Finite Group Databasebeta

← #27205598

Subgroups — #27205598

Order 13184.

552 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#15693050C214yesmaximal, complemented
2#20268339C211yesmaximal, characteristic
3C4⋊Q8×D103C211yesmaximal, characteristic, complemented
4#20268182C214yesmaximal, complemented
5#20268171C211yesmaximal, characteristic, complemented
6#20268170C211yesmaximal, characteristic, complemented
7#20268163C211yesmaximal, characteristic, complemented
8C4×#13110088C211yesmaximal, characteristic, complemented
9#492×C103C211yesmaximal, characteristic, complemented
10C2×#13110104C2212yes—
11C2×Q8×D103C2212yes—
12#15693050—216no—
13C2×Dic412C2214yes—
14C2×#13110095C2214yes—
15C2×#13110093C2214yes—
16C2×#13110088C2212yes—
17#15693021C2211yescharacteristic
18#15693021C2211yescharacteristic
19#15693020—22no—
20#15693019C2212yes—
21#15693008C2212yes—
22#15692992—22no—
23D4×Dic103—22no—
24C4⋊C4×D103—22no—
25C42×D103C2211yescharacteristic
26#15692931C2212yes—
27C4×C103⋊C8C2211yescharacteristic
28C2×SD16×C103C2214yes—
29C4⋊Q8×C103C2211yescharacteristic
30#127×C103C2211yescharacteristic
31C4×C8×C103C2211yescharacteristic
32#13110104—28no—
33C2×Dic206—22no—
34C2×Dic206C2312yes—
35C2×Dic206C2312yes—
36Q8×D103—28no—
37C2×C22⋊D103—22no—
38C22×Dic103—22no—
39C2×C4×D103—22no—
40C2×C4×D103D412yes—
41C2×C4×D103C2311yescharacteristic
42Dic412—28no—
43#13110095—28no—
44#13110093—28no—
45#13110088D418yescomplemented
46C2×C103⋊C8C2312yes—
47C4⋊Dic103—22no—
48C4⋊Dic103—22no—
49Dic103⋊C4—24no—
50C22⋊Dic103—24no—
51C4×Dic103D412yes—
52C4×Dic103C2311yescharacteristic
53C2×Q8×C103C2312yes—
54C2×D4×C103—22no—
55C2×D4×C103C2312yes—
56SD16×C103—28no—
57C2×C8×C103C2312yes—
58C4⋊C4×C103—22no—
59C42×C103C2311yescharacteristic
60C23×C103—22no—
61C22×D103C2×D411yescharacteristic
62Q8×C103—24no—
63D4×C103—24no—
64D4×C103—44no—
65C2×C4×C103—22no—
66C2×C4×C103C2×D412yes—
67C2×C4×C103C2411yescharacteristic
68C22⋊D103—44no—
69C2×Dic103—22no—
70C2×Dic103—22no—
71C2×Dic103—44no—
72C2×Dic103C2×D412yes—
73C2×Dic103C2×D411yescharacteristic
74C4×D103—24no—
75C4×D103—44no—
76C4×D103C2×D414yes—
77Dic206—24no—
78Dic206—24no—
79Dic206—44no—
80C8×C103C2×D414yes—
81C103⋊C8C2×D414yes—
82C22×C103—42no—
83C22×C103—44no—
84C22×C103C22×D411yescharacteristic
85C2×D103—22no—
86C2×D103#12712yes—
87C4×C103—42no—
88C4×C103#13714yescomplemented
89C4×C103C22×D412yes—
90Dic103—22no—
91Dic103—42no—
92Dic103—42no—
93Dic103#12712yes—
94C2×C103—82no—
95C2×C103C2×#12711yescharacteristic
96C2×C103C2×#13712yes—
97D103—22no—
98#3152—1031nomaximal, Sylow
99C103#315211yescharacteristic, complemented, Sylow
100C2×#137—1034no—
101#532—1031no—
102C2×C4⋊Q8—1031no—
103#497—1034no—
104#494—1031no—
105#494—1031no—
106#492—1031no—
107#492D10311yescharacteristic, complemented
108C4×M16—1031no—
109C2×#41—1032no—
110C22×Q8—1032no—
111#137—20616no—
112C2×Q16—1034no—
113C2×Q16—1034no—
114C2×SD16—1034no—
115C2×SD16C2×D10314yes—
116C2×M16—1032no—
117C4⋊Q8—1032no—
118C4⋊Q8—1031no—
119C4⋊Q8—1031no—
120C4⋊Q8—2062no—
121C4⋊Q8C2×D10311yescharacteristic
122#127C2×D10311yescharacteristic
123#124—1032no—
124#121—2062no—
125C4×D4—2062no—
126C2×C4⋊C4—2062no—
127C2×C42—1031no—
128#97—1032no—
129C4×C8—1031no—
130C4×C8C2×D10311yescharacteristic
131#41—2068no—
132C2×Q8—1032no—
133C2×Q8—1032no—
134C2×Q8—2062no—
135C2×Q8—2068no—
136C2×Q8C22×D10312yes—
137C2×D4—22no—
138C2×D4—2062no—
139C2×D4C22×D10312yes—
140C22×C4—1031no—
141C22×C4—1032no—
142C22×C4—2062no—
143C22×C4—2062no—
144Q16—2068no—
145Q16—2068no—
146SD16—28no—
147SD16—2068no—
148M16—1038no—
149C2×C8—1032no—
150C2×C8C22×D10312yes—
151C4⋊C4—22no—
152C4⋊C4—2064no—
153C4⋊C4—2062no—
154C4⋊C4—2062no—
155C22⋊C4—2064no—
156C42—1032no—
157C42—1031no—
158C42C22×D10311yescharacteristic
159C23—22no—
160C23—1031no—
161Q8—24no—
162Q8—4124no—
163Q8—2064no—
164Q8—2064no—
165D4—24no—
166D4—44no—
167D4—4124no—
168C2×C4—22no—
169C2×C4—1031no—
170C2×C4—1034no—
171C2×C4—1032no—
172C2×C4—4124no—
173C2×C4—4124no—
174C2×C4—2062no—
175C2×C4—2062no—
176C2×C4—2064no—
177C2×C4D4×D10312yes—
178C2×C4C23×D10311yescharacteristic
179C8—1034no—
180C8D4×D10314yes—
181C22—44no—
182C22—42no—
183C22—1032no—
184C22—2062no—
185C22C2×D4×D10311yescharacteristic
186C4—42no—
187C4—1032no—
188C4—4122no—
189C4—4122no—
190C4—2062no—
191C4#1569305014yescomplemented
192C4C2×D4×D10312yes—
193C2—82no—
194C2—2062no—
195C2#127×D10311yescharacteristic
196C2C2×#1569305012yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#492×C103C2
socleC22×C103C22×D4
prime radical#20268339C2
hypercenter#492D103
hypocenterC103#3152
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#15693050C2semidirect
3. C4⋊Q8×D103C2semidirect
4. #20268182C2semidirect
5. #20268171C2semidirect
6. #20268170C2semidirect
7. #20268163C2semidirect
8. C4×#13110088C2semidirect
9. #492×C103C2semidirect
45. #13110088D4semidirect
88. C4×C103#137semidirect
99. C103#3152semidirect
107. #492D103semidirect
191. C4#15693050semidirect

Maximal subgroups

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

subgroupindex
C2×#156930502
#202683392
C4⋊Q8×D1032
#202681822
#202681712
#202681702
#202681632
C4×#131100882
#492×C1032
#3152103