Finite Group Databasebeta

← #11920945

Subgroups — #11920945

Order 1152.

402 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 31 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
2C3×#379⋊C3C211yesmaximal, characteristic
3#72989—33nomaximal
4#69497—31nomaximal
5C2×C3×C22⋊A4C2211yescharacteristic
6#64259—41nomaximal
7#5936—36no—
8#5483—31no—
9C3×#379D311yescharacteristic
10#5247—32no—
11#379⋊C3D313yes—
12#4527—32no—
13#4526—31no—
14C3×C22⋊A4Q811yescharacteristic, complemented
15C3×C4×A4—41no—
16C3⋊SL(2,ℤ/4)—42no—
17C3⋊SL(2,ℤ/4)—82no—
18#2029—91noSylow
19C25×C3C2×D311yescharacteristic
20C2×C22⋊A4C2×D313yes—
21A4⋊Q8—123no—
22C2×C3×C22⋊C4—31no—
23C2×C3×C22⋊C4—31no—
24C2×#217—32no—
25C2×#217—32no—
26C2×#217—62no—
27C2×#217—62no—
28#924—61no—
29#924—61no—
30#878—62no—
31#878—62no—
32C2×C3×A4—41no—
33C2×C3×A4—82no—
34#634—161no—
35#543—91no—
36#379—92no—
37#379C3⋊D311yescharacteristic
38#342—91no—
39#342—92no—
40C24×C3—31no—
41C24×C3—31no—
42C24×C3—62no—
43C24×C3—62no—
44C24×C3Dic611yescharacteristic, complemented
45C22⋊A4Dic613yescomplemented
46C22×C3×C4—31no—
47C22×C3×C4S411yescharacteristic
48C22×Dic3—32no—
49C22×Dic3—32no—
50C22×Dic3—62no—
51C2×Dic6—61no—
52C2×Dic6—61no—
53C4×A4—43no—
54SL(2,ℤ/4)—126no—
55SL(2,ℤ/4)—246no—
56C3×C22⋊C4—62no—
57C3×C22⋊C4—62no—
58#217—62no—
59#217—62no—
60#217—62no—
61#217—62no—
62#217—122no—
63#217—122no—
64#217—122no—
65#217—122no—
66C4⋊Dic3—61no—
67C4⋊Dic3—61no—
68Dic3⋊C4—62no—
69Dic3⋊C4—62no—
70C3×A4—41no—
71C3×A4—82no—
72C32×C4—161no—
73C3⋊Dic3—162no—
74C25C2×C3⋊D311yescharacteristic
75C22⋊Q8—182no—
76C22⋊Q8—182no—
77C22⋊Q8—181no—
78C22⋊Q8—181no—
79C2×C22⋊C4—31no—
80C2×C22⋊C4—31no—
81C2×C22⋊C4—92no—
82C2×C22⋊C4—92no—
83C2×C22⋊C4—182no—
84C2×C22⋊C4—182no—
85C23×C3—22no—
86C23×C3—32no—
87C23×C3—32no—
88C23×C3—31no—
89C23×C3—31no—
90C23×C3—62no—
91C23×C3—62no—
92C23×C3—62no—
93C23×C3—62no—
94C23×C3—62no—
95C23×C3—121no—
96C23×C3—121no—
97C23×C3—122no—
98C23×C3—122no—
99C23×C3C2×S411yescharacteristic
100C2×A4—43no—
101C2×A4—86no—
102C2×C3×C4—61no—
103C2×C3×C4—61no—
104C2×C3×C4—121no—
105C2×Dic3—62no—
106C2×Dic3—62no—
107C2×Dic3—122no—
108C2×Dic3—122no—
109C2×Dic3—122no—
110C2×Dic3—122no—
111C2×Dic3—122no—
112Dic6—241no—
113Dic6—241no—
114Dic6—483no—
115C2×C32—161no—
116C24—31no—
117C24—31no—
118C24—62no—
119C24—62no—
120C24#63411yescharacteristic, complemented
121C2×Q8—181no—
122C2×Q8—181no—
123C22×C4—31no—
124C22×C4—92no—
125C22×C4—92no—
126C22×C4—182no—
127C22×C4C3⋊S411yescharacteristic
128C4⋊C4—182no—
129C4⋊C4—182no—
130C4⋊C4—181no—
131C4⋊C4—181no—
132C22⋊C4—62no—
133C22⋊C4—62no—
134C22⋊C4—182no—
135C22⋊C4—182no—
136C22⋊C4—182no—
137C22⋊C4—182no—
138C22⋊C4—362no—
139C22⋊C4—362no—
140C22⋊C4—362no—
141C22⋊C4—362no—
142C22×C3—22no—
143C22×C3—31no—
144C22×C3—31no—
145C22×C3—32no—
146C22×C3—32no—
147C22×C3—62no—
148C22×C3—62no—
149C22×C3—62no—
150C22×C3—62no—
151C22×C3—62no—
152C22×C3—122no—
153C22×C3—121no—
154C22×C3—121no—
155C22×C3—122no—
156C22×C3A4⋊Q811yescharacteristic
157A4—43no—
158A4—86no—
159C3×C4—41no—
160C3×C4—121no—
161C3×C4—163no—
162Dic3—122no—
163Dic3—122no—
164Dic3—242no—
165Dic3—486no—
166C32—161noSylow
167C23—22no—
168C23—32no—
169C23—32no—
170C23—31no—
171C23—31no—
172C23—62no—
173C23—62no—
174C23—62no—
175C23—62no—
176C23—62no—
177C23—121no—
178C23—121no—
179C23—122no—
180C23—122no—
181C23C2×C3⋊S411yescharacteristic
182Q8—721no—
183Q8—721no—
184C2×C4—61no—
185C2×C4—61no—
186C2×C4—121no—
187C2×C4—182no—
188C2×C4—182no—
189C2×C4—362no—
190C2×C4—362no—
191C2×C4—362no—
192C2×C4—362no—
193C2×C4—362no—
194C2×C3—31no—
195C2×C3—31no—
196C2×C3—62no—
197C2×C3—62no—
198C2×C3—163no—
199C2×C3#1020⋊C211yescharacteristic
200C22—22no—
201C22—31no—
202C22—31no—
203C22—32no—
204C22—32no—
205C22—62no—
206C22—62no—
207C22—62no—
208C22—62no—
209C22—62no—
210C22—122no—
211C22—121no—
212C22—121no—
213C22—122no—
214C22#6425911yescharacteristic
215C4—41no—
216C4—121no—
217C4—362no—
218C4—362no—
219C4—722no—
220C3—163no—
221C3#7298911yescharacteristic, complemented
222C2—31no—
223C2—31no—
224C2—62no—
225C2—62no—
226C2#1059363011yescharacteristic
subgroupG/H
center, hypercenterC2#10593630
commutator, prime radical, cosocleC2×C3×C22⋊A4C22
FrattiniC23C2×C3⋊S4
FittingC3×#379D3
socleC23×C3C2×S4
hypocenterC3×C22⋊A4Q8
LCSG ▷ C2×C3×C22⋊A4 ▷ C3×C22⋊A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
14. C3×C22⋊A4Q8semidirect
44. C24×C3Dic6semidirect
45. C22⋊A4Dic6semidirect
120. C24#634semidirect
221. C3#72989semidirect

Maximal subgroups

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

subgroupindex
C3⋊#59362
C3×#379⋊C32
#729893
#694973
#642594