Finite Group Databasebeta

← #27195691

Subgroups — #27195691

Order 13184.

340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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#20268355C211yesmaximal, characteristic
2#20267775C211yesmaximal, characteristic, complemented
3C2×#15692937C212yesmaximal, complemented
4#20267563C212yesmaximal, complemented
5#568×C103C211yesmaximal, characteristic, complemented
6C22×D412C2211yescharacteristic
7C2×#13110089C2212yes—
8#15693017—21no—
9#15693010—21no—
10#15692995—22no—
11#15692989C414yes—
12#15692980C2211yescharacteristic
13#15692940—21no—
14#15692938—21no—
15#15692937—24no—
16C2×#41×C103C2211yescharacteristic
17#131×C103—24no—
18C2×M16×C103—22no—
19C2×M16×C103C2212yes—
20C23×D103C2×C412yes—
21C2×D412—22no—
22C2×D412—21no—
23C2×D412—21no—
24C2×D412—22no—
25C2×C22⋊D103—24no—
26#13110089—22no—
27#13110089—22no—
28C2×C103⋊C8—22no—
29C4⋊Dic103—21no—
30C22⋊Dic103C2×C412yes—
31(C2×D103)⋊C4—24no—
32C4×Dic103—21no—
33#41×C103—22no—
34#41×C103—22no—
35C2×Q8×C103D411yescharacteristic
36C2×D4×C103C2×C412yes—
37C2×D4×C103D411yescharacteristic
38C22×C4×C103D412yes—
39C22×C4×C103C2311yescharacteristic
40M16×C103—24no—
41M16×C103—22no—
42M16×C103D414yescomplemented
43C2×C8×C103—24no—
44C2×C8×C103—22no—
45C23×C103C22⋊C412yes—
46C23×C103C22×C411yescharacteristic
47C22×D103—22no—
48C22×D103—24no—
49C22×D103—82no—
50Q8×C103—22no—
51D4×C103—24no—
52D4×C103—22no—
53C2×C4×C103—22no—
54C2×C4×C103—22no—
55C2×C4×C103C22⋊C412yes—
56C2×C4×C103C2×D412yes—
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103#4112yes—
60C22⋊D103—84no—
61C2×Dic103—22no—
62D412—41no—
63D412—42no—
64D412—41no—
65C8×C103—24no—
66C103⋊C8—42no—
67C22×C103—22no—
68C22×C103—41no—
69C22×C103—42no—
70C22×C103C2×C22⋊C411yescharacteristic
71C22×C103C4×D412yes—
72C2×D103—44no—
73C2×D103—42no—
74C2×D103—84no—
75C4×C103—22no—
76C4×C103#12011yescharacteristic
77C4×C103#12112yes—
78C4×C103#12311yescharacteristic
79Dic103—42no—
80C2×C103—21no—
81C2×C103—22no—
82C2×C103—42no—
83C2×C103#38611yescharacteristic
84D103—82no—
85#1914—1031nomaximal, Sylow
86C103#191411yescharacteristic, complemented, Sylow
87#568D10311yescharacteristic, complemented
88#535—1031no—
89#413—1031no—
90C2×#100—1032no—
91#344—1032no—
92C2×#41C2×D10311yescharacteristic
93C22×D4—1031no—
94#131—24no—
95C2×M16—22no—
96C2×M16—1032no—
97C2×M16C2×D10312yes—
98#127—2061no—
99#124—2061no—
100#121—2062no—
101#120—1034no—
102#117—1031no—
103#101—2061no—
104#100—2061no—
105#100—2064no—
106C24—1032no—
107#41—22no—
108#41—22no—
109C2×Q8D41211yescharacteristic
110C2×D4—2064no—
111C2×D4—2062no—
112C2×D4—2061no—
113C2×D4—2061no—
114C2×D4—2062no—
115C2×D4C4×D10312yes—
116C2×D4D41211yescharacteristic
117C22×C4C22⋊D10312yes—
118C22×C4C22×D10311yescharacteristic
119M16—24no—
120M16—22no—
121M16—2062no—
122M16—2062no—
123M16C22⋊D10314yescomplemented
124C2×C8—24no—
125C2×C8—22no—
126C2×C8—2062no—
127C4⋊C4—2061no—
128C22⋊C4—1032no—
129C22⋊C4—2064no—
130C42—2061no—
131C23—8242no—
132C23—2064no—
133C23—2062no—
134C23(C2×D103)⋊C412yes—
135C23C2×C4×D10311yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—8244no—
140D4—4121no—
141D4—4122no—
142D4—4121no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—2062no—
146C2×C4(C2×D103)⋊C412yes—
147C2×C4C2×C22⋊D10312yes—
148C2×C4C2×C22⋊D10311yescharacteristic
149C2×C4C2×D41211yescharacteristic
150C2×C4#1311010512yes—
151C8—24no—
152C8—4122no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—8244no—
157C22—4124no—
158C22—4122no—
159C22C2×(C2×D103)⋊C411yescharacteristic
160C22C4×C22⋊D10312yes—
161C4—22no—
162C4—4122no—
163C4#1569299011yescharacteristic
164C4#1569299512yes—
165C4#1569300411yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—8242no—
170C2#2026767011yescharacteristic
subgroupG/H
centerC2#20267670
commutatorC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#568×C103C2
socleC2×C103#386
prime radical#20268355C2
cosocleC22×C4×C103C23
hypercenter#568D103
hypocenterC103#1914
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #20267775C2semidirect
3. C2×#15692937C2semidirect
4. #20267563C2semidirect
5. #568×C103C2semidirect
42. M16×C103D4semidirect
86. C103#1914semidirect
87. #568D103semidirect
123. M16C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
#202683552
#202677752
C2×#156929372
#202675632
#568×C1032
#1914103