Finite Group Databasebeta

← #35313713

Subgroups — #35313713

Order 21248.

372 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 83 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#24916174C211yesmaximal, characteristic
2#24909082C212yesmaximal, complemented
3#24905414C211yesmaximal, characteristic, complemented
4#24905400C212yesmaximal, complemented
5C83×#1327C211yesmaximal, characteristic, complemented
6C2×#14581800C411yescharacteristic
7C2×#14581800C2211yescharacteristic
8#19128251C411yescharacteristic
9M32×D83—22no—
10#19127778—22no—
11#19127766—22no—
12#19127669C411yescharacteristic
13#19127669C2211yescharacteristic
14C2×C4×C83⋊C8C411yescharacteristic
15#19127483C2212yes—
16#19127482—22no—
17#423×C83C2211yescharacteristic
18#349×C83C2212yes—
19C2×#13050590C2×C411yescharacteristic
20C2×#13050590C2×C411yescharacteristic
21#14581800—41no—
22#14581800—41no—
23#14581800—41no—
24#14581800—41no—
25C2×#13050573—21no—
26C2×#13050573D412yes—
27C22×C83⋊C8C2×C411yescharacteristic
28C22×C83⋊C8C2×C411yescharacteristic
29C2×C8×D83—21no—
30C2×C8×D83D412yes—
31#14581792C811yescharacteristic
32#14581789C811yescharacteristic
33#14581780C811yescharacteristic
34#14581780C811yescharacteristic
35#14581766—22no—
36C4×D332—22no—
37#14581732—22no—
38#14581731—42no—
39C16×D83—42no—
40(C2×D83)⋊C8—22no—
41(C2×D83)⋊C8—22no—
42C4×C83⋊C8—21no—
43C4×C83⋊C8—21no—
44C2×M16×C83C2×C411yescharacteristic
45C2×M16×C83C2311yescharacteristic
46C2×C42×C83C2×C411yescharacteristic
47M32×C83—22no—
48C4⋊C8×C83—22no—
49#13050590—41no—
50#13050590—41no—
51#13050590—41no—
52#13050590—41no—
53C2×Dic166C2×C811yescharacteristic
54C2×Dic166C2×C811yescharacteristic
55C2×D332—22no—
56C2×D332C2×C811yescharacteristic
57C2×D332C2×C811yescharacteristic
58C2×C22⋊D83—21no—
59C2×C22⋊D83M1612yes—
60C2×C4×D83—21no—
61C2×C4×D83C22⋊C412yes—
62#13050573—42no—
63#13050573—42no—
64C2×C83⋊C8—21no—
65C2×C83⋊C8—21no—
66C2×C83⋊C8—21no—
67C2×C83⋊C8—41no—
68C2×C83⋊C8C22⋊C411yescharacteristic
69C2×C83⋊C8C22⋊C411yescharacteristic
70C8×D83—22no—
71C8×D83—22no—
72C8×D83—41no—
73C8×D83—41no—
74C4⋊Dic83—22no—
75(C2×D83)⋊C4—22no—
76(C2×D83)⋊C4—22no—
77C83⋊C16—42no—
78C22×C4×C83—21no—
79C22×C4×C83C22×C411yescharacteristic
80M16×C83—41no—
81M16×C83—41no—
82C2×C8×C83—21no—
83C2×C8×C83C2×D412yes—
84C42×C83—21no—
85C42×C83C2×C811yescharacteristic
86C42×C83C2×C811yescharacteristic
87C16×C83—42no—
88C23×C83C2×M1611yescharacteristic
89C22×D83—21no—
90C22×D83C22⋊C812yes—
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83—21no—
94C2×C4×C83—21no—
95C2×C4×C83—42no—
96C2×C4×C83C2×C22⋊C411yescharacteristic
97C2×C4×C83C22×C811yescharacteristic
98C22⋊D83—42no—
99C22⋊D83—42no—
100C2×Dic83—21no—
101C2×Dic83C22⋊C812yes—
102D332—41no—
103D332—41no—
104D332—44no—
105C4×D83—22no—
106C4×D83—22no—
107C4×D83—41no—
108C4×D83—41no—
109Dic166—41no—
110Dic166—41no—
111C8×C83—22no—
112C8×C83—41no—
113C83⋊C8—21no—
114C83⋊C8—41no—
115C83⋊C8#9911yescharacteristic
116C83⋊C8#9911yescharacteristic
117C22×C83—21no—
118C22×C83—41no—
119C22×C83C2×C22⋊C811yescharacteristic
120C2×D83—22no—
121C2×D83—42no—
122C2×D83—42no—
123C2×D83—41no—
124C4×C83—22no—
125C4×C83—21no—
126C4×C83—41no—
127C4×C83C2×#9911yescharacteristic
128C4×C83#41311yescharacteristic
129Dic83—22no—
130Dic83—41no—
131#11485—831nomaximal, Sylow
132C2×C83—21no—
133C2×C83—41no—
134C2×C83#145911yescharacteristic
135D83—42no—
136D83—81no—
137#2931—831no—
138#2115—832no—
139#1327—831no—
140#1327D8311yescharacteristic, complemented
141#1321—832no—
142C83#1148511yescharacteristic, complemented, Sylow
143C2×#131—831no—
144C2×#131—831no—
145#532—831no—
146C2×M32—1662no—
147#436—1662no—
148C8×D4—1662no—
149#423C2×D8311yescharacteristic
150#408—831no—
151#408—831no—
152C2×C4×C8—831no—
153#349—832no—
154#349—1662no—
155#349C2×D8312yes—
156C2×#41—831no—
157C2×#41—831no—
158#131—3321no—
159#131—3321no—
160#131—3321no—
161#131—3321no—
162C2×M16—832no—
163C2×M16—1661no—
164C2×M16C4×D8311yescharacteristic
165C2×M16C22×D8311yescharacteristic
166C22×C8—831no—
167C22×C8—831no—
168C22×C8—832no—
169C22×C8—1661no—
170C4⋊Q8—831no—
171#127—831no—
172#124—831no—
173#124—831no—
174#121—1662no—
175C4×D4—1662no—
176C2×C42C4×D8311yescharacteristic
177M32—22no—
178M32—3322no—
179M32—1662no—
180C2×C16—3322no—
181C4⋊C8—22no—
182C22⋊C8—1662no—
183C22⋊C8—1662no—
184C4×C8—1661no—
185C4×C8—1661no—
186#41—3321no—
187#41—3321no—
188#41—3321no—
189#41—3321no—
190C2×Q8—831no—
191C2×Q8—831no—
192C2×D4—832no—
193C2×D4—831no—
194C2×D4—831no—
195C2×D4—1662no—
196C2×D4—1661no—
197C22×C4—21no—
198C22×C4—832no—
199C22×C4—1661no—
200C22×C4C2×C4×D8311yescharacteristic
201M16—41no—
202M16—41no—
203M16—3322no—
204M16—3322no—
205C2×C8—21no—
206C2×C8—3321no—
207C2×C8—3321no—
208C2×C8—3321no—
209C2×C8—831no—
210C2×C8—831no—
211C2×C8—1662no—
212C2×C8—1662no—
213C2×C8—1661no—
214C2×C8—1661no—
215C2×C8—1661no—
216C2×C8D4×D8312yes—
217C4⋊C4—1662no—
218C22⋊C4—1662no—
219C22⋊C4—1662no—
220C42—21no—
221C42C8×D8311yescharacteristic
222C42C8×D8311yescharacteristic
223C16—42no—
224C16—3322no—
225C23—832no—
226C23—1661no—
227C23M16×D8311yescharacteristic
228Q8—3321no—
229Q8—3321no—
230D4—3321no—
231D4—3324no—
232D4—3321no—
233D4—3322no—
234D4—3322no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—3321no—
241C2×C4—3321no—
242C2×C4—832no—
243C2×C4—1661no—
244C2×C4—1662no—
245C2×C4—1662no—
246C2×C4C22⋊C4×D8311yescharacteristic
247C2×C4C2×C8×D8311yescharacteristic
248C8—22no—
249C8—41no—
250C8—3321no—
251C8—831no—
252C8—831no—
253C8—1661no—
254C22—21no—
255C22—41no—
256C22—3322no—
257C22—3322no—
258C22—3321no—
259C22—1662no—
260C22C22⋊C8×D8311yescharacteristic
261C4—22no—
262C4—21no—
263C4—41no—
264C4—3321no—
265C4—1662no—
266C4#99×D8311yescharacteristic
267C4#1912768411yescharacteristic
268C2—21no—
269C2—41no—
270C2—3322no—
271C2—6641no—
272C2#2490578011yescharacteristic
subgroupG/H
centerC4#99×D83
commutatorC2×C4×C83C22×C8
FrattiniC2×M16C22×D83
FittingC83×#1327C2
socleC2×C83#1459
prime radical#19128251C4
cosocleC2×M16×C83C23
hypercenter#1327D83
hypocenterC83#11485
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #24909082C2semidirect
3. #24905414C2semidirect
4. #24905400C2semidirect
5. C83×#1327C2semidirect
140. #1327D83semidirect
142. C83#11485semidirect

Maximal subgroups

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

subgroupindex
#249161742
#249090822
#249054142
#249054002
C83×#13272
#1148583