Finite Group Databasebeta

← #35308567

Subgroups — #35308567

Order 21248.

342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 73 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#24918857C211yesmaximal, characteristic
2#24907637C211yesmaximal, characteristic
3#24906194C212yesmaximal
4#24906079C212yesmaximal
5C83×#1307C211yesmaximal, characteristic
6#19128258C2212yes—
7#19127987—22no—
8#19127959—22no—
9#19127912—22no—
10C2×#14581727—22no—
11#19127725C2211yescharacteristic
12C2×#14581703C2211yescharacteristic
13#19127449—22no—
14#19127446—22no—
15#19127442—24no—
16#432×C83C2212yes—
17#423×C83C2211yescharacteristic
18C2×Dic332—22no—
19C2×#13050574—21no—
20C22×C83⋊C8—21no—
21#14581792D412yes—
22#14581792D412yes—
23#14581784—22no—
24#14581771—22no—
25#14581771—22no—
26C4×Dic166—22no—
27C4×Dic166—22no—
28#14581751—22no—
29#14581727—44no—
30#14581724—22no—
31C4⋊(C83⋊C8)—22no—
32#14581717—24no—
33#14581703—21no—
34#14581703D412yes—
35C2×M16×C83D412yes—
36C2×C42×C83C2311yescharacteristic
37C4⋊C8×C83—22no—
38C4⋊C8×C83—22no—
39C22⋊C8×C83—22no—
40#97×C83—22no—
41C2×Dic166—22no—
42C2×Dic166—22no—
43Dic332—82no—
44#13050574—42no—
45C2×C83⋊C8—22no—
46C2×C83⋊C8—22no—
47C2×C83⋊C8—22no—
48C2×C83⋊C8—41no—
49C4⋊Dic83—22no—
50C4⋊Dic83—22no—
51C4⋊Dic83—22no—
52C4⋊Dic83—22no—
53Dic83⋊C4—42no—
54Dic83⋊C4—42no—
55C22⋊Dic83—42no—
56C4×Dic83—42no—
57C22×C4×C83C2×D411yescharacteristic
58C22×C4×C83#4112yes—
59M16×C83—42no—
60C2×C8×C83—22no—
61C2×C8×C83—42no—
62C42×C83C2×D412yes—
63C42×C83C2×D411yescharacteristic
64C42×C83#4111yescharacteristic
65C23×C83#12411yescharacteristic
66C2×C4×C83—21no—
67C2×C4×C83—21no—
68C2×C4×C83—42no—
69C2×C4×C83#12011yescharacteristic
70C2×C4×C83#12112yes—
71C2×C4×C83#12111yescharacteristic
72C2×C4×C83#12312yes—
73C2×Dic83—42no—
74C2×Dic83—42no—
75Dic166—42no—
76Dic166—42no—
77Dic166—82no—
78C8×C83—42no—
79C8×C83—82no—
80C83⋊C8—24no—
81C83⋊C8—81no—
82C22×C83—22no—
83C22×C83—21no—
84C22×C83#39411yescharacteristic
85C4×C83—22no—
86C4×C83—22no—
87C4×C83—21no—
88C4×C83#45311yescharacteristic
89C4×C83#45611yescharacteristic
90Dic83—82no—
91Dic83—82no—
92#10528—831nomaximal, Sylow
93C2×C83—41no—
94C2×C83#203911yescharacteristic
95C2×C83#204912yes—
96#3255—831no—
97#1849—831no—
98#1559—832no—
99#1531—832no—
100#1307D8311yescharacteristic
101C83#1052811yescharacteristic, complemented, Sylow
102#533—832no—
103#475—1662no—
104#470—1662no—
105#462—1662no—
106#432C2×D8312yes—
107C2×#108—1662no—
108#423—831no—
109#423C2×D8311yescharacteristic
110C2×#97—831no—
111#333—1662no—
112#332—1662no—
113#330—1664no—
114C2×Q16—1662no—
115C2×M16—1661no—
116C2×M16D33212yes—
117C22×C8—1661no—
118C4⋊Q8—832no—
119C4⋊Q8—832no—
120#125—1662no—
121C22⋊Q8—1662no—
122C22⋊Q8—1662no—
123C4×Q8—1662no—
124C4×Q8—1662no—
125#117—1662no—
126C2×C42C22×D8311yescharacteristic
127#108—3324no—
128#106—1662no—
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—1662no—
132#103—1664no—
133C22⋊C8—22no—
134#97—22no—
135#97—832no—
136#97—1661no—
137C2×Q8—1662no—
138C2×Q8—1662no—
139C22×C4C2×D33211yescharacteristic
140C22×C4#1305059012yes—
141Q16—6642no—
142M16—42no—
143M16—3322no—
144C2×C8—22no—
145C2×C8—42no—
146C2×C8—3321no—
147C2×C8—1662no—
148C2×C8—1662no—
149C2×C8—1662no—
150C4⋊C4—3322no—
151C4⋊C4—3322no—
152C4⋊C4—1662no—
153C4⋊C4—1662no—
154C4⋊C4—1662no—
155C4⋊C4—1662no—
156C22⋊C4—3322no—
157C42—3322no—
158C42D4×D8312yes—
159C42D4×D8311yescharacteristic
160C42#1305059111yescharacteristic
161C23#1458178011yescharacteristic
162Q8—3322no—
163Q8—3322no—
164Q8—6642no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—3322no—
169C2×C4—3322no—
170C2×C4#1458176211yescharacteristic
171C2×C4#1458176512yes—
172C2×C4#1458176711yescharacteristic
173C2×C4#1458177712yes—
174C8—42no—
175C8—82no—
176C8—6641no—
177C8—1664no—
178C22—21no—
179C22—22no—
180C22#1912761911yescharacteristic
181C4—21no—
182C4—22no—
183C4—22no—
184C4—6642no—
185C4—6642no—
186C4#1912787111yescharacteristic
187C4#1912788611yescharacteristic
188C2—41no—
189C2#2490868811yescharacteristic
190C2#2490874612yes—
subgroupG/H
centerC22#19127619
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1307C2
socleC22×C83#394
prime radicalC23×C83#124
hypercenter#1307D83
hypocenterC83#10528
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
101. C83#10528semidirect

Maximal subgroups

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

subgroupindex
#249188572
#249076372
#249061942
#249060792
C83×#13072
#1052883