Finite Group Databasebeta

← #24919666

Subgroups — #24919666

Order 10624.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128397C211yesmaximal, characteristic, complemented
2#19128347C211yesmaximal, characteristic, complemented
3#19128056C211yesmaximal, characteristic, complemented
4#19128043C211yesmaximal, characteristic, complemented
5#19128015C211yesmaximal, characteristic, complemented
6#19128002C211yesmaximal, characteristic, complemented
7#19127954C211yesmaximal, characteristic, complemented
8#19127947C211yesmaximal, characteristic, complemented
9#19127917C211yesmaximal, characteristic, complemented
10#19127848C211yesmaximal, characteristic, complemented
11#19127837C211yesmaximal, characteristic, complemented
12C4×D664C211yesmaximal, characteristic, complemented
13#19127707C211yesmaximal, characteristic, complemented
14#19127703C211yesmaximal, characteristic, complemented
15#436×C83C211yesmaximal, characteristic, complemented
16C2×#13050590C2211yescharacteristic
17C22×D332C2211yescharacteristic
18C2×#13050579C2211yescharacteristic, complemented
19C2×D664C2211yescharacteristic
20C2×D664C2211yescharacteristic
21#14581787—21no—
22#14581784C2211yescharacteristic, complemented
23#14581780C2211yescharacteristic
24#14581777—21no—
25#14581774—21no—
26#14581771C2211yescharacteristic
27#14581766C2211yescharacteristic
28#14581766C2211yescharacteristic
29#14581766C2211yescharacteristic, complemented
30#14581765—21no—
31#14581764—21no—
32#14581760—21no—
33C4×D332C2211yescharacteristic
34C4×D332C2211yescharacteristic, complemented
35(C22⋊D83)⋊C4—21no—
36#14581751C2211yescharacteristic
37C2×C4⋊Dic83C2211yescharacteristic, complemented
38C22⋊C4×D83—21no—
39#14581726C2211yescharacteristic, complemented
40#14581726C2211yescharacteristic, complemented
41#14581724C2211yescharacteristic, complemented
42#14581717C2211yescharacteristic, complemented
43#14581717C2211yescharacteristic, complemented
44#14581717C2211yescharacteristic, complemented
45#14581714C2211yescharacteristic
46#14581714C2211yescharacteristic
47#14581714C2211yescharacteristic
48#14581714C2211yescharacteristic
49#14581714C2211yescharacteristic
50#14581714C2211yescharacteristic
51#14581714C2211yescharacteristic, complemented
52C2×M16×C83C2211yescharacteristic
53C2×M16×C83C2211yescharacteristic, complemented
54C4×D4×C83C2211yescharacteristic
55C4⋊C8×C83C2211yescharacteristic, complemented
56C22⋊C8×C83C2211yescharacteristic
57C22⋊C8×C83C2211yescharacteristic, complemented
58C4×C8×C83C2211yescharacteristic, complemented
59C23×D83—21no—
60#13050590—22no—
61#13050590—41no—
62C2×Dic166C2311yescharacteristic
63C2×D332—22no—
64C2×D332—21no—
65C2×D332—41no—
66C2×D332C2311yescharacteristic
67C2×D332C2311yescharacteristic
68C2×D332C2311yescharacteristic
69C2×C22⋊D83—21no—
70C2×C22⋊D83—21no—
71C2×C22⋊D83—21no—
72C2×C22⋊D83—21no—
73C22×Dic83—21no—
74C2×C4×D83—21no—
75C2×C4×D83—21no—
76C2×C4×D83—21no—
77#13050579—41no—
78D664—22no—
79D664—41no—
80C4⋊Dic83—21no—
81C4⋊Dic83C2311yescharacteristic
82C4⋊Dic83C2311yescharacteristic
83C4⋊Dic83C2311yescharacteristic
84C4⋊Dic83C2311yescharacteristic
85Dic83⋊C4—21no—
86Dic83⋊C4—21no—
87Dic83⋊C4—21no—
88C22⋊Dic83—21no—
89C22⋊Dic83—21no—
90(C2×D83)⋊C4—21no—
91(C2×D83)⋊C4—21no—
92(C2×D83)⋊C4—21no—
93(C2×D83)⋊C4—21no—
94(C2×D83)⋊C4—21no—
95(C2×D83)⋊C4—21no—
96(C2×D83)⋊C4—21no—
97C4×Dic83—21no—
98C2×D4×C83D411yescharacteristic
99C22×C4×C83C2311yescharacteristic
100C22×C4×C83C2311yescharacteristic
101M16×C83—41no—
102M16×C83—41no—
103C2×C8×C83C2311yescharacteristic
104C2×C8×C83C2311yescharacteristic
105C2×C8×C83C2311yescharacteristic
106C2×C8×C83C2311yescharacteristic
107C4⋊C4×C83D411yescharacteristic
108C22⋊C4×C83D411yescharacteristic
109C22⋊C4×C83D411yescharacteristic
110C42×C83C2311yescharacteristic
111C23×C83C2×D411yescharacteristic
112C23×C83C2×D411yescharacteristic
113C22×D83—21no—
114C22×D83—21no—
115C22×D83—21no—
116C22×D83—42no—
117C22×D83—42no—
118C22×D83—81no—
119D4×C83—41no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83C2×D411yescharacteristic
125C2×C4×C83C2×D411yescharacteristic
126C2×C4×C83C2×D411yescharacteristic
127C2×C4×C83C2×D411yescharacteristic
128C2×C4×C83C2411yescharacteristic
129C22⋊D83—42no—
130C22⋊D83—42no—
131C22⋊D83—81no—
132C22⋊D83—81no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—81no—
139D332—21no—
140D332—21no—
141D332—21no—
142D332—21no—
143D332—21no—
144D332—42no—
145D332#4112yes—
146C4×D83—42no—
147C4×D83—81no—
148C4×D83—81no—
149Dic166—21no—
150Dic166—21no—
151C8×C83—21no—
152C8×C83—21no—
153C8×C83—21no—
154C8×C83—21no—
155C22×C83—21no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—21no—
161C22×C83C22×D411yescharacteristic
162C2×D83—22no—
163C2×D83—41no—
164C2×D83—41no—
165C2×D83—41no—
166C2×D83—41no—
167C2×D83—41no—
168C2×D83—41no—
169C2×D83—41no—
170C2×D83—41no—
171C2×D83—84no—
172C4×C83—21no—
173C4×C83—21no—
174C4×C83—21no—
175C4×C83—21no—
176C4×C83C2×#4111yescharacteristic
177C4×C83H(5,𝔽2)11yescharacteristic
178Dic83—41no—
179Dic83—41no—
180Dic83—41no—
181Dic83—41no—
182Dic83—41no—
183C2×C83—41no—
184C2×C83—41no—
185C2×C83#54611yescharacteristic
186C2×C83#57511yescharacteristic
187C2×C83#57611yescharacteristic
188D83—42no—
189D83—81no—
190D83—81no—
191#3322—831nomaximal, Sylow
192C83#332211yescharacteristic, complemented, Sylow
193#553—831no—
194#546—831no—
195#488—831no—
196#485—831no—
197#480—831no—
198#478—831no—
199#469—831no—
200#468—831no—
201#463—831no—
202#449—831no—
203#447—831no—
204C4×D8—831no—
205#436D8311yescharacteristic, complemented
206#418—831no—
207#417—831no—
208C2×#41—831no—
209C22×D4—831no—
210C2×SD16—831no—
211C2×D8—831no—
212C2×D8—831no—
213C2×M16C2×D8311yescharacteristic
214C2×M16C2×D8311yescharacteristic, complemented
215#126—1661no—
216#125—831no—
217#124—831no—
218#123—1661no—
219#123—1661no—
220C22⋊Q8—831no—
221#121—831no—
222#121—831no—
223#121—831no—
224#121—1661no—
225#121—1661no—
226#120—1661no—
227C4×D4—831no—
228C4×D4—831no—
229C4×D4—1661no—
230C4×D4C2×D8311yescharacteristic
231#117—831no—
232C2×C4⋊C4—831no—
233C2×C22⋊C4—1661no—
234#107—831no—
235#107—831no—
236#106—831no—
237C4⋊C8C2×D8311yescharacteristic, complemented
238#103—831no—
239#103—831no—
240#103—831no—
241#102—831no—
242#102—831no—
243#102—831no—
244#102—831no—
245#102—831no—
246#102—831no—
247#102—831no—
248C22⋊C8C2×D8311yescharacteristic
249C22⋊C8C2×D8311yescharacteristic, complemented
250C4×C8C2×D8311yescharacteristic, complemented
251C24—1661no—
252#41—3321no—
253#41—1662no—
254C2×Q8—831no—
255C2×D4—3321no—
256C2×D4—831no—
257C2×D4—831no—
258C2×D4—831no—
259C2×D4—1662no—
260C2×D4—1661no—
261C2×D4—1661no—
262C2×D4—1661no—
263C2×D4—1661no—
264C2×D4—1661no—
265C2×D4D33211yescharacteristic
266C22×C4—1661no—
267C22×C4—1661no—
268C22×C4—1661no—
269C22×C4—1661no—
270C22×C4C22×D8311yescharacteristic
271C22×C4C22×D8311yescharacteristic
272SD16—3321no—
273D8—3321no—
274D8—1662no—
275M16—41no—
276M16—41no—
277C2×C8C22×D8311yescharacteristic
278C2×C8C22×D8311yescharacteristic
279C2×C8C22×D8311yescharacteristic
280C2×C8C22×D8311yescharacteristic
281C4⋊C4—831no—
282C4⋊C4—831no—
283C4⋊C4—831no—
284C4⋊C4—831no—
285C4⋊C4—1661no—
286C4⋊C4—1661no—
287C4⋊C4—1661no—
288C4⋊C4—1661no—
289C4⋊C4D33211yescharacteristic
290C22⋊C4—1661no—
291C22⋊C4—1661no—
292C22⋊C4—1661no—
293C22⋊C4—1661no—
294C22⋊C4—1661no—
295C22⋊C4—1661no—
296C22⋊C4—1661no—
297C22⋊C4—1661no—
298C22⋊C4—1661no—
299C22⋊C4D33211yescharacteristic
300C22⋊C4D33211yescharacteristic
301C42—1661no—
302C42C22×D8311yescharacteristic
303C23—3322no—
304C23—3322no—
305C23—6641no—
306C23—1661no—
307C23—1661no—
308C23—1661no—
309C23C2×D33211yescharacteristic
310C23C2×D33211yescharacteristic
311Q8—1661no—
312Q8—1661no—
313D4—41no—
314D4—3322no—
315D4—3322no—
316D4—3322no—
317D4—832no—
318D4—6641no—
319D4—6641no—
320D4—1661no—
321D4—1661no—
322D4—1661no—
323D4—1661no—
324D4—1661no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—3322no—
330C2×C4—6641no—
331C2×C4—6641no—
332C2×C4—6641no—
333C2×C4—1661no—
334C2×C4—1661no—
335C2×C4—1661no—
336C2×C4—1661no—
337C2×C4—1661no—
338C2×C4C2×D33211yescharacteristic
339C2×C4C2×D33211yescharacteristic
340C2×C4C2×D33211yescharacteristic
341C2×C4C2×D33211yescharacteristic
342C2×C4C23×D8311yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—3321no—
354C22—3321no—
355C22—3321no—
356C22—3321no—
357C22—3321no—
358C22—3321no—
359C22—3321no—
360C22—3321no—
361C22—6644no—
362C22—1662no—
363C22C22×D33211yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—3321no—
369C4—3321no—
370C4—3321no—
371C4—3321no—
372C4—3321no—
373C4#41×D8311yescharacteristic
374C4#1458183711yescharacteristic
375C2—41no—
376C2—41no—
377C2—3322no—
378C2—6641no—
379C2—6641no—
380C2#1912834611yescharacteristic
381C2#1912850111yescharacteristic
382C2#1912850611yescharacteristic
subgroupG/H
centerC22C22×D332
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#436×C83C2
socleC22×C83C22×D4
hypercenter#436D83
hypocenterC83#3322
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #19128397C2semidirect
2. #19128347C2semidirect
3. #19128056C2semidirect
4. #19128043C2semidirect
5. #19128015C2semidirect
6. #19128002C2semidirect
7. #19127954C2semidirect
8. #19127947C2semidirect
9. #19127917C2semidirect
10. #19127848C2semidirect
11. #19127837C2semidirect
12. C4×D664C2semidirect
13. #19127707C2semidirect
14. #19127703C2semidirect
15. #436×C83C2semidirect
18. C2×#13050579C22semidirect
22. #14581784C22semidirect
29. #14581766C22semidirect
34. C4×D332C22semidirect
37. C2×C4⋊Dic83C22semidirect
39. #14581726C22semidirect
40. #14581726C22semidirect
41. #14581724C22semidirect
42. #14581717C22semidirect
43. #14581717C22semidirect
44. #14581717C22semidirect
51. #14581714C22semidirect
53. C2×M16×C83C22semidirect
55. C4⋊C8×C83C22semidirect
57. C22⋊C8×C83C22semidirect
58. C4×C8×C83C22semidirect
192. C83#3322semidirect
205. #436D83semidirect
214. C2×M16C2×D83semidirect
237. C4⋊C8C2×D83semidirect
249. C22⋊C8C2×D83semidirect
250. C4×C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283972
#191283472
#191280562
#191280432
#191280152
#191280022
#191279542
#191279472
#191279172
#191278482
#191278372
C4×D6642
#191277072
#191277032
#436×C832
#332283