Finite Group Databasebeta

← #11921035

Subgroups — #11921035

Order 1152.

490 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 47 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⋊#5936C212yesmaximal, complemented
2C2×C3×#120⋊C3C211yesmaximal, characteristic
3#73080—33nomaximal
4#71669—31nomaximal
5C2×C3×C22⋊A4C2211yescharacteristic
6C2×C3⋊SL(2,ℤ/4)—41nomaximal
7C3×#120⋊C3C412yescomplemented
8#5936—36no—
9C2×C3×#120D311yescharacteristic
10#5798—31no—
11C2×#120⋊C3D313yes—
12#5247—32no—
13C2×#834—31no—
14#4527—32no—
15C3×C22⋊A4C2×C411yescharacteristic, complemented
16C22×C3×A4—41no—
17C3⋊SL(2,ℤ/4)—42no—
18C3⋊SL(2,ℤ/4)—82no—
19#1889—91noSylow
20C25×C3C2×D311yescharacteristic
21C2×C22⋊A4C2×D313yes—
22C22×C3×D4—31no—
23C2×SL(2,ℤ/4)—123no—
24C3×#120—32no—
25C3×#120Dic312yescomplemented
26C2×C3×C22⋊C4—31no—
27C2×#217—32no—
28C2×#217—32no—
29C2×#217—61no—
30C2×#217—62no—
31C2×#217—62no—
32D4×Dic3—62no—
33D4×Dic3—62no—
34#926—61no—
35#120⋊C3Dic316yescomplemented
36#834—62no—
37C2×C3×A4—42no—
38C2×C3×A4—41no—
39C2×C3×A4—82no—
40C2×C3⋊Dic3—161no—
41C2×#120C3⋊D311yescharacteristic
42#518—91no—
43C2×#99—91no—
44#379—92no—
45#342—92no—
46C24×C3—31no—
47C24×C3—31no—
48C24×C3—62no—
49C24×C3—62no—
50C24×C3C2×Dic311yescharacteristic, complemented
51C24×C3S411yescharacteristic
52C22⋊A4C2×Dic313yescomplemented
53C22×A4—43no—
54C2×C3×D4—32no—
55C2×C3×D4—32no—
56C2×C3×D4—62no—
57C2×C3×D4—62no—
58C22×C3×C4—31no—
59C22×Dic3—32no—
60C22×Dic3—32no—
61C22×Dic3—61no—
62C22×Dic3—61no—
63C22×Dic3—62no—
64SL(2,ℤ/4)—126no—
65SL(2,ℤ/4)—246no—
66C3×C22⋊C4—32no—
67C3×C22⋊C4—61no—
68#217—62no—
69#217—62no—
70#217—62no—
71#217—62no—
72#217—62no—
73#217—122no—
74#217—122no—
75#217—122no—
76#217—122no—
77C4⋊Dic3—61no—
78C4⋊Dic3—61no—
79C4×Dic3—62no—
80C22×C32—161no—
81C3×A4—41no—
82C3×A4—82no—
83C3⋊Dic3—162no—
84C25C2×C3⋊D311yescharacteristic
85C22×D4—31no—
86#120—32no—
87#120C3⋊Dic312yescomplemented
88C4×D4—182no—
89C4×D4—182no—
90#117—181no—
91C2×C22⋊C4—31no—
92C2×C22⋊C4—92no—
93C2×C22⋊C4—92no—
94C2×C22⋊C4—181no—
95C2×C22⋊C4—182no—
96C2×C22⋊C4—182no—
97#99—182no—
98C23×C3—22no—
99C23×C3—32no—
100C23×C3—32no—
101C23×C3—31no—
102C23×C3—31no—
103C23×C3—62no—
104C23×C3—62no—
105C23×C3—61no—
106C23×C3—61no—
107C23×C3—62no—
108C23×C3—62no—
109C23×C3—62no—
110C23×C3—121no—
111C23×C3—121no—
112C23×C3—122no—
113C23×C3—122no—
114C23×C3SL(2,ℤ/4)12yescomplemented
115C23×C3C2×S411yescharacteristic
116C2×A4—43no—
117C2×A4—46no—
118C2×A4—86no—
119C3×D4—64no—
120C3×D4—64no—
121C2×C3×C4—32no—
122C2×C3×C4—61no—
123C2×C3×C4—61no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—122no—
127C2×Dic3—122no—
128C2×Dic3—122no—
129C2×Dic3—122no—
130C2×Dic3—122no—
131C2×Dic3—241no—
132C2×Dic3—241no—
133C2×Dic3—483no—
134C2×C32—162no—
135C2×C32—161no—
136C24—31no—
137C24—31no—
138C24—62no—
139C24—62no—
140C24C2×C3⋊Dic311yescharacteristic, complemented
141C24C3⋊S411yescharacteristic
142C2×D4—32no—
143C2×D4—32no—
144C2×D4—62no—
145C2×D4—62no—
146C22×C4—31no—
147C22×C4—92no—
148C22×C4—92no—
149C22×C4—181no—
150C22×C4—181no—
151C22×C4—182no—
152C4⋊C4—181no—
153C4⋊C4—181no—
154C22⋊C4—32no—
155C22⋊C4—61no—
156C22⋊C4—182no—
157C22⋊C4—182no—
158C22⋊C4—182no—
159C22⋊C4—182no—
160C22⋊C4—182no—
161C22⋊C4—362no—
162C22⋊C4—362no—
163C22⋊C4—362no—
164C22⋊C4—362no—
165C42—182no—
166C22×C3—22no—
167C22×C3—31no—
168C22×C3—31no—
169C22×C3—32no—
170C22×C3—32no—
171C22×C3—41no—
172C22×C3—62no—
173C22×C3—62no—
174C22×C3—62no—
175C22×C3—62no—
176C22×C3—62no—
177C22×C3—62no—
178C22×C3—121no—
179C22×C3—122no—
180C22×C3—121no—
181C22×C3—121no—
182C22×C3—122no—
183C22×C3—163no—
184C22×C3C2×SL(2,ℤ/4)11yescharacteristic
185A4—43no—
186A4—86no—
187C3×C4—62no—
188Dic3—122no—
189Dic3—122no—
190Dic3—242no—
191Dic3—486no—
192C32—161noSylow
193C23—22no—
194C23—32no—
195C23—32no—
196C23—31no—
197C23—31no—
198C23—62no—
199C23—62no—
200C23—61no—
201C23—61no—
202C23—62no—
203C23—62no—
204C23—62no—
205C23—121no—
206C23—121no—
207C23—122no—
208C23—122no—
209C23C3⋊SL(2,ℤ/4)12yescomplemented
210C23C2×C3⋊S411yescharacteristic
211D4—64no—
212D4—64no—
213C2×C4—32no—
214C2×C4—61no—
215C2×C4—61no—
216C2×C4—182no—
217C2×C4—182no—
218C2×C4—362no—
219C2×C4—362no—
220C2×C4—362no—
221C2×C4—362no—
222C2×C4—362no—
223C2×C4—721no—
224C2×C4—721no—
225C2×C3—31no—
226C2×C3—31no—
227C2×C3—42no—
228C2×C3—62no—
229C2×C3—62no—
230C2×C3—166no—
231C2×C3—163no—
232C2×C3#1020⋊C211yescharacteristic
233C22—22no—
234C22—31no—
235C22—31no—
236C22—32no—
237C22—32no—
238C22—41no—
239C22—62no—
240C22—62no—
241C22—62no—
242C22—62no—
243C22—62no—
244C22—62no—
245C22—121no—
246C22—121no—
247C22—121no—
248C22—122no—
249C22—122no—
250C22C2×C3⋊SL(2,ℤ/4)11yescharacteristic
251C4—62no—
252C4—362no—
253C4—362no—
254C4—722no—
255C3—163no—
256C3#7308011yescharacteristic, complemented
257C2—31no—
258C2—31no—
259C2—42no—
260C2—62no—
261C2—62no—
262C2#1059363011yescharacteristic
subgroupG/H
center, hypercenterC2#10593630
commutator, hypocenterC3×C22⋊A4C2×C4
FrattiniC23C2×C3⋊S4
FittingC2×C3×#120D3
socleC23×C3C2×S4
prime radicalC2×C3×#120⋊C3C2
cosocleC2×C3×C22⋊A4C22
LCSG ▷ C3×C22⋊A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊#5936C2semidirect
7. C3×#120⋊C3C4semidirect
15. C3×C22⋊A4C2×C4semidirect
25. C3×#120Dic3semidirect
35. #120⋊C3Dic3semidirect
50. C24×C3C2×Dic3semidirect
52. C22⋊A4C2×Dic3semidirect
87. #120C3⋊Dic3semidirect
114. C23×C3SL(2,ℤ/4)semidirect
140. C24C2×C3⋊Dic3semidirect
209. C23C3⋊SL(2,ℤ/4)semidirect
256. C3#73080semidirect

Maximal subgroups

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

subgroupindex
C3⋊#59362
C2×C3×#120⋊C32
#730803
#716693
C2×C3⋊SL(2,ℤ/4)4