Finite Group Databasebeta

← #27197862

Subgroups — #27197862

Order 13184.

516 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 197 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
2C2×Q8×Dic103C211yesmaximal, characteristic
3C2×#15692986C211yesmaximal, characteristic
4#20267697C211yesmaximal, characteristic
5#20267678C214yesmaximal
6#20267673C214yesmaximal
7#20267656C211yesmaximal, characteristic
8#20267637C211yesmaximal, characteristic
9#391×C103C211yesmaximal, characteristic
10C22×Dic206C2211yescharacteristic
11#15693019C418yescomplemented
12Q8×Dic103—24no—
13#15692986—24no—
14C2×C4⋊Dic103C2211yescharacteristic
15C2×C4⋊Dic103C2212yes—
16C2×Dic103⋊C4C2212yes—
17C2×Dic103⋊C4C2214yes—
18C2×C4×Dic103C2212yes—
19C2×C4×Dic103C2212yes—
20C2×C4×Dic103C2211yescharacteristic
21C2×C4×Dic103C2211yescharacteristic
22C103⋊#95C2212yes—
23C103⋊#95C2212yes—
24C103⋊#95C2214yes—
25C103⋊#95C2214yes—
26C22×Q8×C103C2211yescharacteristic
27C2×C4⋊C4×C103C2211yescharacteristic
28C2×C42×C103C2211yescharacteristic
29#95×C103C2214yes—
30C2×Dic206—22no—
31C2×Dic206—22no—
32C2×Dic206C2×C414yes—
33C22×Dic103C2312yes—
34C22×Dic103C2312yes—
35C22×Dic103C2312yes—
36C22×Dic103C2311yescharacteristic
37C22×Dic103C2311yescharacteristic
38C4⋊Dic103—22no—
39C4⋊Dic103—24no—
40Dic103⋊C4—24no—
41Dic103⋊C4C2×C4116yes—
42C4×Dic103—24no—
43C4×Dic103—24no—
44C4×Dic103C2×C414yes—
45C4×Dic103D414yes—
46C2×Q8×C103—22no—
47C2×Q8×C103—22no—
48C2×Q8×C103C2×C414yes—
49C22×C4×C103C2312yes—
50C22×C4×C103C2312yes—
51C22×C4×C103C2312yes—
52C22×C4×C103C2311yescharacteristic
53C4⋊C4×C103—22no—
54C42×C103—22no—
55C23×C103C2411yescharacteristic
56Q8×C103—28no—
57C2×C4×C103—22no—
58C2×C4×C103—22no—
59C2×C4×C103—22no—
60C2×C4×C103—22no—
61C2×C4×C103—24no—
62C2×C4×C103—22no—
63C2×C4×C103—22no—
64C2×C4×C103C22×C414yes—
65C2×C4×C103C22×C412yes—
66C2×C4×C103C2×D412yes—
67C2×C4×C103#4112yes—
68C2×Dic103—22no—
69C2×Dic103—22no—
70C2×Dic103—22no—
71C2×Dic103—22no—
72C2×Dic103—22no—
73C2×Dic103—22no—
74C2×Dic103—22no—
75C2×Dic103—24no—
76C2×Dic103C22×C414yes—
77C2×Dic103C22×C414yes—
78C2×Dic103C2×D412yes—
79C2×Dic103C2×D412yes—
80Dic206—28no—
81C22×C103C23×C411yescharacteristic
82C22×C103C22×D411yescharacteristic
83C22×C103C2×#4111yescharacteristic
84C22×C1032−1+412yes—
85C22×C1032−1+412yes—
86C4×C103—24no—
87C4×C103—42no—
88C4×C103—42no—
89C4×C103C4×D414yes—
90Dic103—24no—
91Dic103—24no—
92Dic103—22no—
93Dic103—22no—
94Dic103—42no—
95C2×C103C2×C4×D411yescharacteristic
96C2×C103#51912yes—
97C2×C103#53611yescharacteristic
98C2×C103#53611yescharacteristic
99C2×C103#54112yes—
100#2327—1031nomaximal, Sylow
101C103#232711yescharacteristic, complemented, Sylow
102C2×C4⋊Q8—1031no—
103C2×C4×Q8—1031no—
104C2×C4×Q8—1031no—
105#391—1031no—
106#391D10311yescharacteristic
107#387—1034no—
108#387—1034no—
109#382—1031no—
110#376—1031no—
111C22×Q8—1031no—
112C22×Q8C2×D10311yescharacteristic
113C4⋊Q8—1038no—
114C4×Q8—2064no—
115C4×Q8—2064no—
116C2×C4⋊C4—1034no—
117C2×C4⋊C4—1031no—
118C2×C4⋊C4—1032no—
119C2×C4⋊C4—1032no—
120C2×C4⋊C4C2×D10311yescharacteristic
121C2×C42—1031no—
122C2×C42—1031no—
123C2×C42—1032no—
124C2×C42—1032no—
125C2×C42C2×D10311yescharacteristic
126#95—1032no—
127#95—1032no—
128#95—1034no—
129#95—1034no—
130#95C2×D10314yes—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—1034no—
134C2×Q8—2062no—
135C2×Q8—2062no—
136C2×Q8C4×D10314yes—
137C22×C4—1032no—
138C22×C4—1031no—
139C22×C4—1031no—
140C22×C4—1032no—
141C22×C4—1032no—
142C22×C4C22×D10312yes—
143C22×C4C22×D10312yes—
144C22×C4C22×D10312yes—
145C22×C4C22×D10311yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—10316no—
148C4⋊C4—2064no—
149C4⋊C4—2064no—
150C4⋊C4—2062no—
151C42—22no—
152C42—1034no—
153C42—1034no—
154C42—2064no—
155C42—2064no—
156C23C23×D10311yescharacteristic
157Q8—28no—
158Q8—2068no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—1032no—
167C2×C4—1032no—
168C2×C4—1034no—
169C2×C4—1034no—
170C2×C4—2062no—
171C2×C4—2064no—
172C2×C4—2062no—
173C2×C4—2062no—
174C2×C4—2062no—
175C2×C4—2062no—
176C2×C4—2062no—
177C2×C4—2062no—
178C2×C4C2×C4×D10314yes—
179C2×C4C2×C4×D10312yes—
180C2×C4D4×D10312yes—
181C2×C4#1311010412yes—
182C22C22×C4×D10311yescharacteristic
183C22C2×D4×D10311yescharacteristic
184C22C2×#1311010411yescharacteristic
185C22#1569306812yes—
186C22#1569306912yes—
187C4—24no—
188C4—42no—
189C4—42no—
190C4—4122no—
191C4—2062no—
192C4—2062no—
193C4—2064no—
194C4—2064no—
195C4(C22⋊D103)⋊C414yes—
196C2C2×(C22⋊D103)⋊C411yescharacteristic
197C2#2026826712yes—
198C2#2026836111yescharacteristic
199C2#2026836611yescharacteristic
200C2#2026840112yes—
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#391×C103C2
socle, prime radical, cosocleC23×C103C24
hypercenter#391D103
hypocenterC103#2327
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #15693019C4semidirect
101. C103#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#156930192
C2×Q8×Dic1032
C2×#156929862
#202676972
#202676782
#202676732
#202676562
#202676372
#391×C1032
#2327103