Finite Group Databasebeta

← #35302079

Subgroups — #35302079

Order 21248.

424 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916548C211yesmaximal, characteristic
2#24906090C212yesmaximal
3#24905807C211yesmaximal, characteristic
4#24905319C212yesmaximal
5C83×#2565C211yesmaximal, characteristic
6#19127832—24no—
7#19127758—21no—
8#19127758C2212yes—
9#19127758C2212yes—
10#19127754—21no—
11#19127443—24no—
12#19127427—21no—
13#19127427—21no—
14C2×#125×C83C2211yescharacteristic
15C2×C4×Q8×C83C2211yescharacteristic
16#398×C83—21no—
17#398×C83—21no—
18#391×C83C411yescharacteristic
19#391×C83C411yescharacteristic
20#387×C83—21no—
21#387×C83—21no—
22#384×C83C411yescharacteristic
23#382×C83C411yescharacteristic
24C4×C4⋊C4×C83C2211yescharacteristic
25C4⋊(C83⋊C8)—22no—
26C4⋊(C83⋊C8)—22no—
27C4⋊(C83⋊C8)—22no—
28C4⋊(C83⋊C8)—22no—
29C22⋊(C83⋊C8)—22no—
30C22⋊(C83⋊C8)—22no—
31#14581703—22no—
32#14581703—22no—
33#14581703D414yes—
34C4×C83⋊C8—22no—
35C22×Q8×C83C2×C411yescharacteristic
36#125×C83—22no—
37#125×C83—22no—
38C4×Q8×C83—22no—
39C4×Q8×C83—22no—
40C2×C4⋊C4×C83—21no—
41C2×C4⋊C4×C83—21no—
42C2×C4⋊C4×C83—21no—
43C2×C4⋊C4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83C2×C411yescharacteristic
46C2×C4⋊C4×C83C2×C411yescharacteristic
47C2×C4⋊C4×C83C2×C411yescharacteristic
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C4⋊C4×C83D411yescharacteristic
50C2×C42×C83C2×C411yescharacteristic
51C2×C42×C83C2×C411yescharacteristic
52C2×C42×C83D411yescharacteristic
53C2×C42×C83D411yescharacteristic
54C2×C42×C83C2311yescharacteristic
55#95×C83—21no—
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—21no—
60#95×C83—21no—
61#95×C83—21no—
62C2×C83⋊C8—24no—
63C2×C83⋊C8—42no—
64C2×Q8×C83—22no—
65C2×Q8×C83—22no—
66C2×Q8×C83—41no—
67C22×C4×C83—21no—
68C22×C4×C83—21no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83C22⋊C411yescharacteristic
72C22×C4×C83C22⋊C411yescharacteristic
73C22×C4×C83C22⋊C411yescharacteristic
74C22×C4×C83C22⋊C411yescharacteristic
75C22×C4×C83C22×C411yescharacteristic
76C22×C4×C83C2×D411yescharacteristic
77C22×C4×C83C2×D411yescharacteristic
78C4⋊C4×C83—22no—
79C4⋊C4×C83—22no—
80C4⋊C4×C83—22no—
81C4⋊C4×C83—22no—
82C4⋊C4×C83—22no—
83C4⋊C4×C83—42no—
84C4⋊C4×C83—42no—
85C4⋊C4×C83—42no—
86C4⋊C4×C83—41no—
87C4⋊C4×C83—42no—
88C4⋊C4×C83—41no—
89C42×C83—21no—
90C42×C83—21no—
91C42×C83—21no—
92C42×C83—21no—
93C42×C83—41no—
94C42×C83—41no—
95C42×C83C2×D412yes—
96C42×C83#4112yes—
97C23×C83C2×C22⋊C411yescharacteristic
98Q8×C83—44no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—22no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—41no—
112C2×C4×C83—41no—
113C2×C4×C83—41no—
114C2×C4×C83—41no—
115C2×C4×C83—41no—
116C2×C4×C83—41no—
117C2×C4×C83—41no—
118C2×C4×C83—41no—
119C2×C4×C83—42no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83#10112yes—
124C2×C4×C83C4×D412yes—
125C2×C4×C83#12011yescharacteristic
126C2×C4×C83#12112yes—
127C2×C4×C83#12311yescharacteristic
128C83⋊C8—44no—
129C83⋊C8—82no—
130C22×C83—21no—
131C22×C83—21no—
132C22×C83#38611yescharacteristic
133C22×C83C2×#10111yescharacteristic
134C22×C83#41311yescharacteristic
135C4×C83—22no—
136C4×C83—22no—
137C4×C83—22no—
138C4×C83—21no—
139C4×C83—21no—
140C4×C83—42no—
141C4×C83—41no—
142C4×C83—41no—
143C4×C83—41no—
144C4×C83—81no—
145C4×C83—81no—
146C4×C83—81no—
147#9450—831nomaximal, Sylow
148C2×C83—21no—
149C2×C83—21no—
150C2×C83#188411yescharacteristic
151C2×C83#190111yescharacteristic
152C2×C83#191211yescharacteristic
153#2983—831no—
154#2565D8311yescharacteristic
155#1534—832no—
156#1467—831no—
157#1285—832no—
158C83#945011yescharacteristic, complemented, Sylow
159C2×#125C2×D8311yescharacteristic
160C2×C4×Q8C2×D8311yescharacteristic
161#446—1664no—
162#432—832no—
163#432—832no—
164#432—1661no—
165#431—1661no—
166#398—21no—
167#398—21no—
168#391Dic8311yescharacteristic
169#391Dic8311yescharacteristic
170#387—21no—
171#387—21no—
172#384Dic8311yescharacteristic
173#382Dic8311yescharacteristic
174C4×C4⋊C4C2×D8311yescharacteristic
175#330—1664no—
176#324—1661no—
177#324—1661no—
178C22×Q8C2×Dic8311yescharacteristic
179#125—22no—
180#125—22no—
181C4×Q8—22no—
182C4×Q8—22no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C2×Dic8311yescharacteristic
189C2×C4⋊C4C2×Dic8311yescharacteristic
190C2×C4⋊C4C2×Dic8311yescharacteristic
191C2×C4⋊C4C22⋊D8311yescharacteristic
192C2×C4⋊C4C22⋊D8311yescharacteristic
193C2×C42C2×Dic8311yescharacteristic
194C2×C42C2×Dic8311yescharacteristic
195C2×C42C22⋊D8311yescharacteristic
196C2×C42C22⋊D8311yescharacteristic
197C2×C42C22×D8311yescharacteristic
198C4⋊C8—1662no—
199C4⋊C8—1662no—
200C4⋊C8—1662no—
201C4⋊C8—1662no—
202C22⋊C8—1662no—
203C22⋊C8—1662no—
204#97—834no—
205#97—1662no—
206#97—1662no—
207C4×C8—1662no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊Dic8311yescharacteristic
223C22×C4C22⋊Dic8311yescharacteristic
224C22×C4C22⋊Dic8311yescharacteristic
225C22×C4C22⋊Dic8311yescharacteristic
226C22×C4C22×Dic8311yescharacteristic
227C22×C4C2×C22⋊D8311yescharacteristic
228C22×C4C2×C22⋊D8311yescharacteristic
229C2×C8—3322no—
230C2×C8—1664no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—41no—
247C42—41no—
248C42D4×D8312yes—
249C42#1305058912yes—
250C23C2×C22⋊Dic8311yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4#1458171112yes—
277C2×C4D4×Dic8312yes—
278C2×C4#1458176011yescharacteristic
279C2×C4#1458176412yes—
280C2×C4#1458177311yescharacteristic
281C8—3324no—
282C8—6642no—
283C22—21no—
284C22—21no—
285C22#1912758111yescharacteristic
286C22C2×#1458171111yescharacteristic
287C22#1912768511yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—21no—
292C4—21no—
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2#2490784711yescharacteristic
303C2#2490793211yescharacteristic
304C2#2490800111yescharacteristic
subgroupG/H
centerC22#19127581
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2565C2
socleC22×C83#386
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenter#2565D83
hypocenterC83#9450
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2565

Complements

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

NH ≅ G/Ntype
158. C83#9450semidirect

Maximal subgroups

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

subgroupindex
#249165482
#249060902
#249058072
#249053192
C83×#25652
#945083