Finite Group Databasebeta

← #24914513

Subgroups — #24914513

Order 10624.

442 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127630C211yesmaximal, characteristic, complemented
2#19127627C211yesmaximal, characteristic, complemented
3#19127622C211yesmaximal, characteristic, complemented
4#19127618C211yesmaximal, characteristic
5#19127614C211yesmaximal, characteristic, complemented
6#19127614C211yesmaximal, characteristic, complemented
7#19127603C211yesmaximal, characteristic
8#19127593C211yesmaximal, characteristic, complemented
9#19127590C211yesmaximal, characteristic, complemented
10#19127587C211yesmaximal, characteristic, complemented
11#19127579C211yesmaximal, characteristic
12#19127569C211yesmaximal, characteristic, complemented
13#19127563C211yesmaximal, characteristic, complemented
14#19127558C211yesmaximal, characteristic, complemented
15#387×C83C211yesmaximal, characteristic, complemented
16C22×Dic166C2211yescharacteristic
17C22×D332C2211yescharacteristic
18C22×C4×D83C2211yescharacteristic
19C2×C4⋊Dic83C2211yescharacteristic
20C2×C4⋊Dic83C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×(C2×D83)⋊C4C2211yescharacteristic
23C2×(C2×D83)⋊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
34C83⋊#95C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C2×C4⋊C4×C83C2211yescharacteristic
45C2×C4⋊C4×C83C2211yescharacteristic
46C2×C42×C83C2211yescharacteristic
47#95×C83C2211yescharacteristic
48#95×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51C23×D83C2311yescharacteristic
52C23×D83C2311yescharacteristic
53C2×Dic166—41no—
54C2×Dic166—41no—
55C2×Dic166—41no—
56C2×D332—22no—
57C2×D332—22no—
58C2×D332—41no—
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C2×C4×D83—22no—
66C2×C4×D83—22no—
67C2×C4×D83—41no—
68C4⋊Dic83—41no—
69C4⋊Dic83—41no—
70Dic83⋊C4—41no—
71(C2×D83)⋊C4—22no—
72(C2×D83)⋊C4—22no—
73(C2×D83)⋊C4—41no—
74(C2×D83)⋊C4—41no—
75(C2×D83)⋊C4—41no—
76(C2×D83)⋊C4—41no—
77(C2×D83)⋊C4—41no—
78(C2×D83)⋊C4—41no—
79(C2×D83)⋊C4—41no—
80(C2×D83)⋊C4—41no—
81(C2×D83)⋊C4—41no—
82C4×Dic83—41no—
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C22×C4×C83C2311yescharacteristic
89C22×C4×C83C2311yescharacteristic
90C4⋊C4×C83—22no—
91C4⋊C4×C83—22no—
92C42×C83—22no—
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—21no—
106C22×D83—21no—
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#4112yes—
128C2×C4×C83#4112yes—
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—21no—
146C2×Dic83—21no—
147D332—44no—
148C4×D83—44no—
149Dic166—44no—
150C22×C83C2×#4111yescharacteristic
151C22×C83C2×#4111yescharacteristic
152C22×C83C2×#4111yescharacteristic
153C22×C83H(5,𝔽2)11yescharacteristic
154C22×C83H(5,𝔽2)11yescharacteristic
155C22×C83H(5,𝔽2)11yescharacteristic
156C22×C832−1+411yescharacteristic
157C2×D83—22no—
158C2×D83—22no—
159C2×D83—22no—
160C2×D83—41no—
161C2×D83—41no—
162C2×D83—41no—
163C2×D83—41no—
164C2×D83—41no—
165C2×D83—41no—
166C2×D83—41no—
167C2×D83—41no—
168C2×D83—41no—
169C2×D83—41no—
170C2×D83—41no—
171C4×C83—22no—
172C4×C83—22no—
173C4×C83—41no—
174C4×C83—41no—
175C4×C83—41no—
176C4×C83—41no—
177C4×C83—41no—
178Dic83—41no—
179Dic83—41no—
180Dic83—41no—
181Dic83—41no—
182Dic83—41no—
183Dic83—41no—
184C2×C83#53911yescharacteristic
185C2×C83#54211yescharacteristic
186C2×C83#54211yescharacteristic
187C2×C83#55111yescharacteristic
188C2×C83#55111yescharacteristic
189C2×C83#55511yescharacteristic
190C2×C83#56011yescharacteristic
191D83—42no—
192D83—81no—
193#2737—831nomaximal, Sylow
194C83#273711yescharacteristic, complemented, Sylow
195#397—831no—
196#397—831no—
197#395—831no—
198#394—831no—
199#393—831no—
200#393—831no—
201#390—831no—
202#388—831no—
203#388—831no—
204#387—831no—
205#387D8311yescharacteristic, complemented
206#386—831no—
207#383—831no—
208#381—831no—
209#380—831no—
210C22×Q8—831no—
211C22×D4—831no—
212C23×C4—831no—
213C2×C4⋊C4—831no—
214C2×C4⋊C4—831no—
215C2×C4⋊C4—831no—
216C2×C4⋊C4C2×D8311yescharacteristic
217C2×C4⋊C4C2×D8311yescharacteristic
218C2×C22⋊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×C22⋊C4—831no—
229C2×C42—831no—
230C2×C42C2×D8311yescharacteristic
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#95—831no—
240#95—831no—
241#95C2×D8311yescharacteristic
242#95C2×D8311yescharacteristic
243#95C2×D8311yescharacteristic
244#95C2×D8311yescharacteristic
245C24—831no—
246C24—831no—
247C2×Q8—3321no—
248C2×Q8—3321no—
249C2×Q8—3321no—
250C2×D4—3321no—
251C2×D4—1662no—
252C2×D4—1662no—
253C22×C4—3321no—
254C22×C4—831no—
255C22×C4—831no—
256C22×C4—831no—
257C22×C4—831no—
258C22×C4—831no—
259C22×C4—831no—
260C22×C4—1662no—
261C22×C4—1662no—
262C22×C4C22×D8311yescharacteristic
263C22×C4C22×D8311yescharacteristic
264C22×C4C22×D8311yescharacteristic
265C22×C4C22×D8311yescharacteristic
266C22×C4C22×D8311yescharacteristic
267C22×C4C22×D8311yescharacteristic
268C22×C4C22×D8311yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—3321no—
272C4⋊C4—3321no—
273C4⋊C4—3321no—
274C22⋊C4—3321no—
275C22⋊C4—3321no—
276C22⋊C4—3321no—
277C22⋊C4—3321no—
278C22⋊C4—3321no—
279C22⋊C4—3321no—
280C22⋊C4—3321no—
281C22⋊C4—3321no—
282C22⋊C4—3321no—
283C22⋊C4—1662no—
284C22⋊C4—1662no—
285C42—22no—
286C42—3321no—
287C23—832no—
288C23—1661no—
289C23—1661no—
290C23—1661no—
291C23—1661no—
292C23—1661no—
293C23—1661no—
294C23—1661no—
295C23—1661no—
296C23—1661no—
297C23—1661no—
298C23—1661no—
299C23—1661no—
300C23—1661no—
301C23C23×D8311yescharacteristic
302Q8—3324no—
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—3324no—
324C2×C4—1661no—
325C2×C4—1661no—
326C2×C4—1661no—
327C2×C4—1661no—
328C2×C4—1661no—
329C2×C4—1661no—
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#1305058912yes—
343C2×C4#1305059012yes—
344C22—3321no—
345C22—3321no—
346C22—3321no—
347C22—3321no—
348C22—3321no—
349C22—3321no—
350C22—3321no—
351C22—3321no—
352C22—3321no—
353C22—3321no—
354C22—3321no—
355C22—1662no—
356C22—1662no—
357C22—1662no—
358C22#41×D8311yescharacteristic
359C22C2×#1305058911yescharacteristic
360C22C2×#1305059011yescharacteristic
361C22#1458183811yescharacteristic
362C22#1458183811yescharacteristic
363C22#1458183811yescharacteristic
364C22#1458184011yescharacteristic
365C4—22no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—3321no—
373C4—3321no—
374C4—3321no—
375C4—3321no—
376C4—3321no—
377C4—3321no—
378C2—3322no—
379C2—6641no—
380C2#1912829911yescharacteristic
381C2#1912832311yescharacteristic
382C2#1912832411yescharacteristic
383C2#1912837411yescharacteristic
384C2#1912837511yescharacteristic
385C2#1912841611yescharacteristic
386C2#1912844211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#387×C83C2
prime radicalC22×D332C22
hypercenter#387D83
hypocenterC83#2737
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. #19127630C2semidirect
2. #19127627C2semidirect
3. #19127622C2semidirect
5. #19127614C2semidirect
6. #19127614C2semidirect
8. #19127593C2semidirect
9. #19127590C2semidirect
10. #19127587C2semidirect
12. #19127569C2semidirect
13. #19127563C2semidirect
14. #19127558C2semidirect
15. #387×C83C2semidirect
194. C83#2737semidirect
205. #387D83semidirect

Maximal subgroups

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

subgroupindex
#191276302
#191276272
#191276222
#191276182
#191276142
#191276032
#191275932
#191275902
#191275872
#191275792
#191275692
#191275632
#191275582
#387×C832
#273783