Finite Group Databasebeta

← #24912018

Subgroups — #24912018

Order 10624.

482 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127641C211yesmaximal, characteristic, complemented
2#19127630C211yesmaximal, characteristic, complemented
3#19127630C211yesmaximal, characteristic, complemented
4#19127593C211yesmaximal, characteristic, complemented
5#19127590C211yesmaximal, characteristic, complemented
6#19127583C211yesmaximal, characteristic, complemented
7#19127579C211yesmaximal, characteristic
8#19127579C211yesmaximal, characteristic
9#19127579C211yesmaximal, characteristic
10#19127575C211yesmaximal, characteristic, complemented
11#19127568C211yesmaximal, characteristic, complemented
12#19127560C211yesmaximal, characteristic, complemented
13#19127548C211yesmaximal, characteristic, complemented
14#95×D83C211yesmaximal, characteristic, complemented
15#401×C83C211yesmaximal, characteristic, complemented
16C22×D332C2211yescharacteristic
17C22×C4×D83C2211yescharacteristic
18C22×C4×D83C2211yescharacteristic
19C22×C4×D83C2211yescharacteristic
20C2×C4⋊Dic83C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×(C2×D83)⋊C4C2211yescharacteristic
25C2×(C2×D83)⋊C4C2211yescharacteristic
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×C4×Dic83C2211yescharacteristic
34C2×C4×Dic83C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44#95×C83C2211yescharacteristic
45#95×C83C2211yescharacteristic
46#95×C83C2211yescharacteristic
47#95×C83C2211yescharacteristic
48#95×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51C23×D83C2311yescharacteristic
52C23×D83C2311yescharacteristic
53C2×D332—22no—
54C2×D332—22no—
55C2×D332—22no—
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C2×C4×D83—22no—
63C2×C4×D83—22no—
64C2×C4×D83—22no—
65C2×C4×D83—22no—
66C2×C4×D83—22no—
67C2×C4×D83—41no—
68C2×C4×D83—41no—
69C2×C4×D83—41no—
70C2×C4×D83—41no—
71C4⋊Dic83—41no—
72Dic83⋊C4—22no—
73Dic83⋊C4—41no—
74Dic83⋊C4—41no—
75(C2×D83)⋊C4—22no—
76(C2×D83)⋊C4—22no—
77(C2×D83)⋊C4—22no—
78(C2×D83)⋊C4—22no—
79(C2×D83)⋊C4—22no—
80(C2×D83)⋊C4—41no—
81(C2×D83)⋊C4—41no—
82(C2×D83)⋊C4—41no—
83(C2×D83)⋊C4—41no—
84C4×Dic83—22no—
85C4×Dic83—41no—
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C22×C4×C83C2311yescharacteristic
89C22×C4×C83C2311yescharacteristic
90C22×C4×C83C2311yescharacteristic
91C22×C4×C83C2311yescharacteristic
92C22×C4×C83C2311yescharacteristic
93C23×C83C2411yescharacteristic
94C22×D83—21no—
95C22×D83—21no—
96C22×D83—21no—
97C22×D83—21no—
98C22×D83—21no—
99C22×D83—21no—
100C22×D83—21no—
101C22×D83—21no—
102C22×D83—21no—
103C22×D83—21no—
104C22×D83—21no—
105C22×D83#4112yes—
106C22×D83#4112yes—
107C22×D83#4112yes—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
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×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83—21no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—21no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83—21no—
144C2×Dic83—21no—
145C2×Dic83#4112yes—
146C2×Dic83#4112yes—
147D332—44no—
148C4×D83—44no—
149C4×D83—44no—
150C4×D83—44no—
151C22×C83C2×#4111yescharacteristic
152C22×C83C2×#4111yescharacteristic
153C22×C83C2×#4111yescharacteristic
154C22×C83C2×#4111yescharacteristic
155C22×C83C2×#4111yescharacteristic
156C22×C83H(5,𝔽2)11yescharacteristic
157C22×C83H(5,𝔽2)11yescharacteristic
158C2×D83—22no—
159C2×D83—22no—
160C2×D83—22no—
161C2×D83—22no—
162C2×D83—22no—
163C2×D83—22no—
164C2×D83—41no—
165C2×D83—41no—
166C2×D83—41no—
167C2×D83—41no—
168C2×D83—41no—
169C2×D83—41no—
170C2×D83—41no—
171C2×D83#12614yes—
172C4×C83—41no—
173C4×C83—41no—
174C4×C83—41no—
175C4×C83—41no—
176C4×C83—41no—
177C4×C83—41no—
178C4×C83—41no—
179Dic83—22no—
180Dic83—22no—
181Dic83—41no—
182Dic83—41no—
183Dic83—41no—
184Dic83—41no—
185C2×C83C2×#12611yescharacteristic
186C2×C83#52911yescharacteristic
187C2×C83#53811yescharacteristic
188C2×C83#55111yescharacteristic
189C2×C83#55111yescharacteristic
190C2×C83#55311yescharacteristic
191C2×C83#55311yescharacteristic
192D83—24no—
193D83—81no—
194#2510—831nomaximal, Sylow
195C83#251011yescharacteristic, complemented, Sylow
196#401D8311yescharacteristic, complemented
197#400—831no—
198#397—831no—
199#397—831no—
200#388—831no—
201#388—831no—
202#387—831no—
203#386—831no—
204#386—831no—
205#386—831no—
206#385—831no—
207#383—831no—
208#380—831no—
209C4×C22⋊C4—831no—
210C2×#95—831no—
211C22×D4—831no—
212C23×C4—831no—
213C23×C4—831no—
214C23×C4—831no—
215C2×C4⋊C4—831no—
216C2×C4⋊C4—831no—
217C2×C4⋊C4—831no—
218C2×C4⋊C4—831no—
219C2×C22⋊C4—831no—
220C2×C22⋊C4—831no—
221C2×C22⋊C4—831no—
222C2×C22⋊C4—831no—
223C2×C22⋊C4—831no—
224C2×C22⋊C4—831no—
225C2×C22⋊C4—831no—
226C2×C22⋊C4—831no—
227C2×C22⋊C4—831no—
228C2×C42—831no—
229C2×C42—831no—
230#95—831no—
231#95—831no—
232#95—831no—
233#95—831no—
234#95—831no—
235#95—831no—
236#95—831no—
237#95—831no—
238#95—831no—
239#95C2×D8311yescharacteristic
240#95C2×D8311yescharacteristic
241#95C2×D8311yescharacteristic
242#95C2×D8311yescharacteristic
243#95C2×D8311yescharacteristic
244#95C2×D8311yescharacteristic
245#95C2×D8311yescharacteristic
246C24—831no—
247C24—831no—
248C2×D4—1662no—
249C2×D4—1662no—
250C2×D4—1662no—
251C22×C4—3321no—
252C22×C4—3321no—
253C22×C4—3321no—
254C22×C4—3321no—
255C22×C4—831no—
256C22×C4—831no—
257C22×C4—831no—
258C22×C4—831no—
259C22×C4—831no—
260C22×C4—831no—
261C22×C4—1662no—
262C22×C4—1662no—
263C22×C4—1662no—
264C22×C4—1662no—
265C22×C4—1662no—
266C22×C4C22×D8311yescharacteristic
267C22×C4C22×D8311yescharacteristic
268C22×C4C22×D8311yescharacteristic
269C22×C4C22×D8311yescharacteristic
270C22×C4C22×D8311yescharacteristic
271C22×C4C22×D8311yescharacteristic
272C22×C4C22×D8311yescharacteristic
273C4⋊C4—3321no—
274C4⋊C4—3321no—
275C4⋊C4—3321no—
276C4⋊C4—1662no—
277C22⋊C4—3321no—
278C22⋊C4—3321no—
279C22⋊C4—3321no—
280C22⋊C4—3321no—
281C22⋊C4—1662no—
282C22⋊C4—1662no—
283C22⋊C4—1662no—
284C22⋊C4—1662no—
285C22⋊C4—1662no—
286C42—3321no—
287C42—1662no—
288C23—832no—
289C23—832no—
290C23—832no—
291C23—1661no—
292C23—1661no—
293C23—1661no—
294C23—1661no—
295C23—1661no—
296C23—1661no—
297C23—1661no—
298C23—1661no—
299C23—1661no—
300C23—1661no—
301C23—1661no—
302C23C23×D8311yescharacteristic
303D4—3324no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—3324no—
326C2×C4—3324no—
327C2×C4—3324no—
328C2×C4—832no—
329C2×C4—832no—
330C2×C4—1661no—
331C2×C4—1661no—
332C2×C4—1661no—
333C2×C4—1661no—
334C2×C4—1661no—
335C2×C4—1661no—
336C2×C4—1661no—
337C2×C4—1661no—
338C2×C4—1661no—
339C2×C4—1661no—
340C2×C4—1661no—
341C2×C4—1661no—
342C2×C4—1661no—
343C2×C4—1661no—
344C2×C4—1661no—
345C2×C4—1661no—
346C22—3321no—
347C22—3321no—
348C22—3321no—
349C22—3321no—
350C22—3321no—
351C22—3321no—
352C22—3321no—
353C22—834no—
354C22—1662no—
355C22—1662no—
356C22—1662no—
357C22—1662no—
358C22—1662no—
359C22—1662no—
360C22#41×D8311yescharacteristic
361C22#41×D8311yescharacteristic
362C22#41×D8311yescharacteristic
363C22#41×D8311yescharacteristic
364C22#41×D8311yescharacteristic
365C22#1458183811yescharacteristic
366C22#1458183811yescharacteristic
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—3321no—
375C4—3321no—
376C4—3321no—
377C4—3321no—
378C4—1662no—
379C4—1662no—
380C2—6641no—
381C2—1664no—
382C2#126×D8311yescharacteristic
383C2#1912823411yescharacteristic
384C2#1912829011yescharacteristic
385C2#1912837611yescharacteristic
386C2#1912837611yescharacteristic
387C2#1912840211yescharacteristic
388C2#1912840211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#401×C83C2
prime radicalC22×D332C22
hypercenter#401D83
hypocenterC83#2510
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #401

Complements

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

NH ≅ G/Ntype
1. #19127641C2semidirect
2. #19127630C2semidirect
3. #19127630C2semidirect
4. #19127593C2semidirect
5. #19127590C2semidirect
6. #19127583C2semidirect
10. #19127575C2semidirect
11. #19127568C2semidirect
12. #19127560C2semidirect
13. #19127548C2semidirect
14. #95×D83C2semidirect
15. #401×C83C2semidirect
195. C83#2510semidirect
196. #401D83semidirect

Maximal subgroups

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

subgroupindex
#191276412
#191276302
#191275932
#191275902
#191275832
#191275792
#191275752
#191275682
#191275602
#191275482
#95×D832
#401×C832
#251083