Finite Group Databasebeta

← #45687598

Subgroups — #45687598

Order 33344.

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#30659754C211yesmaximal, characteristic, complemented
2#30659734C211yesmaximal, characteristic, complemented
3#30659704C211yesmaximal, characteristic, complemented
4#30659635C211yesmaximal, characteristic, complemented
5#30659634C211yesmaximal, characteristic, complemented
6#30659624C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C521C211yesmaximal, characteristic, complemented
8#22552365—21no—
9#22552364—21no—
10#22552364C2211yescharacteristic
11C2×D2084—21no—
12C2×D2084C2211yescharacteristic
13C2×C22⋊D521—22no—
14D4×D521—22no—
15D4×D521—21no—
16#22552352—21no—
17#22552349—21no—
18#22552348C2211yescharacteristic, complemented
19C4×Dic521C2211yescharacteristic, complemented
20#41×C521C2211yescharacteristic
21C2×D4×C521C2211yescharacteristic, complemented
22SD16×C521—21no—
23D8×C521—21no—
24M16×C521C2211yescharacteristic, complemented
25C22×D521—22no—
26C22×D521D412yes—
27Dic1042D411yescharacteristic, complemented
28D2084—22no—
29D2084—21no—
30D2084—21no—
31D2084D411yescharacteristic, complemented
32C22⋊D521—22no—
33C22⋊D521—21no—
34C22⋊D521—44no—
35C2×Dic521—21no—
36C4×D521—22no—
37C4×D521—21no—
38#16861960—21no—
39C23×C521—21no—
40Q8×C521D411yescharacteristic, complemented
41D4×C521—21no—
42D4×C521—21no—
43D4×C521—21no—
44D4×C521D411yescharacteristic, complemented
45C2×C4×C521—21no—
46C2×C4×C521C2311yescharacteristic
47C8×C521—21no—
48C22×C521—21no—
49C22×C521—42no—
50C22×C521—41no—
51C22×C521C2×D411yescharacteristic
52C2×D521—22no—
53C2×D521—21no—
54C2×D521—42no—
55C2×D521—82no—
56C4×C521—21no—
57C4×C521C2×D411yescharacteristic
58C4×C521C2×D411yescharacteristic
59Dic521—22no—
60Dic521—21no—
61C2×C521—21no—
62C2×C521—41no—
63C2×C521—81no—
64C2×C521#12011yescharacteristic
65D521—42no—
66D521—41no—
67C521#45311yescharacteristic, complemented, Sylow
68#453—5211nomaximal, Sylow
69H(5,𝔽2)—5211no—
70AGL(1,ℤ/8)—5211no—
71AGL(1,ℤ/8)D52111yescharacteristic, complemented
72#127—5211no—
73#104—5211no—
74#104—5211no—
75#100—5211no—
76#41—5211no—
77#41—10421no—
78#41—10421no—
79#41C2×D52111yescharacteristic
80C2×D4—5211no—
81C2×D4—10421no—
82C2×D4—10422no—
83C2×D4—10421no—
84C2×D4—10422no—
85C2×D4C2×D52111yescharacteristic, complemented
86SD16—21no—
87SD16—10421no—
88D8—21no—
89D8—10421no—
90M16—5211no—
91M16C2×D52111yescharacteristic, complemented
92C42—5211no—
93C23—21no—
94C23—5212no—
95C23—10422no—
96Q8—5211no—
97Q8C22⋊D52111yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—5211no—
102D4—10422no—
103D4—10422no—
104D4—10421no—
105D4—10421no—
106D4—10421no—
107D4—20844no—
108D4C22⋊D52111yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—10422no—
111C2×C4—10421no—
112C2×C4—10421no—
113C2×C4C22×D52111yescharacteristic
114C8—21no—
115C8—10421no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—10421no—
120C22—10422no—
121C22—20842no—
122C22—41682no—
123C22D4×D52111yescharacteristic
124C4—21no—
125C4—10422no—
126C4—10421no—
127C4D4×D52111yescharacteristic
128C4C2×C22⋊D52111yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—20842no—
133C2—20841no—
134C2#3065967611yescharacteristic
subgroupG/H
centerC2#30659676
commutator, cosocleC2×C4×C521C23
FrattiniC2×C4C22×D521
FittingAGL(1,ℤ/8)×C521C2
socleC2×C521#120
hypercenterAGL(1,ℤ/8)D521
hypocenterC521#453
LCSG ▷ C2×C4×C521 ▷ C2×C521 ▷ C521
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30659754C2semidirect
2. #30659734C2semidirect
3. #30659704C2semidirect
4. #30659635C2semidirect
5. #30659634C2semidirect
6. #30659624C2semidirect
7. AGL(1,ℤ/8)×C521C2semidirect
18. #22552348C22semidirect
19. C4×Dic521C22semidirect
21. C2×D4×C521C22semidirect
24. M16×C521C22semidirect
27. Dic1042D4semidirect
31. D2084D4semidirect
40. Q8×C521D4semidirect
44. D4×C521D4semidirect
67. C521#453semidirect
71. AGL(1,ℤ/8)D521semidirect
85. C2×D4C2×D521semidirect
91. M16C2×D521semidirect
97. Q8C22⋊D521semidirect
108. D4C22⋊D521semidirect

Maximal subgroups

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

subgroupindex
#306597542
#306597342
#306597042
#306596352
#306596342
#306596242
AGL(1,ℤ/8)×C5212
#453521