Finite Group Databasebeta

← #35308568

Subgroups — #35308568

Order 21248.

326 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 77 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#24907603C211yesmaximal, characteristic
2#24906193C212yesmaximal
3#24906078C212yesmaximal
4#24905374C211yesmaximal, characteristic
5C83×#3255C211yesmaximal, characteristic
6#19127758C2212yes—
7#19127725C2211yescharacteristic
8C2×#14581703C2211yescharacteristic
9#19127465—22no—
10#19127450—22no—
11#19127447—22no—
12#19127443—24no—
13#533×C83C2212yes—
14#475×C83—22no—
15#470×C83—22no—
16#462×C83—22no—
17#423×C83C2211yescharacteristic
18C2×#13050574—21no—
19C22×C83⋊C8—21no—
20C4⋊(C83⋊C8)—22no—
21C4⋊(C83⋊C8)—22no—
22C22⋊(C83⋊C8)—22no—
23#14581703—22no—
24#14581703—21no—
25#14581703D412yes—
26C2×Q16×C83—22no—
27C2×M16×C83D412yes—
28C4⋊Q8×C83D412yes—
29C4⋊Q8×C83D412yes—
30#125×C83—22no—
31C22⋊Q8×C83—22no—
32C22⋊Q8×C83—22no—
33C4×Q8×C83—22no—
34C4×Q8×C83—22no—
35#117×C83—22no—
36C2×C42×C83C2311yescharacteristic
37#106×C83—22no—
38C4⋊C8×C83—22no—
39#103×C83—24no—
40#13050574—42no—
41C2×C83⋊C8—22no—
42C2×C83⋊C8—41no—
43C2×C83⋊C8—41no—
44C2×C83⋊C8—41no—
45C2×C83⋊C8—42no—
46C2×Q8×C83—22no—
47C2×Q8×C83—22no—
48C22×C4×C83C2×D411yescharacteristic
49C22×C4×C83#4112yes—
50Q16×C83—82no—
51M16×C83—42no—
52C2×C8×C83—22no—
53C4⋊C4×C83—22no—
54C4⋊C4×C83—22no—
55C4⋊C4×C83—22no—
56C4⋊C4×C83—22no—
57C4⋊C4×C83—42no—
58C4⋊C4×C83—42no—
59C22⋊C4×C83—42no—
60C42×C83—42no—
61C42×C83C2×D411yescharacteristic
62C42×C83C2×D412yes—
63C42×C83#4111yescharacteristic
64C23×C83#12411yescharacteristic
65Q8×C83—42no—
66Q8×C83—42no—
67Q8×C83—82no—
68C2×C4×C83—21no—
69C2×C4×C83—21no—
70C2×C4×C83—42no—
71C2×C4×C83—42no—
72C2×C4×C83—42no—
73C2×C4×C83#12011yescharacteristic
74C2×C4×C83#12111yescharacteristic
75C2×C4×C83#12112yes—
76C2×C4×C83#12312yes—
77C8×C83—42no—
78C83⋊C8—42no—
79C83⋊C8—82no—
80C83⋊C8—81no—
81C22×C83—22no—
82C22×C83—21no—
83C22×C83#39411yescharacteristic
84C4×C83—22no—
85C4×C83—22no—
86C4×C83—21no—
87C4×C83—82no—
88C4×C83—82no—
89C4×C83#45411yescharacteristic
90C4×C83#45511yescharacteristic
91#10529—831nomaximal, Sylow
92C2×C83—41no—
93C2×C83#204011yescharacteristic
94C2×C83#204912yes—
95#3255D8311yescharacteristic
96#1838—831no—
97#1559—832no—
98#1531—832no—
99#1307—831no—
100C83#1052911yescharacteristic, complemented, Sylow
101#533C2×D8312yes—
102#475—22no—
103#470—22no—
104#462—22no—
105#432—832no—
106#423—831no—
107#423C2×D8311yescharacteristic
108C2×#97—831no—
109#341—1662no—
110#333—1662no—
111#332—1662no—
112#330—1664no—
113C2×Q16—22no—
114C2×M16—1661no—
115C2×M16C22⋊D8312yes—
116C22×C8—1661no—
117C4⋊Q8C22⋊D8312yes—
118C4⋊Q8C22⋊D8312yes—
119#125—22no—
120C22⋊Q8—22no—
121C22⋊Q8—22no—
122C4×Q8—22no—
123C4×Q8—22no—
124#117—22no—
125C2×C42C22×D8311yescharacteristic
126#106—22no—
127C4⋊C8—22no—
128C4⋊C8—1662no—
129C4⋊C8—1662no—
130#103—24no—
131C22⋊C8—1662no—
132#97—832no—
133#97—1662no—
134#97—1661no—
135C2×Q8—22no—
136C2×Q8—22no—
137C22×C4C2×C22⋊D8311yescharacteristic
138C22×C4#1305058912yes—
139Q16—82no—
140M16—42no—
141M16—3322no—
142C2×C8—22no—
143C2×C8—3321no—
144C2×C8—3321no—
145C2×C8—3321no—
146C2×C8—3322no—
147C2×C8—1662no—
148C4⋊C4—22no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—42no—
153C4⋊C4—42no—
154C22⋊C4—42no—
155C42—42no—
156C42D4×D8311yescharacteristic
157C42C2×C22⋊D8312yes—
158C42#1305058911yescharacteristic
159C23#1458177911yescharacteristic
160Q8—42no—
161Q8—42no—
162Q8—82no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4#1458176111yescharacteristic
169C2×C4#1458176311yescharacteristic
170C2×C4#1458176412yes—
171C2×C4#1458177312yes—
172C8—42no—
173C8—3322no—
174C8—6642no—
175C8—6641no—
176C22—21no—
177C22—22no—
178C22#1912761511yescharacteristic
179C4—21no—
180C4—22no—
181C4—22no—
182C4—82no—
183C4—82no—
184C4#1912787411yescharacteristic
185C4#1912787911yescharacteristic
186C2—41no—
187C2#2490868911yescharacteristic
188C2#2490874012yes—
subgroupG/H
centerC22#19127615
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#3255C2
socleC22×C83#394
prime radicalC23×C83#124
hypercenter#3255D83
hypocenterC83#10529
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
100. C83#10529semidirect

Maximal subgroups

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

subgroupindex
#249076032
#249061932
#249060782
#249053742
C83×#32552
#1052983