Finite Group Databasebeta

← #35308504

Subgroups — #35308504

Order 21248.

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

normal subgroups only

This group has 344 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#24918808C211yesmaximal, characteristic
2#24907582C211yesmaximal, characteristic
3#24906164C212yesmaximal
4#24905976C212yesmaximal
5C83×#1290C211yesmaximal, characteristic
6#19128258C2212yes—
7#19127997—22no—
8#19127942—22no—
9#19127912—22no—
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11#19127547C2211yescharacteristic
12#19127455—22no—
13#19127448—22no—
14#19127446—22no—
15#19127439—24no—
16#432×C83C2212yes—
17C2×C4⋊C8×C83C2211yescharacteristic
18C2×Dic332—22no—
19C22×C83⋊C8—21no—
20#14581792D412yes—
21#14581792D412yes—
22#14581784—22no—
23#14581771—22no—
24#14581771—22no—
25C4×Dic166—22no—
26C4×Dic166—22no—
27#14581751—22no—
28C2×C4×Dic83—21no—
29#14581726—22no—
30C4⋊(C83⋊C8)—22no—
31#14581717—24no—
32C83⋊#95—21no—
33C83⋊#95D412yes—
34C22×C8×C83D412yes—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—22no—
37C4⋊C8×C83—22no—
38C22⋊C8×C83—22no—
39#97×C83—22no—
40C2×Dic166—22no—
41C2×Dic166—22no—
42C22×Dic83—22no—
43Dic332—82no—
44C2×C83⋊C8—42no—
45C2×C83⋊C8—41no—
46C4⋊Dic83—22no—
47C4⋊Dic83—22no—
48C4⋊Dic83—22no—
49C4⋊Dic83—22no—
50Dic83⋊C4—42no—
51Dic83⋊C4—42no—
52C22⋊Dic83—42no—
53C4×Dic83—41no—
54C4×Dic83—41no—
55C4×Dic83—42no—
56C22×C4×C83C2×D411yescharacteristic
57C22×C4×C83C2×D411yescharacteristic
58C22×C4×C83#4111yescharacteristic
59C2×C8×C83—22no—
60C2×C8×C83—42no—
61C2×C8×C83—42no—
62C42×C83C2×D412yes—
63C42×C83#4112yes—
64C23×C83#12111yescharacteristic
65C2×C4×C83—22no—
66C2×C4×C83—21no—
67C2×C4×C83—21no—
68C2×C4×C83—41no—
69C2×C4×C83#12011yescharacteristic
70C2×C4×C83#12112yes—
71C2×C4×C83#12312yes—
72C2×C4×C83#12411yescharacteristic
73C2×Dic83—42no—
74C2×Dic83—42no—
75C2×Dic83—42no—
76C2×Dic83—42no—
77C2×Dic83—42no—
78Dic166—42no—
79Dic166—42no—
80Dic166—82no—
81C8×C83—42no—
82C8×C83—82no—
83C83⋊C8—81no—
84C22×C83—21no—
85C22×C83—21no—
86C22×C83#39411yescharacteristic
87C22×C83#47312yes—
88C4×C83—22no—
89C4×C83—21no—
90C4×C83—22no—
91C4×C83#45411yescharacteristic
92C4×C83#45511yescharacteristic
93Dic83—82no—
94Dic83—82no—
95Dic83—82no—
96#10517—831nomaximal, Sylow
97C2×C83—22no—
98C2×C83#204011yescharacteristic
99C2×C83#204711yescharacteristic
100C2×C83#205311yescharacteristic
101#3249—831no—
102#1832—831no—
103#1552—832no—
104#1506—832no—
105#1290D8311yescharacteristic
106C83#1051711yescharacteristic, complemented, Sylow
107#533—832no—
108#477—1662no—
109#467—1662no—
110#462—1662no—
111#432C2×D8312yes—
112C2×C4⋊C8—831no—
113C2×C4⋊C8C2×D8311yescharacteristic
114#376—831no—
115#336—1662no—
116#332—1662no—
117#332—1662no—
118#328—1664no—
119C2×Q16—1662no—
120C22×C8—1661no—
121C22×C8D33212yes—
122C4⋊Q8—832no—
123C4⋊Q8—832no—
124#125—1662no—
125C22⋊Q8—1662no—
126C22⋊Q8—1662no—
127C4×Q8—1662no—
128C4×Q8—1662no—
129#117—1662no—
130C2×C42—1661no—
131C2×C42C22×D8311yescharacteristic
132#107—1662no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—1662no—
136#103—1664no—
137C22⋊C8—22no—
138#97—22no—
139#95—832no—
140#95—1661no—
141C2×Q8—1662no—
142C2×Q8—1662no—
143C22×C4—1662no—
144C22×C4D4×D8311yescharacteristic
145C22×C4C2×D33211yescharacteristic
146C22×C4#1305059111yescharacteristic
147Q16—6642no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—3322no—
152C2×C8—3321no—
153C4⋊C4—3322no—
154C4⋊C4—3322no—
155C4⋊C4—1662no—
156C4⋊C4—1662no—
157C4⋊C4—1662no—
158C4⋊C4—1662no—
159C22⋊C4—3322no—
160C42—3321no—
161C42—3321no—
162C42—3322no—
163C42D4×D8312yes—
164C42#1305059012yes—
165C23#1458176711yescharacteristic
166Q8—3322no—
167Q8—3322no—
168Q8—6642no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—3322no—
174C2×C4—3322no—
175C2×C4—3322no—
176C2×C4—3322no—
177C2×C4—3322no—
178C2×C4#1458176211yescharacteristic
179C2×C4#1458176512yes—
180C2×C4#1458177712yes—
181C2×C4#1458178011yescharacteristic
182C8—42no—
183C8—82no—
184C8—6641no—
185C22—21no—
186C22—21no—
187C22#1912761911yescharacteristic
188C22#1912797712yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—6642no—
193C4—6642no—
194C4—6642no—
195C4#1912787611yescharacteristic
196C4#1912788111yescharacteristic
197C2—22no—
198C2#2490869311yescharacteristic
199C2#2490873211yescharacteristic
200C2#2490877011yescharacteristic
subgroupG/H
centerC22#19127619
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1290C2
socleC22×C83#394
prime radicalC23×C83#121
hypercenter#1290D83
hypocenterC83#10517
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
106. C83#10517semidirect

Maximal subgroups

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

subgroupindex
#249188082
#249075822
#249061642
#249059762
C83×#12902
#1051783