Finite Group Databasebeta

← #37588937

Subgroups — #37588937

Order 24512.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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#27133836C211yesmaximal, characteristic, complemented
2#27133834C211yesmaximal, characteristic, complemented
3#27133827C211yesmaximal, characteristic, complemented
4#27133827C211yesmaximal, characteristic, complemented
5#27133826C211yesmaximal, characteristic, complemented
6#27133821C211yesmaximal, characteristic, complemented
7#27133815C211yesmaximal, characteristic, complemented
8#27133814C211yesmaximal, characteristic, complemented
9#27133812C211yesmaximal, characteristic, complemented
10#27133811C211yesmaximal, characteristic, complemented
11#27133809C211yesmaximal, characteristic, complemented
12#27133803C211yesmaximal, characteristic, complemented
13C4×C22⋊D383C211yesmaximal, characteristic, complemented
14C22⋊C4×D383C211yesmaximal, characteristic, complemented
15#123×C383C211yesmaximal, characteristic, complemented
16C23×D383C2211yescharacteristic
17C2×Dic766C2211yescharacteristic, complemented
18C2×D1532C2211yescharacteristic
19C2×D1532C2211yescharacteristic
20C2×C22⋊D383C2211yescharacteristic
21C2×C22⋊D383C2211yescharacteristic
22C2×C22⋊D383C2211yescharacteristic
23C2×C22⋊D383C2211yescharacteristic, complemented
24C2×C4×D383C2211yescharacteristic
25C2×C4×D383C2211yescharacteristic
26C2×C4×D383C2211yescharacteristic, complemented
27C4⋊Dic383C2211yescharacteristic, complemented
28C4⋊Dic383C2211yescharacteristic, complemented
29Dic383⋊C4C2211yescharacteristic, complemented
30Dic383⋊C4C2211yescharacteristic, complemented
31C22⋊Dic383C2211yescharacteristic
32C22⋊Dic383C2211yescharacteristic
33C22⋊Dic383C2211yescharacteristic, complemented
34(C2×D383)⋊C4C2211yescharacteristic
35(C2×D383)⋊C4C2211yescharacteristic
36(C2×D383)⋊C4C2211yescharacteristic
37(C2×D383)⋊C4C2211yescharacteristic
38(C2×D383)⋊C4C2211yescharacteristic
39(C2×D383)⋊C4C2211yescharacteristic
40(C2×D383)⋊C4C2211yescharacteristic, complemented
41(C2×D383)⋊C4C2211yescharacteristic, complemented
42C4×Dic383C2211yescharacteristic, complemented
43C4×Dic383C2211yescharacteristic, complemented
44C2×D4×C383C2211yescharacteristic
45C22×C4×C383C2211yescharacteristic, complemented
46C4⋊C4×C383C2211yescharacteristic, complemented
47C4⋊C4×C383C2211yescharacteristic, complemented
48C22⋊C4×C383C2211yescharacteristic
49C22⋊C4×C383C2211yescharacteristic
50C22⋊C4×C383C2211yescharacteristic, complemented
51C22×D383—22no—
52C22×D383—41no—
53C22×D383—41no—
54C22×D383C2311yescharacteristic
55C22×D383C2311yescharacteristic
56C22×D383C2311yescharacteristic
57Dic766—41no—
58D1532—22no—
59D1532—41no—
60C22⋊D383—22no—
61C22⋊D383—41no—
62C22⋊D383—41no—
63C22⋊D383—41no—
64C2×Dic383C2311yescharacteristic
65C2×Dic383C2311yescharacteristic
66C2×Dic383C2311yescharacteristic
67C2×Dic383C2311yescharacteristic
68C2×Dic383C2311yescharacteristic
69C4×D383—41no—
70C4×D383—41no—
71C4×D383—41no—
72C23×C383C2311yescharacteristic
73C23×C383C2311yescharacteristic
74D4×C383—41no—
75C2×C4×C383—41no—
76C2×C4×C383C2311yescharacteristic
77C2×C4×C383C2311yescharacteristic
78C2×C4×C383C2311yescharacteristic
79C2×C4×C383C2311yescharacteristic
80C2×C4×C383C2311yescharacteristic
81C22×C383—21no—
82C22×C383—21no—
83C22×C383—21no—
84C22×C383—21no—
85C22×C383—21no—
86C22×C383—21no—
87C22×C383C2411yescharacteristic
88C2×D383—21no—
89C2×D383—21no—
90C2×D383—21no—
91C2×D383—21no—
92C2×D383—21no—
93C2×D383—21no—
94C2×D383—21no—
95C2×D383—21no—
96C2×D383—44no—
97C2×D383#4112yes—
98C4×C383—21no—
99C4×C383—21no—
100C4×C383—21no—
101C4×C383—21no—
102C4×C383—21no—
103Dic383—21no—
104Dic383—21no—
105Dic383—21no—
106Dic383—21no—
107Dic383—21no—
108C2×C383—41no—
109C2×C383—41no—
110C2×C383C2×#4111yescharacteristic
111C2×C383H(5,𝔽2)11yescharacteristic
112C2×C383H(5,𝔽2)11yescharacteristic
113D383—22no—
114D383—41no—
115D383—41no—
116C383#53811yescharacteristic, complemented, Sylow
117#538—3831nomaximal, Sylow
118#126—3831no—
119#126—3831no—
120#124—3831no—
121#124—3831no—
122#123—3831no—
123#123D38311yescharacteristic, complemented
124C22⋊Q8—3831no—
125#121—3831no—
126#121—3831no—
127#121—3831no—
128#120—3831no—
129#120—3831no—
130C4×D4—3831no—
131C4×D4—3831no—
132C2×C22⋊C4—3831no—
133C24—3831no—
134C2×Q8—3831no—
135C2×D4—3831no—
136C2×D4—3831no—
137C2×D4—3831no—
138C2×D4—3831no—
139C2×D4—3831no—
140C2×D4—3831no—
141C2×D4C2×D38311yescharacteristic
142C22×C4—3831no—
143C22×C4—3831no—
144C22×C4—3831no—
145C22×C4C2×D38311yescharacteristic, complemented
146C4⋊C4—3831no—
147C4⋊C4—3831no—
148C4⋊C4—3831no—
149C4⋊C4—3831no—
150C4⋊C4C2×D38311yescharacteristic, complemented
151C4⋊C4C2×D38311yescharacteristic, complemented
152C22⋊C4—3831no—
153C22⋊C4—3831no—
154C22⋊C4—3831no—
155C22⋊C4—3831no—
156C22⋊C4—3831no—
157C22⋊C4—3831no—
158C22⋊C4—3831no—
159C22⋊C4—3831no—
160C22⋊C4—3831no—
161C22⋊C4—3831no—
162C22⋊C4—3831no—
163C22⋊C4C2×D38311yescharacteristic
164C22⋊C4C2×D38311yescharacteristic
165C22⋊C4C2×D38311yescharacteristic, complemented
166C42—3831no—
167C42—3831no—
168C23—3831no—
169C23—3831no—
170C23—3831no—
171C23—15321no—
172C23—15321no—
173C23—7662no—
174C23C22×D38311yescharacteristic
175C23C22×D38311yescharacteristic
176Q8—15321no—
177D4—41no—
178D4—15321no—
179D4—15321no—
180D4—15321no—
181D4—15321no—
182D4—7662no—
183D4—7662no—
184C2×C4—41no—
185C2×C4—3831no—
186C2×C4—3831no—
187C2×C4—3831no—
188C2×C4—3831no—
189C2×C4—3831no—
190C2×C4—15321no—
191C2×C4—15321no—
192C2×C4—15321no—
193C2×C4C22×D38311yescharacteristic
194C2×C4C22×D38311yescharacteristic
195C2×C4C22×D38311yescharacteristic
196C2×C4C22×D38311yescharacteristic
197C2×C4C22×D38311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—3832no—
205C22—15324no—
206C22—7661no—
207C22—7661no—
208C22—7661no—
209C22—7661no—
210C22—7661no—
211C22—7661no—
212C22—7661no—
213C22—7661no—
214C22C23×D38311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—7661no—
221C4—7661no—
222C4—7661no—
223C4—7661no—
224C4—7661no—
225C2—41no—
226C2—41no—
227C2—15321no—
228C2—15321no—
229C2—7662no—
230C2#41×D38311yescharacteristic
231C2#2713388611yescharacteristic
232C2#2713388711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D383
commutator, socle, cosocleC22×C383C24
Fitting#123×C383C2
hypercenter#123D383
hypocenterC383#538
LCSG ▷ C22×C383 ▷ C383
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #27133836C2semidirect
2. #27133834C2semidirect
3. #27133827C2semidirect
4. #27133827C2semidirect
5. #27133826C2semidirect
6. #27133821C2semidirect
7. #27133815C2semidirect
8. #27133814C2semidirect
9. #27133812C2semidirect
10. #27133811C2semidirect
11. #27133809C2semidirect
12. #27133803C2semidirect
13. C4×C22⋊D383C2semidirect
14. C22⋊C4×D383C2semidirect
15. #123×C383C2semidirect
17. C2×Dic766C22semidirect
23. C2×C22⋊D383C22semidirect
26. C2×C4×D383C22semidirect
27. C4⋊Dic383C22semidirect
28. C4⋊Dic383C22semidirect
29. Dic383⋊C4C22semidirect
30. Dic383⋊C4C22semidirect
33. C22⋊Dic383C22semidirect
40. (C2×D383)⋊C4C22semidirect
41. (C2×D383)⋊C4C22semidirect
42. C4×Dic383C22semidirect
43. C4×Dic383C22semidirect
45. C22×C4×C383C22semidirect
46. C4⋊C4×C383C22semidirect
47. C4⋊C4×C383C22semidirect
50. C22⋊C4×C383C22semidirect
116. C383#538semidirect
123. #123D383semidirect
145. C22×C4C2×D383semidirect
150. C4⋊C4C2×D383semidirect
151. C4⋊C4C2×D383semidirect
165. C22⋊C4C2×D383semidirect

Maximal subgroups

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

subgroupindex
#271338362
#271338342
#271338272
#271338262
#271338212
#271338152
#271338142
#271338122
#271338112
#271338092
#271338032
C4×C22⋊D3832
C22⋊C4×D3832
#123×C3832
#538383