Finite Group Databasebeta

← #28362343

Subgroups — #28362343

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#20295436C212yesmaximal, complemented
2#20295421C211yesmaximal, characteristic
3#20294768C212yesmaximal, complemented
4#20294766C211yesmaximal, characteristic
5#563×C109C211yesmaximal, characteristic
6C2×#13182019—21no—
7C2×#13182017—21no—
8#16812699C2211yescharacteristic
9#16812632—22no—
10#16812630—22no—
11#16812610C2212yes—
12#16812610C2211yescharacteristic
13C4⋊Q8×C109—21no—
14#126×C109—22no—
15#125×C109C2212yes—
16#124×C109C2211yescharacteristic
17#123×C109—21no—
18C22⋊Q8×C109—22no—
19C2×Dic218—21no—
20#13182019—42no—
21#13182017—42no—
22C2×#11724784—22no—
23C2×#11724784—21no—
24C4⋊Dic109—22no—
25C2×Q8×C109—21no—
26C2×Q8×C109D411yescharacteristic
27C2×D4×C109D411yescharacteristic
28C22×C4×C109—21no—
29C4⋊C4×C109—22no—
30C4⋊C4×C109—22no—
31C4⋊C4×C109—22no—
32C4⋊C4×C109D412yes—
33C4⋊C4×C109D412yes—
34C22⋊C4×C109—22no—
35C22⋊C4×C109—21no—
36C22⋊C4×C109—22no—
37C42×C109—21no—
38C42×C109C2311yescharacteristic
39C23×C109—21no—
40Q8×C109—41no—
41Q8×C109—81no—
42D4×C109—41no—
43C2×C4×C109—22no—
44C2×C4×C109—21no—
45C2×C4×C109—22no—
46C2×C4×C109—81no—
47C2×C4×C109C2×D412yes—
48C2×C4×C109C2×D411yescharacteristic
49C2×Dic109—41no—
50Dic218—41no—
51Dic218—41no—
52#11724784—24no—
53#11724784—22no—
54C22×C109—41no—
55C22×C109—42no—
56C22×C109#12011yescharacteristic
57C4×C109—21no—
58C4×C109—22no—
59C4×C109—42no—
60C4×C109—41no—
61C4×C109—42no—
62Dic109—81no—
63C2×C109—81no—
64C2×C109#45311yescharacteristic
65C2×C109#45612yes—
66#1660—1091nomaximal, Sylow
67C109#166011yescharacteristic, complemented, Sylow
68#563D10911yescharacteristic
69#501—1092no—
70#497—1091no—
71#330—1092no—
72#329—1091no—
73C2×Q16—2181no—
74C2×SD16—2181no—
75C4⋊Q8—21no—
76C4⋊Q8—1091no—
77#126—22no—
78#125C2×D10912yes—
79#124C2×D10911yescharacteristic
80#123—21no—
81C22⋊Q8—22no—
82#107—2182no—
83#106—2182no—
84#97—1092no—
85#97—1091no—
86C2×Q8—21no—
87C2×Q8—2181no—
88C2×Q8C22⋊D10911yescharacteristic
89C2×D4C22⋊D10911yescharacteristic
90C22×C4—21no—
91Q16—4362no—
92SD16—4362no—
93C2×C8—2182no—
94C2×C8—2181no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—2182no—
99C4⋊C4C22⋊D10912yes—
100C4⋊C4C22⋊D10912yes—
101C22⋊C4—22no—
102C22⋊C4—21no—
103C22⋊C4—22no—
104C42—21no—
105C42C22×D10911yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—81no—
109Q8—4361no—
110Q8—4361no—
111D4—41no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—81no—
116C2×C4—4361no—
117C2×C4C2×C22⋊D10912yes—
118C2×C4C2×C22⋊D10911yescharacteristic
119C8—2182no—
120C8—2184no—
121C22—41no—
122C22—42no—
123C22#1681266811yescharacteristic
124C4—21no—
125C4—22no—
126C4—42no—
127C4—41no—
128C4—42no—
129C4—8721no—
130C2—81no—
131C2#2029519411yescharacteristic
132C2#2029520912yes—
subgroupG/H
centerC22#16812668
commutator, cosocleC42×C109C23
FrattiniC42C22×D109
Fitting#563×C109C2
socleC22×C109#120
prime radicalC2×D4×C109D4
hypercenter#563D109
hypocenterC109#1660
LCSG ▷ C42×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #20295436C2semidirect
3. #20294768C2semidirect
67. C109#1660semidirect

Maximal subgroups

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

subgroupindex
#202954362
#202954212
#202947682
#202947662
#563×C1092
#1660109