Finite Group Databasebeta

← #27195534

Subgroups — #27195534

Order 13184.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#15693019C211yesmaximal, characteristic
2#20268268C211yesmaximal, characteristic
3#20267800C211yesmaximal, characteristic
4C2×#15692939C211yesmaximal, characteristic
5#20267552C211yesmaximal, characteristic
6#20267550C211yesmaximal, characteristic
7#419×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10#15693019—22no—
11#15693019C414yescomplemented
12C4×Dic206—22no—
13#15692986—22no—
14#15692980C2211yescharacteristic
15#15692977—22no—
16C2×Dic103⋊C4—22no—
17C2×C4×Dic103C2211yescharacteristic
18#15692945—22no—
19#15692939—22no—
20C22×Q8×C103C2211yescharacteristic
21C2×M16×C103C2211yescharacteristic
22#117×C103C2211yescharacteristic
23#103×C103—22no—
24C2×Dic206—21no—
25C2×Dic206—21no—
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206C2×C412yes—
29C2×Dic206D412yes—
30C22×Dic103—21no—
31C22×Dic103D412yes—
32#13110089—21no—
33#13110089—21no—
34C2×C103⋊C8—21no—
35C4⋊Dic103D412yes—
36Dic103⋊C4—24no—
37Dic103⋊C4—28no—
38C22⋊Dic103—21no—
39C4×Dic103—24no—
40C4×Dic103—21no—
41C4×Dic103—21no—
42C4×Dic103C2×C412yes—
43C2×Q8×C103—21no—
44C2×Q8×C103—21no—
45C2×Q8×C103—21no—
46C2×Q8×C103—21no—
47C2×Q8×C103—21no—
48C2×Q8×C103C2×C412yes—
49C22×C4×C103—21no—
50C22×C4×C103C2311yescharacteristic
51M16×C103—21no—
52M16×C103—21no—
53C2×C8×C103—21no—
54C4⋊C4×C103D412yes—
55C22⋊C4×C103—21no—
56C42×C103—21no—
57C23×C103C2×D411yescharacteristic
58Q8×C103—22no—
59Q8×C103—22no—
60Q8×C103—41no—
61Q8×C103—41no—
62C2×C4×C103—22no—
63C2×C4×C103—22no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103C22×C411yescharacteristic
67C2×C4×C103C2×D411yescharacteristic
68C2×C4×C103C2×D411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C2×C4×C103#4111yescharacteristic
71C2×C4×C103#4111yescharacteristic
72C2×Dic103—24no—
73C2×Dic103—22no—
74C2×Dic103—22no—
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103C22⋊C414yes—
78Dic206—22no—
79Dic206—22no—
80Dic206—22no—
81Dic206—22no—
82C8×C103—41no—
83C103⋊C8—41no—
84C22×C103—22no—
85C22×C103C2×C22⋊C411yescharacteristic
86C22×C103#12011yescharacteristic
87C22×C103#12311yescharacteristic
88C4×C103—42no—
89C4×C103—42no—
90C4×C103C4×D411yescharacteristic
91C4×C103C4×D411yescharacteristic
92C4×C103#12111yescharacteristic
93C4×C103#12111yescharacteristic
94Dic103—24no—
95Dic103—24no—
96Dic103—42no—
97C2×C103—21no—
98C2×C103—21no—
99C2×C103#38611yescharacteristic
100C2×C103#45612yes—
101#1886—1031nomaximal, Sylow
102C103#188611yescharacteristic, complemented, Sylow
103C2×C4⋊Q8—1031no—
104#519—1031no—
105#419—1031no—
106#419D10311yescharacteristic
107C2×#101—1031no—
108#339—1031no—
109#339—1031no—
110C22×Q8—1031no—
111C22×Q8C2×D10311yescharacteristic
112C2×M16—1031no—
113C2×M16C2×D10311yescharacteristic
114C4⋊Q8—1034no—
115C4⋊Q8—2062no—
116C4×Q8—2062no—
117C4×Q8—2062no—
118#117—1031no—
119#117—2062no—
120#117C2×D10311yescharacteristic
121C2×C4⋊C4—2062no—
122C2×C42—1031no—
123#103—22no—
124#103—2062no—
125#101—2062no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—1032no—
132C2×Q8—1032no—
133C2×Q8—2061no—
134C2×Q8—2061no—
135C2×Q8—2061no—
136C2×Q8—2061no—
137C2×Q8C4×D10312yes—
138C22×C4—21no—
139C22×C4—1032no—
140C22×C4—2061no—
141C22×C4C22×D10311yescharacteristic
142M16—21no—
143M16—21no—
144M16—2061no—
145M16—2061no—
146C2×C8—21no—
147C2×C8—2061no—
148C4⋊C4—1032no—
149C4⋊C4—2068no—
150C4⋊C4—2064no—
151C4⋊C4C22⋊D10312yes—
152C22⋊C4—21no—
153C22⋊C4—2061no—
154C42—21no—
155C42—1032no—
156C42—2064no—
157C42—2061no—
158C42—2061no—
159C23D4×D10311yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—2062no—
165Q8—2062no—
166Q8—2062no—
167Q8—2062no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—1034no—
173C2×C4—2062no—
174C2×C4—2064no—
175C2×C4—2062no—
176C2×C4—2062no—
177C2×C4—2062no—
178C2×C4C2×C4×D10311yescharacteristic
179C2×C4D4×D10311yescharacteristic
180C2×C4D4×D10311yescharacteristic
181C2×C4C2×C22⋊D10311yescharacteristic
182C2×C4#1311010411yescharacteristic
183C2×C4#1311010511yescharacteristic
184C8—41no—
185C8—4121no—
186C22—22no—
187C22C22⋊C4×D10311yescharacteristic
188C22#1569298911yescharacteristic
189C22#1569300311yescharacteristic
190C4—42no—
191C4—42no—
192C4—4122no—
193C4—2064no—
194C4—2064no—
195C4(C22⋊D103)⋊C411yescharacteristic
196C4C4×C22⋊D10311yescharacteristic
197C4#1569299211yescharacteristic
198C4#1569299411yescharacteristic
199C2—21no—
200C2—21no—
201C2#2026766711yescharacteristic
202C2#2026797212yes—
subgroupG/H
centerC22#15692989
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#419×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
cosocleC22×C4×C103C23
hypercenter#419D103
hypocenterC103#1886
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #15693019C4semidirect
102. C103#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#156930192
#202682682
#202678002
C2×#156929392
#202675522
#202675502
#419×C1032
#1886103