Finite Group Databasebeta

← #27195557

Subgroups — #27195557

Order 13184.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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×#15693002C211yesmaximal, characteristic
2C2×#15692936C211yesmaximal, characteristic
3#20267652C212yesmaximal, complemented
4#20267558C212yesmaximal, complemented
5#518×C103C211yesmaximal, characteristic
6C23×Dic103C2211yescharacteristic
7#15693002—22no—
8#15693002C414yescomplemented
9C2×Dic103⋊C4—21no—
10C2×C22⋊Dic103—21no—
11C2×C22⋊Dic103C2212yes—
12C2×C22⋊Dic103C2211yescharacteristic
13#15692936—22no—
14C103⋊#95—24no—
15C22×D4×C103C2211yescharacteristic
16C4×D4×C103—24no—
17#117×C103—21no—
18C2×C22⋊C4×C103—21no—
19C2×C22⋊C4×C103C2212yes—
20C22×Dic103—22no—
21C22×Dic103—21no—
22C22×Dic103—21no—
23C22×Dic103—21no—
24C22×Dic103—22no—
25C22×Dic103—22no—
26C22×Dic103C2×C412yescomplemented
27Dic103⋊C4—24no—
28C22⋊Dic103—24no—
29C22⋊Dic103—21no—
30C22⋊Dic103—22no—
31C22⋊Dic103—22no—
32C22⋊Dic103C2×C412yescomplemented
33C24×C103D411yescharacteristic
34C24×C103C2311yescharacteristic
35C2×D4×C103—22no—
36C2×D4×C103—22no—
37C2×D4×C103C2×C412yes—
38C2×D4×C103D412yes—
39C22×C4×C103—22no—
40C22×C4×C103D411yescharacteristic
41C22×C4×C103D414yes—
42C4⋊C4×C103—22no—
43C22⋊C4×C103—22no—
44C22⋊C4×C103—22no—
45C22⋊C4×C103—22no—
46C42×C103—22no—
47C23×C103—21no—
48C23×C103—21no—
49C23×C103—42no—
50C23×C103—42no—
51C23×C103C22⋊C412yes—
52C23×C103C22×C411yescharacteristic
53C23×C103C2×D411yescharacteristic
54C23×C103C2×D412yes—
55C23×C103C2×D411yescharacteristic
56C23×C103#4112yes—
57D4×C103—24no—
58D4×C103—24no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—24no—
62C2×C4×C103—44no—
63C2×C4×C103—82no—
64C2×C4×C103C22⋊C412yes—
65C2×Dic103—22no—
66C2×Dic103—22no—
67C2×Dic103—24no—
68C2×Dic103—42no—
69C2×Dic103—41no—
70C2×Dic103—42no—
71C2×Dic103—41no—
72C2×Dic103—44no—
73C2×Dic103—42no—
74C22×C103—24no—
75C22×C103—22no—
76C22×C103—22no—
77C22×C103—41no—
78C22×C103—41no—
79C22×C103—42no—
80C22×C103—42no—
81C22×C103—42no—
82C22×C103—81no—
83C22×C103C2×C22⋊C411yescharacteristic
84C22×C103C4×D412yes—
85C22×C103#12011yescharacteristic
86C22×C103#12112yes—
87C22×C103#12311yescharacteristic
88C4×C103—22no—
89C4×C103—44no—
90Dic103—42no—
91Dic103—42no—
92Dic103—82no—
93C2×C103—21no—
94C2×C103—22no—
95C2×C103—21no—
96C2×C103—22no—
97C2×C103—42no—
98C2×C103#38611yescharacteristic
99C2×C103#45812yes—
100#1890—1031nomaximal, Sylow
101C103#189011yescharacteristic, complemented, Sylow
102C2×#123—1031no—
103#518D10311yescharacteristic
104C2×#99—1031no—
105#381—1032no—
106#342—1032no—
107C22×D4C2×D10311yescharacteristic
108C23×C4—1031no—
109#123—1034no—
110#123—2062no—
111C4×D4—24no—
112#117—21no—
113C2×C4⋊C4—2061no—
114C2×C22⋊C4—21no—
115C2×C22⋊C4—1031no—
116C2×C22⋊C4—1032no—
117C2×C22⋊C4—2061no—
118C2×C22⋊C4C2×D10312yes—
119#99—2062no—
120#95—2064no—
121C24C22⋊D10311yescharacteristic
122C24C22×D10311yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C4×D10312yes—
126C2×D4D41212yes—
127C22×C4—22no—
128C22×C4—1032no—
129C22×C4—2062no—
130C22×C4—2062no—
131C22×C4—2061no—
132C22×C4—2061no—
133C22×C4—2061no—
134C22×C4—2062no—
135C22×C4C22⋊D10311yescharacteristic
136C22×C4C22⋊D10314yes—
137C4⋊C4—22no—
138C4⋊C4—2064no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—1032no—
143C22⋊C4—2062no—
144C22⋊C4—2062no—
145C22⋊C4—2064no—
146C22⋊C4—2061no—
147C42—22no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23(C2×D103)⋊C412yes—
153C23C2×C4×D10311yescharacteristic
154C23C2×C22⋊D10311yescharacteristic
155C23C2×C22⋊D10312yes—
156C23C2×D41211yescharacteristic
157C23#1311010512yes—
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—24no—
163C2×C4—44no—
164C2×C4—82no—
165C2×C4—4124no—
166C2×C4—4122no—
167C2×C4—4122no—
168C2×C4—4121no—
169C2×C4—4122no—
170C2×C4—4121no—
171C2×C4—2062no—
172C2×C4—2062no—
173C2×C4—2064no—
174C2×C4(C2×D103)⋊C412yes—
175C22—24no—
176C22—22no—
177C22—22no—
178C22—41no—
179C22—41no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22C2×(C2×D103)⋊C411yescharacteristic
185C22C4×C22⋊D10312yes—
186C22#1569299011yescharacteristic
187C22#1569299512yes—
188C22#1569300411yescharacteristic
189C4—22no—
190C4—44no—
191C4—8242no—
192C4—4122no—
193C4—4122no—
194C2—22no—
195C2—21no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#2026767011yescharacteristic
200C2#2026798112yes—
subgroupG/H
centerC22#15692990
commutatorC23×C103C22×C4
FrattiniC24C22×D103
Fitting#518×C103C2
socleC22×C103#120
prime radicalC22×D4×C103C22
cosocleC24×C103C23
hypercenter#518D103
hypocenterC103#1890
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
3. #20267652C2semidirect
4. #20267558C2semidirect
8. #15693002C4semidirect
26. C22×Dic103C2×C4semidirect
32. C22⋊Dic103C2×C4semidirect
101. C103#1890semidirect

Maximal subgroups

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

subgroupindex
C2×#156930022
C2×#156929362
#202676522
#202675582
#518×C1032
#1890103