Finite Group Databasebeta

← #35315929

Subgroups — #35315929

Order 21248.

280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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#24918091C211yesmaximal, characteristic
2#24909279C211yesmaximal, characteristic, complemented
3#24905523C212yesmaximal, complemented
4#24905503C212yesmaximal, complemented
5C83×#2153C211yesmaximal, characteristic, complemented
6#19128313C411yescharacteristic
7#19128306C411yescharacteristic
8#19128103C2211yescharacteristic
9#19128074C2211yescharacteristic
10#19128070C411yescharacteristic
11#19128066C411yescharacteristic
12#19127947—21no—
13#19127930—21no—
14#19127803—21no—
15C4×#13050579—21no—
16#19127522C2212yes—
17#19127483—21no—
18#19127479—21no—
19C2×M32×C83—21no—
20#405×C83C2211yescharacteristic
21#364×C83—21no—
22#364×C83C2212yes—
23C2×#13050579—21no—
24C2×#13050579—21no—
25#14581792C2×C411yescharacteristic
26#14581789C2×C411yescharacteristic
27#14581785—41no—
28#14581784C2×C411yescharacteristic
29#14581784C2×C411yescharacteristic
30#14581782—41no—
31#14581777—41no—
32#14581771—21no—
33#14581766—21no—
34#14581765—41no—
35C4×Dic166—21no—
36C4×D332—21no—
37#14581732—22no—
38#14581726—21no—
39#14581724—21no—
40#14581717—21no—
41#14581717—21no—
42#14581714—21no—
43#14581714—21no—
44C2×M16×C83D411yescharacteristic
45C22×C8×C83D411yescharacteristic
46#117×C83C2×C411yescharacteristic
47M32×C83—22no—
48M32×C83—41no—
49C2×C16×C83—41no—
50#97×C83C2×C411yescharacteristic
51#97×C83D411yescharacteristic
52C4×C8×C83D411yescharacteristic
53C4×C8×C83C2311yescharacteristic
54C2×Dic166—21no—
55C2×D332—21no—
56C2×D332—41no—
57C2×C22⋊D83—41no—
58C2×C4×D83—41no—
59#13050579—42no—
60#13050579—41no—
61#13050579—41no—
62C4⋊Dic83—21no—
63C4⋊Dic83—21no—
64C4⋊Dic83—41no—
65Dic83⋊C4—41no—
66Dic83⋊C4—41no—
67Dic83⋊C4—41no—
68Dic83⋊C4—41no—
69C22⋊Dic83—41no—
70(C2×D83)⋊C4—41no—
71(C2×D83)⋊C4—41no—
72C4×Dic83—41no—
73C83⋊C16—42no—
74C22×C4×C83C22⋊C411yescharacteristic
75M16×C83—22no—
76C2×C8×C83—21no—
77C2×C8×C83—21no—
78C2×C8×C83C22⋊C411yescharacteristic
79C2×C8×C83C22⋊C411yescharacteristic
80C2×C8×C83C2×D411yescharacteristic
81C2×C8×C83C2×D411yescharacteristic
82C4⋊C4×C83—21no—
83C22⋊C4×C83—21no—
84C42×C83C22⋊C411yescharacteristic
85C42×C83C22×C411yescharacteristic
86C16×C83—42no—
87C23×C83#10011yescharacteristic
88C22×D83—41no—
89C2×C4×C83—21no—
90C2×C4×C83—21no—
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83#10011yescharacteristic
94C2×C4×C83C2×C22⋊C411yescharacteristic
95C22⋊D83—161no—
96C2×Dic83—41no—
97C2×Dic83—41no—
98C2×Dic83—41no—
99D332—41no—
100D332—41no—
101D332—161no—
102C4×D83—161no—
103Dic166—41no—
104Dic166—41no—
105C8×C83—21no—
106C8×C83—21no—
107C8×C83#13512yes—
108C8×C83AGL(1,ℤ/8)11yescharacteristic
109C8×C83#13711yescharacteristic
110C22×C83—21no—
111C22×C83—41no—
112C22×C83C2×#10011yescharacteristic
113C2×D83—81no—
114C2×D83—81no—
115C2×D83—81no—
116C4×C83—21no—
117C4×C83—41no—
118C4×C83—41no—
119C4×C83#41611yescharacteristic
120C4×C83#41711yescharacteristic
121Dic83—81no—
122Dic83—81no—
123Dic83—81no—
124#11991—831nomaximal, Sylow
125C2×C83—21no—
126C2×C83—41no—
127C2×C83#155111yescharacteristic
128D83—161no—
129#3174—831no—
130#2166—831no—
131#2153D8311yescharacteristic, complemented
132#1366—832no—
133#1359—832no—
134C83#1199111yescharacteristic, complemented, Sylow
135#541—831no—
136#540—831no—
137C2×M32—21no—
138#499—831no—
139#492—831no—
140#491—831no—
141#490—831no—
142#468—1661no—
143#465—1661no—
144#440—1661no—
145C4×SD16—1661no—
146#405C2×D8311yescharacteristic
147#364—21no—
148#364—832no—
149#364C2×D8312yes—
150#349—1661no—
151#347—1661no—
152C2×SD16—1661no—
153C2×SD16—1661no—
154C2×M16D33211yescharacteristic
155C22×C8C22⋊D8311yescharacteristic
156C4⋊Q8—831no—
157#127—831no—
158#126—3321no—
159#125—3321no—
160#125—831no—
161#125—831no—
162#123—3321no—
163C22⋊Q8—1661no—
164#121—3321no—
165#121—1661no—
166C4×Q8—1661no—
167C4×D4—1661no—
168#117C4×D8311yescharacteristic
169M32—22no—
170M32—41no—
171M32—1662no—
172C2×C16—41no—
173#107—1661no—
174#106—1661no—
175#103—1661no—
176#103—1661no—
177#102—1661no—
178#102—1661no—
179#97C4×D8311yescharacteristic
180#97D33211yescharacteristic
181C4×C8C22⋊D8311yescharacteristic
182C4×C8C22×D8311yescharacteristic
183C2×Q8—1661no—
184C2×D4—3321no—
185C2×D4—3321no—
186C2×D4—1661no—
187C22×C4—3321no—
188C22×C4(C2×D83)⋊C411yescharacteristic
189SD16—3322no—
190SD16—3321no—
191SD16—3321no—
192M16—22no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8(C2×D83)⋊C411yescharacteristic
196C2×C8(C2×D83)⋊C411yescharacteristic
197C2×C8C2×C22⋊D8311yescharacteristic
198C2×C8C2×D33211yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—3321no—
201C4⋊C4—3321no—
202C4⋊C4—3321no—
203C4⋊C4—3321no—
204C4⋊C4—3321no—
205C4⋊C4—1661no—
206C4⋊C4—1661no—
207C22⋊C4—21no—
208C22⋊C4—3321no—
209C22⋊C4—3321no—
210C22⋊C4—3321no—
211C42—3321no—
212C42(C2×D83)⋊C411yescharacteristic
213C42C2×C4×D8311yescharacteristic
214C16—42no—
215C16—3322no—
216C23—3321no—
217C23#1458170811yescharacteristic
218Q8—3321no—
219Q8—3321no—
220D4—13281no—
221D4—13281no—
222D4—3321no—
223D4—3321no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—13281no—
229C2×C4—3321no—
230C2×C4—3321no—
231C2×C4—3321no—
232C2×C4#1458170811yescharacteristic
233C2×C4C2×(C2×D83)⋊C411yescharacteristic
234C8—21no—
235C8—21no—
236C8#1458181412yes—
237C8#1458181811yescharacteristic
238C8#1458182311yescharacteristic
239C22—21no—
240C22—41no—
241C22—6641no—
242C22—6641no—
243C22—6641no—
244C22C2×#1458170811yescharacteristic
245C4—21no—
246C4—41no—
247C4—41no—
248C4—6641no—
249C4—6641no—
250C4—6641no—
251C4#1912769811yescharacteristic
252C4#1912770011yescharacteristic
253C2—21no—
254C2—41no—
255C2—13281no—
256C2#2490615611yescharacteristic
subgroupG/H
centerC2#24906156
commutatorC42×C83C22×C4
FrattiniC4×C8C22×D83
FittingC83×#2153C2
socleC2×C83#1551
prime radical#19128306C4
cosocleC4×C8×C83C23
hypercenter#2153D83
hypocenterC83#11991
LCSG ▷ C42×C83 ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2153

Complements

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

NH ≅ G/Ntype
2. #24909279C2semidirect
3. #24905523C2semidirect
4. #24905503C2semidirect
5. C83×#2153C2semidirect
131. #2153D83semidirect
134. C83#11991semidirect

Maximal subgroups

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

subgroupindex
#249180912
#249092792
#249055232
#249055032
C83×#21532
#1199183