Finite Group Databasebeta

← #37583380

Subgroups — #37583380

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#27132990C212yesmaximal, complemented
3#27132985C212yesmaximal, complemented
4#27132914C212yesmaximal, complemented
5#27132899C211yesmaximal, characteristic, complemented
6#27132798C212yesmaximal, complemented
7#27132795C212yesmaximal, complemented
8#27132629C211yesmaximal, characteristic, complemented
9#466×C191C211yesmaximal, characteristic, complemented
10C2×#15690287C2211yescharacteristic
11C2×D4×D191C2212yescomplemented
12C2×D1528C2211yescharacteristic
13C2×#15690272C2212yes—
14C2×#15690271C2211yescharacteristic, complemented
15#20259318—22no—
16#20259308—22no—
17#20259297C2212yes—
18#20259296C2212yescomplemented
19#20259293C2212yes—
20#20259292—22no—
21#20259290—22no—
22#20259280C2212yescomplemented
23#20259256C2211yescharacteristic, complemented
24#20259253C2212yescomplemented
25#20259244C2212yescomplemented
26#20259243C2212yescomplemented
27#20259242C2212yescomplemented
28(C2×D191)⋊C8C2212yescomplemented
29(C2×D191)⋊C8C2212yescomplemented
30C2×D8×C191C2211yescharacteristic
31C22×C8×C191C2211yescharacteristic, complemented
32#121×C191C2212yescomplemented
33#107×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—
51#15690271—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—
63C2×C8×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—21no—
101C22×C191—21no—
102C22×C191—42no—
103C22×C191—42no—
104C22×C191—42no—
105C22×C191C22×D411yescharacteristic
106C2×D191—22no—
107C2×D191—22no—
108C2×D191—22no—
109C2×D191—42no—
110C2×D191—42no—
111C2×D191—42no—
112C2×D191—88no—
113C4×C191—21no—
114C4×C191—42no—
115C4×C191H(5,𝔽2)11yescharacteristic
116C4×C191H(5,𝔽2)11yescharacteristic
117Dic191—22no—
118Dic191—42no—
119C2×C191—41no—
120C2×C191—82no—
121C2×C191#53411yescharacteristic
122C2×C191#57611yescharacteristic
123C2×C191#57611yescharacteristic
124D191—42no—
125D191—82no—
126C191#319911yescharacteristic, complemented, Sylow
127#3199—1911nomaximal, Sylow
128#535—1912no—
129#482—1912no—
130#482—1912no—
131#469—1912no—
132#466—1911no—
133#466D19111yescharacteristic, complemented
134#447—1912no—
135#447—1912no—
136#408—1911no—
137C2×#41—1911no—
138C22×D4—1912no—
139C2×D8—1912no—
140C2×D8—1911no—
141C2×D8C2×D19111yescharacteristic
142C2×M16—1911no—
143C22×C8C2×D19111yescharacteristic, complemented
144#127—3822no—
145#124—3822no—
146#121—1912no—
147#121—1912no—
148#121—1912no—
149#121C2×D19112yescomplemented
150#120—3822no—
151#120—3822no—
152#117—1912no—
153#107—1911no—
154#107C2×D19111yescharacteristic, complemented
155#106—1912no—
156#102—1912no—
157#102—1912no—
158#102—1912no—
159#102C2×D19112yescomplemented
160C22⋊C8—1912no—
161C22⋊C8—1912no—
162C24—3822no—
163#41—7641no—
164#41—7641no—
165C2×Q8—1911no—
166C2×D4—22no—
167C2×D4—3822no—
168C2×D4—3822no—
169C2×D4—3822no—
170C2×D4—3822no—
171C2×D4—1912no—
172C2×D4—1911no—
173C2×D4—1912no—
174C2×D4—7642no—
175C2×D4—7642no—
176C2×D4C22×D19112yes—
177C22×C4—1912no—
178C22×C4C22×D19111yescharacteristic
179D8—41no—
180D8—7641no—
181D8—7642no—
182M16—7641no—
183C2×C8—41no—
184C2×C8—1912no—
185C2×C8C22×D19111yescharacteristic
186C2×C8C22×D19111yescharacteristic
187C4⋊C4—1912no—
188C4⋊C4C22×D19112yes—
189C22⋊C4—22no—
190C22⋊C4—3822no—
191C22⋊C4—3822no—
192C22⋊C4—3822no—
193C22⋊C4—3822no—
194C42—3822no—
195C23—22no—
196C23—3822no—
197C23—1912no—
198C23—15282no—
199C23—15282no—
200C23—7644no—
201C23D4×D19111yescharacteristic
202Q8—7641no—
203D4—22no—
204D4—22no—
205D4—82no—
206D4—3822no—
207D4—3822no—
208D4—15282no—
209D4—15282no—
210D4—15282no—
211D4—7641no—
212D4—7642no—
213D4—7644no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—3822no—
218C2×C4—3822no—
219C2×C4—3822no—
220C2×C4—1912no—
221C2×C4D4×D19111yescharacteristic
222C2×C4C23×D19111yescharacteristic
223C8—21no—
224C8—21no—
225C8—3822no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—3822no—
233C22—3822no—
234C22—3822no—
235C22—15288no—
236C22—7642no—
237C22—7642no—
238C22—7642no—
239C22C2×D4×D19111yescharacteristic
240C4—21no—
241C4—42no—
242C4—3822no—
243C4—7642no—
244C4#2025936711yescharacteristic
245C4#2025936811yescharacteristic
246C2—41no—
247C2—82no—
248C2—15282no—
249C2—7642no—
250C2#2713322111yescharacteristic
251C2#2713346411yescharacteristic
252C2#2713346511yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#466×C191C2
socleC22×C191C22×D4
hypercenter#466D191
hypocenterC191#3199
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #27133229C2semidirect
2. #27132990C2semidirect
3. #27132985C2semidirect
4. #27132914C2semidirect
5. #27132899C2semidirect
6. #27132798C2semidirect
7. #27132795C2semidirect
8. #27132629C2semidirect
9. #466×C191C2semidirect
11. C2×D4×D191C22semidirect
14. C2×#15690271C22semidirect
18. #20259296C22semidirect
22. #20259280C22semidirect
23. #20259256C22semidirect
24. #20259253C22semidirect
25. #20259244C22semidirect
26. #20259243C22semidirect
27. #20259242C22semidirect
28. (C2×D191)⋊C8C22semidirect
29. (C2×D191)⋊C8C22semidirect
31. C22×C8×C191C22semidirect
32. #121×C191C22semidirect
33. #107×C191C22semidirect
34. #102×C191C22semidirect
126. C191#3199semidirect
133. #466D191semidirect
143. C22×C8C2×D191semidirect
149. #121C2×D191semidirect
154. #107C2×D191semidirect
159. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332292
#271329902
#271329852
#271329142
#271328992
#271327982
#271327952
#271326292
#466×C1912
#3199191