Finite Group Databasebeta

← #72219212

Subgroups — #72219212

Order 1024.

117014 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#6342371C212yesmaximal, complemented
2#6342371C211yesmaximal, characteristic, complemented
3#2032594C2115yesmaximal, complemented
4#2032564C2130yesmaximal, complemented
5#2032030C2115yesmaximal, complemented
6C28C2211yescharacteristic, complemented
7C2×#2735C22115yescomplemented
8C2×#2679C22115yescomplemented
9C2×#2846C22130yes—
10C2×#2846C22115yes—
11#16298C22130yescomplemented
12#16255C22130yescomplemented
13#16255C22130yescomplemented
14#16255C22130yescomplemented
15#15947C2215yescomplemented
16#15947C22115yescomplemented
17#15480C22115yescomplemented
18#15297C22130yescomplemented
19#15284C22115yescomplemented
20#15283C22130yescomplemented
21#15283C22115yescomplemented
22#15282C22130yescomplemented
23#15282C22130yescomplemented
24#15281C22130yescomplemented
25#15281C22115yescomplemented
26#15268C22130yescomplemented
27#15268C22130yescomplemented
28#15268C22130yescomplemented
29#14679C22115yescomplemented
30#14679C22130yescomplemented
31#14366C22130yescomplemented
32#14365C22115yescomplemented
33#14358C22130yescomplemented
34#14358C22115yescomplemented
35C27—460no—
36C27C23115yes—
37C22×#120C23130yes—
38C22×#120C23115yes—
39C22×#120C23110yes—
40C22×#120C23115yes—
41C22×#120C23130yes—
42C22×#120C2315yes—
43C22×#120C23115yescomplemented
44#2846—4120no—
45#2846—460no—
46#2735—460no—
47#2679—460no—
48C2×#399C23115yescomplemented
49C2×#397C23115yescomplemented
50C2×#397C23130yescomplemented
51C2×#396C23130yescomplemented
52C2×#394C23130yescomplemented
53C2×#394C23130yescomplemented
54C2×#394C23130yescomplemented
55C2×#390C23130yescomplemented
56C2×#390C23115yescomplemented
57C2×#388C23130yescomplemented
58C2×#388C23130yescomplemented
59C2×#388C23130yescomplemented
60C2×#379C23115yes—
61C2×#379C23130yes—
62C2×#379C23130yes—
63C2×#379C23130yes—
64C2×#379C23130yes—
65C2×#379C23130yes—
66C2×#379C23115yes—
67C2×#379C23115yes—
68C2×#379C23130yes—
69C2×#379C23130yes—
70C2×#379C23130yes—
71C2×#379C23130yes—
72#1440C23130yescomplemented
73#1440C23130yescomplemented
74#1440C23130yescomplemented
75#1439C23130yescomplemented
76#1439C23130yescomplemented
77#1439C23130yescomplemented
78#1439C23130yescomplemented
79#1439C23130yescomplemented
80#1439C23130yescomplemented
81#1439C23130yescomplemented
82#1439C23130yescomplemented
83#1439C23130yescomplemented
84#1438C23130yescomplemented
85#1438C23115yescomplemented
86#1438C23130yescomplemented
87#1438C23130yescomplemented
88#1438C23130yescomplemented
89#1438C23130yescomplemented
90#1438C23115yescomplemented
91#1437C23115yescomplemented
92#1437C23130yescomplemented
93#1437C23115yescomplemented
94#1437C23130yescomplemented
95C26—2120no—
96C26—260no—
97C26—430no—
98C26—460no—
99C26—460no—
100C26—430no—
101C26—460no—
102C26—460no—
103C26—460no—
104C26—4960no—
105C26—4320no—
106C26—4960no—
107C26C2415yes—
108C26C24115yes—
109C26C24115yes—
110C26C2411yescharacteristic, complemented
111C23×D4C24130yes—
112C23×D4C24115yes—
113C2×#120—2120no—
114C2×#120—260no—
115C2×#120—460no—
116C2×#120—460no—
117C2×#120—460no—
118C2×#120—430no—
119C2×#120—460no—
120C2×#120—460no—
121C2×#120—460no—
122C2×#120—460no—
123C2×#120—460no—
124C2×#120—430no—
125C2×#120—430no—
126C2×#120—460no—
127C22×C4⋊C4C24115yescomplemented
128C22×C4⋊C4C24130yescomplemented
129C22×C22⋊C4C24130yes—
130C22×C22⋊C4C24115yes—
131C22×C22⋊C4C24130yes—
132C22×C22⋊C4C24130yes—
133C22×C22⋊C4C24130yes—
134C22×C22⋊C4C24130yes—
135C22×C22⋊C4C24130yes—
136C22×C22⋊C4C24130yes—
137C22×C22⋊C4C24115yes—
138C22×C22⋊C4C24130yes—
139C22×C22⋊C4C24115yes—
140C22×C22⋊C4C24130yes—
141C22×C22⋊C4C24130yescomplemented
142C22×C22⋊C4C24115yescomplemented
143C22×C42C24115yescomplemented
144#399—430no—
145#397—430no—
146#397—460no—
147#396—460no—
148#394—460no—
149#394—460no—
150#394—460no—
151#390—460no—
152#390—430no—
153#388—460no—
154#388—460no—
155#388—460no—
156#379—260no—
157#379—2120no—
158#379—430no—
159#379—460no—
160#379—460no—
161#379—430no—
162#379—460no—
163#379—460no—
164#379—460no—
165#379—460no—
166#379—460no—
167#379—460no—
168C2×#95C24130yescomplemented
169C2×#95C24130yescomplemented
170C2×#95C24115yescomplemented
171C2×#95C24130yescomplemented
172C2×#95C24115yescomplemented
173C2×#95C24130yescomplemented
174C25—260no—
175C25—260no—
176C25—260no—
177C25—230no—
178C25—260no—
179C25—260no—
180C25—230no—
181C25—260no—
182C25—260no—
183C25—260no—
184C25—430no—
185C25—415no—
186C25—415no—
187C25—430no—
188C25—430no—
189C25—430no—
190C25—415no—
191C25—430no—
192C25—415no—
193C25—430no—
194C25—415no—
195C25—4240no—
196C25—4480no—
197C25—4480no—
198C25—4240no—
199C25—4480no—
200C25—4480no—
201C25—4480no—
202C25—4480no—
203C25—4240no—
204C25—4480no—
205C25—4240no—
206C25—4240no—
207C25—4480no—
208C25—4480no—
209C25—4480no—
210C25—4240no—
211C25—4480no—
212C25—4480no—
213C25—4480no—
214C25—4480no—
215C25—415360no—
216C25—4240no—
217C25H(5,𝔽2)160yes—
218C25C2512yes—
219C25C2511yescharacteristic
220C25C25115yes—
221C22×D4—260no—
222C22×D4—230no—
223C22×D4—260no—
224C22×D4—260no—
225C22×D4—260no—
226C22×D4—430no—
227C22×D4—415no—
228C22×D4—430no—
229C22×D4—430no—
230C22×D4—430no—
231C22×D4—430no—
232C22×D4—415no—
233C23×C4C25130yes—
234C23×C4C25115yes—
235#120—8240no—
236#120—8120no—
237#120—8120no—
238#120—8240no—
239#120—8120no—
240#120—880no—
241#120—840no—
242C2×C4⋊C4—415no—
243C2×C4⋊C4—430no—
244C2×C4⋊C4—430no—
245C2×C4⋊C4—415no—
246C2×C4⋊C4—430no—
247C2×C4⋊C4—415no—
248C2×C22⋊C4—260no—
249C2×C22⋊C4—230no—
250C2×C22⋊C4—260no—
251C2×C22⋊C4—260no—
252C2×C22⋊C4—260no—
253C2×C22⋊C4—260no—
254C2×C22⋊C4—260no—
255C2×C22⋊C4—260no—
256C2×C22⋊C4—260no—
257C2×C22⋊C4—230no—
258C2×C22⋊C4—260no—
259C2×C22⋊C4—260no—
260C2×C22⋊C4—260no—
261C2×C22⋊C4—260no—
262C2×C22⋊C4—230no—
263C2×C22⋊C4—430no—
264C2×C22⋊C4—430no—
265C2×C22⋊C4—430no—
266C2×C22⋊C4—430no—
267C2×C22⋊C4—415no—
268C2×C22⋊C4—430no—
269C2×C22⋊C4—430no—
270C2×C22⋊C4—430no—
271C2×C22⋊C4—430no—
272C2×C22⋊C4—430no—
273C2×C22⋊C4—430no—
274C2×C22⋊C4—430no—
275C2×C22⋊C4—430no—
276C2×C22⋊C4—430no—
277C2×C22⋊C4—430no—
278C2×C22⋊C4—430no—
279C2×C22⋊C4—430no—
280C2×C22⋊C4—430no—
281C2×C22⋊C4—415no—
282C2×C22⋊C4—430no—
283C2×C22⋊C4—430no—
284C2×C22⋊C4—430no—
285C2×C22⋊C4—430no—
286C2×C22⋊C4—415no—
287C2×C42—430no—
288C2×C42—415no—
289#95—430no—
290#95—415no—
291#95—430no—
292#95—430no—
293#95—430no—
294#95—415no—
295C24—215no—
296C24—230no—
297C24—230no—
298C24—230no—
299C24—230no—
300C24—215no—
301C24—230no—
302C24—2120no—
303C24—2240no—
304C24—280no—
305C24—240no—
306C24—2120no—
307C24—2240no—
308C24—230no—
309C24—215no—
310C24—4120no—
311C24—460no—
312C24—460no—
313C24—4120no—
314C24—4120no—
315C24—4120no—
316C24—460no—
317C24—4120no—
318C24—4120no—
319C24—4120no—
320C24—4120no—
321C24—460no—
322C24—4120no—
323C24—4120no—
324C24—4120no—
325C24—4120no—
326C24—4120no—
327C24—460no—
328C24—460no—
329C24—4120no—
330C24—4120no—
331C24—4120no—
332C24—4120no—
333C24—4120no—
334C24—460no—
335C24—460no—
336C24—4120no—
337C24—4120no—
338C24—4120no—
339C24—4120no—
340C24—4120no—
341C24—4120no—
342C24—4120no—
343C24—4120no—
344C24—4120no—
345C24—4120no—
346C24—41920no—
347C24—43840no—
348C24—43840no—
349C24—43840no—
350C24—43840no—
351C24—41920no—
352C24—41920no—
353C24—43840no—
354C24—416384no—
355C24—43840no—
356C24—460no—
357C24—440no—
358C24—460no—
359C24—460no—
360C24—4120no—
361C24—460no—
362C24—4120no—
363C24—460no—
364C24—460no—
365C24—830no—
366C24—1615no—
367C24—165no—
368C24C2×H(5,𝔽2)160yes—
369C24C2×H(5,𝔽2)130yes—
370C24C2611yescharacteristic
371C2×D4—4120no—
372C2×D4—460no—
373C2×D4—860no—
374C2×D4—830no—
375C2×D4—830no—
376C2×D4—860no—
377C2×D4—860no—
378C2×D4—860no—
379C2×D4—860no—
380C2×D4—860no—
381C2×D4—860no—
382C2×D4—860no—
383C22×C4—230no—
384C22×C4—215no—
385C22×C4—230no—
386C22×C4—230no—
387C22×C4—230no—
388C22×C4—230no—
389C22×C4—215no—
390C22×C4—230no—
391C22×C4—230no—
392C22×C4—230no—
393C22×C4—230no—
394C22×C4—215no—
395C4⋊C4—1615no—
396C4⋊C4—1630no—
397C22⋊C4—4120no—
398C22⋊C4—460no—
399C22⋊C4—860no—
400C22⋊C4—860no—
401C22⋊C4—860no—
402C22⋊C4—830no—
403C22⋊C4—860no—
404C22⋊C4—860no—
405C22⋊C4—830no—
406C22⋊C4—860no—
407C22⋊C4—860no—
408C22⋊C4—860no—
409C22⋊C4—860no—
410C22⋊C4—830no—
411C42—1615no—
412C23—260no—
413C23—260no—
414C23—260no—
415C23—260no—
416C23—230no—
417C23—230no—
418C23—260no—
419C23—260no—
420C23—260no—
421C23—260no—
422C23—4480no—
423C23—4240no—
424C23—4480no—
425C23—4480no—
426C23—4480no—
427C23—4240no—
428C23—4480no—
429C23—4240no—
430C23—4480no—
431C23—4240no—
432C23—4480no—
433C23—415360no—
434C23—4240no—
435C23—4480no—
436C23—4480no—
437C23—4480no—
438C23—4480no—
439C23—4240no—
440C23—4480no—
441C23—4480no—
442C23—4480no—
443C23—4240no—
444C23—430no—
445C23—415no—
446C23—415no—
447C23—430no—
448C23—430no—
449C23—430no—
450C23—415no—
451C23—415no—
452C23—430no—
453C23—430no—
454C23—430no—
455C23—415no—
456C23—45no—
457C23—410no—
458C23—430no—
459C23—415no—
460C23—1660no—
461C23#3532160yes—
462C23C22×H(5,𝔽2)115yes—
463D4—16120no—
464D4—1660no—
465C2×C4—430no—
466C2×C4—415no—
467C2×C4—415no—
468C2×C4—430no—
469C2×C4—430no—
470C2×C4—430no—
471C2×C4—430no—
472C2×C4—430no—
473C2×C4—430no—
474C2×C4—430no—
475C2×C4—430no—
476C2×C4—415no—
477C22—260no—
478C22—2120no—
479C22—4960no—
480C22—4320no—
481C22—4960no—
482C22—460no—
483C22—430no—
484C22—460no—
485C22—460no—
486C22—460no—
487C22—460no—
488C22—430no—
489C22—830no—
490C22—815no—
491C22—1616no—
492C22C2×#3532115yes—
493C22#62817115yes—
494C22#6281715yes—
495C4—830no—
496C4—815no—
497C2—460no—
498C2—162no—
499C2—161no—
500C2#8108057115yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C26
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #6342371C2semidirect
2. #6342371C2semidirect
3. #2032594C2semidirect
4. #2032564C2semidirect
5. #2032030C2semidirect
6. C28C22semidirect
7. C2×#2735C22semidirect
8. C2×#2679C22semidirect
11. #16298C22semidirect
12. #16255C22semidirect
13. #16255C22semidirect
14. #16255C22semidirect
15. #15947C22semidirect
16. #15947C22semidirect
17. #15480C22semidirect
18. #15297C22semidirect
19. #15284C22semidirect
20. #15283C22semidirect
21. #15283C22semidirect
22. #15282C22semidirect
23. #15282C22semidirect
24. #15281C22semidirect
25. #15281C22semidirect
26. #15268C22semidirect
27. #15268C22semidirect
28. #15268C22semidirect
29. #14679C22semidirect
30. #14679C22semidirect
31. #14366C22semidirect
32. #14365C22semidirect
33. #14358C22semidirect
34. #14358C22semidirect
43. C22×#120C23semidirect
48. C2×#399C23semidirect
49. C2×#397C23semidirect
50. C2×#397C23semidirect
51. C2×#396C23semidirect
52. C2×#394C23semidirect
53. C2×#394C23semidirect
54. C2×#394C23semidirect
55. C2×#390C23semidirect
56. C2×#390C23semidirect
57. C2×#388C23semidirect
58. C2×#388C23semidirect
59. C2×#388C23semidirect
72. #1440C23semidirect
73. #1440C23semidirect
74. #1440C23semidirect
75. #1439C23semidirect
76. #1439C23semidirect
77. #1439C23semidirect
78. #1439C23semidirect
79. #1439C23semidirect
80. #1439C23semidirect
81. #1439C23semidirect
82. #1439C23semidirect
83. #1439C23semidirect
84. #1438C23semidirect
85. #1438C23semidirect
86. #1438C23semidirect
87. #1438C23semidirect
88. #1438C23semidirect
89. #1438C23semidirect
90. #1438C23semidirect
91. #1437C23semidirect
92. #1437C23semidirect
93. #1437C23semidirect
94. #1437C23semidirect
110. C26C24semidirect
127. C22×C4⋊C4C24semidirect
128. C22×C4⋊C4C24semidirect
141. C22×C22⋊C4C24semidirect
142. C22×C22⋊C4C24semidirect
143. C22×C42C24semidirect
168. C2×#95C24semidirect
169. C2×#95C24semidirect
170. C2×#95C24semidirect
171. C2×#95C24semidirect
172. C2×#95C24semidirect
173. C2×#95C24semidirect

Maximal subgroups

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

subgroupindex
#63423712
#20325942
#20325642
#20320302