Finite Group Databasebeta

← #35301926

Subgroups — #35301926

Order 21248.

384 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 99 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#24906181C212yesmaximal
3#24906101C211yesmaximal, characteristic
4#24905334C212yesmaximal
5C83×#2987C211yesmaximal, characteristic
6C2×#14581792C2211yescharacteristic
7#19128071—22no—
8#19128053C414yes—
9#19127758C2212yes—
10#19127709—22no—
11C4×#13050574C2211yescharacteristic
12#19127448—24no—
13#19127443—22no—
14#533×C83C2211yescharacteristic
15#446×C83—24no—
16#433×C83—22no—
17#432×C83C2212yes—
18C22×Dic166—21no—
19C2×#13050574—21no—
20#14581792—22no—
21#14581792—21no—
22#14581792C2×C412yes—
23C2×C4⋊Dic83—22no—
24C4⋊(C83⋊C8)—22no—
25#14581715—28no—
26C22⋊(C83⋊C8)—22no—
27#14581703—21no—
28#14581703—22no—
29C4×C83⋊C8C2×C412yes—
30C4⋊Q8×C83C2×C412yes—
31#125×C83D412yes—
32C22⋊Q8×C83—22no—
33C4×Q8×C83—22no—
34#117×C83D412yes—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—24no—
37C4⋊C8×C83D414yes—
38C22⋊C8×C83—22no—
39#97×C83—22no—
40#97×C83—22no—
41C4×C8×C83—22no—
42C2×Dic166—22no—
43C2×Dic166—44no—
44C2×Dic166—41no—
45C22×Dic83—41no—
46#13050574—42no—
47C2×C83⋊C8—22no—
48C2×C83⋊C8—42no—
49C4⋊Dic83—24no—
50C4⋊Dic83—42no—
51C2×Q8×C83—22no—
52C22×C4×C83C2×D411yescharacteristic
53C22×C4×C83#4112yes—
54C2×C8×C83—24no—
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—44no—
77C83⋊C8—42no—
78C83⋊C8—82no—
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#2987D8311yescharacteristic
94#1556—832no—
95#1537—831no—
96#1291—832no—
97C83#942211yescharacteristic, complemented, Sylow
98#533C2×D8311yescharacteristic
99C2×C4⋊Q8—831no—
100#491—1662no—
101#487—834no—
102#446—24no—
103#433—22no—
104#432—832no—
105#432C2×D8312yes—
106#419—1662no—
107C4×M16—831no—
108#332—1664no—
109#330—1662no—
110C22×Q8—1661no—
111C2×M16—1661no—
112C4⋊Q8—832no—
113C4⋊Q8—1662no—
114C4⋊Q8—1661no—
115C4⋊Q8C4×D8312yes—
116#125D33212yes—
117C22⋊Q8—22no—
118C4×Q8—22no—
119#117C22⋊D8312yes—
120C2×C4⋊C4—1662no—
121C2×C42C22×D8311yescharacteristic
122C4⋊C8—24no—
123C4⋊C8—1662no—
124C4⋊C8C22⋊D8314yes—
125#103—1668no—
126C22⋊C8—22no—
127C22⋊C8—1662no—
128#97—22no—
129#97—22no—
130#97—1662no—
131#97—1661no—
132C4×C8—22no—
133C4×C8—832no—
134C2×Q8—22no—
135C2×Q8—3324no—
136C2×Q8—3321no—
137C2×Q8—1662no—
138C22×C4—3321no—
139C22×C4C2×C22⋊D8311yescharacteristic
140C22×C4#1305059012yes—
141M16—3322no—
142C2×C8—24no—
143C2×C8—3322no—
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
153C42C2×C22⋊D8312yes—
154C42C2×D33211yescharacteristic
155C23#1458177511yescharacteristic
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×C4C4×C22⋊D8312yes—
166C2×C4#1458176111yescharacteristic
167C2×C4#1458176612yes—
168C8—44no—
169C8—3322no—
170C8—6642no—
171C22—21no—
172C22—22no—
173C22#1912758011yescharacteristic
174C4—21no—
175C4—22no—
176C4—22no—
177C4—44no—
178C4—6642no—
179C4#1912787412yes—
180C2—41no—
181C2#2490786611yescharacteristic
182C2#2490793612yes—
subgroupG/H
centerC22#19127580
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2987C2
socleC22×C83#386
prime radicalC23×C83#123
cosocleC2×C42×C83C23
hypercenter#2987D83
hypocenterC83#9422
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2987

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
#249061812
#249061012
#249053342
C83×#29872
#942283