Finite Group Databasebeta

← #27195672

Subgroups — #27195672

Order 13184.

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

normal subgroups only

This group has 344 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, complemented
2#20267796C212yesmaximal, complemented
3#20267765C211yesmaximal, characteristic, complemented
4#20267547C212yesmaximal, complemented
5#535×C103C211yesmaximal, characteristic
6#15693028—24no—
7C2×#13110089—22no—
8C2×#13110089C2212yes—
9#15692980C2212yes—
10#15692942—24no—
11#15692936—22no—
12C2×#41×C103C2211yescharacteristic
13C22×D4×C103C2211yescharacteristic
14#127×C103C412yescomplemented
15#124×C103C412yescomplemented
16#121×C103—22no—
17#120×C103—22no—
18#117×C103C2211yescharacteristic
19#13110089—24no—
20#13110089—22no—
21#13110089—22no—
22C2×C103⋊C8—24no—
23C2×C103⋊C8D414yescomplemented
24C4⋊Dic103—22no—
25C22⋊Dic103—22no—
26C4×Dic103—22no—
27C24×C103—21no—
28#41×C103—22no—
29#41×C103—22no—
30C2×Q8×C103C2×C411yescharacteristic
31C2×D4×C103—24no—
32C2×D4×C103—22no—
33C2×D4×C103—21no—
34C2×D4×C103—22no—
35C2×D4×C103C2×C412yes—
36C2×D4×C103C2×C411yescharacteristic
37C2×D4×C103D412yes—
38C22×C4×C103D412yes—
39C22×C4×C103C2311yescharacteristic
40C4⋊C4×C103—21no—
41C22⋊C4×C103—21no—
42C22⋊C4×C103—24no—
43C42×C103C2×C412yes—
44C23×C103—22no—
45C23×C103—42no—
46C23×C103—82no—
47C23×C103C22⋊C412yes—
48C23×C103C2×D411yescharacteristic
49Q8×C103—22no—
50D4×C103—24no—
51D4×C103—22no—
52D4×C103—24no—
53D4×C103—41no—
54D4×C103—41no—
55D4×C103—84no—
56C2×C4×C103—22no—
57C2×C4×C103—22no—
58C2×C4×C103—22no—
59C2×C4×C103C22⋊C412yes—
60C2×C4×C103C22×C411yescharacteristic
61C2×C4×C103C2×D412yes—
62C2×C4×C103C2×D411yescharacteristic
63C2×C4×C103#4112yes—
64C2×Dic103—42no—
65C103⋊C8—24no—
66C22×C103—22no—
67C22×C103—41no—
68C22×C103—42no—
69C22×C103—44no—
70C22×C103—42no—
71C22×C103—84no—
72C22×C103C2×C22⋊C411yescharacteristic
73C22×C103#12112yes—
74C4×C103—22no—
75C4×C103—42no—
76C4×C103C4×D412yes—
77C4×C103#12011yescharacteristic
78C4×C103#12311yescharacteristic
79Dic103—82no—
80C2×C103—22no—
81C2×C103—21no—
82C2×C103—42no—
83C2×C103—82no—
84C2×C103#38611yescharacteristic
85#1910—1031nomaximal, Sylow
86C103#191011yescharacteristic, complemented, Sylow
87#568—1031no—
88#535D10311yescharacteristic
89#418—1032no—
90#410—1031no—
91H(3,ℤ/4)—1032no—
92C2×#41C2×D10311yescharacteristic
93C22×D4C2×D10311yescharacteristic
94#131—2064no—
95C2×M16—1032no—
96C2×M16—2062no—
97#127Dic10312yescomplemented
98#124Dic10312yescomplemented
99#121—22no—
100#120—22no—
101#117—1032no—
102#117C2×D10311yescharacteristic
103#102—2064no—
104#99—2062no—
105C24—21no—
106#41—22no—
107#41—22no—
108C2×Q8C2×Dic10311yescharacteristic
109C2×D4—24no—
110C2×D4—22no—
111C2×D4—21no—
112C2×D4—22no—
113C2×D4C2×Dic10312yes—
114C2×D4C2×Dic10311yescharacteristic
115C2×D4C22⋊D10312yes—
116C22×C4C22⋊D10312yes—
117C22×C4C22×D10311yescharacteristic
118M16—2064no—
119M16—2062no—
120M16—2062no—
121C2×C8—1034no—
122C2×C8—2064no—
123C4⋊C4—21no—
124C4⋊C4—2062no—
125C22⋊C4—21no—
126C22⋊C4—24no—
127C22⋊C4—2062no—
128C42—2062no—
129C42C2×Dic10312yes—
130C23—22no—
131C23—42no—
132C23—82no—
133C23C22⋊Dic10312yes—
134C23C2×C22⋊D10311yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—24no—
139D4—41no—
140D4—41no—
141D4—84no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—4122no—
146C2×C4C22⋊Dic10312yes—
147C2×C4C22×Dic10311yescharacteristic
148C2×C4D4×D10312yes—
149C2×C4C2×C22⋊D10311yescharacteristic
150C2×C4#1311010412yes—
151C8—2064no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—44no—
156C22—42no—
157C22—84no—
158C22C2×C22⋊Dic10311yescharacteristic
159C22#1569299312yes—
160C4—22no—
161C4—42no—
162C4—8242no—
163C4D4×Dic10312yes—
164C4#1569298911yescharacteristic
165C4#1569300211yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#2026767111yescharacteristic
subgroupG/H
centerC2#20267671
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting, prime radical#535×C103C2
socleC2×C103#386
cosocleC22×C4×C103C23
hypercenter#535D103
hypocenterC103#1910
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20268558C2semidirect
2. #20267796C2semidirect
3. #20267765C2semidirect
4. #20267547C2semidirect
14. #127×C103C4semidirect
15. #124×C103C4semidirect
23. C2×C103⋊C8D4semidirect
86. C103#1910semidirect
97. #127Dic103semidirect
98. #124Dic103semidirect

Maximal subgroups

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

subgroupindex
#202685582
#202677962
#202677652
#202675472
#535×C1032
#1910103