Subgroups — #72338615

Order 4096.

At least 17397 conjugacy classes of subgroups; only the 1081 normal subgroups are shown.

The subgroup lattice has 651 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72338599	C₂	1	1	yes	maximal, characteristic, complemented
2	#72338598	C₂	1	1	yes	maximal, characteristic, complemented
3	#72338584	C₂	1	1	yes	maximal, characteristic, complemented
4	#72338301	C₂	1	1	yes	maximal, characteristic, complemented
5	#72338296	C₂	1	1	yes	maximal, characteristic, complemented
6	#72338207	C₂²	1	1	yes	characteristic
7	#72319673	C₂	1	4	yes	maximal, complemented
8	#72319643	C₂²	1	2	yes	complemented
9	#72318414	C₂	1	4	yes	maximal, complemented
10	#72318404	C₂²	1	2	yes	complemented
11	#72318350	C₂²	1	4	yes	complemented
12	#72318347	C₂²	1	4	yes	complemented
13	#72318200	C₂	1	4	yes	maximal, complemented
14	#72318092	C₂	1	4	yes	maximal, complemented
15	#72318057	C₂²	1	4	yes	complemented
16	#72318055	C₂²	1	4	yes	complemented
17	#72317938	C₂²	1	2	yes	complemented
18	#72317884	C₂²	1	2	yes	complemented
19	#72317872	C₂²	1	2	yes	complemented
20	#72317722	C₂²	1	4	yes	complemented
21	#72306903	C₂²	1	2	yes	complemented
22	#72306901	C₂²	1	2	yes	complemented
23	#72306297	C₂²	1	4	yes	complemented
24	#72302242	C₂²	1	1	yes	characteristic
25	#72256107	C₂	1	1	yes	maximal, characteristic, complemented
26	#72256107	C₂	1	1	yes	maximal, characteristic, complemented
27	#72252021	C₂²	1	1	yes	characteristic
28	#72252021	C₂²	1	1	yes	characteristic
29	#72252020	C₂²	1	1	yes	characteristic
30	#72252020	C₂²	1	1	yes	characteristic
31	#72252010	C₂²	1	4	yes	—
32	#72251980	C₂²	1	2	yes	complemented
33	#72251980	C₂²	1	2	yes	complemented
34	#72251822	C₂	1	8	yes	maximal, complemented
35	#72251812	C₂²	1	16	yes	complemented
36	#72251808	C₂²	1	16	yes	complemented
37	#72251759	C₂²	1	4	yes	complemented
38	#72251681	C₂²	1	4	yes	complemented
39	#72241309	C₂²	1	16	yes	complemented
40	#72237054	C₂²	1	4	yes	complemented
41	#72236657	C₂²	1	4	yes	—
42	#72234146	C₂²	1	2	yes	complemented
43	#72234146	C₂²	1	2	yes	complemented
44	C₂×#7737411	C₂²	1	1	yes	characteristic
45	#72219689	C₂²	1	2	yes	complemented
46	#72216567	C₂²	1	4	yes	complemented
47	#72215568	C₂²	1	4	yes	complemented
48	#72213695	C₂²	1	16	yes	complemented
49	#72213534	C₂²	1	4	yes	complemented
50	#72210575	C₂²	1	4	yes	complemented
51	#10586066	D₄	1	1	yes	characteristic, complemented
52	#10586066	D₄	1	1	yes	characteristic, complemented
53	C₂²×#3498	C₂³	1	1	yes	characteristic
54	C₂³×D₄²	D₄	1	1	yes	characteristic, complemented
55	C₂×#60388	D₄	1	1	yes	characteristic, complemented
56	C₂×#60388	D₄	1	1	yes	characteristic, complemented
57	C₂×#60388	C₂³	1	1	yes	characteristic
58	C₂×#60388	C₂³	1	1	yes	characteristic
59	#7737411	D₄	1	2	yes	complemented
60	#7737411	D₄	1	2	yes	complemented
61	#7737411	C₂³	1	2	yes	—
62	#7737411	C₂³	1	2	yes	—
63	C₂×#52004	D₄	1	2	yes	complemented
64	C₂×#52004	C₂³	1	2	yes	—
65	C₂×#34364	D₄	1	1	yes	characteristic, complemented
66	C₂×#33359	D₄	1	2	yes	complemented
67	C₂×#33359	D₄	1	2	yes	complemented
68	#6437456	D₄	1	2	yes	complemented
69	#6437456	C₂³	1	2	yes	—
70	#6437452	D₄	1	2	yes	complemented
71	#6437452	C₂³	1	2	yes	—
72	#6437449	C₂³	1	2	yes	—
73	#6437445	C₂³	1	2	yes	—
74	#6437437	D₄	1	2	yes	complemented
75	C₂×#23906	D₄	1	2	yes	complemented
76	#6371456	D₄	1	1	yes	characteristic, complemented
77	#6371456	D₄	1	1	yes	characteristic, complemented
78	#6371456	C₂³	1	1	yes	characteristic
79	#6371456	C₂³	1	1	yes	characteristic
80	#6370950	D₄	1	1	yes	characteristic, complemented
81	#6370937	D₄	1	1	yes	characteristic, complemented
82	#6370704	D₄	1	1	yes	characteristic, complemented
83	#6370704	D₄	1	1	yes	characteristic, complemented
84	#500179	C₂³	1	8	yes	—
85	#500177	C₂³	1	8	yes	—
86	#499832	C₂³	1	8	yes	—
87	#499831	C₂³	1	8	yes	—
88	#493431	D₄	1	2	yes	complemented
89	#493431	C₂³	1	2	yes	—
90	#493430	D₄	1	2	yes	complemented
91	#493430	C₂³	1	2	yes	—
92	#493430	C₂³	1	2	yes	—
93	#493430	C₂³	1	2	yes	—
94	#493372	C₂³	1	2	yes	—
95	#493370	D₄	1	2	yes	complemented
96	#493370	D₄	1	2	yes	complemented
97	#493370	C₂³	1	2	yes	—
98	#493365	D₄	1	2	yes	complemented
99	C₂×#12693	D₄	1	2	yes	complemented
100	#451783	C₂³	1	4	yes	complemented
101	#449491	C₂³	1	4	yes	complemented
102	#418772	C₂³	1	4	yes	complemented
103	#418770	C₂³	1	4	yes	complemented
104	#382414	D₄	1	2	yes	complemented
105	#382414	C₂³	1	2	yes	—
106	#361634	D₄	1	2	yes	complemented
107	#361634	C₂³	1	2	yes	—
108	#361631	D₄	1	2	yes	complemented
109	#361631	C₂³	1	2	yes	—
110	#187836	C₂³	1	2	yes	—
111	#187824	C₂³	1	2	yes	—
112	#187811	C₂³	1	2	yes	—
113	#152322	C₂³	1	8	yes	complemented
114	#152319	C₂³	1	8	yes	complemented
115	#152021	C₂³	1	8	yes	complemented
116	#152018	C₂³	1	8	yes	complemented
117	#131979	C₂³	1	16	yes	—
118	#94441	C₂³	1	16	yes	complemented
119	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
120	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
121	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
122	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
123	#62852	C₂×D₄	1	2	yes	—
124	#62842	C₂×D₄	1	2	yes	—
125	#62811	C₂×D₄	1	2	yes	complemented
126	C₂×#3498	C₂×D₄	1	1	yes	characteristic
127	C₂×#3498	C₂×D₄	1	1	yes	characteristic
128	C₂×#3498	C₂×D₄	1	1	yes	characteristic
129	C₂×#3498	C₂×D₄	1	1	yes	characteristic
130	C₂×#3498	C₂×D₄	1	1	yes	characteristic
131	C₂×#3498	C₂×D₄	1	1	yes	characteristic
132	C₂×#3498	C₂×D₄	1	1	yes	characteristic
133	C₂×#3498	C₂×D₄	1	1	yes	characteristic
134	C₂×#3498	C₂×D₄	1	1	yes	characteristic
135	C₂×#3498	C₂×D₄	1	1	yes	characteristic
136	C₂×#3498	C₂×D₄	1	1	yes	characteristic
137	C₂×#3498	C₂×D₄	1	1	yes	characteristic
138	C₂×#3498	#41	1	1	yes	characteristic
139	C₂×#3498	#41	1	1	yes	characteristic
140	C₂×#3498	C₂⁴	1	1	yes	characteristic
141	C₂×#3498	C₂⁴	1	1	yes	characteristic
142	C₂×#3484	C₂×D₄	1	2	yes	complemented
143	C₂²×D₄²	C₂×D₄	1	2	yes	—
144	C₂²×D₄²	C₂×D₄	1	2	yes	—
145	C₂²×D₄²	C₂×D₄	1	2	yes	—
146	C₂²×#535	C₂×D₄	1	1	yes	characteristic
147	C₂²×#535	C₂×D₄	1	1	yes	characteristic
148	C₂²×#535	C₂×D₄	1	1	yes	characteristic
149	C₂²×#535	C₂×D₄	1	1	yes	characteristic
150	C₂²×#535	#41	1	1	yes	characteristic
151	C₂²×#535	C₂⁴	1	1	yes	characteristic
152	C₂²×#532	C₂×D₄	1	1	yes	characteristic
153	C₂²×#532	C₂×D₄	1	1	yes	characteristic
154	C₂²×#532	#41	1	1	yes	characteristic
155	C₂³×#127	C₂×D₄	1	1	yes	characteristic
156	C₂³×#127	C₂×D₄	1	1	yes	characteristic
157	C₂³×#127	C₂×D₄	1	1	yes	characteristic
158	#62652	C₂×D₄	1	1	yes	characteristic, complemented
159	#62652	C₂×D₄	1	1	yes	characteristic, complemented
160	C₂²×C₄×#41	C₂×D₄	1	1	yes	characteristic
161	C₂×#3021	C₂×D₄	1	2	yes	complemented
162	C₂×#3021	C₂⁴	1	2	yes	—
163	C₂×#3019	C₂×D₄	1	2	yes	complemented
164	C₂×#3019	C₂⁴	1	2	yes	—
165	C₂×#3018	C₂×D₄	1	2	yes	—
166	C₂×#3018	C₂×D₄	1	2	yes	complemented
167	C₂²×#453	C₂×D₄	1	2	yes	—
168	C₂²×#453	C₂×D₄	1	2	yes	complemented
169	C₂×#2888	C₂×D₄	1	1	yes	characteristic, complemented
170	C₂×#2888	C₂×D₄	1	1	yes	characteristic, complemented
171	C₂×#2888	C₂×D₄	1	1	yes	characteristic, complemented
172	C₂×#2888	C₂×D₄	1	1	yes	characteristic, complemented
173	#52004	C₂×D₄	1	4	yes	—
174	#52004	C₂×D₄	1	4	yes	—
175	#52004	C₂×D₄	1	4	yes	—
176	#52004	C₂⁴	1	4	yes	—
177	#34364	C₂×D₄	1	2	yes	—
178	#34364	C₂×D₄	1	2	yes	—
179	C₂×#2380	C₂×D₄	1	2	yes	—
180	C₂×#2128	C₂×D₄	1	4	yes	complemented
181	C₂×#2127	C₂×D₄	1	4	yes	complemented
182	C₂×#2127	C₂×D₄	1	4	yes	complemented
183	C₂×#2127	C₂×D₄	1	4	yes	complemented
184	C₂×#2126	C₂×D₄	1	4	yes	—
185	C₂²×#353	C₂×D₄	1	4	yes	—
186	#20956	C₂×D₄	1	2	yes	complemented
187	#20956	C₂⁴	1	2	yes	—
188	#20953	C₂×D₄	1	2	yes	complemented
189	#20953	C₂⁴	1	2	yes	—
190	#20952	C₂×D₄	1	2	yes	—
191	#20952	C₂×D₄	1	2	yes	complemented
192	C₂×#1887	C₂×D₄	1	2	yes	—
193	C₂×#1887	C₂×D₄	1	2	yes	complemented
194	#20694	C₂×D₄	1	2	yes	complemented
195	#20688	C₂×D₄	1	2	yes	complemented
196	#20637	C₂×D₄	1	2	yes	complemented
197	#20632	C₂×D₄	1	2	yes	complemented
198	#20592	C₂×D₄	1	2	yes	—
199	#20592	C₂×D₄	1	2	yes	—
200	#20591	C₂×D₄	1	2	yes	complemented
201	C₂×#1783	C₂×D₄	1	2	yes	complemented
202	C₄×#413	C₂×D₄	1	2	yes	complemented
203	C₄×#410	C₂×D₄	1	2	yes	complemented
204	#12697	C₂⁴	1	4	yes	—
205	#12696	C₂×D₄	1	4	yes	—
206	#12696	C₂×D₄	1	4	yes	—
207	#12696	C₂⁴	1	4	yes	—
208	#12695	C₂×D₄	1	4	yes	complemented
209	#12694	C₂×D₄	1	4	yes	complemented
210	#12693	C₂×D₄	1	4	yes	complemented
211	#12693	C₂×D₄	1	4	yes	complemented
212	#11006	C₂×D₄	1	4	yes	complemented
213	#11006	C₂×D₄	1	4	yes	complemented
214	#11006	C₂×D₄	1	4	yes	complemented
215	#11006	C₂⁴	1	4	yes	—
216	#8522	C₂⁴	1	4	yes	—
217	C₂×#585	C₂²×D₄	1	2	yes	—
218	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
219	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
220	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
221	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
222	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
223	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
224	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
225	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic
226	C₂²×H(5,𝔽₂)	#121	1	1	yes	characteristic
227	C₂²×H(5,𝔽₂)	#121	1	1	yes	characteristic
228	C₂²×H(5,𝔽₂)	#121	1	1	yes	characteristic
229	C₂²×H(5,𝔽₂)	#121	1	1	yes	characteristic
230	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
231	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
232	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
233	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
234	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
235	C₂³×#41	#120	1	1	yes	characteristic
236	C₂³×#41	#120	1	1	yes	characteristic
237	C₂³×#41	#120	1	1	yes	characteristic
238	C₂³×#41	#121	1	1	yes	characteristic
239	C₂³×#41	#121	1	1	yes	characteristic
240	C₂³×#41	#121	1	1	yes	characteristic
241	C₂³×#41	C₂²×D₄	1	1	yes	characteristic
242	C₂⁴×D₄	#120	1	1	yes	characteristic
243	C₂⁴×D₄	#120	1	1	yes	characteristic
244	C₂⁴×D₄	#120	1	1	yes	characteristic
245	C₂⁴×D₄	#120	1	1	yes	characteristic
246	C₂⁴×D₄	#121	1	1	yes	characteristic
247	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
248	C₂×D₄²	C₂²×D₄	1	4	yes	—
249	C₂×#535	#120	1	1	yes	characteristic
250	C₂×#535	#120	1	1	yes	characteristic
251	C₂×#535	#120	1	1	yes	characteristic
252	C₂×#535	#120	1	1	yes	characteristic
253	C₂×#535	#120	1	1	yes	characteristic
254	C₂×#535	#120	1	1	yes	characteristic
255	C₂×#535	#120	1	1	yes	characteristic
256	C₂×#535	#120	1	1	yes	characteristic
257	C₂×#535	#120	1	1	yes	characteristic
258	C₂×#535	#120	1	1	yes	characteristic
259	C₂×#535	#121	1	1	yes	characteristic
260	C₂×#535	#121	1	1	yes	characteristic
261	C₂×#535	#121	1	1	yes	characteristic
262	C₂×#535	#121	1	1	yes	characteristic
263	C₂×#535	#121	1	1	yes	characteristic
264	C₂×#535	#121	1	1	yes	characteristic
265	C₂×#535	#121	1	1	yes	characteristic
266	C₂×#535	#121	1	1	yes	characteristic
267	C₂×#535	#121	1	1	yes	characteristic
268	C₂×#535	#121	1	1	yes	characteristic
269	C₂×#535	#121	1	1	yes	characteristic
270	C₂×#535	#121	1	1	yes	characteristic
271	C₂×#535	#121	1	1	yes	characteristic
272	C₂×#535	#121	1	1	yes	characteristic
273	C₂×#535	#127	1	1	yes	characteristic
274	C₂×#535	#127	1	1	yes	characteristic
275	C₂×#535	#127	1	1	yes	characteristic
276	C₂×#535	#127	1	1	yes	characteristic
277	C₂×#535	#127	1	1	yes	characteristic
278	C₂×#535	#127	1	1	yes	characteristic
279	C₂×#535	C₂²×D₄	1	1	yes	characteristic
280	C₂×#535	C₂²×D₄	1	1	yes	characteristic
281	C₂×#535	C₂²×D₄	1	1	yes	characteristic
282	C₂×#535	C₂²×D₄	1	1	yes	characteristic
283	C₂×#535	C₂²×D₄	1	1	yes	characteristic
284	C₂×#535	C₂²×D₄	1	1	yes	characteristic
285	C₂×#535	C₂²×D₄	1	1	yes	characteristic
286	C₂×#535	C₂²×D₄	1	1	yes	characteristic
287	C₂×#535	C₂²×D₄	1	1	yes	characteristic
288	C₂×#535	C₂²×D₄	1	1	yes	characteristic
289	C₂×#535	C₂²×D₄	1	1	yes	characteristic
290	C₂×#535	C₂²×D₄	1	1	yes	characteristic
291	C₂×#535	C₂²×D₄	1	1	yes	characteristic
292	C₂×#535	C₂²×D₄	1	1	yes	characteristic
293	C₂×#535	C₂×#41	1	1	yes	characteristic
294	C₂×#535	C₂×#41	1	1	yes	characteristic
295	C₂×#535	C₂×#41	1	1	yes	characteristic
296	C₂×#535	C₂⁵	1	1	yes	characteristic
297	C₂×#532	#120	1	1	yes	characteristic
298	C₂×#532	#120	1	1	yes	characteristic
299	C₂×#532	#120	1	1	yes	characteristic
300	C₂×#532	#120	1	1	yes	characteristic
301	C₂×#532	#120	1	1	yes	characteristic
302	C₂×#532	#120	1	1	yes	characteristic
303	C₂×#532	#121	1	1	yes	characteristic
304	C₂×#532	#121	1	1	yes	characteristic
305	C₂×#532	#121	1	1	yes	characteristic
306	C₂×#532	#121	1	1	yes	characteristic
307	C₂×#532	#121	1	1	yes	characteristic
308	C₂×#532	#121	1	1	yes	characteristic
309	C₂×#532	#121	1	1	yes	characteristic
310	C₂×#532	#121	1	1	yes	characteristic
311	C₂×#532	#121	1	1	yes	characteristic
312	C₂×#532	#121	1	1	yes	characteristic
313	C₂×#532	#127	1	1	yes	characteristic
314	C₂×#532	#127	1	1	yes	characteristic
315	C₂×#532	C₂²×D₄	1	1	yes	characteristic
316	C₂×#532	C₂²×D₄	1	1	yes	characteristic
317	C₂×#532	C₂²×D₄	1	1	yes	characteristic
318	C₂×#532	C₂²×D₄	1	1	yes	characteristic
319	C₂×#532	C₂×#41	1	1	yes	characteristic
320	C₂×#532	C₂×#41	1	1	yes	characteristic
321	C₂²×C₄⋊Q₈	#121	1	1	yes	characteristic
322	C₂²×#127	#120	1	1	yes	characteristic
323	C₂²×#127	#120	1	1	yes	characteristic
324	C₂²×#127	#120	1	1	yes	characteristic
325	C₂²×#127	#120	1	1	yes	characteristic
326	C₂²×#127	#120	1	1	yes	characteristic
327	C₂²×#127	#120	1	1	yes	characteristic
328	C₂²×#127	#120	1	1	yes	characteristic
329	C₂²×#127	#120	1	1	yes	characteristic
330	C₂²×#127	#120	1	1	yes	characteristic
331	C₂²×#127	#120	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	1	yes	characteristic
335	C₂²×#127	#121	1	1	yes	characteristic
336	C₂²×#127	#121	1	1	yes	characteristic
337	C₂²×#127	#121	1	1	yes	characteristic
338	C₂²×#127	#121	1	1	yes	characteristic
339	C₂²×#127	#121	1	1	yes	characteristic
340	C₂²×#127	#121	1	1	yes	characteristic
341	C₂²×#127	#121	1	1	yes	characteristic
342	C₂²×#127	#121	1	1	yes	characteristic
343	C₂²×#127	#121	1	1	yes	characteristic
344	C₂²×#127	#127	1	1	yes	characteristic
345	C₂²×#127	#127	1	1	yes	characteristic
346	C₂²×#127	#127	1	1	yes	characteristic
347	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
348	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
349	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
350	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
351	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
352	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
353	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
354	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
355	C₂²×#124	#120	1	1	yes	characteristic
356	C₂²×#124	#121	1	1	yes	characteristic
357	C₂²×#124	#121	1	1	yes	characteristic
358	C₂²×#124	#127	1	1	yes	characteristic
359	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
360	C₂²×#124	C₂×#41	1	1	yes	characteristic
361	#3428	C₂²×D₄	1	2	yes	—
362	C₂×#518	C₂²×D₄	1	2	yes	—
363	C₂×C₄×#41	#120	1	1	yes	characteristic
364	C₂×C₄×#41	#120	1	1	yes	characteristic
365	C₂×C₄×#41	#121	1	1	yes	characteristic
366	C₂×C₄×#41	#121	1	1	yes	characteristic
367	C₂×C₄×#41	#127	1	1	yes	characteristic
368	C₂×C₄×#41	#127	1	1	yes	characteristic
369	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
371	C₂²×#117	#121	1	1	yes	characteristic
372	C₂²×#117	#127	1	1	yes	characteristic
373	C₂²×#117	C₂²×D₄	1	1	yes	characteristic
374	C₂³×C₄²	#120	1	1	yes	characteristic
375	C₂³×C₄²	#121	1	1	yes	characteristic
376	C₂³×C₄²	#127	1	1	yes	characteristic
377	C₂×#413	C₂²×D₄	1	2	yes	—
378	C₂×#413	C₂²×D₄	1	2	yes	—
379	C₂²×#100	C₂²×D₄	1	2	yes	—
380	C₂²×#100	C₂²×D₄	1	2	yes	—
381	#2380	C₂²×D₄	1	4	yes	—
382	C₂×#354	C₂²×D₄	1	8	yes	—
383	C₂×#353	C₂²×D₄	1	8	yes	—
384	#1742	C₂²×D₄	1	4	yes	—
385	#1740	C₂²×D₄	1	4	yes	—
386	C₂²×#41	#392	1	1	yes	characteristic
387	C₂²×#41	#392	1	1	yes	characteristic
388	C₂²×#41	#392	1	1	yes	characteristic
389	C₂²×#41	#392	1	1	yes	characteristic
390	C₂²×#41	#392	1	1	yes	characteristic
391	C₂²×#41	#392	1	1	yes	characteristic
392	C₂²×#41	#392	1	1	yes	characteristic
393	C₂²×#41	#392	1	1	yes	characteristic
394	C₂²×#41	#392	1	1	yes	characteristic
395	C₂²×#41	#392	1	1	yes	characteristic
396	C₂²×#41	#392	1	1	yes	characteristic
397	C₂²×#41	#392	1	1	yes	characteristic
398	C₂²×#41	B(4,𝔽₂)	1	1	yes	characteristic
399	C₂²×#41	B(4,𝔽₂)	1	1	yes	characteristic
400	C₂²×#41	B(4,𝔽₂)	1	1	yes	characteristic
401	C₂²×#41	B(4,𝔽₂)	1	1	yes	characteristic
402	C₂²×#41	C₂×#120	1	1	yes	characteristic
403	C₂²×#41	C₂×#120	1	1	yes	characteristic
404	C₂²×#41	C₂×#120	1	1	yes	characteristic
405	C₂²×#41	C₂×#120	1	1	yes	characteristic
406	C₂²×#41	C₂×#120	1	1	yes	characteristic
407	C₂²×#41	C₂×#120	1	1	yes	characteristic
408	C₂²×#41	C₂×#120	1	1	yes	characteristic
409	C₂²×#41	C₂×#120	1	1	yes	characteristic
410	C₂²×#41	C₂×#121	1	1	yes	characteristic
411	C₂²×#41	C₂×#121	1	1	yes	characteristic
412	C₂²×#41	C₂×#121	1	1	yes	characteristic
413	C₂²×#41	C₂×#121	1	1	yes	characteristic
414	C₂²×#41	C₂×#121	1	1	yes	characteristic
415	C₂²×#41	C₂×#121	1	1	yes	characteristic
416	C₂²×#41	C₂×#121	1	1	yes	characteristic
417	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
418	C₂³×Q₈	#392	1	1	yes	characteristic
419	C₂³×Q₈	B(4,𝔽₂)	1	1	yes	characteristic
420	C₂³×Q₈	C₂×#121	1	1	yes	characteristic
421	C₂³×D₄	#392	1	1	yes	characteristic
422	C₂³×D₄	#392	1	1	yes	characteristic
423	C₂³×D₄	#392	1	1	yes	characteristic
424	C₂³×D₄	#392	1	1	yes	characteristic
425	C₂³×D₄	#392	1	1	yes	characteristic
426	C₂³×D₄	#392	1	1	yes	characteristic
427	C₂³×D₄	#392	1	1	yes	characteristic
428	C₂³×D₄	#392	1	1	yes	characteristic
429	C₂³×D₄	#392	1	1	yes	characteristic
430	C₂³×D₄	#392	1	1	yes	characteristic
431	C₂³×D₄	#392	1	1	yes	characteristic
432	C₂³×D₄	#392	1	1	yes	characteristic
433	C₂³×D₄	#392	1	1	yes	characteristic
434	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
435	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
436	C₂³×D₄	B(4,𝔽₂)	1	1	yes	characteristic
437	C₂³×D₄	C₂×#120	1	1	yes	characteristic
438	C₂³×D₄	C₂×#120	1	1	yes	characteristic
439	C₂³×D₄	C₂×#120	1	1	yes	characteristic
440	C₂³×D₄	C₂×#120	1	1	yes	characteristic
441	C₂³×D₄	C₂×#120	1	1	yes	characteristic
442	C₂³×D₄	C₂×#120	1	1	yes	characteristic
443	C₂³×D₄	C₂×#120	1	1	yes	characteristic
444	C₂³×D₄	C₂×#120	1	1	yes	characteristic
445	C₂³×D₄	C₂×#120	1	1	yes	characteristic
446	C₂³×D₄	C₂×#120	1	1	yes	characteristic
447	C₂³×D₄	C₂×#120	1	1	yes	characteristic
448	C₂³×D₄	C₂×#120	1	1	yes	characteristic
449	C₂³×D₄	C₂×#121	1	1	yes	characteristic
450	C₂³×D₄	C₂×#121	1	1	yes	characteristic
451	C₂³×D₄	C₂×#121	1	1	yes	characteristic
452	C₂³×D₄	C₂×#121	1	1	yes	characteristic
453	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
454	C₂⁴×C₄	#392	1	1	yes	characteristic
455	C₂⁴×C₄	#392	1	1	yes	characteristic
456	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
457	C₂×C₄⋊Q₈	#392	1	1	yes	characteristic
458	C₂×C₄⋊Q₈	#392	1	1	yes	characteristic
459	C₂×C₄⋊Q₈	C₂×#121	1	1	yes	characteristic
460	C₂×C₄⋊Q₈	C₂×#121	1	1	yes	characteristic
461	C₂×#127	#392	1	1	yes	characteristic
462	C₂×#127	#392	1	1	yes	characteristic
463	C₂×#127	#392	1	1	yes	characteristic
464	C₂×#127	#392	1	1	yes	characteristic
465	C₂×#127	#392	1	1	yes	characteristic
466	C₂×#127	#392	1	1	yes	characteristic
467	C₂×#127	#392	1	1	yes	characteristic
468	C₂×#127	#392	1	1	yes	characteristic
469	C₂×#127	#392	1	1	yes	characteristic
470	C₂×#127	#392	1	1	yes	characteristic
471	C₂×#127	#392	1	1	yes	characteristic
472	C₂×#127	#392	1	1	yes	characteristic
473	C₂×#127	#392	1	1	yes	characteristic
474	C₂×#127	#392	1	1	yes	characteristic
475	C₂×#127	C₂×#120	1	1	yes	characteristic
476	C₂×#127	C₂×#120	1	1	yes	characteristic
477	C₂×#127	C₂×#120	1	1	yes	characteristic
478	C₂×#127	C₂×#120	1	1	yes	characteristic
479	C₂×#127	C₂×#120	1	1	yes	characteristic
480	C₂×#127	C₂×#120	1	1	yes	characteristic
481	C₂×#127	C₂×#120	1	1	yes	characteristic
482	C₂×#127	C₂×#120	1	1	yes	characteristic
483	C₂×#127	C₂×#120	1	1	yes	characteristic
484	C₂×#127	C₂×#121	1	1	yes	characteristic
485	C₂×#127	C₂×#121	1	1	yes	characteristic
486	C₂×#127	C₂×#121	1	1	yes	characteristic
487	C₂×#127	C₂×#121	1	1	yes	characteristic
488	C₂×#127	C₂×#121	1	1	yes	characteristic
489	C₂×#127	C₂×#121	1	1	yes	characteristic
490	C₂×#127	C₂×#121	1	1	yes	characteristic
491	C₂×#127	C₂×#121	1	1	yes	characteristic
492	C₂×#127	C₂×#127	1	1	yes	characteristic
493	C₂×#127	C₂×#127	1	1	yes	characteristic
494	C₂×#127	C₂×#127	1	1	yes	characteristic
495	C₂×#127	C₂³×D₄	1	1	yes	characteristic
496	C₂×#127	C₂³×D₄	1	1	yes	characteristic
497	C₂×#124	#392	1	1	yes	characteristic
498	C₂×#124	#392	1	1	yes	characteristic
499	C₂×#124	#392	1	1	yes	characteristic
500	C₂×#124	#392	1	1	yes	characteristic
501	C₂×#124	#392	1	1	yes	characteristic
502	C₂×#124	#392	1	1	yes	characteristic
503	C₂×#124	#392	1	1	yes	characteristic
504	C₂×#124	#392	1	1	yes	characteristic
505	C₂×#124	C₂×#120	1	1	yes	characteristic
506	C₂×#124	C₂×#120	1	1	yes	characteristic
507	C₂×#124	C₂×#120	1	1	yes	characteristic
508	C₂×#124	C₂×#121	1	1	yes	characteristic
509	C₂×#124	C₂×#121	1	1	yes	characteristic
510	C₂×#124	C₂×#121	1	1	yes	characteristic
511	C₂×#124	C₂×#121	1	1	yes	characteristic
512	C₂×#124	C₂×#121	1	1	yes	characteristic
513	C₂×#124	C₂×#121	1	1	yes	characteristic
514	C₂×#124	C₂×#121	1	1	yes	characteristic
515	C₂×#124	C₂×#121	1	1	yes	characteristic
516	C₂×#124	C₂×#127	1	1	yes	characteristic
517	C₂×#124	C₂×#127	1	1	yes	characteristic
518	C₂×#124	C₂×#127	1	1	yes	characteristic
519	C₂×#124	C₂³×D₄	1	1	yes	characteristic
520	C₂×#124	C₂²×#41	1	1	yes	characteristic
521	C₂×#117	#392	1	1	yes	characteristic
522	C₂×#117	#392	1	1	yes	characteristic
523	C₂×#117	#392	1	1	yes	characteristic
524	C₂×#117	#392	1	1	yes	characteristic
525	C₂×#117	C₂×#120	1	1	yes	characteristic
526	C₂×#117	C₂×#121	1	1	yes	characteristic
527	C₂×#117	C₂×#121	1	1	yes	characteristic
528	C₂×#117	C₂×#121	1	1	yes	characteristic
529	C₂×#117	C₂×#127	1	1	yes	characteristic
530	C₂×#117	C₂×#127	1	1	yes	characteristic
531	C₂×#117	C₂×#127	1	1	yes	characteristic
532	C₂×#117	C₂³×D₄	1	1	yes	characteristic
533	C₂²×C₄²	#392	1	1	yes	characteristic
534	C₂²×C₄²	#392	1	1	yes	characteristic
535	C₂²×C₄²	#392	1	1	yes	characteristic
536	C₂²×C₄²	#392	1	1	yes	characteristic
537	C₂²×C₄²	#392	1	1	yes	characteristic
538	C₂²×C₄²	#392	1	1	yes	characteristic
539	C₂²×C₄²	#392	1	1	yes	characteristic
540	C₂²×C₄²	#392	1	1	yes	characteristic
541	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
542	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
543	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
544	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
545	C₂²×C₄²	C₂×#121	1	1	yes	characteristic
546	C₂²×C₄²	C₂×#127	1	1	yes	characteristic
547	C₂²×C₄²	C₂×#127	1	1	yes	characteristic
548	C₂²×C₄²	C₂×#127	1	1	yes	characteristic
549	C₂⁵	#2021	1	1	yes	characteristic
550	C₂⁵	#2021	1	1	yes	characteristic
551	C₂⁵	C₂×B(4,𝔽₂)	1	1	yes	characteristic
552	C₂²×Q₈	#2021	1	1	yes	characteristic
553	C₂²×Q₈	#2021	1	1	yes	characteristic
554	C₂²×Q₈	C₂×#392	1	1	yes	characteristic
555	C₂²×Q₈	C₂×#392	1	1	yes	characteristic
556	C₂²×Q₈	C₂×#392	1	1	yes	characteristic
557	C₂²×Q₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
558	C₂²×Q₈	C₂×B(4,𝔽₂)	1	1	yes	characteristic
559	C₂²×Q₈	C₂²×#121	1	1	yes	characteristic
560	C₂²×D₄	#2021	1	1	yes	characteristic
561	C₂²×D₄	#2021	1	1	yes	characteristic
562	C₂²×D₄	#2021	1	1	yes	characteristic
563	C₂²×D₄	#2021	1	1	yes	characteristic
564	C₂²×D₄	#2021	1	1	yes	characteristic
565	C₂²×D₄	#2021	1	1	yes	characteristic
566	C₂²×D₄	C₂×#392	1	1	yes	characteristic
567	C₂²×D₄	C₂×#392	1	1	yes	characteristic
568	C₂²×D₄	C₂×#392	1	1	yes	characteristic
569	C₂²×D₄	C₂×#392	1	1	yes	characteristic
570	C₂²×D₄	C₂×#392	1	1	yes	characteristic
571	C₂²×D₄	C₂×#392	1	1	yes	characteristic
572	C₂²×D₄	C₂×#392	1	1	yes	characteristic
573	C₂²×D₄	C₂×#392	1	1	yes	characteristic
574	C₂²×D₄	C₂×#392	1	1	yes	characteristic
575	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
576	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
577	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
578	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
579	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
580	C₂²×D₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
581	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
582	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
583	C₂²×D₄	C₂²×#121	1	1	yes	characteristic
584	C₂³×C₄	#2021	1	1	yes	characteristic
585	C₂³×C₄	#2021	1	1	yes	characteristic
586	C₂³×C₄	#2021	1	1	yes	characteristic
587	C₂³×C₄	#2021	1	1	yes	characteristic
588	C₂³×C₄	#2021	1	1	yes	characteristic
589	C₂³×C₄	#2021	1	1	yes	characteristic
590	C₂³×C₄	C₂×#392	1	1	yes	characteristic
591	C₂³×C₄	C₂×#392	1	1	yes	characteristic
592	C₂³×C₄	C₂×#392	1	1	yes	characteristic
593	C₂³×C₄	C₂×#392	1	1	yes	characteristic
594	C₂³×C₄	C₂×#392	1	1	yes	characteristic
595	C₂³×C₄	C₂×#392	1	1	yes	characteristic
596	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
597	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
598	C₂³×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
599	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
600	#127	#3026	1	2	yes	—
601	#127	#3026	1	2	yes	—
602	#127	#3026	1	2	yes	—
603	#127	#3026	1	2	yes	—
604	C₂×C₄²	C₂×#392	1	1	yes	characteristic
605	C₂×C₄²	C₂×#392	1	1	yes	characteristic
606	C₂×C₄²	C₂×#392	1	1	yes	characteristic
607	C₂×C₄²	C₂×#392	1	1	yes	characteristic
608	C₂×C₄²	C₂×#392	1	1	yes	characteristic
609	C₂×C₄²	C₂×#392	1	1	yes	characteristic
610	C₂×C₄²	C₂²×#121	1	1	yes	characteristic
611	C₂×C₄²	C₂²×#127	1	1	yes	characteristic
612	C₂⁴	C₂×#2021	1	1	yes	characteristic
613	C₂⁴	C₂×#2021	1	1	yes	characteristic
614	C₂⁴	C₂×#2021	1	1	yes	characteristic
615	C₂⁴	C₂×#2021	1	1	yes	characteristic
616	C₂⁴	C₂×#2021	1	1	yes	characteristic
617	C₂⁴	C₂×#2021	1	1	yes	characteristic
618	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
619	C₂×D₄	#23444	1	2	yes	—
620	C₂×D₄	#23444	1	2	yes	—
621	C₂×D₄	#33551	1	4	yes	—
622	C₂×D₄	#33551	1	4	yes	—
623	C₂×D₄	C₂×#3026	1	2	yes	—
624	C₂×D₄	C₂×#3026	1	2	yes	—
625	C₂²×C₄	C₂×#2021	1	1	yes	characteristic
626	C₂²×C₄	C₂×#2021	1	1	yes	characteristic
627	C₂²×C₄	C₂×#2021	1	1	yes	characteristic
628	C₂²×C₄	C₂×#2021	1	1	yes	characteristic
629	C₂²×C₄	C₂×#2021	1	1	yes	characteristic
630	C₂²×C₄	C₂×#2021	1	1	yes	characteristic
631	C₂²×C₄	C₂²×#392	1	1	yes	characteristic
632	C₂²×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
633	C₄²	#23444	1	1	yes	characteristic
634	C₄²	#23444	1	1	yes	characteristic
635	C₄²	#23444	1	1	yes	characteristic
636	C₄²	#23444	1	1	yes	characteristic
637	C₂³	#498886	1	2	yes	—
638	C₂³	#498886	1	2	yes	—
639	C₂³	#498886	1	2	yes	—
640	C₂³	C₂²×#2021	1	1	yes	characteristic
641	C₂³	C₂×#33551	1	2	yes	—
642	C₂×C₄	#498886	1	2	yes	—
643	C₂×C₄	C₂×#23444	1	1	yes	characteristic
644	C₂×C₄	C₂×#23444	1	1	yes	characteristic
645	C₂×C₄	C₂×#33551	1	2	yes	—
646	C₂²	C₂×#498886	1	1	yes	characteristic
647	C₂²	C₂×#498886	1	1	yes	characteristic
648	C₂²	#72236431	1	1	yes	characteristic
649	C₂	#72317894	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72317894
commutator, Frattini, cosocle	C₂×#535	C₂⁵
LCS	G ▷ C₂×#535 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂³×#41 ◁ C₂²×#3498 ◁ G
LECS	G ▷ C₂×#535 ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72338599	C₂	semidirect
2. #72338598	C₂	semidirect
3. #72338584	C₂	semidirect
4. #72338301	C₂	semidirect
5. #72338296	C₂	semidirect
7. #72319673	C₂	semidirect
8. #72319643	C₂²	semidirect
9. #72318414	C₂	semidirect
10. #72318404	C₂²	semidirect
11. #72318350	C₂²	semidirect
12. #72318347	C₂²	semidirect
13. #72318200	C₂	semidirect
14. #72318092	C₂	semidirect
15. #72318057	C₂²	semidirect
16. #72318055	C₂²	semidirect
17. #72317938	C₂²	semidirect
18. #72317884	C₂²	semidirect
19. #72317872	C₂²	semidirect
20. #72317722	C₂²	semidirect
21. #72306903	C₂²	semidirect
22. #72306901	C₂²	semidirect
23. #72306297	C₂²	semidirect
25. #72256107	C₂	semidirect
26. #72256107	C₂	semidirect
32. #72251980	C₂²	semidirect
33. #72251980	C₂²	semidirect
34. #72251822	C₂	semidirect
35. #72251812	C₂²	semidirect
36. #72251808	C₂²	semidirect
37. #72251759	C₂²	semidirect
38. #72251681	C₂²	semidirect
39. #72241309	C₂²	semidirect
40. #72237054	C₂²	semidirect
42. #72234146	C₂²	semidirect
43. #72234146	C₂²	semidirect
45. #72219689	C₂²	semidirect
46. #72216567	C₂²	semidirect
47. #72215568	C₂²	semidirect
48. #72213695	C₂²	semidirect
49. #72213534	C₂²	semidirect
50. #72210575	C₂²	semidirect
51. #10586066	D₄	semidirect
52. #10586066	D₄	semidirect
54. C₂³×D₄²	D₄	semidirect
55. C₂×#60388	D₄	semidirect
56. C₂×#60388	D₄	semidirect
59. #7737411	D₄	semidirect
60. #7737411	D₄	semidirect
63. C₂×#52004	D₄	semidirect
65. C₂×#34364	D₄	semidirect
66. C₂×#33359	D₄	semidirect
67. C₂×#33359	D₄	semidirect
68. #6437456	D₄	semidirect
70. #6437452	D₄	semidirect
74. #6437437	D₄	semidirect
75. C₂×#23906	D₄	semidirect
76. #6371456	D₄	semidirect
77. #6371456	D₄	semidirect
80. #6370950	D₄	semidirect
81. #6370937	D₄	semidirect
82. #6370704	D₄	semidirect
83. #6370704	D₄	semidirect
88. #493431	D₄	semidirect
90. #493430	D₄	semidirect
95. #493370	D₄	semidirect
96. #493370	D₄	semidirect
98. #493365	D₄	semidirect
99. C₂×#12693	D₄	semidirect
100. #451783	C₂³	semidirect
101. #449491	C₂³	semidirect
102. #418772	C₂³	semidirect
103. #418770	C₂³	semidirect
104. #382414	D₄	semidirect
106. #361634	D₄	semidirect
108. #361631	D₄	semidirect
113. #152322	C₂³	semidirect
114. #152319	C₂³	semidirect
115. #152021	C₂³	semidirect
116. #152018	C₂³	semidirect
118. #94441	C₂³	semidirect
119. C₂×H(7,𝔽₂)	C₂×D₄	semidirect
120. C₂×H(7,𝔽₂)	C₂×D₄	semidirect
125. #62811	C₂×D₄	semidirect
142. C₂×#3484	C₂×D₄	semidirect
158. #62652	C₂×D₄	semidirect
159. #62652	C₂×D₄	semidirect
161. C₂×#3021	C₂×D₄	semidirect
163. C₂×#3019	C₂×D₄	semidirect
166. C₂×#3018	C₂×D₄	semidirect
168. C₂²×#453	C₂×D₄	semidirect
169. C₂×#2888	C₂×D₄	semidirect
170. C₂×#2888	C₂×D₄	semidirect
171. C₂×#2888	C₂×D₄	semidirect
172. C₂×#2888	C₂×D₄	semidirect
180. C₂×#2128	C₂×D₄	semidirect
181. C₂×#2127	C₂×D₄	semidirect
182. C₂×#2127	C₂×D₄	semidirect
183. C₂×#2127	C₂×D₄	semidirect
186. #20956	C₂×D₄	semidirect
188. #20953	C₂×D₄	semidirect
191. #20952	C₂×D₄	semidirect
193. C₂×#1887	C₂×D₄	semidirect
194. #20694	C₂×D₄	semidirect
195. #20688	C₂×D₄	semidirect
196. #20637	C₂×D₄	semidirect
197. #20632	C₂×D₄	semidirect
200. #20591	C₂×D₄	semidirect
201. C₂×#1783	C₂×D₄	semidirect
202. C₄×#413	C₂×D₄	semidirect
203. C₄×#410	C₂×D₄	semidirect
208. #12695	C₂×D₄	semidirect
209. #12694	C₂×D₄	semidirect
210. #12693	C₂×D₄	semidirect
211. #12693	C₂×D₄	semidirect
212. #11006	C₂×D₄	semidirect
213. #11006	C₂×D₄	semidirect
214. #11006	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72338599	2
#72338598	2
#72338584	2
#72338301	2
#72338296	2
#72319673	2
#72318414	2
#72318200	2
#72318092	2
#72256107	2
#72251822	2