Finite Group Databasebeta

← #131×C22⋊C9 #11919779

Subgroups — #131×C22⋊C9 #11919779

Order 1152.

646 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 646 conjugacy classes of subgroups — too many to draw. Only its 140 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
1#41×C22⋊C9C211yesmaximal, characteristic
2M16×C22⋊C9C213yesmaximal, complemented
3C2×C8×C22⋊C9C213yesmaximal, complemented
4C22×C3×#131C311yesmaximal, characteristic
5Q8×C22⋊C9C411yescharacteristic
6D4×C22⋊C9C413yes—
7C2×C4×C22⋊C9C2213yes—
8C9×#131—41nomaximal
9C8×C22⋊C9C2211yescharacteristic
10C8×C22⋊C9C2213yes—
11C22×C3×#41C2×C311yescharacteristic
12C2×C3×#131—31no—
13C2×C3×#131—33no—
14C2×C3×#131—33no—
15C2×C3×#131—31no—
16C22×C3×M16C2×C313yes—
17C23×C3×C8C2×C313yes—
18C22×C22⋊C9C2×C413yes—
19C9×#41—41no—
20C4×C22⋊C9C2×C413yes—
21C4×C22⋊C9C2311yescharacteristic
22C9×M16—43no—
23C2×C8×C9—43no—
24C22×#131C911yescharacteristic, complemented, Sylow
25C2×C3×#41—33no—
26C2×C3×#41—33no—
27C2×C3×#41—31no—
28C2×C3×#41—31no—
29C22×C3×Q8C3×C411yescharacteristic
30C22×C3×D4C3×C413yes—
31C23×C3×C4C22×C313yes—
32C3×#131—36no—
33C3×#131—36no—
34C3×#131—32no—
35C3×#131—31no—
36C3×#131—33no—
37C3×#131—33no—
38C3×#131A411yescharacteristic
39C2×C3×M16—33no—
40C2×C3×M16—36no—
41C2×C3×M16—33no—
42C22×C3×C8—33no—
43C22×C3×C8—33no—
44C22×C3×C8—33no—
45C22×C3×C8—33no—
46C22×C3×C8C22×C311yescharacteristic
47C22×C3×C8C22×C313yes—
48C2×C22⋊C9—23no—
49C2×C22⋊C9C22×C411yescharacteristic
50Q8×C9—41no—
51D4×C9—43no—
52C2×C4×C9—43no—
53C8×C9—43no—
54C8×C9—41no—
55C22×#41C2×C911yescharacteristic
56C2×#131—31no—
57C2×#131—33no—
58C2×#131—33no—
59C2×#131—31no—
60C22×M16C2×C913yescomplemented
61C23×C8C2×C913yescomplemented
62C24×C3C2×C3×C413yes—
63C3×#41—32no—
64C3×#41—36no—
65C3×#41—36no—
66C3×#41—31no—
67C3×#41—33no—
68C3×#41—33no—
69C3×#41C2×A411yescharacteristic
70C2×C3×Q8—33no—
71C2×C3×Q8—31no—
72C2×C3×D4—33no—
73C2×C3×D4—33no—
74C2×C3×D4—36no—
75C22×C3×C4—33no—
76C22×C3×C4—33no—
77C22×C3×C4—33no—
78C22×C3×C4—33no—
79C22×C3×C4C2×C3×C413yes—
80C22×C3×C4C23×C311yescharacteristic
81C3×M16—36no—
82C3×M16—33no—
83C3×M16—36no—
84C3×M16C2×A413yes—
85C2×C3×C8—36no—
86C2×C3×C8—33no—
87C2×C3×C8—33no—
88C2×C3×C8—33no—
89C2×C3×C8—31no—
90C2×C3×C8—33no—
91C2×C3×C8—31no—
92C2×C3×C8—33no—
93C2×C3×C8C2×A413yes—
94C22×C9—43no—
95C22⋊C9#13111yescharacteristic, direct product factor
96C4×C9—43no—
97C4×C9—41no—
98C2×#41—33no—
99C2×#41—33no—
100C2×#41—31no—
101C2×#41—31no—
102C22×Q8C4×C911yescharacteristic
103C22×D4C4×C913yes—
104C23×C4C22×C913yes—
105#131—36no—
106#131—36no—
107#131—32no—
108#131—31no—
109#131—33no—
110#131—33no—
111#131C22⋊C911yescharacteristic, direct product factor
112C2×M16—33no—
113C2×M16—36no—
114C2×M16—33no—
115C22×C8—33no—
116C22×C8—33no—
117C22×C8—33no—
118C22×C8—33no—
119C22×C8C22×C911yescharacteristic
120C22×C8C22×C913yes—
121C23×C3—23no—
122C23×C3—33no—
123C23×C3—33no—
124C23×C3—63no—
125C23×C3C22×C3×C411yescharacteristic
126C3×Q8—32no—
127C3×Q8—33no—
128C3×Q8C4×A411yescharacteristic
129C3×D4—36no—
130C3×D4—36no—
131C3×D4—33no—
132C3×D4C4×A413yes—
133C2×C3×C4—36no—
134C2×C3×C4—33no—
135C2×C3×C4—33no—
136C2×C3×C4—33no—
137C2×C3×C4—31no—
138C2×C3×C4—33no—
139C2×C3×C4—31no—
140C2×C3×C4—33no—
141C2×C3×C4C22×A413yes—
142C3×C8—31no—
143C3×C8—33no—
144C3×C8C22×A413yes—
145C3×C8C22×A411yescharacteristic
146C2×C9—41no—
147C2×C9—83no—
148C24C2×C4×C913yes—
149#41—32no—
150#41—36no—
151#41—36no—
152#41—31no—
153#41—33no—
154#41—33no—
155#41C2×C22⋊C911yescharacteristic
156C2×Q8—33no—
157C2×Q8—31no—
158C2×D4—33no—
159C2×D4—33no—
160C2×D4—36no—
161C22×C4—33no—
162C22×C4—33no—
163C22×C4—33no—
164C22×C4—33no—
165C22×C4C2×C4×C913yes—
166C22×C4C23×C911yescharacteristic
167M16—36no—
168M16—33no—
169M16—36no—
170M16C2×C22⋊C913yescomplemented
171C2×C8—36no—
172C2×C8—33no—
173C2×C8—31no—
174C2×C8—33no—
175C2×C8—33no—
176C2×C8—33no—
177C2×C8—31no—
178C2×C8—33no—
179C2×C8C2×C22⋊C913yescomplemented
180C22×C3—31no—
181C22×C3—31no—
182C22×C3—33no—
183C22×C3—63no—
184C22×C3—63no—
185C22×C3—63no—
186C22×C3—63no—
187C22×C3C3×#13111yescharacteristic
188C22×C3C2×C4×A413yes—
189C3×C4—31no—
190C3×C4—33no—
191C3×C4C2×C4×A413yes—
192C3×C4C23×A411yescharacteristic
193C9—41noSylow
194C23—23no—
195C23—33no—
196C23—33no—
197C23—63no—
198C23C22×C4×C911yescharacteristic
199Q8—32no—
200Q8—33no—
201Q8C4×C22⋊C911yescharacteristic
202D4—36no—
203D4—36no—
204D4—33no—
205D4C4×C22⋊C913yes—
206C2×C4—36no—
207C2×C4—33no—
208C2×C4—31no—
209C2×C4—33no—
210C2×C4—33no—
211C2×C4—33no—
212C2×C4—31no—
213C2×C4—33no—
214C2×C4C22×C22⋊C913yes—
215C8—31no—
216C8—33no—
217C8C22×C22⋊C911yescharacteristic
218C8C22×C22⋊C913yes—
219C2×C3—23no—
220C2×C3—31no—
221C2×C3—31no—
222C2×C3—63no—
223C2×C3C22×C4×A411yescharacteristic
224C22—31no—
225C22—31no—
226C22—33no—
227C22—63no—
228C22—63no—
229C22—63no—
230C22—63no—
231C22C9×#13111yescharacteristic, complemented
232C22C2×C4×C22⋊C913yes—
233C4—31no—
234C4—33no—
235C4C2×C4×C22⋊C913yes—
236C4C23×C22⋊C911yescharacteristic
237C3A4×#13111yescharacteristic
238C2—23no—
239C2—31no—
240C2—31no—
241C2—63no—
242C2C22×C4×C22⋊C911yescharacteristic
subgroupG/H
centerC3×C8C22×A4
commutatorC23C22×C4×C9
FrattiniC3×C4C23×A4
FittingC22×C3×#131C3
socleC23×C3C22×C3×C4
prime radicalC22×C3×#41C2×C3
cosocleC22×C3×C4C23×C3
hypercenterC3×#131A4
hypocenterC22C9×#131
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C3×C8 ◁ C3×#131

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊C9C2semidirect
3. C2×C8×C22⋊C9C2semidirect
24. C22×#131C9semidirect
60. C22×M16C2×C9semidirect
61. C23×C8C2×C9semidirect
95. C22⋊C9#131direct (N × H)
111. #131C22⋊C9direct (N × H)
170. M16C2×C22⋊C9semidirect
179. C2×C8C2×C22⋊C9semidirect
231. C22C9×#131semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊C92
M16×C22⋊C92
C2×C8×C22⋊C92
C22×C3×#1313
C9×#1314