Finite Group Databasebeta

← #26011675

Subgroups — #26011675

Order 11072.

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#19149726C211yesmaximal, characteristic
2#19149712C211yesmaximal, characteristic, complemented
3#19149709C211yesmaximal, characteristic, complemented
4#19149679C211yesmaximal, characteristic, complemented
5#19149607C211yesmaximal, characteristic, complemented
6#19149597C211yesmaximal, characteristic, complemented
7#104×C173C211yesmaximal, characteristic, complemented
8#14583826—21no—
9#14583826C2211yescharacteristic
10#14583825—22no—
11#14583825—21no—
12C2×Dic346—21no—
13C2×Dic346C2211yescharacteristic
14C2×Dic346C2211yescharacteristic
15Q8×D173—21no—
16Dic692—21no—
17#14583816—21no—
18#14583815—21no—
19#14583814—21no—
20#14583810C2211yescharacteristic
21C4⋊Dic173—22no—
22#41×C173C2211yescharacteristic
23M16×C173C2211yescharacteristic
24C42×C173C2211yescharacteristic
25Dic346—22no—
26Dic346—21no—
27Dic346—21no—
28Dic346—21no—
29Dic346—21no—
30Dic346D411yescharacteristic
31D692D411yescharacteristic
32C22⋊D173—22no—
33C22⋊D173—21no—
34C2×Dic173—22no—
35C2×Dic173—21no—
36C2×Dic173D412yes—
37C4×D173—22no—
38C4×D173—21no—
39#13063436—21no—
40Q8×C173D411yescharacteristic
41D4×C173—21no—
42D4×C173D411yescharacteristic
43C2×C4×C173—21no—
44C2×C4×C173—21no—
45C2×C4×C173C2311yescharacteristic
46C8×C173—21no—
47C22×C173—21no—
48C22×C173C2×D411yescharacteristic
49C2×D173—21no—
50C4×C173—22no—
51C4×C173—21no—
52C4×C173C2×D411yescharacteristic
53C4×C173C2×D411yescharacteristic
54Dic173—21no—
55Dic173—22no—
56Dic173—41no—
57C2×C173—21no—
58C2×C173—41no—
59C2×C173#12011yescharacteristic
60D173—41no—
61C173#45611yescharacteristic, complemented, Sylow
62#456—1731nomaximal, Sylow
632−1+4—1731no—
64#137—1731no—
65#137—1731no—
66C4⋊Q8—1731no—
67#104—1731no—
68#104D17311yescharacteristic, complemented
69#101—1731no—
70#41—3461no—
71#41—3461no—
72#41—3462no—
73#41—1731no—
74#41C2×D17311yescharacteristic
75C2×Q8—3461no—
76C2×Q8—3461no—
77C2×Q8—1731no—
78C2×Q8—1731no—
79Q16—3461no—
80Q16—3461no—
81SD16—3461no—
82SD16—3461no—
83M16—1731no—
84M16C2×D17311yescharacteristic
85C4⋊C4—3462no—
86C42C2×D17311yescharacteristic
87Q8—3462no—
88Q8—3461no—
89Q8—3461no—
90Q8—3461no—
91Q8—3461no—
92Q8—1731no—
93Q8D69211yescharacteristic
94D4—21no—
95D4—3462no—
96D4—3461no—
97D4—1731no—
98D4D69211yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3462no—
102C2×C4—3462no—
103C2×C4—3461no—
104C2×C4—3461no—
105C2×C4—1732no—
106C2×C4C22×D17311yescharacteristic
107C8—21no—
108C8—3461no—
109C22—21no—
110C22—3461no—
111C22D4×D17311yescharacteristic
112C4—22no—
113C4—21no—
114C4—3461no—
115C4—3462no—
116C4—6921no—
117C4D4×D17311yescharacteristic
118C4C2×D69211yescharacteristic
119C2—21no—
120C2—41no—
121C2—6921no—
122C2#1914964911yescharacteristic
subgroupG/H
centerC2#19149649
commutator, cosocleC2×C4×C173C23
FrattiniC2×C4C22×D173
Fitting#104×C173C2
socleC2×C173#120
prime radical#19149726C2
hypercenter#104D173
hypocenterC173#456
LCSG ▷ C2×C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #19149712C2semidirect
3. #19149709C2semidirect
4. #19149679C2semidirect
5. #19149607C2semidirect
6. #19149597C2semidirect
7. #104×C173C2semidirect
61. C173#456semidirect
68. #104D173semidirect

Maximal subgroups

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

subgroupindex
#191497262
#191497122
#191497092
#191496792
#191496072
#191495972
#104×C1732
#456173