Finite Group Databasebeta

← #27206614

Subgroups — #27206614

Order 13184.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#20268408C212yesmaximal, complemented
2#20268079C212yesmaximal, complemented
3#20268075C212yesmaximal, complemented
4#20268049C211yesmaximal, characteristic, complemented
5#20268018C212yesmaximal, complemented
6#20268012C212yesmaximal, complemented
7#20268004C212yesmaximal, complemented
8#20267819C211yesmaximal, characteristic, complemented
9#469×C103C211yesmaximal, characteristic
10C2×Dic412C2211yescharacteristic
11C2×#13110093C2212yes—
12C22×C103⋊C8C2211yescharacteristic
13#15693020C2212yes—
14#15693014—22no—
15#15693008—22no—
16#15693008C2212yes—
17#15693002—22no—
18#15693000C2212yes—
19#15692998—22no—
20#15692986C2212yes—
21D4×Dic103C2212yes—
22#15692980C2211yescharacteristic
23#15692953C2211yescharacteristic
24#15692952C2212yes—
25Dic103⋊C8C2212yes—
26Dic103⋊C8C2212yes—
27#15692946C2212yes—
28#15692944C2212yes—
29#15692942C2212yes—
30C2×D8×C103C2211yescharacteristic
31C2×M16×C103C2211yescharacteristic
32#121×C103C2212yes—
33#106×C103C2211yescharacteristic
34#102×C103C2212yes—
35C2×Dic206—22no—
36C2×Dic206C2312yes—
37C22×Dic103—22no—
38Dic412—41no—
39#13110093—42no—
40C2×C103⋊C8—41no—
41C2×C103⋊C8C2312yes—
42C4⋊Dic103D412yes—
43C4⋊Dic103C2312yes—
44Dic103⋊C4—22no—
45Dic103⋊C4—22no—
46Dic103⋊C4—22no—
47C22⋊Dic103—22no—
48C22⋊Dic103—22no—
49C22⋊Dic103—22no—
50C22⋊Dic103—22no—
51C22⋊Dic103D411yescharacteristic
52C22⋊Dic103D411yescharacteristic
53C4×Dic103—22no—
54C4×Dic103C2312yes—
55C2×D4×C103—22no—
56C2×D4×C103C2312yes—
57C22×C4×C103C2311yescharacteristic
58D8×C103—41no—
59M16×C103—41no—
60C2×C8×C103C2311yescharacteristic
61C2×C8×C103C2311yescharacteristic
62C4⋊C4×C103C2312yes—
63C22⋊C4×C103—22no—
64C23×C103—22no—
65C23×C103C2×D411yescharacteristic
66D4×C103—22no—
67D4×C103—22no—
68D4×C103—82no—
69C2×C4×C103—21no—
70C2×C4×C103—21no—
71C2×C4×C103—22no—
72C2×C4×C103C2×D411yescharacteristic
73C2×C4×C103C2411yescharacteristic
74C2×Dic103—22no—
75C2×Dic103—22no—
76C2×Dic103—82no—
77C2×Dic103C2×D412yes—
78C2×Dic103C2×D412yes—
79Dic206—22no—
80Dic206—22no—
81Dic206—82no—
82C8×C103—21no—
83C8×C103—21no—
84C103⋊C8—22no—
85C22×C103—21no—
86C22×C103—22no—
87C22×C103—42no—
88C22×C103—42no—
89C22×C103—42no—
90C22×C103C22×D411yescharacteristic
91C4×C103—21no—
92C4×C103—42no—
93C4×C103H(5,𝔽2)11yescharacteristic
94C4×C1032−1+411yescharacteristic
95Dic103—22no—
96Dic103—22no—
97Dic103—42no—
98Dic103—42no—
99C2×C103—41no—
100C2×C103—82no—
101C2×C103#53711yescharacteristic
102C2×C103#57712yes—
103#3263—1031nomaximal, Sylow
104C103#326311yescharacteristic, complemented, Sylow
105#542—1032no—
106#476—1032no—
107#475—1032no—
108#470—1031no—
109#469D10311yescharacteristic
110#465—1032no—
111#464—1032no—
112#463—1032no—
113#424—1031no—
114C2×Q16—1031no—
115C2×SD16—1032no—
116C2×D8C2×D10311yescharacteristic
117C2×M16C2×D10311yescharacteristic
118C22×C8—1031no—
119C4⋊Q8—1032no—
120#126—2062no—
121#124—1032no—
122#124—2062no—
123#123—2062no—
124C22⋊Q8—1032no—
125C22⋊Q8—2062no—
126#121C2×D10312yes—
127C4×Q8—1032no—
128C4×D4—1032no—
129#117—1031no—
130#106—1031no—
131#106—1032no—
132#106C2×D10311yescharacteristic
133C4⋊C8—1032no—
134C4⋊C8—1032no—
135#103—1032no—
136#103—1032no—
137#102—1032no—
138#102C2×D10312yes—
139C2×Q8—1032no—
140C2×Q8—2062no—
141C2×D4—22no—
142C2×D4C22×D10312yes—
143C22×C4—2062no—
144C22×C4C22×D10311yescharacteristic
145Q16—4121no—
146SD16—4122no—
147D8—41no—
148M16—41no—
149C2×C8—1032no—
150C2×C8—4121no—
151C2×C8C22×D10311yescharacteristic
152C2×C8C22×D10311yescharacteristic
153C4⋊C4—1032no—
154C4⋊C4—1032no—
155C4⋊C4—2062no—
156C4⋊C4—2062no—
157C4⋊C4—2062no—
158C4⋊C4C22×D10312yes—
159C22⋊C4—22no—
160C22⋊C4—1031no—
161C22⋊C4—1031no—
162C22⋊C4—2062no—
163C22⋊C4—2062no—
164C22⋊C4—2062no—
165C22⋊C4—2062no—
166C42—1032no—
167C42—2062no—
168C23—22no—
169C23D4×D10311yescharacteristic
170Q8—8242no—
171Q8—2062no—
172Q8—2062no—
173D4—22no—
174D4—22no—
175D4—82no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—8242no—
180C2×C4—1032no—
181C2×C4—1032no—
182C2×C4—2062no—
183C2×C4—2062no—
184C2×C4D4×D10311yescharacteristic
185C2×C4C23×D10311yescharacteristic
186C8—21no—
187C8—21no—
188C8—2062no—
189C22—22no—
190C22—21no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22C2×D4×D10311yescharacteristic
195C4—21no—
196C4—42no—
197C4—4122no—
198C4—4122no—
199C4—2062no—
200C4—2062no—
201C4#1569306611yescharacteristic
202C4#1569306811yescharacteristic
203C2—41no—
204C2—82no—
205C2#2026836811yescharacteristic
206C2#2026860112yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting, prime radical#469×C103C2
socleC22×C103C22×D4
hypercenter#469D103
hypocenterC103#3263
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20268408C2semidirect
2. #20268079C2semidirect
3. #20268075C2semidirect
4. #20268049C2semidirect
5. #20268018C2semidirect
6. #20268012C2semidirect
7. #20268004C2semidirect
8. #20267819C2semidirect
104. C103#3263semidirect

Maximal subgroups

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

subgroupindex
#202684082
#202680792
#202680752
#202680492
#202680182
#202680122
#202680042
#202678192
#469×C1032
#3263103