Finite Group Databasebeta

← #27195692

Subgroups — #27195692

Order 13184.

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

normal subgroups only

This group has 340 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#20267775C211yesmaximal, characteristic, complemented
3C2×#15692938C212yesmaximal, complemented
4#20267561C212yesmaximal, complemented
5#535×C103C211yesmaximal, characteristic
6#15693028—24no—
7C2×#13110089—22no—
8C2×#13110089C2212yes—
9C2×#13110089C2212yes—
10#15692940—21no—
11#15692938—24no—
12#15692938—21no—
13C2×#41×C103C2211yescharacteristic
14C22×D4×C103C2211yescharacteristic
15#127×C103—21no—
16#124×C103—21no—
17#121×C103—22no—
18#120×C103C414yes—
19#117×C103C2211yescharacteristic
20#13110089—24no—
21#13110089—22no—
22#13110089—22no—
23#13110089—22no—
24#13110089D414yescomplemented
25C2×C103⋊C8—24no—
26C2×C103⋊C8—22no—
27C2×C103⋊C8—22no—
28C24×C103C2×C412yes—
29#41×C103—22no—
30#41×C103—22no—
31C2×Q8×C103D411yescharacteristic
32C2×D4×C103—24no—
33C2×D4×C103—21no—
34C2×D4×C103—21no—
35C2×D4×C103—22no—
36C2×D4×C103—22no—
37C2×D4×C103C2×C412yes—
38C2×D4×C103D411yescharacteristic
39C22×C4×C103D412yes—
40C22×C4×C103C2311yescharacteristic
41C4⋊C4×C103—21no—
42C22⋊C4×C103—24no—
43C22⋊C4×C103C2×C412yes—
44C42×C103—21no—
45C23×C103—22no—
46C23×C103—24no—
47C23×C103—82no—
48C23×C103C22⋊C412yes—
49C23×C103C22×C411yescharacteristic
50Q8×C103—22no—
51D4×C103—24no—
52D4×C103—22no—
53D4×C103—41no—
54D4×C103—42no—
55D4×C103—41no—
56D4×C103—84no—
57C2×C4×C103—22no—
58C2×C4×C103—22no—
59C2×C4×C103—22no—
60C2×C4×C103C22⋊C412yes—
61C2×C4×C103C2×D412yes—
62C2×C4×C103C2×D411yescharacteristic
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103#4112yes—
65C103⋊C8—24no—
66C103⋊C8—42no—
67C22×C103—22no—
68C22×C103—41no—
69C22×C103—42no—
70C22×C103—44no—
71C22×C103—42no—
72C22×C103—84no—
73C22×C103C2×C22⋊C411yescharacteristic
74C22×C103C4×D412yes—
75C4×C103—22no—
76C4×C103—42no—
77C4×C103#12011yescharacteristic
78C4×C103#12112yes—
79C4×C103#12311yescharacteristic
80C2×C103—21no—
81C2×C103—22no—
82C2×C103—42no—
83C2×C103—82no—
84C2×C103#38611yescharacteristic
85#1914—1031nomaximal, Sylow
86C103#191411yescharacteristic, complemented, Sylow
87#568—1031no—
88#535D10311yescharacteristic
89#413—1031no—
90C2×#100—1032no—
91#344—1032no—
92C2×#41C2×D10311yescharacteristic
93C22×D4C2×D10311yescharacteristic
94#131—2064no—
95C2×M16—1032no—
96C2×M16—1032no—
97C2×M16—2062no—
98#127—21no—
99#124—21no—
100#121—22no—
101#120Dic10314yes—
102#117C2×D10311yescharacteristic
103#101—2061no—
104#100—2064no—
105#100—2061no—
106C24C2×Dic10312yes—
107#41—22no—
108#41—22no—
109C2×Q8C22⋊D10311yescharacteristic
110C2×D4—24no—
111C2×D4—22no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4C2×Dic10312yes—
116C2×D4C22⋊D10311yescharacteristic
117C22×C4C22⋊D10312yes—
118C22×C4C22×D10311yescharacteristic
119M16—1034no—
120M16—2062no—
121M16—2062no—
122M16—2064no—
123M16—2062no—
124C2×C8—2062no—
125C2×C8—2064no—
126C2×C8—2062no—
127C4⋊C4—21no—
128C22⋊C4—24no—
129C22⋊C4C2×Dic10312yes—
130C42—21no—
131C23—22no—
132C23—24no—
133C23—82no—
134C23C22⋊Dic10312yes—
135C23C22×Dic10311yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—41no—
140D4—42no—
141D4—41no—
142D4—84no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4C22⋊Dic10312yes—
147C2×C4D4×D10312yes—
148C2×C4C2×C22⋊D10311yescharacteristic
149C2×C4C2×C22⋊D10311yescharacteristic
150C2×C4#1311010412yes—
151C8—4122no—
152C8—2064no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—44no—
157C22—42no—
158C22—84no—
159C22C2×C22⋊Dic10311yescharacteristic
160C22D4×Dic10312yes—
161C4—22no—
162C4—42no—
163C4#1569298911yescharacteristic
164C4#1569299312yes—
165C4#1569300211yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#2026767111yescharacteristic
subgroupG/H
centerC2#20267671
commutatorC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting, prime radical#535×C103C2
socleC2×C103#386
cosocleC22×C4×C103C23
hypercenter#535D103
hypocenterC103#1914
LCSG ▷ C23×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. #20267775C2semidirect
3. C2×#15692938C2semidirect
4. #20267561C2semidirect
24. #13110089D4semidirect
86. C103#1914semidirect

Maximal subgroups

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

subgroupindex
#202685582
#202677752
C2×#156929382
#202675612
#535×C1032
#1914103