Finite Group Databasebeta

← #24919628

Subgroups — #24919628

Order 10624.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic166C211yesmaximal, characteristic, complemented
2#19128071C211yesmaximal, characteristic, complemented
3#19128042C211yesmaximal, characteristic, complemented
4#19128036C211yesmaximal, characteristic, complemented
5#19128005C211yesmaximal, characteristic, complemented
6#19127945C211yesmaximal, characteristic, complemented
7#19127928C211yesmaximal, characteristic, complemented
8#19127906C211yesmaximal, characteristic, complemented
9#19127839C211yesmaximal, characteristic, complemented
10#19127839C211yesmaximal, characteristic, complemented
11#19127801C211yesmaximal, characteristic, complemented
12#19127773C211yesmaximal, characteristic, complemented
13#19127709C211yesmaximal, characteristic, complemented
14C2×#14581715C211yesmaximal, characteristic, complemented
15#553×C83C211yesmaximal, characteristic
16C22×Dic166C2211yescharacteristic
17C22×Dic166C2211yescharacteristic
18C2×#13050578C2211yescharacteristic
19C2×#13050578C2211yescharacteristic
20C2×#13050578C2211yescharacteristic
21C2×#13050574C2211yescharacteristic
22C22×C83⋊C8C2211yescharacteristic
23#14581792C2211yescharacteristic
24#14581791—21no—
25#14581771C2211yescharacteristic
26#14581771C2211yescharacteristic
27#14581769—21no—
28#14581769—21no—
29C4×Dic166C2211yescharacteristic
30D4×Dic83—21no—
31#14581725C2211yescharacteristic
32#14581725C2211yescharacteristic
33#14581723C2211yescharacteristic
34C4⋊(C83⋊C8)C2211yescharacteristic
35#14581715C2211yescharacteristic
36#14581715C2211yescharacteristic
37#14581715C2211yescharacteristic
38#14581715C2211yescharacteristic
39#14581715C2211yescharacteristic
40#14581715C2211yescharacteristic
41#14581715C2211yescharacteristic
42#14581715C2211yescharacteristic
43#14581715C2211yescharacteristic
44#14581713C2211yescharacteristic
45C22⋊(C83⋊C8)C2211yescharacteristic
46C22⋊(C83⋊C8)C2211yescharacteristic
47#14581703C2211yescharacteristic
48#126×C83—21no—
49#125×C83C2211yescharacteristic
50#123×C83—21no—
51#121×C83—21no—
52#121×C83C2211yescharacteristic
53#121×C83C2211yescharacteristic
54C4×D4×C83—21no—
55C4×D4×C83C2211yescharacteristic
56C4×D4×C83C2211yescharacteristic
57#117×C83C2211yescharacteristic
58C2×C4⋊C4×C83C2211yescharacteristic
59C2×Dic166—22no—
60C2×Dic166—22no—
61C2×Dic166—21no—
62C2×Dic166—21no—
63C2×Dic166—41no—
64C2×Dic166—41no—
65C2×Dic166C2311yescharacteristic
66C2×Dic166C2311yescharacteristic
67C2×Dic166C2311yescharacteristic
68C22×Dic83—21no—
69C22×Dic83—21no—
70#13050578—22no—
71#13050578—41no—
72#13050578—41no—
73#13050574—41no—
74C2×C83⋊C8—41no—
75C2×C83⋊C8C2311yescharacteristic
76C2×C83⋊C8C2311yescharacteristic
77C2×C83⋊C8C2311yescharacteristic
78C2×C83⋊C8C2311yescharacteristic
79C4⋊Dic83—21no—
80C4⋊Dic83—21no—
81C4⋊Dic83C2311yescharacteristic
82Dic83⋊C4—21no—
83Dic83⋊C4—21no—
84Dic83⋊C4—21no—
85C22⋊Dic83—21no—
86C22⋊Dic83—21no—
87C4×Dic83—21no—
88C2×D4×C83—21no—
89C2×D4×C83—21no—
90C2×D4×C83D411yescharacteristic
91C2×D4×C83C2311yescharacteristic
92C22×C4×C83—21no—
93C22×C4×C83—21no—
94C22×C4×C83C2311yescharacteristic
95C22×C4×C83C2311yescharacteristic
96C4⋊C4×C83—21no—
97C4⋊C4×C83—21no—
98C4⋊C4×C83—21no—
99C4⋊C4×C83D411yescharacteristic
100C4⋊C4×C83C2311yescharacteristic
101C4⋊C4×C83C2311yescharacteristic
102C4⋊C4×C83C2311yescharacteristic
103C22⋊C4×C83—21no—
104C22⋊C4×C83—21no—
105C22⋊C4×C83—21no—
106C22⋊C4×C83—21no—
107C22⋊C4×C83D411yescharacteristic
108C22⋊C4×C83D411yescharacteristic
109C42×C83—21no—
110C42×C83C2311yescharacteristic
111C23×C83—21no—
112C23×C83C2×D411yescharacteristic
113C23×C83C2×D411yescharacteristic
114D4×C83—22no—
115D4×C83—21no—
116D4×C83—21no—
117D4×C83—42no—
118D4×C83—81no—
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—81no—
127C2×C4×C83—81no—
128C2×C4×C83C2×D411yescharacteristic
129C2×C4×C83C2×D411yescharacteristic
130C2×C4×C83C2×D411yescharacteristic
131C2×C4×C83C2×D411yescharacteristic
132C2×C4×C83C2411yescharacteristic
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136C2×Dic83—21no—
137C2×Dic83—42no—
138C2×Dic83—42no—
139Dic166—21no—
140Dic166—21no—
141Dic166—21no—
142Dic166—21no—
143Dic166—21no—
144Dic166—42no—
145Dic166—42no—
146Dic166#4112yes—
147C83⋊C8—21no—
148C83⋊C8—21no—
149C83⋊C8—21no—
150C83⋊C8—21no—
151C22×C83—21no—
152C22×C83—21no—
153C22×C83—21no—
154C22×C83—21no—
155C22×C83—21no—
156C22×C83—41no—
157C22×C83—41no—
158C22×C83—41no—
159C22×C83#13712yes—
160C22×C83C22×D411yescharacteristic
161C4×C83—21no—
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—21no—
165C4×C83—41no—
166C4×C83—41no—
167C4×C83—41no—
168C4×C83C2×#4111yescharacteristic
169C4×C83H(5,𝔽2)11yescharacteristic
170Dic83—22no—
171Dic83—41no—
172Dic83—41no—
173Dic83—41no—
174C2×C83—22no—
175C2×C83—41no—
176C2×C83—81no—
177C2×C83#54611yescharacteristic
178C2×C83C2×#13711yescharacteristic
179C2×C83#57711yescharacteristic
180#3320—831nomaximal, Sylow
181C83#332011yescharacteristic, complemented, Sylow
182#553D8311yescharacteristic
183D4×Q8—831no—
184#491—831no—
185#485—831no—
186#484—831no—
187#479—831no—
188#468—831no—
189#465—831no—
190#461—831no—
191#448—831no—
192#448—831no—
193#440—831no—
194#435—831no—
195#419—831no—
196C2×#103—831no—
197C22×Q8—831no—
198C22×Q8—831no—
199C2×SD16—831no—
200C2×SD16—831no—
201C2×SD16—831no—
202C2×M16—831no—
203C22×C8—831no—
204C4⋊Q8—831no—
205C4⋊Q8—1661no—
206#126—21no—
207#125C2×D8311yescharacteristic
208#123—21no—
209C22⋊Q8—831no—
210C22⋊Q8—831no—
211C22⋊Q8—1661no—
212C22⋊Q8—1661no—
213#121—21no—
214#121C2×D8311yescharacteristic
215#121C2×D8311yescharacteristic
216C4×Q8—831no—
217C4×D4—21no—
218C4×D4—1661no—
219C4×D4C2×D8311yescharacteristic
220C4×D4C2×D8311yescharacteristic
221#117C2×D8311yescharacteristic
222C2×C4⋊C4C2×D8311yescharacteristic
223#107—831no—
224#107—831no—
225#106—831no—
226C4⋊C8—831no—
227#103—831no—
228#103—831no—
229#103—831no—
230#103—831no—
231#103—831no—
232#103—831no—
233#103—831no—
234#103—831no—
235#103—831no—
236#102—831no—
237C22⋊C8—831no—
238C22⋊C8—831no—
239#97—831no—
240C2×Q8—3321no—
241C2×Q8—3321no—
242C2×Q8—831no—
243C2×Q8—831no—
244C2×Q8—831no—
245C2×Q8—1662no—
246C2×Q8—1662no—
247C2×Q8—1661no—
248C2×Q8—1661no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D8311yescharacteristic
252C2×D4C22×D8311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1661no—
256C22×C4—1661no—
257C22×C4C22×D8311yescharacteristic
258C22×C4C22×D8311yescharacteristic
259SD16—3321no—
260SD16—3321no—
261SD16—1662no—
262M16—3321no—
263C2×C8—3321no—
264C2×C8—831no—
265C2×C8—831no—
266C2×C8—831no—
267C2×C8—831no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—831no—
272C4⋊C4—1661no—
273C4⋊C4—1661no—
274C4⋊C4—1661no—
275C4⋊C4—1661no—
276C4⋊C4—1661no—
277C4⋊C4C22⋊D8311yescharacteristic
278C4⋊C4C22×D8311yescharacteristic
279C4⋊C4C22×D8311yescharacteristic
280C4⋊C4C22×D8311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1661no—
286C22⋊C4—1661no—
287C22⋊C4C22⋊D8311yescharacteristic
288C22⋊C4C22⋊D8311yescharacteristic
289C42—21no—
290C42—1661no—
291C42C22×D8311yescharacteristic
292C23—21no—
293C23C2×C22⋊D8311yescharacteristic
294C23C2×C22⋊D8311yescharacteristic
295Q8—3322no—
296Q8—3322no—
297Q8—832no—
298Q8—1661no—
299Q8—1661no—
300Q8—1661no—
301Q8—1661no—
302Q8—1661no—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—3322no—
318C2×C4—3322no—
319C2×C4—1661no—
320C2×C4—1661no—
321C2×C4—1661no—
322C2×C4—1661no—
323C2×C4C2×C22⋊D8311yescharacteristic
324C2×C4C2×C22⋊D8311yescharacteristic
325C2×C4C2×C22⋊D8311yescharacteristic
326C2×C4C2×C22⋊D8311yescharacteristic
327C2×C4C23×D8311yescharacteristic
328C8—1661no—
329C8—1661no—
330C8—1661no—
331C8—1661no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1458182212yes—
341C22C22×C22⋊D8311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3321no—
350C4—3321no—
351C4—3321no—
352C4—1662no—
353C4#41×D8311yescharacteristic
354C4#1458183811yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1912833911yescharacteristic
359C2C2×#1458182211yescharacteristic
360C2#1912851211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting, prime radical#553×C83C2
socleC22×C83C22×D4
hypercenter#553D83
hypocenterC83#3320
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×Dic166C2semidirect
2. #19128071C2semidirect
3. #19128042C2semidirect
4. #19128036C2semidirect
5. #19128005C2semidirect
6. #19127945C2semidirect
7. #19127928C2semidirect
8. #19127906C2semidirect
9. #19127839C2semidirect
10. #19127839C2semidirect
11. #19127801C2semidirect
12. #19127773C2semidirect
13. #19127709C2semidirect
14. C2×#14581715C2semidirect
181. C83#3320semidirect

Maximal subgroups

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

subgroupindex
D4×Dic1662
#191280712
#191280422
#191280362
#191280052
#191279452
#191279282
#191279062
#191278392
#191278012
#191277732
#191277092
C2×#145817152
#553×C832
#332083