Finite Group Databasebeta

← #45687616

Subgroups — #45687616

Order 33344.

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

normal subgroups only

This group has 142 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#30659755C211yesmaximal, characteristic
2#30659741C211yesmaximal, characteristic, complemented
3#30659738C211yesmaximal, characteristic, complemented
4#30659708C211yesmaximal, characteristic, complemented
5#30659636C211yesmaximal, characteristic, complemented
6#30659626C211yesmaximal, characteristic, complemented
7#104×C521C211yesmaximal, characteristic, complemented
8#22552364—21no—
9#22552364C2211yescharacteristic
10#22552363—22no—
11#22552363—21no—
12C2×Dic1042—21no—
13C2×Dic1042C2211yescharacteristic
14C2×Dic1042C2211yescharacteristic
15Q8×D521—21no—
16Dic2084—21no—
17#22552354—21no—
18#22552353—21no—
19#22552352—21no—
20#22552348C2211yescharacteristic
21C4⋊Dic521—22no—
22#41×C521C2211yescharacteristic
23M16×C521C2211yescharacteristic
24C42×C521C2211yescharacteristic
25Dic1042—22no—
26Dic1042—21no—
27Dic1042—21no—
28Dic1042—21no—
29Dic1042—21no—
30Dic1042D411yescharacteristic
31D2084D411yescharacteristic
32C22⋊D521—22no—
33C22⋊D521—21no—
34C2×Dic521—22no—
35C2×Dic521—21no—
36C2×Dic521D412yes—
37C4×D521—22no—
38C4×D521—21no—
39#16861960—21no—
40Q8×C521D411yescharacteristic
41D4×C521—21no—
42D4×C521D411yescharacteristic
43C2×C4×C521—21no—
44C2×C4×C521—21no—
45C2×C4×C521C2311yescharacteristic
46C8×C521—21no—
47C22×C521—21no—
48C22×C521C2×D411yescharacteristic
49C2×D521—21no—
50C4×C521—22no—
51C4×C521—21no—
52C4×C521C2×D411yescharacteristic
53C4×C521C2×D411yescharacteristic
54Dic521—21no—
55Dic521—22no—
56Dic521—41no—
57C2×C521—21no—
58C2×C521—41no—
59C2×C521#12011yescharacteristic
60D521—41no—
61C521#45611yescharacteristic, complemented, Sylow
62#456—5211nomaximal, Sylow
632−1+4—5211no—
64#137—5211no—
65#137—5211no—
66C4⋊Q8—5211no—
67#104—5211no—
68#104D52111yescharacteristic, complemented
69#101—5211no—
70#41—5211no—
71#41—10421no—
72#41—10422no—
73#41—10421no—
74#41C2×D52111yescharacteristic
75C2×Q8—5211no—
76C2×Q8—5211no—
77C2×Q8—10421no—
78C2×Q8—10421no—
79Q16—10421no—
80Q16—10421no—
81SD16—10421no—
82SD16—10421no—
83M16—5211no—
84M16C2×D52111yescharacteristic
85C4⋊C4—10422no—
86C42C2×D52111yescharacteristic
87Q8—5211no—
88Q8—10422no—
89Q8—10421no—
90Q8—10421no—
91Q8—10421no—
92Q8—10421no—
93Q8D208411yescharacteristic
94D4—21no—
95D4—5211no—
96D4—10422no—
97D4—10421no—
98D4D208411yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—5212no—
102C2×C4—10422no—
103C2×C4—10422no—
104C2×C4—10421no—
105C2×C4—10421no—
106C2×C4C22×D52111yescharacteristic
107C8—21no—
108C8—10421no—
109C22—21no—
110C22—10421no—
111C22D4×D52111yescharacteristic
112C4—22no—
113C4—21no—
114C4—10422no—
115C4—10421no—
116C4—20841no—
117C4D4×D52111yescharacteristic
118C4C2×D208411yescharacteristic
119C2—21no—
120C2—41no—
121C2—20841no—
122C2#3065967811yescharacteristic
subgroupG/H
centerC2#30659678
commutator, cosocleC2×C4×C521C23
FrattiniC2×C4C22×D521
Fitting#104×C521C2
socleC2×C521#120
prime radical#30659755C2
hypercenter#104D521
hypocenterC521#456
LCSG ▷ C2×C4×C521 ▷ C2×C521 ▷ C521
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #30659741C2semidirect
3. #30659738C2semidirect
4. #30659708C2semidirect
5. #30659636C2semidirect
6. #30659626C2semidirect
7. #104×C521C2semidirect
61. C521#456semidirect
68. #104D521semidirect

Maximal subgroups

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

subgroupindex
#306597552
#306597412
#306597382
#306597082
#306596362
#306596262
#104×C5212
#456521