Finite Group Databasebeta

← C2×#20267938 #27204347

Subgroups — C2×#20267938 #27204347

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×#13110105C211yesmaximal, characteristic, complemented
2C22×#13110094C211yesmaximal, characteristic, complemented
3C22×D824C211yesmaximal, characteristic, complemented
4C2×#15692995C211yesmaximal, characteristic, complemented
5#20267938C218yesmaximal, direct product factor
6C2×#15692946C211yesmaximal, characteristic, complemented
7C2×#15692943C211yesmaximal, characteristic, complemented
8C2×C22⋊C8×C103C211yesmaximal, characteristic, complemented
9C2×#13110105—24no—
10C2×#13110105—24no—
11C2×#13110105—22no—
12C2×#13110105C2214yescomplemented
13C22×Dic206C2211yescharacteristic
14C22×D412C2211yescharacteristic
15C22×D412C2211yescharacteristic
16C22×C22⋊D103—21no—
17C22×C22⋊D103—21no—
18C22×C4×D103—21no—
19C2×#13110094—24no—
20C2×#13110094C2214yescomplemented
21C2×D824—24no—
22C2×D824C2214yescomplemented
23#15692995—22no—
24#15692995C2214yescomplemented
25C2×C4⋊Dic103C2211yescharacteristic
26C2×(C2×D103)⋊C4—21no—
27#15692946C2214yescomplemented
28#15692943C2214yescomplemented
29C23×C4×C103C2211yescharacteristic
30C22×C8×C103C2211yescharacteristic
31C22×C8×C103C2211yescharacteristic
32C22⋊C8×C103C2214yescomplemented
33C23×D103—21no—
34C23×D103—21no—
35#13110105—216no—
36#13110105—28no—
37#13110105—28no—
38C2×Dic206—22no—
39C2×Dic206—21no—
40C2×Dic206D414yescomplemented
41C2×Dic206C2312yes—
42C2×D412—22no—
43C2×D412—21no—
44C2×D412—22no—
45C2×D412—22no—
46C2×D412—21no—
47C2×D412D414yescomplemented
48C2×D412C2312yes—
49C2×D412C2312yes—
50C2×C22⋊D103—28no—
51C2×C22⋊D103—24no—
52C2×C22⋊D103—24no—
53C2×C22⋊D103—44no—
54C22×Dic103—21no—
55C22×Dic103—21no—
56C2×C4×D103—28no—
57C2×C4×D103—24no—
58#13110094—28no—
59D824—28no—
60C4⋊Dic103—21no—
61C4⋊Dic103C2312yes—
62(C2×D103)⋊C4—24no—
63C24×C103D411yescharacteristic
64C22×C4×C103—22no—
65C22×C4×C103—22no—
66C22×C4×C103D412yes—
67C22×C4×C103D411yescharacteristic
68C22×C4×C103C2312yes—
69C22×C4×C103C2311yescharacteristic
70C2×C8×C103—22no—
71C2×C8×C103—22no—
72C2×C8×C103C2312yes—
73C2×C8×C103C2312yes—
74C23×C103—22no—
75C23×C103—22no—
76C23×C103—22no—
77C23×C103C2×D412yes—
78C23×C103C2×D411yescharacteristic
79C22×D103—24no—
80C22×D103—22no—
81C22×D103—22no—
82C22×D103—42no—
83C22×D103—42no—
84C22×D103—42no—
85C22×D103—42no—
86C22×D103—42no—
87C2×C4×C103—22no—
88C2×C4×C103—24no—
89C2×C4×C103—22no—
90C2×C4×C103—22no—
91C2×C4×C103C2×D412yes—
92C2×C4×C103C2×D412yes—
93C2×C4×C103C2×D412yes—
94C2×C4×C103C2×D411yescharacteristic
95C2×C4×C103C2411yescharacteristic
96C22⋊D103—216no—
97C22⋊D103—48no—
98C2×Dic103—24no—
99C2×Dic103—22no—
100C2×Dic103—22no—
101C2×Dic103—42no—
102D412—24no—
103D412—22no—
104D412—22no—
105D412—22no—
106D412—42no—
107D412C2×D414yescomplemented
108C4×D103—216no—
109Dic206—24no—
110Dic206—22no—
111Dic206C2×D414yescomplemented
112C8×C103—22no—
113C8×C103—22no—
114C22×C103—22no—
115C22×C103—22no—
116C22×C103—22no—
117C22×C103—44no—
118C22×C103#12012yes—
119C22×C103#13512yes—
120C22×C103AGL(1,ℤ/8)12yes—
121C22×C103C22×D411yescharacteristic
122C2×D103—24no—
123C2×D103—42no—
124C2×D103—42no—
125C2×D103—48no—
126C2×D103—42no—
127C2×D103—42no—
128C2×D103—42no—
129C2×D103—84no—
130C4×C103—22no—
131C4×C103#12012yes—
132C4×C103C22×D411yescharacteristic
133C4×C103C22×D411yescharacteristic
134Dic103—24no—
135Dic103—42no—
136C2×C103—42no—
137C2×C103#44914yescomplemented
138C2×C103C2×#12011yescharacteristic
139C2×C103C2×#13511yescharacteristic
140C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
141D103—44no—
142D103—82no—
143C2×#449—1031nomaximal, Sylow
144C103C2×#44911yescharacteristic, complemented, Sylow
145C22×#41—1031no—
146C22×SD16—1031no—
147C22×D8—1031no—
148C2×#121—1031no—
149#449—1038no—
150C2×#103—1031no—
151C2×#102—1031no—
152C2×C22⋊C8D10311yescharacteristic, complemented
153C2×#41—1034no—
154C2×#41—2064no—
155C2×#41—2064no—
156C2×#41—2062no—
157C22×Q8—1031no—
158C22×D4—1031no—
159C22×D4—1031no—
160C22×D4—2061no—
161C22×D4—2061no—
162C23×C4—2061no—
163C23×C4C2×D10311yescharacteristic
164C2×SD16—1034no—
165C2×SD16—2064no—
166C2×D8—1034no—
167C2×D8—2064no—
168C22×C8C2×D10311yescharacteristic
169C22×C8C2×D10311yescharacteristic
170#121—1034no—
171#121—2062no—
172C2×C4⋊C4—1031no—
173C2×C22⋊C4—2061no—
174#103—1034no—
175#102—1034no—
176C22⋊C8C2×D10314yescomplemented
177C24—2061no—
178C24—2061no—
179C24D41211yescharacteristic
180#41—2068no—
181#41—2068no—
182#41—20616no—
183C2×Q8—1034no—
184C2×Q8—1032no—
185C2×Q8—2062no—
186C2×Q8—2061no—
187C2×D4—1034no—
188C2×D4—1032no—
189C2×D4—1032no—
190C2×D4—4124no—
191C2×D4—2064no—
192C2×D4—2068no—
193C2×D4—2064no—
194C2×D4—2062no—
195C2×D4—2062no—
196C2×D4—2062no—
197C2×D4—2061no—
198C2×D4—2061no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—2068no—
202C22×C4—2061no—
203C22×C4—2061no—
204C22×C4—2064no—
205C22×C4D41212yes—
206C22×C4D41211yescharacteristic
207C22×C4C22×D10312yes—
208C22×C4C22×D10311yescharacteristic
209SD16—2068no—
210D8—2068no—
211C2×C8—22no—
212C2×C8—22no—
213C2×C8C22×D10312yes—
214C2×C8C22×D10312yes—
215C4⋊C4—1032no—
216C4⋊C4—2061no—
217C22⋊C4—2064no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—4122no—
222C23—4122no—
223C23—4122no—
224C23—4122no—
225C23—4122no—
226C23—2062no—
227C23—2062no—
228C23—2064no—
229C23C2×D41212yes—
230C23C2×D41211yescharacteristic
231Q8—1034no—
232Q8—2062no—
233Q8—2064no—
234D4—1034no—
235D4—4128no—
236D4—4122no—
237D4—20616no—
238D4—2062no—
239D4—2062no—
240D4—2062no—
241D4—2064no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—24no—
246C2×C4—4122no—
247C2×C4—20616no—
248C2×C4—2062no—
249C2×C4—2062no—
250C2×C4—2064no—
251C2×C4D4×D10312yes—
252C2×C4D4×D10312yes—
253C2×C4C2×D41212yes—
254C2×C4C2×D41211yescharacteristic
255C2×C4C23×D10311yescharacteristic
256C8—22no—
257C8—22no—
258C22—22no—
259C22—22no—
260C22—22no—
261C22—44no—
262C22—8244no—
263C22—4122no—
264C22—4122no—
265C22—4122no—
266C22—4122no—
267C22—4122no—
268C22—4128no—
269C22—2064no—
270C22#1569299112yes—
271C22#1569304312yes—
272C22#1569304912yes—
273C22C22×D41211yescharacteristic
274C4—22no—
275C4—4122no—
276C4—2064no—
277C4#1569299112yes—
278C4C2×D4×D10311yescharacteristic
279C4C2×D4×D10311yescharacteristic
280C2—42no—
281C2—8242no—
282C2—4124no—
283C2#2026793814yesdirect product factor
284C2C2×#1569299111yescharacteristic
285C2C2×#1569304311yescharacteristic
286C2C2×#1569304911yescharacteristic
subgroupG/H
centerC23C2×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×C22⋊C8×C103C2
socleC23×C103C2×D4
hypercenterC2×C22⋊C8D103
hypocenterC103C2×#449
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×#13110105C2semidirect
2. C22×#13110094C2semidirect
3. C22×D824C2semidirect
4. C2×#15692995C2semidirect
5. #20267938C2direct (N × H)
6. C2×#15692946C2semidirect
7. C2×#15692943C2semidirect
8. C2×C22⋊C8×C103C2semidirect
12. C2×#13110105C22semidirect
20. C2×#13110094C22semidirect
22. C2×D824C22semidirect
24. #15692995C22semidirect
27. #15692946C22semidirect
28. #15692943C22semidirect
32. C22⋊C8×C103C22semidirect
40. C2×Dic206D4semidirect
47. C2×D412D4semidirect
107. D412C2×D4semidirect
111. Dic206C2×D4semidirect
137. C2×C103#449semidirect
144. C103C2×#449semidirect
152. C2×C22⋊C8D103semidirect
176. C22⋊C8C2×D103semidirect
283. C2#20267938direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131101052
C22×#131100942
C22×D8242
C2×#156929952
#202679382
C2×#156929462
C2×#156929432
C2×C22⋊C8×C1032
C2×#449103