Finite Group Databasebeta

← #35308563

Subgroups — #35308563

Order 21248.

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

normal subgroups only

This group has 342 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#24907637C211yesmaximal, characteristic
2#24906193C212yesmaximal
3#24906078C212yesmaximal
4#24905374C211yesmaximal, characteristic
5C83×#3255C211yesmaximal, characteristic
6#19127758C2212yes—
7C2×#14581727—22no—
8#19127725C2211yescharacteristic
9C2×#14581703C2211yescharacteristic
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—
20#14581727—44no—
21C4⋊(C83⋊C8)—22no—
22C4⋊(C83⋊C8)—22no—
23C22⋊(C83⋊C8)—22no—
24#14581703—22no—
25#14581703—21no—
26#14581703D412yes—
27C2×Q16×C83—22no—
28C2×M16×C83D412yes—
29C4⋊Q8×C83D412yes—
30C4⋊Q8×C83D412yes—
31#125×C83—22no—
32C22⋊Q8×C83—22no—
33C22⋊Q8×C83—22no—
34C4×Q8×C83—22no—
35C4×Q8×C83—22no—
36#117×C83—22no—
37C2×C42×C83C2311yescharacteristic
38#106×C83—22no—
39C4⋊C8×C83—22no—
40#103×C83—24no—
41#13050574—42no—
42C2×C83⋊C8—22no—
43C2×C83⋊C8—22no—
44C2×C83⋊C8—22no—
45C2×C83⋊C8—41no—
46C2×C83⋊C8—42no—
47C2×Q8×C83—22no—
48C2×Q8×C83—22no—
49C22×C4×C83C2×D411yescharacteristic
50C22×C4×C83#4112yes—
51Q16×C83—82no—
52M16×C83—42no—
53C2×C8×C83—22no—
54C4⋊C4×C83—22no—
55C4⋊C4×C83—22no—
56C4⋊C4×C83—22no—
57C4⋊C4×C83—22no—
58C4⋊C4×C83—42no—
59C4⋊C4×C83—42no—
60C22⋊C4×C83—42no—
61C42×C83—42no—
62C42×C83C2×D411yescharacteristic
63C42×C83C2×D412yes—
64C42×C83#4111yescharacteristic
65C23×C83#12411yescharacteristic
66Q8×C83—42no—
67Q8×C83—42no—
68Q8×C83—82no—
69C2×C4×C83—21no—
70C2×C4×C83—21no—
71C2×C4×C83—42no—
72C2×C4×C83—42no—
73C2×C4×C83—42no—
74C2×C4×C83#12011yescharacteristic
75C2×C4×C83#12111yescharacteristic
76C2×C4×C83#12112yes—
77C2×C4×C83#12312yes—
78C8×C83—42no—
79C83⋊C8—24no—
80C83⋊C8—82no—
81C83⋊C8—81no—
82C22×C83—22no—
83C22×C83—21no—
84C22×C83#39411yescharacteristic
85C4×C83—22no—
86C4×C83—22no—
87C4×C83—21no—
88C4×C83—82no—
89C4×C83—82no—
90C4×C83#45311yescharacteristic
91C4×C83#45611yescharacteristic
92#10528—831nomaximal, Sylow
93C2×C83—41no—
94C2×C83#203911yescharacteristic
95C2×C83#204912yes—
96#3255D8311yescharacteristic
97#1849—831no—
98#1559—832no—
99#1531—832no—
100#1307—831no—
101C83#1052811yescharacteristic, complemented, Sylow
102#533C2×D8312yes—
103#475—22no—
104#470—22no—
105#462—22no—
106#432—832no—
107C2×#108—1662no—
108#423—831no—
109#423C2×D8311yescharacteristic
110C2×#97—831no—
111#333—1662no—
112#332—1662no—
113#330—1664no—
114C2×Q16—22no—
115C2×M16—1661no—
116C2×M16C22⋊D8312yes—
117C22×C8—1661no—
118C4⋊Q8C22⋊D8312yes—
119C4⋊Q8C22⋊D8312yes—
120#125—22no—
121C22⋊Q8—22no—
122C22⋊Q8—22no—
123C4×Q8—22no—
124C4×Q8—22no—
125#117—22no—
126C2×C42C22×D8311yescharacteristic
127#108—3324no—
128#106—22no—
129C4⋊C8—22no—
130C4⋊C8—1662no—
131C4⋊C8—1662no—
132#103—24no—
133C22⋊C8—1662no—
134#97—832no—
135#97—1662no—
136#97—1661no—
137C2×Q8—22no—
138C2×Q8—22no—
139C22×C4C2×C22⋊D8311yescharacteristic
140C22×C4#1305058912yes—
141Q16—82no—
142M16—42no—
143M16—3322no—
144C2×C8—22no—
145C2×C8—3321no—
146C2×C8—3322no—
147C2×C8—1662no—
148C2×C8—1662no—
149C2×C8—1662no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C22⋊C4—42no—
157C42—42no—
158C42D4×D8311yescharacteristic
159C42C2×C22⋊D8312yes—
160C42#1305058911yescharacteristic
161C23#1458177911yescharacteristic
162Q8—42no—
163Q8—42no—
164Q8—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4#1458176111yescharacteristic
171C2×C4#1458176311yescharacteristic
172C2×C4#1458176412yes—
173C2×C4#1458177312yes—
174C8—42no—
175C8—6642no—
176C8—6641no—
177C8—1664no—
178C22—21no—
179C22—22no—
180C22#1912761511yescharacteristic
181C4—21no—
182C4—22no—
183C4—22no—
184C4—82no—
185C4—82no—
186C4#1912786911yescharacteristic
187C4#1912788411yescharacteristic
188C2—41no—
189C2#2490868411yescharacteristic
190C2#2490874012yes—
subgroupG/H
centerC22#19127615
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#3255C2
socleC22×C83#394
prime radicalC23×C83#124
hypercenter#3255D83
hypocenterC83#10528
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
101. C83#10528semidirect

Maximal subgroups

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

subgroupindex
#249076372
#249061932
#249060782
#249053742
C83×#32552
#1052883