Finite Group Databasebeta

← #37581802

Subgroups — #37581802

Order 24448.

732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20259370C211yesmaximal, characteristic, complemented
2C2×#20259348C211yesmaximal, characteristic, complemented
3#27133230C211yesmaximal, characteristic, complemented
4#27132807C214yesmaximal, complemented
5#27132800C214yesmaximal, complemented
6#27132672C211yesmaximal, characteristic, complemented
7#27132660C211yesmaximal, characteristic, complemented
8#27132629C211yesmaximal, characteristic, complemented
9C22×SD16×C191C211yesmaximal, characteristic, complemented
10#20259370—24no—
11#20259370—24no—
12C2×#15690288—21no—
13C2×#15690288C2212yescomplemented
14C2×#15690287—22no—
15C2×#15690287C2211yescharacteristic
16C2×#15690287C2211yescharacteristic
17C2×Q8×D191—21no—
18C2×Q8×D191C2212yescomplemented
19#20259348—24no—
20C2×#15690275C2212yes—
21C2×#15690272C2212yes—
22C2×#15690271C2211yescharacteristic
23#20259318—21no—
24#20259309—21no—
25#20259293C2214yes—
26#20259291—22no—
27#20259281C2211yescharacteristic
28#20259247C2212yescomplemented
29#20259246C2214yescomplemented
30#20259244C2212yescomplemented
31(C2×D191)⋊C8C2214yescomplemented
32C22×Q8×C191C2211yescharacteristic
33C22×D4×C191C2211yescharacteristic
34C2×SD16×C191—24no—
35C2×SD16×C191C2214yes—
36C22×C8×C191C2211yescharacteristic
37#15690288—28no—
38#15690288—24no—
39#15690288—24no—
40#15690287—216no—
41#15690287—22no—
42#15690287—22no—
43#15690287—22no—
44#15690287D414yescomplemented
45C2×Dic382—22no—
46C2×Dic382D411yescharacteristic
47C2×Dic382C2311yescharacteristic
48Q8×D191—28no—
49Q8×D191—24no—
50Q8×D191—24no—
51C2×D764—22no—
52C2×D764D411yescharacteristic
53C2×D764C2311yescharacteristic
54C2×C22⋊D191—24no—
55C2×C22⋊D191—21no—
56C2×C22⋊D191D412yes—
57C2×C4×D191—22no—
58C2×C4×D191—22no—
59C2×C4×D191—21no—
60C2×C4×D191C2312yes—
61#15690275—24no—
62#15690272—24no—
63#15690271—22no—
64C2×C191⋊C8C2312yes—
65C4⋊Dic191C2312yes—
66C22⋊Dic191—24no—
67C22⋊Dic191—21no—
68C4×Dic191—21no—
69C24×C191—21no—
70C2×Q8×C191—21no—
71C2×Q8×C191—22no—
72C2×Q8×C191D414yescomplemented
73C2×Q8×C191C2312yes—
74C2×D4×C191—22no—
75C2×D4×C191—22no—
76C2×D4×C191—21no—
77C2×D4×C191C2312yes—
78C22×C4×C191—21no—
79C22×C4×C191C2311yescharacteristic
80SD16×C191—28no—
81C2×C8×C191—22no—
82C2×C8×C191C2312yes—
83C22×D191—21no—
84C22×D191C2×D412yes—
85Dic382—28no—
86Dic382—22no—
87Dic382—21no—
88Dic382C2×D412yes—
89D764—28no—
90D764—22no—
91D764—21no—
92D764C2×D412yes—
93C22⋊D191—24no—
94C22⋊D191—24no—
95C22⋊D191—84no—
96C2×Dic191—21no—
97C2×Dic191—22no—
98C2×Dic191C2×D412yes—
99C4×D191—28no—
100C4×D191—28no—
101C4×D191—24no—
102C4×D191—22no—
103C4×D191—22no—
104C191⋊C8—22no—
105C23×C191—22no—
106C23×C191—42no—
107C23×C191—82no—
108C23×C191C2×D411yescharacteristic
109Q8×C191—24no—
110Q8×C191—22no—
111Q8×C191C2×D414yes—
112D4×C191—22no—
113D4×C191—22no—
114D4×C191—42no—
115C2×C4×C191—24no—
116C2×C4×C191—22no—
117C2×C4×C191C2×D411yescharacteristic
118C2×C4×C191C2×D412yes—
119C2×C4×C191C2×D412yes—
120C2×C4×C191C2411yescharacteristic
121C8×C191—22no—
122C22×C191—22no—
123C22×C191—42no—
124C22×C191—44no—
125C22×C191—84no—
126C22×C191#12012yes—
127C22×C191C22×D411yescharacteristic
128C2×D191—22no—
129C2×D191—22no—
130C2×D191—24no—
131C2×D191—42no—
132C4×C191—24no—
133C4×C191#12012yes—
134C4×C191C22×D411yescharacteristic
135C4×C191C22×D411yescharacteristic
136Dic191—22no—
137Dic191—22no—
138Dic191—42no—
139C2×C191—22no—
140C2×C191—82no—
141C2×C191C2×#12011yescharacteristic
142C2×C191#57712yes—
143D191—42no—
144D191—42no—
145C191#301011yescharacteristic, complemented, Sylow
146#3010—1911nomaximal, Sylow
147C2×2−1+4—1911no—
148C2×AGL(1,ℤ/8)—1911no—
149C22×SD16D19111yescharacteristic, complemented
150#535—1911no—
151#449—1914no—
152#448—1914no—
153#419—1911no—
154#416—1911no—
155#408—1911no—
1562−1+4—3824no—
1572−1+4—3824no—
158C2×#41—3822no—
159C2×#41—3821no—
160C2×#41—1912no—
161C2×#41—1911no—
162C2×#41—1911no—
163C22×Q8—3821no—
164C22×Q8—1912no—
165C22×Q8C2×D19111yescharacteristic
166C22×D4C2×D19111yescharacteristic
167AGL(1,ℤ/8)—3824no—
168C2×SD16—24no—
169C2×SD16—1912no—
170C2×SD16C2×D19114yes—
171C2×D8—1912no—
172C2×M16—1911no—
173C22×C8C2×D19111yescharacteristic
174#127—3821no—
175#124—3821no—
176#121—1914no—
177#120—3822no—
178#117—1911no—
179#103—1914no—
180#103—1912no—
181#102—1912no—
182C22⋊C8—1914no—
183C24—21no—
184#41—38216no—
185#41—3828no—
186#41—3824no—
187#41—3824no—
188#41—3822no—
189#41—3822no—
190#41—3822no—
191#41—1914no—
192C2×Q8—21no—
193C2×Q8—22no—
194C2×Q8—3822no—
195C2×Q8—3828no—
196C2×Q8—3824no—
197C2×Q8—3824no—
198C2×Q8—1911no—
199C2×Q8—1911no—
200C2×Q8C22⋊D19114yescomplemented
201C2×Q8C22×D19112yes—
202C2×D4—22no—
203C2×D4—21no—
204C2×D4—22no—
205C2×D4—3822no—
206C2×D4—3821no—
207C2×D4—3824no—
208C2×D4—1912no—
209C2×D4—1911no—
210C2×D4—1911no—
211C2×D4C22×D19112yes—
212C22×C4—21no—
213C22×C4—3822no—
214C22×C4—3822no—
215C22×C4—3821no—
216C22×C4—1912no—
217C22×C4C22×D19111yescharacteristic
218SD16—28no—
219SD16—3824no—
220D8—3824no—
221M16—3822no—
222C2×C8—22no—
223C2×C8—1912no—
224C2×C8C22×D19112yes—
225C4⋊C4—1912no—
226C22⋊C4—3821no—
227C22⋊C4—3824no—
228C42—3821no—
229C23—22no—
230C23—42no—
231C23—82no—
232C23—3821no—
233C23—1912no—
234C23D4×D19111yescharacteristic
235Q8—22no—
236Q8—24no—
237Q8—3828no—
238Q8—3821no—
239Q8—3822no—
240Q8—1912no—
241Q8C2×C22⋊D19114yes—
242D4—22no—
243D4—22no—
244D4—42no—
245D4—3828no—
246D4—3824no—
247D4—3824no—
248D4—3821no—
249D4—3822no—
250D4—1912no—
251D4—15284no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—3828no—
255C2×C4—3828no—
256C2×C4—3821no—
257C2×C4—3822no—
258C2×C4—3822no—
259C2×C4—3824no—
260C2×C4—3822no—
261C2×C4—1912no—
262C2×C4D4×D19112yes—
263C2×C4D4×D19111yescharacteristic
264C2×C4C2×C22⋊D19112yes—
265C2×C4C23×D19111yescharacteristic
266C8—22no—
267C8—3822no—
268C22—22no—
269C22—44no—
270C22—42no—
271C22—84no—
272C22—3824no—
273C22—3822no—
274C22—3822no—
275C22—7642no—
276C22#2025929012yes—
277C22C2×D4×D19111yescharacteristic
278C4—24no—
279C4—3822no—
280C4—3822no—
281C4—7642no—
282C4#2025929012yes—
283C4C2×D4×D19111yescharacteristic
284C4C22×C22⋊D19111yescharacteristic
285C2—22no—
286C2—82no—
287C2—7642no—
288C2—7642no—
289C2C2×#2025929011yescharacteristic
290C2#2713346912yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC22×SD16×C191C2
socleC22×C191C22×D4
hypercenterC22×SD16D191
hypocenterC191#3010
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#20259370C2semidirect
2. C2×#20259348C2semidirect
3. #27133230C2semidirect
4. #27132807C2semidirect
5. #27132800C2semidirect
6. #27132672C2semidirect
7. #27132660C2semidirect
8. #27132629C2semidirect
9. C22×SD16×C191C2semidirect
13. C2×#15690288C22semidirect
18. C2×Q8×D191C22semidirect
28. #20259247C22semidirect
29. #20259246C22semidirect
30. #20259244C22semidirect
31. (C2×D191)⋊C8C22semidirect
44. #15690287D4semidirect
72. C2×Q8×C191D4semidirect
145. C191#3010semidirect
149. C22×SD16D191semidirect
200. C2×Q8C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593702
C2×#202593482
#271332302
#271328072
#271328002
#271326722
#271326602
#271326292
C22×SD16×C1912
#3010191