Finite Group Databasebeta

← #44470228

Subgroups — #44470228

Order 29888.

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

normal subgroups only

This group has 160 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#28417998C211yesmaximal, characteristic
2#28417937C212yesmaximal, complemented
3#28417934C211yesmaximal, characteristic, complemented
4#28417867C212yesmaximal, complemented
5#99×C467C211yesmaximal, characteristic, complemented
6#21418743—21no—
7#21418742—22no—
8C2×C22⋊D467—21no—
9C2×C22⋊D467C2212yes—
10D4×D467—22no—
11C22×Dic467C2211yescharacteristic, complemented
12C4⋊Dic467—22no—
13Dic467⋊C4—21no—
14C22⋊Dic467—21no—
15C22⋊Dic467C2211yescharacteristic, complemented
16(C2×D467)⋊C4—22no—
17C2×D4×C467C2211yescharacteristic
18C22⋊C4×C467C2212yescomplemented
19C22×D467—21no—
20C22×D467D412yes—
21Dic934—21no—
22D1868—21no—
23C22⋊D467—22no—
24C22⋊D467—22no—
25C22⋊D467—22no—
26C2×Dic467—21no—
27C2×Dic467—22no—
28C2×Dic467—21no—
29C2×Dic467—21no—
30C2×Dic467D412yes—
31C4×D467—22no—
32C23×C467D411yescharacteristic
33C23×C467C2311yescharacteristic
34D4×C467—22no—
35C2×C4×C467—22no—
36C2×C4×C467D411yescharacteristic
37C22×C467—21no—
38C22×C467—41no—
39C22×C467—41no—
40C22×C467C2×D412yes—
41C22×C467C2×D411yescharacteristic
42C2×D467—22no—
43C2×D467—42no—
44C2×D467—81no—
45C4×C467—21no—
46C4×C467—42no—
47Dic467—22no—
48Dic467—41no—
49Dic467—41no—
50C2×C467—21no—
51C2×C467—22no—
52C2×C467—41no—
53C2×C467#12011yescharacteristic
54D467—42no—
55C467#45811yescharacteristic, complemented, Sylow
56#458—4671nomaximal, Sylow
57H(5,𝔽2)—4671no—
58#123—4671no—
59#123—4672no—
60#99—4672no—
61#99D46711yescharacteristic, complemented
62#41—9342no—
63#41—9341no—
64C2×D4—9342no—
65C2×D4—9341no—
66C2×D4—4672no—
67C2×D4C2×D46711yescharacteristic
68C22×C4—4671no—
69C4⋊C4—9342no—
70C4⋊C4—9341no—
71C22⋊C4—9342no—
72C22⋊C4—9341no—
73C22⋊C4—4671no—
74C22⋊C4C2×D46712yescomplemented
75C23—9341no—
76C23—4672no—
77C23D186811yescharacteristic
78C23C22×D46711yescharacteristic
79Q8—9341no—
80D4—22no—
81D4—9341no—
82D4—9342no—
83D4—9342no—
84D4—9342no—
85C2×C4—22no—
86C2×C4—9342no—
87C2×C4—9342no—
88C2×C4—9341no—
89C2×C4—9341no—
90C2×C4—9341no—
91C2×C4—4672no—
92C2×C4D186811yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—18682no—
97C22—37361no—
98C22—9342no—
99C22D4×D46712yes—
100C22C2×D186811yescharacteristic
101C4—21no—
102C4—42no—
103C4—18681no—
104C4—18681no—
105C4—9342no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—18682no—
110C2#2841792311yescharacteristic
subgroupG/H
centerC2#28417923
commutator, cosocleC23×C467C23
FrattiniC23C22×D467
Fitting#99×C467C2
socleC2×C467#120
prime radical#28417998C2
hypercenter#99D467
hypocenterC467#458
LCSG ▷ C23×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #28417937C2semidirect
3. #28417934C2semidirect
4. #28417867C2semidirect
5. #99×C467C2semidirect
11. C22×Dic467C22semidirect
15. C22⋊Dic467C22semidirect
18. C22⋊C4×C467C22semidirect
55. C467#458semidirect
61. #99D467semidirect
74. C22⋊C4C2×D467semidirect

Maximal subgroups

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

subgroupindex
#284179982
#284179372
#284179342
#284178672
#99×C4672
#458467