Subgroups — #72341504

Order 1024.

At least 6259 conjugacy classes of subgroups; only the 653 normal subgroups are shown.

The subgroup lattice has 608 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#8063857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#33553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#2200	C₂	1	1	yes	maximal, characteristic, complemented
4	#6573716	C₂	1	1	yes	maximal, characteristic, complemented
5	#6573713	C₂	1	1	yes	maximal, characteristic, complemented
6	#6573673	C₂	1	1	yes	maximal, characteristic, complemented
7	#511943	C₂	1	1	yes	maximal, characteristic, complemented
8	#511781	C₂	1	1	yes	maximal, characteristic, complemented
9	#511776	C₂	1	1	yes	maximal, characteristic, complemented
10	#503237	C₂	1	1	yes	maximal, characteristic, complemented
11	#503206	C₂	1	1	yes	maximal, characteristic, complemented
12	#503190	C₂	1	1	yes	maximal, characteristic, complemented
13	#501182	C₂	1	1	yes	maximal, characteristic, complemented
14	#501169	C₂	1	1	yes	maximal, characteristic, complemented
15	#501165	C₂	1	1	yes	maximal, characteristic, complemented
16	#501156	C₂	1	1	yes	maximal, characteristic, complemented
17	#501102	C₂	1	1	yes	maximal, characteristic, complemented
18	#501084	C₂	1	1	yes	maximal, characteristic, complemented
19	#500822	C₂	1	1	yes	maximal, characteristic, complemented
20	#500781	C₂	1	1	yes	maximal, characteristic, complemented
21	#500765	C₂	1	1	yes	maximal, characteristic, complemented
22	#499843	C₂	1	1	yes	maximal, characteristic, complemented
23	#499837	C₂	1	1	yes	maximal, characteristic, complemented
24	#499813	C₂	1	1	yes	maximal, characteristic, complemented
25	#499800	C₂	1	1	yes	maximal, characteristic, complemented
26	#499799	C₂	1	1	yes	maximal, characteristic, complemented
27	#499787	C₂	1	1	yes	maximal, characteristic, complemented
28	#497365	C₂	1	1	yes	maximal, characteristic, complemented
29	#497357	C₂	1	1	yes	maximal, characteristic, complemented
30	#497290	C₂	1	1	yes	maximal, characteristic, complemented
31	#495776	C₂	1	1	yes	maximal, characteristic, complemented
32	#62987	C₂²	1	1	yes	characteristic, complemented
33	C₂×#3537	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#560	C₂²	1	1	yes	characteristic, complemented
35	C₂×#3027	C₂²	1	1	yes	characteristic, complemented
36	C₂×#3025	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#458	C₂²	1	1	yes	characteristic, complemented
38	C₂²×B(4,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
39	C₂×#3021	C₂²	1	1	yes	characteristic, complemented
40	C₂²×#453	C₂²	1	1	yes	characteristic, complemented
41	#59126	C₂²	1	1	yes	characteristic, complemented
42	#58990	C₂²	1	1	yes	characteristic, complemented
43	#52031	C₂²	1	1	yes	characteristic, complemented
44	#52013	C₂²	1	1	yes	characteristic, complemented
45	#49564	C₂²	1	1	yes	characteristic, complemented
46	#47932	C₂²	1	1	yes	characteristic, complemented
47	#45487	C₂²	1	1	yes	characteristic, complemented
48	#45455	C₂²	1	1	yes	characteristic, complemented
49	#45452	C₂²	1	1	yes	characteristic, complemented
50	#37674	C₂²	1	1	yes	characteristic
51	#37645	C₂²	1	1	yes	characteristic
52	#36099	C₂²	1	1	yes	characteristic
53	#34518	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×#2200	C₂²	1	1	yes	characteristic, complemented
58	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
59	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
60	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
61	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
62	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
63	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
64	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
65	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
66	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
67	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
68	C₂×#2200	C₂²	1	1	yes	characteristic, complemented
69	C₂×#2196	C₂²	1	1	yes	characteristic, complemented
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×#2128	C₂²	1	1	yes	characteristic, complemented
76	C₂²×#353	C₂²	1	1	yes	characteristic, complemented
77	C₂×#2122	C₂²	1	1	yes	characteristic, complemented
78	C₂×#2120	C₂²	1	1	yes	characteristic, complemented
79	C₂²×#352	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	#32920	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	#32890	C₂²	1	1	yes	characteristic, complemented
89	#32888	C₂²	1	1	yes	characteristic, complemented
90	#25773	C₂²	1	1	yes	characteristic, complemented
91	#25771	C₂²	1	1	yes	characteristic, complemented
92	#25739	C₂²	1	1	yes	characteristic, complemented
93	#24414	C₂²	1	1	yes	characteristic, complemented
94	#24412	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	#24261	C₂²	1	1	yes	characteristic, complemented
101	#24226	C₂²	1	1	yes	characteristic, complemented
102	#23913	C₂²	1	1	yes	characteristic, complemented
103	#23906	C₂²	1	1	yes	characteristic, complemented
104	#23904	C₂²	1	1	yes	characteristic, complemented
105	#23902	C₂²	1	1	yes	characteristic, complemented
106	#23901	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×#458	C₂²	1	1	yes	characteristic, complemented
113	#21473	C₂²	1	1	yes	characteristic, complemented
114	#13423	C₂²	1	1	yes	characteristic, complemented
115	#13422	C₂²	1	1	yes	characteristic, complemented
116	#13422	C₂²	1	1	yes	characteristic, complemented
117	#13422	C₂²	1	1	yes	characteristic, complemented
118	#13420	C₂²	1	1	yes	characteristic, complemented
119	#13419	C₂²	1	1	yes	characteristic, complemented
120	#13347	C₂²	1	1	yes	characteristic, complemented
121	#13347	C₂²	1	1	yes	characteristic, complemented
122	#13347	C₂²	1	1	yes	characteristic, complemented
123	#13346	C₂²	1	1	yes	characteristic, complemented
124	#13346	C₂²	1	1	yes	characteristic, complemented
125	#13346	C₂²	1	1	yes	characteristic, complemented
126	#13346	C₂²	1	1	yes	characteristic, complemented
127	#13346	C₂²	1	1	yes	characteristic, complemented
128	#13346	C₂²	1	1	yes	characteristic, complemented
129	#13346	C₂²	1	1	yes	characteristic, complemented
130	#13346	C₂²	1	1	yes	characteristic, complemented
131	#13346	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	#13223	C₂²	1	1	yes	characteristic, complemented
139	#13223	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	#13089	C₂²	1	1	yes	characteristic, complemented
145	#13089	C₂²	1	1	yes	characteristic, complemented
146	#13088	C₂²	1	1	yes	characteristic, complemented
147	#13088	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	#13047	C₂²	1	1	yes	characteristic, complemented
157	#13047	C₂²	1	1	yes	characteristic, complemented
158	#13047	C₂²	1	1	yes	characteristic, complemented
159	#13044	C₂²	1	1	yes	characteristic, complemented
160	#13044	C₂²	1	1	yes	characteristic, complemented
161	#13044	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	#12964	C₂²	1	1	yes	characteristic, complemented
166	#12961	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	#12794	C₂²	1	1	yes	characteristic, complemented
171	#12762	C₂²	1	1	yes	characteristic, complemented
172	#12762	C₂²	1	1	yes	characteristic, complemented
173	#12762	C₂²	1	1	yes	characteristic, complemented
174	#12762	C₂²	1	1	yes	characteristic, complemented
175	#12762	C₂²	1	1	yes	characteristic, complemented
176	#12759	C₂²	1	1	yes	characteristic, complemented
177	#12759	C₂²	1	1	yes	characteristic, complemented
178	#12697	C₂²	1	1	yes	characteristic, complemented
179	#12693	C₂²	1	1	yes	characteristic, complemented
180	#12691	C₂²	1	1	yes	characteristic, complemented
181	#12689	C₂²	1	1	yes	characteristic, complemented
182	#12688	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×#352	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×#560	C₂³	1	1	yes	characteristic
190	C₂×#560	C₂³	1	1	yes	characteristic
191	C₂×#560	C₂³	1	1	yes	characteristic
192	C₂×#560	C₂³	1	1	yes	characteristic
193	C₂×#560	C₂³	1	1	yes	characteristic
194	#3496	C₂³	1	1	yes	characteristic
195	#3485	C₂³	1	1	yes	characteristic
196	#3484	C₂³	1	1	yes	characteristic
197	C₂×#546	C₂³	1	1	yes	characteristic
198	C₂×D₄²	D₄	1	1	yes	characteristic, complemented
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	C₂²×#127	C₂³	1	1	yes	characteristic
204	C₂×#525	C₂³	1	1	yes	characteristic
205	C₂²×#123	C₂³	1	1	yes	characteristic
206	C₂²×#120	D₄	1	1	yes	characteristic, complemented
207	C₂²×#120	C₂³	1	1	yes	characteristic
208	C₄×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₄	D₄	1	1	yes	characteristic, complemented
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×#458	C₂³	1	1	yes	characteristic
214	C₂×#458	C₂³	1	1	yes	characteristic
215	C₂×#458	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×#453	C₂³	1	1	yes	characteristic
229	C₂×#453	C₂³	1	1	yes	characteristic
230	C₂×#453	C₂³	1	1	yes	characteristic
231	C₂×#453	C₂³	1	1	yes	characteristic
232	C₂×#453	C₂³	1	1	yes	characteristic
233	C₂×#453	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	#2854	D₄	1	1	yes	characteristic, complemented
244	#2850	D₄	1	1	yes	characteristic, complemented
245	#2849	D₄	1	1	yes	characteristic, complemented
246	#2849	D₄	1	1	yes	characteristic, complemented
247	#2846	D₄	1	1	yes	characteristic, complemented
248	#2709	C₂³	1	1	yes	characteristic
249	#2697	C₂³	1	1	yes	characteristic
250	#2679	C₂³	1	1	yes	characteristic
251	#2669	C₂³	1	1	yes	characteristic
252	#2669	C₂³	1	1	yes	characteristic
253	#2669	C₂³	1	1	yes	characteristic
254	#2657	D₄	1	1	yes	characteristic, complemented
255	#2619	D₄	1	1	yes	characteristic, complemented
256	#2617	D₄	1	1	yes	characteristic, complemented
257	#2613	D₄	1	1	yes	characteristic, complemented
258	#2544	D₄	1	1	yes	characteristic, complemented
259	#2541	C₂³	1	1	yes	characteristic
260	#2539	D₄	1	1	yes	characteristic, complemented
261	#2534	C₂³	1	1	yes	characteristic
262	#2435	D₄	1	1	yes	characteristic, complemented
263	#2433	D₄	1	1	yes	characteristic, complemented
264	#2433	D₄	1	1	yes	characteristic, complemented
265	#2433	C₂³	1	1	yes	characteristic
266	#2431	C₂³	1	1	yes	characteristic
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	#2376	C₂³	1	1	yes	characteristic
277	#2366	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×#123	C₂³	1	1	yes	characteristic
284	#2290	D₄	1	1	yes	characteristic, complemented
285	#2200	D₄	1	8	yes	complemented
286	C₂×#353	C₂³	1	1	yes	characteristic
287	C₂×#353	C₂³	1	1	yes	characteristic
288	C₂×#353	C₂³	1	1	yes	characteristic
289	C₂×#353	C₂³	1	1	yes	characteristic
290	C₂×#353	C₂³	1	1	yes	characteristic
291	C₂×#353	C₂³	1	1	yes	characteristic
292	C₂×#353	C₂³	1	1	yes	characteristic
293	C₂×#353	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×#352	C₂³	1	1	yes	characteristic
303	C₂×#352	C₂³	1	1	yes	characteristic
304	C₂×#352	C₂³	1	1	yes	characteristic
305	C₂×#352	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	#1890	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	#1887	C₂³	1	1	yes	characteristic
330	#1887	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	C₂⁴	1	1	yes	characteristic
372	C₂³×D₄	C₂×D₄	1	1	yes	characteristic
373	C₂³×D₄	C₂×D₄	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, complemented
378	C₂³×D₄	C₂⁴	1	1	yes	characteristic
379	C₂⁴×C₄	C₂×D₄	1	1	yes	characteristic
380	C₂⁴×C₄	C₂×D₄	1	1	yes	characteristic, complemented
381	#560	C₂×D₄	1	4	yes	complemented
382	C₂×#127	C₂×D₄	1	1	yes	characteristic
383	C₂×#127	C₂×D₄	1	1	yes	characteristic
384	C₂×#127	C₂×D₄	1	1	yes	characteristic
385	C₂×#127	C₂×D₄	1	1	yes	characteristic, complemented
386	C₂×#127	C₂⁴	1	1	yes	characteristic
387	C₂×#127	C₂⁴	1	1	yes	characteristic
388	C₂×#127	C₂⁴	1	1	yes	characteristic
389	C₂×#124	C₂×D₄	1	1	yes	characteristic
390	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
391	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
392	C₂×#124	C₂×D₄	1	1	yes	characteristic, complemented
393	C₂×#123	C₂×D₄	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	C₂×D₄	1	1	yes	characteristic, complemented
399	C₂×#123	C₂⁴	1	1	yes	characteristic
400	C₂×#123	C₂⁴	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
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×#121	C₂×D₄	1	1	yes	characteristic
406	C₂×#121	C₂×D₄	1	1	yes	characteristic, complemented
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
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	#518	C₂⁴	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂×D₄	1	1	yes	characteristic, complemented
424	C₂×C₄×D₄	C₂⁴	1	1	yes	characteristic
425	C₂×#117	C₂×D₄	1	1	yes	characteristic
426	C₂×#117	C₂×D₄	1	1	yes	characteristic, complemented
427	C₂×#117	C₂×D₄	1	1	yes	characteristic, complemented
428	C₂²×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
429	C₂²×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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, complemented
436	C₂²×C₄²	C₂×D₄	1	1	yes	characteristic
437	C₂²×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
438	#458	C₂×D₄	1	4	yes	complemented
439	B(4,𝔽₂)	C₂×D₄	1	4	yes	complemented
440	#453	C₂×D₄	1	4	yes	complemented
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	#390	C₂×D₄	1	1	yes	characteristic
455	#390	C₂×D₄	1	1	yes	characteristic, complemented
456	#390	C₂×D₄	1	1	yes	characteristic, complemented
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	#381	C₂×D₄	1	1	yes	characteristic, complemented
472	#380	C₂×D₄	1	1	yes	characteristic
473	#380	C₂×D₄	1	1	yes	characteristic, complemented
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
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	#352	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	H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
496	C₂²×Q₈	C₂²×D₄	1	1	yes	characteristic
497	C₂²×D₄	#120	1	1	yes	characteristic
498	C₂²×D₄	#120	1	1	yes	characteristic
499	C₂²×D₄	#120	1	1	yes	characteristic
500	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
501	C₂²×D₄	C₂²×D₄	1	1	yes	characteristic
502	C₂²×D₄	C₂²×D₄	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	C₂⁵	1	1	yes	characteristic
509	C₂³×C₄	C₂²×D₄	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	#123	C₂²×D₄	1	2	yes	—
522	#123	H(5,𝔽₂)	1	2	yes	—
523	#120	C₂²×D₄	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	C₂³×D₄	1	1	yes	characteristic
564	C₂⁴	C₂³×D₄	1	1	yes	characteristic
565	C₂×D₄	D₄²	1	2	yes	—
566	C₂×D₄	C₂³×D₄	1	1	yes	characteristic
567	C₂×D₄	C₂×H(5,𝔽₂)	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	C₂²×C₄	C₂×#120	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	D₄²	1	2	yes	—
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	#33553	1	2	yes	complemented
601	C₂²	D₄×#120	1	1	yes	characteristic
602	C₂²	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
603	C₂²	#60399	1	1	yes	characteristic
604	C₂	D₄×B(4,𝔽₂)	1	1	yes	characteristic
605	C₂	C₂×#33553	1	1	yes	characteristic
606	C₂	#7622887	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. #8063857	C₂	semidirect
2. C₂×#33553	C₂	semidirect
3. C₂²×#2200	C₂	semidirect
4. #6573716	C₂	semidirect
5. #6573713	C₂	semidirect
6. #6573673	C₂	semidirect
7. #511943	C₂	semidirect
8. #511781	C₂	semidirect
9. #511776	C₂	semidirect
10. #503237	C₂	semidirect
11. #503206	C₂	semidirect
12. #503190	C₂	semidirect
13. #501182	C₂	semidirect
14. #501169	C₂	semidirect
15. #501165	C₂	semidirect
16. #501156	C₂	semidirect
17. #501102	C₂	semidirect
18. #501084	C₂	semidirect
19. #500822	C₂	semidirect
20. #500781	C₂	semidirect
21. #500765	C₂	semidirect
22. #499843	C₂	semidirect
23. #499837	C₂	semidirect
24. #499813	C₂	semidirect
25. #499800	C₂	semidirect
26. #499799	C₂	semidirect
27. #499787	C₂	semidirect
28. #497365	C₂	semidirect
29. #497357	C₂	semidirect
30. #497290	C₂	semidirect
31. #495776	C₂	semidirect
32. #62987	C₂²	semidirect
33. C₂×#3537	C₂²	semidirect
34. C₂²×#560	C₂²	semidirect
35. C₂×#3027	C₂²	semidirect
36. C₂×#3025	C₂²	semidirect
37. C₂²×#458	C₂²	semidirect
38. C₂²×B(4,𝔽₂)	C₂²	semidirect
39. C₂×#3021	C₂²	semidirect
40. C₂²×#453	C₂²	semidirect
41. #59126	C₂²	semidirect
42. #58990	C₂²	semidirect
43. #52031	C₂²	semidirect
44. #52013	C₂²	semidirect
45. #49564	C₂²	semidirect
46. #47932	C₂²	semidirect
47. #45487	C₂²	semidirect
48. #45455	C₂²	semidirect
49. #45452	C₂²	semidirect
53. #34518	C₂²	semidirect
55. C₂×#2200	C₂²	semidirect
56. C₂×#2200	C₂²	semidirect
57. C₂×#2200	C₂²	semidirect
58. C₂×#2200	C₂²	semidirect
59. C₂×#2200	C₂²	semidirect
60. C₂×#2200	C₂²	semidirect
61. C₂×#2200	C₂²	semidirect
62. C₂×#2200	C₂²	semidirect
63. C₂×#2200	C₂²	semidirect
64. C₂×#2200	C₂²	semidirect
65. C₂×#2200	C₂²	semidirect
66. C₂×#2200	C₂²	semidirect
67. C₂×#2200	C₂²	semidirect
68. C₂×#2200	C₂²	semidirect
69. C₂×#2196	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×#2128	C₂²	semidirect
76. C₂²×#353	C₂²	semidirect
77. C₂×#2122	C₂²	semidirect
78. C₂×#2120	C₂²	semidirect
79. C₂²×#352	C₂²	semidirect
80. C₂²×AΣL(1,𝔽₁₆)	C₂²	semidirect
81. #32928	C₂²	semidirect
82. #32926	C₂²	semidirect
83. #32920	C₂²	semidirect
84. #32901	C₂²	semidirect
85. #32899	C₂²	semidirect
86. #32898	C₂²	semidirect
87. #32898	C₂²	semidirect
88. #32890	C₂²	semidirect
89. #32888	C₂²	semidirect
90. #25773	C₂²	semidirect
91. #25771	C₂²	semidirect
92. #25739	C₂²	semidirect
93. #24414	C₂²	semidirect
94. #24412	C₂²	semidirect
95. #24407	C₂²	semidirect
96. #24406	C₂²	semidirect
97. #24404	C₂²	semidirect
98. #24404	C₂²	semidirect
99. #24262	C₂²	semidirect
100. #24261	C₂²	semidirect
101. #24226	C₂²	semidirect
102. #23913	C₂²	semidirect
103. #23906	C₂²	semidirect
104. #23904	C₂²	semidirect
105. #23902	C₂²	semidirect
106. #23901	C₂²	semidirect
107. #23900	C₂²	semidirect
108. #22408	C₂²	semidirect
109. #22405	C₂²	semidirect
110. #22405	C₂²	semidirect
111. #21482	C₂²	semidirect
112. C₄×#458	C₂²	semidirect
113. #21473	C₂²	semidirect
114. #13423	C₂²	semidirect
115. #13422	C₂²	semidirect
116. #13422	C₂²	semidirect
117. #13422	C₂²	semidirect
118. #13420	C₂²	semidirect
119. #13419	C₂²	semidirect
120. #13347	C₂²	semidirect
121. #13347	C₂²	semidirect
122. #13347	C₂²	semidirect
123. #13346	C₂²	semidirect
124. #13346	C₂²	semidirect
125. #13346	C₂²	semidirect
126. #13346	C₂²	semidirect
127. #13346	C₂²	semidirect
128. #13346	C₂²	semidirect
129. #13346	C₂²	semidirect
130. #13346	C₂²	semidirect
131. #13346	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. #13223	C₂²	semidirect
139. #13223	C₂²	semidirect
140. #13222	C₂²	semidirect
141. #13221	C₂²	semidirect
142. #13219	C₂²	semidirect
143. #13218	C₂²	semidirect
144. #13089	C₂²	semidirect
145. #13089	C₂²	semidirect
146. #13088	C₂²	semidirect
147. #13088	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. #13047	C₂²	semidirect
157. #13047	C₂²	semidirect
158. #13047	C₂²	semidirect
159. #13044	C₂²	semidirect
160. #13044	C₂²	semidirect
161. #13044	C₂²	semidirect
162. #13041	C₂²	semidirect
163. #13041	C₂²	semidirect
164. #13041	C₂²	semidirect
165. #12964	C₂²	semidirect
166. #12961	C₂²	semidirect
167. #12958	C₂²	semidirect
168. #12799	C₂²	semidirect
169. #12795	C₂²	semidirect
170. #12794	C₂²	semidirect
171. #12762	C₂²	semidirect
172. #12762	C₂²	semidirect
173. #12762	C₂²	semidirect
174. #12762	C₂²	semidirect
175. #12762	C₂²	semidirect
176. #12759	C₂²	semidirect
177. #12759	C₂²	semidirect
178. #12697	C₂²	semidirect
179. #12693	C₂²	semidirect
180. #12691	C₂²	semidirect
181. #12689	C₂²	semidirect
182. #12688	C₂²	semidirect
183. #12687	C₂²	semidirect
184. #12628	C₂²	semidirect
185. #12622	C₂²	semidirect
186. C₄×#352	C₂²	semidirect
198. C₂×D₄²	D₄	semidirect
206. C₂²×#120	D₄	semidirect
209. C₂²×C₄×D₄	D₄	semidirect
243. #2854	D₄	semidirect
244. #2850	D₄	semidirect
245. #2849	D₄	semidirect
246. #2849	D₄	semidirect
247. #2846	D₄	semidirect
254. #2657	D₄	semidirect
255. #2619	D₄	semidirect
256. #2617	D₄	semidirect
257. #2613	D₄	semidirect
258. #2544	D₄	semidirect
260. #2539	D₄	semidirect
262. #2435	D₄	semidirect
263. #2433	D₄	semidirect
264. #2433	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. #2200	D₄	semidirect
377. C₂³×D₄	C₂×D₄	semidirect
380. C₂⁴×C₄	C₂×D₄	semidirect
381. #560	C₂×D₄	semidirect
385. C₂×#127	C₂×D₄	semidirect
390. C₂×#124	C₂×D₄	semidirect
391. C₂×#124	C₂×D₄	semidirect
392. C₂×#124	C₂×D₄	semidirect
397. C₂×#123	C₂×D₄	semidirect
398. C₂×#123	C₂×D₄	semidirect
406. C₂×#121	C₂×D₄	semidirect
416. C₂×#120	C₂×D₄	semidirect
423. C₂×C₄×D₄	C₂×D₄	semidirect
426. C₂×#117	C₂×D₄	semidirect
427. C₂×#117	C₂×D₄	semidirect
428. C₂²×C₄⋊C₄	C₂×D₄	semidirect
435. C₂²×C₂²⋊C₄	C₂×D₄	semidirect
437. C₂²×C₄²	C₂×D₄	semidirect
438. #458	C₂×D₄	semidirect
439. B(4,𝔽₂)	C₂×D₄	semidirect
440. #453	C₂×D₄	semidirect
453. #391	C₂×D₄	semidirect
455. #390	C₂×D₄	semidirect
456. #390	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
471. #381	C₂×D₄	semidirect
473. #380	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. #352	C₂×D₄	semidirect
488. AΣL(1,𝔽₁₆)	C₂×D₄	semidirect
600. C₂²	#33553	semidirect

Maximal subgroups

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

subgroup	index
#8063857	2
C₂×#33553	2
C₂²×#2200	2
#6573716	2
#6573713	2
#6573673	2
#511943	2
#511781	2
#511776	2
#503237	2
#503206	2
#503190	2
#501182	2
#501169	2
#501165	2
#501156	2
#501102	2
#501084	2
#500822	2
#500781	2
#500765	2
#499843	2
#499837	2
#499813	2
#499800	2
#499799	2
#499787	2
#497365	2
#497357	2
#497290	2
#495776	2