Finite Group Databasebeta

← #11798887

Subgroups — #11798887

Order 1152.

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

normal subgroups only

This group has 403 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, complemented
2C2×C3×#828C212yesmaximal, complemented
3#10590886C211yesmaximal, characteristic
4#10589133C211yesmaximal, characteristic, complemented
5#10589115C212yesmaximal, complemented
6#71475—32nomaximal
7C2×C32×Q16C2211yescharacteristic
8Q8×C3⋊Dic3—21no—
9C2×C3×D24C2212yes—
10#63914—21no—
11C2×#3713—21no—
12#63662—21no—
13#63645C2211yescharacteristic
14C8×C3⋊Dic3C2211yescharacteristic
15C3×#828—24no—
16C2×C3×C3⋊C16C2212yes—
17C2×C3×SD32—32no—
18Dic3×Q16—32no—
19Dic3×Q16—61no—
20C2×#828D312yescomplemented
21#5151—32no—
22#4562—32no—
23#4509—32no—
24Dic3⋊C16—32no—
25C2×C32×Q8—21no—
26C2×C3×D12—22no—
27C2×#625—41no—
28C2×#625—41no—
29C32×Q16—21no—
30C32×Q16D412yescomplemented
31C2×C32×C8C2311yescharacteristic
32C4⋊(C3⋊Dic3)—21no—
33C4⋊(C3⋊Dic3)—41no—
34C4×C3⋊Dic3—41no—
35C4×C3⋊Dic3D411yescharacteristic
36C2×C3⋊(C3⋊C8)D411yescharacteristic
37C3×D24—22no—
38C3×D24—22no—
39#3713—42no—
40C3×C3⋊C16—22no—
41#2207—91noSylow
42C2×C3×Q16—21no—
43C2×C3×Q16C2×D312yes—
44C2×C3×D8—32no—
45Q8×Dic3—62no—
46Q8×Dic3—62no—
47#940—62no—
48C2×#213—62no—
49C2×D24C2×D312yes—
50C3×SD32—64no—
51C2×C3×C16—32no—
52#835—62no—
53#835—62no—
54#828—24no—
55#818—32no—
56#818—61no—
57C8×Dic3—32no—
58C8×Dic3—61no—
59C2×C3⋊C16C2×D312yes—
60C22×C3×D3—42no—
61C32×Q8—22no—
62C32×Q8—41no—
63C2×C32×C4—41no—
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3D811yescharacteristic
67C2×C3⋊Dic3D811yescharacteristic
68C3×D12—42no—
69C3×D12—42no—
70#625—82no—
71#625—82no—
72C32×C8C2×D411yescharacteristic
73C32×C8#4111yescharacteristic
74C3⋊(C3⋊C8)—21no—
75C2×SD32—32no—
76#493—91no—
77C4×Q16—91no—
78C4⋊C16—91no—
79#357—92no—
80C2×C3×Q8—22no—
81C2×C3×Q8—22no—
82C2×C3×D4—62no—
83C2×#67—122no—
84C2×#67—122no—
85C2×D12—22no—
86C3×Q16—22no—
87C3×Q16—22no—
88C3×Q16—22no—
89C3×Q16#6714yescomplemented
90C3×D8—62no—
91C3×D8—62no—
92C2×C3×C8—21no—
93C2×C3×C8C22×D312yes—
94#213—124no—
95C4⋊Dic3—62no—
96C4⋊Dic3—62no—
97C4⋊Dic3—122no—
98C4⋊Dic3—122no—
99C4×Dic3—32no—
100C4×Dic3—61no—
101C4×Dic3—122no—
102C4×Dic3—122no—
103C2×C3⋊C8—32no—
104C2×C3⋊C8—61no—
105D24—22no—
106D24—22no—
107C3×C16—62no—
108C3⋊C16—22no—
109C22×C32C2×D811yescharacteristic
110C2×C3×D3—82no—
111C2×C3×D3—82no—
112C2×C3×D3—82no—
113C32×C4—42no—
114C32×C4#12111yescharacteristic
115C32×C4AGL(1,ℤ/8)11yescharacteristic
116C3⋊Dic3—21no—
117C3⋊Dic3—81no—
118C3⋊Dic3SD3212yescomplemented
119C2×Q16D3211yescharacteristic
120C2×D8—32no—
121C2×D8—181no—
122#127—181no—
123C4×Q8—181no—
124SD32—64no—
125C2×C16—32no—
126#107—91no—
127#103—181no—
128C4×C8—91no—
129C23×C3—122no—
130C22×D3—42no—
131C3×Q8—24no—
132C3×Q8—24no—
133C3×Q8—42no—
134C3×Q8—42no—
135C3×D4—122no—
136C3×D4—122no—
137C2×C3×C4—21no—
138C2×C3×C4—42no—
139C2×C3×C4—42no—
140C2×C3×C4D3×D412yes—
141#67—244no—
142#67—244no—
143C2×Dic3—32no—
144C2×Dic3—32no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—122no—
148C2×Dic3—122no—
149D12—42no—
150D12—42no—
151C3×C8—21no—
152C3×C8—21no—
153C3×C8#23712yes—
154C3×C8C2×#6712yes—
155C3⋊C8—62no—
156C3⋊C8—121no—
157C2×C32#45911yescharacteristic
158C2×C32C2×SD3211yescharacteristic
159C2×C32#50911yescharacteristic
160C3×D3—162no—
161C2×Q8—21no—
162C2×D4—62no—
163C2×D4—361no—
164C2×D4—361no—
165Q16—21no—
166Q16#62512yescomplemented
167D8—62no—
168D8—62no—
169D8—362no—
170C2×C8—91no—
171C2×C8C2×D3211yescharacteristic
172C4⋊C4—181no—
173C4⋊C4—361no—
174C42—91no—
175C42—361no—
176C16—62no—
177C22×C3—21no—
178C22×C3—242no—
179C22×C3—242no—
180C22×C3—242no—
181C22×C3D3×D812yes—
182C2×D3—82no—
183C2×D3—82no—
184C2×D3—82no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—44no—
188C3×C4—44no—
189C3×C4#91112yes—
190C3×C4#93912yes—
191Dic3—34no—
192Dic3—62no—
193Dic3—62no—
194Dic3—121no—
195Dic3—242no—
196Dic3—242no—
197C32#220711yescharacteristic, complemented, Sylow
198C23—122no—
199Q8—22no—
200Q8—41no—
201D4—122no—
202D4—122no—
203D4—722no—
204D4—722no—
205C2×C4—41no—
206C2×C4—91no—
207C2×C4—91no—
208C2×C4—361no—
209C2×C4#381111yescharacteristic
210C8—181no—
211C8#380511yescharacteristic
212C8C2×#62511yescharacteristic
213C2×C3—21no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—482no—
217C2×C3D3×SD3212yes—
218C2×C3#491412yes—
219C2×C3#515012yes—
220D3—162no—
221C22—242no—
222C22—242no—
223C22—242no—
224C22#6392611yescharacteristic
225C4—42no—
226C4—92no—
227C4—181no—
228C4—721no—
229C4#6392711yescharacteristic
230C4#6398011yescharacteristic
231C3—21no—
232C3#7147512yescomplemented
233C2—482no—
234C2#1059103911yescharacteristic
235C2#1059104011yescharacteristic
236C2#1059148611yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC2×C32×Q16C22
socleC22×C32C2×D8
prime radical#10590886C2
hypercenterC2×Q16D32
hypocenterC32#2207
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
1. Q16×C3⋊Dic3C2semidirect
2. C2×C3×#828C2semidirect
4. #10589133C2semidirect
5. #10589115C2semidirect
20. C2×#828D3semidirect
30. C32×Q16D4semidirect
89. C3×Q16#67semidirect
118. C3⋊Dic3SD32semidirect
166. Q16#625semidirect
197. C32#2207semidirect
232. C3#71475semidirect

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×#8282
#105908862
#105891332
#105891152
#714753