Finite Group Databasebeta

← #27205766

Subgroups — #27205766

Order 13184.

362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#20268403C211yesmaximal, characteristic, complemented
2#20268190C211yesmaximal, characteristic, complemented
3#20268163C211yesmaximal, characteristic, complemented
4#20268161C211yesmaximal, characteristic, complemented
5#20268155C211yesmaximal, characteristic, complemented
6#20268035C212yesmaximal, complemented
7#20268018C212yesmaximal, complemented
8#20267891C212yesmaximal, complemented
9C4×#13110093C212yesmaximal, complemented
10#20267747C211yesmaximal, characteristic, complemented
11#540×C103C211yesmaximal, characteristic
12C2×#13110093C2212yes—
13C2×#13110093C2212yes—
14C2×#13110089C2211yescharacteristic
15C22×C103⋊C8C2211yescharacteristic
16#15693021C2211yescharacteristic
17#15693014—22no—
18#15693013C2211yescharacteristic
19#15693011—22no—
20#15693000C2212yes—
21C4×Dic206C2212yes—
22#15692954C2212yes—
23#15692952C2212yes—
24#15692944C2212yes—
25#15692944C2212yes—
26#15692942C2212yes—
27#15692942C2212yes—
28#15692932C2211yescharacteristic
29#15692932C2211yescharacteristic
30C4×C103⋊C8C2211yescharacteristic
31C4×C103⋊C8C2211yescharacteristic
32#127×C103C2211yescharacteristic
33#125×C103C2211yescharacteristic
34#123×C103—22no—
35#121×C103—22no—
36#121×C103C2212yes—
37C4×D4×C103C2212yes—
38#117×C103C2211yescharacteristic
39C2×Dic206C2312yes—
40#13110093—24no—
41#13110093—24no—
42#13110089—22no—
43C2×C103⋊C8—22no—
44C2×C103⋊C8C2311yescharacteristic
45C2×C103⋊C8C2311yescharacteristic
46C2×C103⋊C8C2311yescharacteristic
47C2×C103⋊C8C2311yescharacteristic
48C4⋊Dic103—22no—
49C4⋊Dic103C2312yes—
50Dic103⋊C4—22no—
51Dic103⋊C4—22no—
52Dic103⋊C4—22no—
53C22⋊Dic103—22no—
54C4×Dic103—22no—
55C2×D4×C103—22no—
56C2×D4×C103—22no—
57C2×D4×C103C2312yes—
58C22×C4×C103—22no—
59C22×C4×C103C2311yescharacteristic
60C4⋊C4×C103—22no—
61C4⋊C4×C103D412yes—
62C4⋊C4×C103C2312yes—
63C22⋊C4×C103—22no—
64C22⋊C4×C103—22no—
65C22⋊C4×C103D412yes—
66C42×C103C2311yescharacteristic
67C42×C103C2311yescharacteristic
68C23×C103—22no—
69C23×C103C2×D411yescharacteristic
70D4×C103—22no—
71D4×C103—22no—
72D4×C103—82no—
73D4×C103—82no—
74C2×C4×C103—21no—
75C2×C4×C103—21no—
76C2×C4×C103—22no—
77C2×C4×C103—82no—
78C2×C4×C103C2×D412yes—
79C2×C4×C103C2×D412yes—
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2411yescharacteristic
82C2×Dic103—22no—
83C2×Dic103—22no—
84Dic206—22no—
85Dic206—22no—
86C103⋊C8—21no—
87C103⋊C8—21no—
88C103⋊C8#4112yes—
89C103⋊C8#4112yes—
90C22×C103—21no—
91C22×C103—22no—
92C22×C103—42no—
93C22×C103—42no—
94C22×C103—42no—
95C22×C103C22×D411yescharacteristic
96C4×C103—21no—
97C4×C103—22no—
98C4×C103—22no—
99C4×C103—42no—
100C4×C103C2×#4111yescharacteristic
101C4×C103C2×#4111yescharacteristic
102Dic103—42no—
103Dic103—42no—
104C2×C103—41no—
105C2×C103—82no—
106C2×C103#53211yescharacteristic
107C2×C103#57712yes—
108#3174—1031nomaximal, Sylow
109C103#317411yescharacteristic, complemented, Sylow
110#541—1031no—
111#540D10311yescharacteristic
112#499—1031no—
113#492—1031no—
114#491—1031no—
115#490—1031no—
116#468—1032no—
117#465—1032no—
118#440—1032no—
119C4×SD16—1032no—
120#405—1031no—
121C2×SD16—1032no—
122C2×SD16—1032no—
123C2×M16—1031no—
124C22×C8—1031no—
125C4⋊Q8—1031no—
126#127C2×D10311yescharacteristic
127#126—2062no—
128#125—1031no—
129#125—2062no—
130#125C2×D10311yescharacteristic
131#123—22no—
132C22⋊Q8—1032no—
133#121—22no—
134#121C2×D10312yes—
135C4×Q8—1032no—
136C4×D4C2×D10312yes—
137#117C2×D10311yescharacteristic
138#107—1032no—
139#106—1032no—
140#103—1032no—
141#103—1032no—
142#102—1032no—
143#102—1032no—
144#97—1031no—
145#97—1031no—
146C4×C8—1031no—
147C4×C8—1031no—
148C2×Q8—1032no—
149C2×D4—22no—
150C2×D4—22no—
151C2×D4C22×D10312yes—
152C22×C4—22no—
153C22×C4C22×D10311yescharacteristic
154SD16—2064no—
155SD16—2064no—
156M16—2062no—
157C2×C8—1031no—
158C2×C8—1031no—
159C2×C8—1031no—
160C2×C8—1031no—
161C2×C8—2062no—
162C4⋊C4—22no—
163C4⋊C4—1032no—
164C4⋊C4—2062no—
165C4⋊C4—2062no—
166C4⋊C4—2062no—
167C4⋊C4—2062no—
168C4⋊C4C22⋊D10312yes—
169C4⋊C4C22×D10312yes—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—2062no—
173C22⋊C4C22⋊D10312yes—
174C42—2062no—
175C42C22×D10311yescharacteristic
176C42C22×D10311yescharacteristic
177C23—22no—
178C23C2×C22⋊D10311yescharacteristic
179Q8—2062no—
180Q8—2062no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—82no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—2062no—
190C2×C4—2062no—
191C2×C4C2×C22⋊D10312yes—
192C2×C4C2×C22⋊D10312yes—
193C2×C4C2×C22⋊D10311yescharacteristic
194C2×C4C23×D10311yescharacteristic
195C8—1032no—
196C8—1032no—
197C8—2061no—
198C8—2061no—
199C22—21no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22C22×C22⋊D10311yescharacteristic
205C4—21no—
206C4—22no—
207C4—22no—
208C4—42no—
209C4—4122no—
210C4—4122no—
211C4#41×D10311yescharacteristic
212C4#41×D10311yescharacteristic
213C2—41no—
214C2—82no—
215C2#2026833711yescharacteristic
216C2#2026860212yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting, prime radical#540×C103C2
socleC22×C103C22×D4
hypercenter#540D103
hypocenterC103#3174
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20268403C2semidirect
2. #20268190C2semidirect
3. #20268163C2semidirect
4. #20268161C2semidirect
5. #20268155C2semidirect
6. #20268035C2semidirect
7. #20268018C2semidirect
8. #20267891C2semidirect
9. C4×#13110093C2semidirect
10. #20267747C2semidirect
109. C103#3174semidirect

Maximal subgroups

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

subgroupindex
#202684032
#202681902
#202681632
#202681612
#202681552
#202680352
#202680182
#202678912
C4×#131100932
#202677472
#540×C1032
#3174103