Finite Group Databasebeta

← #27205884

Subgroups — #27205884

Order 13184.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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#20268343C212yesmaximal
2#20268188C211yesmaximal, characteristic, complemented
3#20268169C211yesmaximal, characteristic, complemented
4#20268140C212yesmaximal, complemented
5#20268049C211yesmaximal, characteristic
6#20268047C212yesmaximal
7#20267898C211yesmaximal, characteristic, complemented
8#20267897C211yesmaximal, characteristic, complemented
9#20267895C212yesmaximal, complemented
10M16×Dic103C211yesmaximal, characteristic
11#470×C103C211yesmaximal, characteristic
12C2×Dic412C2211yescharacteristic
13C2×#13110095C2212yes—
14C2×#13110089C2211yescharacteristic
15#15693020C2212yes—
16#15693019C2212yes—
17#15693011—22no—
18#15693000C2212yes—
19#15692998—22no—
20Q8×Dic103C2212yes—
21#15692986—22no—
22#15692986C2212yes—
23#15692977—22no—
24C2×C4×Dic103C2211yescharacteristic
25#15692953C2211yescharacteristic
26#15692952C2212yes—
27#15692946C2212yes—
28#15692945C2212yes—
29#15692944C2212yes—
30#15692931C2211yescharacteristic
31#15692931C2211yescharacteristic
32C8×Dic103C2211yescharacteristic
33C8×Dic103C2211yescharacteristic
34C2×Q16×C103C2211yescharacteristic
35C2×M16×C103C2211yescharacteristic
36C22⋊Q8×C103C2212yes—
37#106×C103C2211yescharacteristic
38#103×C103C2212yes—
39C2×Dic206—22no—
40C2×Dic206C2312yes—
41C22×Dic103D412yes—
42Dic412—22no—
43#13110095—24no—
44#13110089—22no—
45C2×C103⋊C8C2311yescharacteristic
46C2×C103⋊C8C2311yescharacteristic
47C4⋊Dic103—22no—
48C4⋊Dic103C2312yes—
49Dic103⋊C4—22no—
50Dic103⋊C4—22no—
51Dic103⋊C4—22no—
52Dic103⋊C4—22no—
53Dic103⋊C4—22no—
54C22⋊Dic103—22no—
55C4×Dic103—22no—
56C4×Dic103—22no—
57C4×Dic103D412yes—
58C4×Dic103C2311yescharacteristic
59C4×Dic103C2311yescharacteristic
60C2×Q8×C103C2312yes—
61C22×C4×C103C2311yescharacteristic
62Q16×C103—22no—
63M16×C103—22no—
64C2×C8×C103C2311yescharacteristic
65C2×C8×C103C2311yescharacteristic
66C4⋊C4×C103—22no—
67C4⋊C4×C103C2312yes—
68C22⋊C4×C103—22no—
69C23×C103C2×D411yescharacteristic
70Q8×C103—22no—
71Q8×C103—22no—
72C2×C4×C103—21no—
73C2×C4×C103—21no—
74C2×C4×C103—22no—
75C2×C4×C103—22no—
76C2×C4×C103C2×D411yescharacteristic
77C2×C4×C103C2411yescharacteristic
78C2×Dic103—24no—
79C2×Dic103—22no—
80C2×Dic103—22no—
81C2×Dic103C2×D412yes—
82C2×Dic103C2×D412yes—
83Dic206—22no—
84Dic206—22no—
85Dic206—44no—
86C8×C103—21no—
87C8×C103#4112yes—
88C103⋊C8—21no—
89C103⋊C8#4112yes—
90C22×C103—21no—
91C22×C103—22no—
92C22×C103C22×D411yescharacteristic
93C4×C103—21no—
94C4×C103—42no—
95C4×C103—42no—
96C4×C103C2×#4111yescharacteristic
97C4×C103C2×#4111yescharacteristic
98Dic103—22no—
99Dic103—42no—
100Dic103—42no—
101Dic103#13714yes—
102C2×C103—41no—
103C2×C103#53211yescharacteristic
104C2×C103C2×#13712yes—
105#3185—1031nomaximal, Sylow
106C103#318511yescharacteristic, complemented, Sylow
107#533—1032no—
108#498—1031no—
109#494—1031no—
110#487—1032no—
111#470—1031no—
112#470—1032no—
113#470D10311yescharacteristic
114#441—1031no—
115#441—1031no—
116#441—1032no—
117C4×M16—1031no—
118C2×Q16—1032no—
119C2×Q16—1031no—
120C2×Q16C2×D10311yescharacteristic
121C2×M16—1031no—
122C2×M16C2×D10311yescharacteristic
123C4⋊Q8—1032no—
124C4⋊Q8—1032no—
125#125—2062no—
126C22⋊Q8—1032no—
127C22⋊Q8—2062no—
128C22⋊Q8C2×D10312yes—
129C4×Q8—1032no—
130C4×Q8—1032no—
131C4×Q8—2062no—
132#117—2062no—
133C2×C42—1031no—
134#106—1031no—
135#106—1032no—
136#106C2×D10311yescharacteristic
137#103—1032no—
138#103—1032no—
139#103—1032no—
140#103C2×D10312yes—
141#97—1031no—
142#97—1031no—
143C4×C8—1031no—
144C4×C8—1031no—
145C2×Q8—1032no—
146C2×Q8—2062no—
147C2×Q8C22×D10312yes—
148C22×C4—1032no—
149C22×C4C22×D10311yescharacteristic
150Q16—22no—
151Q16—2064no—
152Q16—2062no—
153M16—22no—
154M16—2062no—
155C2×C8—1031no—
156C2×C8—1031no—
157C2×C8C22×D10311yescharacteristic
158C2×C8C22×D10311yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—1032no—
161C4⋊C4—2062no—
162C4⋊C4—2062no—
163C4⋊C4—2062no—
164C4⋊C4—2062no—
165C4⋊C4—2062no—
166C4⋊C4—2062no—
167C4⋊C4C22×D10312yes—
168C22⋊C4—22no—
169C22⋊C4—2062no—
170C42—1032no—
171C42—1031no—
172C42—1031no—
173C42—2062no—
174C42—2062no—
175C23D4×D10311yescharacteristic
176Q8—22no—
177Q8—22no—
178Q8—4124no—
179Q8—2062no—
180Q8—2062no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—1032no—
186C2×C4—1032no—
187C2×C4—2064no—
188C2×C4—2062no—
189C2×C4—2062no—
190C2×C4D4×D10311yescharacteristic
191C2×C4C23×D10311yescharacteristic
192C8—21no—
193C8—1032no—
194C8—2061no—
195C8#1311010412yes—
196C22—22no—
197C22—21no—
198C22C2×D4×D10311yescharacteristic
199C4—21no—
200C4—42no—
201C4—42no—
202C4—1034no—
203C4—4122no—
204C4—4122no—
205C4—2062no—
206C4#41×D10311yescharacteristic
207C4C2×#1311010411yescharacteristic
208C2—41no—
209C2#2026833611yescharacteristic
210C2#137×D10312yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#470×C103C2
socleC22×C103C22×D4
prime radicalC23×C103C2×D4
hypercenter#470D103
hypocenterC103#3185
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #20268188C2semidirect
3. #20268169C2semidirect
4. #20268140C2semidirect
7. #20267898C2semidirect
8. #20267897C2semidirect
9. #20267895C2semidirect
106. C103#3185semidirect

Maximal subgroups

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

subgroupindex
#202683432
#202681882
#202681692
#202681402
#202680492
#202680472
#202678982
#202678972
#202678952
M16×Dic1032
#470×C1032
#3185103