Finite Group Databasebeta

← #35307140

Subgroups — #35307140

Order 21248.

528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 113 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#24918411C212yesmaximal
2#24908440C211yesmaximal, characteristic
3#24906144C212yesmaximal
4#24905296C211yesmaximal, characteristic
5C83×#2862C211yesmaximal, characteristic
6#19128258C2211yescharacteristic
7#19128080—22no—
8#19128051—22no—
9#19127908—24no—
10#19127857—24no—
11#19127754C2212yes—
12#19127725C2211yescharacteristic
13#19127461—22no—
14#19127450—24no—
15C2×C4⋊Q8×C83C2212yes—
16#391×C83—24no—
17#382×C83—22no—
18C43×C83C2211yescharacteristic
19C2×#13050580—28no—
20C2×#13050574—21no—
21#14581792D412yes—
22#14581784—21no—
23#14581771—22no—
24C4×Dic166—22no—
25#14581751—21no—
26C4⋊(C83⋊C8)—22no—
27C4⋊(C83⋊C8)D414yes—
28#14581716—28no—
29C22⋊(C83⋊C8)—22no—
30C4×C83⋊C8—22no—
31C22×Q8×C83D414yes—
32C4⋊Q8×C83—22no—
33C4⋊Q8×C83—22no—
34C4⋊Q8×C83—22no—
35C4⋊Q8×C83—22no—
36C2×C4⋊C4×C83—22no—
37C2×C4⋊C4×C83—22no—
38C2×C42×C83—22no—
39C2×C42×C83D412yes—
40C2×C42×C83C2311yescharacteristic
41#95×C83—28no—
42C2×Dic166—22no—
43#13050580—88no—
44#13050574—42no—
45C2×C83⋊C8—24no—
46C2×C83⋊C8—41no—
47C4⋊Dic83—22no—
48C4⋊Dic83—22no—
49Dic83⋊C4—42no—
50C22⋊Dic83—41no—
51C4×Dic83—41no—
52C2×Q8×C83—24no—
53C2×Q8×C83—24no—
54C2×Q8×C83—48no—
55C22×C4×C83—22no—
56C22×C4×C83—24no—
57C22×C4×C83C2×D412yes—
58C22×C4×C83C2×D411yescharacteristic
59C4⋊C4×C83—42no—
60C4⋊C4×C83—42no—
61C4⋊C4×C83—42no—
62C4⋊C4×C83—42no—
63C42×C83—22no—
64C42×C83—44no—
65C42×C83Q1614yescomplemented
66C42×C83C2×D411yescharacteristic
67C42×C83C2×D412yes—
68C42×C83#4111yescharacteristic
69C23×C83#12011yescharacteristic
70Q8×C83—48no—
71Q8×C83—84no—
72C2×C4×C83—24no—
73C2×C4×C83—24no—
74C2×C4×C83—44no—
75C2×C4×C83—48no—
76C2×C4×C83—44no—
77C2×C4×C83#12012yes—
78C2×C4×C83#12111yescharacteristic
79C2×C4×C83#12112yes—
80C2×C4×C83#12711yescharacteristic
81C2×C4×C83C2×Q1612yes—
82C2×C4×C83#13712yes—
83C2×Dic83—42no—
84Dic166—44no—
85C83⋊C8—44no—
86C83⋊C8—81no—
87C22×C83—22no—
88C22×C83#39211yescharacteristic
89C22×C83#45112yes—
90C4×C83—22no—
91C4×C83—44no—
92C4×C83—84no—
93C4×C83#45514yes—
94C4×C83#46212yes—
95C4×C83#49411yescharacteristic
96C4×C83#49711yescharacteristic
97Dic83—82no—
98#10297—831nomaximal, Sylow
99C2×C83—22no—
100C2×C83#200412yes—
101C2×C83#201611yescharacteristic
102#3209—832no—
103#2862D8311yescharacteristic
104#1994—831no—
105#1548—832no—
106#1276—831no—
107C83#1029711yescharacteristic, complemented, Sylow
108#533—831no—
109C2×C4⋊Q8C2×D8312yes—
110#494—1662no—
111#487—1662no—
112#462—1664no—
113#451—1664no—
114#431—832no—
115#423—831no—
116#391—24no—
117#382—22no—
118C43C2×D8311yescharacteristic
119#339—1662no—
120#333—1664no—
121C22×Q8C22⋊D8314yes—
122C2×Q16—1668no—
123C2×M16—1661no—
124C4⋊Q8—22no—
125C4⋊Q8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8—832no—
129#125—1661no—
130C22⋊Q8—1662no—
131C4×Q8—1662no—
132#117—1661no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C42—22no—
136C2×C42C22⋊D8312yes—
137C2×C42C22×D8311yescharacteristic
138C4⋊C8—834no—
139C4⋊C8—1662no—
140#103—1668no—
141C22⋊C8—1662no—
142C4×C8—1662no—
143#95—28no—
144C2×Q8—24no—
145C2×Q8—24no—
146C2×Q8—48no—
147C2×Q8—1662no—
148C22×C4—22no—
149C22×C4—24no—
150C22×C4C2×C22⋊D8312yes—
151C22×C4C2×C22⋊D8311yescharacteristic
152Q16—6648no—
153M16—3322no—
154C2×C8—3321no—
155C2×C8—1664no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—3322no—
161C4⋊C4—1662no—
162C4⋊C4—1662no—
163C22⋊C4—3321no—
164C42—22no—
165C42—44no—
166C42—3321no—
167C42#1305058014yescomplemented
168C42D4×D8311yescharacteristic
169C42D4×D8312yes—
170C42#1305058911yescharacteristic
171C23#1458176111yescharacteristic
172Q8—48no—
173Q8—84no—
174Q8—3324no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—44no—
178C2×C4—48no—
179C2×C4—44no—
180C2×C4—3322no—
181C2×C4#1458176012yes—
182C2×C4#1458176311yescharacteristic
183C2×C4#1458176412yes—
184C2×C4#1458178811yescharacteristic
185C2×C4C2×#1305058012yes—
186C2×C4#1458182312yes—
187C8—3324no—
188C8—6641no—
189C22—22no—
190C22#1912760911yescharacteristic
191C22#1912785712yes—
192C4—22no—
193C4—44no—
194C4—84no—
195C4—6642no—
196C4#1912787814yes—
197C4#1912790812yes—
198C4#1912808011yescharacteristic
199C4#1912809311yescharacteristic
200C2—22no—
201C2#2490849212yes—
202C2#2490856311yescharacteristic
subgroupG/H
centerC22#19127609
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2862C2
socleC22×C83#392
prime radicalC23×C83#120
hypercenter#2862D83
hypocenterC83#10297
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

Complements

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

NH ≅ G/Ntype
65. C42×C83Q16semidirect
107. C83#10297semidirect
167. C42#13050580semidirect

Maximal subgroups

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

subgroupindex
#249184112
#249084402
#249061442
#249052962
C83×#28622
#1029783