Finite Group Databasebeta

← #46830307

Subgroups — #46830307

Order 34624.

198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 45 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×D4×D541C211yesmaximal, characteristic, complemented
2C2×#22575821C211yesmaximal, characteristic, complemented
3#31772599C211yesmaximal, characteristic, complemented
4#31772550C211yesmaximal, characteristic, complemented
5#31772549C211yesmaximal, characteristic, complemented
6#31772540C211yesmaximal, characteristic, complemented
7C2×D8×C541C211yesmaximal, characteristic, complemented
8C23×D541—21no—
9C2×D2164C2211yescharacteristic
10C2×C22⋊D541—21no—
11C2×C22⋊D541—21no—
12D4×D541—22no—
13D4×D541—22no—
14C2×C4×D541C2211yescharacteristic
15#22575821—22no—
16C2×#16864513C2211yescharacteristic, complemented
17C4⋊Dic541C2211yescharacteristic, complemented
18C22⋊Dic541—21no—
19C2×D4×C541C2211yescharacteristic
20C2×D4×C541C2211yescharacteristic, complemented
21D8×C541—22no—
22C2×C8×C541C2211yescharacteristic, complemented
23C22×D541—24no—
24C22×D541—21no—
25C22×D541—42no—
26C22×D541—42no—
27C22×D541D411yescharacteristic
28D2164—21no—
29D2164D412yescomplemented
30C22⋊D541—24no—
31C22⋊D541—42no—
32C2×Dic541—21no—
33C2×Dic541D411yescharacteristic
34C4×D541—21no—
35C4×D541—21no—
36#16864513—21no—
37C23×C541—21no—
38C23×C541—21no—
39D4×C541—21no—
40D4×C541—21no—
41D4×C541—21no—
42D4×C541D412yescomplemented
43C2×C4×C541C2311yescharacteristic
44C8×C541—21no—
45C22×C541—22no—
46C22×C541—41no—
47C22×C541—41no—
48C22×C541—41no—
49C22×C541—41no—
50C22×C541—41no—
51C22×C541C2×D411yescharacteristic
52C2×D541—21no—
53C2×D541—21no—
54C2×D541—22no—
55C2×D541—48no—
56C2×D541—41no—
57C2×D541—41no—
58C2×D541D812yescomplemented
59C4×C541C2×D411yescharacteristic
60C4×C541C2×D411yescharacteristic
61Dic541—21no—
62Dic541—41no—
63C2×C541—42no—
64C2×C541—81no—
65C2×C541#12011yescharacteristic
66C2×C541C2×D811yescharacteristic
67C2×C541AGL(1,ℤ/8)11yescharacteristic
68D541—22no—
69D541—42no—
70C541#44711yescharacteristic, complemented, Sylow
71#447—5411nomaximal, Sylow
72C22×D4—5411no—
73C2×D8—5411no—
74C2×D8D54111yescharacteristic, complemented
75#121—5411no—
76#102—5411no—
77#102—5411no—
78C22⋊C8—5411no—
79C24—10821no—
80C2×D4—5411no—
81C2×D4—10821no—
82C2×D4—10822no—
83C2×D4—10822no—
84C2×D4—10821no—
85C2×D4C2×D54111yescharacteristic
86C2×D4C2×D54111yescharacteristic, complemented
87C22×C4—5411no—
88D8—22no—
89D8—10822no—
90C2×C8—5411no—
91C2×C8C2×D54111yescharacteristic, complemented
92C4⋊C4—5411no—
93C22⋊C4—10821no—
94C23—21no—
95C23—21no—
96C23—5411no—
97C23—10824no—
98C23—10821no—
99C23—21642no—
100C23—21642no—
101D4—21no—
102D4—21no—
103D4—21no—
104D4—5412no—
105D4—10824no—
106D4—10821no—
107D4—21642no—
108D4C22⋊D54112yescomplemented
109C2×C4—5411no—
110C2×C4—10821no—
111C2×C4—10821no—
112C2×C4—10821no—
113C2×C4C22×D54111yescharacteristic
114C8—21no—
115C8—10821no—
116C22—22no—
117C22—41no—
118C22—41no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—5412no—
123C22—10821no—
124C22—10821no—
125C22—10822no—
126C22—21648no—
127C22—21641no—
128C22—21641no—
129C22D4×D54111yescharacteristic
130C4—10821no—
131C4—21641no—
132C4D4×D54111yescharacteristic
133C4C2×C22⋊D54111yescharacteristic
134C2—42no—
135C2—81no—
136C2—10822no—
137C2—21642no—
138C2#3177259611yescharacteristic
139C2D8×D54111yescharacteristic
140C2#3177265211yescharacteristic
subgroupG/H
centerC22D4×D541
commutator, cosocleC2×C4×C541C23
FrattiniC2×C4C22×D541
FittingC2×D8×C541C2
socleC22×C541C2×D4
hypercenterC2×D8D541
hypocenterC541#447
LCSG ▷ C2×C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×D541C2semidirect
2. C2×#22575821C2semidirect
3. #31772599C2semidirect
4. #31772550C2semidirect
5. #31772549C2semidirect
6. #31772540C2semidirect
7. C2×D8×C541C2semidirect
16. C2×#16864513C22semidirect
17. C4⋊Dic541C22semidirect
20. C2×D4×C541C22semidirect
22. C2×C8×C541C22semidirect
29. D2164D4semidirect
42. D4×C541D4semidirect
58. C2×D541D8semidirect
70. C541#447semidirect
74. C2×D8D541semidirect
86. C2×D4C2×D541semidirect
91. C2×C8C2×D541semidirect
108. D4C22⋊D541semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D5412
C2×#225758212
#317725992
#317725502
#317725492
#317725402
C2×D8×C5412
#447541