Finite Group Databasebeta

← #35307508

Subgroups — #35307508

Order 21248.

400 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 97 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#24915826C211yesmaximal, characteristic
2#24908440C211yesmaximal, characteristic
3#24906028C212yesmaximal
4#24905322C212yesmaximal
5C83×#1276C211yesmaximal, characteristic
6#19128258C2211yescharacteristic
7C2×#14581784—21no—
8#19127725C2211yescharacteristic
9#19127599—24no—
10#19127571—21no—
11#19127567C2212yes—
12#19127461—21no—
13#19127461—21no—
14#19127439—24no—
15#431×C83C2212yes—
16C43×C83C2211yescharacteristic
17C2×#13050574—21no—
18#14581792Q812yes—
19#14581784—21no—
20#14581784—42no—
21#14581784—42no—
22#14581771—22no—
23C4×Dic166—22no—
24#14581751—21no—
25C2×C4⋊Dic83—24no—
26C2×C4⋊Dic83—22no—
27C2×Dic83⋊C4—24no—
28C4⋊(C83⋊C8)—22no—
29C83⋊#95—22no—
30C83⋊#95D414yes—
31C2×C42×C83—22no—
32C2×C42×C83D411yescharacteristic
33C2×C42×C83D411yescharacteristic
34C2×C42×C83C2311yescharacteristic
35C4⋊C8×C83—22no—
36C22⋊C8×C83—22no—
37C4×C8×C83—22no—
38C2×Dic166—22no—
39C22×Dic83—24no—
40#13050574—41no—
41#13050574—41no—
42C2×C83⋊C8—41no—
43C4⋊Dic83—22no—
44C4⋊Dic83—22no—
45C4⋊Dic83—48no—
46C4⋊Dic83—42no—
47C4⋊Dic83—42no—
48Dic83⋊C4—48no—
49Dic83⋊C4—42no—
50C22⋊Dic83—41no—
51C4×Dic83—41no—
52C22×C4×C83—21no—
53C22×C4×C83—21no—
54C22×C4×C83C2×D412yes—
55C22×C4×C83C2×D411yescharacteristic
56C2×C8×C83—42no—
57C42×C83—21no—
58C42×C83—21no—
59C42×C83—44no—
60C42×C83SD1612yes—
61C42×C83Q1612yes—
62C42×C83C2×Q811yescharacteristic
63C42×C83#4111yescharacteristic
64C42×C83#4112yes—
65C23×C83#12011yescharacteristic
66C2×C4×C83—24no—
67C2×C4×C83—22no—
68C2×C4×C83—22no—
69C2×C4×C83—42no—
70C2×C4×C83—42no—
71C2×C4×C83C22⋊Q812yes—
72C2×C4×C83C22⋊Q811yescharacteristic
73C2×C4×C83#12412yes—
74C2×C4×C83#12411yescharacteristic
75C2×C4×C83C2×SD1611yescharacteristic
76C2×C4×C83C2×Q1611yescharacteristic
77C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
78C2×C4×C83#13711yescharacteristic
79C2×Dic83—48no—
80C2×Dic83—42no—
81C2×Dic83—44no—
82Dic166—82no—
83C8×C83—82no—
84C83⋊C8—81no—
85C22×C83—22no—
86C22×C83#39311yescharacteristic
87C22×C83#45011yescharacteristic
88C22×C83#45111yescharacteristic
89C4×C83—24no—
90C4×C83—22no—
91C4×C83—22no—
92C4×C83—42no—
93C4×C83#47511yescharacteristic
94C4×C83#47711yescharacteristic
95C4×C83#48711yescharacteristic
96C4×C83#48911yescharacteristic
97Dic83—84no—
98Dic83—82no—
99#10365—831nomaximal, Sylow
100C2×C83—21no—
101C2×C83—21no—
102C2×C83#202411yescharacteristic
103C2×C83#203112yes—
104#2859—831no—
105#1994—831no—
106#1518—832no—
107#1286—832no—
108#1276D8311yescharacteristic
109C83#1036511yescharacteristic, complemented, Sylow
110#533—831no—
111C2×#125—1661no—
112#431C2×D8312yes—
113#423—831no—
114#389—1664no—
115#384—1661no—
116#382—832no—
117C43C2×D8311yescharacteristic
118#339—1661no—
119#339—1661no—
120#328—1664no—
121C2×M16—1661no—
122C4⋊Q8—832no—
123#125—3322no—
124#125—3322no—
125#125—1661no—
126C22⋊Q8—1662no—
127C4×Q8—1662no—
128#117—1661no—
129C2×C4⋊C4—1664no—
130C2×C4⋊C4—1664no—
131C2×C4⋊C4—1662no—
132C2×C42—22no—
133C2×C42D33211yescharacteristic
134C2×C42D33211yescharacteristic
135C2×C42C22×D8311yescharacteristic
136C4⋊C8—22no—
137C4⋊C8—1662no—
138C22⋊C8—22no—
139C4×C8—22no—
140#95—834no—
141#95—1662no—
142C2×Q8—1662no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1664no—
146C22×C4D4×D8312yes—
147C22×C4C2×D33211yescharacteristic
148M16—3321no—
149M16—3321no—
150C2×C8—42no—
151C2×C8—3321no—
152C4⋊C4—3328no—
153C4⋊C4—3328no—
154C4⋊C4—3322no—
155C4⋊C4—3322no—
156C4⋊C4—3322no—
157C4⋊C4—1662no—
158C4⋊C4—1662no—
159C22⋊C4—3321no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—3321no—
164C42#1305057912yes—
165C42Dic33212yes—
166C42Q8×D8311yescharacteristic
167C42#1305058911yescharacteristic
168C42#1305059012yes—
169C23#1458176211yescharacteristic
170Q8—6642no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—3328no—
177C2×C4—3324no—
178C2×C4—3322no—
179C2×C4#1458177012yes—
180C2×C4#1458177211yescharacteristic
181C2×C4#1458177812yes—
182C2×C4#1458178011yescharacteristic
183C2×C4C2×#1305057911yescharacteristic
184C2×C4C2×Dic33211yescharacteristic
185C2×C4#1458182011yescharacteristic
186C2×C4#1458182511yescharacteristic
187C8—82no—
188C8—6641no—
189C22—22no—
190C22#1912761411yescharacteristic
191C22#1912785411yescharacteristic
192C22#1912785911yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—6644no—
198C4—6642no—
199C4#1912798711yescharacteristic
200C4#1912799711yescharacteristic
201C4#1912805211yescharacteristic
202C4#1912806111yescharacteristic
203C2—21no—
204C2—21no—
205C2#2490860511yescharacteristic
206C2#2490863612yes—
subgroupG/H
centerC22#19127614
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1276C2
socleC22×C83#393
prime radicalC23×C83#120
hypercenter#1276D83
hypocenterC83#10365
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
109. C83#10365semidirect

Maximal subgroups

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

subgroupindex
#249158262
#249084402
#249060282
#249053222
C83×#12762
#1036583