Finite Group Databasebeta

← #14581021

Subgroups — #14581021

Order 2624.

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

normal subgroups only

This group has 214 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#13050159C212yesmaximal, complemented
2#13050155C211yesmaximal, characteristic, complemented
3#13050154C212yesmaximal, complemented
4#13050147C212yesmaximal
5#13050144C211yesmaximal, characteristic, complemented
6#13050143C211yesmaximal, characteristic, complemented
7#13050129C211yesmaximal, characteristic, complemented
8C4×C22⋊D41C211yesmaximal, characteristic
9#13050123C212yesmaximal, complemented
10#13050122C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×C41C211yesmaximal, characteristic, complemented
12C22×C4×C41C2212yes—
13C22×C4×C41C2211yescharacteristic
14C2×C22⋊D41C2211yescharacteristic
15C2×C4×D41C2211yescharacteristic
16C2×Dic82C2211yescharacteristic
17C4⋊C4×C41C2211yescharacteristic
18C4⋊C4×C41C2211yescharacteristic
19C4⋊C4×C41C2212yes—
20C22⋊Dic41C2211yescharacteristic
21C22⋊Dic41C2212yes—
22#10620281C2212yes—
23#10620281C2211yescharacteristic
24#10620281C2212yes—
25C4⋊Dic41C2211yescharacteristic
26C4⋊Dic41C2212yes—
27C4⋊Dic41C2212yes—
28#10620279C2211yescharacteristic
29#10620279C2212yes—
30#10620279C2212yes—
31#10620279C2212yes—
32C4×Dic41C2212yes—
33C4×Dic41C2212yes—
34C4×Dic41C2211yescharacteristic
35C23×C41C2311yescharacteristic
36C22×D41C2311yescharacteristic
37C2×C4×C41—24no—
38C2×C4×C41—22no—
39C2×C4×C41C2312yes—
40C2×C4×C41C2311yescharacteristic
41C2×C4×C41C2312yes—
42C2×C4×C41C2311yescharacteristic
43C22⋊D41—22no—
44C2×Dic41C2311yescharacteristic
45C2×Dic41C2311yescharacteristic
46C2×Dic41C2311yescharacteristic
47C2×Dic41C2312yes—
48C2×Dic41C2312yes—
49C4×D41—22no—
50Dic82—22no—
51C22×C41—21no—
52C22×C41—21no—
53C22×C41#4112yes—
54C22×C41C2411yescharacteristic
55C2×D41—21no—
56C2×D41—21no—
57C2×D41—21no—
58C4×C41—22no—
59C4×C41—22no—
60C4×C41—21no—
61C4×C41#4112yes—
62Dic41—22no—
63Dic41—21no—
64Dic41—21no—
65Dic41—21no—
66Dic41—22no—
67C2×C41—22no—
68C2×C41C2×#4111yescharacteristic
69C2×C41C2×#4111yescharacteristic
70C2×C412−1+411yescharacteristic
71D41—41no—
72#552—411nomaximal, Sylow
73C41#55211yescharacteristic, complemented, Sylow
74#126—412no—
75#125—412no—
76#125—411no—
77#123—412no—
78C22⋊Q8—411no—
79C22⋊Q8—411no—
80C4×Q8—411no—
81C4×D4—411no—
82#117—412no—
83#117—411no—
84C2×C4⋊C4D4111yescharacteristic, complemented
85C2×Q8—411no—
86C2×D4—411no—
87C22×C4—411no—
88C22×C4C2×D4112yes—
89C22×C4C2×D4111yescharacteristic
90C4⋊C4—412no—
91C4⋊C4—411no—
92C4⋊C4—412no—
93C4⋊C4—411no—
94C4⋊C4—412no—
95C4⋊C4—412no—
96C4⋊C4—412no—
97C4⋊C4C2×D4111yescharacteristic
98C4⋊C4C2×D4111yescharacteristic
99C4⋊C4C2×D4112yes—
100C22⋊C4—411no—
101C22⋊C4—412no—
102C22⋊C4—412no—
103C22⋊C4—411no—
104C22⋊C4—412no—
105C42—412no—
106C42—412no—
107C42—411no—
108C23—411no—
109C23C22×D4111yescharacteristic
110Q8—822no—
111D4—822no—
112C2×C4—24no—
113C2×C4—22no—
114C2×C4—411no—
115C2×C4—411no—
116C2×C4—412no—
117C2×C4—412no—
118C2×C4—411no—
119C2×C4—822no—
120C2×C4C22×D4112yes—
121C2×C4C22×D4112yes—
122C2×C4C22×D4111yescharacteristic
123C2×C4C22×D4111yescharacteristic
124C22—21no—
125C22—21no—
126C22—821no—
127C22—821no—
128C22—821no—
129C22#1062030812yes—
130C22C23×D4111yescharacteristic
131C4—22no—
132C4—22no—
133C4—21no—
134C4—821no—
135C4—821no—
136C4—822no—
137C4—821no—
138C4—822no—
139C4#1062030612yes—
140C2—22no—
141C2—1641no—
142C2C2×#1062030811yescharacteristic
143C2C2×#1062030611yescharacteristic
144C2#1305021211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
FittingC2×C4⋊C4×C41C2
prime radicalC2×C22⋊D41C22
hypercenterC2×C4⋊C4D41
hypocenterC41#552
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13050159C2semidirect
2. #13050155C2semidirect
3. #13050154C2semidirect
5. #13050144C2semidirect
6. #13050143C2semidirect
7. #13050129C2semidirect
9. #13050123C2semidirect
10. #13050122C2semidirect
11. C2×C4⋊C4×C41C2semidirect
73. C41#552semidirect
84. C2×C4⋊C4D41semidirect

Maximal subgroups

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

subgroupindex
#130501592
#130501552
#130501542
#130501472
#130501442
#130501432
#130501292
C4×C22⋊D412
#130501232
#130501222
C2×C4⋊C4×C412
#55241