Finite Group Databasebeta

← #11921099

Subgroups — #11921099

Order 1152.

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

normal subgroups only

This group has 586 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×D4×A4C211yesmaximal, characteristic
2#10593643C212yesmaximal, complemented
3#73143—33nomaximal
4#72129—31nomaximal
5C23×C3×A4C412yes—
6C3×D4×A4—22no—
7C2×C3×C4×A4C2211yescharacteristic
8C3⋊(A4⋊C8)—22no—
9#63660—41nomaximal
10C23×C3×D4D311yescharacteristic
11C2×D4×A4D313yes—
12#5409—36no—
13C2×#833—32no—
14C2×#833—31no—
15C2×#833—31no—
16#5207—32no—
17C22×C3×A4—22no—
18C22×C3×A4—42no—
19C22×C3×A4C2×C411yescharacteristic
20C2×C32×D4—41no—
21C3×C4×A4D412yes—
22#3748—42no—
23#1783—91noSylow
24C25×C3Dic312yes—
25C23×A4Dic316yes—
26C22×C3×D4—22no—
27C22×C3×D4—31no—
28C22×C3×D4—31no—
29C22×C3×D4—32no—
30C22×C3×D4—62no—
31C23×C3×C4C2×D311yescharacteristic
32D4×A4—26no—
33C2×C4×A4C2×D313yes—
34C2×#208—32no—
35C2×#208—32no—
36A4⋊C8—66no—
37#833—64no—
38#833—62no—
39#833—61no—
40#833—61no—
41#833—123no—
42#830—62no—
43#830—62no—
44C23×C32—42no—
45C2×C3×A4—21no—
46C2×C3×A4—42no—
47C2×C3×A4C22⋊C411yescharacteristic
48C32×D4—82no—
49C2×C32×C4—41no—
50C3⋊(C3⋊C8)—82no—
51C23×D4C3⋊D311yescharacteristic
52C2×#100—92no—
53C2×#100—91no—
54C2×#100—91no—
55#407—92no—
56C24×C3—22no—
57C24×C3—32no—
58C24×C3—32no—
59C24×C3—42no—
60C24×C3—62no—
61C24×C3—122no—
62C24×C3C2×Dic311yescharacteristic
63C22×A4—26no—
64C22×A4—46no—
65C22×A4C2×Dic313yes—
66C2×C3×D4—34no—
67C2×C3×D4—32no—
68C2×C3×D4—31no—
69C2×C3×D4—43no—
70C2×C3×D4—62no—
71C2×C3×D4—62no—
72C2×C3×D4—61no—
73C2×C3×D4—62no—
74C2×C3×D4—64no—
75C2×C3×D4—64no—
76C2×C3×D4S411yescharacteristic
77C22×C3×C4—31no—
78C22×C3×C4—32no—
79C22×C3×C4—31no—
80C22×C3×C4#6712yes—
81C4×A4#6716yes—
82#208—62no—
83#208—62no—
84#208—62no—
85#208—62no—
86#208—126no—
87C2×C3⋊C8—62no—
88C2×C3⋊C8—62no—
89C22×C32—41no—
90C22×C32—82no—
91C22×C32—162no—
92C3×A4#10011yescharacteristic, complemented
93C32×C4—42no—
94C25C3⋊Dic312yes—
95C22×D4—22no—
96C22×D4—31no—
97C22×D4—31no—
98C22×D4—32no—
99C22×D4—62no—
100C23×C4C2×C3⋊D311yescharacteristic
101C2×M16—92no—
102C2×M16—92no—
103#100—184no—
104#100—182no—
105#100—181no—
106#100—181no—
107C22⋊C8—182no—
108C22⋊C8—182no—
109C23×C3—21no—
110C23×C3—31no—
111C23×C3—31no—
112C23×C3—34no—
113C23×C3—32no—
114C23×C3—42no—
115C23×C3—46no—
116C23×C3—62no—
117C23×C3—62no—
118C23×C3—61no—
119C23×C3—62no—
120C23×C3—122no—
121C23×C3—124no—
122C23×C3—122no—
123C23×C3—122no—
124C23×C3—122no—
125C23×C3—122no—
126C23×C3—124no—
127C23×C3#21711yescharacteristic
128C23×C3SL(2,ℤ/4)12yes—
129C2×A4—23no—
130C2×A4—46no—
131C2×A4#21713yes—
132C3×D4—22no—
133C3×D4—64no—
134C3×D4—64no—
135C3×D4—62no—
136C3×D4—86no—
137C2×C3×C4—31no—
138C2×C3×C4—32no—
139C2×C3×C4—32no—
140C2×C3×C4—32no—
141C2×C3×C4—43no—
142C2×C3×C4—61no—
143C2×C3×C4C2×S411yescharacteristic
144C3⋊C8—122no—
145C3⋊C8—122no—
146C3⋊C8—246no—
147C2×C32—41no—
148C2×C32—81no—
149C2×C32—162no—
150C24—22no—
151C24—32no—
152C24—32no—
153C24—42no—
154C24—62no—
155C24—122no—
156C24C2×C3⋊Dic311yescharacteristic
157C2×D4—34no—
158C2×D4—32no—
159C2×D4—31no—
160C2×D4—62no—
161C2×D4—62no—
162C2×D4—61no—
163C2×D4—62no—
164C2×D4—64no—
165C2×D4—64no—
166C2×D4C3⋊S411yescharacteristic
167C22×C4—31no—
168C22×C4—32no—
169C22×C4—31no—
170C22×C4#63812yes—
171M16—182no—
172M16—182no—
173M16—182no—
174M16—182no—
175C2×C8—182no—
176C2×C8—182no—
177C22×C3—22no—
178C22×C3—31no—
179C22×C3—31no—
180C22×C3—32no—
181C22×C3—31no—
182C22×C3—42no—
183C22×C3—43no—
184C22×C3—61no—
185C22×C3—61no—
186C22×C3—61no—
187C22×C3—62no—
188C22×C3—86no—
189C22×C3—122no—
190C22×C3—122no—
191C22×C3—122no—
192C22×C3—122no—
193C22×C3—122no—
194C22×C3—124no—
195C22×C3—124no—
196C22×C3—166no—
197C22×C3#83311yescharacteristic, complemented
198C22×C3C2×SL(2,ℤ/4)11yescharacteristic
199A4#83313yescomplemented
200C3×C4—32no—
201C3×C4—46no—
202C3×C4GL(2,ℤ/4)12yes—
203C32—41noSylow
204C23—21no—
205C23—31no—
206C23—31no—
207C23—34no—
208C23—32no—
209C23—42no—
210C23—62no—
211C23—62no—
212C23—61no—
213C23—62no—
214C23—122no—
215C23—124no—
216C23—122no—
217C23—122no—
218C23—122no—
219C23—122no—
220C23—124no—
221C23#375711yescharacteristic
222C23C3⋊SL(2,ℤ/4)12yes—
223D4—22no—
224D4—64no—
225D4—64no—
226D4—62no—
227C2×C4—31no—
228C2×C4—32no—
229C2×C4—32no—
230C2×C4—32no—
231C2×C4—61no—
232C2×C4C2×C3⋊S411yescharacteristic
233C8—362no—
234C8—362no—
235C2×C3—21no—
236C2×C3—31no—
237C2×C3—31no—
238C2×C3—42no—
239C2×C3—43no—
240C2×C3—61no—
241C2×C3—83no—
242C2×C3—122no—
243C2×C3—166no—
244C2×C3#543211yescharacteristic
245C22—22no—
246C22—31no—
247C22—31no—
248C22—32no—
249C22—31no—
250C22—42no—
251C22—61no—
252C22—61no—
253C22—61no—
254C22—62no—
255C22—122no—
256C22—122no—
257C22—122no—
258C22—122no—
259C22—122no—
260C22—124no—
261C22—124no—
262C22#6366011yescharacteristic, complemented
263C22C2×C3⋊SL(2,ℤ/4)11yescharacteristic
264C4—32no—
265C4#6426912yes—
266C3—43no—
267C3#7314311yescharacteristic, complemented
268C2—21no—
269C2—31no—
270C2—31no—
271C2—42no—
272C2—61no—
273C2—122no—
274C2#1059366611yescharacteristic
subgroupG/H
centerC2#10593666
commutatorC22×C3×A4C2×C4
FrattiniC2×C4C2×C3⋊S4
FittingC23×C3×D4D3
socleC23×C3#217
prime radicalC2×C3×D4×A4C2
cosocleC2×C3×C4×A4C22
hypercenterC2×D4C3⋊S4
hypocenterC3×A4#100
LCSG ▷ C22×C3×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10593643C2semidirect
92. C3×A4#100semidirect
197. C22×C3#833semidirect
199. A4#833semidirect
262. C22#63660semidirect
267. C3#73143semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
#105936432
#731433
#721293
#636604