Subgroups — #72262761

Order 4096.

At least 21493 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	#72262756	C₂	1	4	yes	maximal, complemented
2	#72262755	C₂	1	4	yes	maximal, complemented
3	#72262754	C₂	1	2	yes	maximal, complemented
4	#72262752	C₂	1	2	yes	maximal, complemented
5	#72262747	C₂	1	2	yes	maximal, complemented
6	#72262746	C₂	1	2	yes	maximal, complemented
7	#72262688	C₂	1	1	yes	maximal, characteristic, complemented
8	#72262685	C₂²	1	2	yes	complemented
9	#72262684	C₂²	1	2	yes	complemented
10	#72262682	C₂²	1	2	yes	—
11	#72262681	C₂²	1	2	yes	—
12	#72262579	C₂	1	2	yes	maximal, complemented
13	#72262578	C₂²	1	4	yes	complemented
14	#72262577	C₂²	1	4	yes	complemented
15	#72262576	C₂²	1	4	yes	complemented
16	#72262575	C₂²	1	4	yes	complemented
17	#72262565	C₂²	1	1	yes	characteristic, complemented
18	#72262549	C₂	1	2	yes	maximal, complemented
19	#72262548	C₂²	1	4	yes	complemented
20	#72262547	C₂²	1	4	yes	complemented
21	#72262545	C₂²	1	4	yes	complemented
22	#72262544	C₂²	1	4	yes	complemented
23	#72262532	C₂	1	2	yes	maximal, complemented
24	#72262530	C₂²	1	4	yes	complemented
25	#72262529	C₂²	1	4	yes	complemented
26	#72262528	C₂²	1	4	yes	complemented
27	#72262526	C₂²	1	4	yes	complemented
28	#72262509	C₂²	1	1	yes	characteristic, complemented
29	#72262488	C₂	1	2	yes	maximal, complemented
30	#72262485	C₂²	1	4	yes	complemented
31	#72262484	C₂²	1	4	yes	complemented
32	#72262482	C₂²	1	4	yes	complemented
33	#72262481	C₂²	1	4	yes	complemented
34	#72262463	C₂²	1	1	yes	characteristic, complemented
35	#72238497	C₂²	1	1	yes	characteristic, complemented
36	#72238371	C₂	1	1	yes	maximal, characteristic, complemented
37	#72238370	C₂²	1	2	yes	complemented
38	#72238369	C₂²	1	2	yes	complemented
39	#72238368	C₂²	1	2	yes	complemented
40	#72238367	C₂²	1	2	yes	complemented
41	#72238366	C₂²	1	4	yes	complemented
42	#72237991	C₂	1	1	yes	maximal, characteristic, complemented
43	#72237989	C₂²	1	2	yes	complemented
44	#72237988	C₂²	1	2	yes	complemented
45	#72237987	C₂²	1	4	yes	complemented
46	#72237982	C₂²	1	2	yes	complemented
47	#72237980	C₂²	1	2	yes	complemented
48	#72237585	C₂	1	1	yes	maximal, characteristic, complemented
49	#72237584	C₂²	1	4	yes	complemented
50	#72237583	C₂²	1	2	yes	complemented
51	#72237582	C₂²	1	2	yes	complemented
52	#72237579	C₂²	1	2	yes	complemented
53	#72237471	C₂	1	1	yes	maximal, characteristic, complemented
54	#72237459	C₂²	1	2	yes	complemented
55	#72237039	C₂	1	1	yes	maximal, characteristic, complemented
56	#72237036	C₂²	1	2	yes	—
57	#72237036	C₂²	1	2	yes	complemented
58	#72237034	C₂²	1	1	yes	characteristic, complemented
59	#72237033	C₂²	1	1	yes	characteristic, complemented
60	#72237018	C₂²	1	2	yes	complemented
61	#72237018	C₂²	1	2	yes	complemented
62	#72237017	C₂²	1	2	yes	complemented
63	#72237017	C₂²	1	2	yes	complemented
64	#72235234	C₂²	1	1	yes	characteristic, complemented
65	#72235147	C₂²	1	2	yes	complemented
66	#72234789	C₂	1	1	yes	maximal, characteristic, complemented
67	#72234769	C₂²	1	4	yes	complemented
68	#72234744	C₂²	1	2	yes	complemented
69	#72234724	C₂²	1	2	yes	complemented
70	#72234716	C₂²	1	1	yes	characteristic
71	#72234636	C₂²	1	1	yes	characteristic
72	#72234509	C₂²	1	2	yes	complemented
73	#72232980	C₂²	1	2	yes	complemented
74	#72226029	C₂²	1	2	yes	complemented
75	#72226029	C₂²	1	2	yes	complemented
76	#72225985	C₂²	1	2	yes	complemented
77	#72225870	C₂²	1	1	yes	characteristic, complemented
78	#72225712	C₂²	1	1	yes	characteristic, complemented
79	#72225665	C₂²	1	1	yes	characteristic
80	#72224136	C₂²	1	1	yes	characteristic, complemented
81	#72219314	C₂²	1	1	yes	characteristic, complemented
82	#72219310	C₂²	1	1	yes	characteristic, complemented
83	#10586404	C₂³	1	1	yes	characteristic
84	C₂³×D₄²	D₄	1	1	yes	characteristic
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	#6499871	C₂³	1	2	yes	—
89	#6499869	C₂³	1	2	yes	—
90	#6374128	C₂³	1	1	yes	characteristic
91	#6347363	C₂³	1	4	yes	complemented
92	#5519539	D₄	1	2	yes	complemented
93	#5519537	D₄	1	2	yes	complemented
94	#5118112	D₄	1	2	yes	complemented
95	#5117977	D₄	1	2	yes	complemented
96	#5083490	D₄	1	2	yes	complemented
97	#5083484	D₄	1	2	yes	complemented
98	#5082849	C₂³	1	2	yes	—
99	#5082801	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	#4524223	C₂³	1	2	yes	—
105	#4524032	D₄	1	2	yes	complemented
106	#4466055	D₄	1	2	yes	complemented
107	#4444985	C₂³	1	2	yes	—
108	#4444438	D₄	1	2	yes	complemented
109	#4440064	C₂³	1	2	yes	—
110	#4437473	C₂³	1	2	yes	—
111	#4435227	C₂³	1	1	yes	characteristic
112	#4430405	C₂³	1	1	yes	characteristic
113	#4420586	D₄	1	1	yes	characteristic
114	#4420586	D₄	1	1	yes	characteristic
115	#4420586	C₂³	1	1	yes	characteristic
116	#4420586	C₂³	1	1	yes	characteristic
117	#4381972	D₄	1	2	yes	complemented
118	#4380237	C₂³	1	2	yes	—
119	#4379699	C₂³	1	2	yes	—
120	#2601286	C₂³	1	2	yes	—
121	#2600715	C₂³	1	2	yes	—
122	#2536084	C₂³	1	2	yes	—
123	#2109240	D₄	1	2	yes	complemented
124	#2039918	C₂³	1	2	yes	—
125	#2032565	D₄	1	2	yes	complemented
126	#1495238	D₄	1	2	yes	complemented
127	#1494931	D₄	1	2	yes	complemented
128	#845298	D₄	1	2	yes	complemented
129	#686193	D₄	1	1	yes	characteristic, complemented
130	#663621	C₂³	1	1	yes	characteristic
131	#663621	C₂³	1	1	yes	characteristic
132	#659638	D₄	1	2	yes	complemented
133	#651203	D₄	1	2	yes	complemented
134	#648360	D₄	1	2	yes	complemented
135	#648360	D₄	1	1	yes	characteristic, complemented
136	#647656	D₄	1	1	yes	characteristic
137	#647656	D₄	1	1	yes	characteristic
138	#631841	C₂³	1	2	yes	—
139	#617710	D₄	1	1	yes	characteristic
140	#617710	C₂³	1	1	yes	characteristic
141	#616960	D₄	1	1	yes	characteristic
142	#616960	C₂³	1	1	yes	characteristic
143	#612801	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
147	#347044	C₂³	1	2	yes	—
148	#347044	C₂³	1	2	yes	—
149	#346462	C₂³	1	4	yes	complemented
150	#346452	C₂³	1	4	yes	complemented
151	#346447	C₂³	1	2	yes	—
152	#346447	C₂³	1	2	yes	—
153	#188122	C₂³	1	2	yes	—
154	#188109	C₂³	1	2	yes	—
155	#188109	C₂³	1	1	yes	characteristic
156	#188049	C₂³	1	1	yes	characteristic
157	#185285	C₂³	1	4	yes	complemented
158	#139916	C₂³	1	4	yes	complemented
159	#139914	C₂³	1	4	yes	complemented
160	#139912	C₂³	1	4	yes	—
161	#139912	C₂³	1	4	yes	—
162	#139719	C₂³	1	2	yes	—
163	#139719	C₂³	1	2	yes	—
164	#139717	C₂³	1	2	yes	—
165	#139717	C₂³	1	2	yes	—
166	#139505	C₂³	1	4	yes	complemented
167	#139487	C₂³	1	4	yes	complemented
168	#139478	C₂³	1	4	yes	—
169	#139478	C₂³	1	4	yes	—
170	#139456	C₂³	1	4	yes	complemented
171	#139450	C₂³	1	4	yes	complemented
172	#135475	C₂³	1	4	yes	complemented
173	#135471	C₂³	1	4	yes	complemented
174	#134037	C₂³	1	2	yes	—
175	#134035	C₂³	1	2	yes	—
176	#133826	C₂³	1	2	yes	—
177	#133824	C₂³	1	2	yes	—
178	#133086	C₂³	1	4	yes	complemented
179	#133080	C₂³	1	4	yes	complemented
180	#119544	C₂³	1	4	yes	complemented
181	#115697	C₂³	1	2	yes	—
182	#115633	C₂³	1	2	yes	—
183	#112274	C₂³	1	4	yes	complemented
184	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
185	#62820	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×#534	C₂×D₄	1	1	yes	characteristic
191	C₂²×#534	C₂⁴	1	1	yes	characteristic
192	C₂³×#127	C₂×D₄	1	1	yes	characteristic
193	C₂³×#120	C₂×D₄	1	1	yes	characteristic
194	C₂³×#120	C₂×D₄	1	1	yes	characteristic
195	C₂×#2760	C₂×D₄	1	2	yes	complemented
196	C₂×#2736	C₂×D₄	1	2	yes	complemented
197	C₂×#2733	C₂×D₄	1	2	yes	complemented
198	C₂×#2699	C₂×D₄	1	2	yes	complemented
199	C₂×#2840	C₂×D₄	1	1	yes	characteristic, complemented
200	C₂×#2813	C₂×D₄	1	2	yes	—
201	C₂×#2815	C₂×D₄	1	1	yes	characteristic, complemented
202	C₂×#2849	C₂×D₄	1	1	yes	characteristic
203	C₂×#2849	C₂⁴	1	1	yes	characteristic
204	C₂×#2847	C₂×D₄	1	2	yes	complemented
205	C₂×#2846	C₂×D₄	1	1	yes	characteristic
206	C₂×#2846	C₂×D₄	1	1	yes	characteristic
207	C₂×#2846	C₂×D₄	1	2	yes	—
208	C₂×#2607	C₂×D₄	1	1	yes	characteristic, complemented
209	C₂×#2404	C₂×D₄	1	2	yes	—
210	C₂×#2431	C₂×D₄	1	2	yes	—
211	C₂×#2433	C₂×D₄	1	2	yes	—
212	C₂×#2433	C₂×D₄	1	2	yes	complemented
213	C₂×#2403	C₂×D₄	1	1	yes	characteristic, complemented
214	C₂×#2403	C₂×D₄	1	2	yes	complemented
215	C₂×#2615	C₂×D₄	1	2	yes	—
216	C₂×#2661	C₂⁴	1	2	yes	—
217	C₂×#2613	C₂×D₄	1	1	yes	characteristic
218	C₂×#2613	C₂×D₄	1	1	yes	characteristic
219	C₂×#2613	C₂×D₄	1	2	yes	—
220	C₂×#2613	C₂×D₄	1	1	yes	characteristic
221	C₂×#2613	C₂⁴	1	1	yes	characteristic
222	C₂×#2333	C₂×D₄	1	2	yes	complemented
223	C₂×#2308	C₂×D₄	1	1	yes	characteristic
224	C₂×#2308	C₂×D₄	1	1	yes	characteristic
225	C₂²×#379	C₂×D₄	1	1	yes	characteristic
226	#21747	C₂⁴	1	2	yes	—
227	#17392	C₂⁴	1	4	yes	—
228	#17147	C₂×D₄	1	2	yes	complemented
229	#17140	C₂×D₄	1	2	yes	complemented
230	#17105	C₂×D₄	1	2	yes	complemented
231	#17082	C₂×D₄	1	2	yes	complemented
232	#16214	C₂×D₄	1	2	yes	complemented
233	#16208	C₂×D₄	1	2	yes	complemented
234	#16171	C₂×D₄	1	2	yes	complemented
235	#15964	C₂×D₄	1	2	yes	complemented
236	#15948	C₂×D₄	1	1	yes	characteristic
237	#15948	C₂×D₄	1	1	yes	characteristic
238	#15948	C₂⁴	1	1	yes	characteristic
239	#15948	C₂⁴	1	1	yes	characteristic
240	#15947	C₂×D₄	1	1	yes	characteristic
241	#15947	C₂×D₄	1	1	yes	characteristic
242	#15947	C₂×D₄	1	1	yes	characteristic
243	#15947	C₂×D₄	1	1	yes	characteristic
244	#15856	C₂×D₄	1	2	yes	complemented
245	#15833	C₂×D₄	1	2	yes	complemented
246	#15674	C₂×D₄	1	2	yes	—
247	#15668	C₂×D₄	1	2	yes	—
248	#15668	C₂⁴	1	2	yes	—
249	#15630	C₂×D₄	1	2	yes	complemented
250	#15630	C₂×D₄	1	2	yes	complemented
251	#15480	C₂×D₄	1	2	yes	complemented
252	#15467	C₂×D₄	1	2	yes	complemented
253	#15467	C₂×D₄	1	2	yes	complemented
254	#15467	C₂×D₄	1	2	yes	complemented
255	#15464	C₂×D₄	1	2	yes	—
256	#15412	C₂×D₄	1	2	yes	—
257	#15412	C₂⁴	1	2	yes	—
258	#15340	C₂×D₄	1	2	yes	—
259	#15310	C₂×D₄	1	2	yes	—
260	#15310	C₂×D₄	1	2	yes	—
261	#15310	C₂×D₄	1	2	yes	—
262	#15310	C₂×D₄	1	2	yes	—
263	#15283	C₂×D₄	1	2	yes	—
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	2	yes	—
271	#15261	C₂⁴	1	1	yes	characteristic
272	#15261	C₂⁴	1	1	yes	characteristic
273	#15259	C₂×D₄	1	2	yes	—
274	#15259	C₂×D₄	1	2	yes	—
275	#15258	C₂×D₄	1	1	yes	characteristic
276	#15258	C₂×D₄	1	1	yes	characteristic
277	#15258	C₂×D₄	1	1	yes	characteristic
278	#15258	C₂×D₄	1	1	yes	characteristic
279	#15258	C₂×D₄	1	2	yes	—
280	#15258	C₂×D₄	1	2	yes	—
281	#15258	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	#14659	C₂×D₄	1	2	yes	—
286	#14657	C₂×D₄	1	1	yes	characteristic
287	#14657	C₂×D₄	1	1	yes	characteristic
288	#14652	C₂×D₄	1	2	yes	complemented
289	#14649	C₂×D₄	1	2	yes	complemented
290	#14641	C₂×D₄	1	2	yes	complemented
291	#14641	C₂×D₄	1	2	yes	complemented
292	#14567	C₂×D₄	1	2	yes	complemented
293	#14533	C₂×D₄	1	2	yes	complemented
294	#14507	C₂×D₄	1	2	yes	complemented
295	#14365	C₂×D₄	1	2	yes	complemented
296	#14335	C₂×D₄	1	1	yes	characteristic
297	#14335	C₂×D₄	1	1	yes	characteristic
298	#14295	C₂×D₄	1	2	yes	complemented
299	#14290	C₂×D₄	1	2	yes	—
300	#14287	C₂⁴	1	2	yes	—
301	#14255	C₂×D₄	1	2	yes	—
302	#14246	C₂×D₄	1	2	yes	complemented
303	#14181	C₂×D₄	1	2	yes	complemented
304	#14167	C₂×D₄	1	2	yes	—
305	#14134	C₂×D₄	1	1	yes	characteristic
306	#14134	C₂×D₄	1	1	yes	characteristic
307	#13903	C₂×D₄	1	2	yes	—
308	#13902	C₂×D₄	1	2	yes	—
309	#13902	C₂×D₄	1	2	yes	complemented
310	#13828	C₂×D₄	1	1	yes	characteristic, complemented
311	#13827	C₂×D₄	1	1	yes	characteristic, complemented
312	#13826	C₂×D₄	1	2	yes	complemented
313	#13824	C₂×D₄	1	2	yes	complemented
314	#13807	C₂×D₄	1	1	yes	characteristic, complemented
315	C₂²⋊C₄²	C₂×D₄	1	2	yes	complemented
316	C₂²⋊C₄²	C₂×D₄	1	1	yes	characteristic, complemented
317	C₄×#379	C₂×D₄	1	2	yes	complemented
318	#8553	C₂⁴	1	4	yes	—
319	#8548	C₂⁴	1	2	yes	—
320	#8543	C₂⁴	1	2	yes	—
321	C₂⁷	#120	1	1	yes	characteristic
322	C₂⁷	#120	1	1	yes	characteristic
323	C₂⁷	#120	1	1	yes	characteristic
324	C₂³×#41	#120	1	2	yes	—
325	C₂⁴×D₄	#120	1	1	yes	characteristic
326	C₂⁴×D₄	#120	1	1	yes	characteristic
327	C₂⁴×D₄	#120	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	1	yes	characteristic
331	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂²×#127	#120	1	1	yes	characteristic
333	C₂²×#127	#120	1	1	yes	characteristic
334	C₂²×#127	#120	1	2	yes	—
335	C₂²×#127	#120	1	2	yes	—
336	C₂²×#127	#120	1	2	yes	—
337	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
338	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
339	C₂²×#124	#120	1	2	yes	—
340	C₂²×#123	#120	1	1	yes	characteristic
341	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
342	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
343	C₂²×#123	C₂²×D₄	1	2	yes	—
344	C₂²×#123	C₂⁵	1	1	yes	characteristic
345	C₂²×#121	C₂²×D₄	1	2	yes	—
346	C₂²×#121	C₂²×D₄	1	2	yes	—
347	C₂²×#121	C₂²×D₄	1	2	yes	—
348	C₂²×#120	#120	1	1	yes	characteristic
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	1	yes	characteristic
353	C₂²×#120	#120	1	2	yes	—
354	C₂²×#120	#120	1	2	yes	—
355	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
356	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
357	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
358	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
359	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
360	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
361	C₂²×#120	C₂²×D₄	1	2	yes	—
362	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
363	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
364	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
365	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
366	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
367	C₂³×C₄²	#120	1	1	yes	characteristic
368	C₂×#400	#120	1	2	yes	—
369	C₂×#399	#120	1	2	yes	—
370	C₂×#398	C₂²×D₄	1	2	yes	—
371	C₂×#397	C₂²×D₄	1	2	yes	—
372	C₂×#394	#120	1	2	yes	—
373	C₂×#394	C₂²×D₄	1	2	yes	—
374	C₂×#394	C₂²×D₄	1	2	yes	—
375	C₂×#394	C₂²×D₄	1	2	yes	—
376	C₂×#393	#120	1	2	yes	—
377	C₂×#393	#120	1	2	yes	—
378	C₂×#393	C₂²×D₄	1	2	yes	—
379	C₂×#393	C₂²×D₄	1	2	yes	—
380	C₂×#392	#120	1	2	yes	—
381	C₂×#392	#120	1	2	yes	—
382	C₂×#392	#120	1	2	yes	—
383	C₂×#392	#120	1	2	yes	—
384	C₂×#392	#120	1	2	yes	—
385	C₂×#392	C₂²×D₄	1	2	yes	—
386	C₂×#392	C₂²×D₄	1	2	yes	—
387	C₂×#392	C₂²×D₄	1	2	yes	—
388	C₂×#391	C₂²×D₄	1	2	yes	—
389	C₂×#390	#120	1	2	yes	—
390	C₂×#390	#120	1	2	yes	—
391	C₂×#390	C₂²×D₄	1	2	yes	—
392	C₂×#381	#120	1	2	yes	—
393	C₂×#381	#120	1	2	yes	—
394	C₂×#381	#120	1	1	yes	characteristic
395	C₂×#381	C₂²×D₄	1	1	yes	characteristic
396	C₂×#381	C₂²×D₄	1	1	yes	characteristic
397	C₂×#381	C₂²×D₄	1	1	yes	characteristic
398	C₂×#380	#120	1	2	yes	—
399	C₂×#380	C₂²×D₄	1	2	yes	—
400	C₂×#379	#120	1	1	yes	characteristic
401	C₂×#379	#120	1	1	yes	characteristic
402	C₂×#379	#120	1	1	yes	characteristic
403	C₂×#379	#120	1	1	yes	characteristic
404	C₂×#379	#120	1	1	yes	characteristic
405	C₂×#379	#120	1	2	yes	—
406	C₂×#379	C₂²×D₄	1	1	yes	characteristic
407	C₂×#379	C₂²×D₄	1	1	yes	characteristic
408	C₂×#379	C₂²×D₄	1	2	yes	—
409	C₂×#379	C₂²×D₄	1	2	yes	—
410	C₂×#379	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₂²⋊C₄	#120	1	2	yes	—
412	C₂×C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
414	#1445	C₂²×D₄	1	2	yes	—
415	#1445	C₂²×D₄	1	2	yes	—
416	#1440	C₂²×D₄	1	2	yes	—
417	#1440	C₂²×D₄	1	2	yes	—
418	#1438	#120	1	2	yes	—
419	#1438	#120	1	2	yes	—
420	#1438	#120	1	2	yes	—
421	#1438	#120	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	C₂²×D₄	1	1	yes	characteristic
429	#1438	C₂²×D₄	1	1	yes	characteristic
430	#1438	C₂²×D₄	1	1	yes	characteristic
431	#1438	C₂²×D₄	1	1	yes	characteristic
432	#1437	#120	1	2	yes	—
433	#1437	#120	1	2	yes	—
434	#1437	#120	1	2	yes	—
435	#1437	#120	1	2	yes	—
436	#1437	#120	1	2	yes	—
437	#1437	#120	1	2	yes	—
438	#1437	#120	1	2	yes	—
439	#1437	#120	1	2	yes	—
440	#1437	C₂²×D₄	1	2	yes	—
441	#1437	C₂²×D₄	1	2	yes	—
442	#1437	C₂²×D₄	1	2	yes	—
443	#1437	C₂²×D₄	1	2	yes	—
444	#1437	C₂²×D₄	1	2	yes	—
445	#1437	C₂²×D₄	1	2	yes	—
446	#1436	#120	1	2	yes	—
447	#1436	#120	1	2	yes	—
448	#1436	C₂²×D₄	1	2	yes	—
449	#1436	C₂²×D₄	1	2	yes	—
450	#1436	C₂²×D₄	1	2	yes	—
451	#1436	C₂²×D₄	1	2	yes	—
452	C₂⁶	C₂×#120	1	1	yes	characteristic
453	C₂⁶	C₂×#120	1	1	yes	characteristic
454	C₂⁶	C₂×#120	1	1	yes	characteristic
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	C₂³×Q₈	C₂×#120	1	2	yes	—
461	C₂³×D₄	C₂×#120	1	1	yes	characteristic
462	C₂³×D₄	C₂×#120	1	1	yes	characteristic
463	C₂³×D₄	C₂×#120	1	2	yes	—
464	C₂³×D₄	C₂×#120	1	2	yes	—
465	C₂³×D₄	C₂×#120	1	2	yes	—
466	C₂³×D₄	C₂×#120	1	2	yes	—
467	C₂³×D₄	C₂×#120	1	1	yes	characteristic
468	C₂³×D₄	C₂×#120	1	2	yes	—
469	C₂³×D₄	C₂×#120	1	1	yes	characteristic
470	C₂³×D₄	C₂×#120	1	1	yes	characteristic
471	C₂³×D₄	C₂×#120	1	2	yes	—
472	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
473	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
474	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
475	C₂⁴×C₄	C₂×#120	1	2	yes	—
476	C₂⁴×C₄	C₂³×D₄	1	1	yes	characteristic
477	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
478	C₂²×C₄⋊C₄	C₂×#120	1	2	yes	—
479	C₂²×C₄⋊C₄	C₂³×D₄	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	1	yes	characteristic
483	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
484	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
485	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
486	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
487	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
488	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
489	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
490	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
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	1	yes	characteristic
494	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
495	C₂²×C₂²⋊C₄	C₂³×D₄	1	2	yes	—
496	C₂²×C₂²⋊C₄	C₂³×D₄	1	1	yes	characteristic
497	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
498	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
499	C₂²×C₄²	C₂×#120	1	2	yes	—
500	C₂²×C₄²	C₂×#120	1	2	yes	—
501	C₂²×C₄²	C₂×#120	1	2	yes	—
502	C₂²×C₄²	C₂×#120	1	2	yes	—
503	C₂×#95	C₂×#120	1	2	yes	—
504	C₂×#95	C₂×#120	1	2	yes	—
505	C₂×#95	C₂×#120	1	2	yes	—
506	C₂×#95	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	2	yes	—
515	C₂⁵	#2846	1	1	yes	characteristic
516	C₂⁵	#2846	1	1	yes	characteristic
517	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
518	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
519	C₂⁵	#3026	1	1	yes	characteristic
520	C₂⁵	#3026	1	1	yes	characteristic
521	C₂⁵	C₂²×#120	1	1	yes	characteristic
522	C₂⁵	C₂²×#120	1	1	yes	characteristic
523	C₂³×C₄	#2846	1	2	yes	—
524	C₂³×C₄	#2846	1	1	yes	characteristic
525	C₂³×C₄	C₂²×#120	1	2	yes	—
526	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
527	C₂³×C₄	C₂²×#120	1	2	yes	—
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	C₂²×C₄	#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	#72234102	1	2	yes	—
543	C₂²	#72237402	1	1	yes	characteristic
544	C₂²	#72238342	1	1	yes	characteristic
545	C₂²	#72260545	1	2	yes	—
546	C₂	#72249438	1	1	yes	characteristic
547	C₂	#72262734	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#72237402
commutator, Frattini, cosocle	C₂²×#123	C₂⁵
LCS	G ▷ C₂²×#123 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂²×#534 ◁ G
LECS	G ▷ C₂²×#123 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262756	C₂	semidirect
2. #72262755	C₂	semidirect
3. #72262754	C₂	semidirect
4. #72262752	C₂	semidirect
5. #72262747	C₂	semidirect
6. #72262746	C₂	semidirect
7. #72262688	C₂	semidirect
8. #72262685	C₂²	semidirect
9. #72262684	C₂²	semidirect
12. #72262579	C₂	semidirect
13. #72262578	C₂²	semidirect
14. #72262577	C₂²	semidirect
15. #72262576	C₂²	semidirect
16. #72262575	C₂²	semidirect
17. #72262565	C₂²	semidirect
18. #72262549	C₂	semidirect
19. #72262548	C₂²	semidirect
20. #72262547	C₂²	semidirect
21. #72262545	C₂²	semidirect
22. #72262544	C₂²	semidirect
23. #72262532	C₂	semidirect
24. #72262530	C₂²	semidirect
25. #72262529	C₂²	semidirect
26. #72262528	C₂²	semidirect
27. #72262526	C₂²	semidirect
28. #72262509	C₂²	semidirect
29. #72262488	C₂	semidirect
30. #72262485	C₂²	semidirect
31. #72262484	C₂²	semidirect
32. #72262482	C₂²	semidirect
33. #72262481	C₂²	semidirect
34. #72262463	C₂²	semidirect
35. #72238497	C₂²	semidirect
36. #72238371	C₂	semidirect
37. #72238370	C₂²	semidirect
38. #72238369	C₂²	semidirect
39. #72238368	C₂²	semidirect
40. #72238367	C₂²	semidirect
41. #72238366	C₂²	semidirect
42. #72237991	C₂	semidirect
43. #72237989	C₂²	semidirect
44. #72237988	C₂²	semidirect
45. #72237987	C₂²	semidirect
46. #72237982	C₂²	semidirect
47. #72237980	C₂²	semidirect
48. #72237585	C₂	semidirect
49. #72237584	C₂²	semidirect
50. #72237583	C₂²	semidirect
51. #72237582	C₂²	semidirect
52. #72237579	C₂²	semidirect
53. #72237471	C₂	semidirect
54. #72237459	C₂²	semidirect
55. #72237039	C₂	semidirect
57. #72237036	C₂²	semidirect
58. #72237034	C₂²	semidirect
59. #72237033	C₂²	semidirect
60. #72237018	C₂²	semidirect
61. #72237018	C₂²	semidirect
62. #72237017	C₂²	semidirect
63. #72237017	C₂²	semidirect
64. #72235234	C₂²	semidirect
65. #72235147	C₂²	semidirect
66. #72234789	C₂	semidirect
67. #72234769	C₂²	semidirect
68. #72234744	C₂²	semidirect
69. #72234724	C₂²	semidirect
72. #72234509	C₂²	semidirect
73. #72232980	C₂²	semidirect
74. #72226029	C₂²	semidirect
75. #72226029	C₂²	semidirect
76. #72225985	C₂²	semidirect
77. #72225870	C₂²	semidirect
78. #72225712	C₂²	semidirect
80. #72224136	C₂²	semidirect
81. #72219314	C₂²	semidirect
82. #72219310	C₂²	semidirect
85. C₂×#47031	D₄	semidirect
86. C₂×#46996	D₄	semidirect
91. #6347363	C₂³	semidirect
92. #5519539	D₄	semidirect
93. #5519537	D₄	semidirect
94. #5118112	D₄	semidirect
95. #5117977	D₄	semidirect
96. #5083490	D₄	semidirect
97. #5083484	D₄	semidirect
99. #5082801	D₄	semidirect
102. #5020751	D₄	semidirect
103. #5020747	D₄	semidirect
105. #4524032	D₄	semidirect
106. #4466055	D₄	semidirect
108. #4444438	D₄	semidirect
117. #4381972	D₄	semidirect
123. #2109240	D₄	semidirect
125. #2032565	D₄	semidirect
126. #1495238	D₄	semidirect
127. #1494931	D₄	semidirect
128. #845298	D₄	semidirect
129. #686193	D₄	semidirect
132. #659638	D₄	semidirect
133. #651203	D₄	semidirect
134. #648360	D₄	semidirect
135. #648360	D₄	semidirect
143. #612801	D₄	semidirect
144. #576189	D₄	semidirect
145. #576160	D₄	semidirect
149. #346462	C₂³	semidirect
150. #346452	C₂³	semidirect
157. #185285	C₂³	semidirect
158. #139916	C₂³	semidirect
159. #139914	C₂³	semidirect
166. #139505	C₂³	semidirect
167. #139487	C₂³	semidirect
170. #139456	C₂³	semidirect
171. #139450	C₂³	semidirect
172. #135475	C₂³	semidirect
173. #135471	C₂³	semidirect
178. #133086	C₂³	semidirect
179. #133080	C₂³	semidirect
180. #119544	C₂³	semidirect
183. #112274	C₂³	semidirect
195. C₂×#2760	C₂×D₄	semidirect
196. C₂×#2736	C₂×D₄	semidirect
197. C₂×#2733	C₂×D₄	semidirect
198. C₂×#2699	C₂×D₄	semidirect
199. C₂×#2840	C₂×D₄	semidirect
201. C₂×#2815	C₂×D₄	semidirect
204. C₂×#2847	C₂×D₄	semidirect
208. C₂×#2607	C₂×D₄	semidirect
212. C₂×#2433	C₂×D₄	semidirect
213. C₂×#2403	C₂×D₄	semidirect
214. C₂×#2403	C₂×D₄	semidirect
222. C₂×#2333	C₂×D₄	semidirect
228. #17147	C₂×D₄	semidirect
229. #17140	C₂×D₄	semidirect
230. #17105	C₂×D₄	semidirect
231. #17082	C₂×D₄	semidirect
232. #16214	C₂×D₄	semidirect
233. #16208	C₂×D₄	semidirect
234. #16171	C₂×D₄	semidirect
235. #15964	C₂×D₄	semidirect
244. #15856	C₂×D₄	semidirect
245. #15833	C₂×D₄	semidirect
249. #15630	C₂×D₄	semidirect
250. #15630	C₂×D₄	semidirect
251. #15480	C₂×D₄	semidirect
252. #15467	C₂×D₄	semidirect
253. #15467	C₂×D₄	semidirect
254. #15467	C₂×D₄	semidirect
264. #15267	C₂×D₄	semidirect
265. #15267	C₂×D₄	semidirect
266. #15267	C₂×D₄	semidirect
267. #15267	C₂×D₄	semidirect
288. #14652	C₂×D₄	semidirect
289. #14649	C₂×D₄	semidirect
290. #14641	C₂×D₄	semidirect
291. #14641	C₂×D₄	semidirect
292. #14567	C₂×D₄	semidirect
293. #14533	C₂×D₄	semidirect
294. #14507	C₂×D₄	semidirect
295. #14365	C₂×D₄	semidirect
298. #14295	C₂×D₄	semidirect
302. #14246	C₂×D₄	semidirect
303. #14181	C₂×D₄	semidirect
309. #13902	C₂×D₄	semidirect
310. #13828	C₂×D₄	semidirect
311. #13827	C₂×D₄	semidirect
312. #13826	C₂×D₄	semidirect
313. #13824	C₂×D₄	semidirect
314. #13807	C₂×D₄	semidirect
315. C₂²⋊C₄²	C₂×D₄	semidirect
316. C₂²⋊C₄²	C₂×D₄	semidirect
317. C₄×#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
#72262756	2
#72262755	2
#72262754	2
#72262752	2
#72262747	2
#72262746	2
#72262688	2
#72262579	2
#72262549	2
#72262532	2
#72262488	2
#72238371	2
#72237991	2
#72237585	2
#72237471	2
#72237039	2
#72234789	2