Finite Group Databasebeta

← C2×#20267945 #27204336

Subgroups — C2×#20267945 #27204336

Order 13184.

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

normal subgroups only

This group has 740 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
1C22×Q8×D103C211yesmaximal, characteristic
2C22×#13110095C211yesmaximal, characteristic, complemented
3C2×#15692997C211yesmaximal, characteristic
4#20267945C218yesmaximal, direct product factor
5C2×#15692946C211yesmaximal, characteristic, complemented
6C2×#15692945C211yesmaximal, characteristic, complemented
7C2×(C2×D103)⋊C8C211yesmaximal, characteristic
8C22×Q16×C103C211yesmaximal, characteristic, complemented
9C22×Dic206—21no—
10C22×Dic206C2211yescharacteristic
11C2×Q8×D103—24no—
12C2×Q8×D103—22no—
13C2×Q8×D103—24no—
14C2×Q8×D103C2214yes—
15C22×C4×D103—21no—
16C22×C4×D103C2211yescharacteristic
17C2×#13110095—24no—
18C2×#13110095C2214yescomplemented
19C22×C103⋊C8C2211yescharacteristic
20#15692997—22no—
21#15692997C2214yes—
22C2×C4⋊Dic103C2211yescharacteristic
23C2×Dic103⋊C4—21no—
24C2×(C2×D103)⋊C4—21no—
25#15692946C2214yescomplemented
26#15692945C2214yescomplemented
27(C2×D103)⋊C8C2214yes—
28C22×Q8×C103C2211yescharacteristic
29C22×Q8×C103C2211yescharacteristic
30C2×Q16×C103—24no—
31C2×Q16×C103C2214yescomplemented
32C22×C8×C103C2211yescharacteristic
33C23×D103D411yescharacteristic
34C2×Dic206—28no—
35C2×Dic206—21no—
36C2×Dic206—22no—
37C2×Dic206—24no—
38C2×Dic206D414yes—
39C2×Dic206C2312yes—
40Q8×D103—216no—
41Q8×D103—28no—
42Q8×D103—28no—
43C22×Dic103—21no—
44C22×Dic103—21no—
45C22×Dic103D411yescharacteristic
46C2×C4×D103—28no—
47C2×C4×D103—24no—
48C2×C4×D103—22no—
49C2×C4×D103—22no—
50C2×C4×D103D412yes—
51C2×C4×D103C2312yes—
52#13110095—28no—
53C2×C103⋊C8—22no—
54C2×C103⋊C8C2312yes—
55C4⋊Dic103—21no—
56C4⋊Dic103C2312yes—
57Dic103⋊C4—24no—
58(C2×D103)⋊C4—24no—
59C2×Q8×C103—22no—
60C2×Q8×C103—21no—
61C2×Q8×C103—21no—
62C2×Q8×C103—22no—
63C2×Q8×C103—22no—
64C2×Q8×C103D414yes—
65C2×Q8×C103C2312yes—
66C2×Q8×C103C2312yes—
67C22×C4×C103—21no—
68C22×C4×C103—21no—
69C22×C4×C103C2311yescharacteristic
70Q16×C103—28no—
71C2×C8×C103—22no—
72C2×C8×C103C2312yes—
73C23×C103C2×D411yescharacteristic
74C22×D103—22no—
75C22×D103—22no—
76C22×D103Q1614yescomplemented
77C22×D103C2×D412yes—
78Q8×C103—24no—
79Q8×C103—22no—
80Q8×C103—22no—
81Q8×C103—22no—
82Q8×C103—42no—
83Q8×C103C2×D414yes—
84C2×C4×C103—24no—
85C2×C4×C103—22no—
86C2×C4×C103—22no—
87C2×C4×C103—42no—
88C2×C4×C103C2×D411yescharacteristic
89C2×C4×C103C2×D412yes—
90C2×C4×C103C2×D412yes—
91C2×C4×C103C2411yescharacteristic
92C2×Dic103—24no—
93C2×Dic103—22no—
94C2×Dic103—22no—
95C2×Dic103—22no—
96C2×Dic103—42no—
97C2×Dic103C2×D412yes—
98C4×D103—216no—
99C4×D103—24no—
100C4×D103—22no—
101C4×D103—22no—
102Dic206—216no—
103Dic206—24no—
104Dic206—22no—
105Dic206C2×D414yes—
106C8×C103—22no—
107C103⋊C8—22no—
108C22×C103#12012yes—
109C22×C103C2×Q1612yes—
110C22×C103#13712yes—
111C22×C103C22×D411yescharacteristic
112C2×D103—22no—
113C2×D103—22no—
114C2×D103—28no—
115C2×D103C2×Q1614yescomplemented
116C4×C103—24no—
117C4×C103—42no—
118C4×C103#12012yes—
119C4×C103C22×D411yescharacteristic
120C4×C103C22×D411yescharacteristic
121Dic103—22no—
122Dic103—24no—
123Dic103—42no—
124C2×C103#45114yescomplemented
125C2×C103C2×#12011yescharacteristic
126C2×C103C22×Q1611yescharacteristic
127C2×C103C2×#13711yescharacteristic
128D103—24no—
129C2×#451—1031nomaximal, Sylow
130C103C2×#45111yescharacteristic, complemented, Sylow
131C23×Q8—1031no—
132C22×Q16—1031no—
133C22×Q16D10311yescharacteristic, complemented
134C2×C22⋊Q8—1031no—
135#451—1038no—
136C2×#103—1031no—
137C2×#103—1031no—
138C2×C22⋊C8—1031no—
139C22×Q8—1034no—
140C22×Q8—1031no—
141C22×Q8—2061no—
142C22×Q8—2062no—
143C22×Q8—2064no—
144C22×Q8—2064no—
145C22×Q8C2×D10311yescharacteristic
146C22×Q8C2×D10311yescharacteristic
147C23×C4—1031no—
148C23×C4—2061no—
149C2×Q16—24no—
150C2×Q16—1034no—
151C2×Q16—2064no—
152C2×Q16C2×D10314yescomplemented
153C22×C8—1031no—
154C22×C8C2×D10311yescharacteristic
155C22⋊Q8—1034no—
156C22⋊Q8—2062no—
157C2×C4⋊C4—1031no—
158C2×C4⋊C4—2061no—
159C2×C22⋊C4—2061no—
160#103—1034no—
161#103—1034no—
162C22⋊C8—1034no—
163C24—1031no—
164C2×Q8—21no—
165C2×Q8—22no—
166C2×Q8—21no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—1034no—
170C2×Q8—1032no—
171C2×Q8—2064no—
172C2×Q8—2068no—
173C2×Q8—2068no—
174C2×Q8—20616no—
175C2×Q8—2068no—
176C2×Q8—2061no—
177C2×Q8—2062no—
178C2×Q8C22⋊D10314yes—
179C2×Q8C22×D10312yes—
180C2×Q8C22×D10312yes—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—1031no—
184C22×C4—1032no—
185C22×C4—1032no—
186C22×C4—2064no—
187C22×C4—2068no—
188C22×C4—2061no—
189C22×C4—2061no—
190C22×C4—2062no—
191C22×C4—2062no—
192C22×C4C22×D10311yescharacteristic
193Q16—28no—
194Q16—2068no—
195C2×C8—22no—
196C2×C8—1032no—
197C2×C8—2062no—
198C2×C8C22×D10312yes—
199C4⋊C4—1032no—
200C4⋊C4—2064no—
201C4⋊C4—2061no—
202C22⋊C4—2064no—
203C23—1032no—
204C23—1034no—
205C23—2062no—
206C23—2062no—
207C23D4×D10311yescharacteristic
208Q8—22no—
209Q8—24no—
210Q8—22no—
211Q8—22no—
212Q8—42no—
213Q8—1034no—
214Q8—20616no—
215Q8—2062no—
216Q8—2064no—
217Q8C2×C22⋊D10314yes—
218C2×C4—22no—
219C2×C4—24no—
220C2×C4—22no—
221C2×C4—42no—
222C2×C4—1032no—
223C2×C4—4122no—
224C2×C4—20616no—
225C2×C4—2062no—
226C2×C4—2062no—
227C2×C4—2062no—
228C2×C4—2064no—
229C2×C4—2062no—
230C2×C4—2062no—
231C2×C4—2064no—
232C2×C4D4×D10312yes—
233C2×C4D4×D10311yescharacteristic
234C2×C4C2×C22⋊D10312yes—
235C2×C4C23×D10311yescharacteristic
236C8—22no—
237C8—2062no—
238C22—1034no—
239C22—2062no—
240C22—2068no—
241C22—2062no—
242C22#1569298912yes—
243C22Q16×D10312yes—
244C22#1569305312yes—
245C22C2×D4×D10311yescharacteristic
246C4—24no—
247C4—42no—
248C4—4122no—
249C4—2062no—
250C4—2064no—
251C4#1569298912yes—
252C4C2×D4×D10311yescharacteristic
253C4C22×C22⋊D10311yescharacteristic
254C2—2064no—
255C2#2026794514yesdirect product factor
256C2C2×#1569298911yescharacteristic
257C2C2×Q16×D10311yescharacteristic
258C2C2×#1569305311yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC22×Q16×C103C2
socleC23×C103C2×D4
prime radicalC23×D103D4
hypercenterC22×Q16D103
hypocenterC103C2×#451
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
2. C22×#13110095C2semidirect
4. #20267945C2direct (N × H)
5. C2×#15692946C2semidirect
6. C2×#15692945C2semidirect
8. C22×Q16×C103C2semidirect
18. C2×#13110095C22semidirect
25. #15692946C22semidirect
26. #15692945C22semidirect
31. C2×Q16×C103C22semidirect
76. C22×D103Q16semidirect
115. C2×D103C2×Q16semidirect
124. C2×C103#451semidirect
130. C103C2×#451semidirect
133. C22×Q16D103semidirect
152. C2×Q16C2×D103semidirect
255. C2#20267945direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D1032
C22×#131100952
C2×#156929972
#202679452
C2×#156929462
C2×#156929452
C2×(C2×D103)⋊C82
C22×Q16×C1032
C2×#451103