Finite Group Databasebeta

← C2×#20267940 #27204324

Subgroups — C2×#20267940 #27204324

Order 13184.

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

normal subgroups only

This group has 996 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×D4×D103C211yesmaximal, characteristic
2C22×#13110092C211yesmaximal, characteristic, complemented
3C2×#15692997C211yesmaximal, characteristic, complemented
4#20267940C218yesmaximal, direct product factor
5C2×#15692943C211yesmaximal, characteristic, complemented
6C2×#15692942C211yesmaximal, characteristic, complemented
7C2×(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C103C211yesmaximal, characteristic, complemented
9C24×D103—21no—
10C22×D412C2211yescharacteristic
11C22×C22⋊D103—21no—
12C2×D4×D103—24no—
13C2×D4×D103—22no—
14C2×D4×D103—24no—
15C2×D4×D103C2214yes—
16C22×C4×D103C2211yescharacteristic
17C2×#13110092—24no—
18C2×#13110092C2214yescomplemented
19C22×C103⋊C8C2211yescharacteristic, complemented
20#15692997—22no—
21#15692997C2214yescomplemented
22C2×C4⋊Dic103C2211yescharacteristic, complemented
23C2×Dic103⋊C4—21no—
24C2×(C2×D103)⋊C4—21no—
25#15692943C2214yescomplemented
26#15692942C2214yescomplemented
27(C2×D103)⋊C8C2214yescomplemented
28C22×Q8×C103C2211yescharacteristic, complemented
29C22×D4×C103C2211yescharacteristic
30C2×SD16×C103—24no—
31C2×SD16×C103C2214yescomplemented
32C22×C8×C103C2211yescharacteristic, complemented
33C23×D103—28no—
34C23×D103—21no—
35C23×D103—24no—
36C23×D103—44no—
37C23×D103—44no—
38C23×D103D411yescharacteristic
39C2×D412—21no—
40C2×D412—22no—
41C2×D412D414yes—
42C2×D412C2312yes—
43C2×C22⋊D103—28no—
44C2×C22⋊D103—24no—
45D4×D103—216no—
46D4×D103—28no—
47D4×D103—28no—
48C22×Dic103—21no—
49C22×Dic103D411yescharacteristic
50C2×C4×D103—22no—
51C2×C4×D103—22no—
52C2×C4×D103D412yes—
53C2×C4×D103C2312yes—
54#13110092—28no—
55C2×C103⋊C8—22no—
56C2×C103⋊C8C2312yescomplemented
57C4⋊Dic103—21no—
58C4⋊Dic103C2312yescomplemented
59Dic103⋊C4—24no—
60(C2×D103)⋊C4—24no—
61C24×C103—21no—
62C2×Q8×C103—21no—
63C2×Q8×C103—22no—
64C2×Q8×C103—22no—
65C2×Q8×C103C2312yescomplemented
66C2×D4×C103—21no—
67C2×D4×C103—22no—
68C2×D4×C103D414yes—
69C2×D4×C103C2312yes—
70C22×C4×C103—21no—
71C22×C4×C103C2311yescharacteristic
72SD16×C103—28no—
73C2×C8×C103—22no—
74C2×C8×C103C2312yescomplemented
75C23×C103—24no—
76C23×C103—22no—
77C23×C103—42no—
78C23×C103—42no—
79C23×C103C2×D411yescharacteristic
80C22×D103—22no—
81C22×D103—22no—
82C22×D103—216no—
83C22×D103—24no—
84C22×D103—22no—
85C22×D103—48no—
86C22×D103—432no—
87C22×D103—42no—
88C22×D103—42no—
89C22×D103—48no—
90C22×D103SD1614yescomplemented
91C22×D103C2×D412yes—
92Q8×C103—22no—
93Q8×C103—22no—
94Q8×C103—42no—
95D4×C103—24no—
96D4×C103—22no—
97D4×C103C2×D414yes—
98C2×C4×C103—22no—
99C2×C4×C103—42no—
100C2×C4×C103C2×D411yescharacteristic
101C2×C4×C103C2×D412yes—
102C2×C4×C103C2×D412yes—
103C2×C4×C103C2411yescharacteristic
104C22⋊D103—216no—
105C2×Dic103—22no—
106C2×Dic103—22no—
107C2×Dic103—42no—
108C2×Dic103C2×D412yes—
109D412—24no—
110D412—22no—
111D412C2×D414yes—
112C4×D103—24no—
113C4×D103—22no—
114C4×D103—22no—
115C8×C103—22no—
116C103⋊C8—22no—
117C22×C103—24no—
118C22×C103—42no—
119C22×C103—42no—
120C22×C103—48no—
121C22×C103#12012yes—
122C22×C103C2×SD1612yes—
123C22×C103AGL(1,ℤ/8)12yes—
124C22×C103C22×D411yescharacteristic
125C2×D103—22no—
126C2×D103—22no—
127C2×D103—28no—
128C2×D103—24no—
129C2×D103—432no—
130C2×D103—42no—
131C2×D103—42no—
132C2×D103—48no—
133C2×D103C2×SD1614yescomplemented
134C4×C103—42no—
135C4×C103#12012yes—
136C4×C103C22×D411yescharacteristic
137C4×C103C22×D411yescharacteristic
138Dic103—22no—
139Dic103—42no—
140C2×C103—44no—
141C2×C103#45014yescomplemented
142C2×C103C2×#12011yescharacteristic
143C2×C103C22×SD1611yescharacteristic
144C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
145D103—24no—
146D103—44no—
147C2×#450—1031nomaximal, Sylow
148C103C2×#45011yescharacteristic, complemented, Sylow
149C23×D4—1031no—
150C22×SD16—1031no—
151C22×SD16D10311yescharacteristic, complemented
152C2×C22⋊Q8—1031no—
153#450—1038no—
154C2×#102—1031no—
155C2×#102—1031no—
156C2×C22⋊C8—1031no—
157C25—2061no—
158C22×Q8C2×D10311yescharacteristic, complemented
159C22×D4—1034no—
160C22×D4—1031no—
161C22×D4—2062no—
162C22×D4—2061no—
163C22×D4—2064no—
164C22×D4—2064no—
165C22×D4C2×D10311yescharacteristic
166C23×C4—1031no—
167C2×SD16—24no—
168C2×SD16—1034no—
169C2×SD16—2064no—
170C2×SD16C2×D10314yescomplemented
171C22×C8—1031no—
172C22×C8C2×D10311yescharacteristic, complemented
173C22⋊Q8—1034no—
174C22⋊Q8—2062no—
175C2×C4⋊C4—1031no—
176C2×C4⋊C4—2061no—
177C2×C22⋊C4—2061no—
178#102—1034no—
179#102—1034no—
180C22⋊C8—1034no—
181C24—21no—
182C24—1031no—
183C24—4124no—
184C24—4124no—
185C24—2064no—
186C24—2068no—
187C24—2061no—
188C2×Q8—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8C22×D10312yescomplemented
192C2×D4—22no—
193C2×D4—21no—
194C2×D4—1034no—
195C2×D4—1032no—
196C2×D4—2064no—
197C2×D4—2068no—
198C2×D4—20616no—
199C2×D4—2068no—
200C2×D4—2068no—
201C2×D4—2061no—
202C2×D4—2062no—
203C2×D4C22⋊D10314yes—
204C2×D4C22×D10312yes—
205C22×C4—21no—
206C22×C4—1031no—
207C22×C4—1032no—
208C22×C4—1032no—
209C22×C4—2061no—
210C22×C4—2062no—
211C22×C4—2062no—
212C22×C4C22×D10311yescharacteristic
213SD16—28no—
214SD16—2068no—
215C2×C8—22no—
216C2×C8—1032no—
217C2×C8—2062no—
218C2×C8C22×D10312yescomplemented
219C4⋊C4—1032no—
220C4⋊C4—2064no—
221C4⋊C4—2061no—
222C22⋊C4—2064no—
223C23—22no—
224C23—24no—
225C23—42no—
226C23—42no—
227C23—1032no—
228C23—1034no—
229C23—4128no—
230C23—4128no—
231C23—41232no—
232C23—4122no—
233C23—4122no—
234C23—20616no—
235C23—2062no—
236C23—2064no—
237C23—2062no—
238C23—2062no—
239C23D4×D10311yescharacteristic
240Q8—22no—
241Q8—22no—
242Q8—42no—
243D4—22no—
244D4—24no—
245D4—1034no—
246D4—20616no—
247D4—2062no—
248D4—2064no—
249D4C2×C22⋊D10314yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—1032no—
253C2×C4—4122no—
254C2×C4—2062no—
255C2×C4—2062no—
256C2×C4—2062no—
257C2×C4—2062no—
258C2×C4—2064no—
259C2×C4D4×D10312yes—
260C2×C4D4×D10311yescharacteristic
261C2×C4C2×C22⋊D10312yes—
262C2×C4C23×D10311yescharacteristic
263C8—22no—
264C8—2062no—
265C22—24no—
266C22—42no—
267C22—42no—
268C22—48no—
269C22—1034no—
270C22—41232no—
271C22—4122no—
272C22—4122no—
273C22—4128no—
274C22—2064no—
275C22—2062no—
276C22—2068no—
277C22—2062no—
278C22#1569298912yes—
279C22SD16×D10312yes—
280C22#1569304812yes—
281C22C2×D4×D10311yescharacteristic
282C4—42no—
283C4—4122no—
284C4—2062no—
285C4#1569298912yes—
286C4C2×D4×D10311yescharacteristic
287C4C22×C22⋊D10311yescharacteristic
288C2—44no—
289C2—4124no—
290C2—2064no—
291C2#2026794014yesdirect product factor
292C2C2×#1569298911yescharacteristic
293C2C2×SD16×D10311yescharacteristic
294C2C2×#1569304811yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC22×SD16×C103C2
socleC23×C103C2×D4
prime radicalC22×D4×D103C2
hypercenterC22×SD16D103
hypocenterC103C2×#450
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
2. C22×#13110092C2semidirect
3. C2×#15692997C2semidirect
4. #20267940C2direct (N × H)
5. C2×#15692943C2semidirect
6. C2×#15692942C2semidirect
7. C2×(C2×D103)⋊C8C2semidirect
8. C22×SD16×C103C2semidirect
18. C2×#13110092C22semidirect
19. C22×C103⋊C8C22semidirect
21. #15692997C22semidirect
22. C2×C4⋊Dic103C22semidirect
25. #15692943C22semidirect
26. #15692942C22semidirect
27. (C2×D103)⋊C8C22semidirect
28. C22×Q8×C103C22semidirect
31. C2×SD16×C103C22semidirect
32. C22×C8×C103C22semidirect
56. C2×C103⋊C8C23semidirect
58. C4⋊Dic103C23semidirect
65. C2×Q8×C103C23semidirect
74. C2×C8×C103C23semidirect
90. C22×D103SD16semidirect
133. C2×D103C2×SD16semidirect
141. C2×C103#450semidirect
148. C103C2×#450semidirect
151. C22×SD16D103semidirect
158. C22×Q8C2×D103semidirect
170. C2×SD16C2×D103semidirect
172. C22×C8C2×D103semidirect
191. C2×Q8C22×D103semidirect
218. C2×C8C22×D103semidirect
291. C2#20267940direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1032
C22×#131100922
C2×#156929972
#202679402
C2×#156929432
C2×#156929422
C2×(C2×D103)⋊C82
C22×SD16×C1032
C2×#450103