Finite Group Databasebeta

← #27193270

Subgroups — #27193270

Order 13184.

172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#15692940C211yesmaximal, characteristic
2#20267698C211yesmaximal, characteristic
3C2×#101×C103C211yesmaximal, characteristic
4C2×#13110089—21no—
5C2×C4⋊Dic103C411yescharacteristic
6C2×C4×Dic103C411yescharacteristic
7#15692940—21no—
8#15692940C412yescomplemented
9C103⋊#95—21no—
10C103⋊#95—21no—
11C22×Q8×C103C2211yescharacteristic
12C2×M16×C103—21no—
13#101×C103—21no—
14#101×C103C412yescomplemented
15C22×Dic103—21no—
16C22×Dic103—21no—
17#13110089—22no—
18#13110089—41no—
19C2×C103⋊C8—41no—
20C4⋊Dic103—41no—
21C4×Dic103—41no—
22C2×Q8×C103—41no—
23C2×Q8×C103—41no—
24C2×Q8×C103C2×C411yescharacteristic
25C2×Q8×C103C2×C411yescharacteristic
26C2×Q8×C103D411yescharacteristic
27C2×Q8×C103Q811yescharacteristic
28C22×C4×C103C2×C411yescharacteristic
29C22×C4×C103D411yescharacteristic
30C22×C4×C103D411yescharacteristic
31M16×C103—22no—
32M16×C103—41no—
33C2×C8×C103—41no—
34C23×C103C22⋊C411yescharacteristic
35Q8×C103—41no—
36Q8×C103—41no—
37Q8×C103—41no—
38Q8×C103—41no—
39C2×C4×C103—21no—
40C2×C4×C103—21no—
41C2×C4×C103—21no—
42C2×C4×C103—21no—
43C2×C4×C103—21no—
44C2×C4×C103—21no—
45C2×C4×C103C4211yescharacteristic
46C2×C4×C103C22⋊C411yescharacteristic
47C2×C4×C103C22⋊C411yescharacteristic
48C2×C4×C103C4⋊C411yescharacteristic
49C2×C4×C103C4⋊C411yescharacteristic
50C2×C4×C103C4⋊C411yescharacteristic
51C2×Dic103—22no—
52C2×Dic103—41no—
53C2×Dic103—41no—
54C2×Dic103—42no—
55C2×Dic103—41no—
56C8×C103—42no—
57C103⋊C8—42no—
58C22×C103—21no—
59C22×C103—21no—
60C22×C103#9511yescharacteristic
61C22×C103#9911yescharacteristic
62C22×C103#9911yescharacteristic
63C4×C103—21no—
64C4×C103—21no—
65C4×C103—21no—
66C4×C103—21no—
67C4×C103—21no—
68C4×C103—21no—
69Dic103—42no—
70Dic103—81no—
71C2×C103—21no—
72C2×C103—21no—
73C2×C103#34211yescharacteristic
74C2×C103#35511yescharacteristic
75C2×C103#35611yescharacteristic
76#1394—1031nomaximal, Sylow
77C103#139411yescharacteristic, complemented, Sylow
78C2×#101—1031no—
79C2×#101D10311yescharacteristic
80#391—1031no—
81C22×Q8C2×D10311yescharacteristic
82C2×M16—21no—
83C2×M16—2061no—
84C2×C4⋊C4—1031no—
85C2×C42—1031no—
86#101—21no—
87#101—1032no—
88#101—2061no—
89#101Dic10312yescomplemented
90#95—2061no—
91#95—2061no—
92C2×Q8—41no—
93C2×Q8—41no—
94C2×Q8Dic20611yescharacteristic
95C2×Q8C4×D10311yescharacteristic
96C2×Q8C2×Dic10311yescharacteristic
97C2×Q8C22⋊D10311yescharacteristic
98C22×C4—2061no—
99C22×C4—2061no—
100C22×C4C4×D10311yescharacteristic
101C22×C4D41211yescharacteristic
102C22×C4C22⋊D10311yescharacteristic
103M16—22no—
104M16—41no—
105M16—4121no—
106M16—2062no—
107C2×C8—41no—
108C2×C8—4121no—
109C4⋊C4—4121no—
110C42—4121no—
111C23(C2×D103)⋊C411yescharacteristic
112Q8—41no—
113Q8—41no—
114Q8—41no—
115Q8—41no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—4122no—
123C2×C4—4121no—
124C2×C4—4121no—
125C2×C4—4121no—
126C2×C4—2062no—
127C2×C4C4×Dic10311yescharacteristic
128C2×C4(C2×D103)⋊C411yescharacteristic
129C2×C4C22⋊Dic10311yescharacteristic
130C2×C4Dic103⋊C411yescharacteristic
131C2×C4Dic103⋊C411yescharacteristic
132C2×C4C4⋊Dic10311yescharacteristic
133C8—42no—
134C8—4122no—
135C22—21no—
136C22—21no—
137C22C103⋊#9511yescharacteristic
138C22#1569293511yescharacteristic
139C22#1569293511yescharacteristic
140C4—21no—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—21no—
145C4—21no—
146C4—8241no—
147C4—4122no—
148C2—21no—
149C2—21no—
150C2#2026755711yescharacteristic
151C2#2026758711yescharacteristic
152C2#2026758911yescharacteristic
subgroupG/H
centerC22#15692935
commutatorC2×C4×C103C42
FrattiniC22×Q8C2×D103
FittingC2×#101×C103C2
socleC22×C103#99
prime radicalC23×C103C22⋊C4
cosocleC22×Q8×C103C22
hypercenterC2×#101D103
hypocenterC103#1394
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
8. #15692940C4semidirect
14. #101×C103C4semidirect
77. C103#1394semidirect
89. #101Dic103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929402
#202676982
C2×#101×C1032
#1394103