Finite Group Databasebeta

← #27205801

Subgroups — #27205801

Order 13184.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#20268399C212yesmaximal
2#20268191C211yesmaximal, characteristic, complemented
3#20268169C211yesmaximal, characteristic, complemented
4#20268158C212yesmaximal, complemented
5#20268050C211yesmaximal, characteristic
6#20268046C211yesmaximal, characteristic
7#20268031C212yesmaximal
8#20267899C211yesmaximal, characteristic, complemented
9C4×#13110095C212yesmaximal, complemented
10#20267748C211yesmaximal, characteristic
11#441×C103C211yesmaximal, characteristic, complemented
12C2×Dic412C2211yescharacteristic
13C2×#13110095C2212yes—
14C2×#13110088C2211yescharacteristic
15C2×C8×D103C2211yescharacteristic
16#15693019C2212yes—
17#15693016—22no—
18#15693015—22no—
19#15693013—22no—
20#15693012C2212yes—
21#15693011—22no—
22#15693001C2212yes—
23#15692997C2212yes—
24C4×Dic206C2212yes—
25#15692978C2211yescharacteristic
26#15692954C2212yes—
27#15692953C2211yescharacteristic
28#15692946C2212yes—
29#15692945C2212yes—
30#15692944C2212yes—
31#15692931C2211yescharacteristic
32C4×C103⋊C8C2211yescharacteristic
33C8×Dic103C2211yescharacteristic
34C2×Q16×C103C2211yescharacteristic
35C4×Q8×C103C2212yes—
36#106×C103C2211yescharacteristic
37#103×C103C2212yes—
38#97×C103C2211yescharacteristic
39C2×Dic206C2312yes—
40C2×C4×D103C2311yescharacteristic
41Dic412—22no—
42#13110095—24no—
43#13110088—22no—
44C2×C103⋊C8C2311yescharacteristic
45C2×C103⋊C8C2311yescharacteristic
46C8×D103—22no—
47C4⋊Dic103—22no—
48C4⋊Dic103—22no—
49C4⋊Dic103C2312yes—
50Dic103⋊C4—22no—
51Dic103⋊C4—22no—
52Dic103⋊C4—22no—
53Dic103⋊C4—22no—
54Dic103⋊C4—22no—
55Dic103⋊C4D412yes—
56(C2×D103)⋊C4—22no—
57(C2×D103)⋊C4—22no—
58(C2×D103)⋊C4D412yes—
59C4×Dic103—22no—
60C4×Dic103C2311yescharacteristic
61C2×Q8×C103C2312yes—
62Q16×C103—22no—
63C2×C8×C103C2311yescharacteristic
64C2×C8×C103C2311yescharacteristic
65C4⋊C4×C103—22no—
66C4⋊C4×C103C2312yes—
67C42×C103—22no—
68C42×C103C2311yescharacteristic
69C22×D103C2×D411yescharacteristic
70Q8×C103—22no—
71Q8×C103—22no—
72C2×C4×C103—22no—
73C2×C4×C103—22no—
74C2×C4×C103C2×D412yes—
75C2×C4×C103C2411yescharacteristic
76C2×Dic103—22no—
77C2×Dic103—22no—
78C2×Dic103C2×D412yes—
79C2×Dic103C2×D411yescharacteristic
80C4×D103—21no—
81C4×D103—21no—
82Dic206—22no—
83Dic206—22no—
84C8×C103—21no—
85C8×C103#4112yes—
86C103⋊C8—21no—
87C103⋊C8#4112yes—
88C22×C103C22×D411yescharacteristic
89C2×D103—21no—
90C2×D103—22no—
91C4×C103—22no—
92C4×C103—42no—
93C4×C103—42no—
94C4×C103C2×#4111yescharacteristic
95C4×C103C2×#4111yescharacteristic
96Dic103—21no—
97Dic103—22no—
98Dic103—42no—
99Dic103—42no—
100C2×C103#53211yescharacteristic
101C2×C103#57812yes—
102D103—41no—
103#3177—1031nomaximal, Sylow
104C103#317711yescharacteristic, complemented, Sylow
105#541—1032no—
106#499—1031no—
107#494—1031no—
108#491—1032no—
109#470—1031no—
110#470—1031no—
111#467—1032no—
112#441—1031no—
113#441D10311yescharacteristic, complemented
114C4×Q16—1032no—
115#405—1031no—
116C2×Q16—1032no—
117C2×Q16—1031no—
118C2×Q16C2×D10311yescharacteristic
119C2×M16—1031no—
120C22×C8—1031no—
121C4⋊Q8—1032no—
122#126—2062no—
123#126—2062no—
124#125—1032no—
125#125—2062no—
126#125—2062no—
127C22⋊Q8—1032no—
128C22⋊Q8—1032no—
129C4×Q8—1032no—
130C4×Q8C2×D10312yes—
131#117—1031no—
132#107—1032no—
133#106—1031no—
134#106C2×D10311yescharacteristic
135#103—1032no—
136#103—1032no—
137#103—1032no—
138#103C2×D10312yes—
139#97—1031no—
140#97C2×D10311yescharacteristic
141C4×C8—1031no—
142C4×C8—1031no—
143C2×Q8—1032no—
144C2×Q8C22×D10312yes—
145C22×C4—1031no—
146Q16—22no—
147Q16—2064no—
148Q16—2062no—
149M16—2062no—
150C2×C8—1031no—
151C2×C8—1031no—
152C2×C8—2062no—
153C2×C8C22×D10311yescharacteristic
154C2×C8C22×D10311yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—1032no—
157C4⋊C4—1032no—
158C4⋊C4—2062no—
159C4⋊C4—2062no—
160C4⋊C4—2062no—
161C4⋊C4—2062no—
162C4⋊C4—2062no—
163C4⋊C4—2062no—
164C4⋊C4—2062no—
165C4⋊C4C22×D10312yes—
166C22⋊C4—1032no—
167C22⋊C4—2062no—
168C22⋊C4—2062no—
169C42—22no—
170C42—1031no—
171C42—2062no—
172C42C22×D10311yescharacteristic
173C23—1031no—
174Q8—22no—
175Q8—22no—
176Q8—2062no—
177Q8—2062no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—1032no—
181C2×C4—1031no—
182C2×C4—2062no—
183C2×C4—2062no—
184C2×C4—2061no—
185C2×C4—2061no—
186C2×C4D4×D10312yes—
187C2×C4C23×D10311yescharacteristic
188C8—21no—
189C8—1032no—
190C8—2061no—
191C8#1311010512yes—
192C22—2061no—
193C22—2062no—
194C22C2×D4×D10311yescharacteristic
195C4—22no—
196C4—42no—
197C4—42no—
198C4—4122no—
199C4—4122no—
200C4—2061no—
201C4—2062no—
202C4#41×D10311yescharacteristic
203C4C2×#1311010511yescharacteristic
204C2—4121no—
205C2#2026833811yescharacteristic
206C2#2026860712yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#441×C103C2
socleC22×C103C22×D4
prime radicalC22×D103C2×D4
hypercenter#441D103
hypocenterC103#3177
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #20268191C2semidirect
3. #20268169C2semidirect
4. #20268158C2semidirect
8. #20267899C2semidirect
9. C4×#13110095C2semidirect
11. #441×C103C2semidirect
104. C103#3177semidirect
113. #441D103semidirect

Maximal subgroups

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

subgroupindex
#202683992
#202681912
#202681692
#202681582
#202680502
#202680462
#202680312
#202678992
C4×#131100952
#202677482
#441×C1032
#3177103