Finite Group Databasebeta

← #37583314

Subgroups — #37583314

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#27133176C212yesmaximal, complemented
2#27133003C212yesmaximal, complemented
3#27132990C212yesmaximal, complemented
4#27132899C211yesmaximal, characteristic, complemented
5#27132894C212yesmaximal, complemented
6#27132824C212yesmaximal, complemented
7#27132811C212yesmaximal, complemented
8C2×(C2×D191)⋊C8C211yesmaximal, characteristic, complemented
9#467×C191C211yesmaximal, characteristic, complemented
10C2×#15690288C2212yes—
11C22×C4×D191C2211yescharacteristic
12C2×#15690274C2212yescomplemented
13C2×D1528C2211yescharacteristic, complemented
14C22×C191⋊C8C2211yescharacteristic
15#20259307—22no—
16#20259298C2212yes—
17#20259297C2212yes—
18#20259296C2212yes—
19#20259292—22no—
20#20259284—22no—
21(C22⋊D191)⋊C4—22no—
22#20259280C2212yes—
23#20259256C2211yescharacteristic, complemented
24#20259253C2212yescomplemented
25#20259246C2212yescomplemented
26#20259244C2212yescomplemented
27#20259242C2212yescomplemented
28(C2×D191)⋊C8C2212yes—
29(C2×D191)⋊C8C2212yes—
30C2×Q16×C191C2211yescharacteristic, complemented
31C22×C8×C191C2211yescharacteristic
32C22⋊Q8×C191C2212yes—
33#107×C191C2211yescharacteristic, complemented
34#103×C191C2212yescomplemented
35C23×D191D411yescharacteristic
36#15690288—42no—
37#15690288—42no—
38C2×D764—22no—
39C2×D764—22no—
40C2×D764C2312yes—
41C2×C22⋊D191—22no—
42C22×Dic191D411yescharacteristic
43C2×C4×D191—22no—
44C2×C4×D191—41no—
45C2×C4×D191—41no—
46C2×C4×D191D412yes—
47C2×C4×D191C2312yes—
48#15690274—42no—
49D1528—41no—
50C2×C191⋊C8—41no—
51C2×C191⋊C8C2312yes—
52C4⋊Dic191C2312yes—
53Dic191⋊C4—22no—
54(C2×D191)⋊C4—22no—
55(C2×D191)⋊C4—22no—
56(C2×D191)⋊C4—22no—
57(C2×D191)⋊C4—22no—
58C4×Dic191—22no—
59C2×Q8×C191C2312yes—
60C22×C4×C191C2311yescharacteristic
61Q16×C191—41no—
62C2×C8×C191—41no—
63C2×C8×C191C2311yescharacteristic
64C2×C8×C191C2311yescharacteristic
65C4⋊C4×C191—22no—
66C4⋊C4×C191C2312yes—
67C22⋊C4×C191—22no—
68C22×D191—22no—
69C22×D191—22no—
70C22×D191—41no—
71C22×D191—41no—
72C22×D191C2×D412yes—
73D764—22no—
74D764—22no—
75D764—44no—
76D764—44no—
77C22⋊D191—44no—
78C2×Dic191—22no—
79C2×Dic191—41no—
80C2×Dic191C2×D412yes—
81C4×D191—22no—
82C4×D191—22no—
83C4×D191—42no—
84C4×D191—44no—
85C191⋊C8—22no—
86C23×C191C2×D411yescharacteristic
87Q8×C191—22no—
88Q8×C191—22no—
89C2×C4×C191—21no—
90C2×C4×C191—21no—
91C2×C4×C191—22no—
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#13512yes—
100C22×C191C22×D411yescharacteristic
101C2×D191—22no—
102C2×D191—22no—
103C2×D191—22no—
104C2×D191—44no—
105C2×D191—42no—
106C2×D191—42no—
107C2×D191—42no—
108C4×C191—21no—
109C4×C191—42no—
110C4×C191—42no—
111C4×C191H(5,𝔽2)11yescharacteristic
112C4×C191H(5,𝔽2)11yescharacteristic
113Dic191—22no—
114Dic191—42no—
115C2×C191—22no—
116C2×C191#53411yescharacteristic
117C2×C191C2×#13511yescharacteristic
118C2×C191#57511yescharacteristic
119D191—42no—
120D191—82no—
121C191#319111yescharacteristic, complemented, Sylow
122#3191—1911nomaximal, Sylow
123#525—1912no—
124#485—1912no—
125#482—1912no—
126#467D19111yescharacteristic, complemented
127#466—1911no—
128#465—1912no—
129#452—1912no—
130#449—1912no—
131C2×C22⋊C8—1911no—
132C2×#41—1912no—
133C23×C4—1911no—
134C2×Q16C2×D19111yescharacteristic, complemented
135C2×SD16—1912no—
136C2×D8—1911no—
137C22×C8—1911no—
138C22×C8C2×D19111yescharacteristic
139#123—3822no—
140C22⋊Q8—1912no—
141C22⋊Q8C2×D19112yes—
142#121—1912no—
143#121—1912no—
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#103C2×D19112yescomplemented
153#102—1912no—
154#102—1912no—
155C22⋊C8—1912no—
156C22⋊C8—1912no—
157C24—1911no—
158#41—7642no—
159#41—7642no—
160C2×Q8C22×D19112yes—
161C2×D4—3822no—
162C2×D4—3822no—
163C2×D4—3822no—
164C2×D4—1912no—
165C22×C4—3822no—
166C22×C4—1912no—
167C22×C4—1911no—
168C22×C4—1912no—
169C22×C4—7641no—
170C22×C4—7641no—
171C22×C4C22×D19111yescharacteristic
172Q16—41no—
173SD16—7642no—
174D8—7641no—
175C2×C8—41no—
176C2×C8—1912no—
177C2×C8—7641no—
178C2×C8C22×D19111yescharacteristic
179C2×C8C22×D19111yescharacteristic
180C4⋊C4—22no—
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—3822no—
191C23—3822no—
192C23—1912no—
193C23—7641no—
194C23—7641no—
195C23D4×D19111yescharacteristic
196Q8—22no—
197Q8—22no—
198D4—3822no—
199D4—3822no—
200D4—7644no—
201D4—7644no—
202D4—7644no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—3822no—
208C2×C4—3822no—
209C2×C4—3822no—
210C2×C4—1912no—
211C2×C4—7642no—
212C2×C4—7644no—
213C2×C4—7641no—
214C2×C4D4×D19111yescharacteristic
215C2×C4C23×D19111yescharacteristic
216C8—21no—
217C8—21no—
218C8—3822no—
219C22—21no—
220C22—21no—
221C22—3822no—
222C22—3822no—
223C22—3822no—
224C22—7644no—
225C22—7642no—
226C22—7642no—
227C22—7642no—
228C22#2025934512yes—
229C22C2×D4×D19111yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—3822no—
234C4—7642no—
235C4#2025936711yescharacteristic
236C4#2025936811yescharacteristic
237C2—22no—
238C2—15282no—
239C2—7642no—
240C2#2713322111yescharacteristic
241C2C2×#2025934511yescharacteristic
242C2#2713346011yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#467×C191C2
socleC22×C191C22×D4
hypercenter#467D191
hypocenterC191#3191
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #27133176C2semidirect
2. #27133003C2semidirect
3. #27132990C2semidirect
4. #27132899C2semidirect
5. #27132894C2semidirect
6. #27132824C2semidirect
7. #27132811C2semidirect
8. C2×(C2×D191)⋊C8C2semidirect
9. #467×C191C2semidirect
12. C2×#15690274C22semidirect
13. C2×D1528C22semidirect
23. #20259256C22semidirect
24. #20259253C22semidirect
25. #20259246C22semidirect
26. #20259244C22semidirect
27. #20259242C22semidirect
30. C2×Q16×C191C22semidirect
33. #107×C191C22semidirect
34. #103×C191C22semidirect
121. C191#3191semidirect
126. #467D191semidirect
134. C2×Q16C2×D191semidirect
149. #107C2×D191semidirect
152. #103C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331762
#271330032
#271329902
#271328992
#271328942
#271328242
#271328112
C2×(C2×D191)⋊C82
#467×C1912
#3191191