Finite Group Databasebeta

← #24917653

Subgroups — #24917653

Order 10624.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128323C211yesmaximal, characteristic, complemented
2#19128173C211yesmaximal, characteristic, complemented
3#19128041C211yesmaximal, characteristic, complemented
4#19128027C211yesmaximal, characteristic, complemented
5#19127990C211yesmaximal, characteristic, complemented
6#19127979C211yesmaximal, characteristic, complemented
7#19127919C211yesmaximal, characteristic, complemented
8#19127918C211yesmaximal, characteristic, complemented
9#19127850C211yesmaximal, characteristic, complemented
10#19127836C211yesmaximal, characteristic
11#19127811C211yesmaximal, characteristic, complemented
12#19127799C211yesmaximal, characteristic, complemented
13C4×D664C211yesmaximal, characteristic, complemented
14#19127760C211yesmaximal, characteristic, complemented
15C4×SD16×C83C211yesmaximal, characteristic, complemented
16C2×D4×D83C2211yescharacteristic
17C2×#13050577C2211yescharacteristic
18C2×D664C2211yescharacteristic
19C2×#13050575C2211yescharacteristic
20#14581791C2211yescharacteristic, complemented
21#14581786—21no—
22#14581781C2211yescharacteristic, complemented
23#14581780—21no—
24#14581777—21no—
25#14581770—21no—
26#14581768C2211yescharacteristic
27#14581767C2211yescharacteristic
28C4×D332C2211yescharacteristic
29C4×D332C2211yescharacteristic, complemented
30D4×Dic83C2211yescharacteristic
31#14581754C2211yescharacteristic
32C4×C22⋊D83—21no—
33(C22⋊D83)⋊C4—21no—
34#14581750C2211yescharacteristic
35#14581749C2211yescharacteristic
36C2×(C2×D83)⋊C4—21no—
37C22⋊C4×D83—21no—
38#14581726C2211yescharacteristic, complemented
39#14581725C2211yescharacteristic, complemented
40#14581723C2211yescharacteristic, complemented
41Dic83⋊C8C2211yescharacteristic, complemented
42Dic83⋊C8C2211yescharacteristic, complemented
43#14581716C2211yescharacteristic, complemented
44#14581714C2211yescharacteristic
45#14581714C2211yescharacteristic, complemented
46#14581713C2211yescharacteristic
47#14581712C2211yescharacteristic
48#14581712C2211yescharacteristic, complemented
49(C2×D83)⋊C8C2211yescharacteristic
50(C2×D83)⋊C8C2211yescharacteristic
51#14581703C2211yescharacteristic, complemented
52C2×SD16×C83C2211yescharacteristic
53C4×Q8×C83C2211yescharacteristic, complemented
54C4×D4×C83C2211yescharacteristic
55#106×C83C2211yescharacteristic, complemented
56#103×C83C2211yescharacteristic, complemented
57#102×C83C2211yescharacteristic
58C4×C8×C83C2211yescharacteristic, complemented
59C23×D83—21no—
60C2×Dic166—21no—
61C2×D332—21no—
62C2×D332C2311yescharacteristic
63C2×D332C2311yescharacteristic
64C2×C22⋊D83—21no—
65D4×D83—22no—
66D4×D83—22no—
67C22×Dic83—21no—
68C2×C4×D83—21no—
69C2×C4×D83—21no—
70C2×C4×D83—21no—
71C2×C4×D83C2311yescharacteristic
72#13050577—22no—
73D664—22no—
74#13050575—22no—
75C2×C83⋊C8C2311yescharacteristic
76C2×C83⋊C8C2311yescharacteristic
77C4⋊Dic83C2311yescharacteristic
78C4⋊Dic83C2311yescharacteristic
79Dic83⋊C4—21no—
80Dic83⋊C4—21no—
81Dic83⋊C4D411yescharacteristic
82Dic83⋊C4D411yescharacteristic
83C22⋊Dic83—21no—
84(C2×D83)⋊C4—21no—
85(C2×D83)⋊C4—21no—
86(C2×D83)⋊C4—21no—
87(C2×D83)⋊C4—21no—
88(C2×D83)⋊C4—21no—
89(C2×D83)⋊C4—21no—
90(C2×D83)⋊C4—21no—
91(C2×D83)⋊C4—21no—
92(C2×D83)⋊C4D411yescharacteristic
93(C2×D83)⋊C4D411yescharacteristic
94C4×Dic83—21no—
95C4×Dic83C2311yescharacteristic
96C2×Q8×C83C2311yescharacteristic
97C2×D4×C83C2311yescharacteristic
98C22×C4×C83—21no—
99SD16×C83—22no—
100C2×C8×C83C2311yescharacteristic
101C2×C8×C83C2311yescharacteristic
102C4⋊C4×C83—21no—
103C4⋊C4×C83C2311yescharacteristic
104C4⋊C4×C83C2311yescharacteristic
105C22⋊C4×C83—21no—
106C42×C83—21no—
107C42×C83C2311yescharacteristic
108C23×C83—21no—
109C22×D83—21no—
110C22×D83—24no—
111C22×D83—21no—
112C22×D83—81no—
113C22×D83—81no—
114C22×D83C2×D411yescharacteristic
115Q8×C83—21no—
116Q8×C83—21no—
117D4×C83—21no—
118D4×C83#4112yes—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—81no—
123C2×C4×C83C2×D411yescharacteristic
124C2×C4×C83C2×D411yescharacteristic
125C2×C4×C83C2411yescharacteristic
126C22⋊D83—24no—
127C2×Dic83—21no—
128C2×Dic83—21no—
129C2×Dic83—81no—
130C2×Dic83C2×D411yescharacteristic
131C2×Dic83C2×D411yescharacteristic
132C2×Dic83C2×D411yescharacteristic
133D332—21no—
134D332—21no—
135D332—21no—
136D332—81no—
137D332#4112yes—
138C4×D83—21no—
139C4×D83—21no—
140C4×D83—81no—
141C4×D83—81no—
142C4×D83—81no—
143Dic166—81no—
144C8×C83—21no—
145C8×C83—21no—
146C83⋊C8—21no—
147C83⋊C8—21no—
148C22×C83—22no—
149C22×C83—41no—
150C22×C83—41no—
151C22×C83C22×D411yescharacteristic
152C2×D83—21no—
153C2×D83—22no—
154C2×D83—21no—
155C2×D83—21no—
156C2×D83—41no—
157C2×D83—41no—
158C2×D83—41no—
159C2×D83—41no—
160C2×D83—41no—
161C2×D83—84no—
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—41no—
165C4×C83—41no—
166C4×C83—41no—
167C4×C83C2×#4111yescharacteristic
168C4×C83C2×#4111yescharacteristic
169Dic83—21no—
170Dic83—21no—
171Dic83—21no—
172Dic83—41no—
173Dic83—41no—
174C2×C83—42no—
175C2×C83#52511yescharacteristic
176C2×C83#57611yescharacteristic
177C2×C83#57711yescharacteristic
178D83—41no—
179D83—42no—
180D83—81no—
181#3118—831nomaximal, Sylow
182C83#311811yescharacteristic, complemented, Sylow
183#542—831no—
184#518—831no—
185#485—831no—
186#482—831no—
187#476—831no—
188#474—831no—
189#463—831no—
190#463—831no—
191#450—831no—
192#447—831no—
193#442—831no—
194#440—831no—
195C4×SD16D8311yescharacteristic, complemented
196C4×D8—831no—
197#433—831no—
198C22×D4—831no—
199C2×SD16—831no—
200C2×SD16C2×D8311yescharacteristic
201C2×D8—831no—
202C2×D8—831no—
203C4⋊Q8—831no—
204#126—1661no—
205#124—831no—
206#124—1661no—
207#123—1661no—
208C22⋊Q8—831no—
209C22⋊Q8—1661no—
210#121—831no—
211C4×Q8C2×D8311yescharacteristic, complemented
212C4×D4—831no—
213C4×D4—831no—
214C4×D4—831no—
215C4×D4—831no—
216C4×D4—1661no—
217C4×D4—1661no—
218C4×D4C2×D8311yescharacteristic
219#117—831no—
220#117—831no—
221C2×C22⋊C4—1661no—
222C2×C22⋊C4—1661no—
223#107—831no—
224#107—831no—
225#106—831no—
226#106C2×D8311yescharacteristic, complemented
227C4⋊C8—831no—
228C4⋊C8—831no—
229#103—831no—
230#103C2×D8311yescharacteristic, complemented
231#102—831no—
232#102—831no—
233#102—831no—
234#102—831no—
235#102—831no—
236#102C2×D8311yescharacteristic
237C22⋊C8—831no—
238C22⋊C8—831no—
239#97—831no—
240C4×C8C2×D8311yescharacteristic, complemented
241C24—1661no—
242C2×Q8—1661no—
243C2×Q8C22×D8311yescharacteristic
244C2×D4—831no—
245C2×D4—831no—
246C2×D4—1661no—
247C2×D4—1661no—
248C2×D4—1662no—
249C2×D4—1662no—
250C2×D4C22×D8311yescharacteristic
251C22×C4—21no—
252C22×C4—831no—
253C22×C4—1661no—
254C22×C4—1661no—
255C22×C4—1661no—
256C22×C4—1661no—
257SD16—22no—
258SD16—1662no—
259D8—1662no—
260D8—1662no—
261C2×C8—831no—
262C2×C8—831no—
263C2×C8C22×D8311yescharacteristic
264C2×C8C22×D8311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—831no—
267C4⋊C4—831no—
268C4⋊C4—831no—
269C4⋊C4—831no—
270C4⋊C4—1661no—
271C4⋊C4—1661no—
272C4⋊C4C22×D8311yescharacteristic
273C4⋊C4C22×D8311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—831no—
276C22⋊C4—831no—
277C22⋊C4—1661no—
278C22⋊C4—1661no—
279C22⋊C4—1661no—
280C22⋊C4—1661no—
281C22⋊C4—1661no—
282C22⋊C4—1661no—
283C22⋊C4—1661no—
284C22⋊C4—1661no—
285C22⋊C4—1661no—
286C42—21no—
287C42—831no—
288C42—1661no—
289C42C22×D8311yescharacteristic
290C23—21no—
291C23—831no—
292C23—6641no—
293C23—6641no—
294C23—1664no—
295C23—1661no—
296C23—1661no—
297Q8—21no—
298Q8—21no—
299Q8—6641no—
300D4—21no—
301D4—832no—
302D4—6641no—
303D4—1664no—
304D4—1661no—
305D4—1661no—
306D4—1661no—
307D4#1305059012yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—831no—
313C2×C4—831no—
314C2×C4—831no—
315C2×C4—6641no—
316C2×C4—6641no—
317C2×C4—6641no—
318C2×C4—6641no—
319C2×C4—1661no—
320C2×C4—1661no—
321C2×C4—1661no—
322C2×C4—1661no—
323C2×C4D4×D8311yescharacteristic
324C2×C4D4×D8311yescharacteristic
325C2×C4C23×D8311yescharacteristic
326C8—21no—
327C8—21no—
328C8—1661no—
329C8—1661no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—3321no—
334C22—3321no—
335C22—3321no—
336C22—3321no—
337C22—3321no—
338C22—6644no—
339C22—1661no—
340C22—1662no—
341C22—1661no—
342C22—1661no—
343C22C2×D4×D8311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3321no—
350C4—3321no—
351C4—1661no—
352C4—1661no—
353C4—1661no—
354C4#41×D8311yescharacteristic
355C4C2×#1305059011yescharacteristic
356C2—42no—
357C2—3322no—
358C2—3321no—
359C2—6641no—
360C2#1912821011yescharacteristic
361C2#1912850311yescharacteristic
362C2#1912850711yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC4×SD16×C83C2
socleC22×C83C22×D4
prime radical#19127836C2
hypercenterC4×SD16D83
hypocenterC83#3118
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #19128323C2semidirect
2. #19128173C2semidirect
3. #19128041C2semidirect
4. #19128027C2semidirect
5. #19127990C2semidirect
6. #19127979C2semidirect
7. #19127919C2semidirect
8. #19127918C2semidirect
9. #19127850C2semidirect
11. #19127811C2semidirect
12. #19127799C2semidirect
13. C4×D664C2semidirect
14. #19127760C2semidirect
15. C4×SD16×C83C2semidirect
20. #14581791C22semidirect
22. #14581781C22semidirect
29. C4×D332C22semidirect
38. #14581726C22semidirect
39. #14581725C22semidirect
40. #14581723C22semidirect
41. Dic83⋊C8C22semidirect
42. Dic83⋊C8C22semidirect
43. #14581716C22semidirect
45. #14581714C22semidirect
48. #14581712C22semidirect
51. #14581703C22semidirect
53. C4×Q8×C83C22semidirect
55. #106×C83C22semidirect
56. #103×C83C22semidirect
58. C4×C8×C83C22semidirect
182. C83#3118semidirect
195. C4×SD16D83semidirect
211. C4×Q8C2×D83semidirect
226. #106C2×D83semidirect
230. #103C2×D83semidirect
240. C4×C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283232
#191281732
#191280412
#191280272
#191279902
#191279792
#191279192
#191279182
#191278502
#191278362
#191278112
#191277992
C4×D6642
#191277602
C4×SD16×C832
#311883