Finite Group Databasebeta

← #35308529

Subgroups — #35308529

Order 21248.

402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 99 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#24908441C212yesmaximal
2#24907614C211yesmaximal, characteristic
3#24906153C212yesmaximal
4#24905338C211yesmaximal, characteristic
5C83×#3249C211yesmaximal, characteristic
6#19127725C2212yes—
7C2×C4⋊(C83⋊C8)C2211yescharacteristic
8C2×Dic83⋊C8—22no—
9C42×Dic83C2211yescharacteristic
10#19127460—22no—
11#19127460—22no—
12#19127450—22no—
13#19127447—22no—
14#533×C83C2212yes—
15#477×C83—22no—
16#467×C83—22no—
17#462×C83—22no—
18C2×C4⋊C8×C83C2211yescharacteristic
19C2×#13050574—22no—
20C22×C83⋊C8—21no—
21C2×C4×Dic83—21no—
22C2×C4×Dic83—21no—
23C2×C4×Dic83D411yescharacteristic
24C2×C4×Dic83D411yescharacteristic
25C4⋊(C83⋊C8)—22no—
26C4⋊(C83⋊C8)—22no—
27C4⋊(C83⋊C8)—22no—
28Dic83⋊C8—44no—
29C2×Q16×C83—22no—
30C22×C8×C83D412yes—
31C4⋊Q8×C83D412yes—
32C4⋊Q8×C83D412yes—
33#125×C83—22no—
34C22⋊Q8×C83—22no—
35C22⋊Q8×C83—22no—
36C4×Q8×C83—22no—
37C4×Q8×C83—22no—
38#117×C83—22no—
39C2×C42×C83C2311yescharacteristic
40#107×C83—22no—
41C4⋊C8×C83—22no—
42#103×C83—24no—
43C22×Dic83—21no—
44C22×Dic83—21no—
45#13050574—42no—
46#13050574—42no—
47C2×C83⋊C8—42no—
48C2×C83⋊C8—41no—
49C2×C83⋊C8—42no—
50C4×Dic83—22no—
51C4×Dic83—22no—
52C4×Dic83—21no—
53C4×Dic83—22no—
54C4×Dic83—42no—
55C4×Dic83Q1612yescomplemented
56C2×Q8×C83—22no—
57C2×Q8×C83—22no—
58C22×C4×C83C2×D411yescharacteristic
59C22×C4×C83C2×D411yescharacteristic
60C22×C4×C83#4111yescharacteristic
61Q16×C83—82no—
62C2×C8×C83—22no—
63C2×C8×C83—42no—
64C4⋊C4×C83—22no—
65C4⋊C4×C83—22no—
66C4⋊C4×C83—22no—
67C4⋊C4×C83—22no—
68C4⋊C4×C83—42no—
69C4⋊C4×C83—42no—
70C22⋊C4×C83—42no—
71C42×C83—42no—
72C42×C83C2×D412yes—
73C42×C83#4112yes—
74C23×C83#12111yescharacteristic
75Q8×C83—42no—
76Q8×C83—42no—
77Q8×C83—82no—
78C2×C4×C83—21no—
79C2×C4×C83—21no—
80C2×C4×C83—41no—
81C2×C4×C83—42no—
82C2×C4×C83—42no—
83C2×C4×C83#12011yescharacteristic
84C2×C4×C83#12112yes—
85C2×C4×C83#12312yes—
86C2×C4×C83#12411yescharacteristic
87C2×C4×C83C2×Q1611yescharacteristic
88C2×C4×C83#13511yescharacteristic
89C2×C4×C83#13712yes—
90C2×Dic83—22no—
91C2×Dic83—22no—
92C2×Dic83—22no—
93C2×Dic83—22no—
94C2×Dic83—41no—
95C2×Dic83—41no—
96C8×C83—42no—
97C83⋊C8—81no—
98C83⋊C8—82no—
99C22×C83—21no—
100C22×C83—21no—
101C22×C83#39411yescharacteristic
102C22×C83#46711yescharacteristic
103C22×C83#47011yescharacteristic
104C4×C83—22no—
105C4×C83—21no—
106C4×C83—82no—
107C4×C83—82no—
108C4×C83#45311yescharacteristic
109C4×C83#45611yescharacteristic
110C4×C83#46212yes—
111C4×C83#46412yes—
112Dic83—24no—
113Dic83—42no—
114#10522—831nomaximal, Sylow
115C2×C83—21no—
116C2×C83—21no—
117C2×C83#203911yescharacteristic
118C2×C83#205011yescharacteristic
119C2×C83#205611yescharacteristic
120#3249D8311yescharacteristic
121#1994—832no—
122#1842—831no—
123#1550—832no—
124#1292—831no—
125C83#1052211yescharacteristic, complemented, Sylow
126#533C2×D8312yes—
127#477—22no—
128#467—22no—
129#462—22no—
130#423—832no—
131C2×C4⋊C8—831no—
132C2×C4⋊C8—1662no—
133C2×C4⋊C8C2×D8311yescharacteristic
134C43—831no—
135#339—1662no—
136#339—1662no—
137#333—1662no—
138#332—1662no—
139C2×Q16—22no—
140C2×M16—1662no—
141C22×C8—1661no—
142C22×C8C22⋊D8312yes—
143C4⋊Q8C22⋊D8312yes—
144C4⋊Q8C22⋊D8312yes—
145#125—22no—
146C22⋊Q8—22no—
147C22⋊Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150#117—22no—
151C2×C42—831no—
152C2×C42—831no—
153C2×C42—1661no—
154C2×C42—1661no—
155C2×C42C22×D8311yescharacteristic
156#107—22no—
157C4⋊C8—22no—
158C4⋊C8—3324no—
159C4⋊C8—1662no—
160C4⋊C8—1662no—
161C4⋊C8—1662no—
162#103—24no—
163C2×Q8—22no—
164C2×Q8—22no—
165C22×C4—1661no—
166C22×C4—1661no—
167C22×C4D4×D8311yescharacteristic
168C22×C4C2×C22⋊D8311yescharacteristic
169C22×C4#1305058911yescharacteristic
170Q16—82no—
171M16—3322no—
172M16—3322no—
173C2×C8—22no—
174C2×C8—42no—
175C2×C8—3322no—
176C2×C8—3321no—
177C2×C8—3322no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C22⋊C4—42no—
185C42—42no—
186C42—3322no—
187C42—832no—
188C42—1662no—
189C42—1662no—
190C42—1662no—
191C42—1661no—
192C42C2×C22⋊D8312yes—
193C42#1305058912yes—
194C23#1458176311yescharacteristic
195Q8—42no—
196Q8—42no—
197Q8—82no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—3321no—
204C2×C4—3321no—
205C2×C4—1662no—
206C2×C4—1662no—
207C2×C4—1662no—
208C2×C4—1662no—
209C2×C4#1458176111yescharacteristic
210C2×C4#1458176412yes—
211C2×C4#1458177312yes—
212C2×C4#1458177911yescharacteristic
213C2×C4Q16×D8311yescharacteristic
214C2×C4#1458181511yescharacteristic
215C2×C4#1458182412yes—
216C8—42no—
217C8—6641no—
218C8—6642no—
219C22—21no—
220C22—21no—
221C22#1912761511yescharacteristic
222C22#1912793911yescharacteristic
223C22#1912795611yescharacteristic
224C4—21no—
225C4—22no—
226C4—82no—
227C4—82no—
228C4—3322no—
229C4—1664no—
230C4#1912786911yescharacteristic
231C4#1912788411yescharacteristic
232C4#1912790912yes—
233C4#1912792512yes—
234C2—21no—
235C2—21no—
236C2#2490868411yescharacteristic
237C2#2490874711yescharacteristic
238C2#2490878311yescharacteristic
subgroupG/H
centerC22#19127615
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#3249C2
socleC22×C83#394
prime radicalC23×C83#121
hypercenter#3249D83
hypocenterC83#10522
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3249

Complements

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

NH ≅ G/Ntype
55. C4×Dic83Q16semidirect
125. C83#10522semidirect

Maximal subgroups

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

subgroupindex
#249084412
#249076142
#249061532
#249053382
C83×#32492
#1052283