Finite Group Databasebeta

← #37565428

Subgroups — #37565428

Order 24256.

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

normal subgroups only

This group has 142 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
2#27131364C211yesmaximal, characteristic, complemented
3#27131361C211yesmaximal, characteristic, complemented
4#27131331C211yesmaximal, 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
14C2×Dic758C2211yescharacteristic
15Q8×D379—21no—
16Dic1516—21no—
17#20258596—21no—
18#20258595—21no—
19#20258594—21no—
20#20258590C2211yescharacteristic
21C4⋊Dic379—22no—
22#41×C379C2211yescharacteristic
23M16×C379C2211yescharacteristic
24C42×C379C2211yescharacteristic
25Dic758—22no—
26Dic758—21no—
27Dic758—21no—
28Dic758—21no—
29Dic758—21no—
30Dic758D411yescharacteristic
31D1516D411yescharacteristic
32C22⋊D379—22no—
33C22⋊D379—21no—
34C2×Dic379—22no—
35C2×Dic379—21no—
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—
50C4×C379—22no—
51C4×C379—21no—
52C4×C379C2×D411yescharacteristic
53C4×C379C2×D411yescharacteristic
54Dic379—21no—
55Dic379—22no—
56Dic379—41no—
57C2×C379—21no—
58C2×C379—41no—
59C2×C379#12011yescharacteristic
60D379—41no—
61C379#45611yescharacteristic, complemented, Sylow
62#456—3791nomaximal, Sylow
632−1+4—3791no—
64#137—3791no—
65#137—3791no—
66C4⋊Q8—3791no—
67#104—3791no—
68#104D37911yescharacteristic, complemented
69#101—3791no—
70#41—3791no—
71#41—7581no—
72#41—7582no—
73#41—7581no—
74#41C2×D37911yescharacteristic
75C2×Q8—3791no—
76C2×Q8—3791no—
77C2×Q8—7581no—
78C2×Q8—7581no—
79Q16—7581no—
80Q16—7581no—
81SD16—7581no—
82SD16—7581no—
83M16—3791no—
84M16C2×D37911yescharacteristic
85C4⋊C4—7582no—
86C42C2×D37911yescharacteristic
87Q8—3791no—
88Q8—7582no—
89Q8—7581no—
90Q8—7581no—
91Q8—7581no—
92Q8—7581no—
93Q8D151611yescharacteristic
94D4—21no—
95D4—3791no—
96D4—7582no—
97D4—7581no—
98D4D151611yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3792no—
102C2×C4—7582no—
103C2×C4—7581no—
104C2×C4—7582no—
105C2×C4—7581no—
106C2×C4C22×D37911yescharacteristic
107C8—21no—
108C8—7581no—
109C22—21no—
110C22—7581no—
111C22D4×D37911yescharacteristic
112C4—22no—
113C4—21no—
114C4—15161no—
115C4—7582no—
116C4—7581no—
117C4D4×D37911yescharacteristic
118C4C2×D151611yescharacteristic
119C2—21no—
120C2—41no—
121C2—15161no—
122C2#2713130111yescharacteristic
subgroupG/H
centerC2#27131301
commutator, cosocleC2×C4×C379C23
FrattiniC2×C4C22×D379
Fitting#104×C379C2
socleC2×C379#120
prime radical#27131378C2
hypercenter#104D379
hypocenterC379#456
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
2. #27131364C2semidirect
3. #27131361C2semidirect
4. #27131331C2semidirect
5. #27131259C2semidirect
6. #27131249C2semidirect
7. #104×C379C2semidirect
61. C379#456semidirect
68. #104D379semidirect

Maximal subgroups

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

subgroupindex
#271313782
#271313642
#271313612
#271313312
#271312592
#271312492
#104×C3792
#456379