Finite Group Databasebeta

← #24917645

Subgroups — #24917645

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#19128316C211yesmaximal, characteristic, complemented
2#19128173C211yesmaximal, characteristic, complemented
3#19128045C211yesmaximal, characteristic, complemented
4#19128023C211yesmaximal, characteristic, complemented
5#19127990C211yesmaximal, characteristic, complemented
6#19127979C211yesmaximal, characteristic, complemented
7#19127915C211yesmaximal, characteristic, complemented
8#19127914C211yesmaximal, characteristic, complemented
9#19127853C211yesmaximal, characteristic, complemented
10#19127833C211yesmaximal, characteristic
11#19127803C211yesmaximal, characteristic, complemented
12C4×#13050578C211yesmaximal, characteristic, complemented
13C4×#13050575C211yesmaximal, characteristic, complemented
14#19127763C211yesmaximal, characteristic, complemented
15#442×C83C211yesmaximal, characteristic, complemented
16C2×D4×D83C2211yescharacteristic
17C2×#13050579C2211yescharacteristic
18C2×#13050578C2211yescharacteristic
19C2×#13050575C2211yescharacteristic
20#14581791C2211yescharacteristic, complemented
21#14581785—21no—
22#14581779C2211yescharacteristic, complemented
23#14581778—21no—
24#14581775—21no—
25#14581772C2211yescharacteristic
26#14581771—21no—
27#14581763C2211yescharacteristic
28C4×Dic166C2211yescharacteristic, complemented
29C4×D332C2211yescharacteristic
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#14581717C2211yescharacteristic, complemented
44#14581715C2211yescharacteristic, complemented
45#14581714C2211yescharacteristic
46#14581713C2211yescharacteristic
47#14581713C2211yescharacteristic, complemented
48#14581712C2211yescharacteristic
49(C2×D83)⋊C8C2211yescharacteristic
50(C2×D83)⋊C8C2211yescharacteristic
51C4×C83⋊C8C2211yescharacteristic, complemented
52C2×D8×C83C2211yescharacteristic
53C4×D4×C83C2211yescharacteristic
54C4×D4×C83C2211yescharacteristic, complemented
55#106×C83C2211yescharacteristic, complemented
56#102×C83C2211yescharacteristic
57#102×C83C2211yescharacteristic, complemented
58#97×C83C2211yescharacteristic, complemented
59C23×D83—21no—
60C2×Dic166—21no—
61C2×Dic166C2311yescharacteristic
62C2×D332C2311yescharacteristic
63C2×C22⋊D83—21no—
64C2×C22⋊D83—21no—
65D4×D83—22no—
66D4×D83—22no—
67C22×Dic83—21no—
68C2×C4×D83—21no—
69C2×C4×D83—21no—
70C2×C4×D83C2311yescharacteristic
71#13050579—22no—
72#13050578—22no—
73#13050575—22no—
74C2×C83⋊C8C2311yescharacteristic
75C2×C83⋊C8C2311yescharacteristic
76C4⋊Dic83—21no—
77C4⋊Dic83C2311yescharacteristic
78C4⋊Dic83C2311yescharacteristic
79Dic83⋊C4—21no—
80Dic83⋊C4—21no—
81Dic83⋊C4D411yescharacteristic
82Dic83⋊C4D411yescharacteristic
83C22⋊Dic83—21no—
84C22⋊Dic83—21no—
85C22⋊Dic83—21no—
86C22⋊Dic83—21no—
87(C2×D83)⋊C4—21no—
88(C2×D83)⋊C4—21no—
89(C2×D83)⋊C4—21no—
90(C2×D83)⋊C4—21no—
91(C2×D83)⋊C4D411yescharacteristic
92(C2×D83)⋊C4D411yescharacteristic
93C4×Dic83—21no—
94C4×Dic83—21no—
95C4×Dic83C2311yescharacteristic
96C2×D4×C83C2311yescharacteristic
97C2×D4×C83C2311yescharacteristic
98C22×C4×C83—21no—
99C22×C4×C83—21no—
100D8×C83—22no—
101C2×C8×C83C2311yescharacteristic
102C2×C8×C83C2311yescharacteristic
103C4⋊C4×C83C2311yescharacteristic
104C4⋊C4×C83C2311yescharacteristic
105C22⋊C4×C83—21no—
106C22⋊C4×C83—21no—
107C42×C83C2311yescharacteristic
108C23×C83—21no—
109C23×C83—21no—
110C22×D83—21no—
111C22×D83—24no—
112C22×D83—81no—
113C22×D83—81no—
114C22×D83C2×D411yescharacteristic
115D4×C83—21no—
116D4×C83—21no—
117D4×C83—21no—
118D4×C83#4112yes—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—81no—
122C2×C4×C83—81no—
123C2×C4×C83C2×D411yescharacteristic
124C2×C4×C83C2×D411yescharacteristic
125C2×C4×C83C2411yescharacteristic
126C22⋊D83—24no—
127C22⋊D83—81no—
128C2×Dic83—21no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83—81no—
132C2×Dic83C2×D411yescharacteristic
133C2×Dic83C2×D411yescharacteristic
134C2×Dic83C2×D411yescharacteristic
135D332—21no—
136D332#4112yes—
137C4×D83—21no—
138C4×D83—21no—
139C4×D83—81no—
140C4×D83—81no—
141Dic166—21no—
142Dic166—21no—
143Dic166—81no—
144C8×C83—21no—
145C8×C83—21no—
146C83⋊C8—21no—
147C83⋊C8—21no—
148C22×C83—22no—
149C22×C83—41no—
150C22×C83—41no—
151C22×C83—41no—
152C22×C83—41no—
153C22×C83—41no—
154C22×C83C22×D411yescharacteristic
155C2×D83—21no—
156C2×D83—22no—
157C2×D83—21no—
158C2×D83—21no—
159C2×D83—41no—
160C2×D83—41no—
161C2×D83—84no—
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—41no—
165C4×C83—41no—
166C4×C83C2×#4111yescharacteristic
167C4×C83C2×#4111yescharacteristic
168Dic83—21no—
169Dic83—21no—
170Dic83—21no—
171Dic83—41no—
172Dic83—41no—
173Dic83—41no—
174C2×C83—42no—
175C2×C83—81no—
176C2×C83#52511yescharacteristic
177C2×C83#57611yescharacteristic
178C2×C83#57711yescharacteristic
179D83—41no—
180D83—42no—
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#442D8311yescharacteristic, complemented
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×D8C2×D8311yescharacteristic
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×Q8—831no—
212C4×D4—831no—
213C4×D4—831no—
214C4×D4—831no—
215C4×D4—1661no—
216C4×D4—1661no—
217C4×D4C2×D8311yescharacteristic
218C4×D4C2×D8311yescharacteristic, complemented
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#103—831no—
231#102—831no—
232#102—831no—
233#102—831no—
234#102—831no—
235#102C2×D8311yescharacteristic
236#102C2×D8311yescharacteristic, complemented
237C22⋊C8—831no—
238C22⋊C8—831no—
239#97C2×D8311yescharacteristic, complemented
240C4×C8—831no—
241C24—1661no—
242C2×Q8—831no—
243C2×Q8—1661no—
244C2×D4—831no—
245C2×D4—1661no—
246C2×D4—1662no—
247C2×D4—1661no—
248C2×D4—1662no—
249C2×D4C22×D8311yescharacteristic
250C2×D4C22×D8311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—831no—
254C22×C4—1661no—
255C22×C4—1661no—
256C22×C4—1661no—
257SD16—1662no—
258SD16—1662no—
259D8—22no—
260D8—1662no—
261C2×C8—831no—
262C2×C8—831no—
263C2×C8C22×D8311yescharacteristic
264C2×C8C22×D8311yescharacteristic
265C4⋊C4—831no—
266C4⋊C4—831no—
267C4⋊C4—831no—
268C4⋊C4—831no—
269C4⋊C4—1661no—
270C4⋊C4—1661no—
271C4⋊C4—1661no—
272C4⋊C4C22×D8311yescharacteristic
273C4⋊C4C22×D8311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—831no—
277C22⋊C4—831no—
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—21no—
292C23—831no—
293C23—6641no—
294C23—6641no—
295C23—1664no—
296C23—1661no—
297Q8—6641no—
298Q8—1661no—
299Q8—1661no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—832no—
304D4—6641no—
305D4—1664no—
306D4—1661no—
307D4#1305059012yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—831no—
313C2×C4—831no—
314C2×C4—831no—
315C2×C4—6641no—
316C2×C4—6641no—
317C2×C4—6641no—
318C2×C4—1661no—
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—41no—
334C22—41no—
335C22—41no—
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—3321no—
349C4—3321no—
350C4—3321no—
351C4—1661no—
352C4—1661no—
353C4—1661no—
354C4#41×D8311yescharacteristic
355C4C2×#1305059011yescharacteristic
356C2—42no—
357C2—81no—
358C2—3322no—
359C2—3321no—
360C2#1912821011yescharacteristic
361C2#1912850511yescharacteristic
362C2#1912851111yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#442×C83C2
socleC22×C83C22×D4
prime radical#19127833C2
hypercenter#442D83
hypocenterC83#3118
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #19128316C2semidirect
2. #19128173C2semidirect
3. #19128045C2semidirect
4. #19128023C2semidirect
5. #19127990C2semidirect
6. #19127979C2semidirect
7. #19127915C2semidirect
8. #19127914C2semidirect
9. #19127853C2semidirect
11. #19127803C2semidirect
12. C4×#13050578C2semidirect
13. C4×#13050575C2semidirect
14. #19127763C2semidirect
15. #442×C83C2semidirect
20. #14581791C22semidirect
22. #14581779C22semidirect
28. C4×Dic166C22semidirect
38. #14581726C22semidirect
39. #14581725C22semidirect
40. #14581723C22semidirect
41. Dic83⋊C8C22semidirect
42. Dic83⋊C8C22semidirect
43. #14581717C22semidirect
44. #14581715C22semidirect
47. #14581713C22semidirect
51. C4×C83⋊C8C22semidirect
54. C4×D4×C83C22semidirect
55. #106×C83C22semidirect
57. #102×C83C22semidirect
58. #97×C83C22semidirect
182. C83#3118semidirect
193. #442D83semidirect
218. C4×D4C2×D83semidirect
226. #106C2×D83semidirect
236. #102C2×D83semidirect
239. #97C2×D83semidirect

Maximal subgroups

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

subgroupindex
#191283162
#191281732
#191280452
#191280232
#191279902
#191279792
#191279152
#191279142
#191278532
#191278332
#191278032
C4×#130505782
C4×#130505752
#191277632
#442×C832
#311883