Subgroups — #72317809

Order 1024.

At least 6127 conjugacy classes of subgroups; only the 651 normal subgroups are shown.

The subgroup lattice has 607 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#8040645	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#33559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#33551	C₂	1	1	yes	maximal, characteristic, complemented
4	#6573724	C₂	1	1	yes	maximal, characteristic, complemented
5	#6573716	C₂	1	1	yes	maximal, characteristic, complemented
6	#6573676	C₂	1	1	yes	maximal, characteristic, complemented
7	#511938	C₂	1	1	yes	maximal, characteristic, complemented
8	#511787	C₂	1	1	yes	maximal, characteristic, complemented
9	#511779	C₂	1	1	yes	maximal, characteristic, complemented
10	#503241	C₂	1	1	yes	maximal, characteristic, complemented
11	#503206	C₂	1	1	yes	maximal, characteristic, complemented
12	#503192	C₂	1	1	yes	maximal, characteristic, complemented
13	#501184	C₂	1	1	yes	maximal, characteristic, complemented
14	#501180	C₂	1	1	yes	maximal, characteristic, complemented
15	#501174	C₂	1	1	yes	maximal, characteristic, complemented
16	#501164	C₂	1	1	yes	maximal, characteristic, complemented
17	#501097	C₂	1	1	yes	maximal, characteristic, complemented
18	#501091	C₂	1	1	yes	maximal, characteristic, complemented
19	#500826	C₂	1	1	yes	maximal, characteristic, complemented
20	#500781	C₂	1	1	yes	maximal, characteristic, complemented
21	#500767	C₂	1	1	yes	maximal, characteristic, complemented
22	#499850	C₂	1	1	yes	maximal, characteristic, complemented
23	#499832	C₂	1	1	yes	maximal, characteristic, complemented
24	#499812	C₂	1	1	yes	maximal, characteristic, complemented
25	#499811	C₂	1	1	yes	maximal, characteristic, complemented
26	#499805	C₂	1	1	yes	maximal, characteristic, complemented
27	#499795	C₂	1	1	yes	maximal, characteristic, complemented
28	#497362	C₂	1	1	yes	maximal, characteristic, complemented
29	#497357	C₂	1	1	yes	maximal, characteristic, complemented
30	#497294	C₂	1	1	yes	maximal, characteristic, complemented
31	#495771	C₂	1	1	yes	maximal, characteristic, complemented
32	#62987	C₂²	1	1	yes	characteristic, complemented
33	C₂×#3549	C₂²	1	1	yes	characteristic, complemented
34	C₂×#3532	C₂²	1	1	yes	characteristic, complemented
35	C₂×#3027	C₂²	1	1	yes	characteristic
36	C₂×#3027	C₂²	1	1	yes	characteristic, complemented
37	C₂×#3026	C₂²	1	1	yes	characteristic, complemented
38	C₂²×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
39	C₂×#3019	C₂²	1	1	yes	characteristic
40	C₂×#3018	C₂²	1	1	yes	characteristic, complemented
41	#52031	C₂²	1	1	yes	characteristic, complemented
42	#52004	C₂²	1	1	yes	characteristic, complemented
43	#50165	C₂²	1	1	yes	characteristic, complemented
44	#49562	C₂²	1	1	yes	characteristic, complemented
45	#48812	C₂²	1	1	yes	characteristic, complemented
46	#47848	C₂²	1	1	yes	characteristic, complemented
47	#46276	C₂²	1	1	yes	characteristic, complemented
48	#45479	C₂²	1	1	yes	characteristic, complemented
49	#45439	C₂²	1	1	yes	characteristic, complemented
50	#39332	C₂²	1	1	yes	characteristic
51	#37682	C₂²	1	1	yes	characteristic
52	#37645	C₂²	1	1	yes	characteristic
53	#34468	C₂²	1	1	yes	characteristic, complemented
54	C₂×#2200	C₂²	1	1	yes	characteristic
55	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
56	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
57	C₂×#2199	C₂²	1	1	yes	characteristic
58	C₂×#2199	C₂²	1	1	yes	characteristic, complemented
59	C₂×#2199	C₂²	1	1	yes	characteristic, complemented
60	C₂×#2199	C₂²	1	1	yes	characteristic, complemented
61	C₂×#2199	C₂²	1	1	yes	characteristic, complemented
62	C₂×#2199	C₂²	1	1	yes	characteristic, complemented
63	C₂×#2199	C₂²	1	1	yes	characteristic, complemented
64	C₂×#2199	C₂²	1	1	yes	characteristic, complemented
65	C₂×#2199	C₂²	1	1	yes	characteristic, complemented
66	C₂×#2197	C₂²	1	1	yes	characteristic, complemented
67	C₂×#2197	C₂²	1	1	yes	characteristic, complemented
68	C₂×#2197	C₂²	1	1	yes	characteristic, complemented
69	C₂×#2196	C₂²	1	1	yes	characteristic
70	C₂×#2196	C₂²	1	1	yes	characteristic, complemented
71	C₂×#2196	C₂²	1	1	yes	characteristic, complemented
72	C₂×#2196	C₂²	1	1	yes	characteristic, complemented
73	C₂×#2196	C₂²	1	1	yes	characteristic, complemented
74	C₂×#2196	C₂²	1	1	yes	characteristic, complemented
75	C₂×#2127	C₂²	1	1	yes	characteristic, complemented
76	C₂×#2126	C₂²	1	1	yes	characteristic, complemented
77	C₂×#2122	C₂²	1	1	yes	characteristic, complemented
78	C₂×#2122	C₂²	1	1	yes	characteristic, complemented
79	C₂×#2121	C₂²	1	1	yes	characteristic, complemented
80	C₂²×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
81	#32928	C₂²	1	1	yes	characteristic, complemented
82	#32926	C₂²	1	1	yes	characteristic, complemented
83	#32922	C₂²	1	1	yes	characteristic, complemented
84	#32901	C₂²	1	1	yes	characteristic, complemented
85	#32899	C₂²	1	1	yes	characteristic, complemented
86	#32898	C₂²	1	1	yes	characteristic, complemented
87	#32898	C₂²	1	1	yes	characteristic, complemented
88	#32893	C₂²	1	1	yes	characteristic, complemented
89	#32891	C₂²	1	1	yes	characteristic, complemented
90	#25773	C₂²	1	1	yes	characteristic, complemented
91	#25771	C₂²	1	1	yes	characteristic, complemented
92	#25738	C₂²	1	1	yes	characteristic, complemented
93	#24415	C₂²	1	1	yes	characteristic, complemented
94	#24413	C₂²	1	1	yes	characteristic, complemented
95	#24407	C₂²	1	1	yes	characteristic, complemented
96	#24406	C₂²	1	1	yes	characteristic, complemented
97	#24404	C₂²	1	1	yes	characteristic, complemented
98	#24404	C₂²	1	1	yes	characteristic, complemented
99	#24262	C₂²	1	1	yes	characteristic, complemented
100	#24260	C₂²	1	1	yes	characteristic, complemented
101	#24226	C₂²	1	1	yes	characteristic, complemented
102	#23912	C₂²	1	1	yes	characteristic
103	#23908	C₂²	1	1	yes	characteristic, complemented
104	#23904	C₂²	1	1	yes	characteristic
105	#23904	C₂²	1	1	yes	characteristic, complemented
106	#23903	C₂²	1	1	yes	characteristic, complemented
107	#23900	C₂²	1	1	yes	characteristic, complemented
108	#22408	C₂²	1	1	yes	characteristic, complemented
109	#22405	C₂²	1	1	yes	characteristic, complemented
110	#22405	C₂²	1	1	yes	characteristic, complemented
111	#21482	C₂²	1	1	yes	characteristic, complemented
112	C₄×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
113	#21473	C₂²	1	1	yes	characteristic, complemented
114	#13425	C₂²	1	1	yes	characteristic, complemented
115	#13424	C₂²	1	1	yes	characteristic, complemented
116	#13424	C₂²	1	1	yes	characteristic, complemented
117	#13424	C₂²	1	1	yes	characteristic, complemented
118	#13420	C₂²	1	1	yes	characteristic, complemented
119	#13419	C₂²	1	1	yes	characteristic, complemented
120	#13349	C₂²	1	1	yes	characteristic, complemented
121	#13349	C₂²	1	1	yes	characteristic, complemented
122	#13349	C₂²	1	1	yes	characteristic, complemented
123	#13348	C₂²	1	1	yes	characteristic, complemented
124	#13348	C₂²	1	1	yes	characteristic, complemented
125	#13348	C₂²	1	1	yes	characteristic, complemented
126	#13348	C₂²	1	1	yes	characteristic, complemented
127	#13348	C₂²	1	1	yes	characteristic, complemented
128	#13348	C₂²	1	1	yes	characteristic, complemented
129	#13348	C₂²	1	1	yes	characteristic, complemented
130	#13348	C₂²	1	1	yes	characteristic, complemented
131	#13348	C₂²	1	1	yes	characteristic, complemented
132	#13344	C₂²	1	1	yes	characteristic, complemented
133	#13344	C₂²	1	1	yes	characteristic, complemented
134	#13344	C₂²	1	1	yes	characteristic, complemented
135	#13343	C₂²	1	1	yes	characteristic, complemented
136	#13343	C₂²	1	1	yes	characteristic, complemented
137	#13343	C₂²	1	1	yes	characteristic, complemented
138	#13224	C₂²	1	1	yes	characteristic, complemented
139	#13224	C₂²	1	1	yes	characteristic, complemented
140	#13222	C₂²	1	1	yes	characteristic, complemented
141	#13221	C₂²	1	1	yes	characteristic, complemented
142	#13219	C₂²	1	1	yes	characteristic, complemented
143	#13218	C₂²	1	1	yes	characteristic, complemented
144	#13091	C₂²	1	1	yes	characteristic, complemented
145	#13091	C₂²	1	1	yes	characteristic, complemented
146	#13090	C₂²	1	1	yes	characteristic, complemented
147	#13090	C₂²	1	1	yes	characteristic, complemented
148	#13087	C₂²	1	1	yes	characteristic, complemented
149	#13086	C₂²	1	1	yes	characteristic, complemented
150	#13086	C₂²	1	1	yes	characteristic, complemented
151	#13085	C₂²	1	1	yes	characteristic, complemented
152	#13083	C₂²	1	1	yes	characteristic, complemented
153	#13082	C₂²	1	1	yes	characteristic, complemented
154	#13082	C₂²	1	1	yes	characteristic, complemented
155	#13081	C₂²	1	1	yes	characteristic, complemented
156	#13049	C₂²	1	1	yes	characteristic, complemented
157	#13049	C₂²	1	1	yes	characteristic, complemented
158	#13049	C₂²	1	1	yes	characteristic, complemented
159	#13043	C₂²	1	1	yes	characteristic, complemented
160	#13043	C₂²	1	1	yes	characteristic, complemented
161	#13043	C₂²	1	1	yes	characteristic, complemented
162	#13041	C₂²	1	1	yes	characteristic, complemented
163	#13041	C₂²	1	1	yes	characteristic, complemented
164	#13041	C₂²	1	1	yes	characteristic, complemented
165	#12966	C₂²	1	1	yes	characteristic, complemented
166	#12960	C₂²	1	1	yes	characteristic, complemented
167	#12958	C₂²	1	1	yes	characteristic, complemented
168	#12799	C₂²	1	1	yes	characteristic, complemented
169	#12795	C₂²	1	1	yes	characteristic, complemented
170	#12793	C₂²	1	1	yes	characteristic, complemented
171	#12763	C₂²	1	1	yes	characteristic, complemented
172	#12763	C₂²	1	1	yes	characteristic, complemented
173	#12763	C₂²	1	1	yes	characteristic, complemented
174	#12762	C₂²	1	1	yes	characteristic, complemented
175	#12761	C₂²	1	1	yes	characteristic, complemented
176	#12759	C₂²	1	1	yes	characteristic, complemented
177	#12759	C₂²	1	1	yes	characteristic, complemented
178	#12696	C₂²	1	1	yes	characteristic, complemented
179	#12695	C₂²	1	1	yes	characteristic, complemented
180	#12691	C₂²	1	1	yes	characteristic, complemented
181	#12691	C₂²	1	1	yes	characteristic, complemented
182	#12690	C₂²	1	1	yes	characteristic, complemented
183	#12687	C₂²	1	1	yes	characteristic, complemented
184	#12628	C₂²	1	1	yes	characteristic, complemented
185	#12622	C₂²	1	1	yes	characteristic, complemented
186	C₄×AΣL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic, complemented
187	C₂×#585	C₂³	1	1	yes	characteristic
188	C₂²×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
189	C₂×H(3,𝔽₄)	C₂³	1	1	yes	characteristic
190	C₂×H(3,𝔽₄)	C₂³	1	1	yes	characteristic
191	C₂×H(3,𝔽₄)	C₂³	1	1	yes	characteristic
192	C₂×#560	C₂³	1	1	yes	characteristic
193	#3496	C₂³	1	1	yes	characteristic
194	#3485	C₂³	1	1	yes	characteristic
195	#3484	C₂³	1	1	yes	characteristic
196	C₂×#551	C₂³	1	1	yes	characteristic
197	C₂×#547	D₄	1	1	yes	characteristic, complemented
198	C₂×#546	C₂³	1	1	yes	characteristic
199	C₂×D₄²	C₂³	1	1	yes	characteristic
200	C₂×D₄²	C₂³	1	1	yes	characteristic
201	C₂×#535	C₂³	1	1	yes	characteristic
202	C₂×#535	C₂³	1	1	yes	characteristic
203	C₂×#535	C₂³	1	1	yes	characteristic
204	C₂×#534	C₂³	1	1	yes	characteristic
205	C₂×#532	C₂³	1	1	yes	characteristic
206	C₂²×#121	D₄	1	1	yes	characteristic, complemented
207	C₂²×#120	D₄	1	1	yes	characteristic, complemented
208	C₂²×#120	C₂³	1	1	yes	characteristic
209	C₄×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
210	C₂×#458	C₂³	1	1	yes	characteristic
211	C₂×#458	C₂³	1	1	yes	characteristic
212	C₂×#458	C₂³	1	1	yes	characteristic
213	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
214	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
215	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
216	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
217	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
218	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
219	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
220	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
221	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
222	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
223	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
224	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
225	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
226	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
227	C₂×B(4,𝔽₂)	C₂³	1	1	yes	characteristic
228	C₂×#455	C₂³	1	1	yes	characteristic
229	C₂×#455	C₂³	1	1	yes	characteristic
230	C₂×#455	C₂³	1	1	yes	characteristic
231	C₂×#455	C₂³	1	1	yes	characteristic
232	C₂×#455	C₂³	1	1	yes	characteristic
233	C₂×#455	C₂³	1	1	yes	characteristic
234	C₂×#453	C₂³	1	1	yes	characteristic
235	C₂×#453	C₂³	1	1	yes	characteristic
236	C₂×#453	C₂³	1	1	yes	characteristic
237	C₂×#413	C₂³	1	1	yes	characteristic
238	C₂²×#100	C₂³	1	1	yes	characteristic
239	C₂×#410	C₂³	1	1	yes	characteristic
240	C₂×#410	C₂³	1	1	yes	characteristic
241	C₂²×#99	C₂³	1	1	yes	characteristic
242	C₂²×#99	C₂³	1	1	yes	characteristic
243	#2850	D₄	1	1	yes	characteristic, complemented
244	#2847	D₄	1	1	yes	characteristic, complemented
245	#2846	D₄	1	1	yes	characteristic, complemented
246	#2717	C₂³	1	1	yes	characteristic
247	#2697	C₂³	1	1	yes	characteristic
248	#2684	C₂³	1	1	yes	characteristic
249	#2684	C₂³	1	1	yes	characteristic
250	#2684	C₂³	1	1	yes	characteristic
251	#2679	C₂³	1	1	yes	characteristic
252	#2658	D₄	1	1	yes	characteristic, complemented
253	#2621	D₄	1	1	yes	characteristic, complemented
254	#2617	D₄	1	1	yes	characteristic, complemented
255	#2613	D₄	1	1	yes	characteristic, complemented
256	#2613	D₄	1	1	yes	characteristic, complemented
257	#2613	D₄	1	1	yes	characteristic, complemented
258	#2547	C₂³	1	1	yes	characteristic
259	#2544	D₄	1	1	yes	characteristic, complemented
260	#2539	D₄	1	1	yes	characteristic, complemented
261	#2534	C₂³	1	1	yes	characteristic
262	#2435	C₂³	1	1	yes	characteristic
263	#2433	D₄	1	1	yes	characteristic, complemented
264	#2432	D₄	1	1	yes	characteristic, complemented
265	#2432	C₂³	1	1	yes	characteristic
266	#2431	D₄	1	1	yes	characteristic, complemented
267	#2413	D₄	1	1	yes	characteristic, complemented
268	#2411	D₄	1	1	yes	characteristic, complemented
269	#2410	D₄	1	1	yes	characteristic, complemented
270	#2410	D₄	1	1	yes	characteristic, complemented
271	#2408	C₂³	1	1	yes	characteristic
272	#2406	C₂³	1	1	yes	characteristic
273	#2404	C₂³	1	1	yes	characteristic
274	#2403	C₂³	1	1	yes	characteristic
275	#2403	C₂³	1	1	yes	characteristic
276	#2380	C₂³	1	1	yes	characteristic
277	#2375	C₂³	1	1	yes	characteristic
278	#2358	C₂³	1	1	yes	characteristic
279	#2342	D₄	1	1	yes	characteristic, complemented
280	#2342	D₄	1	1	yes	characteristic, complemented
281	#2328	C₂³	1	1	yes	characteristic
282	#2321	C₂³	1	1	yes	characteristic
283	C₄×#120	C₂³	1	1	yes	characteristic
284	#2290	D₄	1	1	yes	characteristic, complemented
285	#2196	D₄	1	8	yes	complemented
286	C₂×#354	C₂³	1	1	yes	characteristic
287	C₂×#354	C₂³	1	1	yes	characteristic
288	C₂×#354	C₂³	1	1	yes	characteristic
289	C₂×#354	C₂³	1	1	yes	characteristic
290	C₂×#354	C₂³	1	1	yes	characteristic
291	C₂×#354	C₂³	1	1	yes	characteristic
292	C₂×#354	C₂³	1	1	yes	characteristic
293	C₂×#354	C₂³	1	1	yes	characteristic
294	C₂×#353	C₂³	1	1	yes	characteristic
295	C₂×#353	C₂³	1	1	yes	characteristic
296	C₂×#353	C₂³	1	1	yes	characteristic
297	C₂×#353	C₂³	1	1	yes	characteristic
298	C₂×#352	C₂³	1	1	yes	characteristic
299	C₂×#352	C₂³	1	1	yes	characteristic
300	C₂×#352	C₂³	1	1	yes	characteristic
301	C₂×#352	C₂³	1	1	yes	characteristic
302	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
303	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
304	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
305	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
306	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
307	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
308	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
309	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
310	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
311	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
312	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
313	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
314	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
315	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
316	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
317	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
318	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
319	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
320	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
321	C₂×AΣL(1,𝔽₁₆)	C₂³	1	1	yes	characteristic
322	#1890	C₂³	1	1	yes	characteristic
323	#1889	C₂³	1	1	yes	characteristic
324	#1889	C₂³	1	1	yes	characteristic
325	#1889	C₂³	1	1	yes	characteristic
326	#1889	C₂³	1	1	yes	characteristic
327	#1889	C₂³	1	1	yes	characteristic
328	#1887	C₂³	1	1	yes	characteristic
329	#1885	C₂³	1	1	yes	characteristic
330	#1885	C₂³	1	1	yes	characteristic
331	#1867	C₂³	1	1	yes	characteristic
332	#1867	C₂³	1	1	yes	characteristic
333	#1856	C₂³	1	1	yes	characteristic
334	#1800	C₂³	1	1	yes	characteristic
335	#1799	C₂³	1	1	yes	characteristic
336	#1799	C₂³	1	1	yes	characteristic
337	#1792	C₂³	1	1	yes	characteristic
338	#1792	C₂³	1	1	yes	characteristic
339	#1792	C₂³	1	1	yes	characteristic
340	#1790	C₂³	1	1	yes	characteristic
341	#1790	C₂³	1	1	yes	characteristic
342	#1790	C₂³	1	1	yes	characteristic
343	#1790	C₂³	1	1	yes	characteristic
344	#1790	C₂³	1	1	yes	characteristic
345	#1790	C₂³	1	1	yes	characteristic
346	#1785	C₂³	1	1	yes	characteristic
347	#1783	C₂³	1	1	yes	characteristic
348	#1782	C₂³	1	1	yes	characteristic
349	#1782	C₂³	1	1	yes	characteristic
350	#1781	C₂³	1	1	yes	characteristic
351	#1781	C₂³	1	1	yes	characteristic
352	C₄×#100	C₂³	1	1	yes	characteristic
353	C₄×#99	C₂³	1	1	yes	characteristic
354	C₄×#99	C₂³	1	1	yes	characteristic
355	#1393	C₂³	1	1	yes	characteristic
356	#1393	C₂³	1	1	yes	characteristic
357	#1393	C₂³	1	1	yes	characteristic
358	#1393	C₂³	1	1	yes	characteristic
359	#1390	C₂³	1	1	yes	characteristic
360	#1390	C₂³	1	1	yes	characteristic
361	#1390	C₂³	1	1	yes	characteristic
362	#1390	C₂³	1	1	yes	characteristic
363	#1390	C₂³	1	1	yes	characteristic
364	#1390	C₂³	1	1	yes	characteristic
365	#1390	C₂³	1	1	yes	characteristic
366	#1390	C₂³	1	1	yes	characteristic
367	C₂⁶	C₂×D₄	1	1	yes	characteristic
368	C₂×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
369	C₂×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
370	C₂×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
371	C₂²×#41	C₂×D₄	1	1	yes	characteristic
372	C₂²×#41	C₂×D₄	1	1	yes	characteristic, complemented
373	C₂²×#41	C₂⁴	1	1	yes	characteristic
374	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
375	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
376	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
377	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
378	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
379	C₂³×D₄	C₂×D₄	1	1	yes	characteristic, complemented
380	C₂³×D₄	C₂⁴	1	1	yes	characteristic
381	C₂⁴×C₄	C₂×D₄	1	1	yes	characteristic, complemented
382	D₄²	C₂×D₄	1	4	yes	complemented
383	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
384	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
385	C₂×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
386	C₂×#127	C₂×D₄	1	1	yes	characteristic
387	C₂×#127	C₂⁴	1	1	yes	characteristic
388	C₂×#124	C₂×D₄	1	1	yes	characteristic
389	C₂×#124	C₂×D₄	1	1	yes	characteristic
390	C₂×#124	C₂×D₄	1	1	yes	characteristic
391	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
392	C₂×#124	C₂⁴	1	1	yes	characteristic
393	C₂×#124	C₂⁴	1	1	yes	characteristic
394	C₂×#123	C₂×D₄	1	1	yes	characteristic
395	C₂×#123	C₂×D₄	1	1	yes	characteristic
396	C₂×#123	C₂×D₄	1	1	yes	characteristic
397	C₂×#123	C₂×D₄	1	1	yes	characteristic, complemented
398	C₂×#123	C₂⁴	1	1	yes	characteristic
399	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
400	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
402	C₂×#121	C₂×D₄	1	1	yes	characteristic
403	C₂×#121	C₂×D₄	1	1	yes	characteristic
404	C₂×#121	C₂×D₄	1	1	yes	characteristic
405	C₂×#120	C₂×D₄	1	1	yes	characteristic
406	C₂×#120	C₂×D₄	1	1	yes	characteristic
407	C₂×#120	C₂×D₄	1	1	yes	characteristic
408	C₂×#120	C₂×D₄	1	1	yes	characteristic
409	C₂×#120	C₂×D₄	1	1	yes	characteristic
410	C₂×#120	C₂×D₄	1	1	yes	characteristic
411	C₂×#120	C₂×D₄	1	1	yes	characteristic
412	C₂×#120	C₂×D₄	1	1	yes	characteristic
413	C₂×#120	C₂×D₄	1	1	yes	characteristic
414	C₂×#120	C₂×D₄	1	1	yes	characteristic
415	C₂×#120	C₂×D₄	1	1	yes	characteristic, complemented
416	C₂×#120	C₂×D₄	1	1	yes	characteristic, complemented
417	C₂×#120	C₂⁴	1	1	yes	characteristic
418	C₂×#120	C₂⁴	1	1	yes	characteristic
419	C₂×#120	C₂⁴	1	1	yes	characteristic
420	C₂×#120	C₂⁴	1	1	yes	characteristic
421	C₂×#120	C₂⁴	1	1	yes	characteristic
422	#518	C₂⁴	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
424	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
425	C₂×C₄×D₄	C₂⁴	1	1	yes	characteristic
426	C₂×#117	C₂×D₄	1	1	yes	characteristic
427	C₂×#117	C₂×D₄	1	1	yes	characteristic
428	C₂×#117	C₂×D₄	1	1	yes	characteristic, complemented
429	C₂²×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
430	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
431	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
432	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
433	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
434	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
435	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
436	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
437	C₂²×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
438	B(4,𝔽₂)	C₂×D₄	1	4	yes	—
439	B(4,𝔽₂)	C₂×D₄	1	4	yes	—
440	#453	C₂×D₄	1	4	yes	—
441	C₂×#100	C₂⁴	1	1	yes	characteristic
442	C₂×#100	C₂⁴	1	1	yes	characteristic
443	C₂×#100	C₂⁴	1	1	yes	characteristic
444	C₂×#100	C₂⁴	1	1	yes	characteristic
445	C₂×#99	C₂⁴	1	1	yes	characteristic
446	C₂×#99	C₂⁴	1	1	yes	characteristic
447	C₂×#99	C₂⁴	1	1	yes	characteristic
448	C₂×#99	C₂⁴	1	1	yes	characteristic
449	C₂×#99	C₂⁴	1	1	yes	characteristic
450	C₂×#99	C₂⁴	1	1	yes	characteristic
451	C₂×#99	C₂⁴	1	1	yes	characteristic
452	C₂×#99	C₂⁴	1	1	yes	characteristic
453	#391	C₂×D₄	1	1	yes	characteristic, complemented
454	#391	C₂×D₄	1	1	yes	characteristic, complemented
455	#391	C₂×D₄	1	1	yes	characteristic, complemented
456	#390	C₂×D₄	1	1	yes	characteristic
457	#390	C₂×D₄	1	1	yes	characteristic, complemented
458	#390	C₂⁴	1	1	yes	characteristic
459	#386	C₂×D₄	1	1	yes	characteristic
460	#386	C₂×D₄	1	1	yes	characteristic
461	#386	C₂×D₄	1	1	yes	characteristic
462	#386	C₂×D₄	1	1	yes	characteristic, complemented
463	#386	C₂⁴	1	1	yes	characteristic
464	#386	C₂⁴	1	1	yes	characteristic
465	#385	C₂×D₄	1	1	yes	characteristic
466	#385	C₂×D₄	1	1	yes	characteristic, complemented
467	#382	C₂×D₄	1	1	yes	characteristic, complemented
468	#381	C₂×D₄	1	1	yes	characteristic
469	#381	C₂×D₄	1	1	yes	characteristic, complemented
470	#381	C₂×D₄	1	1	yes	characteristic, complemented
471	#380	C₂×D₄	1	1	yes	characteristic
472	#380	C₂×D₄	1	1	yes	characteristic, complemented
473	#379	C₂×D₄	1	1	yes	characteristic
474	#379	C₂×D₄	1	1	yes	characteristic
475	#379	C₂×D₄	1	1	yes	characteristic
476	#379	C₂×D₄	1	1	yes	characteristic
477	#379	C₂×D₄	1	1	yes	characteristic
478	#379	C₂×D₄	1	1	yes	characteristic, complemented
479	#379	C₂×D₄	1	1	yes	characteristic, complemented
480	C₄×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
481	C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
482	C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
483	C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
484	C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
485	#376	C₂×D₄	1	1	yes	characteristic, complemented
486	#353	C₂×D₄	1	4	yes	complemented
487	AΣL(1,𝔽₁₆)	C₂×D₄	1	4	yes	complemented
488	AΣL(1,𝔽₁₆)	C₂×D₄	1	4	yes	complemented
489	C₂⁵	C₂²×D₄	1	1	yes	characteristic
490	C₂⁵	C₂²×D₄	1	1	yes	characteristic
491	C₂⁵	C₂²×D₄	1	1	yes	characteristic
492	C₂⁵	C₂²×D₄	1	1	yes	characteristic
493	C₂⁵	C₂²×D₄	1	1	yes	characteristic
494	C₂⁵	C₂²×D₄	1	1	yes	characteristic
495	C₂⁵	C₂²×D₄	1	1	yes	characteristic
496	H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
497	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
498	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
499	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
500	C₂²×D₄	#120	1	1	yes	characteristic
501	C₂²×D₄	#120	1	1	yes	characteristic
502	C₂²×D₄	#120	1	1	yes	characteristic
503	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
504	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
505	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
506	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
507	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
508	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
509	C₂²×D₄	C₂⁵	1	1	yes	characteristic
510	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
511	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
512	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
513	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
514	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
516	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
517	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
518	C₂³×C₄	C₂²×D₄	1	1	yes	characteristic
519	#127	C₂²×D₄	1	2	yes	—
520	#127	H(5,𝔽₂)	1	2	yes	—
521	#120	C₂²×D₄	1	2	yes	—
522	#120	C₂²×D₄	1	2	yes	—
523	#120	H(5,𝔽₂)	1	2	yes	—
524	#120	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₄⋊C₄	#120	1	1	yes	characteristic
526	C₂×C₄⋊C₄	#120	1	1	yes	characteristic
527	C₂×C₄⋊C₄	#120	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
531	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	#120	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄²	C₂²×D₄	1	1	yes	characteristic
555	#100	C₂²×D₄	1	2	yes	—
556	#99	C₂²×D₄	1	2	yes	—
557	#99	C₂²×D₄	1	2	yes	—
558	C₂⁴	C₂×#120	1	1	yes	characteristic
559	C₂⁴	C₂×#120	1	1	yes	characteristic
560	C₂⁴	C₂×#120	1	1	yes	characteristic
561	C₂⁴	C₂×#120	1	1	yes	characteristic
562	C₂⁴	D₄²	1	2	yes	—
563	C₂⁴	D₄²	1	2	yes	—
564	C₂⁴	C₂³×D₄	1	1	yes	characteristic
565	C₂⁴	C₂³×D₄	1	1	yes	characteristic
566	C₂×D₄	D₄²	1	2	yes	—
567	C₂×D₄	C₂³×D₄	1	1	yes	characteristic
568	C₂×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂²×C₄	C₂×#120	1	1	yes	characteristic
572	C₂²×C₄	C₂×#120	1	1	yes	characteristic
573	C₂²×C₄	C₂×#120	1	1	yes	characteristic
574	C₂²×C₄	C₂×#120	1	1	yes	characteristic
575	C₂²×C₄	C₂×#120	1	1	yes	characteristic
576	C₂²×C₄	C₂×#120	1	1	yes	characteristic
577	C₂²×C₄	C₂×#120	1	1	yes	characteristic
578	C₂²×C₄	C₂×#120	1	1	yes	characteristic
579	C₂²×C₄	C₂³×D₄	1	1	yes	characteristic
580	C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic
581	C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic
582	C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic
583	C₂²⋊C₄	B(4,𝔽₂)	1	1	yes	characteristic
584	C₂²⋊C₄	D₄²	1	2	yes	—
585	C₂²⋊C₄	D₄²	1	2	yes	—
586	C₄²	D₄²	1	2	yes	—
587	C₂³	C₂×B(4,𝔽₂)	1	1	yes	characteristic
588	C₂³	C₂×B(4,𝔽₂)	1	1	yes	characteristic
589	C₂³	C₂²×#120	1	1	yes	characteristic
590	C₂³	C₂×D₄²	1	1	yes	characteristic
591	C₂³	C₂×D₄²	1	1	yes	characteristic
592	C₂³	#3484	1	1	yes	characteristic
593	C₂³	#3484	1	1	yes	characteristic
594	C₂×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
595	C₂×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
596	C₂×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
597	C₂×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
598	C₂×C₄	C₂×D₄²	1	1	yes	characteristic
599	C₂×C₄	#3484	1	1	yes	characteristic
600	C₂²	D₄×#120	1	1	yes	characteristic
601	C₂²	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
602	C₂²	#60399	1	1	yes	characteristic
603	C₂	D₄×B(4,𝔽₂)	1	1	yes	characteristic
604	C₂	#7622876	1	1	yes	characteristic
605	C₂	#7622886	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂⁵
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊C₄ ◁ C₂×#546 ◁ G
LECS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #8040645	C₂	semidirect
2. C₂×#33559	C₂	semidirect
3. C₂×#33551	C₂	semidirect
4. #6573724	C₂	semidirect
5. #6573716	C₂	semidirect
6. #6573676	C₂	semidirect
7. #511938	C₂	semidirect
8. #511787	C₂	semidirect
9. #511779	C₂	semidirect
10. #503241	C₂	semidirect
11. #503206	C₂	semidirect
12. #503192	C₂	semidirect
13. #501184	C₂	semidirect
14. #501180	C₂	semidirect
15. #501174	C₂	semidirect
16. #501164	C₂	semidirect
17. #501097	C₂	semidirect
18. #501091	C₂	semidirect
19. #500826	C₂	semidirect
20. #500781	C₂	semidirect
21. #500767	C₂	semidirect
22. #499850	C₂	semidirect
23. #499832	C₂	semidirect
24. #499812	C₂	semidirect
25. #499811	C₂	semidirect
26. #499805	C₂	semidirect
27. #499795	C₂	semidirect
28. #497362	C₂	semidirect
29. #497357	C₂	semidirect
30. #497294	C₂	semidirect
31. #495771	C₂	semidirect
32. #62987	C₂²	semidirect
33. C₂×#3549	C₂²	semidirect
34. C₂×#3532	C₂²	semidirect
36. C₂×#3027	C₂²	semidirect
37. C₂×#3026	C₂²	semidirect
38. C₂²×B(4,𝔽₂)	C₂²	semidirect
40. C₂×#3018	C₂²	semidirect
41. #52031	C₂²	semidirect
42. #52004	C₂²	semidirect
43. #50165	C₂²	semidirect
44. #49562	C₂²	semidirect
45. #48812	C₂²	semidirect
46. #47848	C₂²	semidirect
47. #46276	C₂²	semidirect
48. #45479	C₂²	semidirect
49. #45439	C₂²	semidirect
53. #34468	C₂²	semidirect
55. C₂×#2200	C₂²	semidirect
56. C₂×#2200	C₂²	semidirect
58. C₂×#2199	C₂²	semidirect
59. C₂×#2199	C₂²	semidirect
60. C₂×#2199	C₂²	semidirect
61. C₂×#2199	C₂²	semidirect
62. C₂×#2199	C₂²	semidirect
63. C₂×#2199	C₂²	semidirect
64. C₂×#2199	C₂²	semidirect
65. C₂×#2199	C₂²	semidirect
66. C₂×#2197	C₂²	semidirect
67. C₂×#2197	C₂²	semidirect
68. C₂×#2197	C₂²	semidirect
70. C₂×#2196	C₂²	semidirect
71. C₂×#2196	C₂²	semidirect
72. C₂×#2196	C₂²	semidirect
73. C₂×#2196	C₂²	semidirect
74. C₂×#2196	C₂²	semidirect
75. C₂×#2127	C₂²	semidirect
76. C₂×#2126	C₂²	semidirect
77. C₂×#2122	C₂²	semidirect
78. C₂×#2122	C₂²	semidirect
79. C₂×#2121	C₂²	semidirect
80. C₂²×AΣL(1,𝔽₁₆)	C₂²	semidirect
81. #32928	C₂²	semidirect
82. #32926	C₂²	semidirect
83. #32922	C₂²	semidirect
84. #32901	C₂²	semidirect
85. #32899	C₂²	semidirect
86. #32898	C₂²	semidirect
87. #32898	C₂²	semidirect
88. #32893	C₂²	semidirect
89. #32891	C₂²	semidirect
90. #25773	C₂²	semidirect
91. #25771	C₂²	semidirect
92. #25738	C₂²	semidirect
93. #24415	C₂²	semidirect
94. #24413	C₂²	semidirect
95. #24407	C₂²	semidirect
96. #24406	C₂²	semidirect
97. #24404	C₂²	semidirect
98. #24404	C₂²	semidirect
99. #24262	C₂²	semidirect
100. #24260	C₂²	semidirect
101. #24226	C₂²	semidirect
103. #23908	C₂²	semidirect
105. #23904	C₂²	semidirect
106. #23903	C₂²	semidirect
107. #23900	C₂²	semidirect
108. #22408	C₂²	semidirect
109. #22405	C₂²	semidirect
110. #22405	C₂²	semidirect
111. #21482	C₂²	semidirect
112. C₄×B(4,𝔽₂)	C₂²	semidirect
113. #21473	C₂²	semidirect
114. #13425	C₂²	semidirect
115. #13424	C₂²	semidirect
116. #13424	C₂²	semidirect
117. #13424	C₂²	semidirect
118. #13420	C₂²	semidirect
119. #13419	C₂²	semidirect
120. #13349	C₂²	semidirect
121. #13349	C₂²	semidirect
122. #13349	C₂²	semidirect
123. #13348	C₂²	semidirect
124. #13348	C₂²	semidirect
125. #13348	C₂²	semidirect
126. #13348	C₂²	semidirect
127. #13348	C₂²	semidirect
128. #13348	C₂²	semidirect
129. #13348	C₂²	semidirect
130. #13348	C₂²	semidirect
131. #13348	C₂²	semidirect
132. #13344	C₂²	semidirect
133. #13344	C₂²	semidirect
134. #13344	C₂²	semidirect
135. #13343	C₂²	semidirect
136. #13343	C₂²	semidirect
137. #13343	C₂²	semidirect
138. #13224	C₂²	semidirect
139. #13224	C₂²	semidirect
140. #13222	C₂²	semidirect
141. #13221	C₂²	semidirect
142. #13219	C₂²	semidirect
143. #13218	C₂²	semidirect
144. #13091	C₂²	semidirect
145. #13091	C₂²	semidirect
146. #13090	C₂²	semidirect
147. #13090	C₂²	semidirect
148. #13087	C₂²	semidirect
149. #13086	C₂²	semidirect
150. #13086	C₂²	semidirect
151. #13085	C₂²	semidirect
152. #13083	C₂²	semidirect
153. #13082	C₂²	semidirect
154. #13082	C₂²	semidirect
155. #13081	C₂²	semidirect
156. #13049	C₂²	semidirect
157. #13049	C₂²	semidirect
158. #13049	C₂²	semidirect
159. #13043	C₂²	semidirect
160. #13043	C₂²	semidirect
161. #13043	C₂²	semidirect
162. #13041	C₂²	semidirect
163. #13041	C₂²	semidirect
164. #13041	C₂²	semidirect
165. #12966	C₂²	semidirect
166. #12960	C₂²	semidirect
167. #12958	C₂²	semidirect
168. #12799	C₂²	semidirect
169. #12795	C₂²	semidirect
170. #12793	C₂²	semidirect
171. #12763	C₂²	semidirect
172. #12763	C₂²	semidirect
173. #12763	C₂²	semidirect
174. #12762	C₂²	semidirect
175. #12761	C₂²	semidirect
176. #12759	C₂²	semidirect
177. #12759	C₂²	semidirect
178. #12696	C₂²	semidirect
179. #12695	C₂²	semidirect
180. #12691	C₂²	semidirect
181. #12691	C₂²	semidirect
182. #12690	C₂²	semidirect
183. #12687	C₂²	semidirect
184. #12628	C₂²	semidirect
185. #12622	C₂²	semidirect
186. C₄×AΣL(1,𝔽₁₆)	C₂²	semidirect
197. C₂×#547	D₄	semidirect
206. C₂²×#121	D₄	semidirect
207. C₂²×#120	D₄	semidirect
243. #2850	D₄	semidirect
244. #2847	D₄	semidirect
245. #2846	D₄	semidirect
252. #2658	D₄	semidirect
253. #2621	D₄	semidirect
254. #2617	D₄	semidirect
255. #2613	D₄	semidirect
256. #2613	D₄	semidirect
257. #2613	D₄	semidirect
259. #2544	D₄	semidirect
260. #2539	D₄	semidirect
263. #2433	D₄	semidirect
264. #2432	D₄	semidirect
266. #2431	D₄	semidirect
267. #2413	D₄	semidirect
268. #2411	D₄	semidirect
269. #2410	D₄	semidirect
270. #2410	D₄	semidirect
279. #2342	D₄	semidirect
280. #2342	D₄	semidirect
284. #2290	D₄	semidirect
285. #2196	D₄	semidirect
372. C₂²×#41	C₂×D₄	semidirect
379. C₂³×D₄	C₂×D₄	semidirect
381. C₂⁴×C₄	C₂×D₄	semidirect
382. D₄²	C₂×D₄	semidirect
383. C₂×C₄⋊Q₈	C₂×D₄	semidirect
384. C₂×C₄⋊Q₈	C₂×D₄	semidirect
385. C₂×C₄⋊Q₈	C₂×D₄	semidirect
391. C₂×#124	C₂×D₄	semidirect
397. C₂×#123	C₂×D₄	semidirect
401. C₂×C₂²⋊Q₈	C₂×D₄	semidirect
415. C₂×#120	C₂×D₄	semidirect
416. C₂×#120	C₂×D₄	semidirect
424. C₂×C₄×D₄	C₂×D₄	semidirect
428. C₂×#117	C₂×D₄	semidirect
429. C₂²×C₄⋊C₄	C₂×D₄	semidirect
436. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
437. C₂²×C₄²	C₂×D₄	semidirect
453. #391	C₂×D₄	semidirect
454. #391	C₂×D₄	semidirect
455. #391	C₂×D₄	semidirect
457. #390	C₂×D₄	semidirect
462. #386	C₂×D₄	semidirect
466. #385	C₂×D₄	semidirect
467. #382	C₂×D₄	semidirect
469. #381	C₂×D₄	semidirect
470. #381	C₂×D₄	semidirect
472. #380	C₂×D₄	semidirect
478. #379	C₂×D₄	semidirect
479. #379	C₂×D₄	semidirect
480. C₄×C₄⋊C₄	C₂×D₄	semidirect
483. C₄×C₂²⋊C₄	C₂×D₄	semidirect
484. C₄×C₂²⋊C₄	C₂×D₄	semidirect
485. #376	C₂×D₄	semidirect
486. #353	C₂×D₄	semidirect
487. AΣL(1,𝔽₁₆)	C₂×D₄	semidirect
488. AΣL(1,𝔽₁₆)	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#8040645	2
C₂×#33559	2
C₂×#33551	2
#6573724	2
#6573716	2
#6573676	2
#511938	2
#511787	2
#511779	2
#503241	2
#503206	2
#503192	2
#501184	2
#501180	2
#501174	2
#501164	2
#501097	2
#501091	2
#500826	2
#500781	2
#500767	2
#499850	2
#499832	2
#499812	2
#499811	2
#499805	2
#499795	2
#497362	2
#497357	2
#497294	2
#495771	2