Finite Group Databasebeta

← #11920006

Subgroups — #11920006

Order 1152.

274 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 50 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
1C4⋊C4×C22⋊C9C211yesmaximal, characteristic
2C4⋊((C22⋊C9)⋊C4)C211yesmaximal, characteristic
3C2×(C22⋊C9)⋊C8C211yesmaximal, characteristic
4#71556—31nomaximal
5C2×C4×C22⋊C9—21no—
6C2×C4×C22⋊C9C2211yescharacteristic
7C2×(C22⋊C9)⋊C4—21no—
8(C22⋊C9)⋊C8C412yescomplemented
9#63367—41nomaximal
10C22×C3×C4⋊C4D311yescharacteristic
11#5212—31no—
12C2×#830—31no—
13C2×#808—31no—
14C2×#808—31no—
15#4529—31no—
16#4529—31no—
17C22×C22⋊C9D411yescharacteristic
18C4×C22⋊C9—41no—
19C4×C22⋊C9C2×C411yescharacteristic
20C4×C22⋊C9Q811yescharacteristic
21(C22⋊C9)⋊C4—41no—
22C9×C4⋊C4—41no—
23C4⋊Dic9—41no—
24C2×C9⋊C8—41no—
25#1853—91noSylow
26C23×C3×C4—21no—
27C23×C3×C4C2×D311yescharacteristic
28C2×C3×C4⋊C4—31no—
29C2×C3×C4⋊C4—31no—
30C2×C3×C4⋊C4—61no—
31C2×#217—61no—
32C2×C4⋊Dic3—31no—
33C2×C4⋊Dic3—31no—
34C22×C3⋊C8—31no—
35C22×C3⋊C8—31no—
36C3⋊#95—61no—
37#830—32no—
38#830—32no—
39#808—62no—
40#808—61no—
41#808—61no—
42C2×C22⋊C9C4⋊C411yescharacteristic
43C2×C22⋊C9SD1611yescharacteristic
44C2×C22⋊C9SD1611yescharacteristic
45C2×C4×C9—41no—
46C2×C4×C9—81no—
47C2×Dic9—81no—
48C9⋊C8—42no—
49C22×C4⋊C4D911yescharacteristic
50C2×#106—91no—
51C2×#106—91no—
52C2×C22⋊C8—91no—
53#380—91no—
54#340—91no—
55#340—91no—
56C24×C3#6711yescharacteristic
57C22×C3×C4—31no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×C3×C4—31no—
61C22×C3×C4—41no—
62C22×C3×C4—61no—
63C22×C3×C4—61no—
64C22×C3×C4—121no—
65C22×C3×C4Dic611yescharacteristic
66C22×C3×C4C4×D311yescharacteristic
67C22×Dic3—61no—
68C22×Dic3—61no—
69C3×C4⋊C4—32no—
70C3×C4⋊C4—31no—
71C3×C4⋊C4—61no—
72C3×C4⋊C4S411yescharacteristic
73#217—121no—
74#217—121no—
75C4⋊Dic3—61no—
76C4⋊Dic3—61no—
77C4⋊Dic3—61no—
78C4⋊Dic3—61no—
79C2×C3⋊C8—32no—
80C2×C3⋊C8—32no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C2×C3⋊C8—61no—
84C2×C3⋊C8—61no—
85C22×C9—41no—
86C22⋊C9#10611yescharacteristic, complemented
87C4×C9—41no—
88C4×C9—41no—
89C4×C9—161no—
90Dic9—161no—
91C23×C4—21no—
92C23×C4C2×D911yescharacteristic
93C22×C8—91no—
94C22×C8—91no—
95C2×C4⋊C4—31no—
96C2×C4⋊C4—31no—
97C2×C4⋊C4—61no—
98C2×C4⋊C4—91no—
99C2×C4⋊C4—91no—
100C2×C22⋊C4—181no—
101#106—182no—
102#106—181no—
103#106—181no—
104C22⋊C8—92no—
105C22⋊C8—92no—
106#95—181no—
107C23×C3—31no—
108C23×C3—31no—
109C23×C3—31no—
110C23×C3—31no—
111C23×C3Dic3⋊C411yescharacteristic
112C23×C3#21411yescharacteristic
113C23×C3#21511yescharacteristic
114C2×C3×C4—21no—
115C2×C3×C4—31no—
116C2×C3×C4—31no—
117C2×C3×C4—31no—
118C2×C3×C4—31no—
119C2×C3×C4—31no—
120C2×C3×C4—31no—
121C2×C3×C4—31no—
122C2×C3×C4—61no—
123C2×C3×C4—61no—
124C2×C3×C4—121no—
125C2×C3×C4—121no—
126C2×C3×C4—121no—
127C2×C3×C4—121no—
128C2×C3×C4C2×S411yescharacteristic
129C2×Dic3—121no—
130C2×Dic3—121no—
131C2×Dic3—121no—
132C2×Dic3—121no—
133C2×Dic3—121no—
134C2×Dic3—121no—
135C3⋊C8—62no—
136C3⋊C8—62no—
137C2×C9—41no—
138C2×C9—41no—
139C2×C9—41no—
140C24#61111yescharacteristic
141C22×C4—31no—
142C22×C4—31no—
143C22×C4—31no—
144C22×C4—31no—
145C22×C4—41no—
146C22×C4—61no—
147C22×C4—61no—
148C22×C4—121no—
149C22×C4—181no—
150C22×C4—181no—
151C22×C4Dic1811yescharacteristic
152C22×C4C4×D911yescharacteristic
153C2×C8—92no—
154C2×C8—92no—
155C2×C8—181no—
156C2×C8—181no—
157C2×C8—181no—
158C2×C8—181no—
159C4⋊C4—32no—
160C4⋊C4—31no—
161C4⋊C4—61no—
162C4⋊C4—181no—
163C4⋊C4—181no—
164C4⋊C4—181no—
165C4⋊C4—181no—
166C4⋊C4(C22⋊C9)⋊C211yescharacteristic
167C22⋊C4—361no—
168C22⋊C4—361no—
169C22×C3—31no—
170C22×C3—31no—
171C22×C3—31no—
172C22×C3—31no—
173C22×C3—31no—
174C22×C3—31no—
175C22×C3—31no—
176C22×C3—31no—
177C22×C3—31no—
178C22×C3—61no—
179C22×C3#80811yescharacteristic
180C22×C3GL(2,ℤ/4)11yescharacteristic
181C3×C4—31no—
182C3×C4—31no—
183C3×C4—41no—
184C3×C4—121no—
185C3×C4A4⋊Q811yescharacteristic
186C3×C4C4×S411yescharacteristic
187Dic3—241no—
188Dic3—241no—
189C9—41noSylow
190C23—31no—
191C23—31no—
192C23—31no—
193C23—31no—
194C23Dic9⋊C411yescharacteristic
195C23#367211yescharacteristic
196C23#367511yescharacteristic
197C2×C4—21no—
198C2×C4—31no—
199C2×C4—31no—
200C2×C4—31no—
201C2×C4—31no—
202C2×C4—31no—
203C2×C4—31no—
204C2×C4—31no—
205C2×C4—61no—
206C2×C4—61no—
207C2×C4—121no—
208C2×C4—121no—
209C2×C4—121no—
210C2×C4—121no—
211C2×C4—361no—
212C2×C4—361no—
213C2×C4—361no—
214C2×C4—361no—
215C2×C4—361no—
216C2×C4—361no—
217C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
218C8—182no—
219C8—182no—
220C2×C3—31no—
221C2×C3—31no—
222C2×C3—31no—
223C2×C3—31no—
224C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
225C2×C3#541411yescharacteristic
226C2×C3#541711yescharacteristic
227C22—31no—
228C22—31no—
229C22—31no—
230C22—31no—
231C22—31no—
232C22—31no—
233C22—31no—
234C22—31no—
235C22—31no—
236C22—61no—
237C22#6336711yescharacteristic, complemented
238C22#6369411yescharacteristic
239C4—31no—
240C4—31no—
241C4—41no—
242C4—121no—
243C4—721no—
244C4—721no—
245C4(C22⋊C9)⋊Q811yescharacteristic
246C4C4×(C22⋊C9)⋊C211yescharacteristic
247C3#7305111yescharacteristic
248C2—31no—
249C2—31no—
250C2—31no—
251C2—31no—
252C2((C22⋊C9)⋊C4)⋊C411yescharacteristic
253C2#1058951611yescharacteristic
254C2#1058951911yescharacteristic
subgroupG/H
centerC22#63694
commutatorC4×C22⋊C9C2×C4
FrattiniC2×C3×C4C2×S4
FittingC22×C3×C4⋊C4D3
socle, prime radicalC24×C3#67
cosocleC2×C4×C22⋊C9C22
hypercenterC4⋊C4(C22⋊C9)⋊C2
hypocenterC22⋊C9#106
LCSG ▷ C4×C22⋊C9 ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
8. (C22⋊C9)⋊C8C4semidirect
86. C22⋊C9#106semidirect
237. C22#63367semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×C22⋊C92
C4⋊((C22⋊C9)⋊C4)2
C2×(C22⋊C9)⋊C82
#715563
#633674