Finite Group Databasebeta

← #27195986

Subgroups — #27195986

Order 13184.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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#20267814C211yesmaximal, characteristic
3C2×#15692940C211yesmaximal, characteristic
4C2×#15692939C211yesmaximal, characteristic
5C2×#15692939C211yesmaximal, characteristic
6M16×Dic103C211yesmaximal, characteristic
7C2×#101×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10C2×#13110089C2211yescharacteristic
11#15693019—21no—
12#15693019—21no—
13#15693019—22no—
14C2×Dic103⋊C4C414yes—
15C2×C4×Dic103C2211yescharacteristic
16Dic103⋊C8—22no—
17#15692940—22no—
18#15692939—22no—
19#15692939—22no—
20#15692931—21no—
21C8×Dic103—21no—
22C22×Q8×C103C2211yescharacteristic
23C2×M16×C103C2211yescharacteristic
24C2×M16×C103C2211yescharacteristic
25#101×C103—22no—
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206—21no—
29C2×Dic206—21no—
30C2×Dic206—21no—
31C2×Dic206—21no—
32C22×Dic103C2×C412yes—
33C22×Dic103C2×C412yes—
34#13110089—21no—
35#13110089—21no—
36#13110089—21no—
37#13110089D412yes—
38C2×C103⋊C8—21no—
39C2×C103⋊C8—21no—
40Dic103⋊C4—24no—
41Dic103⋊C4—24no—
42C4×Dic103D411yescharacteristic
43C4×Dic103D411yescharacteristic
44C4×Dic103D412yes—
45C2×Q8×C103—21no—
46C2×Q8×C103—21no—
47C2×Q8×C103—21no—
48C2×Q8×C103—21no—
49C2×Q8×C103—21no—
50C2×Q8×C103—21no—
51C22×C4×C103C2×C412yes—
52C22×C4×C103C2311yescharacteristic
53M16×C103—21no—
54M16×C103—21no—
55M16×C103—21no—
56M16×C103D412yes—
57C2×C8×C103—21no—
58C2×C8×C103—21no—
59C23×C103C22×C411yescharacteristic
60Q8×C103—41no—
61Q8×C103—41no—
62Q8×C103—41no—
63Q8×C103—41no—
64C2×C4×C103—22no—
65C2×C4×C103—22no—
66C2×C4×C103—22no—
67C2×C4×C103C2×D411yescharacteristic
68C2×C4×C103C2×D411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103#4111yescharacteristic
72C2×C4×C103#4111yescharacteristic
73C2×Dic103—24no—
74C2×Dic103—22no—
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103C22⋊C412yes—
78C2×Dic103C22⋊C412yes—
79Dic206—41no—
80Dic206—41no—
81Dic206—41no—
82Dic206—41no—
83C8×C103—22no—
84C8×C103—41no—
85C103⋊C8—22no—
86C103⋊C8—41no—
87C22×C103—22no—
88C22×C103C2×C22⋊C411yescharacteristic
89C22×C103C4×D411yescharacteristic
90C22×C103C4×D411yescharacteristic
91C4×C103—42no—
92C4×C103#12111yescharacteristic
93C4×C103#12111yescharacteristic
94C4×C103#12411yescharacteristic
95C4×C103#12711yescharacteristic
96Dic103—22no—
97Dic103—42no—
98Dic103#10114yescomplemented
99C2×C103—21no—
100C2×C103—21no—
101C2×C103#39011yescharacteristic
102C2×C103C2×#10112yes—
103#1966—1031nomaximal, Sylow
104C103#196611yescharacteristic, complemented, Sylow
105C2×C4⋊Q8—1031no—
106#423—1031no—
107C2×#101—1031no—
108C2×#101—1031no—
109C2×#101—1031no—
110C2×#101D10311yescharacteristic
111C4×M16—1031no—
112C22×Q8—1031no—
113C22×Q8C2×D10311yescharacteristic
114C2×M16—1031no—
115C2×M16—1031no—
116C2×M16C2×D10311yescharacteristic
117C2×M16C2×D10311yescharacteristic
118C4⋊Q8—2061no—
119C4⋊Q8—2061no—
120C4⋊Q8—2062no—
121C2×C4⋊C4—1034no—
122C2×C42—1031no—
123C4⋊C8—2062no—
124#101—22no—
125#101—2062no—
126#101—2062no—
127#101—2062no—
128#97—2061no—
129C4×C8—2061no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—2061no—
137C2×Q8—2061no—
138C2×Q8—2061no—
139C2×Q8—2061no—
140C2×Q8—2061no—
141C2×Q8—2061no—
142C22×C4—1032no—
143C22×C4—1032no—
144C22×C4C4×D10312yes—
145C22×C4C22×D10311yescharacteristic
146M16—21no—
147M16—21no—
148M16—21no—
149M16—1032no—
150M16—2061no—
151M16—2061no—
152M16—2061no—
153M16C22⋊D10312yes—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—2061no—
157C2×C8—2061no—
158C4⋊C4—2064no—
159C4⋊C4—2064no—
160C42—1031no—
161C42—1031no—
162C42—1032no—
163C23C2×C4×D10311yescharacteristic
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—41no—
168Q8—4121no—
169Q8—4121no—
170Q8—4121no—
171Q8—4121no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—1032no—
176C2×C4—1032no—
177C2×C4—2064no—
178C2×C4—2062no—
179C2×C4—2062no—
180C2×C4—2062no—
181C2×C4D4×D10311yescharacteristic
182C2×C4D4×D10311yescharacteristic
183C2×C4D4×D10311yescharacteristic
184C2×C4C2×C22⋊D10311yescharacteristic
185C2×C4#1311010411yescharacteristic
186C2×C4#1311010511yescharacteristic
187C8—22no—
188C8—41no—
189C8—4121no—
190C8—2062no—
191C22—22no—
192C22C22⋊C4×D10311yescharacteristic
193C22(C22⋊D103)⋊C411yescharacteristic
194C22C4×C22⋊D10311yescharacteristic
195C4—42no—
196C4—1034no—
197C4—4122no—
198C4—2062no—
199C4#1569299311yescharacteristic
200C4#1569299411yescharacteristic
201C4#1569300711yescharacteristic
202C4#1569301711yescharacteristic
203C2—21no—
204C2—21no—
205C2#2026769111yescharacteristic
206C2#101×D10312yes—
subgroupG/H
centerC22C22⋊C4×D103
commutator, prime radicalC23×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×#101×C103C2
socleC22×C103C2×C22⋊C4
cosocleC22×C4×C103C23
hypercenterC2×#101D103
hypocenterC103#1966
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
98. Dic103#101semidirect
104. C103#1966semidirect

Maximal subgroups

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

subgroupindex
C2×#156930192
#202678142
C2×#156929402
C2×#156929392
M16×Dic1032
C2×#101×C1032
#1966103