Finite Group Databasebeta

← #24920547

Subgroups — #24920547

Order 10624.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128436C211yesmaximal, characteristic, complemented
2#19128091C211yesmaximal, characteristic, complemented
3#19128088C211yesmaximal, characteristic, complemented
4#19128083C211yesmaximal, characteristic, complemented
5#19127923C211yesmaximal, characteristic, complemented
6#19127920C211yesmaximal, characteristic, complemented
7#19127916C211yesmaximal, characteristic, complemented
8#19127913C211yesmaximal, characteristic, complemented
9#19127896C211yesmaximal, characteristic, complemented
10#19127893C211yesmaximal, characteristic, complemented
11#19127832C211yesmaximal, characteristic, complemented
12#19127801C211yesmaximal, characteristic, complemented
13#19127799C211yesmaximal, characteristic, complemented
14C4×#13050575C211yesmaximal, characteristic, complemented
15#559×C83C211yesmaximal, characteristic, complemented
16C2×#13050580C2211yescharacteristic
17C2×#13050578C2211yescharacteristic
18C2×#13050578C2211yescharacteristic
19C2×#13050577C2211yescharacteristic
20C2×#13050577C2211yescharacteristic
21C2×#13050575C2211yescharacteristic
22C2×#13050575C2211yescharacteristic
23C2×#13050575C2211yescharacteristic
24C2×#13050575C2211yescharacteristic
25#14581789C2211yescharacteristic
26#14581781—21no—
27#14581780C2211yescharacteristic
28#14581780C2211yescharacteristic
29#14581777—21no—
30#14581777—21no—
31C4×Dic166C2211yescharacteristic
32C4×D332C2211yescharacteristic
33C4×D332C2211yescharacteristic
34#14581754—21no—
35#14581725C2211yescharacteristic
36C4⋊(C83⋊C8)C2211yescharacteristic
37C4⋊(C83⋊C8)C2211yescharacteristic
38C4⋊(C83⋊C8)C2211yescharacteristic
39#14581716C2211yescharacteristic
40#14581715C2211yescharacteristic
41#14581713C2211yescharacteristic
42#14581713C2211yescharacteristic
43#14581712C2211yescharacteristic
44#14581712C2211yescharacteristic
45#14581703C2211yescharacteristic
46#14581703C2211yescharacteristic
47C4×C83⋊C8C2211yescharacteristic
48#127×C83C2211yescharacteristic
49#124×C83—21no—
50#124×C83C2211yescharacteristic
51#124×C83C2211yescharacteristic
52#123×C83—21no—
53#123×C83—21no—
54C4×Q8×C83C2211yescharacteristic
55C4×Q8×C83C2211yescharacteristic
56C4×D4×C83—21no—
57C4×D4×C83C2211yescharacteristic
58C4×D4×C83C2211yescharacteristic
59C2×Dic166C2311yescharacteristic
60C2×D332—21no—
61C2×D332—21no—
62C2×D332C2311yescharacteristic
63C2×D332C2311yescharacteristic
64C2×C4×D83—21no—
65C2×C4×D83—21no—
66#13050580—41no—
67#13050578—22no—
68#13050578—41no—
69#13050577—22no—
70#13050577—41no—
71#13050575—22no—
72#13050575—41no—
73#13050575—41no—
74#13050575—41no—
75C2×C83⋊C8C2311yescharacteristic
76C2×C83⋊C8C2311yescharacteristic
77C2×C83⋊C8C2311yescharacteristic
78C2×C83⋊C8C2311yescharacteristic
79C4⋊Dic83C2311yescharacteristic
80Dic83⋊C4—21no—
81(C2×D83)⋊C4—21no—
82(C2×D83)⋊C4—21no—
83(C2×D83)⋊C4—21no—
84(C2×D83)⋊C4—21no—
85(C2×D83)⋊C4—21no—
86(C2×D83)⋊C4—21no—
87C4×Dic83—21no—
88C2×Q8×C83D411yescharacteristic
89C2×Q8×C83C2311yescharacteristic
90C2×D4×C83—21no—
91C2×D4×C83—21no—
92C2×D4×C83C2311yescharacteristic
93C2×D4×C83C2311yescharacteristic
94C22×C4×C83—21no—
95C22×C4×C83—21no—
96C4⋊C4×C83—21no—
97C4⋊C4×C83D411yescharacteristic
98C4⋊C4×C83D411yescharacteristic
99C4⋊C4×C83D411yescharacteristic
100C4⋊C4×C83C2311yescharacteristic
101C22⋊C4×C83—21no—
102C22⋊C4×C83—21no—
103C22⋊C4×C83—21no—
104C22⋊C4×C83—21no—
105C22⋊C4×C83—21no—
106C22⋊C4×C83—21no—
107C42×C83—21no—
108C42×C83C2311yescharacteristic
109C42×C83C2311yescharacteristic
110C42×C83C2311yescharacteristic
111C23×C83—21no—
112C23×C83—21no—
113C22×D83—21no—
114C22×D83—21no—
115Q8×C83—21no—
116Q8×C83—21no—
117Q8×C83—41no—
118D4×C83—21no—
119D4×C83—21no—
120D4×C83—21no—
121D4×C83—21no—
122D4×C83—42no—
123D4×C83—81no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—81no—
127C2×C4×C83—81no—
128C2×C4×C83C2×D411yescharacteristic
129C2×C4×C83C2×D411yescharacteristic
130C2×C4×C83C2×D411yescharacteristic
131C2×C4×C83C2×D411yescharacteristic
132C2×C4×C83C2×D411yescharacteristic
133C2×C4×C83C2×D411yescharacteristic
134C2×C4×C83C2411yescharacteristic
135C2×Dic83—21no—
136C2×Dic83—21no—
137D332—21no—
138D332—21no—
139D332—21no—
140D332—21no—
141D332—42no—
142D332—81no—
143C4×D83—81no—
144C4×D83—81no—
145Dic166—21no—
146Dic166—21no—
147C83⋊C8—21no—
148C83⋊C8—21no—
149C83⋊C8—21no—
150C83⋊C8#4112yes—
151C22×C83—41no—
152C22×C83—41no—
153C22×C83—41no—
154C22×C83—41no—
155C22×C83—41no—
156C22×C83—41no—
157C22×C83C22×D411yescharacteristic
158C2×D83—41no—
159C2×D83—41no—
160C2×D83—41no—
161C2×D83—41no—
162C2×D83—41no—
163C2×D83—41no—
164C4×C83—21no—
165C4×C83—21no—
166C4×C83—21no—
167C4×C83—21no—
168C4×C83—21no—
169C4×C83—21no—
170C4×C83—41no—
171C4×C83—41no—
172C4×C83C2×#4111yescharacteristic
173C4×C83H(5,𝔽2)11yescharacteristic
174Dic83—41no—
175Dic83—41no—
176C2×C83—81no—
177C2×C83—81no—
178C2×C83#55011yescharacteristic
179C2×C83#57511yescharacteristic
180C2×C83#57611yescharacteristic
181D83—81no—
182D83—81no—
183#3403—831nomaximal, Sylow
184C83#340311yescharacteristic, complemented, Sylow
185#559—831no—
186#559D8311yescharacteristic, complemented
187#496—831no—
188#496—831no—
189#495—831no—
190#464—831no—
191#464—831no—
192#463—831no—
193#463—831no—
194#459—831no—
195#459—831no—
196#446—831no—
197#440—831no—
198#440—831no—
199C4×D8—831no—
200C2×Q16—831no—
201C2×SD16—831no—
202C2×SD16—831no—
203C2×SD16—831no—
204C2×SD16—831no—
205C2×D8—831no—
206C2×D8—831no—
207C2×D8—831no—
208C2×D8—831no—
209#127—831no—
210#127C2×D8311yescharacteristic
211#124—21no—
212#124—831no—
213#124—831no—
214#124—1661no—
215#124C2×D8311yescharacteristic
216#124C2×D8311yescharacteristic
217#123—21no—
218#123—21no—
219#123—1661no—
220#123—1661no—
221C4×Q8—831no—
222C4×Q8C2×D8311yescharacteristic
223C4×Q8C2×D8311yescharacteristic
224C4×D4—21no—
225C4×D4—831no—
226C4×D4—831no—
227C4×D4—1661no—
228C4×D4C2×D8311yescharacteristic
229C4×D4C2×D8311yescharacteristic
230#107—831no—
231C4⋊C8—831no—
232C4⋊C8—831no—
233C4⋊C8—831no—
234#103—831no—
235#103—831no—
236#102—831no—
237#102—831no—
238#102—831no—
239#102—831no—
240#97—831no—
241#97—831no—
242C4×C8—831no—
243C2×Q8—831no—
244C2×Q8C22⋊D8311yescharacteristic
245C2×Q8C22×D8311yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—831no—
249C2×D4—831no—
250C2×D4—1661no—
251C2×D4—1661no—
252C2×D4C22×D8311yescharacteristic
253C2×D4C22×D8311yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—1661no—
257C22×C4—1661no—
258Q16—3321no—
259SD16—3321no—
260SD16—3321no—
261SD16—1662no—
262SD16—1662no—
263D8—3321no—
264D8—3321no—
265D8—3321no—
266D8—1662no—
267C2×C8—831no—
268C2×C8—831no—
269C2×C8—831no—
270C2×C8—831no—
271C4⋊C4—21no—
272C4⋊C4—831no—
273C4⋊C4—1661no—
274C4⋊C4C22⋊D8311yescharacteristic
275C4⋊C4C22⋊D8311yescharacteristic
276C4⋊C4C22⋊D8311yescharacteristic
277C4⋊C4C22×D8311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1661no—
285C22⋊C4—1661no—
286C22⋊C4—1661no—
287C22⋊C4—1661no—
288C22⋊C4—1661no—
289C22⋊C4—1661no—
290C42—21no—
291C42—1661no—
292C42C22×D8311yescharacteristic
293C42C22×D8311yescharacteristic
294C42C22×D8311yescharacteristic
295C23—21no—
296C23—21no—
297C23—1661no—
298C23—1661no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—1661no—
303Q8—1661no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—3322no—
311D4—6641no—
312D4—1661no—
313D4—1661no—
314D4—1661no—
315D4—1661no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—6641no—
321C2×C4—6641no—
322C2×C4—1661no—
323C2×C4—1661no—
324C2×C4C2×C22⋊D8311yescharacteristic
325C2×C4C2×C22⋊D8311yescharacteristic
326C2×C4C2×C22⋊D8311yescharacteristic
327C2×C4C2×C22⋊D8311yescharacteristic
328C2×C4C2×C22⋊D8311yescharacteristic
329C2×C4C2×C22⋊D8311yescharacteristic
330C2×C4C23×D8311yescharacteristic
331C8—832no—
332C8—1661no—
333C8—1661no—
334C8—1661no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—3321no—
342C22—3321no—
343C22—3321no—
344C22—3321no—
345C22—3321no—
346C22—3321no—
347C22C22×C22⋊D8311yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—3321no—
357C4—3321no—
358C4#41×D8311yescharacteristic
359C4#1458183811yescharacteristic
360C2—81no—
361C2—81no—
362C2—6641no—
363C2—6641no—
364C2#1912837011yescharacteristic
365C2#1912849911yescharacteristic
366C2#1912850411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#559×C83C2
socleC22×C83C22×D4
hypercenter#559D83
hypocenterC83#3403
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #19128436C2semidirect
2. #19128091C2semidirect
3. #19128088C2semidirect
4. #19128083C2semidirect
5. #19127923C2semidirect
6. #19127920C2semidirect
7. #19127916C2semidirect
8. #19127913C2semidirect
9. #19127896C2semidirect
10. #19127893C2semidirect
11. #19127832C2semidirect
12. #19127801C2semidirect
13. #19127799C2semidirect
14. C4×#13050575C2semidirect
15. #559×C83C2semidirect
184. C83#3403semidirect
186. #559D83semidirect

Maximal subgroups

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

subgroupindex
#191284362
#191280912
#191280882
#191280832
#191279232
#191279202
#191279162
#191279132
#191278962
#191278932
#191278322
#191278012
#191277992
C4×#130505752
#559×C832
#340383