Finite Group Databasebeta

← #24914740

Subgroups — #24914740

Order 10624.

484 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127640C211yesmaximal, characteristic, complemented
2#19127629C211yesmaximal, characteristic, complemented
3#19127617C211yesmaximal, characteristic, complemented
4#19127617C211yesmaximal, characteristic, complemented
5#19127617C211yesmaximal, characteristic, complemented
6#19127609C211yesmaximal, characteristic
7#19127594C211yesmaximal, characteristic, complemented
8#19127592C211yesmaximal, characteristic, complemented
9#19127591C211yesmaximal, characteristic, complemented
10#19127589C211yesmaximal, characteristic, complemented
11#19127581C211yesmaximal, characteristic, complemented
12#19127578C211yesmaximal, characteristic, complemented
13#19127576C211yesmaximal, characteristic, complemented
14#19127567C211yesmaximal, characteristic, complemented
15#390×C83C211yesmaximal, characteristic, complemented
16C22×C22⋊D83C2211yescharacteristic
17C22×C22⋊D83C2211yescharacteristic
18C23×Dic83C2211yescharacteristic
19C2×C4⋊Dic83C2211yescharacteristic
20C2×C4⋊Dic83C2211yescharacteristic
21C2×C4⋊Dic83C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×C22⋊Dic83C2211yescharacteristic
24C2×C22⋊Dic83C2211yescharacteristic
25C2×C22⋊Dic83C2211yescharacteristic
26C2×C22⋊Dic83C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×(C2×D83)⋊C4C2211yescharacteristic
29C2×(C2×D83)⋊C4C2211yescharacteristic
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×C4×Dic83C2211yescharacteristic
34C83⋊#95C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C22×D4×C83C2211yescharacteristic
45C2×C4⋊C4×C83C2211yescharacteristic
46C2×C22⋊C4×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48C2×C22⋊C4×C83C2211yescharacteristic
49C2×C22⋊C4×C83C2211yescharacteristic
50C2×C42×C83C2211yescharacteristic
51C23×D83C2311yescharacteristic
52C2×C22⋊D83—22no—
53C2×C22⋊D83—41no—
54C2×C22⋊D83—41no—
55C2×C22⋊D83—41no—
56C2×C22⋊D83—41no—
57C2×C22⋊D83—41no—
58C22×Dic83—41no—
59C22×Dic83—41no—
60C22×Dic83—41no—
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C22×Dic83C2311yescharacteristic
66C22×Dic83C2311yescharacteristic
67C22×Dic83C2311yescharacteristic
68C4⋊Dic83—41no—
69C4⋊Dic83—41no—
70C4⋊Dic83—41no—
71Dic83⋊C4—41no—
72C22⋊Dic83—22no—
73C22⋊Dic83—41no—
74C22⋊Dic83—41no—
75C22⋊Dic83—41no—
76C22⋊Dic83—41no—
77(C2×D83)⋊C4—22no—
78(C2×D83)⋊C4—22no—
79(C2×D83)⋊C4—41no—
80(C2×D83)⋊C4—41no—
81(C2×D83)⋊C4—41no—
82C4×Dic83—41no—
83C24×C83C2311yescharacteristic
84C24×C83C2311yescharacteristic
85C2×D4×C83—22no—
86C2×D4×C83—22no—
87C2×D4×C83—41no—
88C22×C4×C83C2311yescharacteristic
89C22×C4×C83C2311yescharacteristic
90C22×C4×C83C2311yescharacteristic
91C22×C4×C83C2311yescharacteristic
92C22×C4×C83C2311yescharacteristic
93C4⋊C4×C83—41no—
94C22⋊C4×C83—22no—
95C22⋊C4×C83—22no—
96C22⋊C4×C83—41no—
97C22⋊C4×C83—41no—
98C42×C83—22no—
99C23×C83—21no—
100C23×C83—21no—
101C23×C83—21no—
102C23×C83—21no—
103C23×C83—21no—
104C23×C83—21no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—21no—
111C23×C83—21no—
112C23×C83#4112yes—
113C23×C83C2411yescharacteristic
114C22×D83—21no—
115C22×D83—21no—
116C22×D83—21no—
117C22×D83—21no—
118C22×D83—21no—
119C22×D83—21no—
120C22×D83—21no—
121D4×C83—44no—
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#4112yes—
136C2×C4×C83#4112yes—
137C22⋊D83—44no—
138C22⋊D83—44no—
139C2×Dic83—21no—
140C2×Dic83—21no—
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—21no—
159C2×Dic83—21no—
160C2×Dic83—44no—
161C22×C83—22no—
162C22×C83—22no—
163C22×C83—22no—
164C22×C83—41no—
165C22×C83—41no—
166C22×C83—41no—
167C22×C83—41no—
168C22×C83—41no—
169C22×C83—41no—
170C22×C83—41no—
171C22×C83—41no—
172C22×C83—41no—
173C22×C83—41no—
174C22×C83—41no—
175C22×C83C2×#4111yescharacteristic
176C22×C83C2×#4111yescharacteristic
177C22×C83C2×#4111yescharacteristic
178C22×C83H(5,𝔽2)11yescharacteristic
179C22×C83H(5,𝔽2)11yescharacteristic
180C22×C83H(5,𝔽2)11yescharacteristic
181C22×C83H(5,𝔽2)11yescharacteristic
182C2×D83—41no—
183C2×D83—41no—
184C2×D83—41no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—41no—
189C4×C83—22no—
190C4×C83—22no—
191C4×C83—41no—
192C4×C83—41no—
193C4×C83—41no—
194Dic83—41no—
195Dic83—41no—
196Dic83—41no—
197Dic83—41no—
198Dic83—41no—
199Dic83—41no—
200Dic83—41no—
201C2×C83—42no—
202C2×C83—81no—
203C2×C83#53811yescharacteristic
204C2×C83#54011yescharacteristic
205C2×C83#54011yescharacteristic
206C2×C83#55111yescharacteristic
207C2×C83#55311yescharacteristic
208C2×C83#55311yescharacteristic
209C2×C83H(3,𝔽4)11yescharacteristic
210D83—81no—
211#2753—831nomaximal, Sylow
212C83#275311yescharacteristic, complemented, Sylow
213#400—831no—
214#397—831no—
215#394—831no—
216#394—831no—
217#394—831no—
218#392—831no—
219#390D8311yescharacteristic, complemented
220#388—831no—
221#388—831no—
222#388—831no—
223#388—831no—
224#386—831no—
225#386—831no—
226#385—831no—
227#382—831no—
228C22×D4—831no—
229C22×D4—831no—
230C22×D4C2×D8311yescharacteristic
231C23×C4—831no—
232C2×C4⋊C4—831no—
233C2×C4⋊C4—831no—
234C2×C4⋊C4—831no—
235C2×C4⋊C4—831no—
236C2×C4⋊C4C2×D8311yescharacteristic
237C2×C22⋊C4—831no—
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⋊C4C2×D8311yescharacteristic
248C2×C22⋊C4C2×D8311yescharacteristic
249C2×C22⋊C4C2×D8311yescharacteristic
250C2×C22⋊C4C2×D8311yescharacteristic
251C2×C42—831no—
252C2×C42C2×D8311yescharacteristic
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#95—831no—
262#95—831no—
263C24—831no—
264C24C22×D8311yescharacteristic
265C24C22×D8311yescharacteristic
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—41no—
269C2×D4—3321no—
270C2×D4—3321no—
271C2×D4—3321no—
272C2×D4—3321no—
273C2×D4—3321no—
274C2×D4—1662no—
275C22×C4—3321no—
276C22×C4—3321no—
277C22×C4—3321no—
278C22×C4—831no—
279C22×C4—831no—
280C22×C4—831no—
281C22×C4—831no—
282C22×C4—831no—
283C22×C4—831no—
284C22×C4—831no—
285C22×C4C22×D8311yescharacteristic
286C22×C4C22×D8311yescharacteristic
287C22×C4C22×D8311yescharacteristic
288C22×C4C22×D8311yescharacteristic
289C22×C4C22×D8311yescharacteristic
290C4⋊C4—41no—
291C4⋊C4—3321no—
292C4⋊C4—3321no—
293C4⋊C4—3321no—
294C4⋊C4—3321no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—3321no—
300C22⋊C4—3321no—
301C22⋊C4—3321no—
302C22⋊C4—3321no—
303C22⋊C4—3321no—
304C22⋊C4—3321no—
305C22⋊C4—3321no—
306C22⋊C4—1662no—
307C22⋊C4—1662no—
308C22⋊C4—1662no—
309C42—22no—
310C42—3321no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—1661no—
325C23—1661no—
326C23—1661no—
327C23—1661no—
328C23—1661no—
329C23—1661no—
330C23—1661no—
331C23#1305059012yes—
332C23C23×D8311yescharacteristic
333D4—44no—
334D4—3324no—
335D4—3324no—
336C2×C4—21no—
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—3324no—
350C2×C4—1661no—
351C2×C4—1661no—
352C2×C4—1661no—
353C2×C4—1661no—
354C2×C4—1661no—
355C2×C4—1661no—
356C2×C4—1661no—
357C2×C4—1661no—
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#1305058912yes—
372C2×C4#1305058912yes—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—3321no—
388C22—3321no—
389C22—3321no—
390C22—3321no—
391C22—3321no—
392C22—3321no—
393C22—3321no—
394C22C2×#1305058911yescharacteristic
395C22C2×#1305058911yescharacteristic
396C22C2×#1305059011yescharacteristic
397C22#1458183711yescharacteristic
398C22#1458183711yescharacteristic
399C22#1458183811yescharacteristic
400C22#1458183811yescharacteristic
401C4—22no—
402C4—22no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—3321no—
407C4—3321no—
408C4—3321no—
409C4—3321no—
410C4—3321no—
411C4—3321no—
412C4—3321no—
413C2—42no—
414C2—81no—
415C2—6641no—
416C2#1912828411yescharacteristic
417C2#1912830411yescharacteristic
418C2#1912830511yescharacteristic
419C2#1912837711yescharacteristic
420C2#1912839711yescharacteristic
421C2#1912840311yescharacteristic
422C2#1912844311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#390×C83C2
prime radical#19127609C2
hypercenter#390D83
hypocenterC83#2753
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #19127640C2semidirect
2. #19127629C2semidirect
3. #19127617C2semidirect
4. #19127617C2semidirect
5. #19127617C2semidirect
7. #19127594C2semidirect
8. #19127592C2semidirect
9. #19127591C2semidirect
10. #19127589C2semidirect
11. #19127581C2semidirect
12. #19127578C2semidirect
13. #19127576C2semidirect
14. #19127567C2semidirect
15. #390×C83C2semidirect
212. C83#2753semidirect
219. #390D83semidirect

Maximal subgroups

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

subgroupindex
#191276402
#191276292
#191276172
#191276092
#191275942
#191275922
#191275912
#191275892
#191275812
#191275782
#191275762
#191275672
#390×C832
#275383