Finite Group Databasebeta

← #24919897

Subgroups — #24919897

Order 10624.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128391C211yesmaximal, characteristic, complemented
2#19128107C211yesmaximal, characteristic, complemented
3#19128036C211yesmaximal, characteristic, complemented
4#19128031C211yesmaximal, characteristic, complemented
5#19128022C211yesmaximal, characteristic, complemented
6#19128012C211yesmaximal, characteristic, complemented
7#19128001C211yesmaximal, characteristic, complemented
8#19127993C211yesmaximal, characteristic, complemented
9#19127945C211yesmaximal, characteristic, complemented
10#19127928C211yesmaximal, characteristic, complemented
11#19127801C211yesmaximal, characteristic, complemented
12#19127773C211yesmaximal, characteristic, complemented
13#19127741C211yesmaximal, characteristic, complemented
14C2×#14581725C211yesmaximal, characteristic, complemented
15#547×C83C211yesmaximal, characteristic
16C2×#13050578C2211yescharacteristic
17C2×#13050574C2211yescharacteristic
18C22×C83⋊C8C2211yescharacteristic
19#14581785—21no—
20#14581784C2211yescharacteristic
21#14581782—21no—
22#14581773—21no—
23#14581771C2211yescharacteristic
24#14581771C2211yescharacteristic
25C4×Dic166C2211yescharacteristic
26#14581751C2211yescharacteristic
27#14581748—21no—
28C2×C4⋊Dic83C2211yescharacteristic
29#14581725C2211yescharacteristic
30#14581725C2211yescharacteristic
31#14581725C2211yescharacteristic
32#14581725C2211yescharacteristic
33#14581725C2211yescharacteristic
34#14581725C2211yescharacteristic
35#14581723C2211yescharacteristic
36#14581723C2211yescharacteristic
37#14581723C2211yescharacteristic
38C4⋊(C83⋊C8)C2211yescharacteristic
39#14581715C2211yescharacteristic
40#14581715C2211yescharacteristic
41#14581715C2211yescharacteristic
42#14581713C2211yescharacteristic
43#14581713C2211yescharacteristic
44#14581713C2211yescharacteristic
45C22⋊(C83⋊C8)C2211yescharacteristic
46C22⋊(C83⋊C8)C2211yescharacteristic
47#14581703C2211yescharacteristic
48C2×#41×C83—21no—
49C4⋊Q8×C83C2211yescharacteristic
50#123×C83—21no—
51#123×C83—21no—
52C22⋊Q8×C83—21no—
53#121×C83C2211yescharacteristic
54#121×C83C2211yescharacteristic
55C4×D4×C83C2211yescharacteristic
56C4×D4×C83C2211yescharacteristic
57C2×C4⋊C4×C83C2211yescharacteristic
58C2×C4⋊C4×C83C2211yescharacteristic
59C2×Dic166C2311yescharacteristic
60C22×Dic83—21no—
61#13050578—22no—
62#13050574—22no—
63C2×C83⋊C8—22no—
64C2×C83⋊C8C2311yescharacteristic
65C2×C83⋊C8C2311yescharacteristic
66C2×C83⋊C8C2311yescharacteristic
67C2×C83⋊C8C2311yescharacteristic
68C4⋊Dic83—21no—
69C4⋊Dic83C2311yescharacteristic
70C4⋊Dic83C2311yescharacteristic
71C4⋊Dic83C2311yescharacteristic
72Dic83⋊C4—21no—
73Dic83⋊C4—21no—
74Dic83⋊C4—21no—
75Dic83⋊C4—21no—
76Dic83⋊C4—21no—
77C22⋊Dic83—21no—
78C22⋊Dic83—21no—
79C22⋊Dic83—21no—
80C4×Dic83—21no—
81C4×Dic83—21no—
82#41×C83—44no—
83C2×Q8×C83—21no—
84C2×D4×C83—21no—
85C2×D4×C83—21no—
86C2×D4×C83D411yescharacteristic
87C2×D4×C83C2311yescharacteristic
88C22×C4×C83—21no—
89C22×C4×C83—21no—
90C22×C4×C83—21no—
91C22×C4×C83C2311yescharacteristic
92C22×C4×C83C2311yescharacteristic
93C4⋊C4×C83—21no—
94C4⋊C4×C83—21no—
95C4⋊C4×C83—21no—
96C4⋊C4×C83D411yescharacteristic
97C4⋊C4×C83C2311yescharacteristic
98C4⋊C4×C83C2311yescharacteristic
99C4⋊C4×C83C2311yescharacteristic
100C22⋊C4×C83—21no—
101C22⋊C4×C83—21no—
102C22⋊C4×C83—21no—
103C22⋊C4×C83D411yescharacteristic
104C22⋊C4×C83D411yescharacteristic
105C42×C83C2311yescharacteristic
106C23×C83—21no—
107C23×C83C2×D411yescharacteristic
108C23×C83C2×D411yescharacteristic
109Q8×C83—42no—
110D4×C83—22no—
111D4×C83—21no—
112D4×C83—21no—
113D4×C83—42no—
114D4×C83—42no—
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—42no—
123C2×C4×C83—42no—
124C2×C4×C83—42no—
125C2×C4×C83C2×D411yescharacteristic
126C2×C4×C83C2×D411yescharacteristic
127C2×C4×C83C2×D411yescharacteristic
128C2×C4×C83C2×D411yescharacteristic
129C2×C4×C83C2411yescharacteristic
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83—21no—
133C2×Dic83—21no—
134C2×Dic83—42no—
135Dic166—21no—
136Dic166—21no—
137C83⋊C8—21no—
138C83⋊C8—21no—
139C83⋊C8—21no—
140C83⋊C8#4112yescomplemented
141C22×C83—21no—
142C22×C83—21no—
143C22×C83—21no—
144C22×C83—21no—
145C22×C83—21no—
146C22×C83—41no—
147C22×C83—41no—
148C22×C83—41no—
149C22×C83AGL(1,ℤ/8)12yes—
150C22×C83C22×D411yescharacteristic
151C4×C83—21no—
152C4×C83—21no—
153C4×C83—21no—
154C4×C83—21no—
155C4×C83—41no—
156C4×C83—41no—
157C4×C83—41no—
158C4×C83C2×#4111yescharacteristic
159C4×C832−1+411yescharacteristic
160Dic83—41no—
161Dic83—41no—
162Dic83—41no—
163Dic83—41no—
164C2×C83—22no—
165C2×C83—41no—
166C2×C83—81no—
167C2×C83#54711yescharacteristic
168C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C83#57811yescharacteristic
170#3343—831nomaximal, Sylow
171C83#334311yescharacteristic, complemented, Sylow
172#552—831no—
173#547D8311yescharacteristic
174#501—831no—
175#484—831no—
176#483—831no—
177#482—831no—
178#480—831no—
179#478—831no—
180#477—831no—
181#468—831no—
182#465—831no—
183#440—831no—
184#435—831no—
185#428—831no—
186C2×#107—831no—
187C2×#41—21no—
188C2×SD16—831no—
189C2×M16—831no—
190C22×C8—831no—
191C4⋊Q8C2×D8311yescharacteristic
192#126—1661no—
193#125—831no—
194#125—1661no—
195#123—21no—
196#123—21no—
197#123—1661no—
198C22⋊Q8—21no—
199C22⋊Q8—831no—
200C22⋊Q8—831no—
201#121C2×D8311yescharacteristic
202#121C2×D8311yescharacteristic
203C4×Q8—831no—
204C4×D4C2×D8311yescharacteristic
205C4×D4C2×D8311yescharacteristic
206#117—831no—
207#117—1661no—
208C2×C4⋊C4—831no—
209C2×C4⋊C4C2×D8311yescharacteristic
210C2×C4⋊C4C2×D8311yescharacteristic
211#107—831no—
212#107—831no—
213#107—831no—
214#107—831no—
215#107—831no—
216#107—831no—
217#106—831no—
218#106—831no—
219#106—831no—
220C4⋊C8—831no—
221#103—831no—
222#103—831no—
223#103—831no—
224#102—831no—
225#102—831no—
226#102—831no—
227C22⋊C8—831no—
228C22⋊C8—831no—
229#97—831no—
230#41—44no—
231C2×Q8—21no—
232C2×Q8—831no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4C22⋊D8311yescharacteristic
236C2×D4C22×D8311yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—1661no—
241C22×C4C22×D8311yescharacteristic
242C22×C4C22×D8311yescharacteristic
243SD16—1662no—
244M16—1662no—
245C2×C8—831no—
246C2×C8—831no—
247C2×C8—831no—
248C2×C8—831no—
249C2×C8—1662no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—831no—
254C4⋊C4—831no—
255C4⋊C4—831no—
256C4⋊C4—1661no—
257C4⋊C4—1661no—
258C4⋊C4—1661no—
259C4⋊C4—1661no—
260C4⋊C4—1661no—
261C4⋊C4—1661no—
262C4⋊C4C22⋊D8311yescharacteristic
263C4⋊C4C22×D8311yescharacteristic
264C4⋊C4C22×D8311yescharacteristic
265C4⋊C4C22×D8311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—1661no—
270C22⋊C4—1661no—
271C22⋊C4—1661no—
272C22⋊C4C22⋊D8311yescharacteristic
273C22⋊C4C22⋊D8311yescharacteristic
274C42—1661no—
275C42—1661no—
276C42C22×D8311yescharacteristic
277C23—21no—
278C23C2×C22⋊D8311yescharacteristic
279C23C2×C22⋊D8311yescharacteristic
280Q8—42no—
281Q8—1661no—
282Q8—1661no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—3322no—
299C2×C4—1661no—
300C2×C4—1661no—
301C2×C4—1661no—
302C2×C4—1661no—
303C2×C4C2×C22⋊D8311yescharacteristic
304C2×C4C2×C22⋊D8311yescharacteristic
305C2×C4C2×C22⋊D8311yescharacteristic
306C2×C4C2×C22⋊D8311yescharacteristic
307C2×C4C23×D8311yescharacteristic
308C8—832no—
309C8—1661no—
310C8—1661no—
311C8—1661no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#1458181812yes—
321C22C22×C22⋊D8311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—3321no—
330C4—3321no—
331C4—3321no—
332C4—3321no—
333C4#41×D8311yescharacteristic
334C4#1458183911yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2#1912835011yescharacteristic
339C2C2×#1458181811yescharacteristic
340C2#1912851611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting, prime radical#547×C83C2
socleC22×C83C22×D4
hypercenter#547D83
hypocenterC83#3343
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #19128391C2semidirect
2. #19128107C2semidirect
3. #19128036C2semidirect
4. #19128031C2semidirect
5. #19128022C2semidirect
6. #19128012C2semidirect
7. #19128001C2semidirect
8. #19127993C2semidirect
9. #19127945C2semidirect
10. #19127928C2semidirect
11. #19127801C2semidirect
12. #19127773C2semidirect
13. #19127741C2semidirect
14. C2×#14581725C2semidirect
140. C83⋊C8#41semidirect
171. C83#3343semidirect

Maximal subgroups

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

subgroupindex
#191283912
#191281072
#191280362
#191280312
#191280222
#191280122
#191280012
#191279932
#191279452
#191279282
#191278012
#191277732
#191277412
C2×#145817252
#547×C832
#334383