Finite Group Databasebeta

← #35301924

Subgroups — #35301924

Order 21248.

384 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 95 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#24917845C211yesmaximal, characteristic
2#24916569C211yesmaximal, characteristic
3#24906179C212yesmaximal
4#24905336C212yesmaximal
5C83×#1537C211yesmaximal, characteristic
6C2×#14581792C2211yescharacteristic
7#19128071—22no—
8#19128053C414yes—
9#19127832—24no—
10#19127762—22no—
11#19127758C2212yes—
12#19127709—22no—
13C4×#13050574C2211yescharacteristic
14#19127446—24no—
15#533×C83C2211yescharacteristic
16#432×C83C2212yes—
17#330×C83—22no—
18C22×Dic166—21no—
19C2×#13050574—21no—
20#14581792—22no—
21#14581792—21no—
22#14581792C2×C412yes—
23C2×C4⋊Dic83—22no—
24C4⋊(C83⋊C8)—24no—
25C4⋊(C83⋊C8)D414yes—
26#14581715—28no—
27C22⋊(C83⋊C8)—22no—
28#14581703—22no—
29#14581703—21no—
30#14581703—22no—
31C4×C83⋊C8—22no—
32C4×C83⋊C8C2×C412yes—
33C4⋊Q8×C83C2×C412yes—
34#125×C83D412yes—
35C22⋊Q8×C83—22no—
36C4×Q8×C83—22no—
37#117×C83D412yes—
38C2×C42×C83C2311yescharacteristic
39C4⋊C8×C83—22no—
40C22⋊C8×C83—22no—
41#97×C83—22no—
42C2×Dic166—22no—
43C2×Dic166—44no—
44C2×Dic166—41no—
45C22×Dic83—41no—
46#13050574—42no—
47C2×C83⋊C8—22no—
48C2×C83⋊C8—24no—
49C4⋊Dic83—24no—
50C4⋊Dic83—42no—
51C2×Q8×C83—22no—
52C22×C4×C83C2×D411yescharacteristic
53C22×C4×C83#4112yes—
54C2×C8×C83—42no—
55C4⋊C4×C83—22no—
56C4⋊C4×C83—24no—
57C4⋊C4×C83C22⋊C414yes—
58C22⋊C4×C83—22no—
59C42×C83—22no—
60C42×C83C22×C411yescharacteristic
61C42×C83C2×D412yes—
62C42×C83C2×D411yescharacteristic
63C23×C83#12311yescharacteristic
64Q8×C83—82no—
65C2×C4×C83—22no—
66C2×C4×C83—24no—
67C2×C4×C83—42no—
68C2×C4×C83C2×C22⋊C411yescharacteristic
69C2×C4×C83C4×D412yes—
70C2×C4×C83#12011yescharacteristic
71C2×C4×C83#12112yes—
72C2×Dic83—42no—
73C2×Dic83—82no—
74Dic166—44no—
75Dic166—82no—
76C8×C83—82no—
77C83⋊C8—42no—
78C83⋊C8—44no—
79C22×C83—21no—
80C22×C83—22no—
81C22×C83#38611yescharacteristic
82C4×C83—21no—
83C4×C83—22no—
84C4×C83—22no—
85C4×C83—44no—
86C4×C83#45412yes—
87Dic83—82no—
88#9422—831nomaximal, Sylow
89C2×C83—41no—
90C2×C83#188811yescharacteristic
91C2×C83#190212yes—
92#3139—831no—
93#2987—831no—
94#1556—832no—
95#1537D8311yescharacteristic
96#1291—832no—
97C83#942211yescharacteristic, complemented, Sylow
98#533C2×D8311yescharacteristic
99C2×C4⋊Q8—831no—
100#491—1662no—
101#487—834no—
102#446—1664no—
103#433—1662no—
104#432—832no—
105#432C2×D8312yes—
106#419—1662no—
107C4×M16—831no—
108#332—1664no—
109#330—22no—
110C22×Q8—1661no—
111C2×M16—1661no—
112C4⋊Q8—832no—
113C4⋊Q8—1662no—
114C4⋊Q8—1661no—
115C4⋊Q8C4×D8312yes—
116#125C22⋊D8312yes—
117C22⋊Q8—22no—
118C4×Q8—22no—
119#117D33212yes—
120C2×C4⋊C4—1662no—
121C2×C42C22×D8311yescharacteristic
122C4⋊C8—22no—
123C4⋊C8—834no—
124C4⋊C8—1664no—
125#103—1668no—
126C22⋊C8—22no—
127C22⋊C8—1662no—
128#97—22no—
129#97—1662no—
130#97—1662no—
131#97—1661no—
132C4×C8—832no—
133C4×C8—1662no—
134C2×Q8—22no—
135C2×Q8—3324no—
136C2×Q8—3321no—
137C2×Q8—1662no—
138C22×C4—3321no—
139C22×C4C2×D33211yescharacteristic
140C22×C4#1305058912yes—
141M16—3322no—
142C2×C8—42no—
143C2×C8—1664no—
144C2×C8—1662no—
145C4⋊C4—24no—
146C4⋊C4—22no—
147C4⋊C4—3322no—
148C4⋊C4—1664no—
149C4⋊C4(C2×D83)⋊C414yes—
150C22⋊C4—22no—
151C42—22no—
152C42C2×C4×D8311yescharacteristic
153C42D4×D8312yes—
154C42C2×C22⋊D8311yescharacteristic
155C23#1458177611yescharacteristic
156Q8—82no—
157Q8—3324no—
158Q8—6642no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—42no—
162C2×C4—3322no—
163C2×C4—6642no—
164C2×C4C2×(C2×D83)⋊C411yescharacteristic
165C2×C4(C22⋊D83)⋊C412yes—
166C2×C4#1458176211yescharacteristic
167C2×C4#1458176412yes—
168C8—82no—
169C8—3322no—
170C8—3324no—
171C22—21no—
172C22—22no—
173C22#1912757811yescharacteristic
174C4—21no—
175C4—22no—
176C4—22no—
177C4—44no—
178C4—6642no—
179C4#1912787612yes—
180C2—41no—
181C2#2490786411yescharacteristic
182C2#2490793412yes—
subgroupG/H
centerC22#19127578
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1537C2
socleC22×C83#386
prime radicalC23×C83#123
cosocleC2×C42×C83C23
hypercenter#1537D83
hypocenterC83#9422
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
97. C83#9422semidirect

Maximal subgroups

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

subgroupindex
#249178452
#249165692
#249061792
#249053362
C83×#15372
#942283