Finite Group Databasebeta

← #37565415

Subgroups — #37565415

Order 24256.

146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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#27131378C211yesmaximal, characteristic, complemented
2#27131357C211yesmaximal, characteristic, complemented
3#27131318C211yesmaximal, characteristic, complemented
4#27131258C211yesmaximal, characteristic, complemented
5#27131257C211yesmaximal, characteristic, complemented
6#27131249C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C379C211yesmaximal, characteristic, complemented
8#20258606—21no—
9#20258606C2211yescharacteristic
10#20258605—22no—
11#20258605—21no—
12C2×Dic758—21no—
13C2×Dic758C2211yescharacteristic
14Q8×D379—21no—
15#20258594—21no—
16#20258591—21no—
17#20258590C2211yescharacteristic
18C22⋊Dic379—22no—
19C4×Dic379C2211yescharacteristic
20#41×C379C2211yescharacteristic
21C2×D4×C379C2211yescharacteristic
22SD16×C379—21no—
23D8×C379—21no—
24M16×C379C2211yescharacteristic
25Dic758—22no—
26Dic758—21no—
27Dic758—21no—
28Dic758D411yescharacteristic
29D1516D411yescharacteristic
30C22⋊D379—22no—
31C22⋊D379—21no—
32C2×Dic379—22no—
33C2×Dic379—21no—
34C2×Dic379D412yes—
35C4×D379—22no—
36C4×D379—21no—
37C379⋊C8—21no—
38C23×C379—21no—
39Q8×C379D411yescharacteristic
40D4×C379—21no—
41D4×C379—21no—
42D4×C379—21no—
43D4×C379D411yescharacteristic
44C2×C4×C379—21no—
45C2×C4×C379C2311yescharacteristic
46C8×C379—21no—
47C22×C379—21no—
48C22×C379—42no—
49C22×C379—41no—
50C22×C379C2×D411yescharacteristic
51C2×D379—21no—
52C4×C379—21no—
53C4×C379C2×D411yescharacteristic
54C4×C379C2×D411yescharacteristic
55Dic379—21no—
56Dic379—22no—
57Dic379—41no—
58C2×C379—21no—
59C2×C379—41no—
60C2×C379—81no—
61C2×C379#12011yescharacteristic
62D379—41no—
63C379#45411yescharacteristic, complemented, Sylow
64#454—3791nomaximal, Sylow
652−1+4—3791no—
66AGL(1,ℤ/8)—3791no—
67AGL(1,ℤ/8)D37911yescharacteristic, complemented
68#124—3791no—
69#104—3791no—
70#104—3791no—
71#101—3791no—
72#41—3791no—
73#41—7581no—
74#41—7582no—
75#41—7581no—
76#41C2×D37911yescharacteristic
77C2×Q8—3791no—
78C2×Q8—7581no—
79C2×Q8—7581no—
80C2×D4C2×D37911yescharacteristic
81SD16—21no—
82SD16—7581no—
83D8—21no—
84D8—7581no—
85M16—3791no—
86M16C2×D37911yescharacteristic
87C22⋊C4—7582no—
88C42—3791no—
89C23—21no—
90Q8—3791no—
91Q8—7582no—
92Q8—7581no—
93Q8—7581no—
94Q8C22⋊D37911yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—3791no—
99D4—7582no—
100D4—7581no—
101D4C22⋊D37911yescharacteristic
102C2×C4—21no—
103C2×C4—3792no—
104C2×C4—7582no—
105C2×C4—7581no—
106C2×C4—7582no—
107C2×C4—7581no—
108C2×C4C22×D37911yescharacteristic
109C8—21no—
110C8—7581no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—7581no—
115C22D4×D37911yescharacteristic
116C4—21no—
117C4—15161no—
118C4—7582no—
119C4—7581no—
120C4D4×D37911yescharacteristic
121C4C2×C22⋊D37911yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—15161no—
126C2#2713129911yescharacteristic
subgroupG/H
centerC2#27131299
commutator, cosocleC2×C4×C379C23
FrattiniC2×C4C22×D379
FittingAGL(1,ℤ/8)×C379C2
socleC2×C379#120
hypercenterAGL(1,ℤ/8)D379
hypocenterC379#454
LCSG ▷ C2×C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #27131378C2semidirect
2. #27131357C2semidirect
3. #27131318C2semidirect
4. #27131258C2semidirect
5. #27131257C2semidirect
6. #27131249C2semidirect
7. AGL(1,ℤ/8)×C379C2semidirect
63. C379#454semidirect
67. AGL(1,ℤ/8)D379semidirect

Maximal subgroups

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

subgroupindex
#271313782
#271313572
#271313182
#271312582
#271312572
#271312492
AGL(1,ℤ/8)×C3792
#454379