Finite Group Databasebeta

← #27197900

Subgroups — #27197900

Order 13184.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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×#15693000C211yesmaximal, characteristic
2#20267695C212yesmaximal, complemented
3#20267685C212yesmaximal
4#20267679C212yesmaximal
5#20267676C212yesmaximal, complemented
6#20267675C212yesmaximal, complemented
7#20267654C211yesmaximal, characteristic
8C4×Dic103⋊C4C212yesmaximal, complemented
9C4×C22⋊C4×C103C211yesmaximal, characteristic
10C22×Dic206C2211yescharacteristic
11#15693000C418yescomplemented
12C2×C4⋊Dic103C2211yescharacteristic
13C2×Dic103⋊C4C2212yes—
14C2×Dic103⋊C4C2212yes—
15C2×Dic103⋊C4C2212yes—
16C2×C22⋊Dic103C2211yescharacteristic
17C2×C22⋊Dic103C2211yescharacteristic
18C2×C22⋊Dic103C2212yes—
19C2×C4×Dic103C2212yes—
20C2×C4×Dic103C2212yes—
21C103⋊#95C2212yes—
22C103⋊#95C2212yes—
23C103⋊#95C2212yes—
24C103⋊#95C2212yes—
25C103⋊#95C2212yes—
26C103⋊#95C2212yes—
27C23×C4×C103C2211yescharacteristic
28C2×C22⋊C4×C103C2212yes—
29C2×C42×C103C2211yescharacteristic
30C2×C42×C103C2211yescharacteristic
31#95×C103C2212yes—
32C2×Dic206—41no—
33C2×Dic206—41no—
34C2×Dic206C2×C414yes—
35C22×Dic103C2312yes—
36C22×Dic103C2312yes—
37C22×Dic103C2312yes—
38C22×Dic103C2312yes—
39C4⋊Dic103C2×C414yes—
40Dic103⋊C4—24no—
41Dic103⋊C4—42no—
42Dic103⋊C4C2×C418yes—
43C22⋊Dic103—41no—
44C22⋊Dic103—41no—
45C22⋊Dic103C2×C418yes—
46C4×Dic103—24no—
47C4×Dic103—42no—
48C24×C103C2311yescharacteristic
49C22×C4×C103—41no—
50C22×C4×C103—41no—
51C22×C4×C103C2×C414yes—
52C22×C4×C103C2312yes—
53C22×C4×C103C2311yescharacteristic
54C22×C4×C103C2311yescharacteristic
55C22×C4×C103C2312yes—
56C22⋊C4×C103—24no—
57C42×C103—41no—
58C42×C103—41no—
59C23×C103—22no—
60C23×C103—21no—
61C23×C103—21no—
62C23×C103—22no—
63C23×C103C22×C412yes—
64C23×C103C2411yescharacteristic
65C2×C4×C103—21no—
66C2×C4×C103—21no—
67C2×C4×C103—22no—
68C2×C4×C103—21no—
69C2×C4×C103—21no—
70C2×C4×C103—22no—
71C2×C4×C103—22no—
72C2×C4×C103—22no—
73C2×C4×C103—22no—
74C2×C4×C103—44no—
75C2×C4×C103C22×C412yes—
76C2×C4×C103C22×C412yes—
77C2×C4×C103#4114yes—
78C2×Dic103—22no—
79C2×Dic103—22no—
80C2×Dic103—22no—
81C2×Dic103—22no—
82C2×Dic103—22no—
83C2×Dic103—22no—
84C2×Dic103—22no—
85C2×Dic103—22no—
86C2×Dic103—22no—
87C2×Dic103—22no—
88C2×Dic103C22×C414yes—
89C2×Dic103C22×C414yes—
90Dic206—44no—
91C22×C103—22no—
92C22×C103—22no—
93C22×C103—22no—
94C22×C103—42no—
95C22×C103—42no—
96C22×C103C23×C411yescharacteristic
97C22×C103C2×#4112yes—
98C22×C103H(5,𝔽2)11yescharacteristic
99C22×C103H(5,𝔽2)11yescharacteristic
100C22×C1032−1+412yes—
101C4×C103—22no—
102C4×C103—22no—
103C4×C103—24no—
104C4×C103—42no—
105Dic103—24no—
106Dic103—24no—
107Dic103—42no—
108Dic103—42no—
109C2×C103—42no—
110C2×C103C4×#4111yescharacteristic
111C2×C103#51811yescharacteristic
112C2×C103#51911yescharacteristic
113C2×C103#53912yes—
114C2×C103#54212yes—
115#2332—1031nomaximal, Sylow
116C103#233211yescharacteristic, complemented, Sylow
117C2×C22⋊Q8—1031no—
118#391—1032no—
119#388—1032no—
120#388—1032no—
121#387—1032no—
122#387—1032no—
123#381—1031no—
124C4×C4⋊C4—1032no—
125C4×C22⋊C4D10311yescharacteristic
126C22×Q8—1031no—
127C23×C4C2×D10311yescharacteristic
128C22⋊Q8—1038no—
129C2×C4⋊C4—1032no—
130C2×C4⋊C4—1031no—
131C2×C4⋊C4—1032no—
132C2×C4⋊C4—1032no—
133C2×C22⋊C4—1032no—
134C2×C22⋊C4—1031no—
135C2×C22⋊C4—1031no—
136C2×C22⋊C4C2×D10312yes—
137C2×C42—1032no—
138C2×C42—1032no—
139C2×C42C2×D10311yescharacteristic
140C2×C42C2×D10311yescharacteristic
141#95—1032no—
142#95—1032no—
143#95—1032no—
144#95—1032no—
145#95—1032no—
146#95—1032no—
147#95C2×D10312yes—
148C24C22×D10311yescharacteristic
149C2×Q8—1034no—
150C2×Q8—4121no—
151C2×Q8—4121no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—1032no—
155C22×C4—1032no—
156C22×C4—1032no—
157C22×C4—1032no—
158C22×C4C4×D10314yes—
159C22×C4C22×D10312yes—
160C22×C4C22×D10311yescharacteristic
161C22×C4C22×D10311yescharacteristic
162C22×C4C22×D10312yes—
163C4⋊C4—1038no—
164C4⋊C4—1034no—
165C4⋊C4—4122no—
166C4⋊C4—2064no—
167C22⋊C4—24no—
168C22⋊C4—1038no—
169C22⋊C4—4121no—
170C22⋊C4—4121no—
171C42—41no—
172C42—41no—
173C42—4122no—
174C42—2064no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—22no—
179C23C2×C4×D10312yes—
180C23C23×D10311yescharacteristic
181Q8—4124no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—1034no—
193C2×C4—1034no—
194C2×C4—2062no—
195C2×C4—2062no—
196C2×C4—2062no—
197C2×C4—2062no—
198C2×C4—2062no—
199C2×C4—2062no—
200C2×C4—2062no—
201C2×C4—2062no—
202C2×C4—2062no—
203C2×C4—2062no—
204C2×C4C2×C4×D10312yes—
205C2×C4C2×C4×D10312yes—
206C2×C4#1311010514yes—
207C22—22no—
208C22—22no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22C22×C4×D10311yescharacteristic
213C22C2×#1311010512yes—
214C22#1569306611yescharacteristic
215C22#1569306611yescharacteristic
216C22#1569306812yes—
217C4—24no—
218C4—22no—
219C4—22no—
220C4—42no—
221C4—4122no—
222C4—4122no—
223C4—2064no—
224C4—2064no—
225C2—42no—
226C2C4×#1311010511yescharacteristic
227C2#2026826411yescharacteristic
228C2#2026826811yescharacteristic
229C2#2026838312yes—
230C2#2026840612yes—
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
FittingC4×C22⋊C4×C103C2
socle, cosocleC23×C103C24
prime radicalC24×C103C23
hypercenterC4×C22⋊C4D103
hypocenterC103#2332
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20267695C2semidirect
5. #20267676C2semidirect
6. #20267675C2semidirect
8. C4×Dic103⋊C4C2semidirect
11. #15693000C4semidirect
116. C103#2332semidirect

Maximal subgroups

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

subgroupindex
C2×#156930002
#202676952
#202676852
#202676792
#202676762
#202676752
#202676542
C4×Dic103⋊C42
C4×C22⋊C4×C1032
#2332103