Finite Group Databasebeta

← #24919420

Subgroups — #24919420

Order 10624.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128352C211yesmaximal, characteristic, complemented
2#19128345C211yesmaximal, characteristic, complemented
3#19128059C211yesmaximal, characteristic, complemented
4#19128031C211yesmaximal, characteristic, complemented
5#19128018C211yesmaximal, characteristic, complemented
6#19127989C211yesmaximal, characteristic, complemented
7#19127953C211yesmaximal, characteristic, complemented
8#19127930C211yesmaximal, characteristic, complemented
9#19127915C211yesmaximal, characteristic, complemented
10#19127847C211yesmaximal, characteristic, complemented
11#19127835C211yesmaximal, characteristic, complemented
12#19127810C211yesmaximal, characteristic, complemented
13#19127772C211yesmaximal, characteristic, complemented
14#19127699C211yesmaximal, characteristic, complemented
15C2×#102×C83C211yesmaximal, characteristic, complemented
16C2×#13050590—21no—
17C2×#13050589C2211yescharacteristic
18C2×#13050579C2211yescharacteristic, complemented
19C2×#13050575C2211yescharacteristic
20C2×#13050575C2211yescharacteristic
21C2×#13050573C2211yescharacteristic, complemented
22#14581791C2211yescharacteristic, complemented
23#14581779C2211yescharacteristic
24#14581777—21no—
25#14581775—21no—
26#14581773—21no—
27#14581771C2211yescharacteristic
28#14581770—21no—
29#14581767C2211yescharacteristic, complemented
30#14581766C2211yescharacteristic
31#14581764—21no—
32#14581763C2211yescharacteristic
33#14581761—21no—
34D4×Dic83C2211yescharacteristic
35#14581754C2211yescharacteristic, complemented
36C4×C22⋊D83C2211yescharacteristic
37C4⋊C4×D83C2211yescharacteristic, complemented
38C2×C22⋊Dic83—21no—
39#14581724C2211yescharacteristic, complemented
40#14581723C2211yescharacteristic, complemented
41#14581723C2211yescharacteristic, complemented
42Dic83⋊C8C2211yescharacteristic, complemented
43#14581717C2211yescharacteristic, complemented
44#14581715C2211yescharacteristic, complemented
45#14581715C2211yescharacteristic, complemented
46#14581714C2211yescharacteristic, complemented
47#14581713C2211yescharacteristic
48#14581713C2211yescharacteristic
49C22⋊(C83⋊C8)C2211yescharacteristic
50(C2×D83)⋊C8C2211yescharacteristic, complemented
51#14581702C2211yescharacteristic, complemented
52C22×D4×C83C2211yescharacteristic
53C22×C8×C83C2211yescharacteristic
54C2×C4⋊C4×C83C2211yescharacteristic
55#102×C83C2211yescharacteristic
56#102×C83C2211yescharacteristic
57#102×C83C2211yescharacteristic
58#102×C83C2211yescharacteristic
59#13050590—44no—
60#13050589—22no—
61#13050589—41no—
62C2×Dic166—21no—
63C2×Dic166C2311yescharacteristic
64C2×D332—21no—
65C2×D332C2311yescharacteristic
66C2×C22⋊D83—21no—
67C2×C22⋊D83—21no—
68C2×C22⋊D83—21no—
69C2×C22⋊D83D411yescharacteristic
70C22×Dic83—21no—
71C22×Dic83—21no—
72C2×C4×D83—21no—
73C2×C4×D83—21no—
74C2×C4×D83C2311yescharacteristic
75#13050579—41no—
76#13050575—22no—
77#13050575—41no—
78#13050573—41no—
79C2×C83⋊C8C2311yescharacteristic
80C2×C83⋊C8C2311yescharacteristic
81C4⋊Dic83C2311yescharacteristic
82C4⋊Dic83C2311yescharacteristic
83Dic83⋊C4—21no—
84Dic83⋊C4—21no—
85Dic83⋊C4—21no—
86Dic83⋊C4D411yescharacteristic
87C22⋊Dic83—21no—
88C22⋊Dic83—21no—
89C22⋊Dic83—21no—
90C22⋊Dic83—21no—
91C22⋊Dic83—21no—
92C22⋊Dic83D411yescharacteristic
93(C2×D83)⋊C4—21no—
94(C2×D83)⋊C4—21no—
95(C2×D83)⋊C4—21no—
96(C2×D83)⋊C4D411yescharacteristic
97C4×Dic83C2311yescharacteristic
98C24×C83—21no—
99C2×D4×C83—22no—
100C2×D4×C83—21no—
101C2×D4×C83—41no—
102C2×D4×C83C2311yescharacteristic
103C2×D4×C83C2311yescharacteristic
104C22×C4×C83—21no—
105C22×C4×C83C2311yescharacteristic
106C2×C8×C83—41no—
107C2×C8×C83C2311yescharacteristic
108C2×C8×C83C2311yescharacteristic
109C4⋊C4×C83—21no—
110C4⋊C4×C83C2311yescharacteristic
111C4⋊C4×C83C2311yescharacteristic
112C23×C83—21no—
113C23×C83—21no—
114C23×C83—42no—
115C23×C83—42no—
116C23×C83—81no—
117C23×C83C2×D411yescharacteristic
118C22×D83—21no—
119C22×D83C2×D411yescharacteristic
120D4×C83—21no—
121D4×C83—21no—
122D4×C83—21no—
123D4×C83—42no—
124D4×C83#4112yescomplemented
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—42no—
130C2×C4×C83C2×D411yescharacteristic
131C2×C4×C83C2411yescharacteristic
132C22⋊D83—22no—
133C22⋊D83—42no—
134C22⋊D83—42no—
135C22⋊D83—81no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—42no—
140C2×Dic83—81no—
141C2×Dic83C2×D411yescharacteristic
142C2×Dic83C2×D411yescharacteristic
143C2×Dic83C2×D411yescharacteristic
144D332—21no—
145D332—21no—
146D332—42no—
147C4×D83—21no—
148C4×D83—21no—
149C4×D83—42no—
150C4×D83—42no—
151Dic166—21no—
152Dic166—21no—
153Dic166—42no—
154C8×C83—21no—
155C8×C83—21no—
156C83⋊C8—21no—
157C83⋊C8—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—22no—
161C22×C83—41no—
162C22×C83—41no—
163C22×C83—41no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—84no—
167C22×C83AGL(1,ℤ/8)12yes—
168C22×C83C22×D411yescharacteristic
169C2×D83—21no—
170C2×D83—21no—
171C2×D83—21no—
172C2×D83—41no—
173C2×D83—41no—
174C2×D83—41no—
175C4×C83—21no—
176C4×C83—41no—
177C4×C83—41no—
178C4×C83C2×#4111yescharacteristic
179C4×C83H(5,𝔽2)11yescharacteristic
180Dic83—21no—
181Dic83—21no—
182Dic83—21no—
183Dic83—41no—
184Dic83—41no—
185Dic83—41no—
186C2×C83—22no—
187C2×C83—42no—
188C2×C83—81no—
189C2×C83#54611yescharacteristic
190C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C83#57711yescharacteristic
192D83—41no—
193D83—81no—
194#3306—831nomaximal, Sylow
195C83#330611yescharacteristic, complemented, Sylow
196#547—831no—
197#546—831no—
198#489—831no—
199#483—831no—
200#481—831no—
201#476—831no—
202#469—831no—
203#465—831no—
204#463—831no—
205#449—831no—
206#447—831no—
207#442—831no—
208#435—831no—
209#417—831no—
210C2×#102D8311yescharacteristic, complemented
211C2×#41—831no—
212C2×#41—1661no—
213C22×D4C2×D8311yescharacteristic
214C2×SD16—831no—
215C2×D8—831no—
216C2×D8—831no—
217C2×M16—831no—
218C22×C8C2×D8311yescharacteristic
219C4⋊Q8—831no—
220#124—831no—
221#123—1661no—
222#123—1661no—
223#123—1661no—
224C22⋊Q8—831no—
225C22⋊Q8—1661no—
226#121—831no—
227#121—831no—
228#121—831no—
229#121—1661no—
230#120—1661no—
231C4×D4—831no—
232C4×D4—831no—
233C4×D4—831no—
234C2×C4⋊C4—831no—
235C2×C4⋊C4C2×D8311yescharacteristic
236C2×C22⋊C4—1661no—
237#106—831no—
238#106—831no—
239#106—831no—
240C4⋊C8—831no—
241#103—831no—
242#103—831no—
243#103—831no—
244#102—831no—
245#102—831no—
246#102—831no—
247#102C2×D8311yescharacteristic
248#102C2×D8311yescharacteristic
249#102C2×D8311yescharacteristic
250#102C2×D8311yescharacteristic
251C22⋊C8—831no—
252C22⋊C8—831no—
253#97—831no—
254C24—21no—
255#41—3324no—
256#41—3321no—
257#41—1662no—
258C2×Q8—831no—
259C2×Q8—1661no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—831no—
264C2×D4—831no—
265C2×D4—1661no—
266C2×D4—1661no—
267C2×D4—1661no—
268C2×D4—1661no—
269C2×D4C22×D8311yescharacteristic
270C2×D4C22×D8311yescharacteristic
271C22×C4—21no—
272C22×C4—831no—
273C22×C4—1661no—
274C22×C4—1661no—
275C22×C4—1661no—
276C22×C4—1661no—
277C22×C4C22×D8311yescharacteristic
278SD16—3321no—
279D8—3321no—
280D8—1662no—
281M16—3321no—
282C2×C8—41no—
283C2×C8—831no—
284C2×C8—831no—
285C2×C8C22×D8311yescharacteristic
286C2×C8C22×D8311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—831no—
289C4⋊C4—831no—
290C4⋊C4—831no—
291C4⋊C4—1661no—
292C4⋊C4—1661no—
293C4⋊C4—1661no—
294C4⋊C4C22×D8311yescharacteristic
295C4⋊C4C22×D8311yescharacteristic
296C22⋊C4—831no—
297C22⋊C4—831no—
298C22⋊C4—1661no—
299C22⋊C4—1661no—
300C22⋊C4—1661no—
301C22⋊C4—1661no—
302C22⋊C4—1661no—
303C22⋊C4—1661no—
304C22⋊C4—1661no—
305C22⋊C4—1661no—
306C42—831no—
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—831no—
313C23—1661no—
314C23D4×D8311yescharacteristic
315Q8—3322no—
316Q8—1661no—
317Q8—1661no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—3322no—
323D4—3322no—
324D4—3322no—
325D4—6641no—
326D4—1662no—
327D4—1661no—
328D4—1661no—
329D4#1305059012yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—3322no—
336C2×C4—3322no—
337C2×C4—3322no—
338C2×C4—831no—
339C2×C4—831no—
340C2×C4—831no—
341C2×C4—6641no—
342C2×C4—1661no—
343C2×C4—1661no—
344C2×C4—1661no—
345C2×C4—1661no—
346C2×C4—1661no—
347C2×C4D4×D8311yescharacteristic
348C2×C4C23×D8311yescharacteristic
349C8—21no—
350C8—21no—
351C8—1661no—
352C8—1661no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—84no—
362C22—3321no—
363C22—3321no—
364C22—3321no—
365C22—1661no—
366C22—1661no—
367C22—1661no—
368C22#1458181612yes—
369C22C2×D4×D8311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—3321no—
374C4—3321no—
375C4—3321no—
376C4—1661no—
377C4—1661no—
378C4—1661no—
379C4C2×#1305059011yescharacteristic
380C4#1458183711yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—3321no—
385C2—6641no—
386C2#1912834111yescharacteristic
387C2C2×#1458181611yescharacteristic
388C2#1912850711yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×#102×C83C2
socleC22×C83C22×D4
hypercenterC2×#102D83
hypocenterC83#3306
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #19128352C2semidirect
2. #19128345C2semidirect
3. #19128059C2semidirect
4. #19128031C2semidirect
5. #19128018C2semidirect
6. #19127989C2semidirect
7. #19127953C2semidirect
8. #19127930C2semidirect
9. #19127915C2semidirect
10. #19127847C2semidirect
11. #19127835C2semidirect
12. #19127810C2semidirect
13. #19127772C2semidirect
14. #19127699C2semidirect
15. C2×#102×C83C2semidirect
18. C2×#13050579C22semidirect
21. C2×#13050573C22semidirect
22. #14581791C22semidirect
29. #14581767C22semidirect
35. #14581754C22semidirect
37. C4⋊C4×D83C22semidirect
39. #14581724C22semidirect
40. #14581723C22semidirect
41. #14581723C22semidirect
42. Dic83⋊C8C22semidirect
43. #14581717C22semidirect
44. #14581715C22semidirect
45. #14581715C22semidirect
46. #14581714C22semidirect
50. (C2×D83)⋊C8C22semidirect
51. #14581702C22semidirect
124. D4×C83#41semidirect
195. C83#3306semidirect
210. C2×#102D83semidirect
329. D4#13050590semidirect

Maximal subgroups

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

subgroupindex
#191283522
#191283452
#191280592
#191280312
#191280182
#191279892
#191279532
#191279302
#191279152
#191278472
#191278352
#191278102
#191277722
#191276992
C2×#102×C832
#330683