Finite Group Databasebeta

← #37566041

Subgroups — #37566041

Order 24256.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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×D379C212yesmaximal, complemented
2#27131363C212yesmaximal, complemented
3#27131360C212yesmaximal, complemented
4#27131358C212yesmaximal, complemented
5#27131355C212yesmaximal, complemented
6#27131353C211yesmaximal, characteristic, complemented
7#27131351C212yesmaximal, complemented
8C2×#20258589C211yesmaximal, characteristic, complemented
9#135×C379C211yesmaximal, characteristic, complemented
10#20258607C2212yes—
11#20258606—22no—
12#20258606C2212yescomplemented
13#20258605—22no—
14#20258605C2212yes—
15Q8×D379C2212yescomplemented
16D4×D379—22no—
17D4×D379C2212yescomplemented
18C2×C4×D379—22no—
19C2×C4×D379C2211yescharacteristic
20Dic1516C2211yescharacteristic, complemented
21#20258596C2212yescomplemented
22#20258595C2212yescomplemented
23#20258594C2212yescomplemented
24#20258593C2212yescomplemented
25D3032C2211yescharacteristic, complemented
26#20258591C2212yescomplemented
27#20258589C2212yescomplemented
28#20258589C2212yescomplemented
29C2×C379⋊C8C2211yescharacteristic, complemented
30#41×C379C2212yescomplemented
31Q16×C379C2211yescharacteristic, complemented
32SD16×C379C2212yescomplemented
33D8×C379C2211yescharacteristic, complemented
34C2×C8×C379C2211yescharacteristic, complemented
35C22×D379—22no—
36C22×D379D411yescharacteristic
37Dic758—22no—
38Dic758C2312yes—
39D1516—22no—
40D1516C2312yes—
41C22⋊D379—22no—
42C22⋊D379—22no—
43C22⋊D379—22no—
44C2×Dic379—22no—
45C2×Dic379D411yescharacteristic
46C4×D379—22no—
47C4×D379—22no—
48C4×D379—22no—
49C4×D379D412yes—
50C4×D379C2312yes—
51C379⋊C8C2312yes—
52Q8×C379C2312yes—
53D4×C379—22no—
54D4×C379C2312yes—
55C2×C4×C379—22no—
56C2×C4×C379C2311yescharacteristic
57C8×C379C2311yescharacteristic
58C8×C379C2311yescharacteristic
59C22×C379—22no—
60C22×C379C2×D411yescharacteristic
61C2×D379—22no—
62C2×D379—41no—
63C2×D379—44no—
64C2×D379C2×D412yes—
65C4×C379—22no—
66C4×C379C2×D411yescharacteristic
67C4×C379C2411yescharacteristic
68Dic379—22no—
69Dic379C2×D412yes—
70C2×C379—21no—
71C2×C379—42no—
72C2×C379C22×D411yescharacteristic
73D379—22no—
74D379—42no—
75C379#57511yescharacteristic, complemented, Sylow
76#575—3791nomaximal, Sylow
77C2×#41—3792no—
78#137—3792no—
79#137—3792no—
80AGL(1,ℤ/8)—3792no—
81AGL(1,ℤ/8)—3792no—
82#135—3792no—
83#135—3791no—
84#135D37911yescharacteristic, complemented
85C2×M16—3791no—
86#41—3792no—
87#41—3792no—
88#41—3792no—
89#41—7582no—
90#41—7582no—
91#41C2×D37912yescomplemented
92C2×Q8—3792no—
93C2×D4—3792no—
94C2×D4—7582no—
95C22×C4—3791no—
96C22×C4—7582no—
97Q16—3792no—
98Q16—3791no—
99Q16C2×D37911yescharacteristic, complemented
100SD16—3792no—
101SD16—3792no—
102SD16—3792no—
103SD16C2×D37912yescomplemented
104D8—3792no—
105D8—3791no—
106D8C2×D37911yescharacteristic, complemented
107M16—3792no—
108M16—3792no—
109C2×C8—3791no—
110C2×C8C2×D37911yescharacteristic, complemented
111C23—3791no—
112C23—7582no—
113Q8—3792no—
114Q8—7582no—
115Q8C22×D37912yes—
116D4—22no—
117D4—3792no—
118D4—7582no—
119D4—7582no—
120D4—7582no—
121D4—7582no—
122D4C22×D37912yes—
123C2×C4—22no—
124C2×C4—3791no—
125C2×C4—3792no—
126C2×C4—3792no—
127C2×C4—7582no—
128C2×C4—7582no—
129C2×C4—7582no—
130C2×C4—7582no—
131C2×C4C22×D37911yescharacteristic
132C8—3792no—
133C8C22×D37911yescharacteristic
134C8C22×D37911yescharacteristic
135C22—22no—
136C22—3792no—
137C22—15161no—
138C22—15164no—
139C22—7582no—
140C22D4×D37911yescharacteristic
141C4—22no—
142C4—3792no—
143C4—7582no—
144C4D4×D37911yescharacteristic
145C4C23×D37911yescharacteristic
146C2—21no—
147C2—42no—
148C2—15162no—
149C2—7582no—
150C2C2×D4×D37911yescharacteristic
subgroupG/H
centerC4D4×D379
commutator, cosocleC4×C379C24
FrattiniC4C23×D379
Fitting#135×C379C2
socleC2×C379C22×D4
hypercenter#135D379
hypocenterC379#575
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D379C2semidirect
2. #27131363C2semidirect
3. #27131360C2semidirect
4. #27131358C2semidirect
5. #27131355C2semidirect
6. #27131353C2semidirect
7. #27131351C2semidirect
8. C2×#20258589C2semidirect
9. #135×C379C2semidirect
12. #20258606C22semidirect
15. Q8×D379C22semidirect
17. D4×D379C22semidirect
20. Dic1516C22semidirect
21. #20258596C22semidirect
22. #20258595C22semidirect
23. #20258594C22semidirect
24. #20258593C22semidirect
25. D3032C22semidirect
26. #20258591C22semidirect
27. #20258589C22semidirect
28. #20258589C22semidirect
29. C2×C379⋊C8C22semidirect
30. #41×C379C22semidirect
31. Q16×C379C22semidirect
32. SD16×C379C22semidirect
33. D8×C379C22semidirect
34. C2×C8×C379C22semidirect
75. C379#575semidirect
84. #135D379semidirect
91. #41C2×D379semidirect
99. Q16C2×D379semidirect
103. SD16C2×D379semidirect
106. D8C2×D379semidirect
110. C2×C8C2×D379semidirect

Maximal subgroups

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

subgroupindex
#41×D3792
#271313632
#271313602
#271313582
#271313552
#271313532
#271313512
C2×#202585892
#135×C3792
#575379