Finite Group Databasebeta

← #11920949

Subgroups — #11920949

Order 1152.

342 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 33 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
1C2×C3⋊#857C211yesmaximal, characteristic
2C3×#384⋊C3C211yesmaximal, characteristic, complemented
3C3⋊#4623C211yesmaximal, characteristic, complemented
4#857⋊C4—33nomaximal
5#69592—31nomaximal
6C4×C3⋊S4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8C3⋊#857C412yescomplemented
9#5504—31no—
10C2×#857—33no—
11C3×#384D311yescharacteristic, complemented
12#4966—31no—
13#4964—31no—
14C2×#805—31no—
15#384⋊C3D313yescomplemented
16#4623—33no—
17#4530—31no—
18#4523—31no—
19C2×C3⋊S4—41no—
20C3×C4×A4—41no—
21C3⋊SL(2,ℤ/4)—41no—
22C3×C42⋊C3C2×C411yescharacteristic, complemented
23#1859—91noSylow
24C2×#235—31no—
25C4×S4—123no—
26C2×C3×C4⋊C4—31no—
27C2×C3×C4⋊C4—31no—
28C2×C3×C42C2×D311yescharacteristic
29C4×#67—61no—
30C4×#67—61no—
31#926—31no—
32C2×#208—31no—
33C2×#208—31no—
34#893—61no—
35#892—61no—
36D3×C4⋊C4—61no—
37#887—61no—
38C2×C42⋊C3C2×D313yes—
39#857—36no—
40#810—61no—
41#809—61no—
42#808—61no—
43#807—61no—
44#805—32no—
45#805—32no—
46C2×C3×A4—41no—
47C3⋊S4—42no—
48C4×C3⋊D3—161no—
49#520—91no—
50#428—91no—
51C2×#104—91no—
52#417—91no—
53#384C3⋊D311yescharacteristic, complemented
54#343—91no—
55#339—91no—
56C2×S4—123no—
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4S411yescharacteristic
60C2×#67—61no—
61#235—32no—
62#235—32no—
63#235—61no—
64#235—61no—
65C2×D12—31no—
66C2×C4×D3—61no—
67C2×C4×D3—61no—
68C2×C4×D3—61no—
69C2×Dic6—31no—
70C4×A4—43no—
71SL(2,ℤ/4)—123no—
72C3×C4⋊C4—61no—
73C3×C4⋊C4—61no—
74C3×C4⋊C4—61no—
75C3×C4⋊C4—61no—
76C3×C42—31no—
77C3×C42C4×D311yescharacteristic, complemented
78#217—61no—
79(C2×D3)⋊C4—61no—
80(C2×D3)⋊C4—61no—
81C4⋊Dic3—31no—
82C4⋊Dic3—31no—
83Dic3⋊C4—61no—
84Dic3⋊C4—61no—
85C4×Dic3—61no—
86C4×Dic3—61no—
87C4×Dic3—61no—
88#208—32no—
89#208—61no—
90#208—61no—
91#208—61no—
92C2×C3⋊C8—61no—
93C2×C3⋊C8—61no—
94C42⋊C3C4×D313yescomplemented
95C2×C3⋊D3—161no—
96C3×A4—41no—
97C32×C4—161no—
98C3⋊Dic3—161no—
99C2×#41—91no—
100C2×M16—91no—
101C2×M16—91no—
102C4×Q8—181no—
103C4×D4—181no—
104C4×D4—181no—
105C4×D4—181no—
106#117—91no—
107#117—181no—
108C2×C4⋊C4—31no—
109C2×C4⋊C4—31no—
110C2×C4⋊C4—181no—
111C2×C42C2×C3⋊D311yescharacteristic
112#107—181no—
113#106—181no—
114#104—92no—
115#104—92no—
116#103—181no—
117#102—181no—
118C23×C3C2×S411yescharacteristic
119C22×D3—61no—
120C2×A4—43no—
121S4—126no—
122C2×C3×C4—31no—
123C2×C3×C4—31no—
124C2×C3×C4—31no—
125C2×C3×C4—31no—
126C2×C3×C4—31no—
127C2×C3×C4—31no—
128C2×C3×C4—61no—
129C2×C3×C4—61no—
130C2×C3×C4—121no—
131#67—62no—
132#67—62no—
133C2×Dic3—61no—
134C2×Dic3—61no—
135C2×Dic3—61no—
136D12—32no—
137D12—61no—
138C4×D3—62no—
139C4×D3—62no—
140C4×D3—241no—
141C4×D3—241no—
142C4×D3—483no—
143Dic6—32no—
144Dic6—61no—
145C3⋊C8—62no—
146C3⋊C8—121no—
147C2×C32—161no—
148C3⋊D3—162no—
149#41—92no—
150#41—92no—
151#41—181no—
152#41—181no—
153C2×Q8—91no—
154C2×D4—91no—
155C2×D4—181no—
156C22×C4—31no—
157C22×C4—31no—
158C22×C4—181no—
159C22×C4—181no—
160C22×C4—181no—
161C22×C4C3⋊S411yescharacteristic
162M16—92no—
163M16—181no—
164M16—181no—
165M16—181no—
166C2×C8—181no—
167C2×C8—181no—
168C4⋊C4—61no—
169C4⋊C4—61no—
170C4⋊C4—61no—
171C4⋊C4—61no—
172C4⋊C4—91no—
173C4⋊C4—91no—
174C4⋊C4—181no—
175C4⋊C4—181no—
176C22⋊C4—181no—
177C22⋊C4—181no—
178C22⋊C4—181no—
179C42—31no—
180C42—181no—
181C42—181no—
182C42—181no—
183C42C4×C3⋊D311yescharacteristic, complemented
184C22×C3—31no—
185C22×C3—31no—
186C22×C3C4×S411yescharacteristic
187C2×D3—62no—
188C2×D3—121no—
189C2×D3—121no—
190C2×D3—483no—
191A4—43no—
192C3×C4—31no—
193C3×C4—31no—
194C3×C4—31no—
195C3×C4—31no—
196C3×C4—41no—
197C3×C4—121no—
198C3×C4—163no—
199Dic3—62no—
200Dic3—121no—
201Dic3—121no—
202Dic3—483no—
203C32—161noSylow
204C23—181no—
205C23C2×C3⋊S411yescharacteristic
206Q8—92no—
207Q8—181no—
208D4—92no—
209D4—181no—
210D4—182no—
211D4—182no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—31no—
216C2×C4—31no—
217C2×C4—31no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—121no—
221C2×C4—182no—
222C2×C4—182no—
223C2×C4—181no—
224C2×C4—181no—
225C2×C4—181no—
226C2×C4—721no—
227C2×C4—721no—
228C8—182no—
229C8—361no—
230C2×C3—31no—
231C2×C3—31no—
232C2×C3—163no—
233C2×C3#857⋊C211yescharacteristic
234D3—122no—
235D3—486no—
236C22—31no—
237C22—31no—
238C22—182no—
239C22—361no—
240C22—361no—
241C22C4×C3⋊S411yescharacteristic
242C4—31no—
243C4—31no—
244C4—31no—
245C4—31no—
246C4—41no—
247C4—121no—
248C4—182no—
249C4—361no—
250C4—361no—
251C3—163no—
252C3#857⋊C411yescharacteristic, complemented
253C2—31no—
254C2—31no—
255C2—362no—
256C2#1059363111yescharacteristic
subgroupG/H
center, hypercenterC2#10593631
commutator, hypocenterC3×C42⋊C3C2×C4
FrattiniC23C2×C3⋊S4
FittingC3×#384D3
socleC23×C3C2×S4
prime radicalC2×C3⋊#857C2
cosocleC2×C3×C42⋊C3C22
LCSG ▷ C3×C42⋊C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C3×#384⋊C3C2semidirect
3. C3⋊#4623C2semidirect
8. C3⋊#857C4semidirect
11. C3×#384D3semidirect
15. #384⋊C3D3semidirect
22. C3×C42⋊C3C2×C4semidirect
53. #384C3⋊D3semidirect
77. C3×C42C4×D3semidirect
94. C42⋊C3C4×D3semidirect
183. C42C4×C3⋊D3semidirect
252. C3#857⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#8572
C3×#384⋊C32
C3⋊#46232
#857⋊C43
#695923
C4×C3⋊S44