Subgroups — #72318703

Order 2048.

At least 13766 conjugacy classes of subgroups; only the 964 normal subgroups are shown.

The subgroup lattice has 619 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72318689	C₂	1	2	yes	maximal, complemented
2	#72318682	C₂	1	1	yes	maximal, characteristic, complemented
3	#72318678	C₂	1	2	yes	maximal, complemented
4	#72318668	C₂	1	2	yes	maximal, complemented
5	#72318659	C₂	1	2	yes	maximal, complemented
6	#72318649	C₂	1	1	yes	maximal, characteristic, complemented
7	#72318637	C₂	1	2	yes	maximal, complemented
8	#72318630	C₂	1	1	yes	maximal, characteristic, complemented
9	#72318622	C₂	1	2	yes	maximal, complemented
10	#72318615	C₂	1	1	yes	maximal, characteristic, complemented
11	#72318605	C₂	1	2	yes	maximal, complemented
12	#72318598	C₂	1	2	yes	maximal, complemented
13	#72318569	C₂	1	1	yes	maximal, characteristic, complemented
14	#72318542	C₂	1	1	yes	maximal, characteristic, complemented
15	#72318279	C₂	1	1	yes	maximal, characteristic, complemented
16	#72318243	C₂	1	1	yes	maximal, characteristic, complemented
17	#72318207	C₂	1	1	yes	maximal, characteristic, complemented
18	#72317855	C₂	1	1	yes	maximal, characteristic, complemented
19	#72311068	C₂	1	1	yes	maximal, characteristic, complemented
20	#72285530	C₂	1	1	yes	maximal, characteristic, complemented
21	#72285519	C₂	1	1	yes	maximal, characteristic, complemented
22	#72252010	C₂	1	1	yes	maximal, characteristic, complemented
23	#72210498	C₂	1	1	yes	maximal, characteristic, complemented
24	#8934366	C₂²	1	1	yes	characteristic
25	#8926850	C₂²	1	1	yes	characteristic
26	#8898948	C₂²	1	2	yes	—
27	#8824175	C₂²	1	2	yes	—
28	#8756105	C₂²	1	1	yes	characteristic
29	#8360950	C₂²	1	2	yes	—
30	#8193898	C₂²	1	1	yes	characteristic
31	#7826509	C₂²	1	2	yes	—
32	#7743196	C₂²	1	1	yes	characteristic
33	#7737411	C₂²	1	1	yes	characteristic
34	#7674604	C₂²	1	1	yes	characteristic
35	#6470243	C₂²	1	2	yes	complemented
36	#6470231	C₂²	1	2	yes	complemented
37	#6437457	C₂²	1	1	yes	characteristic, complemented
38	#6437456	C₂²	1	1	yes	characteristic, complemented
39	#6432958	C₂²	1	1	yes	characteristic, complemented
40	#500190	C₂²	1	2	yes	complemented
41	#500183	C₂²	1	2	yes	complemented
42	#500182	C₂²	1	2	yes	complemented
43	#500178	C₂²	1	1	yes	characteristic, complemented
44	#500177	C₂²	1	1	yes	characteristic
45	#500177	C₂²	1	2	yes	complemented
46	#500177	C₂²	1	1	yes	characteristic, complemented
47	#500177	C₂²	1	1	yes	characteristic, complemented
48	#500172	C₂²	1	2	yes	complemented
49	#500170	C₂²	1	2	yes	complemented
50	#499852	C₂²	1	2	yes	complemented
51	#499849	C₂²	1	2	yes	complemented
52	#499848	C₂²	1	2	yes	complemented
53	#499843	C₂²	1	2	yes	complemented
54	#499838	C₂²	1	2	yes	complemented
55	#499834	C₂²	1	1	yes	characteristic, complemented
56	#499832	C₂²	1	1	yes	characteristic
57	#499832	C₂²	1	2	yes	complemented
58	#499832	C₂²	1	1	yes	characteristic, complemented
59	#499832	C₂²	1	1	yes	characteristic, complemented
60	#496243	C₂²	1	2	yes	complemented
61	#496243	C₂²	1	2	yes	complemented
62	#496237	C₂²	1	2	yes	complemented
63	#496237	C₂²	1	2	yes	complemented
64	#493434	C₂²	1	2	yes	complemented
65	#493431	C₂²	1	1	yes	characteristic, complemented
66	#493431	C₂²	1	1	yes	characteristic, complemented
67	#451038	C₂²	1	1	yes	characteristic, complemented
68	#451037	C₂²	1	1	yes	characteristic, complemented
69	#449527	C₂²	1	1	yes	characteristic, complemented
70	#449492	C₂²	1	1	yes	characteristic, complemented
71	#418124	C₂²	1	1	yes	characteristic, complemented
72	#417813	C₂²	1	1	yes	characteristic, complemented
73	#417568	C₂²	1	1	yes	characteristic, complemented
74	#417566	C₂²	1	1	yes	characteristic, complemented
75	#391714	C₂²	1	1	yes	characteristic, complemented
76	#382444	C₂²	1	1	yes	characteristic, complemented
77	#382443	C₂²	1	1	yes	characteristic, complemented
78	#251857	C₂²	1	2	yes	complemented
79	#251855	C₂²	1	2	yes	complemented
80	#251840	C₂²	1	2	yes	complemented
81	#251838	C₂²	1	2	yes	complemented
82	#245267	C₂²	1	2	yes	complemented
83	#245255	C₂²	1	2	yes	complemented
84	#245234	C₂²	1	2	yes	complemented
85	#245233	C₂²	1	2	yes	complemented
86	#213861	C₂²	1	2	yes	complemented
87	#213837	C₂²	1	2	yes	complemented
88	#213829	C₂²	1	2	yes	complemented
89	#134011	C₂²	1	2	yes	complemented
90	#133905	C₂²	1	2	yes	complemented
91	#133904	C₂²	1	1	yes	characteristic, complemented
92	#133904	C₂²	1	1	yes	characteristic, complemented
93	#133835	C₂²	1	1	yes	characteristic, complemented
94	#133835	C₂²	1	1	yes	characteristic, complemented
95	#133431	C₂²	1	2	yes	complemented
96	#133431	C₂²	1	2	yes	complemented
97	#133428	C₂²	1	2	yes	complemented
98	#133428	C₂²	1	2	yes	complemented
99	#133359	C₂²	1	2	yes	complemented
100	#133359	C₂²	1	2	yes	complemented
101	#133357	C₂²	1	1	yes	characteristic, complemented
102	#133357	C₂²	1	1	yes	characteristic, complemented
103	#133356	C₂²	1	1	yes	characteristic
104	#133356	C₂²	1	1	yes	characteristic
105	#133356	C₂²	1	2	yes	complemented
106	#133356	C₂²	1	2	yes	complemented
107	#133356	C₂²	1	1	yes	characteristic, complemented
108	#133356	C₂²	1	1	yes	characteristic, complemented
109	#133356	C₂²	1	1	yes	characteristic, complemented
110	#133356	C₂²	1	1	yes	characteristic, complemented
111	#133336	C₂²	1	2	yes	complemented
112	#133336	C₂²	1	2	yes	complemented
113	#133335	C₂²	1	2	yes	complemented
114	#133335	C₂²	1	2	yes	complemented
115	#133334	C₂²	1	2	yes	complemented
116	#133334	C₂²	1	2	yes	complemented
117	#133332	C₂²	1	2	yes	complemented
118	#133332	C₂²	1	2	yes	complemented
119	#133311	C₂²	1	2	yes	complemented
120	#133311	C₂²	1	2	yes	complemented
121	#133308	C₂²	1	2	yes	complemented
122	#133308	C₂²	1	2	yes	complemented
123	#62842	C₂³	1	1	yes	characteristic, complemented
124	C₂×#3500	D₄	1	1	yes	characteristic, complemented
125	C₂×#3500	C₂³	1	1	yes	characteristic
126	C₂×#3498	D₄	1	1	yes	characteristic, complemented
127	C₂×#3498	C₂³	1	1	yes	characteristic
128	C₂×#3543	D₄	1	1	yes	characteristic, complemented
129	C₂×#3532	D₄	1	2	yes	complemented
130	C₂²×D₄²	D₄	1	1	yes	characteristic, complemented
131	C₂×#3019	C₂³	1	1	yes	characteristic
132	C₂×#3019	C₂³	1	1	yes	characteristic, complemented
133	C₂²×#455	C₂³	1	1	yes	characteristic, complemented
134	C₂²×#453	C₂³	1	1	yes	characteristic, complemented
135	#59162	C₂³	1	2	yes	—
136	#59126	C₂³	1	2	yes	—
137	#59041	D₄	1	2	yes	complemented
138	#59041	D₄	1	2	yes	complemented
139	C₂×#2684	D₄	1	2	yes	complemented
140	#52054	D₄	1	1	yes	characteristic, complemented
141	#52054	C₂³	1	1	yes	characteristic
142	#52012	C₂³	1	2	yes	—
143	#52004	D₄	1	1	yes	characteristic, complemented
144	#52004	D₄	1	1	yes	characteristic, complemented
145	#52004	D₄	1	1	yes	characteristic, complemented
146	#52004	C₂³	1	1	yes	characteristic
147	#52004	C₂³	1	1	yes	characteristic
148	#52004	C₂³	1	2	yes	—
149	#52004	C₂³	1	1	yes	characteristic
150	#51749	D₄	1	2	yes	complemented
151	#51530	D₄	1	2	yes	complemented
152	#47563	C₂³	1	2	yes	—
153	#46997	C₂³	1	2	yes	—
154	#46996	D₄	1	2	yes	complemented
155	#46387	D₄	1	2	yes	complemented
156	#46385	D₄	1	2	yes	complemented
157	#46384	D₄	1	2	yes	complemented
158	#46324	C₂³	1	2	yes	—
159	#46276	D₄	1	2	yes	complemented
160	#46276	D₄	1	2	yes	complemented
161	#45977	C₂³	1	2	yes	—
162	#37232	C₂³	1	2	yes	—
163	#37119	D₄	1	2	yes	complemented
164	#36737	D₄	1	2	yes	complemented
165	#36717	D₄	1	2	yes	complemented
166	#36714	D₄	1	2	yes	complemented
167	#36702	D₄	1	2	yes	complemented
168	#35676	D₄	1	1	yes	characteristic, complemented
169	#35616	D₄	1	1	yes	characteristic, complemented
170	#35554	C₂³	1	1	yes	characteristic, complemented
171	#35527	C₂³	1	1	yes	characteristic
172	#35527	C₂³	1	2	yes	—
173	#35527	C₂³	1	1	yes	characteristic
174	#35527	C₂³	1	1	yes	characteristic, complemented
175	#35512	D₄	1	2	yes	complemented
176	#35347	C₂³	1	2	yes	—
177	#35346	D₄	1	2	yes	complemented
178	#35346	C₂³	1	2	yes	—
179	#35327	D₄	1	1	yes	characteristic, complemented
180	#35327	C₂³	1	1	yes	characteristic
181	#35272	D₄	1	1	yes	characteristic, complemented
182	#35272	C₂³	1	1	yes	characteristic
183	C₂×#2657	C₂³	1	1	yes	characteristic
184	#34406	D₄	1	2	yes	complemented
185	#34364	D₄	1	1	yes	characteristic, complemented
186	C₂×#2380	D₄	1	1	yes	characteristic, complemented
187	#34070	D₄	1	1	yes	characteristic, complemented
188	#34070	D₄	1	1	yes	characteristic, complemented
189	#33022	C₂³	1	2	yes	complemented
190	#33020	C₂³	1	2	yes	—
191	#33020	C₂³	1	2	yes	complemented
192	#33020	C₂³	1	2	yes	complemented
193	#32900	C₂³	1	2	yes	complemented
194	#32898	C₂³	1	2	yes	—
195	#32898	C₂³	1	2	yes	complemented
196	#32898	C₂³	1	2	yes	complemented
197	#20953	C₂³	1	1	yes	characteristic
198	#20953	C₂³	1	1	yes	characteristic, complemented
199	C₂×#1887	C₂³	1	1	yes	characteristic, complemented
200	C₂×#1885	C₂³	1	1	yes	characteristic, complemented
201	#20690	C₂³	1	1	yes	characteristic, complemented
202	#20592	C₂³	1	1	yes	characteristic, complemented
203	#20592	C₂³	1	1	yes	characteristic, complemented
204	#20586	C₂³	1	2	yes	complemented
205	#20586	C₂³	1	2	yes	complemented
206	#20586	C₂³	1	1	yes	characteristic, complemented
207	#20586	C₂³	1	1	yes	characteristic, complemented
208	#13082	C₂³	1	2	yes	—
209	#13082	C₂³	1	2	yes	—
210	#13082	C₂³	1	2	yes	—
211	#13082	C₂³	1	2	yes	—
212	#13082	C₂³	1	2	yes	complemented
213	#13082	C₂³	1	2	yes	complemented
214	#13082	C₂³	1	2	yes	complemented
215	#13082	C₂³	1	2	yes	complemented
216	#13082	C₂³	1	2	yes	complemented
217	#13082	C₂³	1	2	yes	complemented
218	#13082	C₂³	1	2	yes	complemented
219	#13082	C₂³	1	2	yes	complemented
220	#13080	C₂³	1	2	yes	complemented
221	#13080	C₂³	1	2	yes	complemented
222	#13080	C₂³	1	2	yes	complemented
223	#13080	C₂³	1	2	yes	complemented
224	#12696	C₂³	1	1	yes	characteristic
225	#12696	C₂³	1	1	yes	characteristic
226	#12696	C₂³	1	1	yes	characteristic
227	#12696	C₂³	1	1	yes	characteristic
228	#12696	C₂³	1	2	yes	complemented
229	#12696	C₂³	1	2	yes	complemented
230	#12694	C₂³	1	2	yes	complemented
231	#12694	C₂³	1	2	yes	complemented
232	#12693	C₂³	1	2	yes	complemented
233	#12693	C₂³	1	2	yes	complemented
234	#11167	C₂³	1	1	yes	characteristic, complemented
235	#11167	C₂³	1	1	yes	characteristic, complemented
236	#10989	C₂³	1	1	yes	characteristic
237	#10989	C₂³	1	1	yes	characteristic
238	#10989	C₂³	1	1	yes	characteristic, complemented
239	#10989	C₂³	1	1	yes	characteristic, complemented
240	#10981	C₂³	1	1	yes	characteristic, complemented
241	#10981	C₂³	1	1	yes	characteristic, complemented
242	#10977	C₂³	1	1	yes	characteristic, complemented
243	#10977	C₂³	1	1	yes	characteristic, complemented
244	#10975	C₂³	1	1	yes	characteristic, complemented
245	#10975	C₂³	1	1	yes	characteristic, complemented
246	#9501	C₂³	1	2	yes	complemented
247	#9501	C₂³	1	2	yes	complemented
248	#9497	C₂³	1	2	yes	—
249	#9497	C₂³	1	2	yes	—
250	#9497	C₂³	1	2	yes	complemented
251	#9497	C₂³	1	2	yes	complemented
252	#9497	C₂³	1	2	yes	complemented
253	#9497	C₂³	1	2	yes	complemented
254	#8748	C₂³	1	2	yes	complemented
255	#8748	C₂³	1	2	yes	complemented
256	#8546	C₂³	1	2	yes	complemented
257	#8546	C₂³	1	2	yes	complemented
258	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
259	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
260	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
261	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
262	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
263	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
264	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	—
265	C₂×#560	C₂×D₄	1	2	yes	—
266	C₂×#560	C₂×D₄	1	2	yes	—
267	C₂×#559	C₂×D₄	1	1	yes	characteristic
268	C₂×#551	C₂×D₄	1	2	yes	—
269	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
270	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
271	C₂×D₄²	C₂×D₄	1	1	yes	characteristic
272	C₂×D₄²	C₂×D₄	1	2	yes	—
273	C₂×D₄²	C₂×D₄	1	2	yes	—
274	C₂×#536	C₂×D₄	1	2	yes	—
275	C₂×#536	C₂×D₄	1	1	yes	characteristic
276	C₂×#536	C₂×D₄	1	1	yes	characteristic
277	C₂×#535	C₂×D₄	1	1	yes	characteristic
278	C₂×#535	C₂×D₄	1	1	yes	characteristic
279	C₂×#535	C₂×D₄	1	2	yes	—
280	C₂×#535	C₂×D₄	1	1	yes	characteristic
281	C₂×#535	C₂×D₄	1	1	yes	characteristic
282	C₂×#535	C₂×D₄	1	1	yes	characteristic
283	C₂×#535	C₂×D₄	1	1	yes	characteristic
284	C₂×#535	C₂×D₄	1	1	yes	characteristic
285	C₂×#535	C₂×D₄	1	1	yes	characteristic
286	C₂×#535	C₂⁴	1	1	yes	characteristic
287	C₂×#535	C₂⁴	1	1	yes	characteristic
288	C₂×#534	C₂×D₄	1	2	yes	—
289	C₂×#534	C₂×D₄	1	2	yes	—
290	C₂×#534	C₂×D₄	1	2	yes	—
291	C₂×#532	C₂×D₄	1	1	yes	characteristic
292	C₂×#532	C₂×D₄	1	1	yes	characteristic
293	C₂×#532	C₂×D₄	1	2	yes	—
294	C₂×#532	C₂×D₄	1	1	yes	characteristic
295	C₂×#532	C₂×D₄	1	1	yes	characteristic
296	C₂²×#127	C₂×D₄	1	1	yes	characteristic
297	C₂²×#127	C₂×D₄	1	1	yes	characteristic
298	C₂²×#127	C₂×D₄	1	1	yes	characteristic
299	C₂²×#127	C₂⁴	1	1	yes	characteristic
300	C₂²×#127	C₂⁴	1	1	yes	characteristic
301	C₂²×#124	C₂×D₄	1	1	yes	characteristic
302	C₂²×#124	C₂×D₄	1	1	yes	characteristic
303	C₂²×#124	C₂×D₄	1	2	yes	—
304	C₂²×#124	C₂⁴	1	1	yes	characteristic
305	C₂²×#121	C₂×D₄	1	2	yes	—
306	C₂²×#120	C₂×D₄	1	2	yes	—
307	C₂²×#120	C₂×D₄	1	2	yes	—
308	C₂²×#120	C₂×D₄	1	2	yes	—
309	C₂×#518	C₂⁴	1	1	yes	characteristic
310	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
311	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
312	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
313	C₂×C₄×#41	C₂×D₄	1	1	yes	characteristic
314	C₂²×#100	C₂⁴	1	1	yes	characteristic
315	C₂²×#100	C₂⁴	1	1	yes	characteristic
316	C₂²×#100	C₂⁴	1	1	yes	characteristic
317	C₂²×#100	C₂⁴	1	1	yes	characteristic
318	#2842	C₂×D₄	1	2	yes	—
319	#2840	C₂×D₄	1	2	yes	—
320	#2717	C₂×D₄	1	2	yes	—
321	#2717	C₂×D₄	1	2	yes	—
322	#2717	C₂×D₄	1	2	yes	—
323	#2709	C₂×D₄	1	2	yes	—
324	#2684	C₂×D₄	1	2	yes	—
325	#2684	C₂×D₄	1	2	yes	—
326	#2684	C₂×D₄	1	2	yes	—
327	#2684	C₂×D₄	1	2	yes	—
328	#2684	C₂×D₄	1	2	yes	—
329	#2684	C₂×D₄	1	2	yes	—
330	#2684	C₂×D₄	1	2	yes	—
331	#2684	C₂×D₄	1	2	yes	—
332	#2684	C₂×D₄	1	2	yes	—
333	#2669	C₂×D₄	1	2	yes	—
334	#2669	C₂×D₄	1	2	yes	—
335	#2669	C₂×D₄	1	2	yes	—
336	#2406	C₂×D₄	1	2	yes	—
337	#2406	C₂×D₄	1	2	yes	—
338	#2405	C₂×D₄	1	2	yes	—
339	#2405	C₂×D₄	1	2	yes	—
340	#2405	C₂×D₄	1	2	yes	—
341	#2405	C₂⁴	1	2	yes	—
342	#2404	C₂×D₄	1	2	yes	—
343	#2404	C₂×D₄	1	2	yes	—
344	#2404	C₂×D₄	1	2	yes	—
345	#2404	C₂×D₄	1	2	yes	—
346	#2404	C₂×D₄	1	2	yes	—
347	#2404	C₂×D₄	1	2	yes	—
348	#2403	C₂×D₄	1	2	yes	—
349	#2403	C₂×D₄	1	2	yes	—
350	#2403	C₂×D₄	1	2	yes	—
351	#2403	C₂×D₄	1	2	yes	—
352	#2403	C₂×D₄	1	2	yes	—
353	#2403	C₂×D₄	1	2	yes	—
354	#2403	C₂×D₄	1	2	yes	—
355	#2403	C₂×D₄	1	2	yes	—
356	#2403	C₂×D₄	1	2	yes	—
357	#2403	C₂×D₄	1	2	yes	—
358	#2403	C₂×D₄	1	2	yes	—
359	#2403	C₂⁴	1	2	yes	—
360	#2403	C₂⁴	1	2	yes	—
361	#2403	C₂⁴	1	2	yes	—
362	#2380	C₂×D₄	1	1	yes	characteristic
363	#2380	C₂×D₄	1	1	yes	characteristic
364	#2380	C₂×D₄	1	1	yes	characteristic
365	#2380	C₂×D₄	1	1	yes	characteristic
366	#2380	C₂×D₄	1	2	yes	—
367	#2380	C₂×D₄	1	2	yes	—
368	#2379	C₂×D₄	1	2	yes	—
369	#2372	C₂×D₄	1	2	yes	—
370	#2366	C₂×D₄	1	2	yes	—
371	#2366	C₂×D₄	1	2	yes	—
372	#2312	C₂×D₄	1	2	yes	—
373	#2310	C₂×D₄	1	1	yes	characteristic
374	#2309	C₂×D₄	1	2	yes	—
375	#2309	C₂×D₄	1	2	yes	—
376	#2309	C₂×D₄	1	2	yes	—
377	#2309	C₂×D₄	1	1	yes	characteristic
378	#2309	C₂×D₄	1	1	yes	characteristic
379	#2309	C₂⁴	1	1	yes	characteristic
380	#2309	C₂⁴	1	1	yes	characteristic
381	#2309	C₂⁴	1	1	yes	characteristic
382	#2308	C₂×D₄	1	2	yes	—
383	#2308	C₂×D₄	1	2	yes	—
384	#2308	C₂×D₄	1	2	yes	—
385	#2308	C₂×D₄	1	2	yes	—
386	#2308	C₂×D₄	1	2	yes	—
387	#2308	C₂×D₄	1	2	yes	—
388	#2297	C₂×D₄	1	1	yes	characteristic
389	#2297	C₂×D₄	1	1	yes	characteristic
390	#2297	C₂×D₄	1	1	yes	characteristic
391	#2297	C₂×D₄	1	1	yes	characteristic
392	C₂×#386	C₂×D₄	1	2	yes	—
393	C₂×#386	C₂×D₄	1	2	yes	—
394	#2285	C₂×D₄	1	1	yes	characteristic
395	#2285	C₂×D₄	1	1	yes	characteristic
396	C₂×#376	C₂×D₄	1	1	yes	characteristic
397	#1781	C₂⁴	1	2	yes	—
398	#1781	C₂⁴	1	2	yes	—
399	#1781	C₂⁴	1	2	yes	—
400	#1781	C₂⁴	1	2	yes	—
401	C₂⁶	#120	1	2	yes	—
402	C₂²×#41	#120	1	2	yes	—
403	C₂²×#41	#120	1	1	yes	characteristic
404	C₂²×#41	#120	1	1	yes	characteristic
405	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
406	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
407	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
408	C₂²×#41	C₂²×D₄	1	2	yes	—
409	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
410	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
411	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
412	C₂³×Q₈	#120	1	2	yes	—
413	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
414	C₂³×D₄	#120	1	1	yes	characteristic
415	C₂³×D₄	#120	1	1	yes	characteristic
416	C₂³×D₄	#120	1	2	yes	—
417	C₂³×D₄	C₂²×D₄	1	2	yes	—
418	C₂³×D₄	C₂²×D₄	1	2	yes	—
419	C₂³×D₄	C₂²×D₄	1	2	yes	—
420	C₂³×D₄	C₂²×D₄	1	2	yes	—
421	C₂³×D₄	C₂²×D₄	1	2	yes	—
422	C₂³×D₄	C₂²×D₄	1	2	yes	—
423	C₂³×D₄	C₂²×D₄	1	2	yes	—
424	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
425	C₂³×D₄	C₂²×D₄	1	2	yes	—
426	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
427	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
428	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
429	C₂³×D₄	C₂⁵	1	1	yes	characteristic
430	C₂⁴×C₄	#120	1	2	yes	—
431	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	#120	1	1	yes	characteristic
433	C₂×C₄⋊Q₈	#120	1	2	yes	—
434	C₂×#127	#120	1	1	yes	characteristic
435	C₂×#127	#120	1	1	yes	characteristic
436	C₂×#127	#120	1	1	yes	characteristic
437	C₂×#127	#120	1	1	yes	characteristic
438	C₂×#127	C₂²×D₄	1	1	yes	characteristic
439	C₂×#127	C₂²×D₄	1	1	yes	characteristic
440	C₂×#127	C₂²×D₄	1	2	yes	—
441	C₂×#127	C₂²×D₄	1	1	yes	characteristic
442	C₂×#127	C₂²×D₄	1	1	yes	characteristic
443	C₂×#127	C₂²×D₄	1	1	yes	characteristic
444	C₂×#127	C₂²×D₄	1	1	yes	characteristic
445	C₂×#124	#120	1	1	yes	characteristic
446	C₂×#124	#120	1	1	yes	characteristic
447	C₂×#124	#120	1	1	yes	characteristic
448	C₂×#124	#120	1	1	yes	characteristic
449	C₂×#124	#120	1	2	yes	—
450	C₂×#124	#120	1	1	yes	characteristic
451	C₂×#124	#120	1	1	yes	characteristic
452	C₂×#124	C₂²×D₄	1	2	yes	—
453	C₂×#124	C₂²×D₄	1	2	yes	—
454	C₂×#124	C₂²×D₄	1	1	yes	characteristic
455	C₂×#124	C₂²×D₄	1	1	yes	characteristic
456	C₂×#124	C₂²×D₄	1	2	yes	—
457	C₂×#123	#120	1	2	yes	—
458	C₂×#123	#120	1	2	yes	—
459	C₂×#123	C₂²×D₄	1	2	yes	—
460	C₂×#123	C₂²×D₄	1	2	yes	—
461	C₂×#120	#120	1	1	yes	characteristic
462	C₂×#120	#120	1	2	yes	—
463	C₂×#120	#120	1	2	yes	—
464	C₂×#120	#120	1	2	yes	—
465	C₂×#120	#120	1	2	yes	—
466	C₂×#120	#120	1	2	yes	—
467	C₂×#120	#120	1	1	yes	characteristic
468	C₂×#120	#120	1	2	yes	—
469	C₂×#120	#120	1	1	yes	characteristic
470	C₂×#120	#120	1	1	yes	characteristic
471	C₂×#120	#120	1	2	yes	—
472	C₂×#120	#120	1	2	yes	—
473	C₂×#120	C₂²×D₄	1	2	yes	—
474	C₂×#120	C₂²×D₄	1	2	yes	—
475	C₂×#120	C₂²×D₄	1	2	yes	—
476	C₂×#120	C₂²×D₄	1	2	yes	—
477	C₂×#120	C₂²×D₄	1	2	yes	—
478	C₂×#120	C₂²×D₄	1	2	yes	—
479	C₂×#117	#120	1	2	yes	—
480	C₂×#117	#120	1	1	yes	characteristic
481	C₂×#117	#120	1	1	yes	characteristic
482	C₂×#117	C₂²×D₄	1	1	yes	characteristic
483	C₂×#117	C₂²×D₄	1	1	yes	characteristic
484	C₂×#117	C₂²×D₄	1	1	yes	characteristic
485	C₂×#117	C₂²×D₄	1	1	yes	characteristic
486	C₂²×C₄⋊C₄	#120	1	2	yes	—
487	C₂²×C₂²⋊C₄	#120	1	2	yes	—
488	C₂²×C₂²⋊C₄	#120	1	2	yes	—
489	C₂²×C₂²⋊C₄	#120	1	2	yes	—
490	C₂²×C₂²⋊C₄	#120	1	2	yes	—
491	C₂²×C₂²⋊C₄	#120	1	2	yes	—
492	C₂²×C₂²⋊C₄	#120	1	2	yes	—
493	C₂²×C₂²⋊C₄	#120	1	2	yes	—
494	C₂²×C₂²⋊C₄	#120	1	2	yes	—
495	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
496	C₂²×C₄²	#120	1	1	yes	characteristic
497	C₂²×C₄²	#120	1	1	yes	characteristic
498	C₂²×C₄²	#120	1	2	yes	—
499	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
500	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
501	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
502	#386	#120	1	2	yes	—
503	#386	#120	1	2	yes	—
504	#386	#120	1	2	yes	—
505	#386	#120	1	2	yes	—
506	#386	#120	1	2	yes	—
507	#386	#120	1	2	yes	—
508	#386	#120	1	2	yes	—
509	#386	#120	1	2	yes	—
510	#386	#120	1	2	yes	—
511	#386	#120	1	2	yes	—
512	#386	#120	1	2	yes	—
513	#386	#120	1	2	yes	—
514	#386	C₂²×D₄	1	2	yes	—
515	#386	C₂²×D₄	1	2	yes	—
516	#386	C₂²×D₄	1	2	yes	—
517	#386	C₂²×D₄	1	2	yes	—
518	#386	C₂²×D₄	1	2	yes	—
519	#386	C₂²×D₄	1	2	yes	—
520	#386	C₂²×D₄	1	2	yes	—
521	#386	C₂²×D₄	1	2	yes	—
522	#381	#120	1	2	yes	—
523	#381	#120	1	2	yes	—
524	#381	#120	1	2	yes	—
525	#381	#120	1	2	yes	—
526	#379	C₂²×D₄	1	2	yes	—
527	#379	C₂²×D₄	1	2	yes	—
528	#379	C₂²×D₄	1	2	yes	—
529	#379	C₂²×D₄	1	2	yes	—
530	#379	C₂²×D₄	1	2	yes	—
531	#379	C₂²×D₄	1	2	yes	—
532	C₂⁵	C₂×#120	1	1	yes	characteristic
533	C₂⁵	C₂×#120	1	1	yes	characteristic
534	C₂⁵	C₂×#120	1	2	yes	—
535	C₂⁵	C₂×#120	1	2	yes	—
536	C₂⁵	C₂×#120	1	2	yes	—
537	C₂⁵	C₂×#120	1	2	yes	—
538	C₂⁵	C₂×#120	1	2	yes	—
539	C₂⁵	C₂³×D₄	1	2	yes	—
540	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
541	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
542	C₂²×Q₈	C₂×#120	1	2	yes	—
543	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
544	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
545	C₂²×D₄	C₂×#120	1	2	yes	—
546	C₂²×D₄	C₂×#120	1	1	yes	characteristic
547	C₂²×D₄	C₂×#120	1	1	yes	characteristic
548	C₂²×D₄	C₂×#120	1	2	yes	—
549	C₂²×D₄	C₂×#120	1	2	yes	—
550	C₂²×D₄	C₂×#120	1	2	yes	—
551	C₂²×D₄	C₂×#120	1	2	yes	—
552	C₂²×D₄	C₂×#120	1	1	yes	characteristic
553	C₂²×D₄	C₂×#120	1	1	yes	characteristic
554	C₂²×D₄	C₂×#120	1	1	yes	characteristic
555	C₂²×D₄	C₂×#120	1	1	yes	characteristic
556	C₂²×D₄	C₂×#120	1	1	yes	characteristic
557	C₂²×D₄	C₂×#120	1	1	yes	characteristic
558	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
559	C₂²×D₄	C₂³×D₄	1	2	yes	—
560	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
561	C₂³×C₄	C₂×#120	1	2	yes	—
562	C₂³×C₄	C₂×#120	1	1	yes	characteristic
563	C₂³×C₄	C₂×#120	1	2	yes	—
564	C₂³×C₄	C₂×#120	1	1	yes	characteristic
565	C₂³×C₄	C₂×#120	1	2	yes	—
566	C₂³×C₄	C₂×#120	1	2	yes	—
567	C₂³×C₄	C₂×#120	1	2	yes	—
568	C₂³×C₄	C₂×#120	1	2	yes	—
569	C₂³×C₄	C₂×#120	1	2	yes	—
570	C₂³×C₄	C₂×#120	1	2	yes	—
571	C₂³×C₄	C₂×#120	1	2	yes	—
572	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
584	C₂×C₄²	C₂×#120	1	1	yes	characteristic
585	C₂×C₄²	C₂×#120	1	1	yes	characteristic
586	C₂×C₄²	C₂×#120	1	1	yes	characteristic
587	C₂×C₄²	C₂×#120	1	1	yes	characteristic
588	C₂×C₄²	C₂×#120	1	2	yes	—
589	C₂×C₄²	C₂×#120	1	1	yes	characteristic
590	C₂×C₄²	C₂×#120	1	1	yes	characteristic
591	C₂⁴	#2846	1	1	yes	characteristic
592	C₂⁴	#2846	1	2	yes	—
593	C₂⁴	#2846	1	1	yes	characteristic
594	C₂⁴	C₂²×#120	1	2	yes	—
595	C₂⁴	C₂²×#120	1	2	yes	—
596	C₂⁴	C₂²×#120	1	1	yes	characteristic
597	C₂×D₄	#3026	1	2	yes	—
598	C₂×D₄	#3026	1	2	yes	—
599	C₂²×C₄	#2846	1	2	yes	—
600	C₂²×C₄	#2846	1	1	yes	characteristic
601	C₂²×C₄	#2846	1	1	yes	characteristic
602	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
603	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
604	C₄²	#3026	1	2	yes	—
605	C₄²	#3026	1	2	yes	—
606	C₂³	C₂×#2846	1	1	yes	characteristic
607	C₂³	#60399	1	1	yes	characteristic
608	C₂³	#60399	1	1	yes	characteristic
609	C₂×C₄	C₂×#3026	1	1	yes	characteristic
610	C₂×C₄	C₂×#3026	1	1	yes	characteristic
611	C₂×C₄	C₂×#3026	1	1	yes	characteristic
612	C₂×C₄	C₂×#3026	1	1	yes	characteristic
613	C₂²	#6628892	1	1	yes	characteristic
614	C₂²	#6628892	1	1	yes	characteristic
615	C₂²	#6628896	1	1	yes	characteristic
616	C₂	#72233206	1	2	yes	—
617	C₂	#72234607	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#6628896
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #35527 ◁ 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. #72318689	C₂	semidirect
2. #72318682	C₂	semidirect
3. #72318678	C₂	semidirect
4. #72318668	C₂	semidirect
5. #72318659	C₂	semidirect
6. #72318649	C₂	semidirect
7. #72318637	C₂	semidirect
8. #72318630	C₂	semidirect
9. #72318622	C₂	semidirect
10. #72318615	C₂	semidirect
11. #72318605	C₂	semidirect
12. #72318598	C₂	semidirect
13. #72318569	C₂	semidirect
14. #72318542	C₂	semidirect
15. #72318279	C₂	semidirect
16. #72318243	C₂	semidirect
17. #72318207	C₂	semidirect
18. #72317855	C₂	semidirect
19. #72311068	C₂	semidirect
20. #72285530	C₂	semidirect
21. #72285519	C₂	semidirect
22. #72252010	C₂	semidirect
23. #72210498	C₂	semidirect
35. #6470243	C₂²	semidirect
36. #6470231	C₂²	semidirect
37. #6437457	C₂²	semidirect
38. #6437456	C₂²	semidirect
39. #6432958	C₂²	semidirect
40. #500190	C₂²	semidirect
41. #500183	C₂²	semidirect
42. #500182	C₂²	semidirect
43. #500178	C₂²	semidirect
45. #500177	C₂²	semidirect
46. #500177	C₂²	semidirect
47. #500177	C₂²	semidirect
48. #500172	C₂²	semidirect
49. #500170	C₂²	semidirect
50. #499852	C₂²	semidirect
51. #499849	C₂²	semidirect
52. #499848	C₂²	semidirect
53. #499843	C₂²	semidirect
54. #499838	C₂²	semidirect
55. #499834	C₂²	semidirect
57. #499832	C₂²	semidirect
58. #499832	C₂²	semidirect
59. #499832	C₂²	semidirect
60. #496243	C₂²	semidirect
61. #496243	C₂²	semidirect
62. #496237	C₂²	semidirect
63. #496237	C₂²	semidirect
64. #493434	C₂²	semidirect
65. #493431	C₂²	semidirect
66. #493431	C₂²	semidirect
67. #451038	C₂²	semidirect
68. #451037	C₂²	semidirect
69. #449527	C₂²	semidirect
70. #449492	C₂²	semidirect
71. #418124	C₂²	semidirect
72. #417813	C₂²	semidirect
73. #417568	C₂²	semidirect
74. #417566	C₂²	semidirect
75. #391714	C₂²	semidirect
76. #382444	C₂²	semidirect
77. #382443	C₂²	semidirect
78. #251857	C₂²	semidirect
79. #251855	C₂²	semidirect
80. #251840	C₂²	semidirect
81. #251838	C₂²	semidirect
82. #245267	C₂²	semidirect
83. #245255	C₂²	semidirect
84. #245234	C₂²	semidirect
85. #245233	C₂²	semidirect
86. #213861	C₂²	semidirect
87. #213837	C₂²	semidirect
88. #213829	C₂²	semidirect
89. #134011	C₂²	semidirect
90. #133905	C₂²	semidirect
91. #133904	C₂²	semidirect
92. #133904	C₂²	semidirect
93. #133835	C₂²	semidirect
94. #133835	C₂²	semidirect
95. #133431	C₂²	semidirect
96. #133431	C₂²	semidirect
97. #133428	C₂²	semidirect
98. #133428	C₂²	semidirect
99. #133359	C₂²	semidirect
100. #133359	C₂²	semidirect
101. #133357	C₂²	semidirect
102. #133357	C₂²	semidirect
105. #133356	C₂²	semidirect
106. #133356	C₂²	semidirect
107. #133356	C₂²	semidirect
108. #133356	C₂²	semidirect
109. #133356	C₂²	semidirect
110. #133356	C₂²	semidirect
111. #133336	C₂²	semidirect
112. #133336	C₂²	semidirect
113. #133335	C₂²	semidirect
114. #133335	C₂²	semidirect
115. #133334	C₂²	semidirect
116. #133334	C₂²	semidirect
117. #133332	C₂²	semidirect
118. #133332	C₂²	semidirect
119. #133311	C₂²	semidirect
120. #133311	C₂²	semidirect
121. #133308	C₂²	semidirect
122. #133308	C₂²	semidirect
123. #62842	C₂³	semidirect
124. C₂×#3500	D₄	semidirect
126. C₂×#3498	D₄	semidirect
128. C₂×#3543	D₄	semidirect
129. C₂×#3532	D₄	semidirect
130. C₂²×D₄²	D₄	semidirect
132. C₂×#3019	C₂³	semidirect
133. C₂²×#455	C₂³	semidirect
134. C₂²×#453	C₂³	semidirect
137. #59041	D₄	semidirect
138. #59041	D₄	semidirect
139. C₂×#2684	D₄	semidirect
140. #52054	D₄	semidirect
143. #52004	D₄	semidirect
144. #52004	D₄	semidirect
145. #52004	D₄	semidirect
150. #51749	D₄	semidirect
151. #51530	D₄	semidirect
154. #46996	D₄	semidirect
155. #46387	D₄	semidirect
156. #46385	D₄	semidirect
157. #46384	D₄	semidirect
159. #46276	D₄	semidirect
160. #46276	D₄	semidirect
163. #37119	D₄	semidirect
164. #36737	D₄	semidirect
165. #36717	D₄	semidirect
166. #36714	D₄	semidirect
167. #36702	D₄	semidirect
168. #35676	D₄	semidirect
169. #35616	D₄	semidirect
170. #35554	C₂³	semidirect
174. #35527	C₂³	semidirect
175. #35512	D₄	semidirect
177. #35346	D₄	semidirect
179. #35327	D₄	semidirect
181. #35272	D₄	semidirect
184. #34406	D₄	semidirect
185. #34364	D₄	semidirect
186. C₂×#2380	D₄	semidirect
187. #34070	D₄	semidirect
188. #34070	D₄	semidirect
189. #33022	C₂³	semidirect
191. #33020	C₂³	semidirect
192. #33020	C₂³	semidirect
193. #32900	C₂³	semidirect
195. #32898	C₂³	semidirect
196. #32898	C₂³	semidirect
198. #20953	C₂³	semidirect
199. C₂×#1887	C₂³	semidirect
200. C₂×#1885	C₂³	semidirect
201. #20690	C₂³	semidirect
202. #20592	C₂³	semidirect
203. #20592	C₂³	semidirect
204. #20586	C₂³	semidirect
205. #20586	C₂³	semidirect
206. #20586	C₂³	semidirect
207. #20586	C₂³	semidirect
212. #13082	C₂³	semidirect
213. #13082	C₂³	semidirect
214. #13082	C₂³	semidirect
215. #13082	C₂³	semidirect
216. #13082	C₂³	semidirect
217. #13082	C₂³	semidirect
218. #13082	C₂³	semidirect
219. #13082	C₂³	semidirect
220. #13080	C₂³	semidirect
221. #13080	C₂³	semidirect
222. #13080	C₂³	semidirect
223. #13080	C₂³	semidirect
228. #12696	C₂³	semidirect
229. #12696	C₂³	semidirect
230. #12694	C₂³	semidirect
231. #12694	C₂³	semidirect
232. #12693	C₂³	semidirect
233. #12693	C₂³	semidirect
234. #11167	C₂³	semidirect
235. #11167	C₂³	semidirect
238. #10989	C₂³	semidirect
239. #10989	C₂³	semidirect
240. #10981	C₂³	semidirect
241. #10981	C₂³	semidirect
242. #10977	C₂³	semidirect
243. #10977	C₂³	semidirect
244. #10975	C₂³	semidirect
245. #10975	C₂³	semidirect
246. #9501	C₂³	semidirect
247. #9501	C₂³	semidirect
250. #9497	C₂³	semidirect
251. #9497	C₂³	semidirect
252. #9497	C₂³	semidirect
253. #9497	C₂³	semidirect
254. #8748	C₂³	semidirect
255. #8748	C₂³	semidirect
256. #8546	C₂³	semidirect
257. #8546	C₂³	semidirect

Maximal subgroups

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

subgroup	index
#72318689	2
#72318682	2
#72318678	2
#72318668	2
#72318659	2
#72318649	2
#72318637	2
#72318630	2
#72318622	2
#72318615	2
#72318605	2
#72318598	2
#72318569	2
#72318542	2
#72318279	2
#72318243	2
#72318207	2
#72317855	2
#72311068	2
#72285530	2
#72285519	2
#72252010	2
#72210498	2