Finite Group Databasebeta

← #11919785

Subgroups — #11919785

Order 1152.

610 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 137 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#10593120C211yesmaximal, characteristic
2#568⋊C9C213yesmaximal, complemented
3C2×#131⋊C9C213yesmaximal, complemented
4C3×#3573C311yesmaximal, characteristic
52−1+4⋊C9C413yes—
6#63700C411yescharacteristic
7C2×#41⋊C9C2213yes—
8C9×#131—41nomaximal
9#131⋊C9C2211yescharacteristic, complemented
10#131⋊C9C2213yescomplemented
11C3×#585C2×C311yescharacteristic
12C3×#568—33no—
13C3×#568—31no—
14C3×#568C2×C313yes—
15C2×C3×#131—31no—
16C2×C3×#131—33no—
17C2×C3×#131C2×C313yes—
18C9×#41—41no—
19#41⋊C9C2×C413yes—
20#41⋊C9C2311yescharacteristic
21C2×Q8⋊C9C2×C413yes—
22C9×M16—43no—
23C2×C8×C9—43no—
24#3573C911yescharacteristic, complemented, Sylow
25C3×2−1+4—31no—
26C3×2−1+4C3×C413yes—
27C3×H(5,𝔽2)—33no—
28C3×H(5,𝔽2)C3×C411yescharacteristic
29C2×C3×#41—33no—
30C2×C3×#41—31no—
31C2×C3×#41C22×C313yes—
32C3×#131—36no—
33C3×#131—31no—
34C3×#131—33no—
35C3×#131—36no—
36C3×#131—33no—
37C3×#131—33no—
38C3×#131—33no—
39C3×#131A411yescharacteristic
40C3×#131C22×C311yescharacteristic
41C3×#131C22×C313yes—
42C2×C3×M16—36no—
43C2×C3×M16—33no—
44C2×C3×M16—33no—
45C2×C3×M16—33no—
46C22×C3×C8—32no—
47C22×C3×C8—33no—
48Q8×C9—41no—
49D4×C9—43no—
50C2×C4×C9—43no—
51Q8⋊C9C22×C411yescharacteristic
52C8×C9—43no—
53C8×C9—41no—
54#585C2×C911yescharacteristic
55#568—33no—
56#568—31no—
57#568C2×C913yescomplemented
58C2×#131—31no—
59C2×#131—33no—
60C2×#131C2×C913yescomplemented
61C3×#41—36no—
62C3×#41—31no—
63C3×#41—33no—
64C3×#41—36no—
65C3×#41—33no—
66C3×#41—33no—
67C3×#41—33no—
68C3×#41C2×C3×C413yes—
69C3×#41C2×A411yescharacteristic
70C3×#41C23×C311yescharacteristic
71C2×C3×Q8—33no—
72C2×C3×Q8—31no—
73C2×C3×Q8C2×C3×C413yes—
74C2×C3×D4—33no—
75C2×C3×D4—36no—
76C2×C3×D4—33no—
77C2×C3×D4—33no—
78C22×C3×C4—32no—
79C22×C3×C4—33no—
80C3×M16—36no—
81C3×M16—33no—
82C3×M16—36no—
83C3×M16—33no—
84C3×M16—31no—
85C3×M16C2×A413yes—
86C2×C3×C8—36no—
87C2×C3×C8—33no—
88C2×C3×C8—33no—
89C2×C3×C8—33no—
90C2×C3×C8—33no—
91C2×C3×C8—31no—
92C2×C3×C8C2×A413yes—
93C22×C9—43no—
94C4×C9—43no—
95C4×C9—41no—
962−1+4—31no—
972−1+4C4×C913yes—
98H(5,𝔽2)—33no—
99H(5,𝔽2)C4×C911yescharacteristic
100C2×#41—33no—
101C2×#41—31no—
102C2×#41C22×C913yes—
103#131—36no—
104#131—31no—
105#131—33no—
106#131—36no—
107#131—33no—
108#131—33no—
109#131—33no—
110#131C22⋊C911yescharacteristic
111#131C22×C911yescharacteristic
112#131C22×C913yes—
113C2×M16—36no—
114C2×M16—33no—
115C2×M16—33no—
116C2×M16—33no—
117C22×C8—32no—
118C22×C8—33no—
119C23×C3—32no—
120C23×C3—33no—
121C3×Q8—33no—
122C3×Q8—33no—
123C3×Q8C4×A411yescharacteristic
124C3×Q8C22×C3×C411yescharacteristic
125C3×D4—33no—
126C3×D4—31no—
127C3×D4—36no—
128C3×D4—36no—
129C3×D4—33no—
130C3×D4C4×A413yes—
131C2×C3×C4—36no—
132C2×C3×C4—33no—
133C2×C3×C4—33no—
134C2×C3×C4—33no—
135C2×C3×C4—33no—
136C2×C3×C4—31no—
137C2×C3×C4C22×A413yes—
138C3×C8—33no—
139C3×C8—31no—
140C3×C8C22×A413yes—
141C3×C8C22×A411yescharacteristic
142C2×C9—41no—
143C2×C9—83no—
144#41—36no—
145#41—31no—
146#41—33no—
147#41—36no—
148#41—33no—
149#41—33no—
150#41—33no—
151#41C2×C4×C913yes—
152#41C2×C22⋊C911yescharacteristic
153#41C23×C911yescharacteristic
154C2×Q8—33no—
155C2×Q8—31no—
156C2×Q8C2×C4×C913yes—
157C2×D4—33no—
158C2×D4—36no—
159C2×D4—33no—
160C2×D4—33no—
161C22×C4—32no—
162C22×C4—33no—
163M16—36no—
164M16—33no—
165M16—36no—
166M16—33no—
167M16—31no—
168M16C2×C22⋊C913yes—
169C2×C8—36no—
170C2×C8—33no—
171C2×C8—31no—
172C2×C8—33no—
173C2×C8—33no—
174C2×C8—33no—
175C2×C8C2×C22⋊C913yes—
176C22×C3—33no—
177C22×C3—31no—
178C22×C3—123no—
179C22×C3—122no—
180C22×C3C2×C4×A413yes—
181C3×C4—33no—
182C3×C4—31no—
183C3×C4C2×C4×A413yes—
184C3×C4C23×A411yescharacteristic
185C9—41noSylow
186C23—32no—
187C23—33no—
188Q8—33no—
189Q8—33no—
190Q8C4×C22⋊C911yescharacteristic
191Q8C22×C4×C911yescharacteristic
192D4—33no—
193D4—31no—
194D4—36no—
195D4—36no—
196D4—33no—
197D4C4×C22⋊C913yes—
198C2×C4—36no—
199C2×C4—33no—
200C2×C4—31no—
201C2×C4—33no—
202C2×C4—33no—
203C2×C4—33no—
204C2×C4C22×C22⋊C913yes—
205C8—33no—
206C8—31no—
207C8C22×C22⋊C911yescharacteristic
208C8C22×C22⋊C913yes—
209C2×C3—23no—
210C2×C3—61no—
211C2×C3—63no—
212C2×C3C22×C4×A411yescharacteristic
213C22—33no—
214C22—31no—
215C22—123no—
216C22—122no—
217C22C2×C4×C22⋊C913yes—
218C4—31no—
219C4—33no—
220C4C2×C4×C22⋊C913yes—
221C4C23×C22⋊C911yescharacteristic
222C3#8562911yescharacteristic
223C2—23no—
224C2—61no—
225C2—63no—
226C2C22×C4×C22⋊C911yescharacteristic
subgroupG/H
centerC3×C8C22×A4
commutator, hypocenterQ8C22×C4×C9
FrattiniC3×C4C23×A4
FittingC3×#3573C3
socleC2×C3C22×C4×A4
prime radicalC3×#585C2×C3
cosocleC3×#41C23×C3
hypercenterC3×#131A4
LCSG ▷ Q8
UCSC1 ◁ C3×C8 ◁ C3×#131

Complements

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

NH ≅ G/Ntype
2. #568⋊C9C2semidirect
3. C2×#131⋊C9C2semidirect
9. #131⋊C9C22semidirect
10. #131⋊C9C22semidirect
24. #3573C9semidirect
57. #568C2×C9semidirect
60. C2×#131C2×C9semidirect

Maximal subgroups

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

subgroupindex
#105931202
#568⋊C92
C2×#131⋊C92
C3×#35733
C9×#1314