Finite Group Databasebeta

← #27198323

Subgroups — #27198323

Order 13184.

424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 173 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#20267698C211yesmaximal, characteristic
3#20267695C212yesmaximal
4#20267678C212yesmaximal
5#20267675C212yesmaximal
6#20267673C212yesmaximal
7#20267672C212yesmaximal
8#20267658C212yesmaximal
9#391×C103C211yesmaximal, characteristic
10C22×Dic206C2211yescharacteristic
11#15693019C418yescomplemented
12C2×C4⋊Dic103C2211yescharacteristic
13C2×Dic103⋊C4C2212yes—
14C2×Dic103⋊C4C2212yes—
15C2×Dic103⋊C4C2212yes—
16C2×C4×Dic103C2212yes—
17C2×C4×Dic103C2211yescharacteristic
18C2×C4×Dic103C2211yescharacteristic
19C103⋊#95C2212yes—
20C103⋊#95C2212yes—
21C103⋊#95C2212yes—
22C103⋊#95C2212yes—
23C103⋊#95C2212yes—
24C103⋊#95C2212yes—
25C103⋊#95C2212yes—
26C103⋊#95C2212yes—
27C22×Q8×C103C2211yescharacteristic
28C2×C4⋊C4×C103C2211yescharacteristic
29C2×C42×C103C2211yescharacteristic
30#95×C103C2212yes—
31#95×C103C2212yes—
32C2×Dic206—41no—
33C2×Dic206—41no—
34C2×Dic206C2×C414yes—
35C22×Dic103C2312yes—
36C22×Dic103C2312yes—
37C22×Dic103C2312yes—
38C22×Dic103C2312yes—
39C4⋊Dic103—41no—
40Dic103⋊C4—42no—
41Dic103⋊C4C2×C418yes—
42Dic103⋊C4C2×C418yes—
43C4×Dic103—42no—
44C4×Dic103—41no—
45C4×Dic103C2×C414yes—
46C2×Q8×C103—41no—
47C2×Q8×C103—41no—
48C2×Q8×C103C2×C414yes—
49C22×C4×C103C2312yes—
50C22×C4×C103C2312yes—
51C22×C4×C103C2311yescharacteristic
52C22×C4×C103C2311yescharacteristic
53C22×C4×C103C2311yescharacteristic
54C4⋊C4×C103—41no—
55C42×C103—41no—
56C23×C103C2411yescharacteristic
57Q8×C103—44no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—21no—
62C2×C4×C103—21no—
63C2×C4×C103—21no—
64C2×C4×C103—22no—
65C2×C4×C103—22no—
66C2×C4×C103—22no—
67C2×C4×C103—24no—
68C2×C4×C103—22no—
69C2×C4×C103C22×C412yes—
70C2×C4×C103C22×C412yes—
71C2×C4×C103C22×C412yes—
72C2×Dic103—22no—
73C2×Dic103—22no—
74C2×Dic103—22no—
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103—22no—
78C2×Dic103—22no—
79C2×Dic103—22no—
80C2×Dic103—24no—
81C2×Dic103C22×C414yes—
82C2×Dic103C22×C414yes—
83Dic206—44no—
84C22×C103C23×C411yescharacteristic
85C22×C103H(5,𝔽2)11yescharacteristic
86C22×C103H(5,𝔽2)11yescharacteristic
87C22×C1032−1+412yes—
88C22×C1032−1+412yes—
89C4×C103—22no—
90C4×C103—22no—
91C4×C103—22no—
92C4×C103—42no—
93C4×C103—42no—
94Dic103—24no—
95Dic103—24no—
96Dic103—42no—
97Dic103—42no—
98C2×C103#51811yescharacteristic
99C2×C103#51912yes—
100C2×C103#56311yescharacteristic
101C2×C103#56311yescharacteristic
102C2×C103#56312yes—
103#2381—1031nomaximal, Sylow
104C103#238111yescharacteristic, complemented, Sylow
105C2×C4⋊Q8—1031no—
106#391—1031no—
107#391—1032no—
108#391D10311yescharacteristic
109#387—1032no—
110#387—1032no—
111#387—1032no—
112#387—1032no—
113#383—1032no—
114C22×Q8—1031no—
115C22×Q8C2×D10311yescharacteristic
116C4⋊Q8—1038no—
117C2×C4⋊C4—1032no—
118C2×C4⋊C4—1032no—
119C2×C4⋊C4—1032no—
120C2×C4⋊C4—1031no—
121C2×C4⋊C4C2×D10311yescharacteristic
122C2×C42—1031no—
123C2×C42—1032no—
124C2×C42—1031no—
125C2×C42C2×D10311yescharacteristic
126#95—1032no—
127#95—1032no—
128#95—1032no—
129#95—1032no—
130#95—1032no—
131#95—1032no—
132#95—1032no—
133#95—1032no—
134#95C2×D10312yes—
135#95C2×D10312yes—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—1034no—
139C2×Q8—4121no—
140C2×Q8—4121no—
141C2×Q8C4×D10314yes—
142C22×C4—1032no—
143C22×C4—1032no—
144C22×C4—1032no—
145C22×C4—1032no—
146C22×C4C22×D10312yes—
147C22×C4C22×D10312yes—
148C22×C4C22×D10311yescharacteristic
149C22×C4C22×D10311yescharacteristic
150C22×C4C22×D10311yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—1038no—
153C4⋊C4—1038no—
154C4⋊C4—4122no—
155C4⋊C4—4121no—
156C42—41no—
157C42—1034no—
158C42—4121no—
159C42—4122no—
160C23C23×D10311yescharacteristic
161Q8—44no—
162Q8—4124no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—1034no—
175C2×C4—1034no—
176C2×C4—2062no—
177C2×C4—2062no—
178C2×C4—2062no—
179C2×C4—2064no—
180C2×C4—2062no—
181C2×C4—2062no—
182C2×C4—2062no—
183C2×C4—2062no—
184C2×C4—2062no—
185C2×C4C2×C4×D10312yes—
186C2×C4C2×C4×D10312yes—
187C2×C4C2×C4×D10312yes—
188C22C22×C4×D10311yescharacteristic
189C22#1569306611yescharacteristic
190C22#1569306611yescharacteristic
191C22#1569306812yes—
192C22#1569306912yes—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—4122no—
199C4—4122no—
200C4—2064no—
201C4—2064no—
202C2#2026826411yescharacteristic
203C2#2026826712yes—
204C2#2026854011yescharacteristic
205C2#2026854111yescharacteristic
206C2#2026854212yes—
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#391×C103C2
socle, prime radical, cosocleC23×C103C24
hypercenter#391D103
hypocenterC103#2381
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #15693019C4semidirect
104. C103#2381semidirect

Maximal subgroups

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

subgroupindex
C2×#156930192
#202676982
#202676952
#202676782
#202676752
#202676732
#202676722
#202676582
#391×C1032
#2381103