Subgroups — #72265983

Order 2048.

At least 13941 conjugacy classes of subgroups; only the 1000 normal subgroups are shown.

The subgroup lattice has 559 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72265982	C₂	1	2	yes	maximal, complemented
2	#72265981	C₂	1	4	yes	maximal, complemented
3	#72265980	C₂	1	2	yes	maximal, complemented
4	#72265979	C₂	1	2	yes	maximal, complemented
5	C₂×#133422	C₂	1	1	yes	maximal, characteristic, complemented
6	#72265961	C₂	1	1	yes	maximal, characteristic, complemented
7	#72265940	C₂	1	1	yes	maximal, characteristic, complemented
8	#72265933	C₂	1	1	yes	maximal, characteristic, complemented
9	#72258238	C₂	1	2	yes	maximal, complemented
10	#72258234	C₂	1	2	yes	maximal, complemented
11	#72256110	C₂	1	1	yes	maximal, characteristic, complemented
12	#72249671	C₂	1	4	yes	maximal, complemented
13	#72241074	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#251827	C₂	1	1	yes	maximal, characteristic, complemented
15	#72237832	C₂	1	2	yes	maximal, complemented
16	#72233116	C₂	1	2	yes	maximal, complemented
17	#72233116	C₂	1	2	yes	maximal, complemented
18	C₂²×#3026	C₂²	1	1	yes	characteristic, complemented
19	C₂²×#3026	C₂²	1	1	yes	characteristic, complemented
20	#9061456	C₂²	1	1	yes	characteristic, complemented
21	#9061085	C₂²	1	1	yes	characteristic, complemented
22	#9054448	C₂²	1	1	yes	characteristic, complemented
23	#9041087	C₂²	1	1	yes	characteristic, complemented
24	#8912605	C₂²	1	2	yes	complemented
25	#8905195	C₂²	1	2	yes	complemented
26	#7763449	C₂²	1	2	yes	—
27	#7763449	C₂²	1	2	yes	—
28	#7713911	C₂²	1	1	yes	characteristic
29	C₂×#46996	C₂²	1	1	yes	characteristic
30	#7630443	C₂²	1	1	yes	characteristic
31	C₂×#32898	C₂²	1	2	yes	complemented
32	#6628867	C₂²	1	2	yes	complemented
33	C₂×#20585	C₂²	1	1	yes	characteristic, complemented
34	#499815	C₂²	1	4	yes	complemented
35	#499812	C₂²	1	4	yes	complemented
36	#499807	C₂²	1	4	yes	complemented
37	#499804	C₂²	1	4	yes	complemented
38	#499800	C₂²	1	4	yes	complemented
39	#499795	C₂²	1	4	yes	complemented
40	#499792	C₂²	1	4	yes	complemented
41	#499787	C₂²	1	4	yes	complemented
42	#494713	C₂²	1	2	yes	complemented
43	#494713	C₂²	1	2	yes	complemented
44	C₂×#13086	C₂²	1	2	yes	complemented
45	C₂×#13086	C₂²	1	2	yes	complemented
46	#493357	C₂²	1	2	yes	complemented
47	#493357	C₂²	1	2	yes	complemented
48	#417543	C₂²	1	2	yes	complemented
49	#417543	C₂²	1	2	yes	complemented
50	#417542	C₂²	1	2	yes	complemented
51	#417542	C₂²	1	2	yes	complemented
52	C₂×#11166	C₂²	1	1	yes	characteristic, complemented
53	#357530	C₂²	1	1	yes	characteristic, complemented
54	C₂×#10972	C₂²	1	1	yes	characteristic, complemented
55	#251945	C₂²	1	4	yes	complemented
56	#251940	C₂²	1	2	yes	complemented
57	#251935	C₂²	1	2	yes	complemented
58	#251827	C₂²	1	2	yes	complemented
59	#251827	C₂²	1	4	yes	complemented
60	#251827	C₂²	1	2	yes	complemented
61	C₂×#9495	C₂²	1	2	yes	complemented
62	#201322	C₂²	1	2	yes	complemented
63	C₂×#8751	C₂²	1	1	yes	characteristic, complemented
64	C₂×#8746	C₂²	1	1	yes	characteristic, complemented
65	#133923	C₂²	1	2	yes	complemented
66	#133923	C₂²	1	2	yes	complemented
67	#133922	C₂²	1	2	yes	complemented
68	#133922	C₂²	1	2	yes	complemented
69	#133436	C₂²	1	2	yes	complemented
70	#133435	C₂²	1	2	yes	complemented
71	#133434	C₂²	1	4	yes	complemented
72	#133422	C₂²	1	2	yes	complemented
73	#133422	C₂²	1	4	yes	complemented
74	#133422	C₂²	1	2	yes	complemented
75	#133411	C₂²	1	4	yes	complemented
76	#133410	C₂²	1	4	yes	complemented
77	#133407	C₂²	1	4	yes	complemented
78	#133406	C₂²	1	4	yes	complemented
79	#133395	C₂²	1	4	yes	complemented
80	#133394	C₂²	1	4	yes	complemented
81	#133391	C₂²	1	4	yes	complemented
82	#133390	C₂²	1	4	yes	complemented
83	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
84	C₂×#3532	D₄	1	2	yes	complemented
85	C₂×#3532	D₄	1	2	yes	complemented
86	C₂²×#534	D₄	1	1	yes	characteristic, complemented
87	C₂²×#534	C₂³	1	1	yes	characteristic
88	C₂²×#534	C₂³	1	1	yes	characteristic
89	C₂²×#518	D₄	1	1	yes	characteristic, complemented
90	C₂×#3026	C₂³	1	2	yes	—
91	C₂×#3026	C₂³	1	2	yes	—
92	C₂²×#458	C₂³	1	2	yes	—
93	C₂²×B(4,𝔽₂)	C₂³	1	2	yes	—
94	C₂³×#99	C₂³	1	1	yes	characteristic
95	C₂³×#99	C₂³	1	1	yes	characteristic
96	#59191	D₄	1	2	yes	complemented
97	#59191	C₂³	1	2	yes	—
98	#58990	D₄	1	2	yes	complemented
99	#58990	C₂³	1	2	yes	—
100	#50856	D₄	1	2	yes	complemented
101	#50856	C₂³	1	2	yes	—
102	#50646	D₄	1	2	yes	complemented
103	#50646	C₂³	1	2	yes	—
104	#47848	D₄	1	2	yes	complemented
105	#47848	C₂³	1	2	yes	—
106	#47827	D₄	1	2	yes	complemented
107	#47827	C₂³	1	2	yes	—
108	#47035	D₄	1	1	yes	characteristic, complemented
109	#47035	C₂³	1	1	yes	characteristic
110	#47033	D₄	1	2	yes	complemented
111	#47033	C₂³	1	2	yes	—
112	#47031	D₄	1	1	yes	characteristic, complemented
113	#47031	C₂³	1	1	yes	characteristic
114	#46996	D₄	1	2	yes	complemented
115	#46996	D₄	1	1	yes	characteristic, complemented
116	#46996	D₄	1	1	yes	characteristic, complemented
117	#46996	C₂³	1	1	yes	characteristic
118	#46996	C₂³	1	1	yes	characteristic
119	#46996	C₂³	1	2	yes	—
120	#45455	D₄	1	2	yes	complemented
121	#45455	C₂³	1	2	yes	—
122	#45439	D₄	1	2	yes	complemented
123	#45439	C₂³	1	2	yes	—
124	#37479	D₄	1	1	yes	characteristic, complemented
125	#37454	D₄	1	1	yes	characteristic, complemented
126	#36737	D₄	1	2	yes	complemented
127	#36737	D₄	1	2	yes	complemented
128	#36714	D₄	1	2	yes	complemented
129	#36714	D₄	1	2	yes	complemented
130	C₂×#2840	D₄	1	1	yes	characteristic, complemented
131	#35447	D₄	1	1	yes	characteristic, complemented
132	#35447	D₄	1	1	yes	characteristic, complemented
133	#35447	C₂³	1	1	yes	characteristic
134	#35447	C₂³	1	1	yes	characteristic
135	#35348	D₄	1	1	yes	characteristic, complemented
136	#35348	D₄	1	1	yes	characteristic, complemented
137	#35348	C₂³	1	1	yes	characteristic
138	#35348	C₂³	1	1	yes	characteristic
139	#35222	C₂³	1	2	yes	—
140	C₂×#2403	D₄	1	1	yes	characteristic, complemented
141	C₂×#2403	C₂³	1	2	yes	—
142	#34407	D₄	1	2	yes	complemented
143	#34407	D₄	1	2	yes	complemented
144	#34396	D₄	1	2	yes	complemented
145	C₂×#2315	D₄	1	1	yes	characteristic, complemented
146	C₂×#2308	D₄	1	1	yes	characteristic, complemented
147	C₂×#2308	D₄	1	2	yes	complemented
148	C₂×#2308	C₂³	1	1	yes	characteristic
149	C₂×#2308	C₂³	1	1	yes	characteristic
150	#32898	C₂³	1	4	yes	—
151	#32898	C₂³	1	4	yes	—
152	#32891	C₂³	1	4	yes	—
153	#32888	C₂³	1	4	yes	—
154	C₂×#1783	C₂³	1	2	yes	—
155	#20585	C₂³	1	2	yes	—
156	#20585	C₂³	1	2	yes	—
157	C₂×#1781	C₂³	1	2	yes	—
158	#13090	C₂³	1	4	yes	—
159	#13090	C₂³	1	4	yes	—
160	#13088	C₂³	1	4	yes	—
161	#13088	C₂³	1	4	yes	—
162	#13086	C₂³	1	4	yes	—
163	#13086	C₂³	1	4	yes	—
164	#13086	C₂³	1	4	yes	—
165	#13086	C₂³	1	4	yes	—
166	#12690	C₂³	1	4	yes	—
167	#12690	C₂³	1	4	yes	—
168	#12688	C₂³	1	4	yes	—
169	#12687	C₂³	1	4	yes	—
170	#11166	C₂³	1	2	yes	—
171	#11166	C₂³	1	2	yes	—
172	#10992	C₂³	1	2	yes	—
173	#10991	C₂³	1	2	yes	—
174	#10972	C₂³	1	2	yes	—
175	#10972	C₂³	1	2	yes	—
176	#9495	C₂³	1	4	yes	—
177	#9495	C₂³	1	4	yes	—
178	#9463	C₂³	1	4	yes	—
179	#9459	C₂³	1	4	yes	—
180	#8751	C₂³	1	2	yes	—
181	#8751	C₂³	1	2	yes	—
182	#8746	C₂³	1	2	yes	—
183	#8746	C₂³	1	2	yes	—
184	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
185	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
186	C₂⁴×D₄	C₂×D₄	1	2	yes	—
187	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
189	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
190	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	complemented
191	C₂×#560	C₂×D₄	1	2	yes	complemented
192	C₂×#560	C₂×D₄	1	2	yes	complemented
193	C₂×#551	C₂×D₄	1	2	yes	complemented
194	C₂×#551	C₂×D₄	1	2	yes	complemented
195	C₂×D₄²	C₂×D₄	1	2	yes	complemented
196	C₂×D₄²	C₂×D₄	1	2	yes	complemented
197	C₂×#535	C₂×D₄	1	2	yes	—
198	C₂×#535	C₂×D₄	1	2	yes	—
199	C₂×#534	C₂×D₄	1	2	yes	—
200	C₂×#534	C₂×D₄	1	2	yes	—
201	C₂×#534	C₂×D₄	1	2	yes	—
202	C₂×#534	C₂×D₄	1	2	yes	—
203	C₂×#534	C₂×D₄	1	2	yes	—
204	C₂×#534	C₂×D₄	1	2	yes	—
205	C₂×#534	C₂×D₄	1	1	yes	characteristic
206	C₂×#534	C₂×D₄	1	1	yes	characteristic
207	C₂×#534	C₂⁴	1	1	yes	characteristic
208	C₂×#534	C₂⁴	1	1	yes	characteristic
209	C₂×#525	C₂×D₄	1	2	yes	—
210	C₂²×#123	C₂×D₄	1	2	yes	—
211	C₂²×#123	C₂×D₄	1	1	yes	characteristic
212	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
213	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
214	C₂²×#123	C₂⁴	1	1	yes	characteristic
215	C₂²×#120	C₂×D₄	1	2	yes	—
216	C₂²×#120	C₂×D₄	1	2	yes	—
217	C₂²×#120	C₂×D₄	1	2	yes	—
218	C₂²×#120	C₂×D₄	1	1	yes	characteristic
219	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
220	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
221	C₂²×#120	C₂⁴	1	1	yes	characteristic
222	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
223	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
224	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
225	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
229	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
230	C₂²×#99	C₂⁴	1	2	yes	—
231	C₂²×#99	C₂⁴	1	2	yes	—
232	#2840	C₂×D₄	1	2	yes	complemented
233	#2840	C₂×D₄	1	1	yes	characteristic, complemented
234	#2840	C₂×D₄	1	1	yes	characteristic, complemented
235	#2817	C₂×D₄	1	1	yes	characteristic, complemented
236	#2816	C₂×D₄	1	2	yes	complemented
237	#2815	C₂×D₄	1	1	yes	characteristic, complemented
238	#2717	C₂×D₄	1	2	yes	complemented
239	#2717	C₂×D₄	1	2	yes	complemented
240	#2709	C₂×D₄	1	2	yes	complemented
241	#2709	C₂×D₄	1	2	yes	complemented
242	#2697	C₂×D₄	1	2	yes	complemented
243	#2697	C₂×D₄	1	2	yes	complemented
244	#2697	C₂×D₄	1	2	yes	complemented
245	#2697	C₂×D₄	1	2	yes	complemented
246	#2684	C₂×D₄	1	2	yes	complemented
247	#2684	C₂×D₄	1	2	yes	complemented
248	#2679	C₂×D₄	1	2	yes	complemented
249	#2679	C₂×D₄	1	2	yes	complemented
250	#2679	C₂×D₄	1	2	yes	complemented
251	#2679	C₂×D₄	1	2	yes	complemented
252	#2669	C₂×D₄	1	2	yes	complemented
253	#2669	C₂×D₄	1	2	yes	complemented
254	#2608	C₂×D₄	1	2	yes	complemented
255	#2607	C₂×D₄	1	1	yes	characteristic, complemented
256	#2607	C₂×D₄	1	1	yes	characteristic, complemented
257	#2435	C₂×D₄	1	2	yes	—
258	#2435	C₂×D₄	1	2	yes	—
259	#2435	C₂×D₄	1	2	yes	—
260	#2435	C₂⁴	1	2	yes	—
261	#2433	C₂×D₄	1	2	yes	—
262	#2433	C₂×D₄	1	2	yes	—
263	#2433	C₂×D₄	1	2	yes	—
264	#2433	C₂⁴	1	2	yes	—
265	#2403	C₂×D₄	1	2	yes	—
266	#2403	C₂×D₄	1	2	yes	—
267	#2403	C₂×D₄	1	2	yes	—
268	#2403	C₂×D₄	1	2	yes	—
269	#2403	C₂×D₄	1	2	yes	—
270	#2403	C₂×D₄	1	2	yes	—
271	#2403	C₂×D₄	1	2	yes	complemented
272	#2403	C₂×D₄	1	1	yes	characteristic, complemented
273	#2403	C₂×D₄	1	1	yes	characteristic, complemented
274	#2403	C₂⁴	1	2	yes	—
275	#2403	C₂⁴	1	2	yes	—
276	#2376	C₂×D₄	1	2	yes	complemented
277	#2376	C₂×D₄	1	2	yes	complemented
278	#2375	C₂×D₄	1	2	yes	complemented
279	#2375	C₂×D₄	1	2	yes	complemented
280	#2374	C₂×D₄	1	2	yes	complemented
281	#2374	C₂×D₄	1	2	yes	complemented
282	#2358	C₂×D₄	1	2	yes	complemented
283	#2358	C₂×D₄	1	2	yes	complemented
284	#2333	C₂×D₄	1	2	yes	complemented
285	#2333	C₂×D₄	1	2	yes	complemented
286	#2332	C₂×D₄	1	2	yes	complemented
287	#2332	C₂×D₄	1	2	yes	complemented
288	#2315	C₂×D₄	1	1	yes	characteristic, complemented
289	#2315	C₂×D₄	1	1	yes	characteristic, complemented
290	#2315	C₂×D₄	1	1	yes	characteristic, complemented
291	#2315	C₂×D₄	1	1	yes	characteristic, complemented
292	#2309	C₂×D₄	1	2	yes	—
293	#2309	C₂×D₄	1	2	yes	—
294	#2308	C₂×D₄	1	1	yes	characteristic
295	#2308	C₂×D₄	1	1	yes	characteristic
296	#2308	C₂×D₄	1	1	yes	characteristic
297	#2308	C₂×D₄	1	1	yes	characteristic
298	#2308	C₂×D₄	1	1	yes	characteristic
299	#2308	C₂×D₄	1	1	yes	characteristic
300	#2308	C₂×D₄	1	2	yes	complemented
301	#2308	C₂×D₄	1	2	yes	complemented
302	#2308	C₂×D₄	1	2	yes	complemented
303	#2308	C₂×D₄	1	2	yes	complemented
304	#2308	C₂⁴	1	2	yes	—
305	#2308	C₂⁴	1	1	yes	characteristic
306	#2308	C₂⁴	1	1	yes	characteristic
307	C₂×#386	C₂×D₄	1	2	yes	—
308	C₂×#386	C₂×D₄	1	2	yes	—
309	#2280	C₂×D₄	1	2	yes	—
310	C₂×#381	C₂×D₄	1	1	yes	characteristic
311	C₂×#381	C₂×D₄	1	1	yes	characteristic
312	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
313	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
314	C₂×#379	C₂×D₄	1	1	yes	characteristic
315	C₂×#379	C₂×D₄	1	1	yes	characteristic
316	C₂×#379	C₂×D₄	1	2	yes	—
317	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
318	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
319	#1783	C₂⁴	1	4	yes	—
320	#1781	C₂⁴	1	4	yes	—
321	C₂⁶	#120	1	1	yes	characteristic
322	C₂⁶	#120	1	2	yes	—
323	C₂⁶	C₂²×D₄	1	1	yes	characteristic
324	C₂⁶	C₂²×D₄	1	1	yes	characteristic
325	C₂⁶	C₂²×D₄	1	1	yes	characteristic
326	C₂²×#41	#120	1	2	yes	—
327	C₂³×D₄	#120	1	2	yes	—
328	C₂³×D₄	#120	1	1	yes	characteristic
329	C₂³×D₄	#120	1	1	yes	characteristic
330	C₂³×D₄	#120	1	2	yes	—
331	C₂³×D₄	#120	1	2	yes	—
332	C₂³×D₄	#120	1	2	yes	—
333	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
334	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
335	C₂³×D₄	C₂²×D₄	1	2	yes	—
336	C₂³×D₄	C₂²×D₄	1	2	yes	—
337	C₂³×D₄	C₂²×D₄	1	2	yes	—
338	C₂³×D₄	C₂²×D₄	1	2	yes	—
339	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
340	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
341	C₂³×D₄	C₂²×D₄	1	2	yes	—
342	C₂³×D₄	C₂²×D₄	1	2	yes	—
343	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂³×D₄	C₂⁵	1	1	yes	characteristic
345	C₂⁴×C₄	#120	1	1	yes	characteristic
346	C₂⁴×C₄	#120	1	2	yes	—
347	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
348	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
349	C₂×#127	#120	1	2	yes	—
350	C₂×#127	#120	1	2	yes	—
351	C₂×#127	C₂²×D₄	1	2	yes	—
352	C₂×#127	C₂²×D₄	1	2	yes	—
353	C₂×#124	#120	1	2	yes	—
354	C₂×#124	#120	1	2	yes	—
355	C₂×#124	C₂²×D₄	1	2	yes	—
356	C₂×#124	C₂²×D₄	1	2	yes	—
357	C₂×#123	#120	1	2	yes	—
358	C₂×#123	#120	1	2	yes	—
359	C₂×#123	#120	1	2	yes	—
360	C₂×#123	#120	1	2	yes	—
361	C₂×#123	C₂²×D₄	1	2	yes	—
362	C₂×#123	C₂²×D₄	1	2	yes	—
363	C₂×#123	C₂²×D₄	1	2	yes	—
364	C₂×#123	C₂²×D₄	1	2	yes	—
365	C₂×C₂²⋊Q₈	#120	1	2	yes	—
366	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
367	C₂×#121	#120	1	2	yes	—
368	C₂×#121	C₂²×D₄	1	2	yes	—
369	C₂×#120	#120	1	2	yes	—
370	C₂×#120	#120	1	2	yes	—
371	C₂×#120	#120	1	2	yes	—
372	C₂×#120	#120	1	2	yes	—
373	C₂×#120	#120	1	2	yes	—
374	C₂×#120	#120	1	2	yes	—
375	C₂×#120	#120	1	2	yes	—
376	C₂×#120	#120	1	2	yes	—
377	C₂×#120	C₂²×D₄	1	2	yes	—
378	C₂×#120	C₂²×D₄	1	2	yes	—
379	C₂×#120	C₂²×D₄	1	2	yes	—
380	C₂×#120	C₂²×D₄	1	2	yes	—
381	C₂×#120	C₂²×D₄	1	2	yes	—
382	C₂×#120	C₂²×D₄	1	2	yes	—
383	C₂×#120	C₂²×D₄	1	2	yes	—
384	C₂×#120	C₂²×D₄	1	2	yes	—
385	C₂×#117	#120	1	2	yes	—
386	C₂×#117	#120	1	2	yes	—
387	C₂×#117	#120	1	2	yes	—
388	C₂²×C₂²⋊C₄	#120	1	2	yes	—
389	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
390	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
391	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
392	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
396	C₂²×C₂²⋊C₄	#120	1	2	yes	—
397	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
398	C₂²×C₂²⋊C₄	#120	1	2	yes	—
399	C₂²×C₂²⋊C₄	#120	1	2	yes	—
400	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
401	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
405	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
406	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
412	#390	#120	1	2	yes	—
413	#390	#120	1	2	yes	—
414	#390	#120	1	2	yes	—
415	#390	#120	1	2	yes	—
416	#390	C₂²×D₄	1	2	yes	—
417	#390	C₂²×D₄	1	2	yes	—
418	#390	C₂²×D₄	1	2	yes	—
419	#390	C₂²×D₄	1	2	yes	—
420	#386	#120	1	2	yes	—
421	#386	#120	1	2	yes	—
422	#386	#120	1	2	yes	—
423	#386	#120	1	2	yes	—
424	#386	C₂²×D₄	1	2	yes	—
425	#386	C₂²×D₄	1	2	yes	—
426	#386	C₂²×D₄	1	2	yes	—
427	#386	C₂²×D₄	1	2	yes	—
428	#381	#120	1	1	yes	characteristic
429	#381	#120	1	1	yes	characteristic
430	#381	#120	1	1	yes	characteristic
431	#381	#120	1	1	yes	characteristic
432	#381	C₂²×D₄	1	1	yes	characteristic
433	#381	C₂²×D₄	1	1	yes	characteristic
434	#381	C₂²×D₄	1	1	yes	characteristic
435	#381	C₂²×D₄	1	1	yes	characteristic
436	#379	#120	1	1	yes	characteristic
437	#379	#120	1	1	yes	characteristic
438	#379	#120	1	2	yes	—
439	#379	#120	1	2	yes	—
440	#379	#120	1	1	yes	characteristic
441	#379	#120	1	1	yes	characteristic
442	#379	C₂²×D₄	1	1	yes	characteristic
443	#379	C₂²×D₄	1	1	yes	characteristic
444	#379	C₂²×D₄	1	1	yes	characteristic
445	#379	C₂²×D₄	1	1	yes	characteristic
446	#379	C₂²×D₄	1	2	yes	—
447	#379	C₂²×D₄	1	2	yes	—
448	C₄×C₂²⋊C₄	#120	1	2	yes	—
449	C₄×C₂²⋊C₄	#120	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
451	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
452	C₂⁵	C₂×#120	1	1	yes	characteristic
453	C₂⁵	C₂×#120	1	2	yes	—
454	C₂⁵	C₂×#120	1	1	yes	characteristic
455	C₂⁵	C₂×#120	1	1	yes	characteristic
456	C₂⁵	C₂×#120	1	1	yes	characteristic
457	C₂⁵	C₂×#120	1	1	yes	characteristic
458	C₂⁵	C₂×#120	1	2	yes	—
459	C₂⁵	C₂×#120	1	1	yes	characteristic
460	C₂⁵	C₂×#120	1	1	yes	characteristic
461	C₂⁵	C₂×#120	1	2	yes	—
462	C₂⁵	C₂×#120	1	1	yes	characteristic
463	C₂⁵	C₂×#120	1	2	yes	—
464	C₂⁵	C₂×#120	1	2	yes	—
465	C₂⁵	C₂×#120	1	1	yes	characteristic
466	C₂⁵	C₂³×D₄	1	1	yes	characteristic
467	C₂⁵	C₂³×D₄	1	1	yes	characteristic
468	C₂²×Q₈	C₂×#120	1	2	yes	—
469	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
470	C₂²×D₄	C₂×#120	1	2	yes	—
471	C₂²×D₄	C₂×#120	1	2	yes	—
472	C₂²×D₄	C₂×#120	1	2	yes	—
473	C₂²×D₄	C₂×#120	1	2	yes	—
474	C₂²×D₄	C₂×#120	1	2	yes	—
475	C₂²×D₄	C₂×#120	1	2	yes	—
476	C₂²×D₄	C₂×#120	1	2	yes	—
477	C₂²×D₄	C₂³×D₄	1	2	yes	—
478	C₂²×D₄	C₂³×D₄	1	2	yes	—
479	C₂³×C₄	C₂×#120	1	2	yes	—
480	C₂³×C₄	C₂×#120	1	1	yes	characteristic
481	C₂³×C₄	C₂×#120	1	2	yes	—
482	C₂³×C₄	C₂×#120	1	1	yes	characteristic
483	C₂³×C₄	C₂×#120	1	2	yes	—
484	C₂³×C₄	C₂×#120	1	1	yes	characteristic
485	C₂³×C₄	C₂×#120	1	2	yes	—
486	C₂³×C₄	C₂×#120	1	2	yes	—
487	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
489	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
490	C₂×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
492	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
496	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
498	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
500	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
502	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
504	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
509	C₂×C₄²	C₂×#120	1	2	yes	—
510	C₂×C₄²	C₂×#120	1	2	yes	—
511	C₂×C₄²	C₂×#120	1	2	yes	—
512	C₂×C₄²	C₂×#120	1	2	yes	—
513	C₂⁴	#2846	1	2	yes	—
514	C₂⁴	#2846	1	1	yes	characteristic
515	C₂⁴	#2846	1	1	yes	characteristic
516	C₂⁴	#2846	1	1	yes	characteristic
517	C₂⁴	#2846	1	1	yes	characteristic
518	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
519	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
520	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
521	C₂⁴	#3025	1	1	yes	characteristic
522	C₂⁴	#3025	1	1	yes	characteristic
523	C₂⁴	#3026	1	2	yes	—
524	C₂⁴	#3026	1	2	yes	—
525	C₂⁴	#3027	1	1	yes	characteristic
526	C₂⁴	#3027	1	1	yes	characteristic
527	C₂⁴	C₂²×#120	1	2	yes	—
528	C₂⁴	C₂²×#120	1	1	yes	characteristic
529	C₂⁴	C₂²×#120	1	1	yes	characteristic
530	C₂⁴	C₂²×#120	1	1	yes	characteristic
531	C₂²×C₄	#2846	1	2	yes	—
532	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
533	C₂²×C₄	C₂²×#120	1	2	yes	—
534	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
535	C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
536	C₂³	#32898	1	2	yes	—
537	C₂³	#32898	1	2	yes	—
538	C₂³	#32898	1	2	yes	—
539	C₂³	#32898	1	2	yes	—
540	C₂³	#32899	1	1	yes	characteristic
541	C₂³	#32899	1	1	yes	characteristic
542	C₂³	#32899	1	1	yes	characteristic
543	C₂³	#32899	1	1	yes	characteristic
544	C₂³	C₂×#2846	1	1	yes	characteristic
545	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
546	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
547	C₂³	C₂×#3025	1	1	yes	characteristic
548	C₂³	C₂×#3026	1	1	yes	characteristic
549	C₂³	C₂×#3026	1	1	yes	characteristic
550	C₂³	C₂×#3027	1	1	yes	characteristic
551	C₂²	#347043	1	2	yes	—
552	C₂²	#347043	1	2	yes	—
553	C₂²	C₂×#32898	1	1	yes	characteristic
554	C₂²	C₂×#32898	1	1	yes	characteristic
555	C₂²	C₂×#32899	1	1	yes	characteristic
556	C₂	C₂×#347043	1	1	yes	characteristic
557	C₂	#72240647	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	C₂×#32899
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂×#2308 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72265982	C₂	semidirect
2. #72265981	C₂	semidirect
3. #72265980	C₂	semidirect
4. #72265979	C₂	semidirect
5. C₂×#133422	C₂	semidirect
6. #72265961	C₂	semidirect
7. #72265940	C₂	semidirect
8. #72265933	C₂	semidirect
9. #72258238	C₂	semidirect
10. #72258234	C₂	semidirect
11. #72256110	C₂	semidirect
12. #72249671	C₂	semidirect
13. #72241074	C₂	semidirect
14. C₂×#251827	C₂	semidirect
15. #72237832	C₂	semidirect
16. #72233116	C₂	semidirect
17. #72233116	C₂	semidirect
18. C₂²×#3026	C₂²	semidirect
19. C₂²×#3026	C₂²	semidirect
20. #9061456	C₂²	semidirect
21. #9061085	C₂²	semidirect
22. #9054448	C₂²	semidirect
23. #9041087	C₂²	semidirect
24. #8912605	C₂²	semidirect
25. #8905195	C₂²	semidirect
31. C₂×#32898	C₂²	semidirect
32. #6628867	C₂²	semidirect
33. C₂×#20585	C₂²	semidirect
34. #499815	C₂²	semidirect
35. #499812	C₂²	semidirect
36. #499807	C₂²	semidirect
37. #499804	C₂²	semidirect
38. #499800	C₂²	semidirect
39. #499795	C₂²	semidirect
40. #499792	C₂²	semidirect
41. #499787	C₂²	semidirect
42. #494713	C₂²	semidirect
43. #494713	C₂²	semidirect
44. C₂×#13086	C₂²	semidirect
45. C₂×#13086	C₂²	semidirect
46. #493357	C₂²	semidirect
47. #493357	C₂²	semidirect
48. #417543	C₂²	semidirect
49. #417543	C₂²	semidirect
50. #417542	C₂²	semidirect
51. #417542	C₂²	semidirect
52. C₂×#11166	C₂²	semidirect
53. #357530	C₂²	semidirect
54. C₂×#10972	C₂²	semidirect
55. #251945	C₂²	semidirect
56. #251940	C₂²	semidirect
57. #251935	C₂²	semidirect
58. #251827	C₂²	semidirect
59. #251827	C₂²	semidirect
60. #251827	C₂²	semidirect
61. C₂×#9495	C₂²	semidirect
62. #201322	C₂²	semidirect
63. C₂×#8751	C₂²	semidirect
64. C₂×#8746	C₂²	semidirect
65. #133923	C₂²	semidirect
66. #133923	C₂²	semidirect
67. #133922	C₂²	semidirect
68. #133922	C₂²	semidirect
69. #133436	C₂²	semidirect
70. #133435	C₂²	semidirect
71. #133434	C₂²	semidirect
72. #133422	C₂²	semidirect
73. #133422	C₂²	semidirect
74. #133422	C₂²	semidirect
75. #133411	C₂²	semidirect
76. #133410	C₂²	semidirect
77. #133407	C₂²	semidirect
78. #133406	C₂²	semidirect
79. #133395	C₂²	semidirect
80. #133394	C₂²	semidirect
81. #133391	C₂²	semidirect
82. #133390	C₂²	semidirect
84. C₂×#3532	D₄	semidirect
85. C₂×#3532	D₄	semidirect
86. C₂²×#534	D₄	semidirect
89. C₂²×#518	D₄	semidirect
96. #59191	D₄	semidirect
98. #58990	D₄	semidirect
100. #50856	D₄	semidirect
102. #50646	D₄	semidirect
104. #47848	D₄	semidirect
106. #47827	D₄	semidirect
108. #47035	D₄	semidirect
110. #47033	D₄	semidirect
112. #47031	D₄	semidirect
114. #46996	D₄	semidirect
115. #46996	D₄	semidirect
116. #46996	D₄	semidirect
120. #45455	D₄	semidirect
122. #45439	D₄	semidirect
124. #37479	D₄	semidirect
125. #37454	D₄	semidirect
126. #36737	D₄	semidirect
127. #36737	D₄	semidirect
128. #36714	D₄	semidirect
129. #36714	D₄	semidirect
130. C₂×#2840	D₄	semidirect
131. #35447	D₄	semidirect
132. #35447	D₄	semidirect
135. #35348	D₄	semidirect
136. #35348	D₄	semidirect
140. C₂×#2403	D₄	semidirect
142. #34407	D₄	semidirect
143. #34407	D₄	semidirect
144. #34396	D₄	semidirect
145. C₂×#2315	D₄	semidirect
146. C₂×#2308	D₄	semidirect
147. C₂×#2308	D₄	semidirect
189. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
190. C₂×H(3,𝔽₄)	C₂×D₄	semidirect
191. C₂×#560	C₂×D₄	semidirect
192. C₂×#560	C₂×D₄	semidirect
193. C₂×#551	C₂×D₄	semidirect
194. C₂×#551	C₂×D₄	semidirect
195. C₂×D₄²	C₂×D₄	semidirect
196. C₂×D₄²	C₂×D₄	semidirect
212. C₂²×#123	C₂×D₄	semidirect
213. C₂²×#123	C₂×D₄	semidirect
219. C₂²×#120	C₂×D₄	semidirect
220. C₂²×#120	C₂×D₄	semidirect
222. C₂×#518	C₂×D₄	semidirect
223. C₂×#518	C₂×D₄	semidirect
224. C₂×#518	C₂×D₄	semidirect
225. C₂×#518	C₂×D₄	semidirect
232. #2840	C₂×D₄	semidirect
233. #2840	C₂×D₄	semidirect
234. #2840	C₂×D₄	semidirect
235. #2817	C₂×D₄	semidirect
236. #2816	C₂×D₄	semidirect
237. #2815	C₂×D₄	semidirect
238. #2717	C₂×D₄	semidirect
239. #2717	C₂×D₄	semidirect
240. #2709	C₂×D₄	semidirect
241. #2709	C₂×D₄	semidirect
242. #2697	C₂×D₄	semidirect
243. #2697	C₂×D₄	semidirect
244. #2697	C₂×D₄	semidirect
245. #2697	C₂×D₄	semidirect
246. #2684	C₂×D₄	semidirect
247. #2684	C₂×D₄	semidirect
248. #2679	C₂×D₄	semidirect
249. #2679	C₂×D₄	semidirect
250. #2679	C₂×D₄	semidirect
251. #2679	C₂×D₄	semidirect
252. #2669	C₂×D₄	semidirect
253. #2669	C₂×D₄	semidirect
254. #2608	C₂×D₄	semidirect
255. #2607	C₂×D₄	semidirect
256. #2607	C₂×D₄	semidirect
271. #2403	C₂×D₄	semidirect
272. #2403	C₂×D₄	semidirect
273. #2403	C₂×D₄	semidirect
276. #2376	C₂×D₄	semidirect
277. #2376	C₂×D₄	semidirect
278. #2375	C₂×D₄	semidirect
279. #2375	C₂×D₄	semidirect
280. #2374	C₂×D₄	semidirect
281. #2374	C₂×D₄	semidirect
282. #2358	C₂×D₄	semidirect
283. #2358	C₂×D₄	semidirect
284. #2333	C₂×D₄	semidirect
285. #2333	C₂×D₄	semidirect
286. #2332	C₂×D₄	semidirect
287. #2332	C₂×D₄	semidirect
288. #2315	C₂×D₄	semidirect
289. #2315	C₂×D₄	semidirect
290. #2315	C₂×D₄	semidirect
291. #2315	C₂×D₄	semidirect
300. #2308	C₂×D₄	semidirect
301. #2308	C₂×D₄	semidirect
302. #2308	C₂×D₄	semidirect
303. #2308	C₂×D₄	semidirect
312. C₂×#381	C₂×D₄	semidirect
313. C₂×#381	C₂×D₄	semidirect
317. C₂×#379	C₂×D₄	semidirect
318. C₂×#379	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72265982	2
#72265981	2
#72265980	2
#72265979	2
C₂×#133422	2
#72265961	2
#72265940	2
#72265933	2
#72258238	2
#72258234	2
#72256110	2
#72249671	2
#72241074	2
C₂×#251827	2
#72237832	2
#72233116	2