Finite Group Databasebeta

← #46830341

Subgroups — #46830341

Order 34624.

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

normal subgroups only

This group has 168 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#31772674C211yesmaximal, characteristic, complemented
2#31772654C211yesmaximal, characteristic, complemented
3#31772624C211yesmaximal, characteristic, complemented
4#31772555C211yesmaximal, characteristic, complemented
5#31772554C211yesmaximal, characteristic, complemented
6#31772544C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C541C211yesmaximal, characteristic, complemented
8#22575837—21no—
9#22575836—21no—
10#22575836C2211yescharacteristic
11C2×D2164—21no—
12C2×D2164C2211yescharacteristic
13C2×C22⋊D541—22no—
14D4×D541—21no—
15D4×D541—22no—
16#22575824—21no—
17#22575821—21no—
18#22575820C2211yescharacteristic, complemented
19C4×Dic541C2211yescharacteristic, complemented
20#41×C541C2211yescharacteristic
21C2×D4×C541C2211yescharacteristic, complemented
22SD16×C541—21no—
23D8×C541—21no—
24M16×C541C2211yescharacteristic, complemented
25C22×D541—22no—
26C22×D541D412yes—
27Dic1082D411yescharacteristic, complemented
28D2164—22no—
29D2164—21no—
30D2164—21no—
31D2164D411yescharacteristic, complemented
32C22⋊D541—22no—
33C22⋊D541—21no—
34C22⋊D541—44no—
35C2×Dic541—21no—
36C4×D541—22no—
37C4×D541—21no—
38#16864513—21no—
39C23×C541—21no—
40Q8×C541D411yescharacteristic, complemented
41D4×C541—21no—
42D4×C541—21no—
43D4×C541—21no—
44D4×C541D411yescharacteristic, complemented
45C2×C4×C541—21no—
46C2×C4×C541C2311yescharacteristic
47C8×C541—21no—
48C22×C541—21no—
49C22×C541—42no—
50C22×C541—41no—
51C22×C541C2×D411yescharacteristic
52C2×D541—22no—
53C2×D541—21no—
54C2×D541—42no—
55C2×D541—82no—
56C4×C541—21no—
57C4×C541C2×D411yescharacteristic
58C4×C541C2×D411yescharacteristic
59Dic541—22no—
60Dic541—21no—
61C2×C541—21no—
62C2×C541—41no—
63C2×C541—81no—
64C2×C541#12011yescharacteristic
65D541—42no—
66D541—41no—
67C541#45311yescharacteristic, complemented, Sylow
68#453—5411nomaximal, Sylow
69H(5,𝔽2)—5411no—
70AGL(1,ℤ/8)—5411no—
71AGL(1,ℤ/8)D54111yescharacteristic, complemented
72#127—5411no—
73#104—5411no—
74#104—5411no—
75#100—5411no—
76#41—5411no—
77#41—10821no—
78#41—10821no—
79#41C2×D54111yescharacteristic
80C2×D4—5411no—
81C2×D4—10821no—
82C2×D4—10822no—
83C2×D4—10821no—
84C2×D4—10822no—
85C2×D4C2×D54111yescharacteristic, complemented
86SD16—21no—
87SD16—10821no—
88D8—21no—
89D8—10821no—
90M16—5411no—
91M16C2×D54111yescharacteristic, complemented
92C42—5411no—
93C23—21no—
94C23—5412no—
95C23—10822no—
96Q8—5411no—
97Q8C22⋊D54111yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—5411no—
102D4—10822no—
103D4—10822no—
104D4—10821no—
105D4—10821no—
106D4—10821no—
107D4—21644no—
108D4C22⋊D54111yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—10822no—
111C2×C4—10821no—
112C2×C4—10821no—
113C2×C4C22×D54111yescharacteristic
114C8—21no—
115C8—10821no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—10821no—
120C22—10822no—
121C22—21642no—
122C22—43282no—
123C22D4×D54111yescharacteristic
124C4—21no—
125C4—10822no—
126C4—10821no—
127C4D4×D54111yescharacteristic
128C4C2×C22⋊D54111yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—21642no—
133C2—21641no—
134C2#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#453
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. #31772674C2semidirect
2. #31772654C2semidirect
3. #31772624C2semidirect
4. #31772555C2semidirect
5. #31772554C2semidirect
6. #31772544C2semidirect
7. AGL(1,ℤ/8)×C541C2semidirect
18. #22575820C22semidirect
19. C4×Dic541C22semidirect
21. C2×D4×C541C22semidirect
24. M16×C541C22semidirect
27. Dic1082D4semidirect
31. D2164D4semidirect
40. Q8×C541D4semidirect
44. D4×C541D4semidirect
67. C541#453semidirect
71. AGL(1,ℤ/8)D541semidirect
85. C2×D4C2×D541semidirect
91. M16C2×D541semidirect
97. Q8C22⋊D541semidirect
108. D4C22⋊D541semidirect

Maximal subgroups

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

subgroupindex
#317726742
#317726542
#317726242
#317725552
#317725542
#317725442
AGL(1,ℤ/8)×C5412
#453541