Finite Group Databasebeta

← #35297724

Subgroups — #35297724

Order 21248.

384 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916438C211yesmaximal, characteristic
2#24906226C211yesmaximal, characteristic, complemented
3#24905986C212yesmaximal
4#24905319C212yesmaximal, complemented
5C4×#107×C83C211yesmaximal, characteristic, complemented
6#19128235C2211yescharacteristic
7#19127831C411yescharacteristic, complemented
8C8×Dic166C411yescharacteristic, complemented
9#19127780C411yescharacteristic, complemented
10#19127772—21no—
11C8×D332C411yescharacteristic, complemented
12C8×C22⋊D83—21no—
13#19127760—21no—
14#19127758C2212yes—
15#19127758C2211yescharacteristic
16#19127655—21no—
17#19127454—21no—
18#19127452—21no—
19#19127437—22no—
20#19127434—22no—
21C2×#107×C83—21no—
22C2×C4×C8×C83C2211yescharacteristic
23C4×C4⋊C4×C83C2212yes—
24#340×C83—21no—
25C2×#13050573—21no—
26C2×C8×D83—21no—
27#14581786—21no—
28#14581784Q811yescharacteristic
29#14581780Q811yescharacteristic
30#14581775—21no—
31#14581771D411yescharacteristic
32#14581766D411yescharacteristic
33C4×Dic166C2×C411yescharacteristic
34C4×D332C2×C411yescharacteristic
35C4×C22⋊D83—21no—
36#14581749—21no—
37C4⋊(C83⋊C8)—22no—
38C4⋊(C83⋊C8)C2×C411yescharacteristic
39C4⋊(C83⋊C8)C2×C411yescharacteristic
40Dic83⋊C8—21no—
41Dic83⋊C8—21no—
42C22⋊(C83⋊C8)—21no—
43C22⋊(C83⋊C8)—22no—
44(C2×D83)⋊C8—21no—
45(C2×D83)⋊C8—21no—
46#14581703—21no—
47#14581703—22no—
48#14581702—21no—
49C8×Dic83—21no—
50C22×C8×C83D411yescharacteristic
51C22×C8×C83D411yescharacteristic
52C2×C4⋊C4×C83—22no—
53C2×C42×C83—22no—
54C2×C42×C83C2311yescharacteristic
55#107×C83—24no—
56C4×C8×C83C2×C411yescharacteristic
57C4×C8×C83C2×C411yescharacteristic
58C4×C8×C83D411yescharacteristic
59C4×C8×C83D411yescharacteristic
60#95×C83—22no—
61C2×Dic166C4⋊C411yescharacteristic
62C2×D332C4⋊C411yescharacteristic
63C2×C22⋊D83—21no—
64C2×C4×D83—21no—
65#13050573—42no—
66C2×C83⋊C8—21no—
67C2×C83⋊C8—21no—
68C2×C83⋊C8—42no—
69C8×D83—42no—
70C4⋊Dic83C4⋊C411yescharacteristic
71C4⋊Dic83C4⋊C411yescharacteristic
72Dic83⋊C4—21no—
73Dic83⋊C4—21no—
74Dic83⋊C4—21no—
75Dic83⋊C4—21no—
76C22⋊Dic83—21no—
77(C2×D83)⋊C4—21no—
78(C2×D83)⋊C4—21no—
79(C2×D83)⋊C4—21no—
80(C2×D83)⋊C4—21no—
81C4×Dic83—21no—
82C22×C4×C83—42no—
83C22×C4×C83C2×D411yescharacteristic
84C22×C4×C83C2×D411yescharacteristic
85C22×C4×C83#4111yescharacteristic
86C2×C8×C83—22no—
87C2×C8×C83—41no—
88C2×C8×C83C22⋊C411yescharacteristic
89C2×C8×C83C22⋊C411yescharacteristic
90C2×C8×C83C22⋊C411yescharacteristic
91C2×C8×C83C22⋊C411yescharacteristic
92C4⋊C4×C83—24no—
93C4⋊C4×C83—42no—
94C42×C83—82no—
95C42×C83C22×C411yescharacteristic
96C42×C83C2×D411yescharacteristic
97C42×C83C2×Q811yescharacteristic
98C42×C83#4111yescharacteristic
99C23×C83#12111yescharacteristic
100C22×D83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—41no—
106C2×C4×C83—44no—
107C2×C4×C83—82no—
108C2×C4×C83—82no—
109C2×C4×C83C2×C22⋊C411yescharacteristic
110C2×C4×C83C2×C4⋊C411yescharacteristic
111C2×C4×C83#11711yescharacteristic
112C2×C4×C83#12111yescharacteristic
113C2×C4×C83C22⋊Q811yescharacteristic
114C2×C4×C83C22⋊Q811yescharacteristic
115C22⋊D83—41no—
116C22⋊D83—41no—
117C2×Dic83—21no—
118C2×Dic83—21no—
119C2×Dic83—21no—
120D332—41no—
121C4×D83—41no—
122C4×D83—41no—
123Dic166—41no—
124C8×C83—21no—
125C8×C83—21no—
126C8×C83—21no—
127C8×C83#10412yes—
128C83⋊C8—41no—
129C83⋊C8—41no—
130C83⋊C8—82no—
131C22×C83—21no—
132C22×C83—21no—
133C22×C83#38011yescharacteristic
134C22×C83#47211yescharacteristic
135C22×C83#47311yescharacteristic
136C2×D83—41no—
137C2×D83—41no—
138C2×D83—41no—
139C4×C83—21no—
140C4×C83—21no—
141C4×C83—21no—
142C4×C83—21no—
143C4×C83—21no—
144C4×C83—84no—
145C4×C83C2×#10411yescharacteristic
146C4×C83#42111yescharacteristic
147Dic83—41no—
148Dic83—41no—
149Dic83—41no—
150#8697—831nomaximal, Sylow
151C2×C83—21no—
152C2×C83—21no—
153C2×C83#180611yescharacteristic
154C2×C83#181211yescharacteristic
155C2×C83#181611yescharacteristic
156D83—81no—
157#2966—831no—
158C4×#107D8311yescharacteristic, complemented
159#1568—831no—
160#1509—832no—
161#1285—832no—
162C83#869711yescharacteristic, complemented, Sylow
163#529—831no—
164#446—831no—
165C8×Q8—831no—
166#436—831no—
167#435—1661no—
168C8×D4—831no—
169C8×D4—1661no—
170#433—1661no—
171#432—831no—
172#432—832no—
173C2×#107—21no—
174#405—1661no—
175C2×C4×C8C2×D8311yescharacteristic
176C4×C4⋊C4C2×D8312yes—
177#340—21no—
178#335—1661no—
179#334—1661no—
180#328—1662no—
181#327—1662no—
182C2×M16—1661no—
183C22×C8—1661no—
184C22×C8C22⋊D8311yescharacteristic
185C22×C8C22⋊D8311yescharacteristic
186#126—1661no—
187#125—831no—
188#124—831no—
189#123—1661no—
190C22⋊Q8—831no—
191#121—831no—
192C4×Q8—831no—
193C4×D4—831no—
194C4×D4—1661no—
195#117—1661no—
196C2×C4⋊C4—22no—
197C2×C42—22no—
198C2×C42C22×D8311yescharacteristic
199#107—24no—
200C4⋊C8—831no—
201C4⋊C8—831no—
202C4⋊C8—1661no—
203C4⋊C8—1661no—
204C4⋊C8—1662no—
205C22⋊C8—1662no—
206C22⋊C8—1661no—
207C22⋊C8—1661no—
208C22⋊C8—1661no—
209#97—1661no—
210#97—1661no—
211#97—1662no—
212C4×C8—1661no—
213C4×C8C4×D8311yescharacteristic
214C4×C8C4×D8311yescharacteristic
215C4×C8D33211yescharacteristic
216C4×C8D33211yescharacteristic
217#95—22no—
218C2×Q8—831no—
219C2×D4—831no—
220C2×D4—1661no—
221C22×C4—42no—
222C22×C4—1661no—
223C22×C4D4×D8311yescharacteristic
224C22×C4C2×C22⋊D8311yescharacteristic
225C22×C4#1305058911yescharacteristic
226M16—3322no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—3322no—
230C2×C8—3322no—
231C2×C8—1661no—
232C2×C8—1661no—
233C2×C8(C2×D83)⋊C411yescharacteristic
234C2×C8(C2×D83)⋊C411yescharacteristic
235C2×C8(C2×D83)⋊C411yescharacteristic
236C2×C8(C2×D83)⋊C411yescharacteristic
237C4⋊C4—24no—
238C4⋊C4—42no—
239C4⋊C4—831no—
240C4⋊C4—831no—
241C4⋊C4—1661no—
242C4⋊C4—1661no—
243C4⋊C4—1661no—
244C4⋊C4—1661no—
245C22⋊C4—1661no—
246C22⋊C4—1661no—
247C22⋊C4—1661no—
248C22⋊C4—1661no—
249C22⋊C4—1661no—
250C42—82no—
251C42—1661no—
252C42C2×C4×D8311yescharacteristic
253C42C2×D33211yescharacteristic
254C42Q8×D8311yescharacteristic
255C42#1305059111yescharacteristic
256C23—1661no—
257C23#1458176311yescharacteristic
258Q8—3321no—
259D4—3321no—
260D4—3321no—
261D4—3321no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—44no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—3321no—
271C2×C4—3321no—
272C2×C4—1661no—
273C2×C4—1661no—
274C2×C4—1661no—
275C2×C4C2×(C2×D83)⋊C411yescharacteristic
276C2×C4C4⋊C4×D8311yescharacteristic
277C2×C4#1458175011yescharacteristic
278C2×C4#1458176711yescharacteristic
279C2×C4#1458176811yescharacteristic
280C2×C4#1458177211yescharacteristic
281C8—21no—
282C8—21no—
283C8—21no—
284C8—3321no—
285C8—3321no—
286C8—6642no—
287C8#1458172012yes—
288C22—21no—
289C22—21no—
290C22—3321no—
291C22—3321no—
292C22—3321no—
293C22#1912755811yescharacteristic
294C22#1912796811yescharacteristic
295C22#1912797311yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—84no—
302C4—3321no—
303C4—3321no—
304C4—3321no—
305C4C2×#1458172011yescharacteristic
306C4#1912771911yescharacteristic
307C2—21no—
308C2—21no—
309C2—6641no—
310C2#2490748411yescharacteristic
311C2#2490750611yescharacteristic
312C2#2490752811yescharacteristic
subgroupG/H
centerC22#19127558
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC4×#107×C83C2
socleC22×C83#380
prime radical#14581766D4
cosocleC2×C42×C83C23
hypercenterC4×#107D83
hypocenterC83#8697
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
2. #24906226C2semidirect
4. #24905319C2semidirect
5. C4×#107×C83C2semidirect
7. #19127831C4semidirect
8. C8×Dic166C4semidirect
9. #19127780C4semidirect
11. C8×D332C4semidirect
158. C4×#107D83semidirect
162. C83#8697semidirect

Maximal subgroups

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

subgroupindex
#249164382
#249062262
#249059862
#249053192
C4×#107×C832
#869783