Finite Group Databasebeta

← C2×#27132661 #37581029

Subgroups — C2×#27132661 #37581029

Order 24448.

816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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×#15690286C211yesmaximal, characteristic
2C22×#15690270C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D191C211yesmaximal, characteristic, complemented
4#27132661C218yesmaximal, direct product factor
5C2×#20259247C211yesmaximal, characteristic, complemented
6C2×#20259245C211yesmaximal, characteristic, complemented
7C2×#20259243C211yesmaximal, characteristic, complemented
8C2×#102×C191C211yesmaximal, characteristic, complemented
9C2×#15690286—22no—
10C2×#15690286—24no—
11C2×#15690286C418yescomplemented
12C2×#15690286C2214yes—
13C22×Dic382C2211yescharacteristic
14C22×C22⋊D191—21no—
15C23×Dic191—21no—
16C22×C4×D191—21no—
17C22×C4×D191C2211yescharacteristic
18C2×#15690270—24no—
19C2×#15690270C2214yescomplemented
20C22×C191⋊C8C2211yescharacteristic
21C2×C4⋊Dic191C2211yescharacteristic
22C2×Dic191⋊C4—21no—
23C4⋊C4×D191—22no—
24C4⋊C4×D191C2214yescomplemented
25#20259247C2214yescomplemented
26#20259245C2214yescomplemented
27#20259243C2214yescomplemented
28C22×D4×C191C2211yescharacteristic
29C22×C8×C191C2211yescharacteristic
30C2×C4⋊C4×C191C2211yescharacteristic
31#102×C191C2214yescomplemented
32C23×D191D411yescharacteristic
33#15690286—216no—
34#15690286—28no—
35#15690286C2×C4116yescomplemented
36C2×Dic382—21no—
37C2×Dic382—22no—
38C2×Dic382C2×C414yescomplemented
39C2×Dic382C2312yes—
40C2×C22⋊D191—28no—
41C2×C22⋊D191—24no—
42C22×Dic191—28no—
43C22×Dic191—24no—
44C22×Dic191—21no—
45C22×Dic191—21no—
46C22×Dic191D411yescharacteristic
47C2×C4×D191—24no—
48C2×C4×D191—44no—
49C2×C4×D191C2×C414yes—
50C2×C4×D191D412yes—
51C2×C4×D191D414yes—
52C2×C4×D191C2312yes—
53#15690270—28no—
54C2×C191⋊C8—22no—
55C2×C191⋊C8C2312yes—
56C4⋊Dic191—21no—
57C4⋊Dic191C2312yes—
58Dic191⋊C4—24no—
59C24×C191—21no—
60C2×D4×C191—21no—
61C2×D4×C191—22no—
62C2×D4×C191C2×C414yescomplemented
63C2×D4×C191C2312yes—
64C22×C4×C191—21no—
65C22×C4×C191C2311yescharacteristic
66C2×C8×C191—22no—
67C2×C8×C191C2312yes—
68C4⋊C4×C191—21no—
69C4⋊C4×C191C2312yes—
70C22×D191—22no—
71C22×D191—22no—
72C22×D191C22⋊C414yes—
73C22×D191C2×D412yes—
74Dic382—24no—
75Dic382—22no—
76Dic382C22×C414yescomplemented
77C22⋊D191—216no—
78C2×Dic191—24no—
79C2×Dic191—22no—
80C2×Dic191—216no—
81C2×Dic191—22no—
82C2×Dic191—42no—
83C2×Dic191C22⋊C414yes—
84C2×Dic191C2×D412yes—
85C4×D191—48no—
86C4×D191C22⋊C418yes—
87C4×D191C22×C414yes—
88C4×D191C2×D414yes—
89C191⋊C8—22no—
90C23×C191—24no—
91C23×C191—22no—
92C23×C191—42no—
93C23×C191—42no—
94C23×C191C2×D411yescharacteristic
95D4×C191—24no—
96D4×C191—22no—
97D4×C191C22×C414yescomplemented
98C2×C4×C191—22no—
99C2×C4×C191—42no—
100C2×C4×C191C22×C412yes—
101C2×C4×C191C2×D411yescharacteristic
102C2×C4×C191C2×D412yes—
103C2×C4×C191C2411yescharacteristic
104C8×C191—22no—
105C22×C191—24no—
106C22×C191—42no—
107C22×C191—42no—
108C22×C191—48no—
109C22×C191C2×C22⋊C412yes—
110C22×C191AGL(1,ℤ/8)12yes—
111C22×C191#13712yes—
112C22×C191C22×D411yescharacteristic
113C2×D191—22no—
114C2×D191—22no—
115C2×D191—28no—
116C2×D191C2×C22⋊C414yes—
117C4×C191—42no—
118C4×C191C2×C22⋊C412yes—
119C4×C191C23×C411yescharacteristic
120C4×C191C22×D411yescharacteristic
121Dic191—24no—
122Dic191—42no—
123Dic191C2×C22⋊C414yes—
124C2×C191—44no—
125C2×C191#41714yescomplemented
126C2×C191C22×C22⋊C411yescharacteristic
127C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C191C2×#13711yescharacteristic
129D191—24no—
130C191C2×#41711yescharacteristic, complemented, Sylow
131C2×#417—1911nomaximal, Sylow
132C22×#41—1911no—
133C22×M16—1911no—
134C22×C4⋊C4—1911no—
135#417—1918no—
136C2×#103—1911no—
137C2×#103—1911no—
138C2×#102—1911no—
139C2×#102D19111yescharacteristic, complemented
140C2×#41—3822no—
141C2×#41—3824no—
142C2×#41—1918no—
143C2×#41—1914no—
144C22×Q8—1911no—
145C22×D4—3821no—
146C22×D4C2×D19111yescharacteristic
147C23×C4—3821no—
148C23×C4—3821no—
149C23×C4—1911no—
150C2×M16—3824no—
151C2×M16—1914no—
152C22×C8—1911no—
153C22×C8C2×D19111yescharacteristic
154C2×C4⋊C4—3822no—
155C2×C4⋊C4—3821no—
156C2×C4⋊C4—1911no—
157C2×C4⋊C4—1914no—
158C2×C4⋊C4C2×D19111yescharacteristic
159#103—1914no—
160#103—1914no—
161#102—1914no—
162#102C2×D19114yescomplemented
163C24—21no—
164C24—1911no—
165#41—3828no—
166#41—38216no—
167#41—19116no—
168C2×Q8—3821no—
169C2×Q8—3822no—
170C2×Q8—1914no—
171C2×Q8—1912no—
172C2×D4—22no—
173C2×D4—21no—
174C2×D4—3824no—
175C2×D4—3828no—
176C2×D4C4×D19114yescomplemented
177C2×D4C22×D19112yes—
178C22×C4—21no—
179C22×C4—3824no—
180C22×C4—3821no—
181C22×C4—3824no—
182C22×C4—3828no—
183C22×C4—3821no—
184C22×C4—1911no—
185C22×C4—1914no—
186C22×C4—1912no—
187C22×C4—1914no—
188C22×C4—1912no—
189C22×C4—7644no—
190C22×C4C22×D19111yescharacteristic
191M16—3828no—
192C2×C8—22no—
193C2×C8—3822no—
194C2×C8—1912no—
195C2×C8C22×D19112yes—
196C4⋊C4—21no—
197C4⋊C4—3824no—
198C4⋊C4—3821no—
199C4⋊C4—1912no—
200C4⋊C4C22×D19112yes—
201C23—22no—
202C23—24no—
203C23—42no—
204C23—42no—
205C23—3822no—
206C23—3822no—
207C23—1912no—
208C23—1914no—
209C23D4×D19111yescharacteristic
210Q8—3822no—
211Q8—3824no—
212Q8—1914no—
213D4—22no—
214D4—24no—
215D4—38216no—
216D4C2×C4×D19114yescomplemented
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—3822no—
220C2×C4—3824no—
221C2×C4—38216no—
222C2×C4—3822no—
223C2×C4—1912no—
224C2×C4—1914no—
225C2×C4—1914no—
226C2×C4—1914no—
227C2×C4—1918no—
228C2×C4—7648no—
229C2×C4—7642no—
230C2×C4C2×C4×D19112yes—
231C2×C4D4×D19112yes—
232C2×C4D4×D19111yescharacteristic
233C2×C4C23×D19111yescharacteristic
234C8—22no—
235C8—3822no—
236C22—24no—
237C22—42no—
238C22—42no—
239C22—48no—
240C22—3822no—
241C22—3822no—
242C22—3828no—
243C22—1914no—
244C22C22⋊C4×D19112yes—
245C22#2025934612yes—
246C22#2025935112yes—
247C22C2×D4×D19111yescharacteristic
248C4—42no—
249C4—3824no—
250C4—1914no—
251C4—7642no—
252C4C22⋊C4×D19112yes—
253C4C22×C4×D19111yescharacteristic
254C4C2×D4×D19111yescharacteristic
255C2—44no—
256C2—3824no—
257C2#2713266114yesdirect product factor
258C2C2×C22⋊C4×D19111yescharacteristic
259C2C2×#2025934611yescharacteristic
260C2C2×#2025935111yescharacteristic
subgroupG/H
centerC23D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
FittingC2×#102×C191C2
socleC23×C191C2×D4
prime radicalC22×#15690286C2
cosocleC2×C4×C191C24
hypercenterC2×#102D191
hypocenterC191C2×#417
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C22×#15690270C2semidirect
3. C2×C4⋊C4×D191C2semidirect
4. #27132661C2direct (N × H)
5. C2×#20259247C2semidirect
6. C2×#20259245C2semidirect
7. C2×#20259243C2semidirect
8. C2×#102×C191C2semidirect
11. C2×#15690286C4semidirect
19. C2×#15690270C22semidirect
24. C4⋊C4×D191C22semidirect
25. #20259247C22semidirect
26. #20259245C22semidirect
27. #20259243C22semidirect
31. #102×C191C22semidirect
35. #15690286C2×C4semidirect
38. C2×Dic382C2×C4semidirect
62. C2×D4×C191C2×C4semidirect
76. Dic382C22×C4semidirect
97. D4×C191C22×C4semidirect
125. C2×C191#417semidirect
130. C191C2×#417semidirect
139. C2×#102D191semidirect
162. #102C2×D191semidirect
176. C2×D4C4×D191semidirect
216. D4C2×C4×D191semidirect
257. C2#27132661direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156902862
C22×#156902702
C2×C4⋊C4×D1912
#271326612
C2×#202592472
C2×#202592452
C2×#202592432
C2×#102×C1912
C2×#417191