Finite Group Databasebeta

← #35308602

Subgroups — #35308602

Order 21248.

342 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 85 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#24907600C211yesmaximal, characteristic
2#24906201C212yesmaximal
3#24905918C212yesmaximal
4C83⋊#1309C211yesmaximal, characteristic
5C83×#3255C211yesmaximal, characteristic
6#19127725C2211yescharacteristic
7#19127725C2212yes—
8C2×C4×C83⋊C8C2211yescharacteristic
9#19127465—22no—
10#19127447—22no—
11#19127447—22no—
12Q8⋊(C83⋊C8)—24no—
13#533×C83C2212yes—
14#475×C83—22no—
15#470×C83—22no—
16#462×C83—22no—
17#423×C83C2211yescharacteristic
18C2×#13050574—21no—
19C2×#13050574—22no—
20C22×C83⋊C8—21no—
21C4⋊(C83⋊C8)—22no—
22C4⋊(C83⋊C8)—22no—
23C4⋊(C83⋊C8)—22no—
24C4×C83⋊C8—21no—
25C4×C83⋊C8D412yes—
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—
41#13050574—82no—
42C2×C83⋊C8—22no—
43C2×C83⋊C8—41no—
44C2×C83⋊C8—41no—
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—42no—
69Q8×C83—42no—
70C2×C4×C83—21no—
71C2×C4×C83—21no—
72C2×C4×C83—22no—
73C2×C4×C83—22no—
74C2×C4×C83—42no—
75C2×C4×C83—42no—
76C2×C4×C83#12011yescharacteristic
77C2×C4×C83#12111yescharacteristic
78C2×C4×C83#12112yes—
79C2×C4×C83#12312yes—
80C8×C83—42no—
81C83⋊C8—42no—
82C83⋊C8—81no—
83C83⋊C8—82no—
84C22×C83—22no—
85C22×C83—21no—
86C22×C83#39411yescharacteristic
87C4×C83—22no—
88C4×C83—21no—
89C4×C83—82no—
90C4×C83—82no—
91C4×C83#45411yescharacteristic
92C4×C83#45511yescharacteristic
93C4×C83#47112yes—
94C4×C83#47312yes—
95#10535—831nomaximal, Sylow
96C2×C83—41no—
97C2×C83#204011yescharacteristic
98C2×C83#205212yes—
99#3255D8311yescharacteristic
100#1837—831no—
101#1561—832no—
102#1493—832no—
103#1309—831no—
104C83#1053511yescharacteristic, complemented, Sylow
105#533C2×D8312yes—
106#475—22no—
107#470—22no—
108#462—22no—
109#423—831no—
110#423—832no—
111#423C2×D8311yescharacteristic
112C2×C4×C8—831no—
113#341—1662no—
114#332—1662no—
115#332—1662no—
116Q8⋊C8—1664no—
117C2×Q16—22no—
118C2×M16—1661no—
119C2×M16—1662no—
120C2×M16C22⋊D8312yes—
121C22×C8—1661no—
122C4⋊Q8C22⋊D8312yes—
123C4⋊Q8C22⋊D8312yes—
124#125—22no—
125C22⋊Q8—22no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128C4×Q8—22no—
129#117—22no—
130C2×C42C22×D8311yescharacteristic
131#106—22no—
132C4⋊C8—22no—
133C4⋊C8—1662no—
134C4⋊C8—1662no—
135C4⋊C8—1662no—
136#103—24no—
137C4×C8—832no—
138C4×C8—1661no—
139C2×Q8—22no—
140C2×Q8—22no—
141C22×C4C2×C22⋊D8311yescharacteristic
142C22×C4#1305058912yes—
143Q16—82no—
144M16—42no—
145M16—3322no—
146M16—6642no—
147C2×C8—22no—
148C2×C8—3321no—
149C2×C8—3321no—
150C2×C8—3321no—
151C2×C8—3322no—
152C2×C8—1662no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—22no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C22⋊C4—42no—
160C42—42no—
161C42D4×D8311yescharacteristic
162C42C2×C22⋊D8312yes—
163C42#1305058911yescharacteristic
164C23#1458177911yescharacteristic
165Q8—42no—
166Q8—42no—
167Q8—42no—
168Q8—42no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4#1458176111yescharacteristic
176C2×C4#1458176311yescharacteristic
177C2×C4#1458176412yes—
178C2×C4#1458177312yes—
179C8—42no—
180C8—3322no—
181C8—6641no—
182C8—6642no—
183C22—21no—
184C22—22no—
185C22#1912761511yescharacteristic
186C4—21no—
187C4—22no—
188C4—82no—
189C4—82no—
190C4#1912787411yescharacteristic
191C4#1912787911yescharacteristic
192C4#1912796612yes—
193C4#1912797412yes—
194C2—41no—
195C2#2490868911yescharacteristic
196C2#2490875912yes—
subgroupG/H
centerC22#19127615
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#3255C2
socleC22×C83#394
prime radicalC23×C83#124
hypercenter#3255D83
hypocenterC83#10535
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
104. C83#10535semidirect

Maximal subgroups

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

subgroupindex
#249076002
#249062012
#249059182
C83⋊#13092
C83×#32552
#1053583