Finite Group Databasebeta

← #11921102

Subgroups — #11921102

Order 1152.

458 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 75 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×Q8×A4C211yesmaximal, characteristic
2#10593643C212yesmaximal
3#73146—33nomaximal
4#72133—31nomaximal
5C3×Q8×A4—22no—
6C2×C3×C4×A4C412yes—
7C2×C3×C4×A4C2211yescharacteristic
8C3⋊(A4⋊C8)—22no—
9#63663—41nomaximal
10C23×C3×Q8D311yescharacteristic
11C2×Q8×A4D313yes—
12#5409—36no—
13C2×#836—32no—
14C2×#836—31no—
15C2×#836—31no—
16#5207—32no—
17C22×C3×A4C2×C411yescharacteristic
18C2×C32×Q8—41no—
19C3×C4×A4—22no—
20C3×C4×A4D412yes—
21#3748—42no—
22#1784—91noSylow
23C22×C3×Q8—22no—
24C22×C3×Q8—31no—
25C22×C3×Q8—31no—
26C22×C3×Q8—32no—
27C22×C3×Q8—62no—
28C23×C3×C4Dic312yes—
29C23×C3×C4C2×D311yescharacteristic
30Q8×A4—26no—
31C2×C4×A4Dic316yes—
32C2×C4×A4C2×D313yes—
33C2×#208—32no—
34C2×#208—32no—
35A4⋊C8—66no—
36#836—64no—
37#836—62no—
38#836—61no—
39#836—61no—
40#836—123no—
41#830—62no—
42#830—62no—
43C2×C3×A4—21no—
44C2×C3×A4C22⋊C411yescharacteristic
45C32×Q8—82no—
46C2×C32×C4—42no—
47C2×C32×C4—41no—
48C3⋊(C3⋊C8)—82no—
49C23×Q8C3⋊D311yescharacteristic
50C2×#101—92no—
51C2×#101—91no—
52C2×#101—91no—
53#407—92no—
54C24×C3C2×Dic311yescharacteristic
55C22×A4C2×Dic313yes—
56C2×C3×Q8—34no—
57C2×C3×Q8—32no—
58C2×C3×Q8—31no—
59C2×C3×Q8—43no—
60C2×C3×Q8—61no—
61C2×C3×Q8—62no—
62C2×C3×Q8—62no—
63C2×C3×Q8—62no—
64C2×C3×Q8—64no—
65C2×C3×Q8—64no—
66C2×C3×Q8S411yescharacteristic
67C22×C3×C4—22no—
68C22×C3×C4—31no—
69C22×C3×C4—32no—
70C22×C3×C4—32no—
71C22×C3×C4—31no—
72C22×C3×C4—32no—
73C22×C3×C4—62no—
74C22×C3×C4#6712yes—
75C4×A4—26no—
76C4×A4#6716yes—
77#208—62no—
78#208—62no—
79#208—62no—
80#208—62no—
81#208—126no—
82C2×C3⋊C8—62no—
83C2×C3⋊C8—62no—
84C22×C32—41no—
85C3×A4#10111yescharacteristic, complemented
86C32×C4—42no—
87C32×C4—82no—
88C22×Q8—22no—
89C22×Q8—31no—
90C22×Q8—31no—
91C22×Q8—32no—
92C22×Q8—62no—
93C23×C4C3⋊Dic312yes—
94C23×C4C2×C3⋊D311yescharacteristic
95C2×M16—92no—
96C2×M16—92no—
97#101—184no—
98#101—182no—
99#101—181no—
100#101—181no—
101C22⋊C8—182no—
102C22⋊C8—182no—
103C23×C3—21no—
104C23×C3—31no—
105C23×C3—31no—
106C23×C3—61no—
107C23×C3#21711yescharacteristic
108C2×A4—23no—
109C2×A4#21713yes—
110C3×Q8—22no—
111C3×Q8—64no—
112C3×Q8—64no—
113C3×Q8—62no—
114C3×Q8—86no—
115C2×C3×C4—31no—
116C2×C3×C4—32no—
117C2×C3×C4—32no—
118C2×C3×C4—32no—
119C2×C3×C4—34no—
120C2×C3×C4—32no—
121C2×C3×C4—43no—
122C2×C3×C4—46no—
123C2×C3×C4—62no—
124C2×C3×C4—62no—
125C2×C3×C4—61no—
126C2×C3×C4—62no—
127C2×C3×C4SL(2,ℤ/4)12yes—
128C2×C3×C4C2×S411yescharacteristic
129C3⋊C8—122no—
130C3⋊C8—122no—
131C3⋊C8—246no—
132C2×C32—41no—
133C2×C32—81no—
134C24C2×C3⋊Dic311yescharacteristic
135C2×Q8—34no—
136C2×Q8—31no—
137C2×Q8—32no—
138C2×Q8—61no—
139C2×Q8—62no—
140C2×Q8—62no—
141C2×Q8—62no—
142C2×Q8—64no—
143C2×Q8—64no—
144C2×Q8C3⋊S411yescharacteristic
145C22×C4—22no—
146C22×C4—31no—
147C22×C4—32no—
148C22×C4—32no—
149C22×C4—31no—
150C22×C4—32no—
151C22×C4—62no—
152C22×C4#63812yes—
153M16—182no—
154M16—182no—
155M16—182no—
156M16—182no—
157C2×C8—182no—
158C2×C8—182no—
159C22×C3—31no—
160C22×C3—31no—
161C22×C3—32no—
162C22×C3—31no—
163C22×C3—43no—
164C22×C3—61no—
165C22×C3—61no—
166C22×C3—61no—
167C22×C3#83611yescharacteristic, complemented
168C22×C3C2×SL(2,ℤ/4)11yescharacteristic
169A4#83613yescomplemented
170C3×C4—22no—
171C3×C4—32no—
172C3×C4—46no—
173C3×C4—62no—
174C3×C4—86no—
175C3×C4GL(2,ℤ/4)12yes—
176C32—41noSylow
177C23—21no—
178C23—31no—
179C23—31no—
180C23—61no—
181C23#375711yescharacteristic
182Q8—22no—
183Q8—64no—
184Q8—64no—
185Q8—62no—
186C2×C4—31no—
187C2×C4—32no—
188C2×C4—32no—
189C2×C4—32no—
190C2×C4—34no—
191C2×C4—32no—
192C2×C4—62no—
193C2×C4—62no—
194C2×C4—61no—
195C2×C4—62no—
196C2×C4C3⋊SL(2,ℤ/4)12yes—
197C2×C4C2×C3⋊S411yescharacteristic
198C8—362no—
199C8—362no—
200C2×C3—21no—
201C2×C3—31no—
202C2×C3—31no—
203C2×C3—43no—
204C2×C3—61no—
205C2×C3—83no—
206C2×C3#543211yescharacteristic
207C22—31no—
208C22—31no—
209C22—32no—
210C22—31no—
211C22—61no—
212C22—61no—
213C22—61no—
214C22#6366311yescharacteristic, complemented
215C22C2×C3⋊SL(2,ℤ/4)11yescharacteristic
216C4—22no—
217C4—32no—
218C4—62no—
219C4#6426912yes—
220C3—43no—
221C3#7314611yescharacteristic, complemented
222C2—21no—
223C2—31no—
224C2—31no—
225C2—61no—
226C2#1059366611yescharacteristic
subgroupG/H
centerC2#10593666
commutator, prime radicalC22×C3×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC23×C3×Q8D3
socleC23×C3#217
cosocleC2×C3×C4×A4C22
hypercenterC2×Q8C3⋊S4
hypocenterC3×A4#101
LCSG ▷ C22×C3×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
85. C3×A4#101semidirect
167. C22×C3#836semidirect
169. A4#836semidirect
214. C22#63663semidirect
221. C3#73146semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
#105936432
#731463
#721333
#636634