Finite Group Databasebeta

← #11920409

Subgroups — #11920409

Order 1152.

566 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 96 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
2#10589511C213yesmaximal, complemented
3C2×(C22⋊C9)⋊C8C213yesmaximal, complemented
4#84075—31nomaximal
5Q8×C22⋊C9C411yescharacteristic
6D4×C22⋊C9C413yes—
7C2×C4×C22⋊C9C2213yes—
8#63510—41nomaximal
9(C22⋊C9)⋊C8C2211yescharacteristic
10(C22⋊C9)⋊C8C2213yes—
11C22×C3×#41D311yescharacteristic
12C2×#948—31no—
13C2×#948—31no—
14#5234—33no—
15#5234—33no—
16#5207—33no—
17C2×#830—33no—
18C22×C22⋊C9C2×C413yes—
19C9×#41—41no—
20C4×C22⋊C9C2×C413yes—
21C4×C22⋊C9C2311yescharacteristic
22#3667—43no—
23C2×C9⋊C8—43no—
24#2880—91noSylow
25C2×C3×#41—31no—
26C2×C3×#41—33no—
27C2×C3×#41—31no—
28C2×C3×#41—33no—
29C22×C3×Q8Dic311yescharacteristic
30C22×C3×D4Dic313yes—
31C23×C3×C4C2×D313yes—
32#948—61no—
33#948—63no—
34#948—63no—
35#948—61no—
36C2×#208—33no—
37C2×#208—33no—
38C22×C3⋊C8—33no—
39C22×C3⋊C8—33no—
40#830—33no—
41#830—33no—
42#830—36no—
43#830—31no—
44#830—33no—
45C2×C22⋊C9—23no—
46C2×C22⋊C9C22×C411yescharacteristic
47Q8×C9—41no—
48D4×C9—43no—
49C2×C4×C9—43no—
50C9⋊C8—41no—
51C9⋊C8—43no—
52C22×#41D911yescharacteristic
53C2×#131—91no—
54C2×#131—91no—
55#408—93no—
56#408—93no—
57#407—93no—
58C2×C22⋊C8—93no—
59C24×C3C2×Dic313yes—
60C3×#41—31no—
61C3×#41—33no—
62C3×#41—33no—
63C3×#41—61no—
64C3×#41—63no—
65C3×#41—63no—
66C3×#41S411yescharacteristic
67C2×C3×Q8—31no—
68C2×C3×Q8—33no—
69C2×C3×D4—33no—
70C2×C3×D4—33no—
71C2×C3×D4—36no—
72C22×C3×C4—33no—
73C22×C3×C4—33no—
74C22×C3×C4—33no—
75C22×C3×C4—33no—
76C22×C3×C4C2×Dic313yes—
77C22×C3×C4C22×D311yescharacteristic
78#208—63no—
79#208—63no—
80#208—63no—
81#208—63no—
82C2×C3⋊C8—31no—
83C2×C3⋊C8—31no—
84C2×C3⋊C8—33no—
85C2×C3⋊C8—33no—
86C2×C3⋊C8—63no—
87C2×C3⋊C8—63no—
88C2×C3⋊C8—63no—
89C2×C3⋊C8—63no—
90C22×C9—43no—
91C22⋊C9#13111yescharacteristic, complemented
92C4×C9—43no—
93C4×C9—41no—
94C2×#41—31no—
95C2×#41—33no—
96C2×#41—33no—
97C2×#41—31no—
98C22×Q8Dic911yescharacteristic
99C22×D4Dic913yes—
100C23×C4C2×D913yes—
101#131—181no—
102#131—183no—
103#131—183no—
104#131—181no—
105C2×M16—93no—
106C2×M16—93no—
107C22×C8—93no—
108C22×C8—93no—
109C22⋊C8—93no—
110C22⋊C8—93no—
111C22⋊C8—96no—
112C22⋊C8—91no—
113C22⋊C8—93no—
114C23×C3—23no—
115C23×C3—33no—
116C23×C3—33no—
117C23×C3—63no—
118C23×C3C22×Dic311yescharacteristic
119C3×Q8—33no—
120C3×Q8—61no—
121C3×Q8SL(2,ℤ/4)11yescharacteristic
122C3×D4—36no—
123C3×D4—33no—
124C3×D4—63no—
125C3×D4SL(2,ℤ/4)13yes—
126C2×C3×C4—33no—
127C2×C3×C4—33no—
128C2×C3×C4—33no—
129C2×C3×C4—31no—
130C2×C3×C4—33no—
131C2×C3×C4—31no—
132C2×C3×C4—33no—
133C2×C3×C4—63no—
134C2×C3×C4C2×S413yes—
135C3⋊C8—61no—
136C3⋊C8—63no—
137C3⋊C8—61no—
138C3⋊C8—63no—
139C2×C9—41no—
140C2×C9—83no—
141C24C2×Dic913yes—
142#41—31no—
143#41—33no—
144#41—33no—
145#41—61no—
146#41—63no—
147#41—63no—
148#41(C22⋊C9)⋊C211yescharacteristic
149C2×Q8—31no—
150C2×Q8—33no—
151C2×D4—33no—
152C2×D4—33no—
153C2×D4—36no—
154C22×C4—33no—
155C22×C4—33no—
156C22×C4—33no—
157C22×C4—33no—
158C22×C4C2×Dic913yes—
159C22×C4C22×D911yescharacteristic
160M16—183no—
161M16—183no—
162M16—183no—
163M16—183no—
164C2×C8—91no—
165C2×C8—91no—
166C2×C8—93no—
167C2×C8—93no—
168C2×C8—183no—
169C2×C8—183no—
170C2×C8—183no—
171C2×C8—183no—
172C22×C3—31no—
173C22×C3—31no—
174C22×C3—33no—
175C22×C3—63no—
176C22×C3—63no—
177C22×C3—63no—
178C22×C3—63no—
179C22×C3#94811yescharacteristic
180C22×C3C2×SL(2,ℤ/4)13yes—
181C3×C4—31no—
182C3×C4—33no—
183C3×C4C2×SL(2,ℤ/4)13yes—
184C3×C4C22×S411yescharacteristic
185C9—41noSylow
186C23—23no—
187C23—33no—
188C23—33no—
189C23—63no—
190C23C22×Dic911yescharacteristic
191Q8—33no—
192Q8—61no—
193Q8(C22⋊C9)⋊C411yescharacteristic
194D4—36no—
195D4—33no—
196D4—63no—
197D4(C22⋊C9)⋊C413yes—
198C2×C4—33no—
199C2×C4—31no—
200C2×C4—33no—
201C2×C4—33no—
202C2×C4—33no—
203C2×C4—31no—
204C2×C4—33no—
205C2×C4—63no—
206C2×C4C2×(C22⋊C9)⋊C213yes—
207C8—181no—
208C8—183no—
209C8—181no—
210C8—183no—
211C2×C3—23no—
212C2×C3—31no—
213C2×C3—31no—
214C2×C3—63no—
215C2×C3C22×SL(2,ℤ/4)11yescharacteristic
216C22—31no—
217C22—31no—
218C22—33no—
219C22—63no—
220C22—63no—
221C22—63no—
222C22—63no—
223C22#6351011yescharacteristic, complemented
224C22C2×(C22⋊C9)⋊C413yes—
225C4—31no—
226C4—33no—
227C4C2×(C22⋊C9)⋊C413yes—
228C4C22×(C22⋊C9)⋊C211yescharacteristic
229C3#8551111yescharacteristic
230C2—23no—
231C2—31no—
232C2—31no—
233C2—63no—
234C2C22×(C22⋊C9)⋊C411yescharacteristic
subgroupG/H
centerC4C22×(C22⋊C9)⋊C2
commutatorC2×C22⋊C9C22×C4
FrattiniC3×C4C22×S4
Fitting, prime radicalC22×C3×#41D3
socleC23×C3C22×Dic3
cosocleC4×C22⋊C9C23
hypercenter#41(C22⋊C9)⋊C2
hypocenterC22⋊C9#131
LCSG ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. #10589511C2semidirect
3. C2×(C22⋊C9)⋊C8C2semidirect
91. C22⋊C9#131semidirect
223. C22#63510semidirect

Maximal subgroups

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

subgroupindex
#41×C22⋊C92
#105895112
C2×(C22⋊C9)⋊C82
#840753
#635104