Finite Group Databasebeta

← #35307152

Subgroups — #35307152

Order 21248.

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

normal subgroups only

This group has 576 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#24918607C212yesmaximal
2#24908440C211yesmaximal, characteristic
3#24906135C212yesmaximal
4#24905296C211yesmaximal, characteristic
5C83×#2868C211yesmaximal, characteristic
6#19128258C2211yescharacteristic
7#19128097—22no—
8#19128053—22no—
9#19128031—24no—
10#19127983—24no—
11#19127754C2212yes—
12#19127725C2211yescharacteristic
13#19127461—22no—
14#19127447—24no—
15C2×C4⋊Q8×C83—22no—
16C2×C4⋊Q8×C83C2212yes—
17#384×C83—24no—
18C43×C83C2211yescharacteristic
19C2×#13050574—21no—
20#14581792D412yes—
21#14581784—21no—
22#14581771—22no—
23C4×Dic166—22no—
24#14581751—21no—
25#14581723—28no—
26C4⋊(C83⋊C8)—22no—
27C4⋊(C83⋊C8)D414yes—
28#14581715—28no—
29C22⋊(C83⋊C8)—22no—
30C4×C83⋊C8—22no—
31C22×Q8×C83—22no—
32C4⋊Q8×C83—22no—
33C4⋊Q8×C83—22no—
34C4⋊Q8×C83—22no—
35C4⋊Q8×C83—22no—
36C4⋊Q8×C83—44no—
37C4⋊Q8×C83—44no—
38C2×C4⋊C4×C83—28no—
39C2×C4⋊C4×C83—22no—
40C2×C4⋊C4×C83D414yes—
41C2×C42×C83—22no—
42C2×C42×C83D412yes—
43C2×C42×C83C2311yescharacteristic
44C2×Dic166—22no—
45#13050574—42no—
46C2×C83⋊C8—24no—
47C2×C83⋊C8—41no—
48C4⋊Dic83—22no—
49C4⋊Dic83—22no—
50Dic83⋊C4—42no—
51C22⋊Dic83—41no—
52C4×Dic83—41no—
53C2×Q8×C83—42no—
54C2×Q8×C83—42no—
55C2×Q8×C83—44no—
56C2×Q8×C83—44no—
57C22×C4×C83—22no—
58C22×C4×C83—24no—
59C22×C4×C83C2×D412yes—
60C22×C4×C83C2×D411yescharacteristic
61C4⋊C4×C83—24no—
62C4⋊C4×C83—24no—
63C4⋊C4×C83—416no—
64C4⋊C4×C83—42no—
65C4⋊C4×C83—42no—
66C42×C83—28no—
67C42×C83—22no—
68C42×C83SD1614yes—
69C42×C83C2×D411yescharacteristic
70C42×C83C2×D412yes—
71C42×C83#4111yescharacteristic
72C23×C83#12011yescharacteristic
73Q8×C83—84no—
74Q8×C83—82no—
75Q8×C83—82no—
76C2×C4×C83—28no—
77C2×C4×C83—24no—
78C2×C4×C83—24no—
79C2×C4×C83—44no—
80C2×C4×C83—48no—
81C2×C4×C83#12012yes—
82C2×C4×C83#12111yescharacteristic
83C2×C4×C83#12112yes—
84C2×C4×C83#12711yescharacteristic
85C2×C4×C83C2×SD1612yes—
86C2×C4×C83AGL(1,ℤ/8)12yes—
87C2×Dic83—42no—
88Dic166—44no—
89C83⋊C8—44no—
90C83⋊C8—81no—
91C22×C83—22no—
92C22×C83#39211yescharacteristic
93C22×C83#45012yes—
94C4×C83—28no—
95C4×C83—22no—
96C4×C83—84no—
97C4×C83#45614yes—
98C4×C83#46012yes—
99C4×C83#49211yescharacteristic
100C4×C83#49611yescharacteristic
101Dic83—82no—
102#10299—831nomaximal, Sylow
103C2×C83—22no—
104C2×C83#200512yes—
105C2×C83#201411yescharacteristic
106#3229—832no—
107#2868D8311yescharacteristic
108#1994—831no—
109#1546—832no—
110#1276—831no—
111C83#1029911yescharacteristic, complemented, Sylow
112#533—831no—
113C2×C4⋊Q8—22no—
114C2×C4⋊Q8C2×D8312yes—
115#498—1662no—
116#487—1662no—
117#483—1664no—
118#475—1664no—
119#431—832no—
120#423—831no—
121#384—24no—
122C43C2×D8311yescharacteristic
123#339—1662no—
124#332—1664no—
125C22×Q8—22no—
126C2×M16—1661no—
127C4⋊Q8—22no—
128C4⋊Q8—22no—
129C4⋊Q8—22no—
130C4⋊Q8—22no—
131C4⋊Q8—44no—
132C4⋊Q8—44no—
133C4⋊Q8—832no—
134#125—1661no—
135C22⋊Q8—1662no—
136C4×Q8—1662no—
137#117—1661no—
138C2×C4⋊C4—28no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4C22⋊D8314yes—
141C2×C42—22no—
142C2×C42C22⋊D8312yes—
143C2×C42C22×D8311yescharacteristic
144#106—1668no—
145C4⋊C8—834no—
146C4⋊C8—1662no—
147#103—1668no—
148C22⋊C8—1662no—
149C4×C8—1662no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—44no—
153C2×Q8—44no—
154C2×Q8—1662no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4C2×C22⋊D8312yes—
158C22×C4C2×C22⋊D8311yescharacteristic
159M16—3322no—
160C2×C8—3321no—
161C2×C8—1664no—
162C4⋊C4—24no—
163C4⋊C4—24no—
164C4⋊C4—416no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—3322no—
168C4⋊C4—1662no—
169C4⋊C4—1662no—
170C22⋊C4—3321no—
171C42—28no—
172C42—22no—
173C42—3321no—
174C42#1305057814yes—
175C42D4×D8311yescharacteristic
176C42D4×D8312yes—
177C42#1305058911yescharacteristic
178C23#1458176111yescharacteristic
179Q8—82no—
180Q8—82no—
181Q8—84no—
182Q8—3324no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—48no—
187C2×C4—44no—
188C2×C4—3322no—
189C2×C4#1458176012yes—
190C2×C4#1458176311yescharacteristic
191C2×C4#1458176412yes—
192C2×C4#1458178811yescharacteristic
193C2×C4C2×#1305057812yes—
194C2×C4#1458181812yes—
195C8—3324no—
196C8—6641no—
197C22—22no—
198C22#1912760911yescharacteristic
199C22#1912785212yes—
200C4—28no—
201C4—22no—
202C4—84no—
203C4—6642no—
204C4#1912788314yes—
205C4#1912789812yes—
206C4#1912807311yescharacteristic
207C4#1912808811yescharacteristic
208C2—22no—
209C2#2490849912yes—
210C2#2490855111yescharacteristic
subgroupG/H
centerC22#19127609
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#2868C2
socleC22×C83#392
prime radicalC23×C83#120
hypercenter#2868D83
hypocenterC83#10299
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2868

Complements

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

NH ≅ G/Ntype
111. C83#10299semidirect

Maximal subgroups

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

subgroupindex
#249186072
#249084402
#249061352
#249052962
C83×#28682
#1029983