Finite Group Databasebeta

← #11797583

Subgroups — #11797583

Order 1152.

432 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 131 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#10592843C211yesmaximal, characteristic
2#10592839C211yesmaximal, characteristic, complemented
3#10592606C211yesmaximal, characteristic, complemented
4C32×#350C211yesmaximal, characteristic, complemented
5#10589377C211yesmaximal, characteristic, complemented
6#10589374C211yesmaximal, characteristic, complemented
7#10589368C211yesmaximal, characteristic, complemented
8#69123—34nomaximal
9C32×#131C2211yescharacteristic
10#64159C411yescharacteristic
11#64110C2211yescharacteristic
12C32×M32C2211yescharacteristic
13C2×C32×C16C2211yescharacteristic
14#63664C411yescharacteristic
15#63652C411yescharacteristic
16#63649C411yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18#63639—21no—
19#63639C2211yescharacteristic
20C2×C3⋊(C3⋊C16)—21no—
21C2×C3⋊(C3⋊C16)C2211yescharacteristic
22#63625—21no—
23C16×C3⋊D3—21no—
24#5144—34no—
25#5140—34no—
26#4907—34no—
27C3×#350D314yescomplemented
28#4511—34no—
29#4508—34no—
30#4502—34no—
31C32×#41C2×C411yescharacteristic
32#3828C2×C411yescharacteristic
33C32×M16—21no—
34C32×M16C2×C411yescharacteristic
35C2×C32×C8—21no—
36C2×C32×C8C2311yescharacteristic
37#3756C811yescharacteristic
38#3755C811yescharacteristic
39#3754C811yescharacteristic
40#3753C811yescharacteristic
41C4×C3⋊Dic3C2×C411yescharacteristic
42#3748C2×C411yescharacteristic
43C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
44#3743—21no—
45C8×C3⋊D3—21no—
46C32×C16—21no—
47C32×C16—21no—
48C3⋊(C3⋊C16)—21no—
49C3⋊(C3⋊C16)D411yescharacteristic
50C3⋊(C3⋊C16)D411yescharacteristic
51#2171—91noSylow
52C3×#131C2×D314yes—
53#950—34no—
54#901—34no—
55C3×M32C2×D314yes—
56C2×C3×C16C2×D314yes—
57#837—34no—
58#825—34no—
59#822—34no—
60C8×Dic3—34no—
61#812—34no—
62#812—64no—
63C2×C3⋊C16—34no—
64C2×C3⋊C16—64no—
65#798—64no—
66D3×C16—64no—
67C32×Q8C2×C811yescharacteristic
68C32×D4—21no—
69C32×D4C2×C811yescharacteristic
70C2×C32×C4—21no—
71C2×C32×C4C22×C411yescharacteristic
72#638—21no—
73C2×C3⋊Dic3—21no—
74C4⋊(C3⋊D3)C2×C811yescharacteristic
75C4×C3⋊D3—21no—
76#634C2×C811yescharacteristic
77C32×C8—21no—
78C32×C8C2×D411yescharacteristic
79C32×C8#4111yescharacteristic
80C3⋊(C3⋊C8)—21no—
81C3⋊(C3⋊C8)C2×C811yescharacteristic
82C3⋊(C3⋊C8)C2×C811yescharacteristic
83#504—91no—
84#504—91no—
85#443—91no—
86#364—91no—
87#350—91no—
88#350C3⋊D311yescharacteristic, complemented
89#346—91no—
90C3×#41C4×D314yes—
91#235—34no—
92C3×M16—24no—
93C3×M16C4×D314yes—
94C2×C3×C8—24no—
95C2×C3×C8C22×D314yes—
96#216—34no—
97#215—34no—
98#214—34no—
99#213—34no—
100C4×Dic3—34no—
101#208—34no—
102C2×C3⋊C8—34no—
103ΓL(1,𝔽25)—64no—
104D3×C8—64no—
105C3×C16—24no—
106C3×C16—24no—
107C3⋊C16—34no—
108C3⋊C16—34no—
109C3⋊C16—64no—
110C22×C32—21no—
111C22×C32#13111yescharacteristic
112C2×C3⋊D3—21no—
113C32×C4—21no—
114C32×C4C4×D411yescharacteristic
115C32×C4C22×C811yescharacteristic
116C3⋊Dic3—21no—
117C3⋊Dic3—41no—
118#135—91no—
119#131—91no—
120#131C2×C3⋊D311yescharacteristic
121M32—91no—
122M32—181no—
123M32—181no—
124M32C2×C3⋊D311yescharacteristic
125C2×C16—91no—
126C2×C16—181no—
127C2×C16—181no—
128C2×C16C2×C3⋊D311yescharacteristic
129#108—91no—
130#104—91no—
131#104—91no—
132C4×C8—91no—
133C3×Q8D3×C814yes—
134C3×D4—24no—
135C3×D4D3×C814yes—
136C2×C3×C4—24no—
137C2×C3×C4C2×C4×D314yes—
138#67—64no—
139C2×Dic3—64no—
140D12—34no—
141C4×D3—64no—
142Dic6—34no—
143C3×C8—24no—
144C3×C8D3×D414yes—
145C3×C8#23714yes—
146C3⋊C8—34no—
147C3⋊C8—34no—
148C3⋊C8—64no—
149C2×C32—21no—
150C2×C32—41no—
151C2×C32C8×D411yescharacteristic
152C3⋊D3—41no—
153#41—91no—
154#41C4×C3⋊D311yescharacteristic
155Q16—91no—
156SD16—91no—
157SD16—91no—
158D8—91no—
159M16—21no—
160M16—91no—
161M16—181no—
162M16C4×C3⋊D311yescharacteristic
163C2×C8—21no—
164C2×C8—91no—
165C2×C8—181no—
166C2×C8C22×C3⋊D311yescharacteristic
167C42—91no—
168C16—21no—
169C16—21no—
170C16—91no—
171C16—91no—
172C16—181no—
173C22×C3—24no—
174C22×C3#90714yes—
175C2×D3—64no—
176C3×C4—24no—
177C3×C4#67⋊C414yes—
178C3×C4C2×D3×C814yes—
179Dic3—64no—
180Dic3—124no—
181C32#217111yescharacteristic, complemented, Sylow
182Q8—91no—
183Q8C8×C3⋊D311yescharacteristic
184D4—21no—
185D4—91no—
186D4—181no—
187D4C8×C3⋊D311yescharacteristic
188C2×C4—21no—
189C2×C4—181no—
190C2×C4—181no—
191C2×C4C2×C4×C3⋊D311yescharacteristic
192C8—21no—
193C8—91no—
194C8—91no—
195C8—181no—
196C8D4×C3⋊D311yescharacteristic
197C8#383011yescharacteristic
198C2×C3—24no—
199C2×C3—44no—
200C2×C3#67⋊C814yes—
201D3—124no—
202C22—21no—
203C22—181no—
204C22#6411611yescharacteristic
205C4—21no—
206C4—181no—
207C4—361no—
208C4#6409011yescharacteristic
209C4C2×C8×C3⋊D311yescharacteristic
210C3#6912314yescomplemented
211C2—21no—
212C2—41no—
213C2—361no—
214C2#1059242411yescharacteristic
subgroupG/H
centerC8D4×C3⋊D3
commutatorC32×C4C22×C8
FrattiniC2×C8C22×C3⋊D3
FittingC32×#350C2
socleC2×C32C8×D4
prime radical#64159C4
cosocleC2×C32×C8C23
hypercenter#350C3⋊D3
hypocenterC32#2171
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8 ◁ #350

Complements

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

NH ≅ G/Ntype
2. #10592839C2semidirect
3. #10592606C2semidirect
4. C32×#350C2semidirect
5. #10589377C2semidirect
6. #10589374C2semidirect
7. #10589368C2semidirect
27. C3×#350D3semidirect
88. #350C3⋊D3semidirect
181. C32#2171semidirect
210. C3#69123semidirect

Maximal subgroups

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

subgroupindex
#105928432
#105928392
#105926062
C32×#3502
#105893772
#105893742
#105893682
#691233