Finite Group Databasebeta

← #37583382

Subgroups — #37583382

Order 24448.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#27133229C212yesmaximal, complemented
2#27132989C212yesmaximal, complemented
3#27132986C212yesmaximal, complemented
4#27132916C211yesmaximal, characteristic, complemented
5#27132897C212yesmaximal, complemented
6#27132798C212yesmaximal, complemented
7#27132795C212yesmaximal, complemented
8#27132631C211yesmaximal, characteristic, complemented
9#469×C191C211yesmaximal, characteristic, complemented
10C2×#15690287C2211yescharacteristic
11C2×D4×D191C2212yescomplemented
12C2×D1528C2211yescharacteristic
13C2×#15690272C2212yes—
14C22×C191⋊C8C2211yescharacteristic, complemented
15#20259318—22no—
16#20259308—22no—
17#20259297C2212yes—
18#20259296C2212yescomplemented
19#20259293C2212yes—
20#20259292—22no—
21#20259290—22no—
22#20259280C2212yescomplemented
23#20259255C2212yescomplemented
24#20259254C2211yescharacteristic, complemented
25#20259244C2212yescomplemented
26#20259243C2212yescomplemented
27#20259242C2212yescomplemented
28(C2×D191)⋊C8C2212yescomplemented
29(C2×D191)⋊C8C2212yescomplemented
30C2×D8×C191C2211yescharacteristic
31C2×M16×C191C2211yescharacteristic, complemented
32#121×C191C2212yescomplemented
33#106×C191C2211yescharacteristic, complemented
34#102×C191C2212yescomplemented
35C23×D191—22no—
36#15690287—41no—
37#15690287—41no—
38C2×Dic382D411yescharacteristic
39C2×D764—22no—
40C2×D764D411yescharacteristic
41C2×D764C2312yes—
42C2×C22⋊D191—22no—
43C2×C22⋊D191—22no—
44C2×C22⋊D191—22no—
45C2×C22⋊D191D412yes—
46D4×D191—42no—
47D4×D191—42no—
48C2×C4×D191C2312yes—
49D1528—41no—
50#15690272—42no—
51C2×C191⋊C8—41no—
52C2×C191⋊C8C2312yes—
53C4⋊Dic191C2312yes—
54C22⋊Dic191—22no—
55(C2×D191)⋊C4—22no—
56(C2×D191)⋊C4—22no—
57(C2×D191)⋊C4—22no—
58C4×Dic191—22no—
59C2×D4×C191—22no—
60C2×D4×C191C2312yes—
61C22×C4×C191C2311yescharacteristic
62D8×C191—41no—
63M16×C191—41no—
64C2×C8×C191C2311yescharacteristic
65C2×C8×C191C2311yescharacteristic
66C4⋊C4×C191C2312yes—
67C22⋊C4×C191—22no—
68C22×D191—22no—
69C22×D191—44no—
70C22×D191—82no—
71C22×D191—82no—
72C22×D191C2×D412yes—
73Dic382—41no—
74D764—22no—
75D764—22no—
76D764—41no—
77D764—82no—
78C22⋊D191—42no—
79C22⋊D191—44no—
80C22⋊D191—82no—
81C22⋊D191—82no—
82C2×Dic191—22no—
83C2×Dic191C2×D412yes—
84C4×D191—22no—
85C4×D191—22no—
86C191⋊C8—22no—
87C23×C191—22no—
88C23×C191C2×D411yescharacteristic
89D4×C191—22no—
90D4×C191—22no—
91D4×C191—82no—
92C2×C4×C191—21no—
93C2×C4×C191—21no—
94C2×C4×C191—22no—
95C2×C4×C191C2×D411yescharacteristic
96C2×C4×C191C2411yescharacteristic
97C8×C191—21no—
98C8×C191—21no—
99C22×C191—21no—
100C22×C191—22no—
101C22×C191—42no—
102C22×C191—42no—
103C22×C191—42no—
104C22×C191C22×D411yescharacteristic
105C2×D191—22no—
106C2×D191—22no—
107C2×D191—22no—
108C2×D191—42no—
109C2×D191—42no—
110C2×D191—42no—
111C2×D191—88no—
112C4×C191—21no—
113C4×C191—42no—
114C4×C191H(5,𝔽2)11yescharacteristic
115C4×C191H(5,𝔽2)11yescharacteristic
116Dic191—22no—
117Dic191—42no—
118C2×C191—41no—
119C2×C191—82no—
120C2×C191#53411yescharacteristic
121C2×C191#57612yes—
122D191—42no—
123D191—82no—
124C191#319911yescharacteristic, complemented, Sylow
125#3199—1911nomaximal, Sylow
126#535—1912no—
127#482—1912no—
128#482—1912no—
129#469—1911no—
130#469D19111yescharacteristic, complemented
131#466—1912no—
132#447—1912no—
133#447—1912no—
134#408—1911no—
135C2×#41—1911no—
136C22×D4—1912no—
137C2×D8—1912no—
138C2×D8—1911no—
139C2×D8C2×D19111yescharacteristic
140C2×M16C2×D19111yescharacteristic, complemented
141C22×C8—1911no—
142#127—3822no—
143#124—3822no—
144#121—1912no—
145#121—1912no—
146#121—1912no—
147#121C2×D19112yescomplemented
148#120—3822no—
149#120—3822no—
150#117—1912no—
151#107—1912no—
152#106—1911no—
153#106C2×D19111yescharacteristic, complemented
154#102—1912no—
155#102—1912no—
156#102—1912no—
157#102C2×D19112yescomplemented
158C22⋊C8—1912no—
159C22⋊C8—1912no—
160C24—3822no—
161#41—7641no—
162#41—7641no—
163C2×Q8—1911no—
164C2×D4—22no—
165C2×D4—3822no—
166C2×D4—3822no—
167C2×D4—3822no—
168C2×D4—3822no—
169C2×D4—1912no—
170C2×D4—1911no—
171C2×D4—1912no—
172C2×D4—7642no—
173C2×D4—7642no—
174C2×D4C22×D19112yes—
175C22×C4—1912no—
176C22×C4C22×D19111yescharacteristic
177D8—41no—
178D8—7641no—
179D8—7642no—
180M16—41no—
181C2×C8—1912no—
182C2×C8—7641no—
183C2×C8C22×D19111yescharacteristic
184C2×C8C22×D19111yescharacteristic
185C4⋊C4—1912no—
186C4⋊C4C22×D19112yes—
187C22⋊C4—22no—
188C22⋊C4—3822no—
189C22⋊C4—3822no—
190C22⋊C4—3822no—
191C22⋊C4—3822no—
192C42—3822no—
193C23—22no—
194C23—3822no—
195C23—1912no—
196C23—15282no—
197C23—15282no—
198C23—7644no—
199C23D4×D19111yescharacteristic
200Q8—7641no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—3822no—
205D4—3822no—
206D4—15282no—
207D4—15282no—
208D4—15282no—
209D4—7641no—
210D4—7642no—
211D4—7644no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—3822no—
216C2×C4—3822no—
217C2×C4—3822no—
218C2×C4—1912no—
219C2×C4D4×D19111yescharacteristic
220C2×C4C23×D19111yescharacteristic
221C8—21no—
222C8—21no—
223C8—3822no—
224C22—22no—
225C22—21no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—3822no—
230C22—3822no—
231C22—3822no—
232C22—15288no—
233C22—7642no—
234C22—7642no—
235C22—7642no—
236C22C2×D4×D19111yescharacteristic
237C4—21no—
238C4—42no—
239C4—3822no—
240C4—7642no—
241C4#2025936711yescharacteristic
242C4#2025936811yescharacteristic
243C2—41no—
244C2—82no—
245C2—15282no—
246C2—7642no—
247C2#2713322111yescharacteristic
248C2#2713346712yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#469×C191C2
socleC22×C191C22×D4
hypercenter#469D191
hypocenterC191#3199
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. #27133229C2semidirect
2. #27132989C2semidirect
3. #27132986C2semidirect
4. #27132916C2semidirect
5. #27132897C2semidirect
6. #27132798C2semidirect
7. #27132795C2semidirect
8. #27132631C2semidirect
9. #469×C191C2semidirect
11. C2×D4×D191C22semidirect
14. C22×C191⋊C8C22semidirect
18. #20259296C22semidirect
22. #20259280C22semidirect
23. #20259255C22semidirect
24. #20259254C22semidirect
25. #20259244C22semidirect
26. #20259243C22semidirect
27. #20259242C22semidirect
28. (C2×D191)⋊C8C22semidirect
29. (C2×D191)⋊C8C22semidirect
31. C2×M16×C191C22semidirect
32. #121×C191C22semidirect
33. #106×C191C22semidirect
34. #102×C191C22semidirect
124. C191#3199semidirect
130. #469D191semidirect
140. C2×M16C2×D191semidirect
147. #121C2×D191semidirect
153. #106C2×D191semidirect
157. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332292
#271329892
#271329862
#271329162
#271328972
#271327982
#271327952
#271326312
#469×C1912
#3199191