Finite Group Databasebeta

← #37583307

Subgroups — #37583307

Order 24448.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 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#27133173C212yesmaximal, complemented
2#27133006C212yesmaximal, complemented
3#27132985C212yesmaximal, complemented
4#27132904C211yesmaximal, characteristic, complemented
5#27132890C212yesmaximal, complemented
6#27132826C212yesmaximal, complemented
7#27132805C212yesmaximal, complemented
8C2×(C2×D191)⋊C8C211yesmaximal, characteristic, complemented
9#466×C191C211yesmaximal, characteristic, complemented
10C2×#15690286C2212yes—
11C22×C4×D191C2211yescharacteristic
12C2×Dic764C2211yescharacteristic, complemented
13C2×#15690275C2212yescomplemented
14C22×C191⋊C8C2211yescharacteristic
15#20259304—22no—
16#20259302C2212yes—
17#20259301C2212yes—
18#20259293C2212yes—
19#20259290—22no—
20D4×Dic191—22no—
21(C22⋊D191)⋊C4—22no—
22#20259280C2212yes—
23#20259256C2211yescharacteristic, complemented
24#20259253C2212yescomplemented
25#20259247C2212yescomplemented
26#20259245C2212yescomplemented
27#20259243C2212yescomplemented
28(C2×D191)⋊C8C2212yes—
29(C2×D191)⋊C8C2212yes—
30C2×D8×C191C2211yescharacteristic, complemented
31C22×C8×C191C2211yescharacteristic
32#121×C191C2212yes—
33#107×C191C2211yescharacteristic, complemented
34#102×C191C2212yescomplemented
35C23×D191D411yescharacteristic
36#15690286—42no—
37#15690286—42no—
38C2×Dic382C2312yes—
39C2×C22⋊D191—22no—
40C2×C22⋊D191—22no—
41C22×Dic191—22no—
42C22×Dic191D411yescharacteristic
43C2×C4×D191—41no—
44C2×C4×D191—41no—
45C2×C4×D191D412yes—
46C2×C4×D191C2312yes—
47Dic764—41no—
48#15690275—42no—
49C2×C191⋊C8—41no—
50C2×C191⋊C8C2312yes—
51C4⋊Dic191—22no—
52C4⋊Dic191C2312yes—
53Dic191⋊C4—22no—
54C22⋊Dic191—22no—
55C22⋊Dic191—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—41no—
70C22×D191—41no—
71C22×D191C2×D412yes—
72Dic382—22no—
73Dic382—22no—
74C22⋊D191—44no—
75C22⋊D191—44no—
76C2×Dic191—22no—
77C2×Dic191—22no—
78C2×Dic191—41no—
79C2×Dic191—44no—
80C2×Dic191C2×D412yes—
81C4×D191—22no—
82C4×D191—22no—
83C4×D191—42no—
84C191⋊C8—22no—
85C23×C191—22no—
86C23×C191C2×D411yescharacteristic
87D4×C191—22no—
88D4×C191—22no—
89D4×C191—44no—
90C2×C4×C191—21no—
91C2×C4×C191—21no—
92C2×C4×C191—22no—
93C2×C4×C191C2×D411yescharacteristic
94C2×C4×C191C2411yescharacteristic
95C8×C191—21no—
96C8×C191—21no—
97C22×C191—21no—
98C22×C191—21no—
99C22×C191—42no—
100C22×C191—42no—
101C22×C191—42no—
102C22×C191#13512yes—
103C22×C191C22×D411yescharacteristic
104C2×D191—22no—
105C2×D191—22no—
106C2×D191—22no—
107C2×D191—44no—
108C4×C191—21no—
109C4×C191—42no—
110C4×C191H(5,𝔽2)11yescharacteristic
111C4×C191H(5,𝔽2)11yescharacteristic
112Dic191—22no—
113Dic191—42no—
114Dic191—42no—
115C2×C191—22no—
116C2×C191—82no—
117C2×C191#53411yescharacteristic
118C2×C191C2×#13511yescharacteristic
119C2×C191#57511yescharacteristic
120D191—42no—
121C191#319111yescharacteristic, complemented, Sylow
122#3191—1911nomaximal, Sylow
123#525—1912no—
124#485—1912no—
125#482—1912no—
126#467—1911no—
127#466D19111yescharacteristic, complemented
128#465—1912no—
129#452—1912no—
130#449—1912no—
131C2×C22⋊C8—1911no—
132C2×#41—1912no—
133C23×C4—1911no—
134C2×Q16—1911no—
135C2×SD16—1912no—
136C2×D8C2×D19111yescharacteristic, complemented
137C22×C8—1911no—
138C22×C8C2×D19111yescharacteristic
139#123—3822no—
140C22⋊Q8—1912no—
141C22⋊Q8—1912no—
142#121—1912no—
143#121C2×D19112yes—
144#120—3822no—
145C4×D4—3822no—
146C4×D4—3822no—
147#117—1912no—
148#107—1911no—
149#107C2×D19111yescharacteristic, complemented
150#106—1912no—
151#103—1912no—
152#103—1912no—
153#102—1912no—
154#102C2×D19112yescomplemented
155C22⋊C8—1912no—
156C22⋊C8—1912no—
157C24—1911no—
158#41—7642no—
159#41—7642no—
160C2×Q8—1912no—
161C2×D4—22no—
162C2×D4—3822no—
163C2×D4—3822no—
164C2×D4C22×D19112yes—
165C22×C4—3822no—
166C22×C4—1912no—
167C22×C4—1911no—
168C22×C4—1912no—
169C22×C4—7641no—
170C22×C4—7641no—
171C22×C4C22×D19111yescharacteristic
172Q16—7641no—
173SD16—7642no—
174D8—41no—
175C2×C8—41no—
176C2×C8—1912no—
177C2×C8—7641no—
178C2×C8C22×D19111yescharacteristic
179C2×C8C22×D19111yescharacteristic
180C4⋊C4—3822no—
181C4⋊C4—3822no—
182C4⋊C4—1912no—
183C4⋊C4C22×D19112yes—
184C22⋊C4—22no—
185C22⋊C4—3822no—
186C22⋊C4—3822no—
187C22⋊C4—3822no—
188C22⋊C4—3822no—
189C42—3822no—
190C23—22no—
191C23—3822no—
192C23—1912no—
193C23—7641no—
194C23—7641no—
195C23D4×D19111yescharacteristic
196Q8—3822no—
197Q8—3822no—
198D4—22no—
199D4—22no—
200D4—44no—
201D4—7644no—
202D4—7644no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—3822no—
207C2×C4—3822no—
208C2×C4—3822no—
209C2×C4—3822no—
210C2×C4—1912no—
211C2×C4—7642no—
212C2×C4—7641no—
213C2×C4—7644no—
214C2×C4D4×D19111yescharacteristic
215C2×C4C23×D19111yescharacteristic
216C8—21no—
217C8—21no—
218C8—3822no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—3822no—
225C22—3822no—
226C22—3822no—
227C22—7644no—
228C22#2025934112yes—
229C22C2×D4×D19111yescharacteristic
230C4—21no—
231C4—42no—
232C4—3822no—
233C4—7642no—
234C4—7642no—
235C4#2025936711yescharacteristic
236C4#2025936811yescharacteristic
237C2—22no—
238C2—82no—
239C2—7642no—
240C2#2713322111yescharacteristic
241C2C2×#2025934111yescharacteristic
242C2#2713346011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#466×C191C2
socleC22×C191C22×D4
hypercenter#466D191
hypocenterC191#3191
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. #27133173C2semidirect
2. #27133006C2semidirect
3. #27132985C2semidirect
4. #27132904C2semidirect
5. #27132890C2semidirect
6. #27132826C2semidirect
7. #27132805C2semidirect
8. C2×(C2×D191)⋊C8C2semidirect
9. #466×C191C2semidirect
12. C2×Dic764C22semidirect
13. C2×#15690275C22semidirect
23. #20259256C22semidirect
24. #20259253C22semidirect
25. #20259247C22semidirect
26. #20259245C22semidirect
27. #20259243C22semidirect
30. C2×D8×C191C22semidirect
33. #107×C191C22semidirect
34. #102×C191C22semidirect
121. C191#3191semidirect
127. #466D191semidirect
136. C2×D8C2×D191semidirect
149. #107C2×D191semidirect
154. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331732
#271330062
#271329852
#271329042
#271328902
#271328262
#271328052
C2×(C2×D191)⋊C82
#466×C1912
#3191191