Subgroups — #72262721

Order 4096.

At least 21564 conjugacy classes of subgroups; only the 981 normal subgroups are shown.

The subgroup lattice has 549 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262719	C₂	1	1	yes	maximal, characteristic, complemented
2	#72262715	C₂	1	4	yes	maximal, complemented
3	#72262714	C₂	1	4	yes	maximal, complemented
4	#72262713	C₂	1	2	yes	maximal, complemented
5	#72262708	C₂	1	2	yes	maximal, complemented
6	#72262707	C₂	1	2	yes	maximal, complemented
7	#72262706	C₂²	1	2	yes	complemented
8	#72262688	C₂	1	1	yes	maximal, characteristic, complemented
9	#72262680	C₂²	1	2	yes	complemented
10	#72262679	C₂²	1	2	yes	complemented
11	#72262678	C₂²	1	2	yes	—
12	#72262573	C₂	1	2	yes	maximal, complemented
13	#72262572	C₂²	1	4	yes	complemented
14	#72262570	C₂²	1	4	yes	complemented
15	#72262569	C₂²	1	4	yes	complemented
16	#72262565	C₂²	1	1	yes	characteristic, complemented
17	#72262542	C₂	1	2	yes	maximal, complemented
18	#72262523	C₂	1	2	yes	maximal, complemented
19	#72262522	C₂²	1	2	yes	complemented
20	#72262522	C₂²	1	4	yes	complemented
21	#72262519	C₂²	1	4	yes	complemented
22	#72262518	C₂²	1	4	yes	complemented
23	#72262516	C₂²	1	4	yes	complemented
24	#72262509	C₂²	1	1	yes	characteristic, complemented
25	#72262480	C₂	1	2	yes	maximal, complemented
26	#72262478	C₂²	1	2	yes	complemented
27	#72262475	C₂²	1	4	yes	complemented
28	#72262463	C₂²	1	1	yes	characteristic, complemented
29	#72256396	C₂²	1	4	yes	complemented
30	#72238497	C₂²	1	1	yes	characteristic, complemented
31	#72238470	C₂	1	2	yes	maximal, complemented
32	#72238469	C₂²	1	4	yes	complemented
33	#72238468	C₂²	1	2	yes	complemented
34	#72238467	C₂²	1	4	yes	complemented
35	#72238466	C₂²	1	2	yes	—
36	#72238449	C₂	1	1	yes	maximal, characteristic, complemented
37	#72238448	C₂²	1	2	yes	complemented
38	#72238438	C₂²	1	4	yes	complemented
39	#72238361	C₂	1	1	yes	maximal, characteristic, complemented
40	#72237489	C₂²	1	2	yes	complemented
41	#72237488	C₂²	1	2	yes	complemented
42	#72237487	C₂²	1	2	yes	complemented
43	#72237486	C₂²	1	2	yes	complemented
44	#72237039	C₂	1	1	yes	maximal, characteristic, complemented
45	#72237034	C₂²	1	1	yes	characteristic, complemented
46	#72237033	C₂²	1	1	yes	characteristic
47	#72235234	C₂²	1	1	yes	characteristic, complemented
48	#72234717	C₂	1	1	yes	maximal, characteristic, complemented
49	#72234716	C₂²	1	1	yes	characteristic
50	#72234713	C₂²	1	2	yes	complemented
51	#72234711	C₂²	1	2	yes	complemented
52	#72234711	C₂²	1	4	yes	complemented
53	#72234710	C₂²	1	2	yes	complemented
54	#72234639	C₂	1	1	yes	maximal, characteristic, complemented
55	#72234638	C₂²	1	2	yes	complemented
56	#72234637	C₂²	1	2	yes	complemented
57	#72234636	C₂²	1	1	yes	characteristic
58	#72234623	C₂²	1	2	yes	complemented
59	#72234606	C₂²	1	2	yes	complemented
60	#72234515	C₂²	1	2	yes	complemented
61	#72234515	C₂²	1	2	yes	complemented
62	#72234515	C₂²	1	4	yes	complemented
63	#72234108	C₂²	1	2	yes	—
64	#72234108	C₂²	1	2	yes	complemented
65	#72234108	C₂²	1	4	yes	complemented
66	#72233790	C₂²	1	4	yes	complemented
67	#72233067	C₂²	1	4	yes	complemented
68	#72232836	C₂²	1	2	yes	complemented
69	#72232806	C₂²	1	4	yes	complemented
70	#72232714	C₂²	1	4	yes	complemented
71	#72225989	C₂²	1	4	yes	complemented
72	#72225987	C₂²	1	2	yes	—
73	#72225870	C₂²	1	1	yes	characteristic, complemented
74	#72225712	C₂²	1	1	yes	characteristic
75	#72225665	C₂²	1	1	yes	characteristic
76	#72224136	C₂²	1	1	yes	characteristic, complemented
77	#72219314	C₂²	1	1	yes	characteristic, complemented
78	#72219311	C₂²	1	1	yes	characteristic, complemented
79	#72215671	C₂²	1	2	yes	complemented
80	#72215671	C₂²	1	2	yes	complemented
81	#72210587	C₂²	1	2	yes	—
82	#72210587	C₂²	1	2	yes	complemented
83	#10586404	C₂³	1	1	yes	characteristic
84	C₂³×D₄²	D₄	1	1	yes	characteristic, complemented
85	C₂×#47031	D₄	1	1	yes	characteristic, complemented
86	C₂×#46996	D₄	1	1	yes	characteristic, complemented
87	C₂×#34980	C₂³	1	1	yes	characteristic
88	#6499870	C₂³	1	2	yes	—
89	#6499870	C₂³	1	4	yes	complemented
90	#6499867	C₂³	1	2	yes	—
91	#6374128	C₂³	1	1	yes	characteristic
92	#5509417	D₄	1	2	yes	complemented
93	#5509416	D₄	1	2	yes	complemented
94	#5065227	C₂³	1	2	yes	—
95	#5065226	D₄	1	2	yes	complemented
96	#5065079	D₄	1	2	yes	complemented
97	#5065025	D₄	1	2	yes	complemented
98	#5036282	D₄	1	2	yes	complemented
99	#5036078	D₄	1	2	yes	complemented
100	#5025772	C₂³	1	1	yes	characteristic
101	#5024691	C₂³	1	1	yes	characteristic
102	#5020751	D₄	1	1	yes	characteristic, complemented
103	#5020747	D₄	1	1	yes	characteristic, complemented
104	#4466151	D₄	1	2	yes	complemented
105	#4466053	D₄	1	2	yes	complemented
106	#4466035	C₂³	1	2	yes	—
107	#4435227	C₂³	1	2	yes	—
108	#4435227	C₂³	1	1	yes	characteristic
109	#4433768	C₂³	1	2	yes	—
110	#4430405	C₂³	1	1	yes	characteristic
111	#4421183	D₄	1	2	yes	complemented
112	#4420586	D₄	1	1	yes	characteristic, complemented
113	#4420586	D₄	1	1	yes	characteristic, complemented
114	#4420586	C₂³	1	1	yes	characteristic
115	#4420586	C₂³	1	1	yes	characteristic
116	#4420586	C₂³	1	2	yes	—
117	#4380225	C₂³	1	2	yes	—
118	#4379766	D₄	1	2	yes	complemented
119	#4379716	C₂³	1	2	yes	—
120	#2600505	D₄	1	2	yes	complemented
121	#2379496	C₂³	1	2	yes	—
122	#2109018	C₂³	1	2	yes	—
123	#2080819	C₂³	1	2	yes	—
124	#2032535	D₄	1	2	yes	complemented
125	#2031999	C₂³	1	2	yes	—
126	#1452828	D₄	1	2	yes	complemented
127	#1448671	D₄	1	2	yes	complemented
128	#846058	D₄	1	2	yes	complemented
129	#686193	D₄	1	1	yes	characteristic, complemented
130	#663621	D₄	1	1	yes	characteristic, complemented
131	#663621	D₄	1	1	yes	characteristic, complemented
132	#659149	D₄	1	2	yes	complemented
133	#650612	D₄	1	2	yes	complemented
134	#648360	D₄	1	1	yes	characteristic, complemented
135	#647656	D₄	1	2	yes	complemented
136	#647656	C₂³	1	1	yes	characteristic
137	#647656	C₂³	1	1	yes	characteristic
138	#617710	D₄	1	1	yes	characteristic, complemented
139	#617710	C₂³	1	1	yes	characteristic
140	#616969	C₂³	1	2	yes	—
141	#616960	D₄	1	1	yes	characteristic, complemented
142	#616960	C₂³	1	1	yes	characteristic
143	#612424	D₄	1	2	yes	complemented
144	#576189	D₄	1	1	yes	characteristic, complemented
145	#576160	D₄	1	1	yes	characteristic, complemented
146	#556752	D₄	1	1	yes	characteristic, complemented
147	#347042	C₂³	1	2	yes	—
148	#347042	C₂³	1	2	yes	—
149	#346466	C₂³	1	4	yes	complemented
150	#346446	C₂³	1	2	yes	—
151	#346446	C₂³	1	2	yes	—
152	#346446	C₂³	1	4	yes	complemented
153	#188122	C₂³	1	2	yes	—
154	#188109	C₂³	1	1	yes	characteristic
155	#188049	C₂³	1	2	yes	—
156	#188049	C₂³	1	1	yes	characteristic
157	#187934	C₂³	1	4	yes	complemented
158	#139830	C₂³	1	4	yes	complemented
159	#139718	C₂³	1	2	yes	—
160	#139718	C₂³	1	2	yes	—
161	#139718	C₂³	1	4	yes	complemented
162	#139716	C₂³	1	4	yes	—
163	#139716	C₂³	1	2	yes	—
164	#139716	C₂³	1	4	yes	—
165	#139716	C₂³	1	2	yes	—
166	#139506	C₂³	1	4	yes	complemented
167	#139504	C₂³	1	4	yes	—
168	#139504	C₂³	1	4	yes	—
169	#139504	C₂³	1	4	yes	complemented
170	#139504	C₂³	1	4	yes	complemented
171	#139484	C₂³	1	4	yes	complemented
172	#135561	C₂³	1	4	yes	complemented
173	#135507	C₂³	1	4	yes	complemented
174	#134036	C₂³	1	2	yes	—
175	#134036	C₂³	1	4	yes	complemented
176	#134033	C₂³	1	2	yes	—
177	#133825	C₂³	1	2	yes	—
178	#133825	C₂³	1	4	yes	complemented
179	#133822	C₂³	1	2	yes	—
180	#119550	C₂³	1	4	yes	complemented
181	#115690	C₂³	1	2	yes	—
182	#115631	C₂³	1	2	yes	—
183	#115631	C₂³	1	4	yes	complemented
184	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
185	#62817	C₂⁴	1	2	yes	—
186	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic
187	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic
188	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic
189	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic
190	C₂²×D₄²	C₂×D₄	1	2	yes	complemented
191	C₂²×#534	C₂×D₄	1	1	yes	characteristic
192	C₂²×#534	C₂⁴	1	1	yes	characteristic
193	C₂³×#127	C₂×D₄	1	1	yes	characteristic
194	C₂³×#120	C₂×D₄	1	1	yes	characteristic
195	C₂³×#120	C₂×D₄	1	1	yes	characteristic
196	C₂³×#120	C₂×D₄	1	2	yes	complemented
197	C₂×#2697	C₂×D₄	1	2	yes	complemented
198	C₂×#2668	C₂×D₄	1	2	yes	complemented
199	C₂×#2840	C₂×D₄	1	1	yes	characteristic, complemented
200	C₂×#2815	C₂×D₄	1	2	yes	—
201	C₂×#2815	C₂×D₄	1	1	yes	characteristic, complemented
202	C₂×#2815	C₂×D₄	1	2	yes	complemented
203	C₂×#2812	C₂×D₄	1	2	yes	complemented
204	C₂×#2849	C₂×D₄	1	1	yes	characteristic
205	C₂×#2849	C₂×D₄	1	1	yes	characteristic
206	C₂×#2846	C₂×D₄	1	2	yes	—
207	C₂×#2846	C₂×D₄	1	1	yes	characteristic
208	C₂×#2846	C₂⁴	1	1	yes	characteristic
209	C₂×#2607	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂×#2539	C₂×D₄	1	2	yes	—
211	C₂×#2410	C₂×D₄	1	2	yes	—
212	C₂×#2403	C₂×D₄	1	2	yes	—
213	C₂×#2403	C₂×D₄	1	1	yes	characteristic, complemented
214	C₂×#2403	C₂×D₄	1	2	yes	complemented
215	C₂×#2619	C₂×D₄	1	2	yes	—
216	C₂×#2613	C₂×D₄	1	1	yes	characteristic
217	C₂×#2613	C₂×D₄	1	1	yes	characteristic
218	C₂×#2613	C₂×D₄	1	2	yes	—
219	C₂×#2613	C₂×D₄	1	1	yes	characteristic
220	C₂×#2613	C₂⁴	1	1	yes	characteristic
221	C₂×#2613	C₂⁴	1	2	yes	—
222	C₂×#2308	C₂×D₄	1	1	yes	characteristic
223	C₂×#2308	C₂×D₄	1	1	yes	characteristic
224	C₂×#2308	C₂×D₄	1	2	yes	complemented
225	C₂²×#379	C₂×D₄	1	1	yes	characteristic
226	#21746	C₂⁴	1	2	yes	—
227	#21746	C₂⁴	1	4	yes	—
228	#17272	C₂×D₄	1	2	yes	complemented
229	#17147	C₂×D₄	1	2	yes	complemented
230	#17136	C₂×D₄	1	2	yes	complemented
231	#17102	C₂×D₄	1	2	yes	complemented
232	#15984	C₂×D₄	1	2	yes	—
233	#15982	C₂×D₄	1	2	yes	—
234	#15950	C₂×D₄	1	2	yes	—
235	#15948	C₂×D₄	1	2	yes	—
236	#15948	C₂×D₄	1	1	yes	characteristic
237	#15948	C₂×D₄	1	1	yes	characteristic
238	#15948	C₂×D₄	1	1	yes	characteristic
239	#15948	C₂×D₄	1	1	yes	characteristic
240	#15948	C₂×D₄	1	2	yes	—
241	#15948	C₂×D₄	1	2	yes	complemented
242	#15947	C₂×D₄	1	1	yes	characteristic
243	#15947	C₂×D₄	1	1	yes	characteristic
244	#15947	C₂×D₄	1	2	yes	—
245	#15947	C₂×D₄	1	2	yes	complemented
246	#15947	C₂⁴	1	1	yes	characteristic
247	#15947	C₂⁴	1	1	yes	characteristic
248	#15669	C₂×D₄	1	2	yes	—
249	#15669	C₂×D₄	1	2	yes	—
250	#15649	C₂×D₄	1	2	yes	complemented
251	#15636	C₂×D₄	1	2	yes	complemented
252	#15561	C₂×D₄	1	2	yes	complemented
253	#15539	C₂×D₄	1	2	yes	complemented
254	#15412	C₂×D₄	1	2	yes	—
255	#15412	C₂×D₄	1	2	yes	—
256	#15310	C₂×D₄	1	2	yes	—
257	#15310	C₂×D₄	1	2	yes	—
258	#15284	C₂×D₄	1	2	yes	complemented
259	#15284	C₂×D₄	1	2	yes	complemented
260	#15283	C₂×D₄	1	2	yes	—
261	#15283	C₂⁴	1	2	yes	—
262	#15281	C₂×D₄	1	2	yes	complemented
263	#15281	C₂×D₄	1	2	yes	complemented
264	#15267	C₂×D₄	1	2	yes	complemented
265	#15267	C₂×D₄	1	2	yes	complemented
266	#15267	C₂×D₄	1	2	yes	complemented
267	#15267	C₂×D₄	1	2	yes	complemented
268	#15261	C₂×D₄	1	1	yes	characteristic
269	#15261	C₂×D₄	1	1	yes	characteristic
270	#15261	C₂×D₄	1	1	yes	characteristic
271	#15261	C₂×D₄	1	1	yes	characteristic
272	#15261	C₂×D₄	1	2	yes	complemented
273	#15258	C₂×D₄	1	1	yes	characteristic
274	#15258	C₂×D₄	1	1	yes	characteristic
275	#15258	C₂×D₄	1	2	yes	—
276	#15258	C₂×D₄	1	2	yes	complemented
277	#15258	C₂⁴	1	2	yes	—
278	#15258	C₂⁴	1	1	yes	characteristic
279	#15258	C₂⁴	1	1	yes	characteristic
280	#15257	C₂×D₄	1	2	yes	—
281	#15257	C₂×D₄	1	2	yes	—
282	#15257	C₂×D₄	1	2	yes	—
283	#15257	C₂×D₄	1	2	yes	—
284	#14706	C₂×D₄	1	2	yes	—
285	#14679	C₂×D₄	1	2	yes	complemented
286	#14661	C₂×D₄	1	2	yes	complemented
287	#14657	C₂×D₄	1	2	yes	—
288	#14657	C₂×D₄	1	1	yes	characteristic
289	#14657	C₂×D₄	1	1	yes	characteristic
290	#14657	C₂×D₄	1	2	yes	complemented
291	#14567	C₂×D₄	1	2	yes	complemented
292	#14567	C₂×D₄	1	2	yes	complemented
293	#14506	C₂×D₄	1	2	yes	complemented
294	#14445	C₂×D₄	1	2	yes	complemented
295	#14365	C₂×D₄	1	2	yes	complemented
296	#14358	C₂×D₄	1	2	yes	complemented
297	#14335	C₂×D₄	1	1	yes	characteristic
298	#14335	C₂×D₄	1	1	yes	characteristic
299	#14290	C₂×D₄	1	2	yes	—
300	#14262	C₂×D₄	1	2	yes	complemented
301	#14255	C₂×D₄	1	2	yes	—
302	#14255	C₂⁴	1	2	yes	—
303	#14253	C₂×D₄	1	2	yes	complemented
304	#14207	C₂×D₄	1	2	yes	complemented
305	#14136	C₂×D₄	1	2	yes	—
306	#14134	C₂×D₄	1	1	yes	characteristic
307	#14134	C₂×D₄	1	1	yes	characteristic
308	#14134	C₂×D₄	1	2	yes	complemented
309	#13868	C₂×D₄	1	2	yes	—
310	#13867	C₂×D₄	1	2	yes	—
311	#13867	C₂×D₄	1	2	yes	complemented
312	#13828	C₂×D₄	1	1	yes	characteristic, complemented
313	#13827	C₂×D₄	1	1	yes	characteristic, complemented
314	#13807	C₂×D₄	1	2	yes	complemented
315	#13807	C₂×D₄	1	1	yes	characteristic, complemented
316	C₂²⋊C₄²	C₂×D₄	1	2	yes	complemented
317	C₂²⋊C₄²	C₂×D₄	1	1	yes	characteristic, complemented
318	#8547	C₂⁴	1	2	yes	—
319	#8547	C₂⁴	1	4	yes	—
320	#8541	C₂⁴	1	2	yes	—
321	C₂⁷	#120	1	1	yes	characteristic
322	C₂⁷	#120	1	1	yes	characteristic
323	C₂⁷	C₂²×D₄	1	1	yes	characteristic
324	C₂⁴×D₄	#120	1	1	yes	characteristic
325	C₂⁴×D₄	#120	1	1	yes	characteristic
326	C₂⁴×D₄	#120	1	1	yes	characteristic
327	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
328	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
329	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
330	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
331	C₂⁵×C₄	#120	1	1	yes	characteristic
332	C₂²×#127	#120	1	1	yes	characteristic
333	C₂²×#127	#120	1	1	yes	characteristic
334	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
335	C₂²×#127	C₂²×D₄	1	2	yes	—
336	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
337	C₂²×#123	#120	1	1	yes	characteristic
338	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
339	C₂²×#123	C₂²×D₄	1	2	yes	—
340	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
341	C₂²×#123	C₂²×D₄	1	2	yes	—
342	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
343	C₂²×#121	#120	1	2	yes	—
344	C₂²×#121	C₂²×D₄	1	2	yes	—
345	C₂²×#121	C₂²×D₄	1	2	yes	—
346	C₂²×#120	#120	1	1	yes	characteristic
347	C₂²×#120	#120	1	1	yes	characteristic
348	C₂²×#120	#120	1	2	yes	—
349	C₂²×#120	#120	1	1	yes	characteristic
350	C₂²×#120	#120	1	1	yes	characteristic
351	C₂²×#120	#120	1	1	yes	characteristic
352	C₂²×#120	#120	1	2	yes	—
353	C₂²×#120	#120	1	2	yes	—
354	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
355	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
356	C₂²×#120	C₂²×D₄	1	2	yes	—
357	C₂²×#120	C₂²×D₄	1	2	yes	—
358	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
359	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
360	C₂²×#120	C₂²×D₄	1	2	yes	—
361	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
362	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
363	C₂²×#120	C₂²×D₄	1	2	yes	—
364	C₂²×#120	C₂⁵	1	1	yes	characteristic
365	C₂²×#117	#120	1	2	yes	—
366	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
367	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
368	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
369	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
370	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
371	C₂³×C₄²	#120	1	1	yes	characteristic
372	C₂×#399	#120	1	2	yes	—
373	C₂×#399	C₂²×D₄	1	2	yes	—
374	C₂×#397	#120	1	2	yes	—
375	C₂×#397	C₂²×D₄	1	2	yes	—
376	C₂×#394	#120	1	2	yes	—
377	C₂×#394	#120	1	2	yes	—
378	C₂×#392	#120	1	2	yes	—
379	C₂×#392	#120	1	2	yes	—
380	C₂×#392	C₂²×D₄	1	2	yes	—
381	C₂×#392	C₂²×D₄	1	2	yes	—
382	C₂×#392	C₂²×D₄	1	2	yes	—
383	C₂×#392	C₂²×D₄	1	2	yes	—
384	C₂×#390	#120	1	2	yes	—
385	C₂×#390	C₂²×D₄	1	2	yes	—
386	C₂×#386	#120	1	2	yes	—
387	C₂×#386	#120	1	2	yes	—
388	C₂×#386	#120	1	2	yes	—
389	C₂×#385	#120	1	2	yes	—
390	C₂×#382	#120	1	2	yes	—
391	C₂×#381	#120	1	2	yes	—
392	C₂×#381	#120	1	2	yes	—
393	C₂×#381	#120	1	1	yes	characteristic
394	C₂×#381	#120	1	1	yes	characteristic
395	C₂×#381	#120	1	1	yes	characteristic
396	C₂×#381	C₂²×D₄	1	1	yes	characteristic
397	C₂×#381	C₂²×D₄	1	2	yes	—
398	C₂×#379	#120	1	1	yes	characteristic
399	C₂×#379	#120	1	1	yes	characteristic
400	C₂×#379	#120	1	1	yes	characteristic
401	C₂×#379	#120	1	2	yes	—
402	C₂×#379	#120	1	2	yes	—
403	C₂×#379	#120	1	2	yes	—
404	C₂×#379	#120	1	2	yes	—
405	C₂×#379	C₂²×D₄	1	1	yes	characteristic
406	C₂×#379	C₂²×D₄	1	1	yes	characteristic
407	C₂×#379	C₂²×D₄	1	2	yes	—
408	C₂×#379	C₂²×D₄	1	2	yes	—
409	C₂×#379	C₂²×D₄	1	1	yes	characteristic
410	C₂×#379	C₂²×D₄	1	1	yes	characteristic
411	C₂×#379	C₂²×D₄	1	2	yes	—
412	C₂×#379	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₂²⋊C₄	#120	1	2	yes	—
414	#1445	#120	1	2	yes	—
415	#1445	#120	1	2	yes	—
416	#1440	#120	1	2	yes	—
417	#1440	#120	1	2	yes	—
418	#1440	#120	1	2	yes	—
419	#1440	#120	1	2	yes	—
420	#1440	C₂²×D₄	1	2	yes	—
421	#1440	C₂²×D₄	1	2	yes	—
422	#1438	#120	1	2	yes	—
423	#1438	#120	1	2	yes	—
424	#1438	#120	1	2	yes	—
425	#1438	#120	1	2	yes	—
426	#1438	#120	1	2	yes	—
427	#1438	#120	1	2	yes	—
428	#1438	#120	1	2	yes	—
429	#1438	#120	1	2	yes	—
430	#1438	C₂²×D₄	1	2	yes	—
431	#1438	C₂²×D₄	1	1	yes	characteristic
432	#1438	C₂²×D₄	1	1	yes	characteristic
433	#1438	C₂²×D₄	1	2	yes	—
434	#1438	C₂²×D₄	1	2	yes	—
435	#1438	C₂²×D₄	1	2	yes	—
436	#1438	C₂²×D₄	1	1	yes	characteristic
437	#1438	C₂²×D₄	1	1	yes	characteristic
438	#1438	C₂²×D₄	1	2	yes	—
439	#1438	C₂²×D₄	1	2	yes	—
440	#1437	#120	1	2	yes	—
441	#1437	#120	1	2	yes	—
442	#1437	#120	1	2	yes	—
443	#1437	#120	1	2	yes	—
444	#1437	C₂²×D₄	1	2	yes	—
445	#1437	C₂²×D₄	1	2	yes	—
446	#1437	C₂²×D₄	1	2	yes	—
447	#1437	C₂²×D₄	1	2	yes	—
448	#1437	C₂²×D₄	1	2	yes	—
449	#1437	C₂²×D₄	1	2	yes	—
450	#1436	#120	1	2	yes	—
451	#1436	#120	1	2	yes	—
452	C₂⁶	C₂×#120	1	1	yes	characteristic
453	C₂⁶	C₂×#120	1	1	yes	characteristic
454	C₂⁶	C₂×#120	1	2	yes	—
455	C₂⁶	C₂×#120	1	1	yes	characteristic
456	C₂⁶	C₂×#120	1	1	yes	characteristic
457	C₂⁶	C₂×#120	1	1	yes	characteristic
458	C₂⁶	C₂×#120	1	1	yes	characteristic
459	C₂⁶	C₂×#120	1	1	yes	characteristic
460	C₂⁶	C₂³×D₄	1	1	yes	characteristic
461	C₂³×D₄	C₂×#120	1	2	yes	—
462	C₂³×D₄	C₂×#120	1	2	yes	—
463	C₂³×D₄	C₂×#120	1	1	yes	characteristic
464	C₂³×D₄	C₂×#120	1	1	yes	characteristic
465	C₂³×D₄	C₂×#120	1	2	yes	—
466	C₂³×D₄	C₂×#120	1	1	yes	characteristic
467	C₂³×D₄	C₂×#120	1	1	yes	characteristic
468	C₂³×D₄	C₂×#120	1	1	yes	characteristic
469	C₂³×D₄	C₂×#120	1	2	yes	—
470	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
471	C₂³×D₄	C₂³×D₄	1	2	yes	—
472	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
473	C₂⁴×C₄	C₂×#120	1	2	yes	—
474	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
475	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
476	C₂⁴×C₄	C₂×#120	1	2	yes	—
477	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
478	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
479	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
480	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
481	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	2	yes	—
482	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
483	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
484	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
485	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
486	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
487	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
488	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
489	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
490	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
491	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
492	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
493	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
494	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
495	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
496	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
497	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
498	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
499	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
500	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
501	C₂²×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
502	C₂²×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
503	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
504	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
505	C₂²×C₄²	C₂×#120	1	2	yes	—
506	C₂²×C₄²	C₂×#120	1	2	yes	—
507	C₂×#95	C₂×#120	1	2	yes	—
508	C₂×#95	C₂×#120	1	2	yes	—
509	C₂×#95	C₂×#120	1	2	yes	—
510	C₂×#95	C₂×#120	1	2	yes	—
511	C₂×#95	C₂×#120	1	2	yes	—
512	C₂×#95	C₂×#120	1	2	yes	—
513	C₂⁵	#2846	1	1	yes	characteristic
514	C₂⁵	#2846	1	1	yes	characteristic
515	C₂⁵	#2846	1	1	yes	characteristic
516	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
517	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
518	C₂⁵	#3026	1	1	yes	characteristic
519	C₂⁵	#3026	1	1	yes	characteristic
520	C₂⁵	C₂²×#120	1	1	yes	characteristic
521	C₂⁵	C₂²×#120	1	1	yes	characteristic
522	C₂⁵	C₂²×#120	1	2	yes	—
523	C₂³×C₄	#2846	1	2	yes	—
524	C₂³×C₄	#2846	1	1	yes	characteristic
525	C₂³×C₄	#2846	1	2	yes	—
526	C₂³×C₄	C₂²×#120	1	2	yes	—
527	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
529	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	2	yes	—
530	C₂⁴	#32898	1	1	yes	characteristic
531	C₂⁴	#32898	1	1	yes	characteristic
532	C₂⁴	#32898	1	1	yes	characteristic
533	C₂⁴	#32898	1	1	yes	characteristic
534	C₂⁴	C₂×#2846	1	1	yes	characteristic
535	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
536	C₂⁴	C₂×#3026	1	1	yes	characteristic
537	C₂⁴	#60399	1	4	yes	—
538	C₂³	#511790	1	2	yes	—
539	C₂³	C₂×#32898	1	1	yes	characteristic
540	C₂³	#6628896	1	2	yes	—
541	C₂²	C₂×#511790	1	1	yes	characteristic
542	C₂²	#72216366	1	2	yes	—
543	C₂²	#72237402	1	1	yes	characteristic
544	C₂²	#72238342	1	1	yes	characteristic
545	C₂²	#72249650	1	2	yes	—
546	C₂	#72249438	1	1	yes	characteristic
547	C₂	#72256105	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#72237402
commutator, Frattini, cosocle	C₂²×#120	C₂⁵
LCS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×#534 ◁ G
LECS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262719	C₂	semidirect
2. #72262715	C₂	semidirect
3. #72262714	C₂	semidirect
4. #72262713	C₂	semidirect
5. #72262708	C₂	semidirect
6. #72262707	C₂	semidirect
7. #72262706	C₂²	semidirect
8. #72262688	C₂	semidirect
9. #72262680	C₂²	semidirect
10. #72262679	C₂²	semidirect
12. #72262573	C₂	semidirect
13. #72262572	C₂²	semidirect
14. #72262570	C₂²	semidirect
15. #72262569	C₂²	semidirect
16. #72262565	C₂²	semidirect
17. #72262542	C₂	semidirect
18. #72262523	C₂	semidirect
19. #72262522	C₂²	semidirect
20. #72262522	C₂²	semidirect
21. #72262519	C₂²	semidirect
22. #72262518	C₂²	semidirect
23. #72262516	C₂²	semidirect
24. #72262509	C₂²	semidirect
25. #72262480	C₂	semidirect
26. #72262478	C₂²	semidirect
27. #72262475	C₂²	semidirect
28. #72262463	C₂²	semidirect
29. #72256396	C₂²	semidirect
30. #72238497	C₂²	semidirect
31. #72238470	C₂	semidirect
32. #72238469	C₂²	semidirect
33. #72238468	C₂²	semidirect
34. #72238467	C₂²	semidirect
36. #72238449	C₂	semidirect
37. #72238448	C₂²	semidirect
38. #72238438	C₂²	semidirect
39. #72238361	C₂	semidirect
40. #72237489	C₂²	semidirect
41. #72237488	C₂²	semidirect
42. #72237487	C₂²	semidirect
43. #72237486	C₂²	semidirect
44. #72237039	C₂	semidirect
45. #72237034	C₂²	semidirect
47. #72235234	C₂²	semidirect
48. #72234717	C₂	semidirect
50. #72234713	C₂²	semidirect
51. #72234711	C₂²	semidirect
52. #72234711	C₂²	semidirect
53. #72234710	C₂²	semidirect
54. #72234639	C₂	semidirect
55. #72234638	C₂²	semidirect
56. #72234637	C₂²	semidirect
58. #72234623	C₂²	semidirect
59. #72234606	C₂²	semidirect
60. #72234515	C₂²	semidirect
61. #72234515	C₂²	semidirect
62. #72234515	C₂²	semidirect
64. #72234108	C₂²	semidirect
65. #72234108	C₂²	semidirect
66. #72233790	C₂²	semidirect
67. #72233067	C₂²	semidirect
68. #72232836	C₂²	semidirect
69. #72232806	C₂²	semidirect
70. #72232714	C₂²	semidirect
71. #72225989	C₂²	semidirect
73. #72225870	C₂²	semidirect
76. #72224136	C₂²	semidirect
77. #72219314	C₂²	semidirect
78. #72219311	C₂²	semidirect
79. #72215671	C₂²	semidirect
80. #72215671	C₂²	semidirect
82. #72210587	C₂²	semidirect
84. C₂³×D₄²	D₄	semidirect
85. C₂×#47031	D₄	semidirect
86. C₂×#46996	D₄	semidirect
89. #6499870	C₂³	semidirect
92. #5509417	D₄	semidirect
93. #5509416	D₄	semidirect
95. #5065226	D₄	semidirect
96. #5065079	D₄	semidirect
97. #5065025	D₄	semidirect
98. #5036282	D₄	semidirect
99. #5036078	D₄	semidirect
102. #5020751	D₄	semidirect
103. #5020747	D₄	semidirect
104. #4466151	D₄	semidirect
105. #4466053	D₄	semidirect
111. #4421183	D₄	semidirect
112. #4420586	D₄	semidirect
113. #4420586	D₄	semidirect
118. #4379766	D₄	semidirect
120. #2600505	D₄	semidirect
124. #2032535	D₄	semidirect
126. #1452828	D₄	semidirect
127. #1448671	D₄	semidirect
128. #846058	D₄	semidirect
129. #686193	D₄	semidirect
130. #663621	D₄	semidirect
131. #663621	D₄	semidirect
132. #659149	D₄	semidirect
133. #650612	D₄	semidirect
134. #648360	D₄	semidirect
135. #647656	D₄	semidirect
138. #617710	D₄	semidirect
141. #616960	D₄	semidirect
143. #612424	D₄	semidirect
144. #576189	D₄	semidirect
145. #576160	D₄	semidirect
146. #556752	D₄	semidirect
149. #346466	C₂³	semidirect
152. #346446	C₂³	semidirect
157. #187934	C₂³	semidirect
158. #139830	C₂³	semidirect
161. #139718	C₂³	semidirect
166. #139506	C₂³	semidirect
169. #139504	C₂³	semidirect
170. #139504	C₂³	semidirect
171. #139484	C₂³	semidirect
172. #135561	C₂³	semidirect
173. #135507	C₂³	semidirect
175. #134036	C₂³	semidirect
178. #133825	C₂³	semidirect
180. #119550	C₂³	semidirect
183. #115631	C₂³	semidirect
190. C₂²×D₄²	C₂×D₄	semidirect
196. C₂³×#120	C₂×D₄	semidirect
197. C₂×#2697	C₂×D₄	semidirect
198. C₂×#2668	C₂×D₄	semidirect
199. C₂×#2840	C₂×D₄	semidirect
201. C₂×#2815	C₂×D₄	semidirect
202. C₂×#2815	C₂×D₄	semidirect
203. C₂×#2812	C₂×D₄	semidirect
209. C₂×#2607	C₂×D₄	semidirect
213. C₂×#2403	C₂×D₄	semidirect
214. C₂×#2403	C₂×D₄	semidirect
224. C₂×#2308	C₂×D₄	semidirect
228. #17272	C₂×D₄	semidirect
229. #17147	C₂×D₄	semidirect
230. #17136	C₂×D₄	semidirect
231. #17102	C₂×D₄	semidirect
241. #15948	C₂×D₄	semidirect
245. #15947	C₂×D₄	semidirect
250. #15649	C₂×D₄	semidirect
251. #15636	C₂×D₄	semidirect
252. #15561	C₂×D₄	semidirect
253. #15539	C₂×D₄	semidirect
258. #15284	C₂×D₄	semidirect
259. #15284	C₂×D₄	semidirect
262. #15281	C₂×D₄	semidirect
263. #15281	C₂×D₄	semidirect
264. #15267	C₂×D₄	semidirect
265. #15267	C₂×D₄	semidirect
266. #15267	C₂×D₄	semidirect
267. #15267	C₂×D₄	semidirect
272. #15261	C₂×D₄	semidirect
276. #15258	C₂×D₄	semidirect
285. #14679	C₂×D₄	semidirect
286. #14661	C₂×D₄	semidirect
290. #14657	C₂×D₄	semidirect
291. #14567	C₂×D₄	semidirect
292. #14567	C₂×D₄	semidirect
293. #14506	C₂×D₄	semidirect
294. #14445	C₂×D₄	semidirect
295. #14365	C₂×D₄	semidirect
296. #14358	C₂×D₄	semidirect
300. #14262	C₂×D₄	semidirect
303. #14253	C₂×D₄	semidirect
304. #14207	C₂×D₄	semidirect
308. #14134	C₂×D₄	semidirect
311. #13867	C₂×D₄	semidirect
312. #13828	C₂×D₄	semidirect
313. #13827	C₂×D₄	semidirect
314. #13807	C₂×D₄	semidirect
315. #13807	C₂×D₄	semidirect
316. C₂²⋊C₄²	C₂×D₄	semidirect
317. C₂²⋊C₄²	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72262719	2
#72262715	2
#72262714	2
#72262713	2
#72262708	2
#72262707	2
#72262688	2
#72262573	2
#72262542	2
#72262523	2
#72262480	2
#72238470	2
#72238449	2
#72238361	2
#72237039	2
#72234717	2
#72234639	2