Finite Group Databasebeta

← #135×D383 #37589129

Subgroups — #135×D383 #37589129

Order 24512.

266 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 101 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#41×D383C212yesmaximal, complemented
2#27133864C211yesmaximal, characteristic, complemented
3#27133863C211yesmaximal, characteristic, complemented
4#27133862C212yesmaximal, complemented
5#27133861C212yesmaximal, complemented
6#27133860C211yesmaximal, characteristic, complemented
7Q16×D383C211yesmaximal, characteristic, complemented
8SD16×D383C212yesmaximal, complemented
9D8×D383C211yesmaximal, characteristic, complemented
10C2×C8×D383C211yesmaximal, characteristic, complemented
11#135×C383C211yesmaximal, characteristic, complemented
12#20259458C2212yescomplemented
13#20259457—22no—
14#20259457C2212yescomplemented
15#20259456—22no—
16#20259456C2212yescomplemented
17Q8×D383C2212yes—
18D4×D383—22no—
19D4×D383C2212yes—
20C2×C4×D383—22no—
21C2×C4×D383C2211yescharacteristic
22Dic1532C2211yescharacteristic, complemented
23#20259447C2212yescomplemented
24#20259446C2212yescomplemented
25#20259445C2212yescomplemented
26#20259444C2212yescomplemented
27D3064C2211yescharacteristic, complemented
28#20259442C2212yescomplemented
29C2×C383⋊C8C2211yescharacteristic, complemented
30C8×D383C2211yescharacteristic
31C8×D383C2211yescharacteristic
32C8×D383C2211yescharacteristic, complemented
33C8×D383C2211yescharacteristic, complemented
34#41×C383C2212yescomplemented
35Q16×C383C2211yescharacteristic, complemented
36SD16×C383C2212yescomplemented
37D8×C383C2211yescharacteristic, complemented
38C2×C8×C383C2211yescharacteristic, complemented
39C22×D383—22no—
40C22×D383D411yescharacteristic
41Dic766—22no—
42Dic766C2312yes—
43D1532—22no—
44D1532C2312yes—
45C22⋊D383—22no—
46C22⋊D383—22no—
47C22⋊D383—22no—
48C2×Dic383—22no—
49C2×Dic383D411yescharacteristic
50C4×D383—22no—
51C4×D383—22no—
52C4×D383—22no—
53C4×D383D411yescharacteristic
54C4×D383D411yescharacteristic
55C4×D383C2311yescharacteristic
56C4×D383C2311yescharacteristic
57C383⋊C8C2311yescharacteristic
58C383⋊C8C2311yescharacteristic
59Q8×C383C2312yes—
60D4×C383—22no—
61D4×C383C2312yes—
62C2×C4×C383—22no—
63C2×C4×C383C2311yescharacteristic
64C8×C383C2311yescharacteristic
65C8×C383C2311yescharacteristic
66C22×C383—22no—
67C22×C383C2×D411yescharacteristic
68C2×D383—22no—
69C2×D383—22no—
70C2×D383—44no—
71C2×D383C2×D411yescharacteristic
72C2×D383C2×D411yescharacteristic
73C4×C383—22no—
74C4×C383C2×D411yescharacteristic
75C4×C383C2411yescharacteristic
76Dic383—22no—
77Dic383C2×D411yescharacteristic
78Dic383C2×D411yescharacteristic
79C2×C383—21no—
80C2×C383—42no—
81C2×C383C22×D411yescharacteristic
82D383—21no—
83D383—42no—
84D383#13512yesdirect product factor
85C383C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—3831nomaximal, Sylow
87C2×#41—3832no—
88#135—3832no—
89#135—3831no—
90#135—3832no—
91#135—3831no—
92#135—3831no—
93#135D38311yescharacteristic, direct product factor
94C2×Q16—3831no—
95C2×SD16—3832no—
96C2×D8—3831no—
97C22×C8—3831no—
98#41—3832no—
99#41—3832no—
100#41—3832no—
101#41—7662no—
102#41—7662no—
103#41C2×D38312yescomplemented
104C2×Q8—3832no—
105C2×D4—3832no—
106C2×D4—7662no—
107C22×C4—3831no—
108C22×C4—7662no—
109Q16—3832no—
110Q16—3831no—
111Q16C2×D38311yescharacteristic, complemented
112SD16—3832no—
113SD16—3832no—
114SD16—3832no—
115SD16C2×D38312yescomplemented
116D8—3832no—
117D8—3831no—
118D8C2×D38311yescharacteristic, complemented
119C2×C8—3831no—
120C2×C8—3831no—
121C2×C8—3831no—
122C2×C8—3831no—
123C2×C8—3831no—
124C2×C8C2×D38311yescharacteristic, complemented
125C23—3831no—
126C23—7662no—
127Q8—3832no—
128Q8—7662no—
129Q8C22×D38312yes—
130D4—22no—
131D4—3832no—
132D4—7662no—
133D4—7662no—
134D4—7662no—
135D4—7662no—
136D4C22×D38312yes—
137C2×C4—22no—
138C2×C4—3831no—
139C2×C4—3831no—
140C2×C4—3831no—
141C2×C4—3831no—
142C2×C4—3831no—
143C2×C4—7662no—
144C2×C4—7662no—
145C2×C4—7662no—
146C2×C4—7662no—
147C2×C4C22×D38311yescharacteristic
148C8—3831no—
149C8—3831no—
150C8C22×D38311yescharacteristic
151C8C22×D38311yescharacteristic
152C22—22no—
153C22—3831no—
154C22—3831no—
155C22—15324no—
156C22—7662no—
157C22—7662no—
158C22D4×D38311yescharacteristic
159C4—22no—
160C4—3831no—
161C4—3831no—
162C4—7662no—
163C4D4×D38311yescharacteristic
164C4C23×D38311yescharacteristic
165C2—21no—
166C2—42no—
167C2—3832no—
168C2—15322no—
169C2—7661no—
170C2C2×D4×D38311yescharacteristic
subgroupG/H
centerC4D4×D383
commutator, cosocleC4×C383C24
FrattiniC4C23×D383
Fitting#135×C383C2
socleC2×C383C22×D4
hypercenter#135D383
hypocenterC383C2×#135
LCSG ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D383C2semidirect
2. #27133864C2semidirect
3. #27133863C2semidirect
4. #27133862C2semidirect
5. #27133861C2semidirect
6. #27133860C2semidirect
7. Q16×D383C2semidirect
8. SD16×D383C2semidirect
9. D8×D383C2semidirect
10. C2×C8×D383C2semidirect
11. #135×C383C2semidirect
12. #20259458C22semidirect
14. #20259457C22semidirect
16. #20259456C22semidirect
22. Dic1532C22semidirect
23. #20259447C22semidirect
24. #20259446C22semidirect
25. #20259445C22semidirect
26. #20259444C22semidirect
27. D3064C22semidirect
28. #20259442C22semidirect
29. C2×C383⋊C8C22semidirect
32. C8×D383C22semidirect
33. C8×D383C22semidirect
34. #41×C383C22semidirect
35. Q16×C383C22semidirect
36. SD16×C383C22semidirect
37. D8×C383C22semidirect
38. C2×C8×C383C22semidirect
84. D383#135direct (N × H)
85. C383C2×#135semidirect
93. #135D383direct (N × H)
103. #41C2×D383semidirect
111. Q16C2×D383semidirect
115. SD16C2×D383semidirect
118. D8C2×D383semidirect
124. C2×C8C2×D383semidirect

Maximal subgroups

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

subgroupindex
#41×D3832
#271338642
#271338632
#271338622
#271338612
#271338602
Q16×D3832
SD16×D3832
D8×D3832
C2×C8×D3832
#135×C3832
C2×#135383