Finite Group Databasebeta

← #37565418

Subgroups — #37565418

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#27131359C211yesmaximal, characteristic, complemented
3#27131356C211yesmaximal, characteristic, complemented
4#27131319C211yesmaximal, characteristic, complemented
5#27131259C211yesmaximal, characteristic, complemented
6#27131249C211yesmaximal, characteristic, complemented
7#104×C379C211yesmaximal, characteristic, complemented
8#20258606—21no—
9#20258606C2211yescharacteristic
10#20258605—22no—
11#20258605—21no—
12C2×Dic758—21no—
13C2×Dic758C2211yescharacteristic
14Q8×D379—21no—
15C2×D1516C2211yescharacteristic
16#20258595—21no—
17#20258593—21no—
18D3032—21no—
19#20258591—21no—
20#20258590C2211yescharacteristic
21(C2×D379)⋊C4—22no—
22#41×C379C2211yescharacteristic
23M16×C379C2211yescharacteristic
24C42×C379C2211yescharacteristic
25C22×D379—21no—
26Dic758—22no—
27Dic758—21no—
28Dic758—21no—
29Dic758D411yescharacteristic
30D1516—21no—
31D1516—21no—
32D1516D411yescharacteristic
33C22⋊D379—22no—
34C22⋊D379—21no—
35C2×Dic379—22no—
36C2×Dic379D412yes—
37C4×D379—22no—
38C4×D379—21no—
39C379⋊C8—21no—
40Q8×C379D411yescharacteristic
41D4×C379—21no—
42D4×C379D411yescharacteristic
43C2×C4×C379—21no—
44C2×C4×C379—21no—
45C2×C4×C379C2311yescharacteristic
46C8×C379—21no—
47C22×C379—21no—
48C22×C379C2×D411yescharacteristic
49C2×D379—21no—
50C2×D379—42no—
51C2×D379—41no—
52C4×C379—21no—
53C4×C379—41no—
54C4×C379C2×D411yescharacteristic
55C4×C379C2×D411yescharacteristic
56Dic379—21no—
57Dic379—22no—
58C2×C379—21no—
59C2×C379—41no—
60C2×C379#12011yescharacteristic
61D379—41no—
62D379—81no—
63C379#45411yescharacteristic, complemented, Sylow
64#454—3791nomaximal, Sylow
652−1+4—3791no—
66AGL(1,ℤ/8)—3791no—
67AGL(1,ℤ/8)—3791no—
68#124—3791no—
69#104—3791no—
70#104D37911yescharacteristic, complemented
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×D4—3791no—
81SD16—7581no—
82SD16—7581no—
83D8—7581no—
84D8—7581no—
85M16—3791no—
86M16C2×D37911yescharacteristic
87C22⋊C4—7582no—
88C42C2×D37911yescharacteristic
89C23—7581no—
90Q8—3791no—
91Q8—7582no—
92Q8—7581no—
93Q8—7581no—
94Q8D151611yescharacteristic
95D4—21no—
96D4—3791no—
97D4—7582no—
98D4—7581no—
99D4—7581no—
100D4—7581no—
101D4D151611yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—3792no—
105C2×C4—7582no—
106C2×C4—7582no—
107C2×C4—7581no—
108C2×C4C22×D37911yescharacteristic
109C8—21no—
110C8—7581no—
111C22—21no—
112C22—15162no—
113C22—15161no—
114C22—7581no—
115C22D4×D37911yescharacteristic
116C4—21no—
117C4—41no—
118C4—7582no—
119C4—7581no—
120C4D4×D37911yescharacteristic
121C4C2×D151611yescharacteristic
122C2—21no—
123C2—41no—
124C2—30321no—
125C2—15161no—
126C2#2713130111yescharacteristic
subgroupG/H
centerC2#27131301
commutator, cosocleC2×C4×C379C23
FrattiniC2×C4C22×D379
Fitting#104×C379C2
socleC2×C379#120
hypercenter#104D379
hypocenterC379#454
LCSG ▷ C2×C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
1. #27131378C2semidirect
2. #27131359C2semidirect
3. #27131356C2semidirect
4. #27131319C2semidirect
5. #27131259C2semidirect
6. #27131249C2semidirect
7. #104×C379C2semidirect
63. C379#454semidirect
70. #104D379semidirect

Maximal subgroups

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

subgroupindex
#271313782
#271313592
#271313562
#271313192
#271312592
#271312492
#104×C3792
#454379