Finite Group Databasebeta

← #46830346

Subgroups — #46830346

Order 34624.

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

normal subgroups only

This group has 146 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#31772675C211yesmaximal, characteristic, complemented
2#31772654C211yesmaximal, characteristic, complemented
3#31772615C211yesmaximal, characteristic, complemented
4#31772555C211yesmaximal, characteristic, complemented
5#31772554C211yesmaximal, characteristic, complemented
6#31772546C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C541C211yesmaximal, characteristic, complemented
8#22575836—21no—
9#22575836C2211yescharacteristic
10#22575835—21no—
11#22575835—22no—
12C2×Dic1082—21no—
13C2×Dic1082C2211yescharacteristic
14Q8×D541—21no—
15#22575824—21no—
16#22575821—21no—
17#22575820C2211yescharacteristic
18C22⋊Dic541—22no—
19C4×Dic541C2211yescharacteristic
20#41×C541C2211yescharacteristic
21C2×D4×C541C2211yescharacteristic
22SD16×C541—21no—
23D8×C541—21no—
24M16×C541C2211yescharacteristic
25Dic1082—22no—
26Dic1082—21no—
27Dic1082—21no—
28Dic1082D411yescharacteristic
29D2164D411yescharacteristic
30C22⋊D541—22no—
31C22⋊D541—21no—
32C2×Dic541—22no—
33C2×Dic541—21no—
34C2×Dic541D412yes—
35C4×D541—22no—
36C4×D541—21no—
37#16864513—21no—
38C23×C541—21no—
39Q8×C541D411yescharacteristic
40D4×C541—21no—
41D4×C541—21no—
42D4×C541—21no—
43D4×C541D411yescharacteristic
44C2×C4×C541—21no—
45C2×C4×C541C2311yescharacteristic
46C8×C541—21no—
47C22×C541—21no—
48C22×C541—42no—
49C22×C541—41no—
50C22×C541C2×D411yescharacteristic
51C2×D541—21no—
52C4×C541—21no—
53C4×C541C2×D411yescharacteristic
54C4×C541C2×D411yescharacteristic
55Dic541—21no—
56Dic541—22no—
57Dic541—41no—
58C2×C541—21no—
59C2×C541—41no—
60C2×C541—81no—
61C2×C541#12011yescharacteristic
62D541—41no—
63C541#45411yescharacteristic, complemented, Sylow
64#454—5411nomaximal, Sylow
652−1+4—5411no—
66AGL(1,ℤ/8)—5411no—
67AGL(1,ℤ/8)D54111yescharacteristic, complemented
68#124—5411no—
69#104—5411no—
70#104—5411no—
71#101—5411no—
72#41—5411no—
73#41—10821no—
74#41—10822no—
75#41—10821no—
76#41C2×D54111yescharacteristic
77C2×Q8—5411no—
78C2×Q8—10821no—
79C2×Q8—10821no—
80C2×D4C2×D54111yescharacteristic
81SD16—21no—
82SD16—10821no—
83D8—21no—
84D8—10821no—
85M16—5411no—
86M16C2×D54111yescharacteristic
87C22⋊C4—10822no—
88C42—5411no—
89C23—21no—
90Q8—5411no—
91Q8—10822no—
92Q8—10821no—
93Q8—10821no—
94Q8C22⋊D54111yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—5411no—
99D4—10822no—
100D4—10821no—
101D4C22⋊D54111yescharacteristic
102C2×C4—21no—
103C2×C4—5412no—
104C2×C4—10822no—
105C2×C4—10822no—
106C2×C4—10821no—
107C2×C4—10821no—
108C2×C4C22×D54111yescharacteristic
109C8—21no—
110C8—10821no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—10821no—
115C22D4×D54111yescharacteristic
116C4—21no—
117C4—10822no—
118C4—10821no—
119C4—21641no—
120C4D4×D54111yescharacteristic
121C4C2×C22⋊D54111yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—21641no—
126C2#3177259611yescharacteristic
subgroupG/H
centerC2#31772596
commutator, cosocleC2×C4×C541C23
FrattiniC2×C4C22×D541
FittingAGL(1,ℤ/8)×C541C2
socleC2×C541#120
hypercenterAGL(1,ℤ/8)D541
hypocenterC541#454
LCSG ▷ C2×C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #31772675C2semidirect
2. #31772654C2semidirect
3. #31772615C2semidirect
4. #31772555C2semidirect
5. #31772554C2semidirect
6. #31772546C2semidirect
7. AGL(1,ℤ/8)×C541C2semidirect
63. C541#454semidirect
67. AGL(1,ℤ/8)D541semidirect

Maximal subgroups

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

subgroupindex
#317726752
#317726542
#317726152
#317725552
#317725542
#317725462
AGL(1,ℤ/8)×C5412
#454541