Finite Group Databasebeta

← #27204378

Subgroups — #27204378

Order 13184.

738 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 173 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×#15693052C212yesmaximal, complemented
2#20268302C211yesmaximal, characteristic
3#20267947C214yesmaximal, complemented
4#20267930C214yesmaximal, complemented
5#20267800C212yesmaximal, complemented
6#20267755C211yesmaximal, characteristic, complemented
7C23×Q8×C103C211yesmaximal, characteristic, complemented
8C2×#13110105C2211yescharacteristic
9#15693052—28no—
10C2×#13110095C2214yescomplemented
11C2×#13110092C2214yescomplemented
12C2×#13110089C2212yes—
13#15693004—21no—
14#15693000C2212yes—
15#15692995C2212yes—
16#15692990—21no—
17C4×C22⋊D103—22no—
18#15692980C2211yescharacteristic
19#15692945C2218yescomplemented
20C22⋊(C103⋊C8)C2214yes—
21C22×Q8×C103—28no—
22C22×Q8×C103—22no—
23C22×Q8×C103—21no—
24C22×Q8×C103C2214yes—
25C22×Q8×C103C2212yes—
26C23×C4×C103—21no—
27C23×C4×C103C2211yescharacteristic
28#13110105—24no—
29C2×Dic206C2311yescharacteristic
30C2×D412C2311yescharacteristic
31C2×C22⋊D103—21no—
32C2×C22⋊D103—22no—
33C2×C4×D103—21no—
34#13110095—28no—
35#13110092—28no—
36#13110089—24no—
37C2×C103⋊C8C2314yes—
38C4⋊Dic103C2312yes—
39Dic103⋊C4—22no—
40C22⋊Dic103—21no—
41C22⋊Dic103—22no—
42(C2×D103)⋊C4—22no—
43C4×Dic103—21no—
44C24×C103D411yescharacteristic
45C2×Q8×C103—216no—
46C2×Q8×C103—28no—
47C2×Q8×C103—216no—
48C2×Q8×C103—24no—
49C2×Q8×C103—24no—
50C2×Q8×C103—22no—
51C2×Q8×C103D418yescomplemented
52C2×Q8×C103C2314yes—
53C22×C4×C103—28no—
54C22×C4×C103—24no—
55C22×C4×C103—22no—
56C22×C4×C103—24no—
57C22×C4×C103D412yes—
58C22×C4×C103D411yescharacteristic
59C22×C4×C103C2312yes—
60C22×C4×C103C2311yescharacteristic
61C23×C103—22no—
62C23×C103—24no—
63C23×C103C2×D411yescharacteristic
64C23×C103C2×D412yes—
65C22×D103—21no—
66Q8×C103—216no—
67Q8×C103—28no—
68Q8×C103—24no—
69Q8×C103C2×D418yes—
70C2×C4×C103—216no—
71C2×C4×C103—28no—
72C2×C4×C103—22no—
73C2×C4×C103—24no—
74C2×C4×C103—24no—
75C2×C4×C103—24no—
76C2×C4×C103C2×D412yes—
77C2×C4×C103C2×D411yescharacteristic
78C2×C4×C103C2×D414yes—
79C2×C4×C103C2411yescharacteristic
80C22⋊D103—42no—
81C22⋊D103—44no—
82C2×Dic103—22no—
83C2×Dic103—21no—
84D412—22no—
85C4×D103—42no—
86Dic206—22no—
87C103⋊C8—24no—
88C22×C103—28no—
89C22×C103—22no—
90C22×C103—22no—
91C22×C103—22no—
92C22×C103#12012yes—
93C22×C103#13714yescomplemented
94C22×C103C22×D411yescharacteristic
95C2×D103—41no—
96C2×D103—42no—
97C4×C103—28no—
98C4×C103—22no—
99C4×C103#12012yes—
100C4×C103C22×D412yes—
101Dic103—41no—
102Dic103—42no—
103C2×C103—22no—
104C2×C103—24no—
105C2×C103C2×#12011yescharacteristic
106C2×C103C2×#13712yes—
107D103—81no—
108#3004—1031nomaximal, Sylow
109C103#300411yescharacteristic, complemented, Sylow
110C23×Q8D10311yescharacteristic, complemented
111C2×#137—1032no—
112#525—1031no—
113#451—1034no—
114#448—1034no—
115#419—1032no—
116#407—1031no—
117C2×#41—1031no—
118C22×Q8—28no—
119C22×Q8—22no—
120C22×Q8—21no—
121C22×Q8C2×D10314yes—
122C22×Q8C2×D10312yes—
123C23×C4—21no—
124C23×C4C2×D10311yescharacteristic
125#137—2068no—
126C2×Q16—1034no—
127C2×SD16—1034no—
128C2×M16—1032no—
129#123—2061no—
130C22⋊Q8—1032no—
131#121—1032no—
132#120—2061no—
133C4×D4—2062no—
134#117—1031no—
135#103—1038no—
136C22⋊C8—1034no—
137C24C22⋊D10311yescharacteristic
138#41—2064no—
139C2×Q8—216no—
140C2×Q8—28no—
141C2×Q8—216no—
142C2×Q8—24no—
143C2×Q8—22no—
144C2×Q8—24no—
145C2×Q8—1031no—
146C2×Q8C22⋊D10318yescomplemented
147C2×Q8C22×D10314yes—
148C2×D4—1031no—
149C2×D4—2062no—
150C2×D4—2061no—
151C22×C4—28no—
152C22×C4—24no—
153C22×C4—22no—
154C22×C4—24no—
155C22×C4—2061no—
156C22×C4C22⋊D10312yes—
157C22×C4C22⋊D10311yescharacteristic
158C22×C4C22×D10312yes—
159C22×C4C22×D10311yescharacteristic
160Q16—2068no—
161SD16—2068no—
162M16—2064no—
163C2×C8—1034no—
164C4⋊C4—1032no—
165C4⋊C4—2062no—
166C22⋊C4—2061no—
167C22⋊C4—2062no—
168C22⋊C4—2062no—
169C42—2061no—
170C23—22no—
171C23—24no—
172C23—2061no—
173C23C2×C22⋊D10311yescharacteristic
174C23C2×C22⋊D10312yes—
175Q8—216no—
176Q8—24no—
177Q8—28no—
178Q8—2062no—
179Q8C2×C22⋊D10318yes—
180D4—4122no—
181D4—4124no—
182D4—2062no—
183C2×C4—216no—
184C2×C4—24no—
185C2×C4—28no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—4122no—
190C2×C4—2062no—
191C2×C4—2061no—
192C2×C4C2×C22⋊D10312yes—
193C2×C4C2×C22⋊D10314yes—
194C2×C4C2×C22⋊D10311yescharacteristic
195C2×C4C23×D10311yescharacteristic
196C8—2064no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—4122no—
202C22—4121no—
203C22#1569299012yes—
204C22#1569305214yescomplemented
205C22C22×C22⋊D10311yescharacteristic
206C4—28no—
207C4—22no—
208C4—4122no—
209C4—4121no—
210C4#1569299012yes—
211C4C22×C22⋊D10312yes—
212C2—22no—
213C2—24no—
214C2—8241no—
215C2C2×#1569299011yescharacteristic
216C2C2×#1569305212yes—
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC23×Q8×C103C2
socleC22×C103C22×D4
prime radical#20268302C2
hypercenterC23×Q8D103
hypocenterC103#3004
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#15693052C2semidirect
3. #20267947C2semidirect
4. #20267930C2semidirect
5. #20267800C2semidirect
6. #20267755C2semidirect
7. C23×Q8×C103C2semidirect
10. C2×#13110095C22semidirect
11. C2×#13110092C22semidirect
19. #15692945C22semidirect
51. C2×Q8×C103D4semidirect
93. C22×C103#137semidirect
109. C103#3004semidirect
110. C23×Q8D103semidirect
146. C2×Q8C22⋊D103semidirect
204. C22#15693052semidirect

Maximal subgroups

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

subgroupindex
C2×#156930522
#202683022
#202679472
#202679302
#202678002
#202677552
C23×Q8×C1032
#3004103