Finite Group Databasebeta

← #27195667

Subgroups — #27195667

Order 13184.

312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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#20268558C211yesmaximal, characteristic
2#20267800C212yesmaximal, complemented
3#20267765C211yesmaximal, characteristic
4#20267547C212yesmaximal, complemented
5#536×C103C211yesmaximal, characteristic
6#15693028—24no—
7C2×#13110089—22no—
8C2×#13110089C2212yes—
9#15692980C2212yes—
10#15692945—24no—
11#15692936—22no—
12C2×#41×C103C2211yescharacteristic
13C22×Q8×C103C2211yescharacteristic
14C4⋊Q8×C103C412yescomplemented
15#124×C103C412yescomplemented
16#123×C103—22no—
17C22⋊Q8×C103—22no—
18#117×C103C2211yescharacteristic
19#13110089—24no—
20#13110089—22no—
21#13110089—22no—
22C2×C103⋊C8—24no—
23C2×C103⋊C8D414yes—
24C4⋊Dic103—22no—
25C22⋊Dic103—22no—
26C4×Dic103—22no—
27#41×C103—22no—
28#41×C103—22no—
29C2×Q8×C103—21no—
30C2×Q8×C103—22no—
31C2×Q8×C103—22no—
32C2×Q8×C103C2×C412yes—
33C2×Q8×C103C2×C411yescharacteristic
34C2×D4×C103C2×C411yescharacteristic
35C2×D4×C103D412yes—
36C22×C4×C103—21no—
37C22×C4×C103D412yes—
38C22×C4×C103C2311yescharacteristic
39C4⋊C4×C103—24no—
40C4⋊C4×C103—21no—
41C22⋊C4×C103—24no—
42C22⋊C4×C103—21no—
43C42×C103C2×C412yes—
44C23×C103C22⋊C412yes—
45C23×C103C2×D411yescharacteristic
46Q8×C103—22no—
47Q8×C103—24no—
48Q8×C103—41no—
49Q8×C103—41no—
50D4×C103—24no—
51D4×C103—22no—
52C2×C4×C103—22no—
53C2×C4×C103—22no—
54C2×C4×C103—22no—
55C2×C4×C103—22no—
56C2×C4×C103—42no—
57C2×C4×C103C22⋊C412yes—
58C2×C4×C103C22×C411yescharacteristic
59C2×C4×C103C2×D412yes—
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103#4112yes—
62C2×Dic103—42no—
63C103⋊C8—24no—
64C22×C103—22no—
65C22×C103—41no—
66C22×C103—42no—
67C22×C103C2×C22⋊C411yescharacteristic
68C22×C103#12112yes—
69C4×C103—22no—
70C4×C103—42no—
71C4×C103—42no—
72C4×C103C4×D412yes—
73C4×C103#12011yescharacteristic
74C4×C103#12311yescharacteristic
75Dic103—82no—
76C2×C103—22no—
77C2×C103—21no—
78C2×C103—42no—
79C2×C103#38611yescharacteristic
80#1909—1031nomaximal, Sylow
81C103#190911yescharacteristic, complemented, Sylow
82#568—1031no—
83#536D10311yescharacteristic
84#419—1032no—
85#410—1031no—
86H(3,ℤ/4)—1032no—
87C2×#41C2×D10311yescharacteristic
88C22×Q8C2×D10311yescharacteristic
89#131—2064no—
90C2×M16—1032no—
91C2×M16—2062no—
92C4⋊Q8Dic10312yescomplemented
93#124Dic10312yescomplemented
94#123—22no—
95C22⋊Q8—22no—
96#117—1032no—
97#117C2×D10311yescharacteristic
98#103—2064no—
99#99—2062no—
100#41—22no—
101#41—22no—
102C2×Q8—21no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8C2×Dic10312yes—
106C2×Q8C2×Dic10311yescharacteristic
107C2×D4C2×Dic10311yescharacteristic
108C2×D4C22⋊D10312yes—
109C22×C4—21no—
110C22×C4C22⋊D10312yes—
111C22×C4C22×D10311yescharacteristic
112M16—2064no—
113M16—2062no—
114M16—2062no—
115C2×C8—1034no—
116C2×C8—2064no—
117C4⋊C4—24no—
118C4⋊C4—21no—
119C4⋊C4—2062no—
120C22⋊C4—24no—
121C22⋊C4—21no—
122C22⋊C4—2062no—
123C42—2062no—
124C42C2×Dic10312yes—
125C23C22⋊Dic10312yes—
126C23C2×C22⋊D10311yescharacteristic
127Q8—22no—
128Q8—24no—
129Q8—41no—
130Q8—41no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—4122no—
139C2×C4C22⋊Dic10312yes—
140C2×C4C22×Dic10311yescharacteristic
141C2×C4D4×D10312yes—
142C2×C4C2×C22⋊D10311yescharacteristic
143C2×C4#1311010412yes—
144C8—2064no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×C22⋊Dic10311yescharacteristic
149C22#1569299312yes—
150C4—22no—
151C4—42no—
152C4—42no—
153C4—8242no—
154C4D4×Dic10312yes—
155C4#1569298911yescharacteristic
156C4#1569300211yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#2026767111yescharacteristic
subgroupG/H
centerC2#20267671
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#536×C103C2
socleC2×C103#386
prime radicalC2×#41×C103C22
cosocleC22×C4×C103C23
hypercenter#536D103
hypocenterC103#1909
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #20267800C2semidirect
4. #20267547C2semidirect
14. C4⋊Q8×C103C4semidirect
15. #124×C103C4semidirect
81. C103#1909semidirect
92. C4⋊Q8Dic103semidirect
93. #124Dic103semidirect

Maximal subgroups

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

subgroupindex
#202685582
#202678002
#202677652
#202675472
#536×C1032
#1909103