Finite Group Databasebeta

← #37581369

Subgroups — #37581369

Order 24448.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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
2#27133135C212yesmaximal, complemented
3#27132776C211yesmaximal, characteristic, complemented
4#27132775C211yesmaximal, characteristic, complemented
5#27132774C211yesmaximal, characteristic, complemented
6C4×#15690272C212yesmaximal, complemented
7#27132743C212yesmaximal, complemented
8#27132698C211yesmaximal, characteristic, complemented
9#27132666C212yesmaximal, complemented
10#27132620C211yesmaximal, characteristic, complemented
11#442×C191C211yesmaximal, characteristic, complemented
12C2×D4×D191C2212yes—
13C2×D1528C2211yescharacteristic
14C2×#15690272C2212yes—
15D8×D191C418yescomplemented
16C2×#15690270C2211yescharacteristic
17C2×C8×D191C2211yescharacteristic
18C4×D764C2212yescomplemented
19D4×Dic191C2212yescomplemented
20#20259284C2212yescomplemented
21C4×C22⋊D191—22no—
22(C22⋊D191)⋊C4—22no—
23#20259280C2212yes—
24#20259279C2211yescharacteristic
25C2×(C2×D191)⋊C4—22no—
26C22⋊C4×D191—22no—
27#20259255C2212yescomplemented
28#20259254C2211yescharacteristic, complemented
29#20259244C2212yescomplemented
30#20259243C2212yescomplemented
31#20259242C2212yescomplemented
32#20259232C2211yescharacteristic, complemented
33C4×C191⋊C8C2211yescharacteristic, complemented
34C8×Dic191C2211yescharacteristic, 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×D191C2311yescharacteristic
49D1528C2×C414yescomplemented
50#15690272C2×C418yescomplemented
51#15690270—22no—
52C2×C191⋊C8C2311yescharacteristic
53C2×C191⋊C8C2311yescharacteristic
54C8×D191C2×C414yescomplemented
55C4⋊Dic191C2312yes—
56Dic191⋊C4D412yes—
57C22⋊Dic191—22no—
58(C2×D191)⋊C4—22no—
59(C2×D191)⋊C4—22no—
60(C2×D191)⋊C4—22no—
61(C2×D191)⋊C4D412yes—
62C4×Dic191—22no—
63C4×Dic191C2311yescharacteristic
64C2×D4×C191C2312yes—
65C22×C4×C191—22no—
66D8×C191C2×C414yescomplemented
67C2×C8×C191C2311yescharacteristic
68C2×C8×C191C2311yescharacteristic
69C4⋊C4×C191C2312yes—
70C22⋊C4×C191—22no—
71C42×C191C2311yescharacteristic
72C22×D191—22no—
73C22×D191—28no—
74C22×D191—82no—
75C22×D191—82no—
76C22×D191C2×D411yescharacteristic
77D764—22no—
78D764C22×C414yes—
79C22⋊D191—28no—
80C2×Dic191—22no—
81C2×Dic191—82no—
82C2×Dic191C2×D412yes—
83C2×Dic191C2×D411yescharacteristic
84C4×D191—82no—
85C4×D191—82no—
86C4×D191C22×C412yes—
87C4×D191#4112yes—
88C191⋊C8—21no—
89C191⋊C8C22×C412yes—
90C23×C191—22no—
91D4×C191—22no—
92D4×C191C22×C414yes—
93C2×C4×C191—22no—
94C2×C4×C191—82no—
95C2×C4×C191C2×D412yes—
96C2×C4×C191C2411yescharacteristic
97C8×C191—21no—
98C8×C191C22×C412yes—
99C22×C191—24no—
100C22×C191—42no—
101C22×C191—42no—
102C22×C191C22×D411yescharacteristic
103C2×D191—22no—
104C2×D191—24no—
105C2×D191—42no—
106C2×D191—42no—
107C2×D191—88no—
108C2×D191C4×D412yes—
109C4×C191—22no—
110C4×C191—42no—
111C4×C191C23×C411yescharacteristic
112C4×C191C2×#4111yescharacteristic
113Dic191—22no—
114Dic191—42no—
115Dic191C4×D412yes—
116C2×C191—44no—
117C2×C191C2×C4×D411yescharacteristic
118C2×C191#57612yes—
119D191—22no—
120D191—44no—
121C191#294811yescharacteristic, complemented, Sylow
122#2948—1911nomaximal, Sylow
123C22×D8—1911no—
124#518—1912no—
125#442—1911no—
126#442—1911no—
127#442—1911no—
128#442D19111yescharacteristic, complemented
129C4×D8—1912no—
130C4×D8—1912no—
131#427—1911no—
132#418—1912no—
133#405—1911no—
134C22×D4—1912no—
135C2×D8—1912no—
136C2×D8—1918no—
137C2×D8—1911no—
138C2×D8C2×D19111yescharacteristic
139C2×M16—1911no—
140C22×C8—1911no—
141C4×D4—3822no—
142C4×D4—3822no—
143C4×D4—1912no—
144C4×D4—1912no—
145C4×D4—1912no—
146C4×D4C2×D19112yescomplemented
147#117—1912no—
148#117—1911no—
149C2×C22⋊C4—3822no—
150C2×C22⋊C4—3822no—
151#107—1912no—
152#106—1911no—
153#106C2×D19111yescharacteristic, complemented
154#102—1912no—
155#102—1912no—
156#102—1912no—
157#102C2×D19112yescomplemented
158#97—1911no—
159#97C2×D19111yescharacteristic, complemented
160C4×C8—1911no—
161C4×C8—1911no—
162C24—3822no—
163C2×D4—3824no—
164C2×D4—3822no—
165C2×D4—1918no—
166C2×D4—1912no—
167C2×D4C22×D19112yes—
168C22×C4—22no—
169C22×C4—3822no—
170C22×C4—3822no—
171C22×C4—3822no—
172C22×C4—1911no—
173D8—1918no—
174D8—1914no—
175D8C4×D19114yescomplemented
176M16—3822no—
177C2×C8—1911no—
178C2×C8—1911no—
179C2×C8—1914no—
180C2×C8C22×D19111yescharacteristic
181C2×C8C22×D19111yescharacteristic
182C4⋊C4—1912no—
183C4⋊C4—1912no—
184C4⋊C4C22×D19112yes—
185C22⋊C4—22no—
186C22⋊C4—3822no—
187C22⋊C4—3822no—
188C22⋊C4—3822no—
189C22⋊C4—3822no—
190C22⋊C4—1912no—
191C42—3822no—
192C42—1911no—
193C42C22×D19111yescharacteristic
194C23—22no—
195C23—3828no—
196C23—3822no—
197C23—1911no—
198C23—15282no—
199C23—15282no—
200D4—22no—
201D4—3828no—
202D4—3822no—
203D4—1914no—
204D4C2×C4×D19114yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—3822no—
208C2×C4—1912no—
209C2×C4—1911no—
210C2×C4—1912no—
211C2×C4—1912no—
212C2×C4—15282no—
213C2×C4—15282no—
214C2×C4—15282no—
215C2×C4D4×D19112yes—
216C2×C4C23×D19111yescharacteristic
217C8—21no—
218C8—3821no—
219C8—1912no—
220C8C2×C4×D19112yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—3822no—
225C22—3824no—
226C22—1912no—
227C22—15288no—
228C22—7642no—
229C22—7642no—
230C22C2×D4×D19111yescharacteristic
231C4—22no—
232C4—42no—
233C4—3822no—
234C4—1912no—
235C4—7642no—
236C4C22×C4×D19111yescharacteristic
237C4#41×D19111yescharacteristic
238C2—44no—
239C2—3822no—
240C2—7644no—
241C2C4×D4×D19111yescharacteristic
242C2#2713346712yes—
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
hypocenterC191#2948
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. #27133135C2semidirect
3. #27132776C2semidirect
4. #27132775C2semidirect
5. #27132774C2semidirect
6. C4×#15690272C2semidirect
7. #27132743C2semidirect
8. #27132698C2semidirect
9. #27132666C2semidirect
10. #27132620C2semidirect
11. #442×C191C2semidirect
15. D8×D191C4semidirect
18. C4×D764C22semidirect
19. D4×Dic191C22semidirect
20. #20259284C22semidirect
27. #20259255C22semidirect
28. #20259254C22semidirect
29. #20259244C22semidirect
30. #20259243C22semidirect
31. #20259242C22semidirect
32. #20259232C22semidirect
33. C4×C191⋊C8C22semidirect
34. C8×Dic191C22semidirect
36. C4×D4×C191C22semidirect
37. #106×C191C22semidirect
38. #102×C191C22semidirect
39. #97×C191C22semidirect
44. D4×D191C2×C4semidirect
49. D1528C2×C4semidirect
50. #15690272C2×C4semidirect
54. C8×D191C2×C4semidirect
66. D8×C191C2×C4semidirect
121. C191#2948semidirect
128. #442D191semidirect
146. C4×D4C2×D191semidirect
153. #106C2×D191semidirect
157. #102C2×D191semidirect
159. #97C2×D191semidirect
175. D8C4×D191semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1912
#271331352
#271327762
#271327752
#271327742
C4×#156902722
#271327432
#271326982
#271326662
#271326202
#442×C1912
#2948191