Finite Group Databasebeta

← #37566042

Subgroups — #37566042

Order 24256.

262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#20258606C211yesmaximal, characteristic, complemented
2#27131362C212yesmaximal, complemented
3#27131361C212yesmaximal, complemented
4#27131357C212yesmaximal, complemented
5#27131356C212yesmaximal, complemented
6#27131351C214yesmaximal, complemented
7C2×#20258590C211yesmaximal, characteristic, complemented
8C2×#41×C379C211yesmaximal, characteristic, complemented
9#20258606—21no—
10#20258606—21no—
11#20258606C2212yes—
12#20258606C2212yescomplemented
13C2×Dic758C2211yescharacteristic, complemented
14C2×D1516C2211yescharacteristic, complemented
15C2×C22⋊D379—21no—
16C2×C4×D379—21no—
17#20258596C2214yescomplemented
18#20258594C2214yescomplemented
19#20258593C2214yescomplemented
20#20258591C2214yescomplemented
21#20258590C2212yescomplemented
22#20258590C2212yescomplemented
23C2×C379⋊C8C2212yescomplemented
24#41×C379—21no—
25#41×C379—21no—
26#41×C379C2212yes—
27#41×C379C2212yescomplemented
28C2×Q8×C379C2211yescharacteristic, complemented
29C2×D4×C379—21no—
30C2×D4×C379C2211yescharacteristic, complemented
31C22×C4×C379—21no—
32C22×C4×C379C2211yescharacteristic
33C22×D379—21no—
34Dic758—21no—
35Dic758C2312yes—
36D1516—21no—
37D1516C2312yes—
38C22⋊D379—22no—
39C22⋊D379—22no—
40C2×Dic379—21no—
41C4×D379—22no—
42C4×D379—22no—
43C379⋊C8C2314yes—
44C23×C379—21no—
45C23×C379D411yescharacteristic
46Q8×C379—21no—
47Q8×C379C2312yes—
48D4×C379—22no—
49D4×C379—22no—
50D4×C379—21no—
51D4×C379C2312yes—
52C2×C4×C379—21no—
53C2×C4×C379—22no—
54C2×C4×C379—22no—
55C2×C4×C379D411yescharacteristic
56C2×C4×C379D411yescharacteristic
57C2×C4×C379D411yescharacteristic
58C2×C4×C379C2311yescharacteristic
59C2×C4×C379C2311yescharacteristic
60C2×C4×C379C2311yescharacteristic
61C22×C379—22no—
62C22×C379—41no—
63C22×C379—42no—
64C22×C379C2×D411yescharacteristic
65C22×C379C2×D411yescharacteristic
66C22×C379C2×D411yescharacteristic
67C2×D379—22no—
68C2×D379—42no—
69C4×C379—22no—
70C4×C379C2×D411yescharacteristic
71C4×C379C2×D411yescharacteristic
72C4×C379C2×D411yescharacteristic
73C4×C379C2411yescharacteristic
74Dic379—22no—
75C2×C379—21no—
76C2×C379—21no—
77C2×C379—21no—
78C2×C379—42no—
79C2×C379C22×D411yescharacteristic
80D379—42no—
81C379#57511yescharacteristic, complemented, Sylow
82#575—3791nomaximal, Sylow
83C2×#41—3791no—
84C2×#41D37911yescharacteristic, complemented
85#137—3792no—
86#137—3792no—
87AGL(1,ℤ/8)—3792no—
88AGL(1,ℤ/8)—3792no—
89#135—3794no—
90C2×M16—3791no—
91#41—21no—
92#41—21no—
93#41—3792no—
94#41—3792no—
95#41—7581no—
96#41—7581no—
97#41C2×D37912yes—
98#41C2×D37912yescomplemented
99C2×Q8—3791no—
100C2×Q8C2×D37911yescharacteristic, complemented
101C2×D4—21no—
102C2×D4—3791no—
103C2×D4—7581no—
104C2×D4C2×D37911yescharacteristic, complemented
105C22×C4—21no—
106C22×C4—7581no—
107C22×C4C2×D37911yescharacteristic
108Q16—3794no—
109SD16—3794no—
110SD16—3794no—
111D8—3794no—
112M16—3792no—
113M16—3792no—
114C2×C8—3792no—
115C23—21no—
116C23—7581no—
117C23C22⋊D37911yescharacteristic
118Q8—21no—
119Q8—3792no—
120Q8—7581no—
121Q8C22×D37912yes—
122D4—22no—
123D4—22no—
124D4—21no—
125D4—3792no—
126D4—7582no—
127D4—7582no—
128D4—7581no—
129D4C22×D37912yes—
130C2×C4—21no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—7581no—
134C2×C4—7582no—
135C2×C4—7582no—
136C2×C4C22⋊D37911yescharacteristic
137C2×C4C22⋊D37911yescharacteristic
138C2×C4C22⋊D37911yescharacteristic
139C2×C4C22×D37911yescharacteristic
140C2×C4C22×D37911yescharacteristic
141C2×C4C22×D37911yescharacteristic
142C8—3794no—
143C22—22no—
144C22—41no—
145C22—42no—
146C22—15162no—
147C22—7582no—
148C22C2×C22⋊D37911yescharacteristic
149C22C2×C22⋊D37911yescharacteristic
150C22C2×C22⋊D37911yescharacteristic
151C4—22no—
152C4—7582no—
153C4C2×C22⋊D37911yescharacteristic
154C4C2×C22⋊D37911yescharacteristic
155C4C2×C22⋊D37911yescharacteristic
156C4C23×D37911yescharacteristic
157C2—21no—
158C2—21no—
159C2—21no—
160C2—42no—
161C2—15162no—
162C2C22×C22⋊D37911yescharacteristic
subgroupG/H
centerC4C2×C22⋊D379
commutator, cosocleC4×C379C24
FrattiniC4C23×D379
FittingC2×#41×C379C2
socleC2×C379C22×D4
hypercenterC2×#41D379
hypocenterC379#575
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#20258606C2semidirect
2. #27131362C2semidirect
3. #27131361C2semidirect
4. #27131357C2semidirect
5. #27131356C2semidirect
6. #27131351C2semidirect
7. C2×#20258590C2semidirect
8. C2×#41×C379C2semidirect
12. #20258606C22semidirect
13. C2×Dic758C22semidirect
14. C2×D1516C22semidirect
17. #20258596C22semidirect
18. #20258594C22semidirect
19. #20258593C22semidirect
20. #20258591C22semidirect
21. #20258590C22semidirect
22. #20258590C22semidirect
23. C2×C379⋊C8C22semidirect
27. #41×C379C22semidirect
28. C2×Q8×C379C22semidirect
30. C2×D4×C379C22semidirect
81. C379#575semidirect
84. C2×#41D379semidirect
98. #41C2×D379semidirect
100. C2×Q8C2×D379semidirect
104. C2×D4C2×D379semidirect

Maximal subgroups

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

subgroupindex
C2×#202586062
#271313622
#271313612
#271313572
#271313562
#271313512
C2×#202585902
C2×#41×C3792
#575379