Finite Group Databasebeta

← #11922833

Subgroups — #11922833

Order 1152.

634 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 99 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×C42×A4C211yesmaximal, characteristic
2C4⋊(C3⋊SL(2,ℤ/4))C212yesmaximal
3#10593645C214yesmaximal
4#85284—33nomaximal
5#82074—31nomaximal
6C2×C3×C4×A4C2212yes—
7C2×C3×C4×A4C2211yescharacteristic
8C2×C3⋊SL(2,ℤ/4)C2214yes—
9#64079—41nomaximal
10C22×C3×C42D311yescharacteristic
11C2×#870—31no—
12C42×A4D313yes—
13C4⋊SL(2,ℤ/4)—36no—
14SL(2,ℤ/4)⋊C4—312no—
15#5212—32no—
16#5210—34no—
17#4936—31no—
18#4933—34no—
19#4928—32no—
20C22×C3×A4C2311yescharacteristic
21C3×C4×A4—22no—
22C3×C4×A4Q812yes—
23C3⋊SL(2,ℤ/4)—24no—
24C32×C42—41no—
25C4⋊(C3⋊Dic3)—42no—
26#3750—44no—
27#2851—91noSylow
28C23×C3×C4C2×D312yes—
29C23×C3×C4C2×D311yescharacteristic
30C2×C4×A4C2×D316yes—
31C2×C4×A4C2×D313yes—
32C2×SL(2,ℤ/4)—312no—
33C2×C3×C42—31no—
34C2×C3×C42—31no—
35C2×C3×C42—32no—
36C2×#217—34no—
37C2×C4⋊Dic3—32no—
38C2×C4⋊Dic3—32no—
39C2×Dic3⋊C4—34no—
40C2×Dic3⋊C4—34no—
41#870—61no—
42#870—62no—
43#870—61no—
44#870—123no—
45C3⋊#95—34no—
46C3⋊#95—34no—
47C3⋊#95—34no—
48C2×C3×A4C2×Q811yescharacteristic
49C2×C3×A4#4112yes—
50C2×C32×C4—41no—
51C2×C32×C4—42no—
52C2×C3⋊Dic3—44no—
53C2×#125—91no—
54C22×C42C3⋊D311yescharacteristic
55#389—92no—
56#387—94no—
57#385—94no—
58#382—91no—
59#380—92no—
60C24×C3C22×D311yescharacteristic
61C22×A4C22×D313yes—
62C22×C3×C4—22no—
63C22×C3×C4—31no—
64C22×C3×C4—31no—
65C22×C3×C4—32no—
66C22×C3×C4—32no—
67C22×C3×C4—32no—
68C22×C3×C4—62no—
69C22×C3×C4Dic612yes—
70C22×Dic3—34no—
71C22×Dic3—34no—
72C4×A4—26no—
73C4×A4Dic616yes—
74SL(2,ℤ/4)—612no—
75C3×C42—32no—
76C3×C42—31no—
77C3×C42—43no—
78C3×C42—61no—
79C3×C42S411yescharacteristic
80#217—64no—
81#217—64no—
82C4⋊Dic3—62no—
83C4⋊Dic3—64no—
84C4⋊Dic3—62no—
85C4⋊Dic3—126no—
86Dic3⋊C4—64no—
87Dic3⋊C4—68no—
88Dic3⋊C4—64no—
89Dic3⋊C4—1212no—
90C22×C32—41no—
91C3×A4#12511yescharacteristic, complemented
92C32×C4—42no—
93C32×C4—82no—
94C3⋊Dic3—84no—
95C23×C4C2×C3⋊D312yes—
96C23×C4C2×C3⋊D311yescharacteristic
97#125—181no—
98#125—182no—
99#125—181no—
100C2×C4⋊C4—92no—
101C2×C4⋊C4—94no—
102C2×C4⋊C4—92no—
103C2×C4⋊C4—94no—
104C2×C22⋊C4—94no—
105C2×C42—31no—
106C2×C42—32no—
107C2×C42—31no—
108#95—94no—
109#95—94no—
110#95—94no—
111C23×C3—31no—
112C23×C3—32no—
113C23×C3—31no—
114C23×C3C2×Dic611yescharacteristic
115C23×C3#23512yes—
116C2×A4C2×Dic613yes—
117C2×A4#23516yes—
118C2×C3×C4—31no—
119C2×C3×C4—32no—
120C2×C3×C4—32no—
121C2×C3×C4—32no—
122C2×C3×C4—34no—
123C2×C3×C4—32no—
124C2×C3×C4—43no—
125C2×C3×C4—46no—
126C2×C3×C4—62no—
127C2×C3×C4—62no—
128C2×C3×C4—61no—
129C2×C3×C4—62no—
130C2×C3×C4C2×S412yes—
131C2×C3×C4C2×S411yescharacteristic
132C2×Dic3—64no—
133C2×Dic3—64no—
134C2×Dic3—64no—
135C2×Dic3—64no—
136C2×Dic3—64no—
137C2×Dic3—64no—
138C2×Dic3—1212no—
139C2×C32—41no—
140C2×C32—42no—
141C24C22×C3⋊D311yescharacteristic
142C22×C4—22no—
143C22×C4—31no—
144C22×C4—31no—
145C22×C4—32no—
146C22×C4—32no—
147C22×C4—32no—
148C22×C4—62no—
149C22×C4—94no—
150C22×C4—94no—
151C22×C4#63412yes—
152C4⋊C4—184no—
153C4⋊C4—182no—
154C4⋊C4—188no—
155C4⋊C4—184no—
156C4⋊C4—184no—
157C4⋊C4—182no—
158C22⋊C4—184no—
159C22⋊C4—184no—
160C42—32no—
161C42—31no—
162C42—61no—
163C42C3⋊S411yescharacteristic
164C22×C3—31no—
165C22×C3—32no—
166C22×C3—31no—
167C22×C3—31no—
168C22×C3—32no—
169C22×C3—32no—
170C22×C3—43no—
171C22×C3—61no—
172C22×C3#87011yescharacteristic, complemented
173C22×C3C22×S411yescharacteristic
174A4#87013yescomplemented
175C3×C4—22no—
176C3×C4—32no—
177C3×C4—46no—
178C3×C4—62no—
179C3×C4—86no—
180C3×C4A4⋊Q812yes—
181Dic3—124no—
182Dic3—124no—
183Dic3—2412no—
184C32—41noSylow
185C23—31no—
186C23—32no—
187C23—31no—
188C23C2×#63411yescharacteristic
189C23#382812yes—
190C2×C4—31no—
191C2×C4—32no—
192C2×C4—32no—
193C2×C4—32no—
194C2×C4—34no—
195C2×C4—32no—
196C2×C4—62no—
197C2×C4—62no—
198C2×C4—61no—
199C2×C4—62no—
200C2×C4—184no—
201C2×C4—184no—
202C2×C4—184no—
203C2×C4—184no—
204C2×C4—184no—
205C2×C4—184no—
206C2×C4C2×C3⋊S412yes—
207C2×C4C2×C3⋊S411yescharacteristic
208C2×C3—32no—
209C2×C3—31no—
210C2×C3—31no—
211C2×C3—43no—
212C2×C3—46no—
213C2×C3C2×A4⋊Q811yescharacteristic
214C2×C3#591212yes—
215C22—31no—
216C22—32no—
217C22—31no—
218C22—31no—
219C22—32no—
220C22—32no—
221C22—61no—
222C22#6407911yescharacteristic, complemented
223C22C22×C3⋊S411yescharacteristic
224C4—22no—
225C4—32no—
226C4—62no—
227C4—364no—
228C4—364no—
229C4#6425912yes—
230C3—43no—
231C3#8528411yescharacteristic, complemented
232C2—32no—
233C2—31no—
234C2—31no—
235C2C2×#6425911yescharacteristic
236C2#1059657512yes—
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, prime radical, cosocleC22×C3×A4C23
FittingC22×C3×C42D3
socleC24×C3C22×D3
hypercenterC42C3⋊S4
hypocenterC3×A4#125
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
91. C3×A4#125semidirect
172. C22×C3#870semidirect
174. A4#870semidirect
222. C22#64079semidirect
231. C3#85284semidirect

Maximal subgroups

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

subgroupindex
C3×C42×A42
C4⋊(C3⋊SL(2,ℤ/4))2
#105936452
#852843
#820743
#640794