Finite Group Databasebeta

← #37583457

Subgroups — #37583457

Order 24448.

488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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#27133218C211yesmaximal, characteristic, complemented
2#127×D191C211yesmaximal, characteristic
3#27133037C211yesmaximal, characteristic, complemented
4#27133010C211yesmaximal, characteristic, complemented
5#27133009C211yesmaximal, characteristic, complemented
6#27132861C214yesmaximal, complemented
7#27132812C214yesmaximal, complemented
8#27132714C211yesmaximal, characteristic, complemented
9#492×C191C211yesmaximal, characteristic, complemented
10C2×D4×D191—21no—
11C2×D4×D191—21no—
12C2×D4×D191C2212yes—
13C2×#15690274C2214yescomplemented
14#20259322C2211yescharacteristic, complemented
15#20259319C2211yescharacteristic
16#20259318—21no—
17#20259318—21no—
18#20259318C2212yes—
19#20259313—21no—
20#20259302—21no—
21#20259298C2212yes—
22Q8×Dic191C2212yescomplemented
23#20259287—21no—
24#20259280—21no—
25C42×D191C2211yescharacteristic
26Dic191⋊C8C2212yescomplemented
27#20259244C2214yescomplemented
28#20259243C2214yescomplemented
29(C2×D191)⋊C8C2212yes—
30C4×C191⋊C8C2211yescharacteristic, complemented
31C2×SD16×C191C2214yescomplemented
32C4⋊Q8×C191C2211yescharacteristic, complemented
33#127×C191C2211yescharacteristic
34C4×C8×C191C2211yescharacteristic, complemented
35C23×D191—22no—
36C2×Dic382—21no—
37C2×D764—21no—
38C2×D764—21no—
39C2×D764C2312yes—
40C2×C22⋊D191—22no—
41C2×C22⋊D191—22no—
42C2×C22⋊D191—22no—
43D4×D191—44no—
44D4×D191—44no—
45D4×D191—44no—
46C2×C4×D191D411yescharacteristic
47C2×C4×D191D411yescharacteristic
48C2×C4×D191C2311yescharacteristic
49#15690274—44no—
50C2×C191⋊C8C2312yes—
51C4⋊Dic191—22no—
52C4⋊Dic191—21no—
53C4⋊Dic191C2312yes—
54Dic191⋊C4—22no—
55(C2×D191)⋊C4—22no—
56C4×Dic191—22no—
57C4×Dic191D411yescharacteristic
58C4×Dic191D411yescharacteristic
59C4×Dic191C2311yescharacteristic
60C2×Q8×C191C2312yes—
61C2×D4×C191—21no—
62C2×D4×C191—21no—
63C2×D4×C191C2312yes—
64SD16×C191—44no—
65C2×C8×C191C2312yes—
66C4⋊C4×C191—21no—
67C4⋊C4×C191—21no—
68C42×C191C2311yescharacteristic
69C22×D191—22no—
70C22×D191—44no—
71C22×D191—44no—
72C22×D191—44no—
73C22×D191C2×D411yescharacteristic
74Dic382—42no—
75D764—24no—
76D764—42no—
77D764—42no—
78C22⋊D191—44no—
79C22⋊D191—44no—
80C22⋊D191—44no—
81C2×Dic191—22no—
82C2×Dic191C2×D411yescharacteristic
83C2×Dic191C2×D411yescharacteristic
84C2×Dic191C2×D411yescharacteristic
85C4×D191—22no—
86C4×D191—22no—
87C4×D191SD1614yescomplemented
88C191⋊C8—22no—
89C23×C191—22no—
90Q8×C191—24no—
91D4×C191—24no—
92D4×C191—42no—
93D4×C191—42no—
94C2×C4×C191—22no—
95C2×C4×C191C2×D411yescharacteristic
96C2×C4×C191C2×D411yescharacteristic
97C2×C4×C191C2411yescharacteristic
98C8×C191—22no—
99C22×C191—42no—
100C22×C191—42no—
101C22×C191—42no—
102C22×C191C22×D411yescharacteristic
103C2×D191—21no—
104C2×D191—21no—
105C2×D191—42no—
106C2×D191—42no—
107C2×D191—42no—
108C2×D191—88no—
109C2×D191C2×SD1612yes—
110C4×C191—42no—
111C4×C191C2×SD1612yes—
112C4×C191AGL(1,ℤ/8)12yes—
113C4×C191H(5,𝔽2)12yes—
114Dic191—21no—
115Dic191—21no—
116Dic191—42no—
117Dic191C2×SD1612yes—
118C2×C191—82no—
119C2×C191#53511yescharacteristic
120C2×C191C22×SD1611yescharacteristic
121C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
122D191—22no—
123D191—82no—
124C191#320811yescharacteristic, complemented, Sylow
125#3208—1911nomaximal, Sylow
126#533—1911no—
127C2×#127—1911no—
128#492—1911no—
129#492D19111yescharacteristic, complemented
130#486—1911no—
131#486—1911no—
132#460—1914no—
133#450—1914no—
134#431—1911no—
135C22×D4—3821no—
136C22×D4—3821no—
137C22×D4—1912no—
138C2×SD16—1914no—
139C2×SD16C2×D19114yescomplemented
140C4⋊Q8—1911no—
141C4⋊Q8C2×D19111yescharacteristic, complemented
142#127—3821no—
143#127—3821no—
144#127—1912no—
145#127—1911no—
146#127C2×D19111yescharacteristic
147#125—3821no—
148C22⋊Q8—3821no—
149C22⋊Q8—1912no—
150C4×Q8—3821no—
151C4×Q8—1912no—
152#117—3821no—
153C2×C42—1911no—
154C4⋊C8—1912no—
155#102—1914no—
156#102—1914no—
157C22⋊C8—1912no—
158C4×C8—1911no—
159C4×C8C2×D19111yescharacteristic, complemented
160C24—3822no—
161C2×Q8—3821no—
162C2×Q8C22×D19112yes—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—3822no—
166C2×D4—3822no—
167C2×D4—3822no—
168C2×D4—3821no—
169C2×D4—3821no—
170C2×D4—1912no—
171C2×D4—7644no—
172C2×D4—7644no—
173C2×D4—7644no—
174C2×D4C22×D19112yes—
175C22×C4—1911no—
176C22×C4—1911no—
177C22×C4—1911no—
178SD16—44no—
179SD16—7644no—
180C2×C8—1912no—
181C2×C8C22×D19112yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—3822no—
185C4⋊C4—3822no—
186C4⋊C4—3821no—
187C4⋊C4—1912no—
188C22⋊C4—3822no—
189C42—3822no—
190C42—1911no—
191C42—1911no—
192C42—1911no—
193C42C22×D19111yescharacteristic
194C23—22no—
195C23—3822no—
196C23—1911no—
197C23—7644no—
198C23—7644no—
199C23—7644no—
200Q8—24no—
201Q8—7642no—
202D4—24no—
203D4—42no—
204D4—42no—
205D4—3824no—
206D4—7644no—
207D4—7644no—
208D4—7644no—
209D4—7642no—
210D4—7642no—
211C2×C4—22no—
212C2×C4—3822no—
213C2×C4—3822no—
214C2×C4—3822no—
215C2×C4—1911no—
216C2×C4—1911no—
217C2×C4—1911no—
218C2×C4—1914no—
219C2×C4D4×D19111yescharacteristic
220C2×C4D4×D19111yescharacteristic
221C2×C4C23×D19111yescharacteristic
222C8—22no—
223C8—3822no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22—3821no—
228C22—3821no—
229C22—1912no—
230C22—15288no—
231C22—7642no—
232C22—7642no—
233C22—7642no—
234C22C2×D4×D19111yescharacteristic
235C4—42no—
236C4—3821no—
237C4—3821no—
238C4—1912no—
239C4—7642no—
240C4SD16×D19112yes—
241C4#2025934912yes—
242C4#2025936712yes—
243C2—82no—
244C2—3822no—
245C2—15282no—
246C2#2713322611yescharacteristic
247C2C2×SD16×D19111yescharacteristic
248C2C2×#2025934911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#492×C191C2
socleC22×C191C22×D4
prime radical#127×D191C2
hypercenter#492D191
hypocenterC191#3208
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #27133218C2semidirect
3. #27133037C2semidirect
4. #27133010C2semidirect
5. #27133009C2semidirect
6. #27132861C2semidirect
7. #27132812C2semidirect
8. #27132714C2semidirect
9. #492×C191C2semidirect
13. C2×#15690274C22semidirect
14. #20259322C22semidirect
22. Q8×Dic191C22semidirect
26. Dic191⋊C8C22semidirect
27. #20259244C22semidirect
28. #20259243C22semidirect
30. C4×C191⋊C8C22semidirect
31. C2×SD16×C191C22semidirect
32. C4⋊Q8×C191C22semidirect
34. C4×C8×C191C22semidirect
87. C4×D191SD16semidirect
124. C191#3208semidirect
129. #492D191semidirect
139. C2×SD16C2×D191semidirect
141. C4⋊Q8C2×D191semidirect
159. C4×C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332182
#127×D1912
#271330372
#271330102
#271330092
#271328612
#271328122
#271327142
#492×C1912
#3208191