Finite Group Databasebeta

← #35314803

Subgroups — #35314803

Order 21248.

358 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#14581711C211yesmaximal, characteristic
2#24905787C211yesmaximal, characteristic
3#24905490C212yesmaximal
4#24905469C212yesmaximal
5C83×#2634C211yesmaximal, characteristic
6#19127754—21no—
7C2×#14581711—21no—
8C4×#13050574—21no—
9#19127470C2212yes—
10#19127427—21no—
11#19127427C2212yes—
12C2×#125×C83C411yescharacteristic
13C2×C4×Q8×C83C2211yescharacteristic
14#400×C83—21no—
15#400×C83C411yescharacteristic
16#400×C83C2211yescharacteristic
17#398×C83C411yescharacteristic
18#398×C83C2211yescharacteristic
19#395×C83—21no—
20#387×C83—21no—
21#387×C83—21no—
22#383×C83C411yescharacteristic
23C2×#13050574—22no—
24C4⋊(C83⋊C8)—41no—
25#14581711—24no—
26C22⋊(C83⋊C8)—22no—
27#14581703—41no—
28C4×C83⋊C8—41no—
29C4×C83⋊C8—41no—
30C22×Q8×C83D411yescharacteristic
31#125×C83—41no—
32#125×C83—41no—
33C4×Q8×C83—41no—
34C4×Q8×C83—41no—
35C2×C4⋊C4×C83—21no—
36C2×C4⋊C4×C83—21no—
37C2×C4⋊C4×C83—21no—
38C2×C4⋊C4×C83—21no—
39C2×C4⋊C4×C83C2×C411yescharacteristic
40C2×C4⋊C4×C83C2×C411yescharacteristic
41C2×C4⋊C4×C83C2×C411yescharacteristic
42C2×C4⋊C4×C83D411yescharacteristic
43C2×C4⋊C4×C83C2311yescharacteristic
44C2×C42×C83C2×C411yescharacteristic
45C2×C42×C83D411yescharacteristic
46C2×C42×C83D411yescharacteristic
47#95×C83—21no—
48#95×C83—21no—
49#95×C83—21no—
50#95×C83—21no—
51#95×C83—21no—
52#95×C83—21no—
53#95×C83—21no—
54#95×C83—21no—
55#95×C83C2×C411yescharacteristic
56#95×C83C2×C411yescharacteristic
57#13050574—24no—
58#13050574—42no—
59C2×C83⋊C8—42no—
60C2×C83⋊C8—42no—
61C2×Q8×C83—22no—
62C2×Q8×C83—22no—
63C2×Q8×C83—41no—
64C22×C4×C83—21no—
65C22×C4×C83—21no—
66C22×C4×C83—21no—
67C22×C4×C83—21no—
68C22×C4×C83C22⋊C411yescharacteristic
69C22×C4×C83C22⋊C411yescharacteristic
70C22×C4×C83C22⋊C411yescharacteristic
71C22×C4×C83C22⋊C411yescharacteristic
72C22×C4×C83C22×C411yescharacteristic
73C22×C4×C83C2×D411yescharacteristic
74C22×C4×C83C2×D411yescharacteristic
75C4⋊C4×C83—41no—
76C4⋊C4×C83—41no—
77C4⋊C4×C83—41no—
78C4⋊C4×C83—41no—
79C4⋊C4×C83—41no—
80C4⋊C4×C83—42no—
81C4⋊C4×C83—41no—
82C4⋊C4×C83—41no—
83C4⋊C4×C83—42no—
84C4⋊C4×C83—42no—
85C42×C83—21no—
86C42×C83—21no—
87C42×C83—21no—
88C42×C83—21no—
89C42×C83—21no—
90C42×C83—21no—
91C23×C83C2×C22⋊C411yescharacteristic
92Q8×C83—44no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—41no—
104C2×C4×C83—41no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—41no—
109C2×C4×C83—41no—
110C2×C4×C83—41no—
111C2×C4×C83—42no—
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#9911yescharacteristic
119C2×C4×C83#9911yescharacteristic
120C2×C4×C83#10412yes—
121C2×C4×C83#13512yes—
122C83⋊C8—44no—
123C83⋊C8—82no—
124C22×C83—21no—
125C22×C83—21no—
126C22×C83C2×#9911yescharacteristic
127C22×C83#41611yescharacteristic
128C22×C83C2×#10411yescharacteristic
129C4×C83—21no—
130C4×C83—21no—
131C4×C83—22no—
132C4×C83—22no—
133C4×C83—41no—
134C4×C83—41no—
135C4×C83—41no—
136C4×C83—41no—
137C4×C83—81no—
138C4×C83—81no—
139C4×C83—81no—
140C4×C83—81no—
141#11740—831nomaximal, Sylow
142C2×C83—21no—
143C2×C83—21no—
144C2×C83#150111yescharacteristic
145C2×C83#212311yescharacteristic
146C2×C83#213311yescharacteristic
147#2634D8311yescharacteristic
148C4×#101—831no—
149#1461—831no—
150#1353—832no—
151#1346—832no—
152C83#1174011yescharacteristic, complemented, Sylow
153C2×#125Dic8311yescharacteristic
154C2×C4×Q8C2×D8311yescharacteristic
155#431—1661no—
156C2×#101—1661no—
157C4×M16—1661no—
158#400—21no—
159#400Dic8311yescharacteristic
160#400C2×D8311yescharacteristic
161#398Dic8311yescharacteristic
162#398C2×D8311yescharacteristic
163#395—21no—
164#387—21no—
165#387—21no—
166#383Dic8311yescharacteristic
167#343—832no—
168#324—832no—
169#324—1661no—
170C22×Q8C22⋊D8311yescharacteristic
171C2×M16—1662no—
172#125—41no—
173#125—41no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4C2×Dic8311yescharacteristic
181C2×C4⋊C4C2×Dic8311yescharacteristic
182C2×C4⋊C4C2×Dic8311yescharacteristic
183C2×C4⋊C4C22⋊D8311yescharacteristic
184C2×C4⋊C4C22×D8311yescharacteristic
185C2×C42C2×Dic8311yescharacteristic
186C2×C42C22⋊D8311yescharacteristic
187C2×C42C22⋊D8311yescharacteristic
188C4⋊C8—3321no—
189#101—1664no—
190C22⋊C8—1662no—
191#97—3321no—
192C4×C8—3321no—
193C4×C8—3321no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95C2×Dic8311yescharacteristic
203#95C2×Dic8311yescharacteristic
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4C22⋊Dic8311yescharacteristic
212C22×C4C22⋊Dic8311yescharacteristic
213C22×C4C22⋊Dic8311yescharacteristic
214C22×C4C22⋊Dic8311yescharacteristic
215C22×C4C22×Dic8311yescharacteristic
216C22×C4C2×C22⋊D8311yescharacteristic
217C22×C4C2×C22⋊D8311yescharacteristic
218M16—3322no—
219M16—1664no—
220C2×C8—3322no—
221C2×C8—3322no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—42no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C23C2×C22⋊Dic8311yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#1458170711yescharacteristic
266C2×C4#1458170711yescharacteristic
267C2×C4#1458171912yes—
268C2×C4#1458181212yes—
269C8—3324no—
270C8—6642no—
271C22—21no—
272C22—21no—
273C22C2×#1458170711yescharacteristic
274C22#1912769711yescharacteristic
275C22C2×#1458171911yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2#2490595411yescharacteristic
291C2#2490911711yescharacteristic
292C2#2490915211yescharacteristic
subgroupG/H
centerC22C2×#14581707
commutatorC22×C4×C83C22×C4
FrattiniC2×C4⋊C4C22×D83
FittingC83×#2634C2
socleC22×C83C2×#99
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C4⋊C4×C83C23
hypercenter#2634D83
hypocenterC83#11740
LCSG ▷ C22×C4×C83 ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2634

Complements

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

NH ≅ G/Ntype
152. C83#11740semidirect

Maximal subgroups

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

subgroupindex
C4×#145817112
#249057872
#249054902
#249054692
C83×#26342
#1174083