Finite Group Databasebeta

← #11782562

Subgroups — #11782562

Order 1152.

373 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 373 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#4681C212yesmaximal
2#10590312C211yesmaximal, characteristic
3#10590312C211yesmaximal, characteristic
4#10590290C212yesmaximal
5C8×C3⋊(C3⋊C8)C211yesmaximal, characteristic
6#71214—32nomaximal
7C3×#869C2212yes—
8C3×#869C2212yes—
9C32×C4×C8C2211yescharacteristic
10C4×C3⋊(C3⋊C8)C2211yescharacteristic
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×#816—24no—
13#63576—22no—
14#63576—22no—
15#63565—24no—
16C3×#487—32no—
17#5093—32no—
18#5079—32no—
19#5078—32no—
20#5078—32no—
21#4681D312yes—
22C8×C3⋊C8—32no—
23C8×C3⋊C8—61no—
24C2×C3×Dic6—22no—
25C2×C3×Dic6—22no—
26C2×C32×C8D412yes—
27C32×C42C2311yescharacteristic
28C2×C3⋊(C3⋊C8)D412yes—
29C2×C3⋊(C3⋊C8)D412yes—
30C3×C4⋊Dic3—22no—
31C3×C4⋊Dic3—22no—
32C3×C4⋊Dic3—22no—
33C3×C4⋊Dic3—22no—
34#1710—91noSylow
35C3×C4⋊Q8—32no—
36C3×C4⋊Q8—32no—
37#869C2×D312yes—
38#869C2×D312yes—
39C3×#103—64no—
40C3×C4×C8—21no—
41C3×C4×C8C2×D312yes—
42#835—64no—
43#816—24no—
44#810—64no—
45#807—64no—
46#807—64no—
47C4×C3⋊C8—32no—
48C4×C3⋊C8—32no—
49C4×C3⋊C8—61no—
50C4×C3⋊C8—61no—
51C2×C32×C4C2×D411yescharacteristic
52C2×C32×C4C2×D411yescharacteristic
53C2×C32×C4C2×D411yescharacteristic
54C2×C3×Dic3—42no—
55C2×C3×Dic3—42no—
56C3×Dic6—44no—
57C3×Dic6—44no—
58C32×C8—22no—
59C3⋊(C3⋊C8)—22no—
60C3⋊(C3⋊C8)Q1614yes—
61#500—91no—
62#500—91no—
63#487—32no—
64#487—92no—
65C82—91no—
66C2×C3×Q8—62no—
67C2×C3×Q8—62no—
68C2×Dic6—22no—
69C2×Dic6—22no—
70C2×C3×C8—22no—
71C2×C3×C8#6714yes—
72C3×C4⋊C4—62no—
73C3×C4⋊C4—62no—
74C3×C4⋊C4—62no—
75C3×C4⋊C4—62no—
76C3×C42—21no—
77C3×C42C22×D312yes—
78C4⋊Dic3—22no—
79C4⋊Dic3—22no—
80C4⋊Dic3—22no—
81C4⋊Dic3—22no—
82C2×C3⋊C8—34no—
83C2×C3⋊C8—34no—
84C2×C3⋊C8—62no—
85C2×C3⋊C8—62no—
86C22×C32#12711yescharacteristic
87C32×C4C2×Q1612yes—
88C32×C4#13512yes—
89C32×C4#13512yes—
90C3×Dic3—82no—
91C3×Dic3—82no—
92C4⋊Q8—32no—
93C4⋊Q8—32no—
94#107—182no—
95#107—182no—
96#103—64no—
97#103—184no—
98C4×C8—91no—
99C4×C8—91no—
100C4×C8D3211yescharacteristic
101C3×Q8—124no—
102C3×Q8—124no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—122no—
107C2×C3×C4—122no—
108C2×C3×C4D3×D412yes—
109C2×C3×C4D3×D412yes—
110C2×C3×C4C2×#6712yes—
111C2×Dic3—42no—
112C2×Dic3—42no—
113Dic6—44no—
114Dic6—44no—
115C3×C8—24no—
116C3×C8—24no—
117C3⋊C8—38no—
118C3⋊C8—64no—
119C3⋊C8—64no—
120C3⋊C8—64no—
121C2×C32#49411yescharacteristic
122C2×C32#49511yescharacteristic
123C2×C32#49511yescharacteristic
124C2×Q8—62no—
125C2×Q8—62no—
126C2×C8—92no—
127C2×C8—92no—
128C2×C8#62512yes—
129C4⋊C4—62no—
130C4⋊C4—62no—
131C4⋊C4—62no—
132C4⋊C4—62no—
133C42C2×D3211yescharacteristic
134C22×C3—21no—
135C22×C3#94012yes—
136C3×C4—22no—
137C3×C4—22no—
138C3×C4—22no—
139C3×C4—242no—
140C3×C4—242no—
141C3×C4#91614yes—
142C3×C4D3×Q1614yes—
143C3×C4#95014yes—
144Dic3—82no—
145Dic3—82no—
146C32#171011yescharacteristic, complemented, Sylow
147Q8—124no—
148Q8—124no—
149C2×C4—122no—
150C2×C4—122no—
151C2×C4#380211yescharacteristic
152C2×C4#380211yescharacteristic
153C2×C4C2×#62511yescharacteristic
154C8—22no—
155C8—94no—
156C8—182no—
157C2×C3—21no—
158C2×C3—21no—
159C2×C3—21no—
160C2×C3#505912yes—
161C2×C3#516812yes—
162C2×C3#518312yes—
163C22#6391411yescharacteristic
164C4—242no—
165C4—242no—
166C4#6380212yes—
167C4#6380912yes—
168C4#6382212yes—
169C3—21no—
170C3#7121412yescomplemented
171C2#1059035311yescharacteristic
172C2#1059086711yescharacteristic
173C2#1059090511yescharacteristic
subgroupG/H
centerC22#63914
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#127
hypercenterC4×C8D32
hypocenterC32#1710
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
146. C32#1710semidirect
170. C3#71214semidirect

Maximal subgroups

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

subgroupindex
C3×#46812
#105903122
#105902902
C8×C3⋊(C3⋊C8)2
#712143