Finite Group Databasebeta

← #35307151

Subgroups — #35307151

Order 21248.

576 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 111 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#24918604C212yesmaximal
2#24915861C211yesmaximal, characteristic
3#24906136C212yesmaximal
4#24905296C211yesmaximal, characteristic
5C83×#1994C211yesmaximal, characteristic
6C2×#14581792—22no—
7C2×#14581792C2212yes—
8#19128097—22no—
9#19128051—22no—
10#19128029—24no—
11#19127986—24no—
12#19127754C2212yes—
13#19127571—24no—
14#19127448—24no—
15#533×C83C2211yescharacteristic
16#423×C83C2211yescharacteristic
17C43×C83C2211yescharacteristic
18#339×C83—22no—
19C22×Dic166—22no—
20#14581792—22no—
21#14581792—22no—
22#14581792—22no—
23#14581792—22no—
24#14581792—44no—
25#14581792—44no—
26C2×C4⋊Dic83—28no—
27C2×C4⋊Dic83—22no—
28C2×C4⋊Dic83D414yes—
29#14581723—28no—
30C4⋊(C83⋊C8)D414yes—
31#14581716—28no—
32C22⋊(C83⋊C8)—22no—
33C4×C83⋊C8—22no—
34C2×M16×C83—21no—
35C4⋊Q8×C83D412yes—
36#125×C83—21no—
37C22⋊Q8×C83—22no—
38C4×Q8×C83—22no—
39#117×C83—21no—
40C2×C42×C83—22no—
41C2×C42×C83D412yes—
42C2×C42×C83C2311yescharacteristic
43C4⋊C8×C83—22no—
44C2×Dic166—42no—
45C2×Dic166—42no—
46C2×Dic166—44no—
47C2×Dic166—44no—
48C22×Dic83—24no—
49C2×C83⋊C8—24no—
50C4⋊Dic83—24no—
51C4⋊Dic83—24no—
52C4⋊Dic83—416no—
53C4⋊Dic83—42no—
54C4⋊Dic83—42no—
55C2×Q8×C83—22no—
56C22×C4×C83—22no—
57C22×C4×C83C2×D412yes—
58C22×C4×C83C2×D411yescharacteristic
59M16×C83—42no—
60C2×C8×C83—41no—
61C4⋊C4×C83—22no—
62C4⋊C4×C83—22no—
63C4⋊C4×C83—42no—
64C22⋊C4×C83—41no—
65C42×C83—28no—
66C42×C83—22no—
67C42×C83—41no—
68C42×C83SD1614yes—
69C42×C83C2×D412yes—
70C42×C83C2×D411yescharacteristic
71C42×C83#4111yescharacteristic
72C23×C83#12011yescharacteristic
73Q8×C83—44no—
74C2×C4×C83—28no—
75C2×C4×C83—24no—
76C2×C4×C83—24no—
77C2×C4×C83—42no—
78C2×C4×C83#12012yes—
79C2×C4×C83#12112yes—
80C2×C4×C83#12111yescharacteristic
81C2×C4×C83#12711yescharacteristic
82C2×C4×C83C2×SD1612yes—
83C2×C4×C83AGL(1,ℤ/8)12yes—
84C2×Dic83—44no—
85C2×Dic83—48no—
86Dic166—84no—
87Dic166—82no—
88Dic166—82no—
89C8×C83—81no—
90C83⋊C8—44no—
91C22×C83—22no—
92C22×C83#39211yescharacteristic
93C22×C83#45012yes—
94C4×C83—28no—
95C4×C83—22no—
96C4×C83—82no—
97C4×C83#45614yes—
98C4×C83#46012yes—
99C4×C83#49211yescharacteristic
100C4×C83#49611yescharacteristic
101Dic83—84no—
102#10299—831nomaximal, Sylow
103C2×C83—22no—
104C2×C83#200512yes—
105C2×C83#201411yescharacteristic
106#3229—832no—
107#2868—831no—
108#1994D8311yescharacteristic
109#1546—832no—
110#1276—831no—
111C83#1029911yescharacteristic, complemented, Sylow
112#533C2×D8311yescharacteristic
113C2×C4⋊Q8—832no—
114C2×C4⋊Q8—1662no—
115#498—1662no—
116#487—1662no—
117#483—1664no—
118#475—1664no—
119#431—832no—
120#423C2×D8311yescharacteristic
121#384—1664no—
122C43C2×D8311yescharacteristic
123#339—22no—
124#332—1664no—
125C22×Q8—1662no—
126C2×M16—21no—
127C4⋊Q8—3324no—
128C4⋊Q8—3324no—
129C4⋊Q8—1662no—
130C4⋊Q8—1662no—
131C4⋊Q8—1662no—
132C4⋊Q8—1662no—
133C4⋊Q8D33212yes—
134#125—21no—
135C22⋊Q8—22no—
136C4×Q8—22no—
137#117—21no—
138C2×C4⋊C4—834no—
139C2×C4⋊C4—1668no—
140C2×C4⋊C4—1662no—
141C2×C42—22no—
142C2×C42C22⋊D8312yes—
143C2×C42C22×D8311yescharacteristic
144#106—1668no—
145C4⋊C8—22no—
146C4⋊C8—834no—
147#103—1668no—
148C22⋊C8—1662no—
149C4×C8—1662no—
150C2×Q8—22no—
151C2×Q8—3322no—
152C2×Q8—3322no—
153C2×Q8—3324no—
154C2×Q8—3324no—
155C22×C4—22no—
156C22×C4—1664no—
157C22×C4D4×D8312yes—
158C22×C4C2×C22⋊D8311yescharacteristic
159M16—42no—
160C2×C8—41no—
161C2×C8—1664no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—33216no—
166C4⋊C4—3322no—
167C4⋊C4—3322no—
168C4⋊C4—1664no—
169C4⋊C4—1664no—
170C22⋊C4—41no—
171C42—28no—
172C42—22no—
173C42—41no—
174C42#1305057714yes—
175C42D4×D8312yes—
176C42C2×D33211yescharacteristic
177C42#1305059011yescharacteristic
178C23#1458176011yescharacteristic
179Q8—44no—
180Q8—6642no—
181Q8—6642no—
182Q8—6644no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—42no—
187C2×C4—3328no—
188C2×C4—3324no—
189C2×C4#1458176212yes—
190C2×C4#1458176512yes—
191C2×C4#1458176611yescharacteristic
192C2×C4#1458178811yescharacteristic
193C2×C4C2×#1305057712yes—
194C2×C4#1458181712yes—
195C8—81no—
196C8—3324no—
197C22—22no—
198C22#1912761011yescharacteristic
199C22#1912785112yes—
200C4—28no—
201C4—22no—
202C4—82no—
203C4—6644no—
204C4#1912788514yes—
205C4#1912790112yes—
206C4#1912807511yescharacteristic
207C4#1912809111yescharacteristic
208C2—22no—
209C2#2490849812yes—
210C2#2490855011yescharacteristic
subgroupG/H
centerC22#19127610
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1994C2
socleC22×C83#392
prime radicalC23×C83#120
hypercenter#1994D83
hypocenterC83#10299
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

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
#249186042
#249158612
#249061362
#249052962
C83×#19942
#1029983