Finite Group Databasebeta

← #28362355

Subgroups — #28362355

Order 13952.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#20295396C211yesmaximal, characteristic, complemented
2#20295385C212yesmaximal, complemented
3#20294768C211yesmaximal, characteristic, complemented
4#20294766C212yesmaximal, complemented
5#562×C109C211yesmaximal, characteristic
6#16812699C2211yescharacteristic
7#16812623—22no—
8#16812622—22no—
9#16812620—22no—
10#16812610C2211yescharacteristic
11#16812610C2212yes—
12#125×C109C2211yescharacteristic
13#124×C109C2212yes—
14#123×C109—22no—
15C22⋊Q8×C109—22no—
16#121×C109—22no—
17C2×Dic218—21no—
18C2×#11724784—22no—
19C2×#11724784—21no—
20C4⋊Dic109—22no—
21C2×Q8×C109D412yes—
22C2×D4×C109—22no—
23C2×D4×C109D412yes—
24C22×C4×C109—22no—
25C4⋊C4×C109—22no—
26C4⋊C4×C109—22no—
27C4⋊C4×C109D412yes—
28C22⋊C4×C109—22no—
29C22⋊C4×C109—22no—
30C22⋊C4×C109—22no—
31C42×C109C2311yescharacteristic
32C23×C109—22no—
33Q8×C109—42no—
34D4×C109—42no—
35D4×C109—82no—
36C2×C4×C109—22no—
37C2×C4×C109—22no—
38C2×C4×C109—82no—
39C2×C4×C109C2×D411yescharacteristic
40C2×C4×C109C2×D412yes—
41C2×Dic109—41no—
42Dic218—42no—
43#11724784—41no—
44#11724784—42no—
45C22×C109—42no—
46C22×C109—42no—
47C22×C109—42no—
48C22×C109#12011yescharacteristic
49C4×C109—21no—
50C4×C109—22no—
51C4×C109—42no—
52C4×C109—42no—
53Dic109—81no—
54C2×C109—82no—
55C2×C109#45411yescharacteristic
56C2×C109#45512yes—
57#1662—1091nomaximal, Sylow
58C109#166211yescharacteristic, complemented, Sylow
59#562D10911yescharacteristic
60#491—1091no—
61#489—1092no—
62#330—1091no—
63#329—1092no—
64C4⋊Q8—1091no—
65#125C2×D10911yescharacteristic
66#124C2×D10912yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—2182no—
71#103—2182no—
72#102—2182no—
73#97—1091no—
74#97—1092no—
75C2×Q8—2181no—
76C2×Q8C22⋊D10912yes—
77C2×D4—22no—
78C2×D4C22⋊D10912yes—
79C22×C4—22no—
80C2×C8—2182no—
81C2×C8—2181no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—2182no—
85C4⋊C4C22⋊D10912yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D10911yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—4362no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—4361no—
99C2×C4C2×C22⋊D10911yescharacteristic
100C2×C4C2×C22⋊D10912yes—
101C8—4361no—
102C8—4362no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1681266811yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—8721no—
112C2—82no—
113C2#2029519911yescharacteristic
114C2#2029520412yes—
subgroupG/H
centerC22#16812668
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting, prime radical#562×C109C2
socleC22×C109#120
hypercenter#562D109
hypocenterC109#1662
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #20295396C2semidirect
2. #20295385C2semidirect
3. #20294768C2semidirect
4. #20294766C2semidirect
58. C109#1662semidirect

Maximal subgroups

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

subgroupindex
#202953962
#202953852
#202947682
#202947662
#562×C1092
#1662109