138	#72235269	C₂	1	1	yes	maximal, characteristic, complemented
139	#72235258	C₂²	1	1	yes	characteristic, complemented
140	#72235258	C₂²	1	1	yes	characteristic, complemented
141	#72235253	C₂²	1	1	yes	characteristic
142	#72235246	C₂²	1	1	yes	characteristic
143	#72235242	C₂²	1	1	yes	characteristic, complemented
144	#72235238	C₂²	1	1	yes	characteristic
145	#72235238	C₂²	1	1	yes	characteristic
146	#72235234	C₂²	1	1	yes	characteristic
147	#72235130	C₂²	1	1	yes	characteristic, complemented
148	#72234953	C₂²	1	1	yes	characteristic, complemented
149	#72231692	C₂²	1	1	yes	characteristic, complemented
150	#72231692	C₂²	1	1	yes	characteristic, complemented
151	C₂×#511771	C₂²	1	1	yes	characteristic
152	C₂×#511771	C₂²	1	1	yes	characteristic
153	#72225745	C₂²	1	1	yes	characteristic, complemented
154	#72225741	C₂²	1	1	yes	characteristic, complemented
155	#72225736	C₂²	1	1	yes	characteristic, complemented
156	#72225735	C₂²	1	1	yes	characteristic, complemented
157	#72225712	C₂²	1	1	yes	characteristic, complemented
158	#72225657	C₂²	1	1	yes	characteristic
159	#72225657	C₂²	1	1	yes	characteristic
160	#72225647	C₂²	1	1	yes	characteristic
161	#72225647	C₂²	1	1	yes	characteristic
162	#72225646	C₂²	1	1	yes	characteristic
163	#72225646	C₂²	1	1	yes	characteristic
164	#72225610	C₂²	1	1	yes	characteristic
165	#72225610	C₂²	1	1	yes	characteristic
166	#72225610	C₂²	1	1	yes	characteristic, complemented
167	#72225610	C₂²	1	1	yes	characteristic, complemented
168	#72219645	C₂²	1	1	yes	characteristic
169	#72219640	C₂²	1	1	yes	characteristic
170	#72219377	C₂²	1	1	yes	characteristic, complemented
171	#72219345	C₂²	1	1	yes	characteristic, complemented
172	#72219345	C₂²	1	1	yes	characteristic, complemented
173	#72219158	C₂²	1	1	yes	characteristic, complemented
174	#72218840	C₂²	1	1	yes	characteristic, complemented
175	#72218840	C₂²	1	1	yes	characteristic, complemented
176	#72218838	C₂²	1	1	yes	characteristic, complemented
177	#72218838	C₂²	1	1	yes	characteristic, complemented
178	#72218521	C₂²	1	1	yes	characteristic, complemented
179	#72218521	C₂²	1	1	yes	characteristic, complemented
180	#72218391	C₂²	1	1	yes	characteristic, complemented
181	#72218391	C₂²	1	1	yes	characteristic, complemented
182	#72218121	C₂²	1	1	yes	characteristic
183	#72218121	C₂²	1	1	yes	characteristic
184	#72218114	C₂²	1	1	yes	characteristic
185	#72218114	C₂²	1	1	yes	characteristic
186	C₂×#139750	C₂²	1	1	yes	characteristic, complemented
187	#10586404	C₂³	1	1	yes	characteristic
188	C₂×#62832	C₂³	1	1	yes	characteristic
189	C₂³×D₄²	C₂³	1	1	yes	characteristic
190	#7642244	C₂³	1	1	yes	characteristic
191	#7642244	C₂³	1	1	yes	characteristic
192	#7642244	C₂³	1	1	yes	characteristic
193	#7642244	C₂³	1	1	yes	characteristic
194	C₂×#35390	C₂³	1	1	yes	characteristic
195	#7626230	C₂³	1	1	yes	characteristic
196	C₂×#32873	C₂³	1	1	yes	characteristic
197	#6628987	D₄	1	2	yes	complemented
198	#6437999	D₄	1	2	yes	complemented
199	C₂×#23895	C₂³	1	1	yes	characteristic
200	C₂×#23895	C₂³	1	1	yes	characteristic
201	#6437621	C₂³	1	1	yes	characteristic
202	#6437621	C₂³	1	1	yes	characteristic
203	#6437621	C₂³	1	1	yes	characteristic
204	#6437621	C₂³	1	1	yes	characteristic
205	#6437621	C₂³	1	1	yes	characteristic
206	#6437621	C₂³	1	1	yes	characteristic
207	C₂×#23900	C₂³	1	1	yes	characteristic
208	C₂×#23900	C₂³	1	1	yes	characteristic
209	C₂×#23900	C₂³	1	1	yes	characteristic
210	C₂×#23900	C₂³	1	1	yes	characteristic
211	C₂×#23897	C₂³	1	1	yes	characteristic
212	C₂×#23906	C₂³	1	1	yes	characteristic
213	C₂×#23906	C₂³	1	1	yes	characteristic
214	#6432949	D₄	1	2	yes	complemented
215	#6431795	C₂³	1	1	yes	characteristic
216	#6374251	C₂³	1	1	yes	characteristic
217	C₂×#21776	C₂³	1	1	yes	characteristic
218	C₂×#21776	C₂³	1	1	yes	characteristic
219	C₂×#21776	C₂³	1	1	yes	characteristic
220	#6374128	C₂³	1	1	yes	characteristic
221	#6374128	C₂³	1	1	yes	characteristic
222	#6371558	C₂³	1	1	yes	characteristic
223	#617710	C₂³	1	1	yes	characteristic
224	#617710	C₂³	1	1	yes	characteristic
225	#616960	C₂³	1	1	yes	characteristic
226	#616960	C₂³	1	1	yes	characteristic
227	#555899	C₂³	1	1	yes	characteristic
228	C₂×#12707	C₂³	1	1	yes	characteristic
229	C₂×#12707	C₂³	1	1	yes	characteristic
230	C₂×#12707	C₂³	1	1	yes	characteristic
231	C₂×#12707	C₂³	1	1	yes	characteristic
232	C₂×#12705	C₂³	1	1	yes	characteristic
233	C₂×#12705	C₂³	1	1	yes	characteristic
234	C₂×#12705	C₂³	1	1	yes	characteristic
235	C₂×#12705	C₂³	1	1	yes	characteristic
236	C₂×#12705	C₂³	1	1	yes	characteristic
237	C₂×#12705	C₂³	1	1	yes	characteristic
238	C₂×#12693	C₂³	1	1	yes	characteristic
239	C₂×#12693	C₂³	1	1	yes	characteristic
240	C₂×#12693	C₂³	1	1	yes	characteristic
241	C₂×#12693	C₂³	1	1	yes	characteristic
242	#493357	C₂³	1	1	yes	characteristic
243	#493357	C₂³	1	1	yes	characteristic
244	#493357	C₂³	1	1	yes	characteristic
245	#493357	C₂³	1	1	yes	characteristic
246	C₂×#12687	C₂³	1	1	yes	characteristic
247	C₂×#12687	C₂³	1	1	yes	characteristic
248	C₂×#12687	C₂³	1	1	yes	characteristic
249	C₂×#12687	C₂³	1	1	yes	characteristic
250	C₂×#12687	C₂³	1	1	yes	characteristic
251	C₂×#12687	C₂³	1	1	yes	characteristic
252	C₂×#12687	C₂³	1	1	yes	characteristic
253	C₂×#12687	C₂³	1	1	yes	characteristic
254	#405481	D₄	1	2	yes	complemented
255	#405306	D₄	1	2	yes	complemented
256	#405274	D₄	1	2	yes	complemented
257	#394273	D₄	1	2	yes	complemented
258	#394058	D₄	1	2	yes	complemented
259	#394058	D₄	1	2	yes	complemented
260	#393532	D₄	1	2	yes	complemented
261	#392030	C₂³	1	1	yes	characteristic
262	#382544	C₂³	1	1	yes	characteristic
263	#382544	C₂³	1	1	yes	characteristic
264	#382544	C₂³	1	1	yes	characteristic
265	#382436	C₂³	1	1	yes	characteristic
266	#382434	C₂³	1	1	yes	characteristic
267	#382422	C₂³	1	1	yes	characteristic
268	#382422	C₂³	1	1	yes	characteristic
269	#380554	D₄	1	2	yes	complemented
270	#374004	D₄	1	2	yes	complemented
271	#373640	C₂³	1	1	yes	characteristic
272	#373637	C₂³	1	1	yes	characteristic
273	#373637	C₂³	1	1	yes	characteristic
274	#359558	C₂³	1	1	yes	characteristic
275	#359558	C₂³	1	1	yes	characteristic
276	#359549	C₂³	1	1	yes	characteristic
277	#359549	C₂³	1	1	yes	characteristic
278	#359549	C₂³	1	1	yes	characteristic
279	#359549	C₂³	1	1	yes	characteristic
280	#359549	C₂³	1	1	yes	characteristic
281	#359549	C₂³	1	1	yes	characteristic
282	#359501	C₂³	1	1	yes	characteristic
283	#359501	C₂³	1	1	yes	characteristic
284	#359501	C₂³	1	1	yes	characteristic
285	#359501	C₂³	1	1	yes	characteristic
286	#359458	C₂³	1	1	yes	characteristic
287	#359458	C₂³	1	1	yes	characteristic
288	#359442	C₂³	1	1	yes	characteristic
289	#359442	C₂³	1	1	yes	characteristic
290	#359442	C₂³	1	1	yes	characteristic
291	#359442	C₂³	1	1	yes	characteristic
292	#359442	C₂³	1	1	yes	characteristic
293	#359442	C₂³	1	1	yes	characteristic
294	#355098	C₂³	1	1	yes	characteristic
295	#355096	C₂³	1	1	yes	characteristic
296	#188109	C₂³	1	1	yes	characteristic
297	#188109	C₂³	1	1	yes	characteristic
298	#188049	C₂³	1	1	yes	characteristic
299	#188049	C₂³	1	1	yes	characteristic
300	C₂×#8546	C₂³	1	1	yes	characteristic
301	C₂×#8546	C₂³	1	1	yes	characteristic
302	C₂×#8541	C₂³	1	1	yes	characteristic
303	C₂×#8541	C₂³	1	1	yes	characteristic
304	#187944	C₂³	1	1	yes	characteristic
305	#187944	C₂³	1	1	yes	characteristic
306	#187944	C₂³	1	1	yes	characteristic
307	#187944	C₂³	1	1	yes	characteristic
308	#187944	C₂³	1	1	yes	characteristic
309	#187944	C₂³	1	1	yes	characteristic
310	#186835	C₂³	1	1	yes	characteristic
311	#186835	C₂³	1	1	yes	characteristic
312	#146479	C₂³	1	1	yes	characteristic
313	#146479	C₂³	1	1	yes	characteristic
314	#146479	C₂³	1	1	yes	characteristic
315	#146479	C₂³	1	1	yes	characteristic
316	#146475	C₂³	1	1	yes	characteristic
317	#146475	C₂³	1	1	yes	characteristic
318	#146475	C₂³	1	1	yes	characteristic
319	#146475	C₂³	1	1	yes	characteristic
320	#146475	C₂³	1	1	yes	characteristic
321	#146475	C₂³	1	1	yes	characteristic
322	#144387	D₄	1	4	yes	complemented
323	#144386	D₄	1	4	yes	complemented
324	#128033	C₂³	1	1	yes	characteristic
325	#128033	C₂³	1	1	yes	characteristic
326	#128033	C₂³	1	1	yes	characteristic
327	#128033	C₂³	1	1	yes	characteristic
328	C₂×#7316	C₂³	1	1	yes	characteristic
329	C₂×#7316	C₂³	1	1	yes	characteristic
330	C₂×#7316	C₂³	1	1	yes	characteristic
331	C₂×#7316	C₂³	1	1	yes	characteristic
332	C₂×#7314	C₂³	1	1	yes	characteristic
333	C₂×#7314	C₂³	1	1	yes	characteristic
334	C₂×#7314	C₂³	1	1	yes	characteristic
335	C₂×#7314	C₂³	1	1	yes	characteristic
336	C₂×#7311	C₂³	1	1	yes	characteristic
337	C₂×#7311	C₂³	1	1	yes	characteristic
338	C₂×#7310	C₂³	1	1	yes	characteristic
339	C₂×#7310	C₂³	1	1	yes	characteristic
340	C₂×#7310	C₂³	1	1	yes	characteristic
341	C₂×#7310	C₂³	1	1	yes	characteristic
342	C₂×#7310	C₂³	1	1	yes	characteristic
343	C₂×#7310	C₂³	1	1	yes	characteristic
344	#128009	C₂³	1	1	yes	characteristic
345	#128009	C₂³	1	1	yes	characteristic
346	#128009	C₂³	1	1	yes	characteristic
347	#128009	C₂³	1	1	yes	characteristic
348	#108238	C₂³	1	1	yes	characteristic
349	#108238	C₂³	1	1	yes	characteristic
350	#107114	C₂³	1	1	yes	characteristic
351	#107114	C₂³	1	1	yes	characteristic
352	#107114	C₂³	1	1	yes	characteristic
353	#107114	C₂³	1	1	yes	characteristic
354	#107114	C₂³	1	1	yes	characteristic
355	#107114	C₂³	1	1	yes	characteristic
356	#62842	C₂×D₄	1	1	yes	characteristic
357	C₂×#3484	C₂⁴	1	1	yes	characteristic
358	C₂×#3484	C₂⁴	1	1	yes	characteristic
359	C₂×#3484	C₂⁴	1	1	yes	characteristic
360	C₂×#3484	C₂⁴	1	1	yes	characteristic
361	C₂²×#534	C₂×D₄	1	1	yes	characteristic
362	C₂²×#534	C₂⁴	1	1	yes	characteristic
363	C₂²×#534	C₂⁴	1	1	yes	characteristic
364	C₂³×#127	C₂⁴	1	1	yes	characteristic
365	C₂³×#120	C₂×D₄	1	1	yes	characteristic
366	C₂³×#120	C₂×D₄	1	1	yes	characteristic
367	C₂³×#120	C₂⁴	1	1	yes	characteristic
368	C₂³×#120	C₂⁴	1	1	yes	characteristic
369	#62652	C₂×D₄	1	1	yes	characteristic
370	C₂×#3026	C₂×D₄	1	2	yes	—
371	C₂²×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
372	C₂²×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
373	C₂×#2883	C₂×D₄	1	1	yes	characteristic
374	C₂×#2883	C₂×D₄	1	1	yes	characteristic
375	C₂×#2883	C₂×D₄	1	1	yes	characteristic
376	C₂×#2883	C₂×D₄	1	2	yes	—
377	C₂×#2846	C₂×D₄	1	2	yes	—
378	#35350	C₂×D₄	1	2	yes	—
379	#35348	C₂×D₄	1	2	yes	—
380	#35348	C₂×D₄	1	2	yes	—
381	#35346	C₂×D₄	1	2	yes	—
382	#34992	C₂×D₄	1	2	yes	—
383	#34980	C₂×D₄	1	2	yes	—
384	#34980	C₂×D₄	1	2	yes	—
385	#34171	C₂⁴	1	1	yes	characteristic
386	#34171	C₂⁴	1	1	yes	characteristic
387	#34171	C₂⁴	1	1	yes	characteristic
388	#34171	C₂⁴	1	1	yes	characteristic
389	C₂×#2273	C₂×D₄	1	1	yes	characteristic
390	#23906	C₂×D₄	1	4	yes	—
391	#23901	C₂×D₄	1	2	yes	complemented
392	#23900	C₂×D₄	1	2	yes	complemented
393	C₂×#1913	C₂×D₄	1	2	yes	—
394	C₂×#1913	C₂×D₄	1	2	yes	—
395	C₂×#1898	C₂×D₄	1	2	yes	—
396	C₂×#1898	C₂×D₄	1	2	yes	—
397	#20960	C₂×D₄	1	2	yes	—
398	C₂×#1889	C₂×D₄	1	2	yes	—
399	C₂×#1889	C₂×D₄	1	2	yes	—
400	C₂×#1889	C₂×D₄	1	2	yes	—
401	C₂×#1889	C₂×D₄	1	2	yes	—
402	C₂×#1889	C₂×D₄	1	2	yes	—
403	C₂×#1889	C₂×D₄	1	2	yes	—
404	#20889	C₂×D₄	1	2	yes	—
405	C₂×#1828	C₂×D₄	1	2	yes	—
406	C₂×#1819	C₂×D₄	1	2	yes	—
407	#20633	C₂×D₄	1	2	yes	—
408	#20609	C₂×D₄	1	2	yes	—
409	C₂×#1783	C₂⁴	1	1	yes	characteristic
410	C₂×#1783	C₂⁴	1	1	yes	characteristic
411	C₂×#1783	C₂⁴	1	1	yes	characteristic
412	C₂×#1783	C₂⁴	1	1	yes	characteristic
413	C₂×#1781	C₂×D₄	1	2	yes	—
414	C₂×#1781	C₂×D₄	1	2	yes	—
415	C₂×#1781	C₂⁴	1	1	yes	characteristic
416	C₂×#1781	C₂⁴	1	1	yes	characteristic
417	C₂×#1781	C₂⁴	1	1	yes	characteristic
418	C₂×#1781	C₂⁴	1	1	yes	characteristic
419	C₂×#1781	C₂⁴	1	1	yes	characteristic
420	C₂×#1781	C₂⁴	1	1	yes	characteristic
421	C₂×#1781	C₂⁴	1	1	yes	characteristic
422	C₂×#1781	C₂⁴	1	1	yes	characteristic
423	C₂×#1781	C₂⁴	1	1	yes	characteristic
424	C₂×#1781	C₂⁴	1	1	yes	characteristic
425	C₂×#1781	C₂⁴	1	1	yes	characteristic
426	C₂×#1781	C₂⁴	1	1	yes	characteristic
427	#20354	C₂×D₄	1	1	yes	characteristic
428	#20354	C₂×D₄	1	1	yes	characteristic
429	#20354	C₂×D₄	1	1	yes	characteristic
430	#15261	C₂×D₄	1	2	yes	—
431	#15261	#41	1	2	yes	complemented
432	#15258	C₂×D₄	1	2	yes	—
433	#15258	#41	1	2	yes	complemented
434	#14679	C₂×D₄	1	2	yes	—
435	#14335	C₂⁴	1	1	yes	characteristic
436	#14335	C₂⁴	1	1	yes	characteristic
437	#12693	C₂×D₄	1	4	yes	—
438	#12688	C₂×D₄	1	2	yes	complemented
439	#12687	C₂×D₄	1	2	yes	complemented
440	#10768	C₂×D₄	1	2	yes	—
441	#10754	C₂×D₄	1	2	yes	—
442	#10754	C₂×D₄	1	2	yes	—
443	#10735	C₂×D₄	1	2	yes	—
444	#10735	C₂×D₄	1	2	yes	—
445	#8534	C₂×D₄	1	4	yes	complemented
446	#7304	C₂×D₄	1	4	yes	complemented
447	C₂⁷	C₂²×D₄	1	1	yes	characteristic
448	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
449	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
450	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
451	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
452	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	1	yes	characteristic
453	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
454	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
455	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
456	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
457	#3484	C₂²×D₄	1	2	yes	—
458	#3484	H(5,𝔽₂)	1	2	yes	—
459	C₂×#534	C₂²×D₄	1	2	yes	—
460	C₂²×#127	C₂²×D₄	1	2	yes	—
461	C₂²×#127	C₂×#41	1	2	yes	—
462	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
463	C₂²×#123	C₂×#41	1	1	yes	characteristic
464	C₂²×#123	H(5,𝔽₂)	1	1	yes	characteristic
465	C₂²×#123	H(5,𝔽₂)	1	1	yes	characteristic
466	C₂²×#120	#120	1	2	yes	—
467	C₂²×#120	#120	1	2	yes	—
468	C₂²×#120	C₂²×D₄	1	2	yes	—
469	C₂²×#120	C₂²×D₄	1	2	yes	—
470	C₂²×#120	C₂²×D₄	1	2	yes	—
471	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
472	C₂²×#120	C₂×#41	1	1	yes	characteristic
473	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
474	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
475	C₂×#518	C₂²×D₄	1	1	yes	characteristic
476	C₂×#518	C₂²×D₄	1	1	yes	characteristic
477	C₂×#518	C₂²×D₄	1	1	yes	characteristic
478	C₂×#518	C₂²×D₄	1	1	yes	characteristic
479	C₂×#518	C₂²×D₄	1	1	yes	characteristic
480	C₂×#518	C₂²×D₄	1	1	yes	characteristic
481	C₂×#518	C₂²×D₄	1	1	yes	characteristic
482	C₂×#518	C₂²×D₄	1	1	yes	characteristic
483	C₂×#518	C₂²×D₄	1	1	yes	characteristic
484	C₂×#518	H(5,𝔽₂)	1	1	yes	characteristic
485	C₂×#518	H(5,𝔽₂)	1	1	yes	characteristic
486	C₂×#518	H(5,𝔽₂)	1	1	yes	characteristic
487	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
488	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
489	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
490	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
491	C₂³×C₄²	H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²×#99	C₂²×D₄	1	2	yes	—
493	C₂²×#99	C₂²×D₄	1	2	yes	—
494	C₂²×#99	C₂²×D₄	1	2	yes	—
495	C₂²×#99	C₂²×D₄	1	2	yes	—
496	#2315	#120	1	2	yes	—
497	#2315	#120	1	2	yes	—
498	#2308	#120	1	2	yes	—
499	#2308	#120	1	2	yes	—
500	#2308	C₂²×D₄	1	2	yes	—
501	C₂×#379	#120	1	2	yes	—
502	C₂×#379	#120	1	2	yes	—
503	C₂×#379	C₂²×D₄	1	2	yes	—
504	C₂×#379	C₂²×D₄	1	2	yes	—
505	C₂×#379	C₂²×D₄	1	2	yes	—
506	#1783	C₂²×D₄	1	2	yes	—
507	#1781	C₂²×D₄	1	2	yes	—
508	#1781	C₂²×D₄	1	2	yes	—
509	#1781	H(5,𝔽₂)	1	2	yes	—
510	#1438	C₂²×D₄	1	2	yes	—
511	#1438	C₂×#41	1	2	yes	—
512	C₂⁶	C₂×#120	1	2	yes	—
513	C₂⁶	D₄²	1	1	yes	characteristic
514	C₂⁶	#546	1	1	yes	characteristic
515	C₂⁶	C₂³×D₄	1	1	yes	characteristic
516	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂×H(5,𝔽₂)	D₄²	1	2	yes	—
518	C₂³×D₄	C₂×#120	1	2	yes	—
519	C₂³×D₄	#546	1	2	yes	—
520	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
521	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
522	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
523	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
524	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂³×D₄	#585	1	1	yes	characteristic
531	C₂³×D₄	#585	1	1	yes	characteristic
532	C₂⁴×C₄	D₄²	1	1	yes	characteristic
533	C₂⁴×C₄	#546	1	1	yes	characteristic
534	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
535	#518	D₄²	1	2	yes	—
536	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
537	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
538	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
539	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
540	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
541	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
542	C₂²×C₂²⋊C₄	#546	1	1	yes	characteristic
543	C₂²×C₂²⋊C₄	#546	1	1	yes	characteristic
544	C₂²×C₄²	#546	1	2	yes	—
545	C₂×#99	D₄²	1	4	yes	—
546	#381	B(4,𝔽₂)	1	4	yes	complemented
547	#379	B(4,𝔽₂)	1	4	yes	complemented
548	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
549	C₂⁵	C₂²×#120	1	1	yes	characteristic
550	C₂⁵	C₂×D₄²	1	1	yes	characteristic
551	C₂⁵	C₂×#546	1	1	yes	characteristic
552	C₂⁵	#3484	1	1	yes	characteristic
553	C₂⁵	#3484	1	1	yes	characteristic
554	C₂⁵	#3484	1	1	yes	characteristic
555	C₂⁵	#3484	1	1	yes	characteristic
556	C₂⁵	#3484	1	1	yes	characteristic
557	C₂⁵	#3484	1	1	yes	characteristic
558	C₂⁵	#3485	1	1	yes	characteristic
559	C₂⁵	#3490	1	1	yes	characteristic
560	C₂⁵	#3534	1	1	yes	characteristic
561	C₂⁵	#3558	1	1	yes	characteristic
562	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
563	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
564	C₂²×D₄	D₄×#41	1	1	yes	characteristic
565	C₂²×D₄	D₄×#41	1	1	yes	characteristic
566	C₂²×D₄	#3484	1	1	yes	characteristic
567	C₂²×D₄	#3484	1	1	yes	characteristic
568	C₂²×D₄	#3488	1	1	yes	characteristic
569	C₂²×D₄	#3488	1	1	yes	characteristic
570	C₂²×D₄	#3488	1	1	yes	characteristic
571	C₂²×D₄	#3496	1	1	yes	characteristic
572	C₂²×D₄	#3519	1	1	yes	characteristic
573	C₂²×D₄	#3519	1	1	yes	characteristic
574	C₂²×D₄	#3532	1	1	yes	characteristic
575	C₂²×D₄	#3534	1	1	yes	characteristic
576	C₂²×D₄	#3543	1	1	yes	characteristic
577	C₂²×D₄	#3558	1	1	yes	characteristic
578	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
579	C₂³×C₄	C₂×#546	1	1	yes	characteristic
580	C₂³×C₄	#3484	1	1	yes	characteristic
581	C₂³×C₄	#3484	1	1	yes	characteristic
582	C₂³×C₄	#3532	1	1	yes	characteristic
583	C₂³×C₄	#3534	1	1	yes	characteristic
584	C₂³×C₄	#3542	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
587	C₂⁴	#35346	1	1	yes	characteristic
588	C₂⁴	D₄×#120	1	1	yes	characteristic
589	C₂⁴	#36212	1	1	yes	characteristic
590	C₂⁴	#43023	1	1	yes	characteristic
591	C₂⁴	#43095	1	1	yes	characteristic
592	C₂⁴	#43098	1	1	yes	characteristic
593	C₂⁴	#43118	1	1	yes	characteristic
594	C₂⁴	#43118	1	1	yes	characteristic
595	C₂⁴	#44877	1	1	yes	characteristic
596	C₂⁴	#47826	1	1	yes	characteristic
597	C₂⁴	#58991	1	1	yes	characteristic
598	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
599	C₂⁴	#60399	1	2	yes	—
600	C₂²×C₄	#47830	1	1	yes	characteristic
601	C₂²×C₄	#51889	1	1	yes	characteristic
602	C₂²×C₄	#59004	1	1	yes	characteristic
603	C₂²×C₄	#59123	1	1	yes	characteristic
604	C₂³	#1418391	1	1	yes	characteristic
605	C₂³	#6499867	1	1	yes	characteristic
606	C₂³	#6499874	1	1	yes	characteristic
607	C₂³	#6499874	1	1	yes	characteristic
608	C₂³	#6499876	1	1	yes	characteristic
609	C₂³	#6499876	1	1	yes	characteristic
610	C₂³	#6499892	1	1	yes	characteristic
611	C₂³	D₄×B(4,𝔽₂)	1	2	yes	—
612	C₂³	#6595772	1	2	yes	—
613	C₂²	#72225637	1	1	yes	characteristic
614	C₂²	#72240626	1	1	yes	characteristic
615	C₂²	#72240628	1	1	yes	characteristic
616	C₂²	#72240631	1	1	yes	characteristic
617	C₂²	#72240643	1	1	yes	characteristic
618	C₂²	#72251243	1	1	yes	characteristic
619	C₂²	#72251367	1	1	yes	characteristic
620	C₂	#72251541	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72251541
commutator, Frattini, cosocle	C₂⁴×D₄	C₂⁵
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×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. #72256177	C₂	semidirect
2. #72256175	C₂	semidirect
3. #72256173	C₂	semidirect
4. #72256172	C₂	semidirect
5. #72256169	C₂	semidirect
6. #72256166	C₂	semidirect
7. #72256163	C₂	semidirect
8. #72256158	C₂	semidirect
9. #72256156	C₂²	semidirect
10. #72256156	C₂²	semidirect
11. #72256147	C₂	semidirect
12. #72256142	C₂	semidirect
13. #72256138	C₂	semidirect
14. #72256137	C₂²	semidirect
15. #72256135	C₂	semidirect
16. #72256132	C₂²	semidirect
17. #72256129	C₂	semidirect
18. #72256126	C₂²	semidirect
19. #72256121	C₂	semidirect
20. #72256119	C₂²	semidirect
21. #72256116	C₂	semidirect
22. #72256113	C₂²	semidirect
23. #72256111	C₂²	semidirect
24. #72256106	C₂	semidirect
25. #72256103	C₂²	semidirect
26. #72256103	C₂²	semidirect
27. #72256078	C₂	semidirect
28. #72256070	C₂	semidirect
29. #72256060	C₂	semidirect
30. #72256048	C₂²	semidirect
31. #72256043	C₂²	semidirect
32. #72256017	C₂	semidirect
33. #72256005	C₂²	semidirect
34. #72256004	C₂²	semidirect
35. #72255990	C₂²	semidirect
36. #72255986	C₂²	semidirect
37. #72255977	C₂²	semidirect
38. #72255974	C₂	semidirect
39. #72255971	C₂²	semidirect
40. #72255971	C₂²	semidirect
41. #72255947	C₂²	semidirect
42. #72255947	C₂²	semidirect
43. #72255942	C₂	semidirect
44. #72255939	C₂²	semidirect
45. #72255939	C₂²	semidirect
46. #72255900	C₂	semidirect
49. #72255894	C₂	semidirect
52. #72255891	C₂²	semidirect
53. #72255878	C₂²	semidirect
54. #72255871	C₂²	semidirect
55. #72255867	C₂²	semidirect
56. #72255860	C₂²	semidirect
57. #72255857	C₂	semidirect
58. #72255853	C₂²	semidirect
59. #72255853	C₂²	semidirect
60. #72255849	C₂²	semidirect
61. #72255846	C₂	semidirect
62. #72255841	C₂²	semidirect
63. #72255841	C₂²	semidirect
64. #72255838	C₂²	semidirect
65. #72255838	C₂²	semidirect
66. #72255829	C₂²	semidirect
67. #72255826	C₂²	semidirect
68. #72255819	C₂²	semidirect
69. #72255803	C₂²	semidirect
70. #72255793	C₂²	semidirect
71. #72255785	C₂²	semidirect
72. #72255777	C₂²	semidirect
75. #72255774	C₂²	semidirect
76. #72255771	C₂²	semidirect
79. #72255754	C₂²	semidirect
80. #72252596	C₂	semidirect
81. #72252595	C₂	semidirect
82. #72251552	C₂²	semidirect
83. #72251550	C₂²	semidirect
84. #72251501	C₂²	semidirect
85. #72251499	C₂²	semidirect
86. #72251476	C₂²	semidirect
87. #72251475	C₂²	semidirect
88. #72251463	C₂²	semidirect
89. #72251185	C₂	semidirect
90. #72251171	C₂²	semidirect
91. #72251028	C₂²	semidirect
92. #72251028	C₂²	semidirect
93. #72249647	C₂²	semidirect
94. #72249638	C₂²	semidirect
95. #72249638	C₂²	semidirect
96. #72249626	C₂²	semidirect
97. #72249626	C₂²	semidirect
98. #72249623	C₂²	semidirect
99. #72249623	C₂²	semidirect
100. #72249606	C₂²	semidirect
101. #72249606	C₂²	semidirect
102. #72249591	C₂²	semidirect
104. #72249584	C₂²	semidirect
105. #72246299	C₂²	semidirect
106. C₂×#493480	C₂²	semidirect
108. #72240083	C₂²	semidirect
109. C₂×#144633	C₂²	semidirect
110. #72238974	C₂²	semidirect
111. C₂×#144631	C₂²	semidirect
112. #72238613	C₂²	semidirect
113. #72238611	C₂²	semidirect
114. #72238609	C₂²	semidirect
115. #72238443	C₂²	semidirect
116. #72238349	C₂²	semidirect
117. #72238349	C₂²	semidirect
118. #72237903	C₂²	semidirect
119. #72237900	C₂²	semidirect
120. #72237829	C₂²	semidirect
121. #72237639	C₂	semidirect
122. #72237638	C₂²	semidirect
123. #72237637	C₂²	semidirect
124. #72237476	C₂²	semidirect
125. #72237473	C₂²	semidirect
126. #72237473	C₂²	semidirect
127. #72237472	C₂²	semidirect
128. #72237467	C₂²	semidirect
129. #72237467	C₂²	semidirect
130. #72237374	C₂²	semidirect
131. #72237034	C₂²	semidirect
132. #72237033	C₂²	semidirect
133. #72236948	C₂²	semidirect
134. #72236636	C₂²	semidirect
135. #72236521	C₂²	semidirect
136. #72236508	C₂²	semidirect
137. #72236233	C₂²	semidirect
138. #72235269	C₂	semidirect
139. #72235258	C₂²	semidirect
140. #72235258	C₂²	semidirect
143. #72235242	C₂²	semidirect
147. #72235130	C₂²	semidirect
148. #72234953	C₂²	semidirect
149. #72231692	C₂²	semidirect
150. #72231692	C₂²	semidirect
153. #72225745	C₂²	semidirect
154. #72225741	C₂²	semidirect
155. #72225736	C₂²	semidirect
156. #72225735	C₂²	semidirect
157. #72225712	C₂²	semidirect
166. #72225610	C₂²	semidirect
167. #72225610	C₂²	semidirect
170. #72219377	C₂²	semidirect
171. #72219345	C₂²	semidirect
172. #72219345	C₂²	semidirect
173. #72219158	C₂²	semidirect
174. #72218840	C₂²	semidirect
175. #72218840	C₂²	semidirect
176. #72218838	C₂²	semidirect
177. #72218838	C₂²	semidirect
178. #72218521	C₂²	semidirect
179. #72218521	C₂²	semidirect
180. #72218391	C₂²	semidirect
181. #72218391	C₂²	semidirect
186. C₂×#139750	C₂²	semidirect
197. #6628987	D₄	semidirect
198. #6437999	D₄	semidirect
214. #6432949	D₄	semidirect
254. #405481	D₄	semidirect
255. #405306	D₄	semidirect
256. #405274	D₄	semidirect
257. #394273	D₄	semidirect
258. #394058	D₄	semidirect
259. #394058	D₄	semidirect
260. #393532	D₄	semidirect
269. #380554	D₄	semidirect
270. #374004	D₄	semidirect
322. #144387	D₄	semidirect
323. #144386	D₄	semidirect
391. #23901	C₂×D₄	semidirect
392. #23900	C₂×D₄	semidirect
431. #15261	#41	semidirect
433. #15258	#41	semidirect
438. #12688	C₂×D₄	semidirect
439. #12687	C₂×D₄	semidirect
445. #8534	C₂×D₄	semidirect
446. #7304	C₂×D₄	semidirect
546. #381	B(4,𝔽₂)	semidirect
547. #379	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
#72256177	2
#72256175	2
#72256173	2
#72256172	2
#72256169	2
#72256166	2
#72256163	2
#72256158	2
#72256147	2
#72256142	2
#72256138	2
#72256135	2
#72256129	2
#72256121	2
#72256116	2
#72256106	2
#72256078	2
#72256070	2
#72256060	2
#72256017	2
#72255974	2
#72255942	2
#72255900	2
#72255894	2
#72255857	2
#72255846	2
#72252596	2
#72252595	2
#72251185	2
#72237639	2
#72235269	2