Finite Group Databasebeta

← C2×#20268172 #27205562

Subgroups — C2×#20268172 #27205562

Order 13184.

592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#13110095C211yesmaximal, characteristic, complemented
2C22×#13110094C211yesmaximal, characteristic, complemented
3C22×#13110090C211yesmaximal, characteristic
4C2×#15693010C211yesmaximal, characteristic, complemented
5C2×#15693008C211yesmaximal, characteristic, complemented
6#20268172C218yesmaximal, direct product factor
7C2×C8×Dic103C211yesmaximal, characteristic, complemented
8C22×SD16×C103C211yesmaximal, characteristic, complemented
9C22×Dic206C2211yescharacteristic
10C22×D412C2211yescharacteristic
11C2×#13110095—24no—
12C2×#13110095C2214yescomplemented
13C2×#13110094—24no—
14C2×#13110094C2214yescomplemented
15C2×#13110090—24no—
16C2×#13110090C2214yes—
17C22×C103⋊C8C2211yescharacteristic
18#15693010—22no—
19#15693010C2214yescomplemented
20#15693008—22no—
21#15693008C2214yescomplemented
22C2×C22⋊Dic103—22no—
23C2×(C2×D103)⋊C4—22no—
24C2×C4×Dic103C2211yescharacteristic
25C8×Dic103C2214yescomplemented
26C22×Q8×C103C2211yescharacteristic
27C22×D4×C103C2211yescharacteristic
28C2×SD16×C103—24no—
29C2×SD16×C103C2214yescomplemented
30C22×C8×C103C2211yescharacteristic
31C23×D103—21no—
32C2×Dic206—22no—
33C2×Dic206—22no—
34C2×Dic206—21no—
35C2×Dic206C2312yes—
36C2×D412—22no—
37C2×D412—22no—
38C2×D412—21no—
39C2×D412C2312yes—
40C22×Dic103—21no—
41C22×Dic103D412yes—
42#13110095—28no—
43#13110094—28no—
44#13110090—28no—
45C2×C103⋊C8D414yes—
46C2×C103⋊C8C2312yes—
47C22⋊Dic103—28no—
48(C2×D103)⋊C4—28no—
49C4×Dic103D412yes—
50C4×Dic103C2312yes—
51C24×C103—21no—
52C2×Q8×C103—21no—
53C2×Q8×C103—22no—
54C2×Q8×C103—22no—
55C2×Q8×C103C2312yes—
56C2×D4×C103—22no—
57C2×D4×C103—22no—
58C2×D4×C103—21no—
59C2×D4×C103C2312yes—
60C22×C4×C103—21no—
61C22×C4×C103C2311yescharacteristic
62SD16×C103—28no—
63C2×C8×C103D414yes—
64C2×C8×C103C2312yes—
65C23×C103—22no—
66C23×C103—42no—
67C23×C103—44no—
68C23×C103C2×D411yescharacteristic
69C22×D103—22no—
70C22×D103—42no—
71C22×D103—44no—
72Q8×C103—22no—
73Q8×C103—22no—
74Q8×C103—42no—
75D4×C103—22no—
76D4×C103—22no—
77D4×C103—42no—
78C2×C4×C103—22no—
79C2×C4×C103—42no—
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2×D412yes—
82C2×C4×C103C2×D412yes—
83C2×C4×C103C2411yescharacteristic
84C2×Dic103—24no—
85C2×Dic103—22no—
86C2×Dic103—42no—
87C2×Dic103C2×D414yes—
88D412—22no—
89D412—22no—
90D412—42no—
91Dic206—22no—
92Dic206—22no—
93Dic206—42no—
94C8×C103C2×D414yes—
95C103⋊C8C2×D414yes—
96C22×C103—42no—
97C22×C103—44no—
98C22×C103—84no—
99C22×C103#12712yes—
100C22×C103#13514yes—
101C22×C103C22×D411yescharacteristic
102C2×D103—42no—
103C2×D103—44no—
104C2×D103—84no—
105C4×C103—42no—
106C4×C103#12712yes—
107C4×C103C22×D411yescharacteristic
108C4×C103C22×D411yescharacteristic
109Dic103—24no—
110Dic103—42no—
111C2×C103—82no—
112C2×C103#49514yescomplemented
113C2×C103C2×#12711yescharacteristic
114C2×C103C2×#13512yes—
115D103—82no—
116C2×#495—1031nomaximal, Sylow
117C103C2×#49511yescharacteristic, complemented, Sylow
118C22×Q16—1031no—
119C22×SD16—1031no—
120C22×SD16D10311yescharacteristic, complemented
121C22×D8—1031no—
122C2×#124—1031no—
123C2×#124—1031no—
124#495—1038no—
125C2×C4×C8—1031no—
126C22×Q8—1031no—
127C22×Q8C2×D10311yescharacteristic
128C22×D4—1031no—
129C22×D4C2×D10311yescharacteristic
130C2×Q16—1034no—
131C2×Q16—2064no—
132C2×SD16—24no—
133C2×SD16—1034no—
134C2×SD16—2064no—
135C2×SD16C2×D10314yescomplemented
136C2×D8—1034no—
137C2×D8—2064no—
138C22×C8—1031no—
139C22×C8C2×D10311yescharacteristic
140#124—1034no—
141#124—1034no—
142#124—2062no—
143#124—2062no—
144C2×C22⋊C4—2062no—
145C2×C22⋊C4—2062no—
146C2×C42—1031no—
147C4×C8—1034no—
148C24—21no—
149C24—2061no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—1032no—
154C2×Q8—2062no—
155C2×Q8—2062no—
156C2×Q8—2061no—
157C2×Q8C22×D10312yes—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4—1032no—
162C2×D4—2061no—
163C2×D4—2062no—
164C2×D4—2062no—
165C2×D4C22×D10312yes—
166C22×C4—21no—
167C22×C4—1032no—
168C22×C4—2061no—
169C22×C4C22×D10311yescharacteristic
170Q16—2068no—
171SD16—28no—
172SD16—2068no—
173D8—2068no—
174C2×C8—1034no—
175C2×C8—1032no—
176C2×C8C22⋊D10314yes—
177C2×C8C22×D10312yes—
178C22⋊C4—2068no—
179C22⋊C4—2068no—
180C42—1032no—
181C42—1032no—
182C23—22no—
183C23—42no—
184C23—44no—
185C23—4122no—
186C23—4124no—
187C23—2062no—
188C23D4×D10311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—4122no—
193Q8—2062no—
194Q8—2062no—
195D4—22no—
196D4—22no—
197D4—42no—
198D4—4122no—
199D4—2062no—
200D4—2062no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—1034no—
204C2×C4—4122no—
205C2×C4—2062no—
206C2×C4—2064no—
207C2×C4D4×D10312yes—
208C2×C4D4×D10311yescharacteristic
209C2×C4C2×C22⋊D10312yes—
210C2×C4C23×D10311yescharacteristic
211C8—1034no—
212C8C2×C22⋊D10314yes—
213C22—44no—
214C22—42no—
215C22—84no—
216C22—8244no—
217C22—4124no—
218C22—4122no—
219C22#1569301712yes—
220C22#1569304214yes—
221C22C2×D4×D10311yescharacteristic
222C4—42no—
223C4—4122no—
224C4—2064no—
225C4#1569301712yes—
226C4C2×D4×D10311yescharacteristic
227C4C22×C22⋊D10311yescharacteristic
228C2—82no—
229C2—8242no—
230C2#2026817214yesdirect product factor
231C2C2×#1569301711yescharacteristic
232C2C2×#1569304212yes—
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC22×SD16×C103C2
socleC23×C103C2×D4
prime radicalC22×#13110090C2
hypercenterC22×SD16D103
hypocenterC103C2×#495
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#13110095C2semidirect
2. C22×#13110094C2semidirect
4. C2×#15693010C2semidirect
5. C2×#15693008C2semidirect
6. #20268172C2direct (N × H)
7. C2×C8×Dic103C2semidirect
8. C22×SD16×C103C2semidirect
12. C2×#13110095C22semidirect
14. C2×#13110094C22semidirect
19. #15693010C22semidirect
21. #15693008C22semidirect
25. C8×Dic103C22semidirect
29. C2×SD16×C103C22semidirect
112. C2×C103#495semidirect
117. C103C2×#495semidirect
120. C22×SD16D103semidirect
135. C2×SD16C2×D103semidirect
230. C2#20268172direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131100952
C22×#131100942
C22×#131100902
C2×#156930102
C2×#156930082
#202681722
C2×C8×Dic1032
C22×SD16×C1032
C2×#495103