Finite Group Databasebeta

← #24917652

Subgroups — #24917652

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#19128325C211yesmaximal, characteristic, complemented
2#19128173C211yesmaximal, characteristic, complemented
3#19128045C211yesmaximal, characteristic, complemented
4#19128027C211yesmaximal, characteristic, complemented
5#19127978C211yesmaximal, characteristic, complemented
6#19127917C211yesmaximal, characteristic, complemented
7#19127916C211yesmaximal, characteristic, complemented
8#19127853C211yesmaximal, characteristic, complemented
9#19127836C211yesmaximal, characteristic
10#19127812C211yesmaximal, characteristic, complemented
11#19127798C211yesmaximal, characteristic, complemented
12#19127788C211yesmaximal, characteristic, complemented
13#19127781C211yesmaximal, characteristic, complemented
14#19127761C211yesmaximal, characteristic, complemented
15#476×C83C211yesmaximal, characteristic, complemented
16C2×D4×D83C2211yescharacteristic
17C2×#13050579C2211yescharacteristic
18C2×#13050578C2211yescharacteristic
19C2×D664C2211yescharacteristic
20C2×#13050575C2211yescharacteristic
21#14581787—21no—
22#14581781—21no—
23#14581780C2211yescharacteristic, complemented
24#14581777—21no—
25#14581772C2211yescharacteristic
26#14581768—21no—
27#14581767C2211yescharacteristic
28#14581757C2211yescharacteristic, complemented
29C4×D332C2211yescharacteristic
30D4×Dic83C2211yescharacteristic
31#14581754C2211yescharacteristic
32#14581754C2211yescharacteristic, complemented
33C4×C22⋊D83—21no—
34(C22⋊D83)⋊C4—21no—
35#14581750C2211yescharacteristic
36#14581749C2211yescharacteristic
37C2×(C2×D83)⋊C4—21no—
38C22⋊C4×D83—21no—
39#14581725C2211yescharacteristic, complemented
40#14581725C2211yescharacteristic, complemented
41C4⋊(C83⋊C8)C2211yescharacteristic, complemented
42#14581717C2211yescharacteristic, complemented
43#14581715C2211yescharacteristic, complemented
44#14581714C2211yescharacteristic, complemented
45#14581712C2211yescharacteristic
46#14581712C2211yescharacteristic
47#14581712C2211yescharacteristic, complemented
48(C2×D83)⋊C8C2211yescharacteristic
49(C2×D83)⋊C8C2211yescharacteristic
50#14581702C2211yescharacteristic, complemented
51C8×Dic83C2211yescharacteristic, complemented
52C4⋊Q8×C83C2211yescharacteristic, complemented
53C4×D4×C83C2211yescharacteristic
54#106×C83C2211yescharacteristic, complemented
55#106×C83C2211yescharacteristic, complemented
56C4⋊C8×C83C2211yescharacteristic, complemented
57#102×C83C2211yescharacteristic
58#102×C83C2211yescharacteristic
59C23×D83—21no—
60C2×Dic166C2311yescharacteristic
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#13050579—22no—
73#13050578—22no—
74D664—22no—
75#13050575—22no—
76C2×C83⋊C8C2311yescharacteristic
77C2×C83⋊C8C2311yescharacteristic
78C4⋊Dic83—21no—
79C4⋊Dic83C2311yescharacteristic
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×Dic83—21no—
96C4×Dic83C2311yescharacteristic
97C2×Q8×C83—21no—
98C2×D4×C83C2311yescharacteristic
99C22×C4×C83—21no—
100C2×C8×C83C2311yescharacteristic
101C2×C8×C83C2311yescharacteristic
102C4⋊C4×C83—21no—
103C4⋊C4×C83C2311yescharacteristic
104C4⋊C4×C83C2311yescharacteristic
105C4⋊C4×C83C2311yescharacteristic
106C22⋊C4×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—81no—
116D4×C83—21no—
117D4×C83#4112yes—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—81no—
122C2×C4×C83C2×D411yescharacteristic
123C2×C4×C83C2×D411yescharacteristic
124C2×C4×C83C2411yescharacteristic
125C22⋊D83—24no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—81no—
129C2×Dic83C2×D411yescharacteristic
130C2×Dic83C2×D411yescharacteristic
131C2×Dic83C2×D411yescharacteristic
132D332—21no—
133D332—21no—
134D332—21no—
135D332—81no—
136D332#4112yes—
137C4×D83—21no—
138C4×D83—21no—
139C4×D83—81no—
140C4×D83—81no—
141C4×D83—81no—
142Dic166—21no—
143Dic166—21no—
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#476D8311yescharacteristic, complemented
188#474—831no—
189#463—831no—
190#463—831no—
191#450—831no—
192#447—831no—
193#442—831no—
194#440—831no—
195C4×SD16—831no—
196C4×D8—831no—
197#433—831no—
198C22×D4—831no—
199C2×SD16—831no—
200C2×SD16—831no—
201C2×D8—831no—
202C2×D8—831no—
203C4⋊Q8C2×D8311yescharacteristic, complemented
204#126—1661no—
205#124—831no—
206#124—1661no—
207#123—1661no—
208C22⋊Q8—831no—
209C22⋊Q8—1661no—
210#121—831no—
211C4×Q8—831no—
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#106C2×D8311yescharacteristic, complemented
226#106C2×D8311yescharacteristic, complemented
227C4⋊C8—831no—
228C4⋊C8C2×D8311yescharacteristic, complemented
229#103—831no—
230#103—831no—
231#102—831no—
232#102—831no—
233#102—831no—
234#102—831no—
235#102C2×D8311yescharacteristic
236#102C2×D8311yescharacteristic
237C22⋊C8—831no—
238C22⋊C8—831no—
239#97—831no—
240C4×C8—831no—
241C24—1661no—
242C2×Q8—21no—
243C2×Q8—831no—
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—1662no—
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—1661no—
270C4⋊C4—1661no—
271C4⋊C4C22×D8311yescharacteristic
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—831no—
287C42—1661no—
288C42—1661no—
289C42C22×D8311yescharacteristic
290C23—21no—
291C23—831no—
292C23—6641no—
293C23—6641no—
294C23—1664no—
295C23—1661no—
296C23—1661no—
297Q8—81no—
298Q8—1661no—
299Q8—1661no—
300D4—21no—
301D4—832no—
302D4—6641no—
303D4—1664no—
304D4—1661no—
305D4—1661no—
306D4—1661no—
307D4#1305059112yes—
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×#1305059111yescharacteristic
356C2—42no—
357C2—3322no—
358C2—3321no—
359C2—6641no—
360C2#1912821411yescharacteristic
361C2#1912850511yescharacteristic
362C2#1912850711yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#476×C83C2
socleC22×C83C22×D4
prime radical#19127836C2
hypercenter#476D83
hypocenterC83#3118
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #19128325C2semidirect
2. #19128173C2semidirect
3. #19128045C2semidirect
4. #19128027C2semidirect
5. #19127978C2semidirect
6. #19127917C2semidirect
7. #19127916C2semidirect
8. #19127853C2semidirect
10. #19127812C2semidirect
11. #19127798C2semidirect
12. #19127788C2semidirect
13. #19127781C2semidirect
14. #19127761C2semidirect
15. #476×C83C2semidirect
23. #14581780C22semidirect
28. #14581757C22semidirect
32. #14581754C22semidirect
39. #14581725C22semidirect
40. #14581725C22semidirect
41. C4⋊(C83⋊C8)C22semidirect
42. #14581717C22semidirect
43. #14581715C22semidirect
44. #14581714C22semidirect
47. #14581712C22semidirect
50. #14581702C22semidirect
51. C8×Dic83C22semidirect
52. C4⋊Q8×C83C22semidirect
54. #106×C83C22semidirect
55. #106×C83C22semidirect
56. C4⋊C8×C83C22semidirect
182. C83#3118semidirect
187. #476D83semidirect
203. C4⋊Q8C2×D83semidirect
225. #106C2×D83semidirect
226. #106C2×D83semidirect
228. C4⋊C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283252
#191281732
#191280452
#191280272
#191279782
#191279172
#191279162
#191278532
#191278362
#191278122
#191277982
#191277882
#191277812
#191277612
#476×C832
#311883