Finite Group Databasebeta

← #11798949

Subgroups — #11798949

Order 1152.

363 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 363 conjugacy classes of subgroups — too many to draw. Only its 82 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
1Q16×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#829C212yesmaximal
3#10590905C211yesmaximal, characteristic
4#10589133C211yesmaximal, characteristic
5#10589118C212yesmaximal
6#71497—32nomaximal
7C2×C32×Q16C2211yescharacteristic
8Q8×C3⋊Dic3—21no—
9C2×C3×Dic12C2212yes—
10#63873—21no—
11C2×#3718—21no—
12#63662—21no—
13#63645C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15C3×#829—24no—
16C2×C3×C3⋊C16C2212yes—
17C2×C3×Q32—32no—
18#5183—32no—
19Dic3×Q16—32no—
20Dic3×Q16—61no—
21C2×#829D312yes—
22#4564—32no—
23#4503—32no—
24Dic3⋊C16—32no—
25C2×C32×Q8—21no—
26C2×C3×Dic6—22no—
27C32×Q16—21no—
28C32×Q16D412yes—
29C2×C32×C8C2311yescharacteristic
30C4⋊(C3⋊Dic3)—21no—
31C4⋊(C3⋊Dic3)—41no—
32C4×C3⋊Dic3—41no—
33C4×C3⋊Dic3D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×Dic12—22no—
36C3×Dic12—22no—
37#3724—41no—
38#3724—41no—
39#3718—42no—
40C3×C3⋊C16—22no—
41#2209—91noSylow
42C2×C3×Q16—21no—
43C2×C3×Q16—32no—
44C2×C3×Q16C2×D312yes—
45Q8×Dic3—62no—
46Q8×Dic3—62no—
47#944—62no—
48C2×#216—62no—
49C2×Dic12C2×D312yes—
50C3×Q32—64no—
51C2×C3×C16—32no—
52#835—62no—
53#835—62no—
54#829—24no—
55#818—32no—
56#818—61no—
57C8×Dic3—32no—
58C8×Dic3—61no—
59C2×C3⋊C16C2×D312yes—
60C32×Q8—22no—
61C32×Q8—41no—
62C2×C32×C4—41no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3D811yescharacteristic
66C2×C3⋊Dic3D811yescharacteristic
67C2×C3×Dic3—42no—
68C3×Dic6—42no—
69C3×Dic6—42no—
70C32×C8C2×D411yescharacteristic
71C32×C8#4111yescharacteristic
72C3⋊(C3⋊C8)—21no—
73C2×Q32—32no—
74#494—91no—
75C4×Q16—91no—
76C4⋊C16—91no—
77#358—92no—
78C2×C3×Q8—22no—
79C2×C3×Q8—22no—
80C2×C3×Q8—62no—
81C2×Dic6—22no—
82C3×Q16—22no—
83C3×Q16—22no—
84C3×Q16—22no—
85C3×Q16—62no—
86C3×Q16—62no—
87C3×Q16#6714yes—
88C2×C3×C8—21no—
89C2×C3×C8C22×D312yes—
90#216—124no—
91C4⋊Dic3—62no—
92C4⋊Dic3—62no—
93C4⋊Dic3—122no—
94C4⋊Dic3—122no—
95Dic3⋊C4—122no—
96Dic3⋊C4—122no—
97C4×Dic3—32no—
98C4×Dic3—61no—
99C4×Dic3—122no—
100C4×Dic3—122no—
101C2×C3⋊C8—32no—
102C2×C3⋊C8—61no—
103Dic12—22no—
104Dic12—22no—
105C3×C16—62no—
106C3⋊C16—22no—
107C22×C32C2×D811yescharacteristic
108C32×C4—42no—
109C32×C4#12111yescharacteristic
110C32×C4AGL(1,ℤ/8)11yescharacteristic
111C3⋊Dic3—21no—
112C3⋊Dic3—81no—
113C3⋊Dic3Q3212yescomplemented
114C3×Dic3—82no—
115C2×Q16—32no—
116C2×Q16—181no—
117C2×Q16D3211yescharacteristic
118C4⋊Q8—181no—
119C4×Q8—181no—
120Q32—64no—
121C2×C16—32no—
122#107—91no—
123#103—181no—
124C4×C8—91no—
125C3×Q8—24no—
126C3×Q8—24no—
127C3×Q8—42no—
128C3×Q8—42no—
129C3×Q8—122no—
130C3×Q8—122no—
131C2×C3×C4—21no—
132C2×C3×C4—42no—
133C2×C3×C4—42no—
134C2×C3×C4—122no—
135C2×C3×C4D3×D412yes—
136C2×Dic3—32no—
137C2×Dic3—32no—
138C2×Dic3—42no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—122no—
142C2×Dic3—122no—
143Dic6—42no—
144Dic6—42no—
145C3×C8—21no—
146C3×C8—21no—
147C3×C8#23712yes—
148C3×C8C2×#6712yes—
149C3⋊C8—62no—
150C3⋊C8—121no—
151C2×C32#45911yescharacteristic
152C2×C32C2×Q3211yescharacteristic
153C2×C32#51011yescharacteristic
154C2×Q8—21no—
155C2×Q8—62no—
156Q16—21no—
157Q16—62no—
158Q16—62no—
159Q16—362no—
160Q16#62512yes—
161C2×C8—91no—
162C2×C8C2×D3211yescharacteristic
163C4⋊C4—181no—
164C4⋊C4—361no—
165C4⋊C4—361no—
166C4⋊C4—361no—
167C42—91no—
168C42—361no—
169C16—62no—
170C22×C3—21no—
171C22×C3D3×D812yes—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—44no—
175C3×C4—44no—
176C3×C4—242no—
177C3×C4#91112yes—
178C3×C4#93912yes—
179Dic3—34no—
180Dic3—62no—
181Dic3—62no—
182Dic3—82no—
183Dic3—121no—
184Dic3—242no—
185Dic3—242no—
186C32#220911yescharacteristic, complemented, Sylow
187Q8—22no—
188Q8—41no—
189Q8—122no—
190Q8—122no—
191C2×C4—41no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—122no—
195C2×C4—361no—
196C2×C4#381111yescharacteristic
197C8—181no—
198C8#380511yescharacteristic
199C8C2×#62511yescharacteristic
200C2×C3—21no—
201C2×C3—21no—
202C2×C3—21no—
203C2×C3D3×Q3212yes—
204C2×C3#491812yes—
205C2×C3#515012yes—
206C22#6392611yescharacteristic
207C4—42no—
208C4—92no—
209C4—181no—
210C4—242no—
211C4—721no—
212C4#6392711yescharacteristic
213C4#6398011yescharacteristic
214C3—21no—
215C3#7149712yescomplemented
216C2#1059104311yescharacteristic
217C2#1059104411yescharacteristic
218C2#1059148611yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socle, prime radicalC22×C32C2×D8
hypercenterC2×Q16D32
hypocenterC32#2209
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
113. C3⋊Dic3Q32semidirect
186. C32#2209semidirect
215. C3#71497semidirect

Maximal subgroups

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

subgroupindex
Q16×C3⋊Dic32
C2×C3×#8292
#105909052
#105891332
#105891182
#714973