Finite Group Databasebeta

← #44505597

Subgroups — #44505597

Order 30848.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#29507889C211yesmaximal, characteristic
2#29507512C211yesmaximal, characteristic, complemented
3#329×C241C211yesmaximal, characteristic, complemented
4#21440690C411yescharacteristic, complemented
5#21440668—21no—
6#21440570—21no—
7#21440561C411yescharacteristic, complemented
8#21440557—21no—
9#124×C241C2211yescharacteristic
10#97×C241—21no—
11#16838771—41no—
12#16838770—21no—
13#16838770—41no—
14Q8×D241—41no—
15#16838758—41no—
16#16838755—41no—
17#16838754—21no—
18C22⋊Dic241—41no—
19C2×Q8×C241C2×C411yescharacteristic
20C2×D4×C241D411yescharacteristic
21C2×C8×C241—41no—
22C22⋊C4×C241—41no—
23C42×C241D411yescharacteristic
24Dic482—21no—
25Dic482—41no—
26D964—21no—
27D964—41no—
28C22⋊D241—41no—
29C2×Dic241—81no—
30C4×D241—41no—
31C4×D241—42no—
32#14515349—41no—
33C23×C241—21no—
34Q8×C241—41no—
35D4×C241—41no—
36C2×C4×C241—21no—
37C2×C4×C241—21no—
38C2×C4×C241C22⋊C411yescharacteristic
39C8×C241—42no—
40C22×C241—41no—
41C22×C241—81no—
42C22×C241#9911yescharacteristic
43C2×D241—41no—
44C4×C241—21no—
45C4×C241—41no—
46C4×C241—41no—
47Dic241—41no—
48Dic241—161no—
49C2×C241—21no—
50C2×C241—81no—
51C2×C241AΣL(1,𝔽16)11yescharacteristic
52D241—81no—
53C241#140411yescharacteristic, complemented, Sylow
54#1404—2411nomaximal, Sylow
55#454—2411no—
56#354—2411no—
57#329D24111yescharacteristic, complemented
582−1+4—2411no—
59AGL(1,ℤ/8)—4821no—
60#124C2×D24111yescharacteristic
61#104—4821no—
62#101—2411no—
63#99—4821no—
64#97—21no—
65#41—9641no—
66#41—9641no—
67#41—4821no—
68C2×Q8—9641no—
69C2×Q8C4×D24111yescharacteristic
70C2×D4D96411yescharacteristic
71SD16—9641no—
72D8—9641no—
73M16—4821no—
74C2×C8—41no—
75C22⋊C4—41no—
76C22⋊C4—9641no—
77C42C22⋊D24111yescharacteristic
78C23—21no—
79Q8—41no—
80Q8—9641no—
81Q8—4821no—
82D4—41no—
83D4—9641no—
84D4—9641no—
85D4—4821no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—19281no—
89C2×C4—9641no—
90C2×C4—9642no—
91C2×C4#1683874711yescharacteristic
92C8—42no—
93C8—9641no—
94C22—41no—
95C22—81no—
96C22—9641no—
97C22#2144055611yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—38561no—
102C4—9641no—
103C2—21no—
104C2—81no—
105C2—19281no—
106C2#2950750511yescharacteristic
subgroupG/H
centerC2#29507505
commutatorC2×Q8×C241C2×C4
Frattini#124C2×D241
Fitting#329×C241C2
socleC2×C241AΣL(1,𝔽16)
prime radical#29507889C2
cosocle#124×C241C22
hypercenter#329D241
hypocenterC241#1404
LCSG ▷ C2×Q8×C241 ▷ C2×C4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #29507512C2semidirect
3. #329×C241C2semidirect
4. #21440690C4semidirect
7. #21440561C4semidirect
53. C241#1404semidirect
57. #329D241semidirect

Maximal subgroups

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

subgroupindex
#295078892
#295075122
#329×C2412
#1404241