Finite Group Databasebeta

← #442×D191 #37581309

Subgroups — #442×D191 #37581309

Order 24448.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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
1C2×D8×D191C211yesmaximal, characteristic
2C4×D4×D191C212yesmaximal, complemented
3#27132776C211yesmaximal, characteristic, complemented
4#27132775C211yesmaximal, characteristic, complemented
5#27132774C211yesmaximal, characteristic, complemented
6#27132773C212yesmaximal, complemented
7#27132772C212yesmaximal, complemented
8#106×D191C211yesmaximal, characteristic, complemented
9#102×D191C212yesmaximal, complemented
10#97×D191C211yesmaximal, characteristic, complemented
11#442×C191C211yesmaximal, characteristic, complemented
12C2×D4×D191C2212yes—
13C22×C4×D191—22no—
14C2×D1528C2211yescharacteristic
15C2×#15690272C2212yes—
16D8×D191C418yescomplemented
17C2×C8×D191C2211yescharacteristic
18C2×C8×D191C2211yescharacteristic
19C4×D764C2212yescomplemented
20D4×Dic191C2212yescomplemented
21#20259284C2212yescomplemented
22C4×C22⋊D191—22no—
23(C22⋊D191)⋊C4—22no—
24C4⋊C4×D191C2212yes—
25C22⋊C4×D191—22no—
26C42×D191C2211yescharacteristic
27#20259254C2211yescharacteristic, complemented
28#20259253C2212yescomplemented
29#20259244C2212yescomplemented
30#20259243C2212yescomplemented
31#20259242C2212yescomplemented
32#20259233C2211yescharacteristic, complemented
33#20259232C2211yescharacteristic, complemented
34#20259232C2211yescharacteristic, complemented
35C2×D8×C191C2211yescharacteristic
36C4×D4×C191C2212yescomplemented
37#106×C191C2211yescharacteristic, complemented
38#102×C191C2212yescomplemented
39#97×C191C2211yescharacteristic, complemented
40C23×D191—22no—
41C2×D764C2312yes—
42C2×C22⋊D191—22no—
43D4×D191—24no—
44D4×D191C2×C418yescomplemented
45C22×Dic191—22no—
46C2×C4×D191—22no—
47C2×C4×D191—22no—
48C2×C4×D191—22no—
49C2×C4×D191—48no—
50C2×C4×D191D412yes—
51C2×C4×D191C2311yescharacteristic
52D1528C2×C414yescomplemented
53#15690272C2×C418yescomplemented
54C2×C191⋊C8C2311yescharacteristic
55C2×C191⋊C8C2311yescharacteristic
56C8×D191—22no—
57C8×D191C2×C414yescomplemented
58C4⋊Dic191C2312yes—
59Dic191⋊C4—22no—
60C22⋊Dic191—22no—
61(C2×D191)⋊C4—22no—
62(C2×D191)⋊C4—22no—
63C4×Dic191D412yes—
64C4×Dic191C2311yescharacteristic
65C2×D4×C191C2312yes—
66C22×C4×C191—22no—
67D8×C191C2×C414yescomplemented
68C2×C8×C191C2311yescharacteristic
69C2×C8×C191C2311yescharacteristic
70C4⋊C4×C191C2312yes—
71C22⋊C4×C191—22no—
72C42×C191C2311yescharacteristic
73C22×D191—22no—
74C22×D191—28no—
75C22×D191—44no—
76C22×D191—44no—
77C22×D191C2×D411yescharacteristic
78D764—22no—
79D764C22×C414yescomplemented
80C22⋊D191—28no—
81C2×Dic191—22no—
82C2×Dic191—44no—
83C2×Dic191C2×D412yes—
84C2×Dic191C2×D411yescharacteristic
85C4×D191—24no—
86C4×D191—44no—
87C4×D191—44no—
88C4×D191—44no—
89C4×D191C22×C412yes—
90C4×D191#4112yes—
91C191⋊C8—21no—
92C191⋊C8C22×C412yescomplemented
93C23×C191—22no—
94D4×C191—22no—
95D4×C191C22×C414yescomplemented
96C2×C4×C191—22no—
97C2×C4×C191—44no—
98C2×C4×C191C2×D412yes—
99C2×C4×C191C2411yescharacteristic
100C8×C191—21no—
101C8×C191C22×C412yescomplemented
102C22×C191—24no—
103C22×C191—42no—
104C22×C191—42no—
105C22×C191C22×D411yescharacteristic
106C2×D191—24no—
107C2×D191—42no—
108C2×D191—42no—
109C2×D191—416no—
110C2×D191C4×D412yes—
111C2×D191AGL(1,ℤ/8)14yes—
112C4×C191—22no—
113C4×C191—42no—
114C4×C191C23×C411yescharacteristic
115C4×C191C2×#4111yescharacteristic
116Dic191—22no—
117Dic191—42no—
118Dic191C4×D412yes—
119C2×C191—44no—
120C2×C191C2×C4×D411yescharacteristic
121C2×C191C2×AGL(1,ℤ/8)12yes—
122D191—44no—
123D191#44214yesdirect product factor
124C191C2×#44211yescharacteristic, complemented, Sylow
125C2×#442—1911nomaximal, Sylow
126C22×D8—1911no—
127C2×C4×D4—1912no—
128#442—1911no—
129#442—1912no—
130#442—1911no—
131#442—1912no—
132#442—1911no—
133#442D19111yescharacteristic, direct product factor
134C2×#106—1911no—
135C2×#102—1912no—
136C2×#97—1911no—
137C22×D4—1912no—
138C23×C4—3822no—
139C2×D8—1912no—
140C2×D8—1918no—
141C2×D8—1911no—
142C2×D8C2×D19111yescharacteristic
143C22×C8—1911no—
144C22×C8—1911no—
145C4×D4—3822no—
146C4×D4—3822no—
147C4×D4—1912no—
148C4×D4—1912no—
149C4×D4—1912no—
150C4×D4C2×D19112yescomplemented
151C2×C4⋊C4—1912no—
152C2×C22⋊C4—3822no—
153C2×C42—1911no—
154#106—1911no—
155#106—1912no—
156#106C2×D19111yescharacteristic, complemented
157#102—1912no—
158#102—1912no—
159#102—1912no—
160#102C2×D19112yescomplemented
161#97—1911no—
162#97—1911no—
163#97—1911no—
164#97C2×D19111yescharacteristic, complemented
165C24—3822no—
166C2×D4—3824no—
167C2×D4—3822no—
168C2×D4—1918no—
169C2×D4—1912no—
170C2×D4C22×D19112yes—
171C22×C4—22no—
172C22×C4—3822no—
173C22×C4—3822no—
174C22×C4—3822no—
175C22×C4—3822no—
176C22×C4—1912no—
177C22×C4—1911no—
178C22×C4—7648no—
179D8—1918no—
180D8—1914no—
181D8C4×D19114yescomplemented
182C2×C8—3822no—
183C2×C8—1911no—
184C2×C8—1911no—
185C2×C8—1914no—
186C2×C8C22×D19111yescharacteristic
187C2×C8C22×D19111yescharacteristic
188C4⋊C4—3822no—
189C4⋊C4—1912no—
190C4⋊C4C22×D19112yes—
191C22⋊C4—22no—
192C22⋊C4—3822no—
193C22⋊C4—3822no—
194C22⋊C4—3822no—
195C42—1912no—
196C42—1911no—
197C42C22×D19111yescharacteristic
198C23—22no—
199C23—3828no—
200C23—3822no—
201C23—1911no—
202C23—7644no—
203C23—7644no—
204D4—22no—
205D4—3828no—
206D4—3822no—
207D4—1914no—
208D4C2×C4×D19114yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—3824no—
212C2×C4—3822no—
213C2×C4—1912no—
214C2×C4—1911no—
215C2×C4—1912no—
216C2×C4—1912no—
217C2×C4—7644no—
218C2×C4—7644no—
219C2×C4—7644no—
220C2×C4—7644no—
221C2×C4D4×D19112yes—
222C2×C4C23×D19111yescharacteristic
223C8—21no—
224C8—3821no—
225C8—1912no—
226C8C2×C4×D19112yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—3824no—
231C22—1914no—
232C22—1912no—
233C22—76416no—
234C22—7642no—
235C22—7642no—
236C22C2×D4×D19111yescharacteristic
237C4—22no—
238C4—42no—
239C4—3822no—
240C4—1912no—
241C4—7642no—
242C4C22×C4×D19111yescharacteristic
243C4#41×D19111yescharacteristic
244C2—44no—
245C2—1914no—
246C2—7644no—
247C2C4×D4×D19111yescharacteristic
248C2AGL(1,ℤ/8)×D19112yes—
subgroupG/H
centerC22C2×D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
Fitting#442×C191C2
socleC22×C191C22×D4
prime radicalC2×D8×D191C2
cosocleC2×C4×C191C24
hypercenter#442D191
hypocenterC191C2×#442
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D191C2semidirect
3. #27132776C2semidirect
4. #27132775C2semidirect
5. #27132774C2semidirect
6. #27132773C2semidirect
7. #27132772C2semidirect
8. #106×D191C2semidirect
9. #102×D191C2semidirect
10. #97×D191C2semidirect
11. #442×C191C2semidirect
16. D8×D191C4semidirect
19. C4×D764C22semidirect
20. D4×Dic191C22semidirect
21. #20259284C22semidirect
27. #20259254C22semidirect
28. #20259253C22semidirect
29. #20259244C22semidirect
30. #20259243C22semidirect
31. #20259242C22semidirect
32. #20259233C22semidirect
33. #20259232C22semidirect
34. #20259232C22semidirect
36. C4×D4×C191C22semidirect
37. #106×C191C22semidirect
38. #102×C191C22semidirect
39. #97×C191C22semidirect
44. D4×D191C2×C4semidirect
52. D1528C2×C4semidirect
53. #15690272C2×C4semidirect
57. C8×D191C2×C4semidirect
67. D8×C191C2×C4semidirect
79. D764C22×C4semidirect
92. C191⋊C8C22×C4semidirect
95. D4×C191C22×C4semidirect
101. C8×C191C22×C4semidirect
123. D191#442direct (N × H)
124. C191C2×#442semidirect
133. #442D191direct (N × H)
150. C4×D4C2×D191semidirect
156. #106C2×D191semidirect
160. #102C2×D191semidirect
164. #97C2×D191semidirect
181. D8C4×D191semidirect
208. D4C2×C4×D191semidirect
226. C8C2×C4×D191semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1912
C4×D4×D1912
#271327762
#271327752
#271327742
#271327732
#271327722
#106×D1912
#102×D1912
#97×D1912
#442×C1912
C2×#442191