Finite Group Databasebeta

← #24914685

Subgroups — #24914685

Order 10624.

498 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127641C211yesmaximal, characteristic, complemented
2#19127629C211yesmaximal, characteristic, complemented
3#19127623C211yesmaximal, characteristic, complemented
4#19127617C211yesmaximal, characteristic, complemented
5#19127610C211yesmaximal, characteristic
6#19127601C211yesmaximal, characteristic, complemented
7#19127590C211yesmaximal, characteristic, complemented
8#19127579C211yesmaximal, characteristic, complemented
9#19127579C211yesmaximal, characteristic, complemented
10#19127577C211yesmaximal, characteristic, complemented
11#19127577C211yesmaximal, characteristic, complemented
12#19127572C211yesmaximal, characteristic, complemented
13#19127568C211yesmaximal, characteristic, complemented
14#19127563C211yesmaximal, characteristic, complemented
15#397×C83C211yesmaximal, characteristic, complemented
16C22×D332C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C22×C22⋊D83C2211yescharacteristic
19C22×C4×D83C2211yescharacteristic
20C22×C4×D83C2211yescharacteristic
21C2×C4⋊Dic83C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×C22⋊Dic83C2211yescharacteristic
25C2×C22⋊Dic83C2211yescharacteristic
26C2×(C2×D83)⋊C4C2211yescharacteristic
27C2×(C2×D83)⋊C4C2211yescharacteristic
28C2×(C2×D83)⋊C4C2211yescharacteristic
29C2×(C2×D83)⋊C4C2211yescharacteristic
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×C4×Dic83C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C2×C4⋊C4×C83C2211yescharacteristic
45C2×C22⋊C4×C83C2211yescharacteristic
46C2×C22⋊C4×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48#95×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51C23×D83C2311yescharacteristic
52C23×D83C2311yescharacteristic
53C2×D332—22no—
54C2×D332—22no—
55C2×D332—41no—
56C2×C22⋊D83—22no—
57C2×C22⋊D83—22no—
58C2×C22⋊D83—22no—
59C2×C22⋊D83—41no—
60C2×C22⋊D83—41no—
61C2×C22⋊D83—41no—
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C22×Dic83C2311yescharacteristic
68C2×C4×D83—22no—
69C2×C4×D83—41no—
70C2×C4×D83—41no—
71C2×C4×D83—41no—
72C2×C4×D83—41no—
73C2×C4×D83—41no—
74C4⋊Dic83—41no—
75Dic83⋊C4—41no—
76Dic83⋊C4—41no—
77C22⋊Dic83—41no—
78C22⋊Dic83—41no—
79(C2×D83)⋊C4—22no—
80(C2×D83)⋊C4—22no—
81(C2×D83)⋊C4—41no—
82(C2×D83)⋊C4—41no—
83(C2×D83)⋊C4—41no—
84(C2×D83)⋊C4—41no—
85(C2×D83)⋊C4—41no—
86(C2×D83)⋊C4—41no—
87C4×Dic83—22no—
88C24×C83C2311yescharacteristic
89C22×C4×C83C2311yescharacteristic
90C22×C4×C83C2311yescharacteristic
91C22×C4×C83C2311yescharacteristic
92C22×C4×C83C2311yescharacteristic
93C22×C4×C83C2311yescharacteristic
94C22×C4×C83C2311yescharacteristic
95C4⋊C4×C83—41no—
96C22⋊C4×C83—41no—
97C22⋊C4×C83—41no—
98C22⋊C4×C83—41no—
99C23×C83—21no—
100C23×C83—21no—
101C23×C83—21no—
102C23×C83—21no—
103C23×C83—21no—
104C23×C83—21no—
105C23×C83—21no—
106C23×C83C2411yescharacteristic
107C22×D83—21no—
108C22×D83—21no—
109C22×D83—21no—
110C22×D83—21no—
111C22×D83—21no—
112C22×D83—21no—
113C22×D83—21no—
114C22×D83—21no—
115C22×D83—21no—
116C22×D83—21no—
117C22×D83—21no—
118C22×D83—21no—
119C22×D83#4112yes—
120C22×D83#4112yes—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—21no—
139C22⋊D83—44no—
140C22⋊D83—44no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83—21no—
144C2×Dic83—21no—
145C2×Dic83—21no—
146C2×Dic83—21no—
147C2×Dic83—21no—
148C2×Dic83—21no—
149C2×Dic83—21no—
150C2×Dic83—21no—
151C2×Dic83—21no—
152C2×Dic83—21no—
153C2×Dic83—21no—
154C2×Dic83—21no—
155C2×Dic83—21no—
156C2×Dic83—21no—
157C2×Dic83—21no—
158C2×Dic83#4112yes—
159D332—44no—
160C4×D83—44no—
161C4×D83—44no—
162C22×C83—41no—
163C22×C83—41no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—41no—
167C22×C83—41no—
168C22×C83—41no—
169C22×C83C2×#4111yescharacteristic
170C22×C83C2×#4111yescharacteristic
171C22×C83C2×#4111yescharacteristic
172C22×C83H(5,𝔽2)11yescharacteristic
173C22×C83H(5,𝔽2)11yescharacteristic
174C22×C83H(5,𝔽2)11yescharacteristic
175C22×C83H(5,𝔽2)11yescharacteristic
176C2×D83—22no—
177C2×D83—22no—
178C2×D83—22no—
179C2×D83—22no—
180C2×D83—22no—
181C2×D83—22no—
182C2×D83—41no—
183C2×D83—41no—
184C2×D83—41no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—41no—
189C2×D83—41no—
190C4×C83—41no—
191C4×C83—41no—
192C4×C83—41no—
193C4×C83—41no—
194C4×C83—41no—
195C4×C83—41no—
196Dic83—22no—
197Dic83—41no—
198Dic83—41no—
199Dic83—41no—
200Dic83—41no—
201Dic83—41no—
202C2×C83—81no—
203C2×C83#53811yescharacteristic
204C2×C83#53811yescharacteristic
205C2×C83#54011yescharacteristic
206C2×C83#55111yescharacteristic
207C2×C83#55111yescharacteristic
208C2×C83#55311yescharacteristic
209C2×C83#56011yescharacteristic
210D83—42no—
211D83—42no—
212#2749—831nomaximal, Sylow
213C83#274911yescharacteristic, complemented, Sylow
214#400—831no—
215#397—831no—
216#397D8311yescharacteristic, complemented
217#396—831no—
218#394—831no—
219#392—831no—
220#390—831no—
221#388—831no—
222#386—831no—
223#386—831no—
224#386—831no—
225#386—831no—
226#385—831no—
227#383—831no—
228#381—831no—
229C22×D4—831no—
230C22×D4—831no—
231C22×D4—831no—
232C23×C4—831no—
233C23×C4—831no—
234C2×C4⋊C4—831no—
235C2×C4⋊C4—831no—
236C2×C4⋊C4—831no—
237C2×C4⋊C4C2×D8311yescharacteristic
238C2×C22⋊C4—831no—
239C2×C22⋊C4—831no—
240C2×C22⋊C4—831no—
241C2×C22⋊C4—831no—
242C2×C22⋊C4—831no—
243C2×C22⋊C4—831no—
244C2×C22⋊C4—831no—
245C2×C22⋊C4—831no—
246C2×C22⋊C4—831no—
247C2×C22⋊C4—831no—
248C2×C22⋊C4C2×D8311yescharacteristic
249C2×C22⋊C4C2×D8311yescharacteristic
250C2×C22⋊C4C2×D8311yescharacteristic
251C2×C42—831no—
252#95—831no—
253#95—831no—
254#95—831no—
255#95—831no—
256#95—831no—
257#95—831no—
258#95—831no—
259#95—831no—
260#95—831no—
261#95C2×D8311yescharacteristic
262#95C2×D8311yescharacteristic
263#95C2×D8311yescharacteristic
264C24—831no—
265C24—831no—
266C24C22×D8311yescharacteristic
267C2×D4—3321no—
268C2×D4—3321no—
269C2×D4—3321no—
270C2×D4—3321no—
271C2×D4—1662no—
272C2×D4—1662no—
273C2×D4—1662no—
274C2×D4—1662no—
275C2×D4—1662no—
276C22×C4—3321no—
277C22×C4—3321no—
278C22×C4—3321no—
279C22×C4—3321no—
280C22×C4—3321no—
281C22×C4—831no—
282C22×C4—831no—
283C22×C4—831no—
284C22×C4—831no—
285C22×C4—831no—
286C22×C4—831no—
287C22×C4—1662no—
288C22×C4C22×D8311yescharacteristic
289C22×C4C22×D8311yescharacteristic
290C22×C4C22×D8311yescharacteristic
291C22×C4C22×D8311yescharacteristic
292C22×C4C22×D8311yescharacteristic
293C22×C4C22×D8311yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—3321no—
296C4⋊C4—3321no—
297C4⋊C4—3321no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—3321no—
302C22⋊C4—3321no—
303C22⋊C4—3321no—
304C22⋊C4—3321no—
305C22⋊C4—3321no—
306C22⋊C4—3321no—
307C22⋊C4—3321no—
308C22⋊C4—3321no—
309C22⋊C4—1662no—
310C22⋊C4—1662no—
311C42—1662no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—832no—
320C23—832no—
321C23—1661no—
322C23—1661no—
323C23—1661no—
324C23—1661no—
325C23—1661no—
326C23—1661no—
327C23—1661no—
328C23—1661no—
329C23—1661no—
330C23—1661no—
331C23—1661no—
332C23—1661no—
333C23C23×D8311yescharacteristic
334D4—3324no—
335D4—3324no—
336D4—3324no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—3324no—
356C2×C4—3324no—
357C2×C4—832no—
358C2×C4—1661no—
359C2×C4—1661no—
360C2×C4—1661no—
361C2×C4—1661no—
362C2×C4—1661no—
363C2×C4—1661no—
364C2×C4—1661no—
365C2×C4—1661no—
366C2×C4—1661no—
367C2×C4—1661no—
368C2×C4—1661no—
369C2×C4—1661no—
370C2×C4—1661no—
371C2×C4—1661no—
372C2×C4—1661no—
373C2×C4—1661no—
374C2×C4—1661no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—3321no—
383C22—3321no—
384C22—3321no—
385C22—3321no—
386C22—3321no—
387C22—3321no—
388C22—3321no—
389C22—3321no—
390C22—1662no—
391C22—1662no—
392C22—1662no—
393C22—1662no—
394C22—1662no—
395C22—1662no—
396C22#41×D8311yescharacteristic
397C22#41×D8311yescharacteristic
398C22#41×D8311yescharacteristic
399C22#1458183711yescharacteristic
400C22#1458183711yescharacteristic
401C22#1458183811yescharacteristic
402C22#1458183811yescharacteristic
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—3321no—
410C4—3321no—
411C4—3321no—
412C4—3321no—
413C4—3321no—
414C4—1662no—
415C2—81no—
416C2—3322no—
417C2—3322no—
418C2#1912828711yescharacteristic
419C2#1912829011yescharacteristic
420C2#1912830311yescharacteristic
421C2#1912837611yescharacteristic
422C2#1912838111yescharacteristic
423C2#1912839611yescharacteristic
424C2#1912843911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#397×C83C2
prime radical#19127610C2
hypercenter#397D83
hypocenterC83#2749
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #19127641C2semidirect
2. #19127629C2semidirect
3. #19127623C2semidirect
4. #19127617C2semidirect
6. #19127601C2semidirect
7. #19127590C2semidirect
8. #19127579C2semidirect
9. #19127579C2semidirect
10. #19127577C2semidirect
11. #19127577C2semidirect
12. #19127572C2semidirect
13. #19127568C2semidirect
14. #19127563C2semidirect
15. #397×C83C2semidirect
213. C83#2749semidirect
216. #397D83semidirect

Maximal subgroups

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

subgroupindex
#191276412
#191276292
#191276232
#191276172
#191276102
#191276012
#191275902
#191275792
#191275772
#191275722
#191275682
#191275632
#397×C832
#274983