Finite Group Databasebeta

← #35308912

Subgroups — #35308912

Order 21248.

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

normal subgroups only

This group has 382 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#24915738C211yesmaximal, characteristic
2#24907631C212yesmaximal
3#24907596C211yesmaximal, characteristic
4#24905345C212yesmaximal
5C83×#1295C211yesmaximal, characteristic
6C2×#14581726—22no—
7C2×#14581724—22no—
8C2×#14581703C2211yescharacteristic
9#19127635—22no—
10#19127634—22no—
11#19127633—22no—
12#19127571C2211yescharacteristic
13#19127567C2212yes—
14#19127463—22no—
15C2×#97×C83C2212yes—
16#382×C83C2211yescharacteristic
17C22×C83⋊C8—21no—
18C2×C4⋊Dic83—22no—
19C2×C4⋊Dic83—21no—
20C2×C4⋊Dic83—22no—
21C2×C4⋊Dic83D412yes—
22C2×C4⋊Dic83D412yes—
23C2×Dic83⋊C4—22no—
24C2×Dic83⋊C4—22no—
25#14581726—44no—
26#14581724—44no—
27#14581703—21no—
28#14581703Q812yes—
29C83⋊#95—22no—
30C83⋊#95—22no—
31C83⋊#95—22no—
32C22×C8×C83—22no—
33C2×C4⋊C4×C83D412yes—
34C2×C42×C83C2311yescharacteristic
35#97×C83—22no—
36#97×C83Q814yes—
37#95×C83—22no—
38C22×Dic83—22no—
39C22×Dic83—22no—
40C22×Dic83—41no—
41C2×C83⋊C8—22no—
42C2×C83⋊C8—41no—
43C2×C83⋊C8—41no—
44C4⋊Dic83—42no—
45C4⋊Dic83—42no—
46C4⋊Dic83—42no—
47C4⋊Dic83—42no—
48C4⋊Dic83—42no—
49C4⋊Dic83—82no—
50Dic83⋊C4—82no—
51Dic83⋊C4—82no—
52C22×C4×C83—22no—
53C22×C4×C83C2×D412yes—
54C22×C4×C83C2×D411yescharacteristic
55C2×C8×C83—24no—
56C2×C8×C83—24no—
57C2×C8×C83—24no—
58C4⋊C4×C83—42no—
59C42×C83C2×Q811yescharacteristic
60C42×C83C2×Q812yes—
61C42×C83#4111yescharacteristic
62C23×C83#12011yescharacteristic
63C2×C4×C83—22no—
64C2×C4×C83—21no—
65C2×C4×C83—21no—
66C2×C4×C83—22no—
67C2×C4×C83—42no—
68C2×C4×C83—42no—
69C2×C4×C83—42no—
70C2×C4×C83C22⋊Q812yes—
71C2×C4×C83C22⋊Q811yescharacteristic
72C2×C4×C83C4⋊Q812yes—
73C2×C4×C83C4⋊Q811yescharacteristic
74C2×Dic83—42no—
75C2×Dic83—42no—
76C2×Dic83—42no—
77C2×Dic83—42no—
78C2×Dic83—42no—
79C2×Dic83—42no—
80C2×Dic83—82no—
81C2×Dic83—81no—
82C8×C83—28no—
83C83⋊C8—42no—
84C22×C83#39511yescharacteristic
85C22×C83#45312yes—
86C22×C83#45411yescharacteristic
87C22×C83#45511yescharacteristic
88C22×C83#45612yes—
89C4×C83—22no—
90C4×C83—22no—
91C4×C83—21no—
92C4×C83—21no—
93C4×C83—82no—
94Dic83—82no—
95Dic83—82no—
96Dic83—161no—
97#10585—831nomaximal, Sylow
98C2×C83#165611yescharacteristic
99C2×C83#166112yes—
100C2×C83#166311yescharacteristic
101C2×C83#206012yes—
102C2×C83#206111yescharacteristic
103#2845—831no—
104#1847—832no—
105#1836—831no—
106#1295—832no—
107#1295D8311yescharacteristic
108C83#1058511yescharacteristic, complemented, Sylow
109C2×#107—1662no—
110C2×#106—1662no—
111C2×#97—831no—
112C2×#97C2×D8312yes—
113#398—1662no—
114#398—1662no—
115#398—1662no—
116#384—831no—
117#382—832no—
118#382C2×D8311yescharacteristic
119#340—1662no—
120C22×C8—22no—
121C22×C8—1661no—
122C2×C4⋊C4—832no—
123C2×C4⋊C4—832no—
124C2×C4⋊C4—1662no—
125C2×C4⋊C4—1661no—
126C2×C4⋊C4—1662no—
127C2×C4⋊C4—1662no—
128C2×C4⋊C4—1662no—
129C2×C4⋊C4D33212yes—
130C2×C42C22×D8311yescharacteristic
131#107—3324no—
132#106—3324no—
133#97—22no—
134#97—832no—
135#97—1661no—
136#97Dic16614yes—
137#95—22no—
138#95—1662no—
139#95—1662no—
140#95—1662no—
141C22×C4—22no—
142C22×C4—3321no—
143C22×C4—1662no—
144C22×C4—1662no—
145C22×C4D4×D8312yes—
146C22×C4C2×D33211yescharacteristic
147C2×C8—24no—
148C2×C8—24no—
149C2×C8—24no—
150C2×C8—3321no—
151C2×C8—3321no—
152C2×C8—1662no—
153C4⋊C4—42no—
154C4⋊C4—3322no—
155C4⋊C4—3322no—
156C4⋊C4—3322no—
157C4⋊C4—3322no—
158C4⋊C4—3322no—
159C4⋊C4—6642no—
160C4⋊C4—6642no—
161C4⋊C4—6642no—
162C42Q8×D8311yescharacteristic
163C42C2×Dic16612yes—
164C42#1305058911yescharacteristic
165C23#1458176211yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—3322no—
174C2×C4—3322no—
175C2×C4—3322no—
176C2×C4—3322no—
177C2×C4—3322no—
178C2×C4—3322no—
179C2×C4—6642no—
180C2×C4—6641no—
181C2×C4#1458176912yes—
182C2×C4#1458177211yescharacteristic
183C2×C4#1458179112yes—
184C2×C4#1458179211yescharacteristic
185C8—28no—
186C8—3322no—
187C22#1912762211yescharacteristic
188C22#1912787012yes—
189C22#1912787611yescharacteristic
190C22#1912788111yescharacteristic
191C22#1912788512yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—13281no—
198C4—6642no—
199C4—6642no—
200C2#2490675811yescharacteristic
201C2#2490678312yes—
202C2#2490679211yescharacteristic
203C2#2490880712yes—
204C2#2490881411yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1295C2
socle, prime radicalC23×C83#120
hypercenter#1295D83
hypocenterC83#10585
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
108. C83#10585semidirect

Maximal subgroups

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

subgroupindex
#249157382
#249076312
#249075962
#249053452
C83×#12952
#1058583