Finite Group Databasebeta

← #24915670

Subgroups — #24915670

Order 10624.

400 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127643C211yesmaximal, characteristic, complemented
2#19127637C211yesmaximal, characteristic, complemented
3#19127637C211yesmaximal, characteristic, complemented
4#19127635C211yesmaximal, characteristic, complemented
5#19127632C211yesmaximal, characteristic, complemented
6#19127629C211yesmaximal, characteristic, complemented
7#19127629C211yesmaximal, characteristic, complemented
8#19127624C211yesmaximal, characteristic, complemented
9#19127624C211yesmaximal, characteristic, complemented
10#19127615C211yesmaximal, characteristic
11#19127615C211yesmaximal, characteristic
12#19127596C211yesmaximal, characteristic, complemented
13#19127595C211yesmaximal, characteristic, complemented
14#19127589C211yesmaximal, characteristic, complemented
15#394×C83C211yesmaximal, characteristic
16C2×C4⋊Dic83C2211yescharacteristic
17C2×C4⋊Dic83C2211yescharacteristic
18C2×Dic83⋊C4C2211yescharacteristic
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×C22⋊Dic83C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C2×C22⋊Dic83C2211yescharacteristic
31C2×C22⋊Dic83C2211yescharacteristic
32C2×C22⋊Dic83C2211yescharacteristic
33C2×C22⋊Dic83C2211yescharacteristic
34C2×C4×Dic83C2211yescharacteristic
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
50#95×C83C2211yescharacteristic
51C22×Dic83C2311yescharacteristic
52C22×Dic83C2311yescharacteristic
53C22×Dic83C2311yescharacteristic
54C22×Dic83C2311yescharacteristic
55C22×Dic83C2311yescharacteristic
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C4⋊Dic83—41no—
60C4⋊Dic83—41no—
61Dic83⋊C4—22no—
62Dic83⋊C4—41no—
63Dic83⋊C4—41no—
64Dic83⋊C4—41no—
65Dic83⋊C4—41no—
66Dic83⋊C4—41no—
67Dic83⋊C4—41no—
68Dic83⋊C4—41no—
69C22⋊Dic83—22no—
70C22⋊Dic83—22no—
71C22⋊Dic83—41no—
72C22⋊Dic83—41no—
73C22⋊Dic83—41no—
74C22⋊Dic83—41no—
75C22⋊Dic83—41no—
76C22⋊Dic83—41no—
77C4×Dic83—41no—
78C24×C83C2311yescharacteristic
79C24×C83C2311yescharacteristic
80C2×D4×C83—41no—
81C2×D4×C83—41no—
82C2×D4×C83—41no—
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C4⋊C4×C83—41no—
89C22⋊C4×C83—41no—
90C22⋊C4×C83—41no—
91C22⋊C4×C83—41no—
92C22⋊C4×C83—41no—
93C23×C83—21no—
94C23×C83—21no—
95C23×C83—21no—
96C23×C83—21no—
97C23×C83—21no—
98C23×C83—21no—
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×C83C2411yescharacteristic
108D4×C83—44no—
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×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—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—21no—
146C2×Dic83—21no—
147C2×Dic83#4112yes—
148C22×C83—41no—
149C22×C83—41no—
150C22×C83—41no—
151C22×C83—41no—
152C22×C83—41no—
153C22×C83—41no—
154C22×C83—41no—
155C22×C83—41no—
156C22×C83—41no—
157C22×C83—41no—
158C22×C83—41no—
159C22×C83—41no—
160C22×C83—41no—
161C22×C83—41no—
162C22×C83C2×#4111yescharacteristic
163C22×C83H(5,𝔽2)11yescharacteristic
164C22×C83H(5,𝔽2)11yescharacteristic
165C22×C83H(5,𝔽2)11yescharacteristic
166C22×C83H(5,𝔽2)11yescharacteristic
167C22×C832−1+411yescharacteristic
168C22×C832−1+411yescharacteristic
169C4×C83—41no—
170C4×C83—41no—
171C4×C83—41no—
172C4×C83—41no—
173C4×C83—41no—
174Dic83—22no—
175Dic83—41no—
176Dic83—41no—
177Dic83—41no—
178Dic83—41no—
179Dic83—41no—
180Dic83—41no—
181Dic83—41no—
182C2×C83—81no—
183C2×C83—81no—
184C2×C83#53911yescharacteristic
185C2×C83#54011yescharacteristic
186C2×C83#54211yescharacteristic
187C2×C83#56011yescharacteristic
188C2×C83#56211yescharacteristic
189C2×C83#56211yescharacteristic
190C2×C83#56311yescharacteristic
191#2837—831nomaximal, Sylow
192C83#283711yescharacteristic, complemented, Sylow
193#400—831no—
194#399—831no—
195#399—831no—
196#398—831no—
197#398—831no—
198#397—831no—
199#397—831no—
200#396—831no—
201#396—831no—
202#394—831no—
203#394—831no—
204#394D8311yescharacteristic
205#389—831no—
206#388—831no—
207#388—831no—
208C22×D4C2×D8311yescharacteristic
209C2×C4⋊C4—831no—
210C2×C4⋊C4—831no—
211C2×C4⋊C4—831no—
212C2×C4⋊C4—831no—
213C2×C4⋊C4—831no—
214C2×C4⋊C4—831no—
215C2×C4⋊C4—831no—
216C2×C4⋊C4—831no—
217C2×C4⋊C4—831no—
218C2×C4⋊C4—831no—
219C2×C4⋊C4C2×D8311yescharacteristic
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⋊C4C2×D8311yescharacteristic
229C2×C22⋊C4C2×D8311yescharacteristic
230C2×C22⋊C4C2×D8311yescharacteristic
231C2×C22⋊C4C2×D8311yescharacteristic
232C2×C42—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#95—831no—
242#95C2×D8311yescharacteristic
243C24C22×D8311yescharacteristic
244C24C22×D8311yescharacteristic
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—831no—
249C22×C4—831no—
250C22×C4—831no—
251C22×C4—831no—
252C22×C4—831no—
253C22×C4—831no—
254C22×C4—831no—
255C22×C4—831no—
256C22×C4C22×D8311yescharacteristic
257C22×C4C22×D8311yescharacteristic
258C22×C4C22×D8311yescharacteristic
259C22×C4C22×D8311yescharacteristic
260C22×C4C22×D8311yescharacteristic
261C4⋊C4—41no—
262C4⋊C4—3321no—
263C4⋊C4—3321no—
264C4⋊C4—3321no—
265C4⋊C4—3321no—
266C4⋊C4—3321no—
267C4⋊C4—3321no—
268C4⋊C4—3321no—
269C4⋊C4—3321no—
270C4⋊C4—3321no—
271C4⋊C4—1662no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—3321no—
277C22⋊C4—3321no—
278C22⋊C4—3321no—
279C22⋊C4—3321no—
280C22⋊C4—3321no—
281C22⋊C4—3321no—
282C22⋊C4—1662no—
283C22⋊C4—1662no—
284C42—3321no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23C23×D8311yescharacteristic
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
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—832no—
317C2×C4—1661no—
318C2×C4—1661no—
319C2×C4—1661no—
320C2×C4—1661no—
321C2×C4—1661no—
322C2×C4—1661no—
323C2×C4—1661no—
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—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22#41×D8311yescharacteristic
355C22#1458183711yescharacteristic
356C22#1458183711yescharacteristic
357C22#1458183711yescharacteristic
358C22#1458183711yescharacteristic
359C22#1458183911yescharacteristic
360C22#1458183911yescharacteristic
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—3321no—
367C4—3321no—
368C4—3321no—
369C4—3321no—
370C4—3321no—
371C4—3321no—
372C4—3321no—
373C4—1662no—
374C2—81no—
375C2—81no—
376C2#1912829411yescharacteristic
377C2#1912830111yescharacteristic
378C2#1912831911yescharacteristic
379C2#1912844011yescharacteristic
380C2#1912844611yescharacteristic
381C2#1912844611yescharacteristic
382C2#1912845111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#394×C83C2
prime radicalC22×D4×C83C22
hypercenter#394D83
hypocenterC83#2837
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #19127643C2semidirect
2. #19127637C2semidirect
3. #19127637C2semidirect
4. #19127635C2semidirect
5. #19127632C2semidirect
6. #19127629C2semidirect
7. #19127629C2semidirect
8. #19127624C2semidirect
9. #19127624C2semidirect
12. #19127596C2semidirect
13. #19127595C2semidirect
14. #19127589C2semidirect
192. C83#2837semidirect

Maximal subgroups

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

subgroupindex
#191276432
#191276372
#191276352
#191276322
#191276292
#191276242
#191276152
#191275962
#191275952
#191275892
#394×C832
#283783