Finite Group Databasebeta

← #27203620

Subgroups — #27203620

Order 13184.

756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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×#15693066C211yesmaximal, characteristic
2#20268557C212yesmaximal, complemented
3#20267773C212yesmaximal, complemented
4#20267772C214yesmaximal, complemented
5C2×#15692938C211yesmaximal, characteristic, complemented
6#100×D103C214yesmaximal, complemented
7C2×#100×C103C211yesmaximal, characteristic, complemented
8#15693066—24no—
9#15693066—24no—
10C2×#13110105C2211yescharacteristic
11C2×#13110105C2211yescharacteristic
12C2×#13110104C412yes—
13C2×#13110104C2212yes—
14C22×C22⋊D103C414yes—
15C2×D4×D103C412yes—
16C2×D4×D103C2212yes—
17#15693029—24no—
18#15693027—24no—
19C2×#13110089C2212yescomplemented
20M16×D103C2218yescomplemented
21#15692939C2214yescomplemented
22#15692938C2214yescomplemented
23#15692937C2214yescomplemented
24C22×D4×C103C2211yescharacteristic
25C2×M16×C103C2212yescomplemented
26#100×C103C2214yescomplemented
27C23×D103C2×C414yes—
28#13110105—22no—
29#13110105—22no—
30#13110105D414yes—
31#13110105D414yes—
32#13110104—28no—
33#13110104—28no—
34C2×Dic206C2×C411yescharacteristic
35C2×Dic206C2311yescharacteristic
36C2×D412C2×C411yescharacteristic
37C2×D412C2311yescharacteristic
38C2×C22⋊D103—28no—
39C2×C22⋊D103—28no—
40C2×C22⋊D103C2×C414yes—
41C2×C22⋊D103C2×C414yes—
42C2×C22⋊D103C2×C412yes—
43C2×C22⋊D103C2×C412yes—
44D4×D103—28no—
45D4×D103—28no—
46C22×Dic103C2×C414yes—
47C2×C4×D103C2×C412yes—
48C2×C4×D103C2312yes—
49#13110089—22no—
50#13110089C2314yes—
51#13110088—28no—
52C2×C103⋊C8—22no—
53C8×D103—28no—
54C24×C103C2×C412yes—
55C2×D4×C103—22no—
56C2×D4×C103—22no—
57C2×D4×C103C2×C412yes—
58C2×D4×C103C2312yes—
59C22×C4×C103C2311yescharacteristic
60M16×C103—22no—
61M16×C103C2314yes—
62C2×C8×C103—22no—
63C23×C103—22no—
64C23×C103—22no—
65C23×C103—82no—
66C23×C103C22×C414yes—
67C23×C103C22×C411yescharacteristic
68C22×D103—28no—
69C22×D103—84no—
70C22×D103C22×C412yes—
71C22×D103C22×C412yes—
72D4×C103—24no—
73D4×C103—24no—
74C2×C4×C103C22×C411yescharacteristic
75C2×C4×C103C2×D412yes—
76C2×C4×C103C2×D412yes—
77C2×C4×C103C2411yescharacteristic
78C22⋊D103—22no—
79C22⋊D103—22no—
80C22⋊D103—28no—
81C22⋊D103—28no—
82C22⋊D103C22⋊C414yes—
83C22⋊D103C22⋊C414yes—
84C2×Dic103—28no—
85C2×Dic103C22×C412yes—
86C2×Dic103C22×C412yes—
87D412—22no—
88D412C22⋊C414yes—
89C4×D103—24no—
90C4×D103C2×D418yes—
91Dic206—22no—
92Dic206C22⋊C414yes—
93C8×C103—24no—
94C103⋊C8—24no—
95C22×C103—24no—
96C22×C103—41no—
97C22×C103—44no—
98C22×C103—82no—
99C22×C103—82no—
100C22×C103C2×C22⋊C411yescharacteristic
101C22×C103C2×C22⋊C411yescharacteristic
102C22×C103C23×C411yescharacteristic
103C2×D103—22no—
104C2×D103—42no—
105C2×D103—42no—
106C2×D103—88no—
107C2×D103C2×C22⋊C414yes—
108C4×C103C2×C22⋊C412yes—
109C4×C103C22×D412yes—
110Dic103—22no—
111Dic103C2×C22⋊C414yes—
112C2×C103—21no—
113C2×C103—21no—
114C2×C103—21no—
115C2×C103—44no—
116C2×C103C22×C22⋊C411yescharacteristic
117D103—24no—
118D103—42no—
119#2888—1031nomaximal, Sylow
120C103#288811yescharacteristic, complemented, Sylow
121C2×H(5,𝔽2)—1031no—
122#568—1032no—
123#413—1032no—
124#413—1034no—
125C2×#100—1031no—
126C2×#100—1034no—
127C2×#100D10311yescharacteristic, complemented
128H(5,𝔽2)—2064no—
129H(5,𝔽2)—2064no—
130C2×#41—1032no—
131C2×#41—1032no—
132C2×#41—1031no—
133C2×#41—1031no—
134C22×D4—1034no—
135C22×D4—1032no—
136C22×D4—1032no—
137C22×D4C2×D10311yescharacteristic
138#131—2064no—
139#131—2064no—
140C2×M16—1032no—
141C2×M16—1038no—
142C2×M16C2×D10312yescomplemented
143#101—1034no—
144#100—1034no—
145#100—1034no—
146#100C2×D10314yescomplemented
147C24—1034no—
148C24C4×D10312yes—
149#41—1034no—
150#41—1034no—
151#41—2068no—
152#41—2068no—
153#41—2062no—
154#41—2062no—
155C2×Q8—1031no—
156C2×Q8—1031no—
157C2×D4—22no—
158C2×D4—22no—
159C2×D4—1032no—
160C2×D4—1034no—
161C2×D4—1034no—
162C2×D4—1032no—
163C2×D4—1031no—
164C2×D4—1031no—
165C2×D4—2068no—
166C2×D4—2068no—
167C2×D4—2068no—
168C2×D4—2068no—
169C2×D4C4×D10312yes—
170C2×D4C22×D10312yes—
171C22×C4—1032no—
172C22×C4—1034no—
173C22×C4—1032no—
174C22×C4C22×D10311yescharacteristic
175M16—22no—
176M16—1034no—
177M16—2068no—
178M16—2062no—
179M16C22×D10314yes—
180C2×C8—22no—
181C2×C8—2068no—
182C2×C8—2062no—
183C23—22no—
184C23—22no—
185C23—82no—
186C23—8244no—
187C23—1032no—
188C23—1032no—
189C23—2068no—
190C23C2×C4×D10314yes—
191C23C2×C4×D10311yescharacteristic
192Q8—1034no—
193Q8—2062no—
194D4—24no—
195D4—24no—
196D4—1034no—
197D4—1034no—
198D4—1034no—
199D4—2068no—
200D4—2068no—
201D4—2062no—
202D4—2062no—
203D4—2062no—
204C2×C4—1032no—
205C2×C4—1038no—
206C2×C4—1032no—
207C2×C4—2068no—
208C2×C4—2064no—
209C2×C4C2×C4×D10311yescharacteristic
210C2×C4D4×D10312yes—
211C2×C4D4×D10312yes—
212C2×C4C23×D10311yescharacteristic
213C8—24no—
214C8—2064no—
215C22—24no—
216C22—41no—
217C22—44no—
218C22—82no—
219C22—82no—
220C22—8248no—
221C22—1034no—
222C22—4122no—
223C22—4122no—
224C22—2062no—
225C22C22⋊C4×D10311yescharacteristic
226C22C22⋊C4×D10311yescharacteristic
227C22C22×C4×D10311yescharacteristic
228C4—1034no—
229C4—2062no—
230C4C22⋊C4×D10312yes—
231C4C2×D4×D10312yes—
232C2—21no—
233C2—21no—
234C2—21no—
235C2—44no—
236C2—4122no—
237C2—2064no—
238C2C2×C22⋊C4×D10311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D103
commutatorC22×C103C23×C4
FrattiniC2×C4C23×D103
FittingC2×#100×C103C2
socleC2×C103C22×C22⋊C4
prime radicalC2×#15693066C2
cosocleC2×C4×C103C24
hypercenterC2×#100D103
hypocenterC103#2888
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #20268557C2semidirect
3. #20267773C2semidirect
4. #20267772C2semidirect
5. C2×#15692938C2semidirect
6. #100×D103C2semidirect
7. C2×#100×C103C2semidirect
19. C2×#13110089C22semidirect
20. M16×D103C22semidirect
21. #15692939C22semidirect
22. #15692938C22semidirect
23. #15692937C22semidirect
25. C2×M16×C103C22semidirect
26. #100×C103C22semidirect
120. C103#2888semidirect
127. C2×#100D103semidirect
142. C2×M16C2×D103semidirect
146. #100C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930662
#202685572
#202677732
#202677722
C2×#156929382
#100×D1032
C2×#100×C1032
#2888103