Subgroups — #72338586

Order 4096.

Only the 4177 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 678 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338585	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338584	C₂	1	2	yes	maximal, complemented
3	#72338583	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338579	C₂	1	1	yes	maximal, characteristic, complemented
5	#72338578	C₂²	1	1	yes	characteristic
6	#72338576	C₂	1	4	yes	maximal, complemented
7	#72338575	C₂²	1	2	yes	complemented
8	#72338207	C₂²	1	1	yes	characteristic, complemented
9	#72317785	C₂	1	16	yes	maximal, complemented
10	#72317775	C₂²	1	32	yes	complemented
11	#72317770	C₂²	1	8	yes	complemented
12	#72317757	C₂²	1	8	yes	complemented
13	#72317732	C₂²	1	8	yes	complemented
14	#72317722	C₂²	1	8	yes	complemented
15	#72317711	C₂²	1	8	yes	complemented
16	#72306961	C₂	1	8	yes	maximal, complemented
17	#72306954	C₂²	1	4	yes	complemented
18	#72306949	C₂²	1	8	yes	complemented
19	#72306941	C₂	1	2	yes	maximal, complemented
20	#72306939	C₂²	1	1	yes	characteristic, complemented
21	#72306935	C₂	1	4	yes	maximal, complemented
22	#72306931	C₂	1	2	yes	maximal, complemented
23	#72306905	C₂²	1	2	yes	complemented
24	#72306903	C₂²	1	4	yes	complemented
25	#72306901	C₂²	1	4	yes	complemented
26	#72306882	C₂²	1	8	yes	complemented
27	#72306880	C₂²	1	16	yes	complemented
28	#72306437	C₂²	1	4	yes	complemented
29	#72306375	C₂²	1	4	yes	complemented
30	#72306361	C₂²	1	2	yes	complemented
31	#72306324	C₂²	1	2	yes	complemented
32	#72306310	C₂²	1	2	yes	complemented
33	#72305972	C₂²	1	2	yes	—
34	#72281710	C₂²	1	8	yes	complemented
35	#72256107	C₂	1	2	yes	maximal, complemented
36	#72252021	C₂²	1	2	yes	complemented
37	#72252020	C₂²	1	2	yes	—
38	#72252013	C₂²	1	4	yes	complemented
39	#72252010	C₂²	1	8	yes	complemented
40	#72251980	C₂²	1	4	yes	complemented
41	C₂×#72216600	C₂	1	4	yes	maximal, complemented
42	C₂×#512862	C₂²	1	8	yes	complemented
43	C₂×#152602	C₂²	1	8	yes	complemented
44	C₂×#7487865	C₂²	1	4	yes	—
45	C₂×#153189	C₂²	1	16	yes	complemented
46	C₂×#152103	C₂²	1	4	yes	complemented
47	C₂×#152679	C₂²	1	8	yes	complemented
48	#72249464	C₂²	1	8	yes	complemented
49	#72236657	C₂²	1	8	yes	complemented
50	#72234146	C₂²	1	4	yes	—
51	C₂×#6348967	C₂²	1	2	yes	complemented
52	C₂×#511771	C₂²	1	4	yes	complemented
53	C₂×#7737411	C₂²	1	1	yes	characteristic, complemented
54	#72216611	C₂	1	16	yes	maximal, complemented
55	#72216603	C₂²	1	32	yes	complemented
56	#72216601	C₂²	1	128	yes	complemented
57	#72216600	C₂²	1	32	yes	complemented
58	#72216600	C₂²	1	32	yes	complemented
59	#72216589	C₂²	1	32	yes	complemented
60	#72216584	C₂²	1	32	yes	complemented
61	#72216577	C₂²	1	32	yes	complemented
62	#72216567	C₂²	1	8	yes	complemented
63	#72216138	C₂²	1	1	yes	characteristic, complemented
64	#72215721	C₂²	1	8	yes	complemented
65	#72215568	C₂²	1	8	yes	complemented
66	#72213685	C₂²	1	8	yes	complemented
67	#72213671	C₂²	1	32	yes	complemented
68	#72213519	C₂²	1	8	yes	complemented
69	#72213428	C₂²	1	8	yes	complemented
70	#72210575	C₂²	1	8	yes	complemented
71	#10586066	D₄	1	2	yes	complemented
72	#10585995	D₄	1	1	yes	characteristic, complemented
73	C₂²×#3498	C₂³	1	1	yes	characteristic
74	C₂³×D₄²	C₂³	1	1	yes	characteristic, complemented
75	#10576178	C₂³	1	8	yes	complemented
76	C₂×#61110	C₂³	1	4	yes	—
77	#10575560	D₄	1	4	yes	complemented
78	#10575560	C₂³	1	4	yes	—
79	#10575552	D₄	1	2	yes	complemented
80	#10575552	C₂³	1	2	yes	—
81	#10575547	D₄	1	4	yes	complemented
82	#10575547	C₂³	1	4	yes	—
83	#10575509	D₄	1	2	yes	complemented
84	C₂×#60798	C₂³	1	2	yes	—
85	#10575254	D₄	1	1	yes	characteristic, complemented
86	#10575254	C₂³	1	1	yes	characteristic
87	#10575219	D₄	1	1	yes	characteristic, complemented
88	#10575219	C₂³	1	1	yes	characteristic
89	C₂×#60388	D₄	1	2	yes	complemented
90	C₂×#60388	C₂³	1	2	yes	—
91	#10574126	D₄	1	1	yes	characteristic, complemented
92	#7737411	C₂³	1	2	yes	—
93	#7737411	C₂³	1	4	yes	complemented
94	#7737411	C₂³	1	2	yes	complemented
95	C₂×#52004	C₂³	1	4	yes	complemented
96	C₂×#34364	C₂³	1	1	yes	characteristic, complemented
97	C₂²×#2196	C₂³	1	8	yes	—
98	C₂×#33359	C₂³	1	4	yes	complemented
99	#7504294	C₂³	1	8	yes	complemented
100	#7504292	C₂³	1	8	yes	complemented
101	C₂×#31282	C₂³	1	8	yes	—
102	#7487871	C₂³	1	32	yes	complemented
103	#7487865	C₂³	1	16	yes	—
104	#7487865	C₂³	1	16	yes	—
105	#6437456	D₄	1	4	yes	complemented
106	#6437456	D₄	1	4	yes	complemented
107	#6437456	C₂³	1	4	yes	—
108	#6437456	C₂³	1	4	yes	—
109	#6437452	D₄	1	4	yes	complemented
110	#6437452	C₂³	1	4	yes	—
111	#6437449	C₂³	1	4	yes	—
112	#6437445	D₄	1	4	yes	complemented
113	#6437445	C₂³	1	4	yes	—
114	#6437437	D₄	1	4	yes	complemented
115	C₂×#23906	D₄	1	4	yes	complemented
116	C₂×#23906	C₂³	1	4	yes	—
117	#6407636	C₂³	1	8	yes	complemented
118	C₂×#23361	C₂³	1	4	yes	—
119	#6371456	D₄	1	2	yes	complemented
120	#6371456	C₂³	1	2	yes	—
121	#6370704	D₄	1	2	yes	complemented
122	#6348967	C₂³	1	8	yes	complemented
123	#6348967	C₂³	1	8	yes	complemented
124	C₂×#18529	C₂³	1	4	yes	complemented
125	C₂×#18524	C₂³	1	4	yes	—
126	C₂×#17741	C₂³	1	2	yes	complemented
127	#512862	C₂³	1	64	yes	complemented
128	#512663	C₂³	1	32	yes	complemented
129	C₂×#13595	C₂³	1	8	yes	complemented
130	C₂×#13584	C₂³	1	8	yes	—
131	C₂×#13561	C₂³	1	16	yes	—
132	#512122	C₂³	1	16	yes	complemented
133	#512119	C₂³	1	16	yes	complemented
134	#511771	C₂³	1	16	yes	complemented
135	#511771	C₂³	1	16	yes	complemented
136	#501097	C₂³	1	32	yes	complemented
137	#501096	C₂³	1	32	yes	complemented
138	#500179	C₂³	1	16	yes	complemented
139	#500177	C₂³	1	16	yes	complemented
140	#499832	C₂³	1	16	yes	—
141	#499831	C₂³	1	16	yes	—
142	#494596	C₂³	1	8	yes	—
143	#494370	C₂³	1	8	yes	complemented
144	C₂×#12759	C₂³	1	8	yes	complemented
145	#493431	C₂³	1	4	yes	complemented
146	#493430	C₂³	1	4	yes	—
147	#493430	C₂³	1	4	yes	complemented
148	#493372	C₂³	1	4	yes	complemented
149	#493370	C₂³	1	4	yes	complemented
150	C₂×#12693	C₂³	1	4	yes	complemented
151	#246957	C₂³	1	32	yes	complemented
152	#246930	C₂³	1	16	yes	complemented
153	#246927	C₂³	1	16	yes	—
154	#200885	C₂³	1	8	yes	complemented
155	#200876	C₂³	1	8	yes	complemented
156	#200851	C₂³	1	4	yes	—
157	#200848	C₂³	1	4	yes	complemented
158	#187836	C₂³	1	4	yes	complemented
159	#187824	C₂³	1	2	yes	—
160	#187824	C₂³	1	2	yes	complemented
161	#187811	C₂³	1	4	yes	complemented
162	#153305	C₂³	1	128	yes	complemented
163	#153189	C₂³	1	128	yes	complemented
164	#152717	C₂³	1	32	yes	complemented
165	#152716	C₂³	1	32	yes	complemented
166	#152679	C₂³	1	32	yes	complemented
167	#152679	C₂³	1	32	yes	complemented
168	#152602	C₂³	1	64	yes	complemented
169	#152477	C₂³	1	64	yes	complemented
170	#152323	C₂³	1	16	yes	complemented
171	#152322	C₂³	1	16	yes	complemented
172	#152191	C₂³	1	64	yes	complemented
173	#152103	C₂³	1	16	yes	complemented
174	#152103	C₂³	1	16	yes	complemented
175	#152069	C₂³	1	16	yes	complemented
176	#152049	C₂³	1	16	yes	complemented
177	#152018	C₂³	1	16	yes	complemented
178	#152017	C₂³	1	16	yes	complemented
179	C₂×#7493	C₂³	1	16	yes	complemented
180	C₂×H(7,𝔽₂)	C₂×D₄	1	2	yes	—
181	C₂³×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
182	#62852	C₂×D₄	1	4	yes	complemented
183	#62842	C₂×D₄	1	4	yes	—
184	#62842	C₂×D₄	1	4	yes	complemented
185	#62815	C₂×D₄	1	2	yes	—
186	#62814	C₂×D₄	1	4	yes	complemented
187	#62813	C₂×D₄	1	1	yes	characteristic
188	#62812	C₂×D₄	1	1	yes	characteristic
189	#62811	C₂×D₄	1	4	yes	complemented
190	C₂×#3498	C₂×D₄	1	1	yes	characteristic
191	C₂×#3498	C₂×D₄	1	1	yes	characteristic
192	C₂×#3498	C₂×D₄	1	2	yes	—
193	C₂×#3498	C₂×D₄	1	2	yes	—
194	C₂×#3498	C₂×D₄	1	2	yes	—
195	C₂×#3498	C₂×D₄	1	2	yes	—
196	C₂×#3498	C₂×D₄	1	2	yes	—
197	C₂×#3498	C₂⁴	1	1	yes	characteristic
198	C₂×#3498	C₂⁴	1	1	yes	characteristic
199	C₂×#3498	C₂⁴	1	2	yes	—
200	C₂×#3484	C₂×D₄	1	4	yes	—
201	C₂×#3484	C₂×D₄	1	4	yes	complemented
202	C₂²×D₄²	C₂⁴	1	2	yes	—
203	C₂²×D₄²	C₂⁴	1	2	yes	—
204	C₂²×D₄²	C₂⁴	1	2	yes	—
205	#62686	C₂×D₄	1	4	yes	complemented
206	C₂²×#535	C₂×D₄	1	2	yes	—
207	C₂²×#535	C₂×D₄	1	2	yes	—
208	C₂²×#535	C₂⁴	1	2	yes	—
209	C₂×#3444	C₂×D₄	1	2	yes	—
210	C₂²×#532	C₂×D₄	1	1	yes	characteristic
211	C₂²×#532	C₂×D₄	1	2	yes	—
212	C₂³×#127	C₂×D₄	1	2	yes	—
213	C₂³×#127	C₂⁴	1	1	yes	characteristic
214	#62652	C₂×D₄	1	2	yes	—
215	C₂²×C₄×#41	C₂×D₄	1	1	yes	characteristic
216	#61110	C₂⁴	1	16	yes	—
217	#60806	C₂×D₄	1	8	yes	—
218	#60806	C₂×D₄	1	8	yes	complemented
219	#60806	C₂×D₄	1	8	yes	complemented
220	#60806	C₂⁴	1	8	yes	—
221	#60802	C₂×D₄	1	8	yes	complemented
222	#60799	C₂×D₄	1	8	yes	complemented
223	#60798	C₂×D₄	1	4	yes	—
224	#60798	C₂×D₄	1	4	yes	—
225	#60798	C₂⁴	1	4	yes	—
226	#60798	C₂⁴	1	4	yes	—
227	#60644	C₂×D₄	1	4	yes	—
228	#60644	C₂×D₄	1	4	yes	complemented
229	#60644	C₂×D₄	1	4	yes	complemented
230	#60644	C₂⁴	1	4	yes	—
231	#60639	C₂×D₄	1	2	yes	—
232	#60639	C₂×D₄	1	2	yes	—
233	C₂×#3151	C₂×D₄	1	2	yes	—
234	C₂×#3151	C₂⁴	1	2	yes	—
235	#60619	C₂×D₄	1	4	yes	—
236	#60619	C₂×D₄	1	4	yes	complemented
237	#60619	C₂×D₄	1	4	yes	complemented
238	#60619	C₂⁴	1	4	yes	—
239	#60618	C₂×D₄	1	2	yes	—
240	#60618	C₂×D₄	1	2	yes	—
241	C₂×#3138	C₂×D₄	1	2	yes	—
242	C₂×#3138	C₂⁴	1	2	yes	—
243	C₂×#3021	C₂×D₄	1	4	yes	complemented
244	C₂×#3021	C₂⁴	1	4	yes	—
245	C₂×#3019	C₂×D₄	1	4	yes	—
246	C₂×#3019	C₂×D₄	1	4	yes	—
247	C₂×#3019	C₂×D₄	1	4	yes	complemented
248	C₂×#3019	C₂⁴	1	4	yes	—
249	C₂×#3018	C₂×D₄	1	4	yes	—
250	C₂×#3018	C₂×D₄	1	4	yes	complemented
251	C₂²×#453	C₂×D₄	1	4	yes	—
252	C₂²×#453	C₂×D₄	1	4	yes	—
253	C₂²×#453	C₂×D₄	1	4	yes	complemented
254	C₂²×#453	C₂⁴	1	4	yes	—
255	#60125	C₂×D₄	1	4	yes	complemented
256	#60124	C₂×D₄	1	4	yes	complemented
257	#60123	C₂×D₄	1	2	yes	—
258	C₂×#2920	C₂×D₄	1	2	yes	—
259	C₂×#2888	C₂×D₄	1	2	yes	—
260	C₂×#2888	C₂×D₄	1	2	yes	—
261	C₄×#568	C₂×D₄	1	1	yes	characteristic
262	C₄×#568	C₂×D₄	1	1	yes	characteristic
263	#52004	C₂⁴	1	8	yes	—
264	#52004	C₂⁴	1	8	yes	—
265	#34364	C₂⁴	1	2	yes	—
266	#34364	C₂⁴	1	2	yes	—
267	C₂×#2380	C₂⁴	1	2	yes	—
268	C₂×#2196	C₂⁴	1	32	yes	—
269	C₂×#2128	C₂⁴	1	8	yes	—
270	C₂×#2127	C₂⁴	1	8	yes	—
271	C₂²×#353	C₂⁴	1	8	yes	—
272	#31282	C₂⁴	1	32	yes	—
273	#23913	C₂×D₄	1	8	yes	complemented
274	#23913	C₂⁴	1	8	yes	—
275	#23912	C₂×D₄	1	8	yes	complemented
276	#23912	C₂×D₄	1	8	yes	complemented
277	#23912	C₂×D₄	1	8	yes	complemented
278	#23912	C₂⁴	1	8	yes	—
279	#23908	C₂×D₄	1	8	yes	—
280	#23908	C₂×D₄	1	8	yes	complemented
281	#23907	C₂×D₄	1	8	yes	complemented
282	#23906	C₂×D₄	1	8	yes	—
283	#23906	C₂×D₄	1	8	yes	—
284	#23906	C₂×D₄	1	8	yes	—
285	#23906	C₂×D₄	1	8	yes	complemented
286	#23906	C₂×D₄	1	8	yes	complemented
287	#23906	C₂⁴	1	8	yes	—
288	#23906	C₂⁴	1	8	yes	—
289	#23361	C₂⁴	1	16	yes	—
290	#20956	C₂×D₄	1	4	yes	complemented
291	#20956	C₂⁴	1	4	yes	—
292	#20953	C₂×D₄	1	4	yes	—
293	#20953	C₂×D₄	1	4	yes	—
294	#20953	C₂×D₄	1	4	yes	complemented
295	#20953	C₂⁴	1	4	yes	—
296	#20952	C₂×D₄	1	4	yes	—
297	#20952	C₂×D₄	1	4	yes	complemented
298	C₂×#1887	C₂×D₄	1	4	yes	—
299	C₂×#1887	C₂×D₄	1	4	yes	—
300	C₂×#1887	C₂×D₄	1	4	yes	complemented
301	C₂×#1887	C₂⁴	1	4	yes	—
302	#20592	C₂×D₄	1	4	yes	—
303	#20592	C₂×D₄	1	4	yes	complemented
304	#20592	C₂×D₄	1	4	yes	complemented
305	#20591	C₂×D₄	1	4	yes	complemented
306	C₂×#1783	C₂×D₄	1	4	yes	—
307	C₂×#1783	C₂×D₄	1	4	yes	complemented
308	#18529	C₂⁴	1	16	yes	—
309	#18524	C₂⁴	1	16	yes	—
310	#17741	C₂⁴	1	4	yes	—
311	#17741	C₂⁴	1	4	yes	—
312	C₂×#1555	C₂⁴	1	4	yes	—
313	#13595	C₂⁴	1	32	yes	—
314	#13584	C₂⁴	1	32	yes	—
315	#13561	C₂⁴	1	64	yes	—
316	#13049	C₂⁴	1	32	yes	—
317	#12966	C₂⁴	1	32	yes	—
318	#12759	C₂⁴	1	32	yes	—
319	#12697	C₂⁴	1	8	yes	—
320	#12696	C₂⁴	1	8	yes	—
321	#12693	C₂⁴	1	8	yes	—
322	#12693	C₂⁴	1	8	yes	—
323	#9428	C₂⁴	1	16	yes	—
324	#9425	C₂⁴	1	16	yes	—
325	#8522	C₂⁴	1	8	yes	—
326	#8522	C₂⁴	1	8	yes	—
327	#7493	C₂⁴	1	64	yes	—
328	C₂×#585	C₂²×D₄	1	4	yes	—
329	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
330	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
331	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
332	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
333	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
334	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
335	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
336	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
337	C₂²×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
338	C₂²×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
339	C₂³×#41	#120	1	2	yes	—
340	C₂³×#41	#120	1	2	yes	—
341	C₂³×#41	#120	1	1	yes	characteristic
342	C₂³×#41	C₂²×D₄	1	2	yes	—
343	C₂⁴×D₄	#120	1	2	yes	—
344	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
345	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
346	#3485	C₂²×D₄	1	8	yes	—
347	#3484	C₂²×D₄	1	8	yes	—
348	#3484	C₂²×D₄	1	8	yes	—
349	#3484	C₂²×D₄	1	8	yes	—
350	C₂×D₄²	C₂⁵	1	4	yes	—
351	#3458	C₂²×D₄	1	4	yes	—
352	#3455	C₂²×D₄	1	8	yes	—
353	#3449	C₂²×D₄	1	4	yes	—
354	C₂×#535	#120	1	2	yes	—
355	C₂×#535	#120	1	2	yes	—
356	C₂×#535	#120	1	2	yes	—
357	C₂×#535	#120	1	2	yes	—
358	C₂×#535	#120	1	2	yes	—
359	C₂×#535	#120	1	2	yes	—
360	C₂×#535	#120	1	2	yes	—
361	C₂×#535	#120	1	2	yes	—
362	C₂×#535	C₂²×D₄	1	2	yes	—
363	C₂×#535	C₂²×D₄	1	2	yes	—
364	C₂×#535	C₂²×D₄	1	2	yes	—
365	C₂×#535	C₂²×D₄	1	2	yes	—
366	C₂×#535	C₂²×D₄	1	2	yes	—
367	C₂×#535	C₂²×D₄	1	2	yes	—
368	C₂×#535	C₂²×D₄	1	2	yes	—
369	C₂×#535	C₂²×D₄	1	2	yes	—
370	C₂×#535	C₂²×D₄	1	2	yes	—
371	C₂×#535	C₂²×D₄	1	2	yes	—
372	C₂×#535	C₂²×D₄	1	2	yes	—
373	C₂×#535	C₂²×D₄	1	2	yes	—
374	C₂×#535	C₂²×D₄	1	2	yes	—
375	C₂×#535	C₂²×D₄	1	2	yes	—
376	C₂×#535	C₂⁵	1	2	yes	—
377	C₂×#535	C₂⁵	1	2	yes	—
378	#3444	C₂²×D₄	1	4	yes	—
379	#3444	C₂²×D₄	1	4	yes	—
380	C₂×#533	C₂²×D₄	1	2	yes	—
381	C₂×#532	#120	1	2	yes	—
382	C₂×#532	#120	1	2	yes	—
383	C₂×#532	#120	1	2	yes	—
384	C₂×#532	#120	1	2	yes	—
385	C₂×#532	#120	1	2	yes	—
386	C₂×#532	#120	1	1	yes	characteristic
387	C₂×#532	#120	1	1	yes	characteristic
388	C₂×#532	C₂²×D₄	1	2	yes	—
389	C₂×#532	C₂²×D₄	1	2	yes	—
390	C₂×#532	C₂²×D₄	1	2	yes	—
391	C₂×#532	C₂²×D₄	1	2	yes	—
392	C₂×#532	C₂²×D₄	1	2	yes	—
393	C₂×#532	C₂²×D₄	1	1	yes	characteristic
394	C₂×#532	C₂²×D₄	1	1	yes	characteristic
395	C₂×#532	C₂²×D₄	1	2	yes	—
396	C₂²×C₄⋊Q₈	#120	1	1	yes	characteristic
397	C₂²×#127	#120	1	2	yes	—
398	C₂²×#127	#120	1	2	yes	—
399	C₂²×#127	#120	1	2	yes	—
400	C₂²×#127	#120	1	2	yes	—
401	C₂²×#127	#120	1	1	yes	characteristic
402	C₂²×#127	#120	1	2	yes	—
403	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
404	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
405	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
406	C₂²×#127	C₂²×D₄	1	2	yes	—
407	C₂²×#127	C₂²×D₄	1	2	yes	—
408	C₂²×#127	C₂²×D₄	1	2	yes	—
409	C₂²×#127	C₂²×D₄	1	2	yes	—
410	C₂²×#127	C₂²×D₄	1	2	yes	—
411	C₂²×#127	C₂²×D₄	1	2	yes	—
412	C₂²×#127	C₂²×D₄	1	2	yes	—
413	C₂²×#127	C₂²×D₄	1	2	yes	—
414	C₂²×#127	C₂⁵	1	1	yes	characteristic
415	C₂²×#127	C₂⁵	1	1	yes	characteristic
416	C₂²×#127	C₂⁵	1	1	yes	characteristic
417	C₂²×#124	#120	1	2	yes	—
418	C₂²×#124	C₂²×D₄	1	2	yes	—
419	C₂²×#124	C₂²×D₄	1	2	yes	—
420	#3428	C₂²×D₄	1	4	yes	—
421	C₂×#518	C₂²×D₄	1	4	yes	—
422	C₂×#518	C₂²×D₄	1	4	yes	—
423	C₂×C₄×#41	#120	1	1	yes	characteristic
424	C₂×C₄×#41	#120	1	1	yes	characteristic
425	C₂×C₄×#41	#120	1	2	yes	—
426	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×#41	C₂²×D₄	1	2	yes	—
429	C₂²×#117	#120	1	1	yes	characteristic
430	C₂²×#117	C₂²×D₄	1	2	yes	—
431	C₂³×C₄²	#120	1	2	yes	—
432	C₂³×C₄²	C₂²×D₄	1	1	yes	characteristic
433	#3153	C₂²×D₄	1	8	yes	—
434	#3153	C₂²×D₄	1	8	yes	—
435	#3151	C₂²×D₄	1	4	yes	—
436	#3151	C₂²×D₄	1	4	yes	—
437	#3151	C₂²×D₄	1	4	yes	—
438	#3151	H(5,𝔽₂)	1	8	yes	—
439	#3151	C₂⁵	1	4	yes	—
440	C₂×#493	H(5,𝔽₂)	1	4	yes	—
441	C₂×#492	H(5,𝔽₂)	1	4	yes	—
442	#3140	C₂²×D₄	1	8	yes	—
443	#3140	C₂²×D₄	1	8	yes	—
444	#3138	C₂²×D₄	1	4	yes	—
445	#3138	C₂²×D₄	1	4	yes	—
446	#3138	C₂²×D₄	1	4	yes	—
447	#3138	C₂⁵	1	4	yes	—
448	C₂×#455	C₂²×D₄	1	8	yes	—
449	C₂×#455	C₂²×D₄	1	8	yes	—
450	C₂×#453	C₂²×D₄	1	8	yes	—
451	C₂×#453	C₂²×D₄	1	8	yes	—
452	C₂×#453	C₂²×D₄	1	8	yes	—
453	C₂×#453	C₂²×D₄	1	8	yes	—
454	C₂×#453	C₂²×D₄	1	8	yes	—
455	C₂×#453	C₂⁵	1	8	yes	—
456	#2921	C₂²×D₄	1	8	yes	—
457	#2920	C₂²×D₄	1	4	yes	—
458	#2920	C₂²×D₄	1	4	yes	—
459	C₂×#413	C₂²×D₄	1	4	yes	—
460	C₂×#413	C₂²×D₄	1	4	yes	—
461	C₂²×#100	C₂²×D₄	1	4	yes	—
462	C₂²×#100	C₂²×D₄	1	4	yes	—
463	C₂²×#100	C₂²×D₄	1	4	yes	—
464	C₂²×#100	C₂²×D₄	1	4	yes	—
465	#2873	C₂²×D₄	1	4	yes	—
466	#2873	C₂²×D₄	1	4	yes	—
467	C₂×C₄×M₁₆	C₂²×D₄	1	2	yes	—
468	C₂×C₄×M₁₆	C₂²×D₄	1	2	yes	—
469	#2380	C₂⁵	1	4	yes	—
470	C₂×#353	C₂⁵	1	16	yes	—
471	#1887	C₂²×D₄	1	8	yes	—
472	#1887	C₂²×D₄	1	8	yes	—
473	#1887	C₂²×D₄	1	8	yes	—
474	#1887	C₂²×D₄	1	8	yes	—
475	#1887	C₂²×D₄	1	8	yes	—
476	#1887	C₂⁵	1	8	yes	—
477	#1885	C₂²×D₄	1	8	yes	—
478	#1885	C₂²×D₄	1	8	yes	—
479	#1785	C₂²×D₄	1	8	yes	—
480	#1783	C₂²×D₄	1	8	yes	—
481	#1783	C₂²×D₄	1	8	yes	—
482	#1783	C₂²×D₄	1	8	yes	—
483	#1555	C₂⁵	1	8	yes	—
484	C₂×H(5,𝔽₂)	C₂³×D₄	1	8	yes	—
485	C₂²×#41	B(4,𝔽₂)	1	1	yes	characteristic
486	C₂²×#41	B(4,𝔽₂)	1	1	yes	characteristic
487	C₂²×#41	B(4,𝔽₂)	1	2	yes	—
488	C₂²×#41	C₂×#120	1	1	yes	characteristic
489	C₂²×#41	C₂×#120	1	1	yes	characteristic
490	C₂²×#41	C₂×#120	1	2	yes	—
491	C₂²×#41	C₂×#120	1	2	yes	—
492	C₂²×#41	C₂×#120	1	2	yes	—
493	C₂²×#41	C₂×#120	1	2	yes	—
494	C₂²×#41	C₂×#120	1	2	yes	—
495	C₂²×#41	C₂×#120	1	2	yes	—
496	C₂²×#41	C₂×#120	1	2	yes	—
497	C₂²×#41	C₂×#120	1	2	yes	—
498	C₂²×#41	C₂×#120	1	2	yes	—
499	C₂²×#41	C₂×#120	1	2	yes	—
500	C₂²×#41	C₂×#120	1	2	yes	—
501	C₂²×#41	C₂³×D₄	1	2	yes	—
502	C₂²×#41	C₂³×D₄	1	2	yes	—
503	C₂³×Q₈	B(4,𝔽₂)	1	1	yes	characteristic
504	C₂³×Q₈	C₂×#120	1	2	yes	—
505	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
506	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
507	C₂³×D₄	C₂×#120	1	2	yes	—
508	C₂³×D₄	C₂×#120	1	2	yes	—
509	C₂³×D₄	C₂×#120	1	2	yes	—
510	C₂³×D₄	C₂×#120	1	2	yes	—
511	C₂³×D₄	C₂×#120	1	2	yes	—
512	C₂³×D₄	C₂×#120	1	2	yes	—
513	C₂³×D₄	C₂×#120	1	2	yes	—
514	C₂³×D₄	C₂×#120	1	2	yes	—
515	C₂³×D₄	C₂×#120	1	2	yes	—
516	C₂³×D₄	C₂×#120	1	2	yes	—
517	C₂³×D₄	C₂³×D₄	1	2	yes	—
518	C₂³×D₄	C₂³×D₄	1	2	yes	—
519	C₂³×D₄	C₂³×D₄	1	2	yes	—
520	C₂³×D₄	C₂³×D₄	1	2	yes	—
521	C₂³×D₄	C₂³×D₄	1	2	yes	—
522	C₂⁴×C₄	C₂×#120	1	2	yes	—
523	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
524	#533	C₂³×D₄	1	4	yes	—
525	#532	#534	1	4	yes	complemented
526	#532	C₂³×D₄	1	4	yes	—
527	C₂×C₄⋊Q₈	C₂×#120	1	1	yes	characteristic
528	C₂×C₄⋊Q₈	C₂×#120	1	1	yes	characteristic
529	C₂×C₄⋊Q₈	C₂×#120	1	2	yes	—
530	C₂×C₄⋊Q₈	#534	1	2	yes	complemented
531	C₂×#127	C₂×#120	1	1	yes	characteristic
532	C₂×#127	C₂×#120	1	1	yes	characteristic
533	C₂×#127	C₂×#120	1	2	yes	—
534	C₂×#127	C₂×#120	1	2	yes	—
535	C₂×#127	C₂×#120	1	2	yes	—
536	C₂×#127	C₂×#120	1	2	yes	—
537	C₂×#127	C₂×#120	1	2	yes	—
538	C₂×#127	C₂×#120	1	2	yes	—
539	C₂×#127	C₂×#120	1	2	yes	—
540	C₂×#127	C₂×#120	1	2	yes	—
541	C₂×#127	C₂×#120	1	2	yes	—
542	C₂×#127	C₂×#120	1	2	yes	—
543	C₂×#127	#534	1	2	yes	complemented
544	C₂×#127	C₂³×D₄	1	1	yes	characteristic
545	C₂×#127	C₂³×D₄	1	1	yes	characteristic
546	C₂×#127	C₂³×D₄	1	1	yes	characteristic
547	C₂×#127	C₂³×D₄	1	2	yes	—
548	C₂×#127	C₂³×D₄	1	2	yes	—
549	C₂×#127	C₂³×D₄	1	2	yes	—
550	C₂×#127	C₂³×D₄	1	2	yes	—
551	C₂×#127	C₂³×D₄	1	2	yes	—
552	C₂×#127	C₂×H(5,𝔽₂)	1	4	yes	—
553	C₂×#127	C₂×H(5,𝔽₂)	1	4	yes	—
554	C₂×#127	C₂⁶	1	1	yes	characteristic
555	C₂×#124	C₂×#120	1	2	yes	—
556	C₂×#124	C₂×#120	1	2	yes	—
557	C₂×#124	C₂×#120	1	2	yes	—
558	C₂×#124	C₂×#120	1	2	yes	—
559	C₂×#124	C₂×#120	1	2	yes	—
560	C₂×#124	C₂×#120	1	2	yes	—
561	C₂×#124	C₂×#120	1	2	yes	—
562	C₂×#124	C₂×#120	1	2	yes	—
563	C₂×#124	C₂³×D₄	1	2	yes	—
564	C₂×#124	C₂³×D₄	1	2	yes	—
565	C₂×#124	C₂³×D₄	1	2	yes	—
566	C₂×#124	C₂³×D₄	1	2	yes	—
567	#518	C₂³×D₄	1	8	yes	—
568	C₂×#117	C₂×#120	1	1	yes	characteristic
569	C₂×#117	C₂×#120	1	1	yes	characteristic
570	C₂×#117	C₂×#120	1	2	yes	—
571	C₂×#117	C₂×#120	1	2	yes	—
572	C₂×#117	C₂×#120	1	2	yes	—
573	C₂×#117	C₂³×D₄	1	2	yes	—
574	C₂×#117	C₂³×D₄	1	2	yes	—
575	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
576	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
577	C₂²×C₄²	C₂×#120	1	2	yes	—
578	C₂²×C₄²	C₂×#120	1	2	yes	—
579	C₂²×C₄²	C₂×#120	1	2	yes	—
580	C₂²×C₄²	C₂×#120	1	2	yes	—
581	C₂²×C₄²	C₂×#120	1	2	yes	—
582	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
583	C₂²×C₄²	C₂³×D₄	1	1	yes	characteristic
584	C₂²×C₄²	C₂³×D₄	1	1	yes	characteristic
585	C₂²×C₄²	C₂³×D₄	1	1	yes	characteristic
586	#493	#534	1	8	yes	complemented
587	#493	C₂×H(5,𝔽₂)	1	8	yes	—
588	#492	#534	1	8	yes	complemented
589	#492	C₂×H(5,𝔽₂)	1	8	yes	—
590	C₂×#100	C₂³×D₄	1	8	yes	—
591	C₂×#100	C₂³×D₄	1	8	yes	—
592	C₄×M₁₆	#534	1	4	yes	complemented
593	C₄×M₁₆	C₂³×D₄	1	4	yes	—
594	C₄×M₁₆	C₂³×D₄	1	4	yes	—
595	C₂×C₄×C₈	#534	1	4	yes	complemented
596	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
597	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
598	C₂²×Q₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
599	C₂²×Q₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
600	C₂²×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
601	C₂²×Q₈	C₂²×#120	1	2	yes	—
602	C₂²×Q₈	C₂²×#120	1	2	yes	—
603	C₂²×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
604	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
605	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
606	C₂²×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
607	C₂²×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
608	C₂²×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
609	C₂²×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
610	C₂²×D₄	C₂²×#120	1	2	yes	—
611	C₂²×D₄	C₂²×#120	1	2	yes	—
612	C₂²×D₄	C₂²×#120	1	2	yes	—
613	C₂²×D₄	C₂²×#120	1	2	yes	—
614	C₂²×D₄	C₂²×#120	1	2	yes	—
615	C₂²×D₄	#3484	1	8	yes	—
616	C₂²×D₄	C₂⁴×D₄	1	2	yes	—
617	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
618	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
619	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
620	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
621	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
622	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
623	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
624	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
625	C₂³×C₄	C₂²×#120	1	2	yes	—
626	C₂³×C₄	C₂²×#120	1	2	yes	—
627	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
628	C₄⋊Q₈	C₂×#534	1	4	yes	—
629	#127	C₂×#534	1	4	yes	—
630	#127	C₂×#534	1	4	yes	—
631	#127	#3484	1	4	yes	—
632	#127	#3484	1	4	yes	—
633	#127	C₂²×H(5,𝔽₂)	1	4	yes	—
634	C₂×C₄²	#3026	1	4	yes	—
635	C₂×C₄²	C₂²×#120	1	1	yes	characteristic
636	C₂×C₄²	C₂²×#120	1	1	yes	characteristic
637	C₂×C₄²	C₂²×#120	1	1	yes	characteristic
638	C₂×C₄²	C₂²×#120	1	2	yes	—
639	C₂×C₄²	C₂²×#120	1	2	yes	—
640	C₂×C₄²	C₂×#534	1	2	yes	—
641	C₂×C₄²	C₂×#534	1	2	yes	—
642	C₂×C₄²	C₂⁴×D₄	1	1	yes	characteristic
643	C₄×C₈	C₂×#534	1	8	yes	—
644	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
645	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
646	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
647	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
648	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
649	C₂×D₄	#33551	1	8	yes	—
650	C₂×D₄	#34980	1	4	yes	—
651	C₂×D₄	C₂×#3484	1	4	yes	—
652	C₂²×C₄	#34980	1	2	yes	—
653	C₂²×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
654	C₂²×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
655	C₂²×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
656	C₂²×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
657	C₂²×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
658	C₂²×C₄	C₂×#3026	1	2	yes	—
659	C₂²×C₄	C₂³×#120	1	1	yes	characteristic
660	C₄²	#34980	1	1	yes	characteristic
661	C₄²	#34980	1	1	yes	characteristic
662	C₄²	C₂×#3026	1	2	yes	—
663	C₄²	C₂×#3026	1	2	yes	—
664	C₄²	C₂²×#534	1	2	yes	—
665	C₂³	#6470225	1	2	yes	—
666	C₂³	C₂×#33551	1	4	yes	—
667	C₂³	C₂×#33551	1	4	yes	—
668	C₂³	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
669	C₂×C₄	#6470225	1	2	yes	—
670	C₂×C₄	C₂×#33551	1	4	yes	—
671	C₂×C₄	C₂×#34980	1	1	yes	characteristic
672	C₂×C₄	C₂²×#3026	1	1	yes	characteristic
673	C₂²	#72210575	1	4	yes	—
674	C₂²	C₂²×#33551	1	2	yes	—
675	C₂²	C₂×#6470225	1	1	yes	characteristic
676	C₂	C₂×#72210575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#72210575
commutator, Frattini, cosocle	C₂×#127	C₂⁶
LCS	G ▷ C₂×#127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂³×#41 ◁ C₂²×#3498 ◁ G
LECS	G ▷ C₂×#127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72338585	C₂	semidirect
2. #72338584	C₂	semidirect
3. #72338583	C₂	semidirect
4. #72338579	C₂	semidirect
6. #72338576	C₂	semidirect
7. #72338575	C₂²	semidirect
8. #72338207	C₂²	semidirect
9. #72317785	C₂	semidirect
10. #72317775	C₂²	semidirect
11. #72317770	C₂²	semidirect
12. #72317757	C₂²	semidirect
13. #72317732	C₂²	semidirect
14. #72317722	C₂²	semidirect
15. #72317711	C₂²	semidirect
16. #72306961	C₂	semidirect
17. #72306954	C₂²	semidirect
18. #72306949	C₂²	semidirect
19. #72306941	C₂	semidirect
20. #72306939	C₂²	semidirect
21. #72306935	C₂	semidirect
22. #72306931	C₂	semidirect
23. #72306905	C₂²	semidirect
24. #72306903	C₂²	semidirect
25. #72306901	C₂²	semidirect
26. #72306882	C₂²	semidirect
27. #72306880	C₂²	semidirect
28. #72306437	C₂²	semidirect
29. #72306375	C₂²	semidirect
30. #72306361	C₂²	semidirect
31. #72306324	C₂²	semidirect
32. #72306310	C₂²	semidirect
34. #72281710	C₂²	semidirect
35. #72256107	C₂	semidirect
36. #72252021	C₂²	semidirect
38. #72252013	C₂²	semidirect
39. #72252010	C₂²	semidirect
40. #72251980	C₂²	semidirect
41. C₂×#72216600	C₂	semidirect
42. C₂×#512862	C₂²	semidirect
43. C₂×#152602	C₂²	semidirect
45. C₂×#153189	C₂²	semidirect
46. C₂×#152103	C₂²	semidirect
47. C₂×#152679	C₂²	semidirect
48. #72249464	C₂²	semidirect
49. #72236657	C₂²	semidirect
51. C₂×#6348967	C₂²	semidirect
52. C₂×#511771	C₂²	semidirect
53. C₂×#7737411	C₂²	semidirect
54. #72216611	C₂	semidirect
55. #72216603	C₂²	semidirect
56. #72216601	C₂²	semidirect
57. #72216600	C₂²	semidirect
58. #72216600	C₂²	semidirect
59. #72216589	C₂²	semidirect
60. #72216584	C₂²	semidirect
61. #72216577	C₂²	semidirect
62. #72216567	C₂²	semidirect
63. #72216138	C₂²	semidirect
64. #72215721	C₂²	semidirect
65. #72215568	C₂²	semidirect
66. #72213685	C₂²	semidirect
67. #72213671	C₂²	semidirect
68. #72213519	C₂²	semidirect
69. #72213428	C₂²	semidirect
70. #72210575	C₂²	semidirect
71. #10586066	D₄	semidirect
72. #10585995	D₄	semidirect
74. C₂³×D₄²	C₂³	semidirect
75. #10576178	C₂³	semidirect
77. #10575560	D₄	semidirect
79. #10575552	D₄	semidirect
81. #10575547	D₄	semidirect
83. #10575509	D₄	semidirect
85. #10575254	D₄	semidirect
87. #10575219	D₄	semidirect
89. C₂×#60388	D₄	semidirect
91. #10574126	D₄	semidirect
93. #7737411	C₂³	semidirect
94. #7737411	C₂³	semidirect
95. C₂×#52004	C₂³	semidirect
96. C₂×#34364	C₂³	semidirect
98. C₂×#33359	C₂³	semidirect
99. #7504294	C₂³	semidirect
100. #7504292	C₂³	semidirect
102. #7487871	C₂³	semidirect
105. #6437456	D₄	semidirect
106. #6437456	D₄	semidirect
109. #6437452	D₄	semidirect
112. #6437445	D₄	semidirect
114. #6437437	D₄	semidirect
115. C₂×#23906	D₄	semidirect
117. #6407636	C₂³	semidirect
119. #6371456	D₄	semidirect
121. #6370704	D₄	semidirect
122. #6348967	C₂³	semidirect
123. #6348967	C₂³	semidirect
124. C₂×#18529	C₂³	semidirect
126. C₂×#17741	C₂³	semidirect
127. #512862	C₂³	semidirect
128. #512663	C₂³	semidirect
129. C₂×#13595	C₂³	semidirect
132. #512122	C₂³	semidirect
133. #512119	C₂³	semidirect
134. #511771	C₂³	semidirect
135. #511771	C₂³	semidirect
136. #501097	C₂³	semidirect
137. #501096	C₂³	semidirect
138. #500179	C₂³	semidirect
139. #500177	C₂³	semidirect
143. #494370	C₂³	semidirect
144. C₂×#12759	C₂³	semidirect
145. #493431	C₂³	semidirect
147. #493430	C₂³	semidirect
148. #493372	C₂³	semidirect
149. #493370	C₂³	semidirect
150. C₂×#12693	C₂³	semidirect
151. #246957	C₂³	semidirect
152. #246930	C₂³	semidirect
154. #200885	C₂³	semidirect
155. #200876	C₂³	semidirect
157. #200848	C₂³	semidirect
158. #187836	C₂³	semidirect
160. #187824	C₂³	semidirect
161. #187811	C₂³	semidirect
162. #153305	C₂³	semidirect
163. #153189	C₂³	semidirect
164. #152717	C₂³	semidirect
165. #152716	C₂³	semidirect
166. #152679	C₂³	semidirect
167. #152679	C₂³	semidirect
168. #152602	C₂³	semidirect
169. #152477	C₂³	semidirect
170. #152323	C₂³	semidirect
171. #152322	C₂³	semidirect
172. #152191	C₂³	semidirect
173. #152103	C₂³	semidirect
174. #152103	C₂³	semidirect
175. #152069	C₂³	semidirect
176. #152049	C₂³	semidirect
177. #152018	C₂³	semidirect
178. #152017	C₂³	semidirect
179. C₂×#7493	C₂³	semidirect
182. #62852	C₂×D₄	semidirect
184. #62842	C₂×D₄	semidirect
186. #62814	C₂×D₄	semidirect
189. #62811	C₂×D₄	semidirect
201. C₂×#3484	C₂×D₄	semidirect
205. #62686	C₂×D₄	semidirect
218. #60806	C₂×D₄	semidirect
219. #60806	C₂×D₄	semidirect
221. #60802	C₂×D₄	semidirect
222. #60799	C₂×D₄	semidirect
228. #60644	C₂×D₄	semidirect
229. #60644	C₂×D₄	semidirect
236. #60619	C₂×D₄	semidirect
237. #60619	C₂×D₄	semidirect
243. C₂×#3021	C₂×D₄	semidirect
247. C₂×#3019	C₂×D₄	semidirect
250. C₂×#3018	C₂×D₄	semidirect
253. C₂²×#453	C₂×D₄	semidirect
255. #60125	C₂×D₄	semidirect
256. #60124	C₂×D₄	semidirect
273. #23913	C₂×D₄	semidirect
275. #23912	C₂×D₄	semidirect
276. #23912	C₂×D₄	semidirect
277. #23912	C₂×D₄	semidirect
280. #23908	C₂×D₄	semidirect
281. #23907	C₂×D₄	semidirect
285. #23906	C₂×D₄	semidirect
286. #23906	C₂×D₄	semidirect
290. #20956	C₂×D₄	semidirect
294. #20953	C₂×D₄	semidirect
297. #20952	C₂×D₄	semidirect
300. C₂×#1887	C₂×D₄	semidirect
303. #20592	C₂×D₄	semidirect
304. #20592	C₂×D₄	semidirect
305. #20591	C₂×D₄	semidirect
307. C₂×#1783	C₂×D₄	semidirect
525. #532	#534	semidirect
530. C₂×C₄⋊Q₈	#534	semidirect
543. C₂×#127	#534	semidirect
586. #493	#534	semidirect
588. #492	#534	semidirect
592. C₄×M₁₆	#534	semidirect
595. C₂×C₄×C₈	#534	semidirect

Maximal subgroups

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

subgroup	index
#72338585	2
#72338584	2
#72338583	2
#72338579	2
#72338576	2
#72317785	2
#72306961	2
#72306941	2
#72306935	2
#72306931	2
#72256107	2
C₂×#72216600	2
#72216611	2