Finite Group Databasebeta

← #37582166

Subgroups — #37582166

Order 24448.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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, complemented
2C2×#20259330C211yesmaximal, characteristic, complemented
3#27133229C212yesmaximal, complemented
4#27132917C211yesmaximal, characteristic, complemented
5#27132916C211yesmaximal, characteristic, complemented
6#27132913C211yesmaximal, characteristic, complemented
7#27132898C212yesmaximal, complemented
8#27132897C212yesmaximal, complemented
9#27132698C211yesmaximal, characteristic, complemented
10#27132666C212yesmaximal, complemented
11#469×C191C211yesmaximal, characteristic, complemented
12C2×#15690287C2211yescharacteristic
13C2×D4×D191C2212yes—
14C2×D1528C2211yescharacteristic
15C2×#15690272C2212yes—
16D8×D191—24no—
17#20259330—24no—
18C2×#15690270C2211yescharacteristic
19C2×#15690270C2211yescharacteristic, complemented
20C22×C191⋊C8C2211yescharacteristic, complemented
21C2×C8×D191C2211yescharacteristic
22C2×C8×D191C2211yescharacteristic, complemented
23#20259318—22no—
24#20259308—22no—
25#20259297C2212yescomplemented
26#20259296C2212yescomplemented
27#20259293C2212yescomplemented
28#20259292—22no—
29#20259290—22no—
30#20259280C2212yes—
31#20259255C2212yescomplemented
32#20259254C2211yescharacteristic, complemented
33#20259244C2212yescomplemented
34#20259243C2212yescomplemented
35#20259242C2212yescomplemented
36C2×D8×C191C2211yescharacteristic
37C2×M16×C191C2211yescharacteristic, complemented
38#121×C191C2212yescomplemented
39#106×C191C2211yescharacteristic, complemented
40#102×C191C2212yescomplemented
41C23×D191—22no—
42#15690287—22no—
43#15690287—22no—
44C2×Dic382D411yescharacteristic
45C2×D764—22no—
46C2×D764D411yescharacteristic
47C2×D764C2312yes—
48C2×C22⋊D191—22no—
49C2×C22⋊D191—22no—
50C2×C22⋊D191—22no—
51C2×C22⋊D191D411yescharacteristic
52C2×C22⋊D191D411yescharacteristic
53D4×D191—24no—
54D4×D191—24no—
55C2×C4×D191C2311yescharacteristic
56C2×C4×D191C2311yescharacteristic
57D1528—22no—
58#15690272—24no—
59#15690270—22no—
60#15690270—22no—
61C2×C191⋊C8—22no—
62C2×C191⋊C8C2311yescharacteristic
63C2×C191⋊C8C2311yescharacteristic
64C8×D191—22no—
65C8×D191D414yescomplemented
66C4⋊Dic191C2312yes—
67C22⋊Dic191—22no—
68(C2×D191)⋊C4—22no—
69(C2×D191)⋊C4—22no—
70(C2×D191)⋊C4—22no—
71C4×Dic191—22no—
72C2×D4×C191—22no—
73C2×D4×C191C2312yes—
74C22×C4×C191C2311yescharacteristic
75D8×C191—22no—
76M16×C191—22no—
77C2×C8×C191C2311yescharacteristic
78C2×C8×C191C2311yescharacteristic
79C4⋊C4×C191C2312yes—
80C22⋊C4×C191—22no—
81C22×D191—22no—
82C22×D191—44no—
83C22×D191—82no—
84C22×D191—82no—
85C22×D191C2×D411yescharacteristic
86C22×D191C2×D411yescharacteristic
87Dic382—22no—
88D764—22no—
89D764—22no—
90D764—22no—
91D764—82no—
92C22⋊D191—22no—
93C22⋊D191—22no—
94C22⋊D191—44no—
95C22⋊D191—82no—
96C22⋊D191—82no—
97C2×Dic191—22no—
98C2×Dic191C2×D411yescharacteristic
99C2×Dic191C2×D411yescharacteristic
100C4×D191—21no—
101C4×D191—21no—
102C4×D191C2×D412yes—
103C4×D191#4112yes—
104C191⋊C8—21no—
105C191⋊C8C2×D412yes—
106C23×C191—22no—
107C23×C191C2×D411yescharacteristic
108D4×C191—22no—
109D4×C191—22no—
110D4×C191—82no—
111C2×C4×C191—21no—
112C2×C4×C191—21no—
113C2×C4×C191—22no—
114C2×C4×C191C2×D411yescharacteristic
115C2×C4×C191C2411yescharacteristic
116C8×C191—21no—
117C8×C191C2×D412yes—
118C22×C191—21no—
119C22×C191—22no—
120C22×C191—42no—
121C22×C191—42no—
122C22×C191—42no—
123C22×C191C22×D411yescharacteristic
124C2×D191—22no—
125C2×D191—21no—
126C2×D191—22no—
127C2×D191—42no—
128C2×D191—42no—
129C2×D191—42no—
130C2×D191—88no—
131C2×D191#12112yes—
132C4×C191—21no—
133C4×C191—42no—
134C4×C191C22×D411yescharacteristic
135C4×C191C2×#4111yescharacteristic
136Dic191—21no—
137Dic191—42no—
138Dic191#12112yes—
139C2×C191—41no—
140C2×C191—82no—
141C2×C191C2×#12111yescharacteristic
142C2×C191#57612yes—
143D191—22no—
144D191—41no—
145D191—82no—
146C191#305811yescharacteristic, complemented, Sylow
147#3058—1911nomaximal, Sylow
148C22×D8—1911no—
149C2×#131—1911no—
150#535—1912no—
151#469—1911no—
152#469—1911no—
153#469—1911no—
154#469D19111yescharacteristic, complemented
155#466—1912no—
156#466—1912no—
157#427—1911no—
158#418—1912no—
159C2×#41—1911no—
160C22×D4—1912no—
161C2×D8—3824no—
162C2×D8—1912no—
163C2×D8—1911no—
164C2×D8C2×D19111yescharacteristic
165#131—3824no—
166C2×M16—1911no—
167C2×M16—1911no—
168C2×M16C2×D19111yescharacteristic, complemented
169C22×C8—1911no—
170C22×C8—1911no—
171C22×C8—1911no—
172#127—3822no—
173#124—3822no—
174#121—1912no—
175#121—1912no—
176#121—1912no—
177#121C2×D19112yescomplemented
178#120—3822no—
179#120—3822no—
180#117—1912no—
181#107—1912no—
182#106—1911no—
183#106C2×D19111yescharacteristic, complemented
184#102—1912no—
185#102—1912no—
186#102—1912no—
187#102C2×D19112yescomplemented
188C24—3822no—
189#41—3822no—
190#41—3822no—
191C2×Q8—1911no—
192C2×D4—22no—
193C2×D4—3822no—
194C2×D4—3822no—
195C2×D4—3822no—
196C2×D4—3824no—
197C2×D4—3824no—
198C2×D4—3822no—
199C2×D4—1911no—
200C2×D4—1911no—
201C2×D4—1911no—
202C2×D4—1912no—
203C2×D4C22×D19112yes—
204C22×C4—1911no—
205C22×C4—1911no—
206C22×C4C22×D19111yescharacteristic
207D8—22no—
208D8—3824no—
209D8—3822no—
210M16—22no—
211M16—3822no—
212M16—3822no—
213C2×C8—3822no—
214C2×C8—3822no—
215C2×C8—1911no—
216C2×C8—1911no—
217C2×C8—1914no—
218C2×C8C22×D19111yescharacteristic
219C2×C8C22×D19111yescharacteristic
220C4⋊C4—1912no—
221C4⋊C4C22×D19112yes—
222C22⋊C4—22no—
223C22⋊C4—3822no—
224C22⋊C4—3822no—
225C22⋊C4—3822no—
226C22⋊C4—3822no—
227C42—3822no—
228C23—22no—
229C23—3822no—
230C23—1911no—
231C23—1911no—
232C23—15282no—
233C23—15282no—
234C23—7644no—
235C23D4×D19111yescharacteristic
236Q8—3822no—
237D4—22no—
238D4—22no—
239D4—82no—
240D4—3822no—
241D4—3822no—
242D4—3822no—
243D4—3822no—
244D4—3822no—
245D4—15282no—
246D4—15282no—
247D4—15282no—
248D4—7644no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—3821no—
253C2×C4—3821no—
254C2×C4—3822no—
255C2×C4—1911no—
256C2×C4—1911no—
257C2×C4—1912no—
258C2×C4—1912no—
259C2×C4D4×D19111yescharacteristic
260C2×C4C23×D19111yescharacteristic
261C8—21no—
262C8—3821no—
263C8—1912no—
264C8D4×D19112yes—
265C22—22no—
266C22—21no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—3822no—
271C22—3822no—
272C22—3821no—
273C22—1912no—
274C22—15288no—
275C22—7642no—
276C22—7642no—
277C22—7642no—
278C22C2×D4×D19111yescharacteristic
279C4—21no—
280C4—42no—
281C4—3821no—
282C4—1912no—
283C4—7642no—
284C4C2×D4×D19111yescharacteristic
285C4#41×D19111yescharacteristic
286C2—41no—
287C2—82no—
288C2—3822no—
289C2—15282no—
290C2—7641no—
291C2#121×D19111yescharacteristic
292C2#2713346712yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#469×C191C2
socleC22×C191C22×D4
hypercenter#469D191
hypocenterC191#3058
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D191C2semidirect
2. C2×#20259330C2semidirect
3. #27133229C2semidirect
4. #27132917C2semidirect
5. #27132916C2semidirect
6. #27132913C2semidirect
7. #27132898C2semidirect
8. #27132897C2semidirect
9. #27132698C2semidirect
10. #27132666C2semidirect
11. #469×C191C2semidirect
19. C2×#15690270C22semidirect
20. C22×C191⋊C8C22semidirect
22. C2×C8×D191C22semidirect
25. #20259297C22semidirect
26. #20259296C22semidirect
27. #20259293C22semidirect
31. #20259255C22semidirect
32. #20259254C22semidirect
33. #20259244C22semidirect
34. #20259243C22semidirect
35. #20259242C22semidirect
37. C2×M16×C191C22semidirect
38. #121×C191C22semidirect
39. #106×C191C22semidirect
40. #102×C191C22semidirect
65. C8×D191D4semidirect
146. C191#3058semidirect
154. #469D191semidirect
168. C2×M16C2×D191semidirect
177. #121C2×D191semidirect
183. #106C2×D191semidirect
187. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1912
C2×#202593302
#271332292
#271329172
#271329162
#271329132
#271328982
#271328972
#271326982
#271326662
#469×C1912
#3058191