Finite Group Databasebeta

← #35308534

Subgroups — #35308534

Order 21248.

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

normal subgroups only

This group has 382 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#24907579C211yesmaximal, characteristic
3#24906153C212yesmaximal
4#24905338C211yesmaximal, characteristic
5C83×#3249C211yesmaximal, characteristic
6#19127725C2212yes—
7C2×C4⋊(C83⋊C8)C2211yescharacteristic
8C42×Dic83C2211yescharacteristic
9#19127460—22no—
10#19127460—22no—
11#19127455—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—
28C2×Q16×C83—22no—
29C22×C8×C83D412yes—
30C4⋊Q8×C83D412yes—
31C4⋊Q8×C83D412yes—
32#125×C83—22no—
33C22⋊Q8×C83—22no—
34C22⋊Q8×C83—22no—
35C4×Q8×C83—22no—
36C4×Q8×C83—22no—
37#117×C83—22no—
38C2×C42×C83C2311yescharacteristic
39#107×C83—22no—
40C4⋊C8×C83—22no—
41#103×C83—24no—
42C22×Dic83—21no—
43C22×Dic83—21no—
44#13050574—42no—
45#13050574—42no—
46C2×C83⋊C8—42no—
47C2×C83⋊C8—41no—
48C2×C83⋊C8—42no—
49C4×Dic83—21no—
50C4×Dic83—22no—
51C4×Dic83—42no—
52C4×Dic83—41no—
53C4×Dic83—41no—
54C4×Dic83Q1612yescomplemented
55C2×Q8×C83—22no—
56C2×Q8×C83—22no—
57C22×C4×C83C2×D411yescharacteristic
58C22×C4×C83C2×D411yescharacteristic
59C22×C4×C83#4111yescharacteristic
60Q16×C83—82no—
61C2×C8×C83—22no—
62C2×C8×C83—42no—
63C4⋊C4×C83—22no—
64C4⋊C4×C83—22no—
65C4⋊C4×C83—22no—
66C4⋊C4×C83—22no—
67C4⋊C4×C83—42no—
68C4⋊C4×C83—42no—
69C22⋊C4×C83—42no—
70C42×C83—42no—
71C42×C83C2×D412yes—
72C42×C83#4112yes—
73C23×C83#12111yescharacteristic
74Q8×C83—42no—
75Q8×C83—42no—
76Q8×C83—82no—
77C2×C4×C83—21no—
78C2×C4×C83—21no—
79C2×C4×C83—41no—
80C2×C4×C83—42no—
81C2×C4×C83—42no—
82C2×C4×C83#12011yescharacteristic
83C2×C4×C83#12112yes—
84C2×C4×C83#12312yes—
85C2×C4×C83#12411yescharacteristic
86C2×C4×C83C2×Q1611yescharacteristic
87C2×C4×C83#13511yescharacteristic
88C2×C4×C83#13712yes—
89C2×Dic83—22no—
90C2×Dic83—22no—
91C2×Dic83—41no—
92C2×Dic83—41no—
93C2×Dic83—41no—
94C2×Dic83—41no—
95C8×C83—42no—
96C83⋊C8—81no—
97C83⋊C8—82no—
98C22×C83—21no—
99C22×C83—21no—
100C22×C83#39411yescharacteristic
101C22×C83#46711yescharacteristic
102C22×C83#47011yescharacteristic
103C4×C83—22no—
104C4×C83—21no—
105C4×C83—82no—
106C4×C83—82no—
107C4×C83#45411yescharacteristic
108C4×C83#45511yescharacteristic
109C4×C83#46212yes—
110C4×C83#46412yes—
111Dic83—42no—
112Dic83—42no—
113#10523—831nomaximal, Sylow
114C2×C83—21no—
115C2×C83—21no—
116C2×C83#204011yescharacteristic
117C2×C83#205011yescharacteristic
118C2×C83#205611yescharacteristic
119#3249D8311yescharacteristic
120#1994—832no—
121#1831—831no—
122#1550—832no—
123#1292—831no—
124C83#1052311yescharacteristic, complemented, Sylow
125#533C2×D8312yes—
126#477—22no—
127#467—22no—
128#462—22no—
129#423—832no—
130C2×C4⋊C8—831no—
131C2×C4⋊C8C2×D8311yescharacteristic
132C43—831no—
133#339—1662no—
134#339—1662no—
135#336—1662no—
136#333—1662no—
137#332—1662no—
138C2×Q16—22no—
139C2×M16—1662no—
140C22×C8—1661no—
141C22×C8C22⋊D8312yes—
142C4⋊Q8C22⋊D8312yes—
143C4⋊Q8C22⋊D8312yes—
144#125—22no—
145C22⋊Q8—22no—
146C22⋊Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149#117—22no—
150C2×C42—831no—
151C2×C42—831no—
152C2×C42—1661no—
153C2×C42—1661no—
154C2×C42C22×D8311yescharacteristic
155#107—22no—
156C4⋊C8—22no—
157C4⋊C8—1662no—
158C4⋊C8—1662no—
159C4⋊C8—1662no—
160#103—24no—
161C2×Q8—22no—
162C2×Q8—22no—
163C22×C4—1661no—
164C22×C4—1661no—
165C22×C4D4×D8311yescharacteristic
166C22×C4C2×C22⋊D8311yescharacteristic
167C22×C4#1305058911yescharacteristic
168Q16—82no—
169M16—3322no—
170M16—3322no—
171C2×C8—22no—
172C2×C8—42no—
173C2×C8—3322no—
174C2×C8—3321no—
175C2×C8—3322no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C22⋊C4—42no—
183C42—42no—
184C42—3321no—
185C42—3321no—
186C42—3322no—
187C42—832no—
188C42—1662no—
189C42—1661no—
190C42C2×C22⋊D8312yes—
191C42#1305058912yes—
192C23#1458176311yescharacteristic
193Q8—42no—
194Q8—42no—
195Q8—82no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—3321no—
202C2×C4—3321no—
203C2×C4—3321no—
204C2×C4—3321no—
205C2×C4—1662no—
206C2×C4—1662no—
207C2×C4#1458176111yescharacteristic
208C2×C4#1458176412yes—
209C2×C4#1458177312yes—
210C2×C4#1458177911yescharacteristic
211C2×C4Q16×D8311yescharacteristic
212C2×C4#1458181511yescharacteristic
213C2×C4#1458182412yes—
214C8—42no—
215C8—6641no—
216C8—6642no—
217C22—21no—
218C22—21no—
219C22#1912761511yescharacteristic
220C22#1912793911yescharacteristic
221C22#1912795611yescharacteristic
222C4—21no—
223C4—22no—
224C4—82no—
225C4—82no—
226C4—3322no—
227C4—3322no—
228C4#1912787411yescharacteristic
229C4#1912787911yescharacteristic
230C4#1912790912yes—
231C4#1912792512yes—
232C2—21no—
233C2—21no—
234C2#2490868911yescharacteristic
235C2#2490874711yescharacteristic
236C2#2490878311yescharacteristic
subgroupG/H
centerC22#19127615
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#3249C2
socleC22×C83#394
prime radicalC23×C83#121
hypercenter#3249D83
hypocenterC83#10523
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
54. C4×Dic83Q16semidirect
124. C83#10523semidirect

Maximal subgroups

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

subgroupindex
#249084412
#249075792
#249061532
#249053382
C83×#32492
#1052383