Finite Group Databasebeta

← #37565425

Subgroups — #37565425

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#27131362C211yesmaximal, characteristic, complemented
3#27131329C211yesmaximal, characteristic, complemented
4#27131258C211yesmaximal, characteristic, complemented
5#27131257C211yesmaximal, characteristic, complemented
6#27131249C211yesmaximal, characteristic, complemented
7#137×C379C211yesmaximal, characteristic, complemented
8#20258606—21no—
9#20258606C2211yescharacteristic
10#20258605—22no—
11#20258605—21no—
12C2×Dic758—21no—
13C2×Dic758C2211yescharacteristic
14Q8×D379—21no—
15#20258596—21no—
16#20258593—21no—
17#20258590C2211yescharacteristic
18Dic379⋊C4—22no—
19C4×Dic379C2211yescharacteristic
20#41×C379C2211yescharacteristic
21C2×Q8×C379C2211yescharacteristic
22Q16×C379—21no—
23SD16×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—
38Q8×C379—21no—
39Q8×C379—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—21no—
51C4×C379—41no—
52C4×C379C2×D411yescharacteristic
53C4×C379C2×D411yescharacteristic
54Dic379—22no—
55Dic379—21no—
56Dic379—22no—
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#137D37911yescharacteristic, complemented
66C4⋊Q8—3791no—
67#104—3791no—
68#104—3791no—
69#101—3791no—
70#41—3791no—
71#41—7581no—
72#41—7582no—
73#41—7581no—
74#41C2×D37911yescharacteristic
75C2×Q8—3791no—
76C2×Q8—7581no—
77C2×Q8—7581no—
78C2×Q8C2×D37911yescharacteristic
79Q16—21no—
80Q16—7581no—
81SD16—21no—
82SD16—7581no—
83M16—3791no—
84M16C2×D37911yescharacteristic
85C4⋊C4—7582no—
86C42—3791no—
87Q8—21no—
88Q8—21no—
89Q8—3791no—
90Q8—7582no—
91Q8—7581no—
92Q8—7581no—
93Q8C22⋊D37911yescharacteristic
94D4—21no—
95D4—3791no—
96D4—7582no—
97D4—7581no—
98D4C22⋊D37911yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3792no—
102C2×C4—7582no—
103C2×C4—7582no—
104C2×C4—7581no—
105C2×C4—7581no—
106C2×C4C22×D37911yescharacteristic
107C8—21no—
108C8—7581no—
109C22—21no—
110C22—7581no—
111C22D4×D37911yescharacteristic
112C4—21no—
113C4—41no—
114C4—7582no—
115C4—7582no—
116C4—7581no—
117C4D4×D37911yescharacteristic
118C4C2×C22⋊D37911yescharacteristic
119C2—21no—
120C2—41no—
121C2—15161no—
122C2#2713129911yescharacteristic
subgroupG/H
centerC2#27131299
commutator, cosocleC2×C4×C379C23
FrattiniC2×C4C22×D379
Fitting#137×C379C2
socleC2×C379#120
prime radical#27131378C2
hypercenter#137D379
hypocenterC379#456
LCSG ▷ C2×C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #27131362C2semidirect
3. #27131329C2semidirect
4. #27131258C2semidirect
5. #27131257C2semidirect
6. #27131249C2semidirect
7. #137×C379C2semidirect
61. C379#456semidirect
65. #137D379semidirect

Maximal subgroups

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

subgroupindex
#271313782
#271313622
#271313292
#271312582
#271312572
#271312492
#137×C3792
#456379