Finite Group Databasebeta

← #28362076

Subgroups — #28362076

Order 13952.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#20295657C211yesmaximal, characteristic
2#20295362C212yesmaximal
3#20294965C211yesmaximal, characteristic
4#20294764C212yesmaximal
5#324×C109C211yesmaximal, characteristic
6#16812698—22no—
7#16812690—22no—
8#16812678—21no—
9#16812678C2212yes—
10#16812658—21no—
11C2×C4⋊Dic109C2211yescharacteristic
12#16812633—22no—
13#16812624—22no—
14#16812606—21no—
15#16812606—21no—
16#16812606C2211yescharacteristic
17C2×C4⋊C4×C109C2211yescharacteristic
18C22⋊C8×C109C2212yes—
19C2×Dic218—21no—
20C2×Dic218D412yes—
21C22×Dic109—21no—
22C22×Dic109—21no—
23C4⋊Dic109—21no—
24C4⋊Dic109—21no—
25C4⋊Dic109—21no—
26C4⋊Dic109—22no—
27C4⋊Dic109D412yes—
28#13182008—22no—
29#13182008—22no—
30C22⋊Dic109—22no—
31C4×Dic109—22no—
32C22×C4×C109D411yescharacteristic
33C22×C4×C109D411yescharacteristic
34C22×C4×C109C2311yescharacteristic
35C2×C8×C109—22no—
36C4⋊C4×C109—22no—
37C23×C109C2×D411yescharacteristic
38C2×C4×C109—21no—
39C2×C4×C109—21no—
40C2×C4×C109—21no—
41C2×C4×C109—41no—
42C2×C4×C109—41no—
43C2×C4×C109Q1612yes—
44C2×C4×C109C2×D412yes—
45C2×Dic109—22no—
46C2×Dic109—22no—
47C2×Dic109—41no—
48C2×Dic109—41no—
49C2×Dic109—42no—
50C2×Dic109—41no—
51C2×Dic109—41no—
52Dic218—42no—
53Dic218—81no—
54C8×C109—42no—
55C22×C109—21no—
56C22×C109—21no—
57C22×C109#12011yescharacteristic
58C22×C109C2×Q1611yescharacteristic
59C22×C109#13711yescharacteristic
60C4×C109—22no—
61C4×C109—22no—
62C4×C109—41no—
63Dic109—42no—
64Dic109—42no—
65Dic109—81no—
66Dic109—81no—
67C2×C109—21no—
68C2×C109—21no—
69C2×C109#45111yescharacteristic
70C2×C109#45411yescharacteristic
71C2×C109#45811yescharacteristic
72#1617—1091nomaximal, Sylow
73C109#161711yescharacteristic, complemented, Sylow
74#544—1091no—
75#484—1092no—
76#400—1091no—
77#328—1092no—
78#324D10911yescharacteristic
79C4⋊Q8—2182no—
80#125—2182no—
81C22⋊Q8—1092no—
82C22⋊Q8—2181no—
83#117—2181no—
84C2×C4⋊C4—1091no—
85C2×C4⋊C4C2×D10911yescharacteristic
86#107—2182no—
87#103—2182no—
88C22⋊C8C2×D10912yes—
89#95—1091no—
90#95—2181no—
91#95—2181no—
92C2×Q8—1092no—
93C2×Q8—2181no—
94C22×C4—2181no—
95C22×C4—2181no—
96C22×C4D43611yescharacteristic
97C22×C4D43611yescharacteristic
98C22×C4C22×D10911yescharacteristic
99C2×C8—22no—
100C4⋊C4—22no—
101C4⋊C4—1092no—
102C4⋊C4—2182no—
103C4⋊C4—2181no—
104C4⋊C4—2181no—
105C4⋊C4—2181no—
106C4⋊C4—2182no—
107C4⋊C4—2182no—
108C22⋊C4—2182no—
109C42—2182no—
110C23C2×D43611yescharacteristic
111Q8—8721no—
112Q8—4362no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—4361no—
119C2×C4—4361no—
120C2×C4—4362no—
121C2×C4—4361no—
122C2×C4—4361no—
123C2×C4—2182no—
124C2×C4—2182no—
125C2×C4Dic43612yes—
126C2×C4D4×D10912yes—
127C8—42no—
128C22—21no—
129C22—21no—
130C22#1681266911yescharacteristic
131C22C2×Dic43611yescharacteristic
132C22#1681273211yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—8721no—
137C4—8721no—
138C4—4362no—
139C4—4362no—
140C2—21no—
141C2—21no—
142C2#2029518411yescharacteristic
143C2#2029520111yescharacteristic
144C2#2029521711yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#324×C109C2
socleC22×C109#120
prime radicalC23×C109C2×D4
hypercenter#324D109
hypocenterC109#1617
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
73. C109#1617semidirect

Maximal subgroups

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

subgroupindex
#202956572
#202953622
#202949652
#202947642
#324×C1092
#1617109