Finite Group Databasebeta

← #44505596

Subgroups — #44505596

Order 30848.

112 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 25 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#29507512C211yesmaximal, characteristic, complemented
2#29507457C211yesmaximal, characteristic, complemented
3#454×C241C211yesmaximal, characteristic
4#21440557—21no—
5#21440553—21no—
62−1+4×C241C411yescharacteristic, complemented
7AGL(1,ℤ/8)×C241—21no—
8#124×C241C2211yescharacteristic
9#104×C241—21no—
10#101×C241C411yescharacteristic, complemented
11C2×#14515349—41no—
12C22⋊Dic241—41no—
13#41×C241—21no—
14#41×C241—41no—
15#41×C241—41no—
16C2×Q8×C241—41no—
17C2×Q8×C241C2×C411yescharacteristic
18C2×D4×C241D411yescharacteristic
19SD16×C241—41no—
20D8×C241—41no—
21M16×C241—21no—
22C22⋊C4×C241—41no—
23C42×C241D411yescharacteristic
24C2×Dic241—81no—
25#14515349—42no—
26C23×C241—21no—
27Q8×C241—21no—
28Q8×C241—41no—
29Q8×C241—41no—
30D4×C241—21no—
31D4×C241—41no—
32D4×C241—41no—
33D4×C241—41no—
34C2×C4×C241—21no—
35C2×C4×C241—21no—
36C2×C4×C241—41no—
37C2×C4×C241—42no—
38C2×C4×C241C22⋊C411yescharacteristic
39C8×C241—41no—
40C22×C241—41no—
41C22×C241—41no—
42C22×C241—81no—
43C22×C241#9911yescharacteristic
44C4×C241—21no—
45C4×C241—41no—
46C4×C241—41no—
47C4×C241—41no—
48Dic241—161no—
49C2×C241—21no—
50C2×C241—81no—
51C2×C241—81no—
52C2×C241AΣL(1,𝔽16)11yescharacteristic
53C241#140411yescharacteristic, complemented, Sylow
54#1404—2411nomaximal, Sylow
55#454D24111yescharacteristic
56#354—2411no—
57#329—2411no—
582−1+4Dic24111yescharacteristic, complemented
59AGL(1,ℤ/8)—21no—
60#124C2×D24111yescharacteristic
61#104—21no—
62#101Dic24111yescharacteristic, complemented
63#99—4821no—
64#97—4821no—
65#41—21no—
66#41—41no—
67#41—41no—
68C2×Q8—41no—
69C2×Q8C2×Dic24111yescharacteristic
70C2×D4C22⋊D24111yescharacteristic
71SD16—41no—
72D8—41no—
73M16—21no—
74C2×C8—9641no—
75C22⋊C4—41no—
76C22⋊C4—9641no—
77C42C22⋊D24111yescharacteristic
78C23—21no—
79Q8—21no—
80Q8—41no—
81Q8—41no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—41no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—41no—
89C2×C4—42no—
90C2×C4—19281no—
91C2×C4C22⋊Dic24111yescharacteristic
92C8—41no—
93C8—9642no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22#2144055711yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—41no—
102C4—38561no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#2950750411yescharacteristic
subgroupG/H
centerC2#29507504
commutatorC2×Q8×C241C2×C4
Frattini#124C2×D241
Fitting, prime radical#454×C241C2
socleC2×C241AΣL(1,𝔽16)
cosocle#124×C241C22
hypercenter#454D241
hypocenterC241#1404
LCSG ▷ C2×Q8×C241 ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #29507512C2semidirect
2. #29507457C2semidirect
6. 2−1+4×C241C4semidirect
10. #101×C241C4semidirect
53. C241#1404semidirect
58. 2−1+4Dic241semidirect
62. #101Dic241semidirect

Maximal subgroups

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

subgroupindex
#295075122
#295074572
#454×C2412
#1404241