Finite Group Databasebeta

← C2×#20267935 #27204344

Subgroups — C2×#20267935 #27204344

Order 13184.

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

normal subgroups only

This group has 812 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×#13110106C211yesmaximal, characteristic, complemented
2C22×#13110090C211yesmaximal, characteristic, complemented
3C2×#15692992C211yesmaximal, characteristic, complemented
4#20267935C218yesmaximal, direct product factor
5C2×#15692945C211yesmaximal, characteristic, complemented
6C2×#15692943C211yesmaximal, characteristic, complemented
7C2×(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C103C211yesmaximal, characteristic, complemented
9C2×#13110106—24no—
10C2×#13110106—22no—
11C2×#13110106—24no—
12C2×#13110106C2214yescomplemented
13C22×D412—21no—
14C22×D412C2211yescharacteristic
15C22×C22⋊D103—21no—
16C22×C4×D103—21no—
17C22×C4×D103C2211yescharacteristic
18C2×#13110090—24no—
19C2×#13110090C2214yescomplemented
20C22×C103⋊C8C2211yescharacteristic
21#15692992—22no—
22#15692992C2214yescomplemented
23C2×C4⋊Dic103C2211yescharacteristic
24C2×C22⋊Dic103—21no—
25#15692945C2214yescomplemented
26#15692943C2214yescomplemented
27(C2×D103)⋊C8C2214yescomplemented
28C22×Q8×C103C2211yescharacteristic
29C22×D4×C103C2211yescharacteristic
30C2×SD16×C103—24no—
31C2×SD16×C103C2214yescomplemented
32C22×C8×C103C2211yescharacteristic
33C23×D103—21no—
34C23×D103D411yescharacteristic
35#13110106—216no—
36#13110106—28no—
37#13110106—28no—
38C2×D412—28no—
39C2×D412—24no—
40C2×D412—21no—
41C2×D412—22no—
42C2×D412D414yescomplemented
43C2×D412C2312yes—
44C2×C22⋊D103—24no—
45C2×C22⋊D103—44no—
46C22×Dic103—21no—
47C22×Dic103D411yescharacteristic
48C2×C4×D103—28no—
49C2×C4×D103—22no—
50C2×C4×D103—22no—
51C2×C4×D103—24no—
52C2×C4×D103D412yes—
53C2×C4×D103C2312yes—
54#13110090—28no—
55C2×C103⋊C8—22no—
56C2×C103⋊C8C2312yes—
57C4⋊Dic103—21no—
58C4⋊Dic103C2312yes—
59C22⋊Dic103—24no—
60C24×C103—21no—
61C2×Q8×C103—22no—
62C2×Q8×C103—21no—
63C2×Q8×C103D414yescomplemented
64C2×Q8×C103C2312yes—
65C2×D4×C103—22no—
66C2×D4×C103—22no—
67C2×D4×C103—21no—
68C2×D4×C103C2312yes—
69C22×C4×C103—21no—
70C22×C4×C103C2311yescharacteristic
71SD16×C103—28no—
72C2×C8×C103—22no—
73C2×C8×C103C2312yes—
74C23×C103—22no—
75C23×C103—42no—
76C23×C103—42no—
77C23×C103—42no—
78C23×C103C2×D411yescharacteristic
79C22×D103—22no—
80C22×D103—24no—
81C22×D103—22no—
82C22×D103—22no—
83C22×D103—22no—
84C22×D103—42no—
85C22×D103—42no—
86C22×D103C2×D412yes—
87Q8×C103—24no—
88Q8×C103—22no—
89Q8×C103C2×D414yescomplemented
90D4×C103—22no—
91D4×C103—22no—
92D4×C103—42no—
93C2×C4×C103—24no—
94C2×C4×C103—22no—
95C2×C4×C103C2×D411yescharacteristic
96C2×C4×C103C2×D412yes—
97C2×C4×C103C2×D412yes—
98C2×C4×C103C2411yescharacteristic
99C22⋊D103—48no—
100C2×Dic103—22no—
101C2×Dic103—22no—
102C2×Dic103—42no—
103C2×Dic103C2×D412yes—
104D412—216no—
105D412—24no—
106D412—22no—
107D412C2×D414yescomplemented
108C4×D103—216no—
109C4×D103—24no—
110C4×D103—22no—
111C4×D103—22no—
112C8×C103—22no—
113C103⋊C8—22no—
114C22×C103—42no—
115C22×C103—42no—
116C22×C103—42no—
117C22×C103—84no—
118C22×C103#12012yes—
119C22×C103#13512yes—
120C22×C103AGL(1,ℤ/8)12yes—
121C22×C103C22×D411yescharacteristic
122C2×D103—22no—
123C2×D103—24no—
124C2×D103—22no—
125C2×D103—22no—
126C2×D103—42no—
127C2×D103—42no—
128C2×D103—44no—
129C2×D103—48no—
130C4×C103—24no—
131C4×C103#12012yes—
132C4×C103C22×D411yescharacteristic
133C4×C103C22×D411yescharacteristic
134Dic103—22no—
135Dic103—42no—
136C2×C103—82no—
137C2×C103#44914yescomplemented
138C2×C103C2×#12011yescharacteristic
139C2×C103C2×#13511yescharacteristic
140C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
141D103—42no—
142D103—44no—
143C2×#449—1031nomaximal, Sylow
144C103C2×#44911yescharacteristic, complemented, Sylow
145C22×#41—1031no—
146C22×SD16D10311yescharacteristic, complemented
147C22×D8—1031no—
148C2×#121—1031no—
149#449—1038no—
150C2×#103—1031no—
151C2×#102—1031no—
152C2×C22⋊C8—1031no—
153C2×#41—1034no—
154C2×#41—2062no—
155C2×#41—2064no—
156C2×#41—2064no—
157C22×Q8C2×D10311yescharacteristic
158C22×D4—1031no—
159C22×D4—2061no—
160C22×D4—2061no—
161C22×D4C2×D10311yescharacteristic
162C23×C4—1031no—
163C23×C4—2061no—
164C2×SD16—24no—
165C2×SD16C2×D10314yescomplemented
166C2×D8—1034no—
167C2×D8—2064no—
168C22×C8—1031no—
169C22×C8C2×D10311yescharacteristic
170#121—1034no—
171#121—2062no—
172C2×C4⋊C4—1031no—
173C2×C22⋊C4—2061no—
174#103—1034no—
175#102—1034no—
176C22⋊C8—1034no—
177C24—21no—
178C24—1031no—
179C24—2061no—
180#41—2068no—
181#41—20616no—
182#41—2068no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8C22⋊D10314yescomplemented
186C2×Q8C22×D10312yes—
187C2×D4—22no—
188C2×D4—21no—
189C2×D4—22no—
190C2×D4—1034no—
191C2×D4—1032no—
192C2×D4—4124no—
193C2×D4—2064no—
194C2×D4—2068no—
195C2×D4—2064no—
196C2×D4—2061no—
197C2×D4—2062no—
198C2×D4C22×D10312yes—
199C22×C4—21no—
200C22×C4—1031no—
201C22×C4—1032no—
202C22×C4—1032no—
203C22×C4—2064no—
204C22×C4—2068no—
205C22×C4—2061no—
206C22×C4—2062no—
207C22×C4—2062no—
208C22×C4C22×D10311yescharacteristic
209SD16—28no—
210D8—2068no—
211C2×C8—22no—
212C2×C8—1032no—
213C2×C8—2062no—
214C2×C8C22×D10312yes—
215C4⋊C4—1032no—
216C4⋊C4—2061no—
217C22⋊C4—2064no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23—42no—
222C23—1032no—
223C23—4122no—
224C23—4122no—
225C23—2062no—
226C23—2064no—
227C23—2062no—
228C23—2062no—
229C23—2062no—
230C23D4×D10311yescharacteristic
231Q8—22no—
232Q8—24no—
233Q8C2×C22⋊D10314yescomplemented
234D4—22no—
235D4—22no—
236D4—42no—
237D4—1034no—
238D4—4128no—
239D4—20616no—
240D4—2062no—
241D4—2064no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—1032no—
245C2×C4—4122no—
246C2×C4—20616no—
247C2×C4—2062no—
248C2×C4—2062no—
249C2×C4—2062no—
250C2×C4—2062no—
251C2×C4—2064no—
252C2×C4D4×D10312yes—
253C2×C4D4×D10311yescharacteristic
254C2×C4C2×C22⋊D10312yes—
255C2×C4C23×D10311yescharacteristic
256C8—22no—
257C8—2062no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—84no—
262C22—4122no—
263C22—4122no—
264C22—4128no—
265C22—4124no—
266C22—2062no—
267C22—2062no—
268C22—2064no—
269C22—2062no—
270C22#1569298912yes—
271C22#1569304212yes—
272C22#1569304812yes—
273C22C2×D4×D10311yescharacteristic
274C4—24no—
275C4—4122no—
276C4—2062no—
277C4#1569298912yes—
278C4C2×D4×D10311yescharacteristic
279C4C22×C22⋊D10311yescharacteristic
280C2—82no—
281C2—4124no—
282C2—4122no—
283C2#2026793514yesdirect product factor
284C2C2×#1569298911yescharacteristic
285C2C2×#1569304211yescharacteristic
286C2C2×#1569304811yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC22×SD16×C103C2
socleC23×C103C2×D4
hypercenterC22×SD16D103
hypocenterC103C2×#449
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×#13110106C2semidirect
2. C22×#13110090C2semidirect
3. C2×#15692992C2semidirect
4. #20267935C2direct (N × H)
5. C2×#15692945C2semidirect
6. C2×#15692943C2semidirect
7. C2×(C2×D103)⋊C8C2semidirect
8. C22×SD16×C103C2semidirect
12. C2×#13110106C22semidirect
19. C2×#13110090C22semidirect
22. #15692992C22semidirect
25. #15692945C22semidirect
26. #15692943C22semidirect
27. (C2×D103)⋊C8C22semidirect
31. C2×SD16×C103C22semidirect
42. C2×D412D4semidirect
63. C2×Q8×C103D4semidirect
89. Q8×C103C2×D4semidirect
107. D412C2×D4semidirect
137. C2×C103#449semidirect
144. C103C2×#449semidirect
146. C22×SD16D103semidirect
165. C2×SD16C2×D103semidirect
185. C2×Q8C22⋊D103semidirect
233. Q8C2×C22⋊D103semidirect
283. C2#20267935direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131101062
C22×#131100902
C2×#156929922
#202679352
C2×#156929452
C2×#156929432
C2×(C2×D103)⋊C82
C22×SD16×C1032
C2×#449103