Finite Group Databasebeta

← #11772754

Subgroups — #11772754

Order 1152.

264 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 20 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#10592941C211yesmaximal, characteristic
2#10590212C211yesmaximal, characteristic, complemented
3#10590210C211yesmaximal, characteristic, complemented
4C32×H(5,𝔽2)C411yescharacteristic
5#64160—21no—
6#64145C2211yescharacteristic
7#63780—21no—
8#63777—21no—
9#63664—21no—
10#63660C411yescharacteristic
11#5242—62no—
12C32×#41—21no—
13C32×#41—41no—
14C2×C32×D4—41no—
15C2×C32×D4—41no—
16C2×C32×D4C2×C411yescharacteristic
17C2×#634D411yescharacteristic
18#3792—41no—
19C2×#622—41no—
20#3757—41no—
21#3756—41no—
22#3754—41no—
23C4×C3⋊Dic3D411yescharacteristic
24#3748—21no—
25#1403—91nomaximal, Sylow
26C3×H(5,𝔽2)—22no—
27#951—64no—
28#936—62no—
29#837—64no—
30#833—62no—
31C23×C32—21no—
32C23×C32—41no—
33C32×Q8—21no—
34C32×D4—21no—
35C32×D4—41no—
36C32×D4—42no—
37C32×D4—41no—
38C2×C32×C4—41no—
39C2×C32×C4—41no—
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C3⋊Dic3—21no—
42C2×C3⋊Dic3—21no—
43#634—41no—
44#622—42no—
45#622—81no—
46C3⋊(C3⋊C8)—41no—
47#455—91no—
48#355—91no—
49#329—91no—
50C3×#41—24no—
51C3×#41—44no—
52C2×C3×D4—22no—
53C2×C3×D4—44no—
54C2×C3×D4—44no—
55C2×Dic6—62no—
56#217—124no—
57#216—124no—
58#214—124no—
59C4×Dic3—62no—
60#208—64no—
61C22×C32—41no—
62C22×C32—41no—
63C22×C32—81no—
64C22×C32—161no—
65C22×C32#9911yescharacteristic
66C32×C4—21no—
67C32×C4—41no—
68C3⋊Dic3—41no—
69C3⋊Dic3—41no—
70H(5,𝔽2)#15711yescharacteristic
71#137—181no—
72#124—91no—
73#104—181no—
74#101—181no—
75#100—91no—
76#97—181no—
77C23×C3—24no—
78C23×C3—44no—
79C3×Q8—24no—
80C3×D4—24no—
81C3×D4—44no—
82C3×D4—44no—
83C3×D4—48no—
84C2×C3×C4—22no—
85C2×C3×C4—44no—
86C2×C3×C4—44no—
87C2×Dic3—122no—
88C2×Dic3—122no—
89Dic6—124no—
90C3⋊C8—124no—
91C2×C32—21no—
92C2×C32—81no—
93C2×C32—81no—
94C2×C32AΣL(1,𝔽16)11yescharacteristic
95#41—21no—
96#41—41no—
97C2×Q8—91no—
98C2×D4—41no—
99C2×D4—41no—
100C2×D4C2×#15711yescharacteristic
101Q16—361no—
102SD16—361no—
103M16—181no—
104M16—361no—
105C2×C8—361no—
106C22⋊C4—361no—
107C42—91no—
108C22×C3—22no—
109C22×C3—44no—
110C22×C3—44no—
111C22×C3—84no—
112C22×C3—164no—
113C3×C4—24no—
114C3×C4—44no—
115Dic3—242no—
116Dic3—242no—
117C32#140311yescharacteristic, complemented, Sylow
118C23—21no—
119C23—41no—
120Q8—21no—
121Q8—361no—
122D4—21no—
123D4—41no—
124D4—42no—
125D4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—181no—
129C2×C4—181no—
130C2×C4C22⋊#15711yescharacteristic
131C8—361no—
132C8—362no—
133C8—721no—
134C2×C3—22no—
135C2×C3—42no—
136C2×C3—84no—
137C2×C3—84no—
138C22—41no—
139C22—41no—
140C22—81no—
141C22—161no—
142C22#6378611yescharacteristic
143C4—21no—
144C4—41no—
145C4—361no—
146C4—361no—
147C3—22no—
148C2—21no—
149C2—81no—
150C2—81no—
151C2#1059022311yescharacteristic
subgroupG/H
centerC2#10590223
commutatorC2×C32×D4C2×C4
FrattiniC2×D4C2×#157
Fitting, prime radicalC32×H(5,𝔽2)C4
socleC2×C32AΣL(1,𝔽16)
cosocle#64145C22
hypercenterH(5,𝔽2)#157
hypocenterC32#1403
LCSG ▷ C2×C32×D4 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. #10590212C2semidirect
3. #10590210C2semidirect
117. C32#1403semidirect

Maximal subgroups

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

subgroupindex
#105929412
#105902122
#105902102
#14039