Finite Group Databasebeta

← #24919463

Subgroups — #24919463

Order 10624.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128372C211yesmaximal, characteristic, complemented
2#19128067C211yesmaximal, characteristic, complemented
3#19128025C211yesmaximal, characteristic, complemented
4#19128014C211yesmaximal, characteristic, complemented
5#19128005C211yesmaximal, characteristic, complemented
6#19127952C211yesmaximal, characteristic, complemented
7#19127935C211yesmaximal, characteristic, complemented
8#19127896C211yesmaximal, characteristic, complemented
9#19127844C211yesmaximal, characteristic, complemented
10#19127844C211yesmaximal, characteristic, complemented
11#19127801C211yesmaximal, characteristic, complemented
12#19127773C211yesmaximal, characteristic, complemented
13#19127700C211yesmaximal, characteristic, complemented
14#19127695C211yesmaximal, characteristic, complemented
15#553×C83C211yesmaximal, characteristic, complemented
16C2×#13050590C2211yescharacteristic
17C2×#13050590C2211yescharacteristic
18C2×#13050578C2211yescharacteristic
19C2×#13050575C2211yescharacteristic
20C2×#13050575C2211yescharacteristic
21C2×#13050574C2211yescharacteristic
22C22×C83⋊C8C2211yescharacteristic
23#14581789C2211yescharacteristic
24#14581788—21no—
25#14581766C2211yescharacteristic
26#14581766C2211yescharacteristic
27#14581765—21no—
28#14581765—21no—
29C4×Dic166C2211yescharacteristic
30#14581754—21no—
31#14581725C2211yescharacteristic
32#14581725C2211yescharacteristic
33#14581723C2211yescharacteristic
34C4⋊(C83⋊C8)C2211yescharacteristic
35#14581715C2211yescharacteristic
36#14581715C2211yescharacteristic
37#14581715C2211yescharacteristic
38#14581713C2211yescharacteristic
39#14581712C2211yescharacteristic
40#14581712C2211yescharacteristic
41#14581712C2211yescharacteristic
42#14581712C2211yescharacteristic
43#14581712C2211yescharacteristic
44#14581712C2211yescharacteristic
45C22⋊(C83⋊C8)C2211yescharacteristic
46C22⋊(C83⋊C8)C2211yescharacteristic
47#14581703C2211yescharacteristic
48#126×C83—21no—
49#125×C83C2211yescharacteristic
50#123×C83—21no—
51#121×C83—21no—
52#121×C83C2211yescharacteristic
53#121×C83C2211yescharacteristic
54C4×D4×C83—21no—
55C4×D4×C83C2211yescharacteristic
56C4×D4×C83C2211yescharacteristic
57#117×C83C2211yescharacteristic
58C2×C4⋊C4×C83C2211yescharacteristic
59#13050590—22no—
60#13050590—22no—
61#13050590—41no—
62#13050590—41no—
63C2×Dic166C2311yescharacteristic
64C2×D332—21no—
65C2×D332—21no—
66C2×D332C2311yescharacteristic
67C2×D332C2311yescharacteristic
68C2×C22⋊D83—21no—
69C2×C22⋊D83—21no—
70C2×C22⋊D83—21no—
71C2×C22⋊D83—21no—
72C2×C4×D83—21no—
73C2×C4×D83—21no—
74#13050578—22no—
75#13050575—41no—
76#13050575—41no—
77#13050574—41no—
78C2×C83⋊C8—41no—
79C2×C83⋊C8C2311yescharacteristic
80C2×C83⋊C8C2311yescharacteristic
81C2×C83⋊C8C2311yescharacteristic
82C2×C83⋊C8C2311yescharacteristic
83C4⋊Dic83C2311yescharacteristic
84Dic83⋊C4—21no—
85(C2×D83)⋊C4—21no—
86(C2×D83)⋊C4—21no—
87C4×Dic83—21no—
88C2×D4×C83—21no—
89C2×D4×C83—21no—
90C2×D4×C83D411yescharacteristic
91C2×D4×C83C2311yescharacteristic
92C22×C4×C83—21no—
93C22×C4×C83—21no—
94C22×C4×C83C2311yescharacteristic
95C22×C4×C83C2311yescharacteristic
96C4⋊C4×C83—21no—
97C4⋊C4×C83—21no—
98C4⋊C4×C83—21no—
99C4⋊C4×C83D411yescharacteristic
100C4⋊C4×C83C2311yescharacteristic
101C4⋊C4×C83C2311yescharacteristic
102C4⋊C4×C83C2311yescharacteristic
103C22⋊C4×C83—21no—
104C22⋊C4×C83—21no—
105C22⋊C4×C83—21no—
106C22⋊C4×C83—21no—
107C22⋊C4×C83D411yescharacteristic
108C22⋊C4×C83D411yescharacteristic
109C42×C83—21no—
110C42×C83C2311yescharacteristic
111C23×C83—21no—
112C23×C83C2×D411yescharacteristic
113C23×C83C2×D411yescharacteristic
114C22×D83—21no—
115C22×D83—21no—
116D4×C83—21no—
117D4×C83—21no—
118D4×C83—41no—
119D4×C83—42no—
120D4×C83—81no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—81no—
129C2×C4×C83—81no—
130C2×C4×C83C2×D411yescharacteristic
131C2×C4×C83C2×D411yescharacteristic
132C2×C4×C83C2×D411yescharacteristic
133C2×C4×C83C2×D411yescharacteristic
134C2×C4×C83C2411yescharacteristic
135C22⋊D83—42no—
136C22⋊D83—42no—
137C22⋊D83—81no—
138C22⋊D83—81no—
139C2×Dic83—21no—
140C2×Dic83—21no—
141D332—21no—
142D332—21no—
143D332—21no—
144D332—21no—
145D332—42no—
146D332—81no—
147C4×D83—42no—
148C4×D83—42no—
149Dic166—21no—
150Dic166#4112yes—
151C83⋊C8—21no—
152C83⋊C8—21no—
153C83⋊C8—21no—
154C83⋊C8—21no—
155C22×C83—21no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—21no—
161C22×C83—41no—
162C22×C83—41no—
163C22×C83—41no—
164C22×C83C22×D411yescharacteristic
165C2×D83—41no—
166C2×D83—41no—
167C2×D83—41no—
168C2×D83—41no—
169C2×D83—41no—
170C2×D83—41no—
171C4×C83—21no—
172C4×C83—21no—
173C4×C83—21no—
174C4×C83—21no—
175C4×C83—41no—
176C4×C83—41no—
177C4×C83—41no—
178C4×C83C2×#4111yescharacteristic
179C4×C83H(5,𝔽2)11yescharacteristic
180Dic83—22no—
181Dic83—41no—
182C2×C83—41no—
183C2×C83—41no—
184C2×C83—81no—
185C2×C83#54611yescharacteristic
186C2×C83#57511yescharacteristic
187C2×C83#57611yescharacteristic
188D83—81no—
189D83—81no—
190#3309—831nomaximal, Sylow
191C83#330911yescharacteristic, complemented, Sylow
192#553D8311yescharacteristic, complemented
193#550—831no—
194#490—831no—
195#482—831no—
196#480—831no—
197#479—831no—
198#469—831no—
199#466—831no—
200#459—831no—
201#449—831no—
202#449—831no—
203#440—831no—
204#435—831no—
205#417—831no—
206#416—831no—
207C2×#41—831no—
208C2×#41—831no—
209C2×SD16—831no—
210C2×D8—831no—
211C2×D8—831no—
212C2×M16—831no—
213C22×C8—831no—
214#127—831no—
215#127—1661no—
216#126—21no—
217#125C2×D8311yescharacteristic
218#123—21no—
219#121—21no—
220#121—831no—
221#121—831no—
222#121—1661no—
223#121—1661no—
224#121C2×D8311yescharacteristic
225#121C2×D8311yescharacteristic
226C4×Q8—831no—
227C4×D4—21no—
228C4×D4—1661no—
229C4×D4C2×D8311yescharacteristic
230C4×D4C2×D8311yescharacteristic
231#117C2×D8311yescharacteristic
232C2×C4⋊C4C2×D8311yescharacteristic
233#107—831no—
234#107—831no—
235#106—831no—
236C4⋊C8—831no—
237#103—831no—
238#103—831no—
239#103—831no—
240#102—831no—
241#102—831no—
242#102—831no—
243#102—831no—
244#102—831no—
245#102—831no—
246#102—831no—
247C22⋊C8—831no—
248C22⋊C8—831no—
249#97—831no—
250#41—3321no—
251#41—3321no—
252#41—1662no—
253#41—1662no—
254C2×Q8—831no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—831no—
258C2×D4—831no—
259C2×D4—1661no—
260C2×D4—1661no—
261C2×D4—1661no—
262C2×D4—1661no—
263C2×D4—1661no—
264C2×D4—1661no—
265C2×D4C22⋊D8311yescharacteristic
266C2×D4C22×D8311yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1661no—
270C22×C4—1661no—
271C22×C4C22×D8311yescharacteristic
272C22×C4C22×D8311yescharacteristic
273SD16—1662no—
274D8—3321no—
275D8—3321no—
276M16—3321no—
277C2×C8—3321no—
278C2×C8—831no—
279C2×C8—831no—
280C2×C8—831no—
281C2×C8—831no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—831no—
286C4⋊C4—1661no—
287C4⋊C4C22⋊D8311yescharacteristic
288C4⋊C4C22×D8311yescharacteristic
289C4⋊C4C22×D8311yescharacteristic
290C4⋊C4C22×D8311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—1661no—
296C22⋊C4—1661no—
297C22⋊C4C22⋊D8311yescharacteristic
298C22⋊C4C22⋊D8311yescharacteristic
299C42—21no—
300C42—1661no—
301C42C22×D8311yescharacteristic
302C23—21no—
303C23—1661no—
304C23—1661no—
305C23C2×C22⋊D8311yescharacteristic
306C23C2×C22⋊D8311yescharacteristic
307Q8—832no—
308Q8—1661no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—3322no—
315D4—3322no—
316D4—3322no—
317D4—6641no—
318D4—6641no—
319D4—6641no—
320D4—1661no—
321D4—1661no—
322D4—1661no—
323D4—1661no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—3322no—
334C2×C4—3322no—
335C2×C4—1661no—
336C2×C4—1661no—
337C2×C4C2×C22⋊D8311yescharacteristic
338C2×C4C2×C22⋊D8311yescharacteristic
339C2×C4C2×C22⋊D8311yescharacteristic
340C2×C4C2×C22⋊D8311yescharacteristic
341C2×C4C23×D8311yescharacteristic
342C8—1661no—
343C8—1661no—
344C8—1661no—
345C8—1661no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—3321no—
356C22—3321no—
357C22—3321no—
358C22—3321no—
359C22—3321no—
360C22—3321no—
361C22C22×C22⋊D8311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—3321no—
370C4—1662no—
371C4#41×D8311yescharacteristic
372C4#1458183811yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—6641no—
377C2—6641no—
378C2#1912833911yescharacteristic
379C2#1912849911yescharacteristic
380C2#1912850411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#553×C83C2
socleC22×C83C22×D4
hypercenter#553D83
hypocenterC83#3309
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #19128372C2semidirect
2. #19128067C2semidirect
3. #19128025C2semidirect
4. #19128014C2semidirect
5. #19128005C2semidirect
6. #19127952C2semidirect
7. #19127935C2semidirect
8. #19127896C2semidirect
9. #19127844C2semidirect
10. #19127844C2semidirect
11. #19127801C2semidirect
12. #19127773C2semidirect
13. #19127700C2semidirect
14. #19127695C2semidirect
15. #553×C83C2semidirect
191. C83#3309semidirect
192. #553D83semidirect

Maximal subgroups

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

subgroupindex
#191283722
#191280672
#191280252
#191280142
#191280052
#191279522
#191279352
#191278962
#191278442
#191278012
#191277732
#191277002
#191276952
#553×C832
#330983