Finite Group Databasebeta

← #46830309

Subgroups — #46830309

Order 34624.

198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#22575821C212yesmaximal, complemented
2#31772602C211yesmaximal, characteristic, complemented
3#31772549C212yesmaximal, complemented
4C22⋊#16864513C211yesmaximal, characteristic, complemented
5C22×D4×C541C211yesmaximal, characteristic, complemented
6C2×D2164C2211yescharacteristic, complemented
7C2×C22⋊D541—21no—
8#22575821—24no—
9C2×#16864513C2212yescomplemented
10C4⋊Dic541C2211yescharacteristic, complemented
11#22575813—21no—
12C24×C541—21no—
13C2×D4×C541—24no—
14C2×D4×C541—21no—
15C2×D4×C541C2212yes—
16C22×C4×C541C2211yescharacteristic
17C22×D541—21no—
18D2164—22no—
19C22⋊D541—42no—
20C2×Dic541—21no—
21#16864513—22no—
22C23×C541—24no—
23C23×C541—22no—
24C23×C541—42no—
25C23×C541—42no—
26C23×C541D411yescharacteristic
27D4×C541—24no—
28D4×C541—22no—
29D4×C541D414yescomplemented
30C2×C4×C541—22no—
31C2×C4×C541D411yescharacteristic
32C2×C4×C541C2311yescharacteristic
33C22×C541—21no—
34C22×C541—21no—
35C22×C541—24no—
36C22×C541—48no—
37C22×C541—42no—
38C22×C541—42no—
39C22×C541D812yescomplemented
40C22×C541C2×D411yescharacteristic
41C2×D541—41no—
42C2×D541—41no—
43C2×D541—41no—
44C4×C541—21no—
45C4×C541C2×D412yes—
46Dic541—41no—
47C2×C541—22no—
48C2×C541—44no—
49C2×C541#12011yescharacteristic
50C2×C541C2×D811yescharacteristic
51C2×C541AGL(1,ℤ/8)11yescharacteristic
52D541—81no—
53C541#44711yescharacteristic, complemented, Sylow
54#447—5411nomaximal, Sylow
55C22×D4D54111yescharacteristic, complemented
56C2×D8—5412no—
57#121—5411no—
58#102—5412no—
59C22⋊C8—5411no—
60C24—21no—
61C2×D4—24no—
62C2×D4—21no—
63C2×D4—5411no—
64C2×D4—10821no—
65C2×D4C2×D54112yes—
66C22×C4C2×D54111yescharacteristic
67D8—10824no—
68C2×C8—5412no—
69C4⋊C4—5411no—
70C22⋊C4—10821no—
71C23—24no—
72C23—22no—
73C23—42no—
74C23—42no—
75C23—10821no—
76C23C22⋊D54111yescharacteristic
77D4—24no—
78D4—22no—
79D4—10822no—
80D4—21642no—
81D4C22⋊D54114yescomplemented
82C2×C4—22no—
83C2×C4—10821no—
84C2×C4C22⋊D54111yescharacteristic
85C2×C4C22×D54111yescharacteristic
86C8—10822no—
87C22—21no—
88C22—21no—
89C22—24no—
90C22—48no—
91C22—42no—
92C22—42no—
93C22—21641no—
94C22—21641no—
95C22—21641no—
96C22#2257582112yescomplemented
97C22C2×C22⋊D54111yescharacteristic
98C4—21no—
99C4—21641no—
100C4C2×C22⋊D54112yes—
101C2—22no—
102C2—44no—
103C2—43281no—
104C2#3177259711yescharacteristic
105C2C2×#2257582111yescharacteristic
106C2#3177265411yescharacteristic
subgroupG/H
centerC22C2×C22⋊D541
commutator, cosocleC2×C4×C541C23
FrattiniC2×C4C22×D541
FittingC22×D4×C541C2
socleC22×C541C2×D4
hypercenterC22×D4D541
hypocenterC541#447
LCSG ▷ C2×C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22575821C2semidirect
2. #31772602C2semidirect
3. #31772549C2semidirect
4. C22⋊#16864513C2semidirect
5. C22×D4×C541C2semidirect
6. C2×D2164C22semidirect
9. C2×#16864513C22semidirect
10. C4⋊Dic541C22semidirect
29. D4×C541D4semidirect
39. C22×C541D8semidirect
53. C541#447semidirect
55. C22×D4D541semidirect
81. D4C22⋊D541semidirect
96. C22#22575821semidirect

Maximal subgroups

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

subgroupindex
C2×#225758212
#317726022
#317725492
C22⋊#168645132
C22×D4×C5412
#447541