Finite Group Databasebeta

← #27193274

Subgroups — #27193274

Order 13184.

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

normal subgroups only

This group has 162 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#20267765C211yesmaximal, characteristic
2#20267758C211yesmaximal, characteristic
3#413×C103C211yesmaximal, characteristic
4C2×#13110089C411yescharacteristic, complemented
5C22×C103⋊C8C411yescharacteristic, complemented
6#15692980—21no—
7#15692936—21no—
8#15692936C412yes—
9C22⋊(C103⋊C8)—21no—
10C22⋊(C103⋊C8)—21no—
11C2×#41×C103C2211yescharacteristic
12C2×M16×C103—21no—
13#101×C103C412yescomplemented
14#100×C103—21no—
15#13110089—41no—
16C2×C103⋊C8—21no—
17C2×C103⋊C8—21no—
18C2×C103⋊C8—41no—
19C4⋊Dic103—41no—
20C22⋊Dic103—22no—
21C4×Dic103—41no—
22#41×C103—41no—
23#41×C103—41no—
24C2×Q8×C103C2×C411yescharacteristic
25C2×D4×C103C2×C411yescharacteristic
26C2×D4×C103D411yescharacteristic
27C2×D4×C103Q811yescharacteristic
28C22×C4×C103C2×C411yescharacteristic
29C22×C4×C103D411yescharacteristic
30C22×C4×C103D411yescharacteristic
31M16×C103—22no—
32M16×C103—41no—
33C2×C8×C103—41no—
34C23×C103C22⋊C411yescharacteristic
35C23×C103C4⋊C411yescharacteristic
36C23×C103C4⋊C411yescharacteristic
37Q8×C103—41no—
38D4×C103—41no—
39D4×C103—41no—
40D4×C103—41no—
41C2×C4×C103—21no—
42C2×C4×C103—21no—
43C2×C4×C103—21no—
44C2×C4×C103—21no—
45C2×C4×C103—21no—
46C2×C4×C103—21no—
47C2×C4×C103C4211yescharacteristic
48C2×C4×C103C22⋊C411yescharacteristic
49C2×C4×C103C22⋊C411yescharacteristic
50C2×C4×C103C4⋊C411yescharacteristic
51C2×Dic103—42no—
52C8×C103—42no—
53C103⋊C8—41no—
54C103⋊C8—41no—
55C22×C103—21no—
56C22×C103—21no—
57C22×C103—21no—
58C22×C103—41no—
59C22×C103—41no—
60C22×C103—41no—
61C22×C103#9511yescharacteristic
62C4×C103—21no—
63C4×C103—21no—
64C4×C103—21no—
65C4×C103#9911yescharacteristic
66C4×C103#9911yescharacteristic
67Dic103—82no—
68C2×C103—21no—
69C2×C103—41no—
70C2×C103—41no—
71C2×C103—41no—
72C2×C103#34211yescharacteristic
73#1395—1031nomaximal, Sylow
74C103#139511yescharacteristic, complemented, Sylow
75#413D10311yescharacteristic
76#410—1031no—
77#408—1031no—
78C2×#41C2×D10311yescharacteristic
79C2×M16—21no—
80C2×M16—1031no—
81C22×C8—1031no—
82#117—2061no—
83#101Dic10312yescomplemented
84#100—21no—
85#99—1032no—
86#99—2061no—
87C22⋊C8—2061no—
88C22⋊C8—2061no—
89#41—41no—
90#41—41no—
91C2×Q8C2×Dic10311yescharacteristic
92C2×D4Dic20611yescharacteristic
93C2×D4C4×D10311yescharacteristic
94C2×D4C22⋊D10311yescharacteristic
95C22×C4C4×D10311yescharacteristic
96C22×C4D41211yescharacteristic
97C22×C4C22⋊D10311yescharacteristic
98M16—22no—
99M16—41no—
100M16—4121no—
101C2×C8—41no—
102C2×C8—4121no—
103C2×C8—2061no—
104C2×C8—2061no—
105C4⋊C4—4121no—
106C22⋊C4—2062no—
107C42—4121no—
108C23(C2×D103)⋊C411yescharacteristic
109C23Dic103⋊C411yescharacteristic
110C23Dic103⋊C411yescharacteristic
111Q8—41no—
112D4—41no—
113D4—41no—
114D4—41no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—4122no—
122C2×C4C4×Dic10311yescharacteristic
123C2×C4(C2×D103)⋊C411yescharacteristic
124C2×C4C22⋊Dic10311yescharacteristic
125C2×C4C4⋊Dic10311yescharacteristic
126C8—42no—
127C8—4121no—
128C8—4121no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22—41no—
133C22—41no—
134C22—41no—
135C22C103⋊#9511yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—8242no—
140C4#1569293511yescharacteristic
141C4#1569293511yescharacteristic
142C2—21no—
143C2—41no—
144C2—41no—
145C2—41no—
146C2#2026755711yescharacteristic
subgroupG/H
centerC4#15692935
commutatorC2×C4×C103C42
FrattiniC2×#41C2×D103
Fitting#413×C103C2
socleC2×C103#342
prime radical, cosocleC2×#41×C103C22
hypercenter#413D103
hypocenterC103#1395
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
4. C2×#13110089C4semidirect
5. C22×C103⋊C8C4semidirect
13. #101×C103C4semidirect
74. C103#1395semidirect
83. #101Dic103semidirect

Maximal subgroups

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

subgroupindex
#202677652
#202677582
#413×C1032
#1395103