Finite Group Databasebeta

← #11799455

Subgroups — #11799455

Order 1152.

432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 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#10592891C211yesmaximal, characteristic, complemented
2C2×#63655C211yesmaximal, characteristic, complemented
3#10592606C211yesmaximal, characteristic, complemented
4#10592596C211yesmaximal, characteristic
5C32×#362C211yesmaximal, characteristic, complemented
6#10589382C211yesmaximal, characteristic, complemented
7#10589359C211yesmaximal, characteristic, complemented
8#69271—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10#64151—21no—
11#64117—21no—
12C2×#3745C2211yescharacteristic
13#64110C2211yescharacteristic
14C32×M32C2211yescharacteristic
15C32×#108C2211yescharacteristic
16#63663—21no—
17#63655—21no—
18#63655—21no—
19#63650—21no—
20#63646C2211yescharacteristic
21C2×C3⋊(C3⋊C16)C2211yescharacteristic
22#63625—21no—
23C16×C3⋊D3—21no—
24#5192—34no—
25C2×#828—34no—
26#4907—34no—
27#4897—34no—
28C3×#362D314yescomplemented
29#4516—34no—
30#4493—34no—
31C2×C32×Q8—21no—
32#3828D411yescharacteristic
33C2×C4⋊(C3⋊D3)—21no—
34C32×Q16—21no—
35C32×Q16—21no—
36C32×M16—21no—
37C2×C32×C8C2311yescharacteristic
38#3756—41no—
39#3755—41no—
40#3748—21no—
41#3748D411yescharacteristic
42#3745—21no—
43#3745—21no—
44#3745—41no—
45#3744—41no—
46#3743—21no—
47C8×C3⋊D3—21no—
48C32×C16—21no—
49C3⋊(C3⋊C16)D411yescharacteristic
50C3⋊(C3⋊C16)D411yescharacteristic
51#2223—91noSylow
52C2×C3×Q16C2×D314yes—
53#942—64no—
54#908—64no—
55C2×D24—34no—
56#901—34no—
57C3×M32C2×D314yes—
58C3×#108C2×D314yes—
59#836—64no—
60#828—64no—
61#828—64no—
62#823—64no—
63#819—34no—
64C2×C3⋊C16—34no—
65#798—64no—
66D3×C16—64no—
67C22×C3⋊D3—41no—
68C32×Q8—41no—
69C32×Q8—41no—
70C2×C32×C4—41no—
71C2×C32×C4C2×D411yescharacteristic
72#638—21no—
73C4⋊(C3⋊D3)—41no—
74C4⋊(C3⋊D3)—41no—
75C4⋊(C3⋊D3)D811yescharacteristic
76C4×C3⋊D3—21no—
77#634D811yescharacteristic
78C32×C8—41no—
79C32×C8C2×D411yescharacteristic
80C32×C8#4111yescharacteristic
81C3⋊(C3⋊C8)—21no—
82C3⋊(C3⋊C8)—41no—
83C2×SD32—91no—
84#504—91no—
85#473—91no—
86#472—91no—
87#368—91no—
88#362C3⋊D311yescharacteristic, complemented
89#361—91no—
90C2×C3×Q8—24no—
91#235—34no—
92C2×D12—64no—
93C3×Q16—24no—
94C3×Q16—24no—
95C3×M16—24no—
96C2×C3×C8C22×D314yes—
97#216—124no—
98#215—124no—
99#208—34no—
100#208—64no—
101D24—64no—
102D24—64no—
103D24—124no—
104#204—124no—
105ΓL(1,𝔽25)—64no—
106D3×C8—64no—
107C3×C16—24no—
108C3⋊C16—34no—
109C3⋊C16—34no—
110C22×C32#13511yescharacteristic
111C2×C3⋊D3—21no—
112C2×C3⋊D3—81no—
113C2×C3⋊D3—161no—
114C32×C4—81no—
115C32×C4#12111yescharacteristic
116C32×C4C2×D811yescharacteristic
117C3⋊Dic3—21no—
118#137—181no—
119AGL(1,ℤ/8)—181no—
120C2×Q16C2×C3⋊D311yescharacteristic
121C2×D8—91no—
122#131—91no—
123SD32—181no—
124SD32—181no—
125M32—181no—
126M32C2×C3⋊D311yescharacteristic
127C2×C16—91no—
128C2×C16—181no—
129#108—91no—
130#108C2×C3⋊D311yescharacteristic
131#101—181no—
132#100—181no—
133C22×D3—124no—
134C3×Q8—44no—
135C3×Q8—44no—
136C2×C3×C4—44no—
137C2×C3×C4D3×D414yes—
138#67—64no—
139D12—34no—
140D12—124no—
141D12—124no—
142C4×D3—64no—
143Dic6—34no—
144C3×C8—44no—
145C3×C8#23514yes—
146C3×C8D3×D414yes—
147C3⋊C8—64no—
148C3⋊C8—124no—
149C2×C32—21no—
150C2×C32#46611yescharacteristic
151C3⋊D3—41no—
152C3⋊D3—161no—
153#41—91no—
154C2×Q8—21no—
155C2×D4—181no—
156Q16—21no—
157Q16—21no—
158Q16—361no—
159SD16—361no—
160SD16—361no—
161D8—181no—
162D8—181no—
163D8—361no—
164M16—21no—
165M16—91no—
166M16—181no—
167M16—181no—
168C2×C8—181no—
169C2×C8C22×C3⋊D311yescharacteristic
170C16—21no—
171C16—91no—
172C16—91no—
173C22×C3#91614yes—
174C2×D3—64no—
175C2×D3—244no—
176C2×D3—484no—
177C3×C4—84no—
178C3×C4#88414yes—
179C3×C4D3×D814yes—
180Dic3—64no—
181C32#222311yescharacteristic, complemented, Sylow
182C23—361no—
183Q8—41no—
184Q8—41no—
185Q8—91no—
186D4—91no—
187D4—181no—
188D4—361no—
189D4—361no—
190C2×C4—41no—
191C2×C4—181no—
192C2×C4D4×C3⋊D311yescharacteristic
193C8—41no—
194C8—181no—
195C8—361no—
196C8#382811yescharacteristic
197C8D4×C3⋊D311yescharacteristic
198C2×C3—24no—
199C2×C3#477514yes—
200D3—124no—
201D3—484no—
202C22—181no—
203C22—721no—
204C22—1441no—
205C22#6412511yescharacteristic
206C4—81no—
207C4—181no—
208C4#6409311yescharacteristic
209C4D8×C3⋊D311yescharacteristic
210C3#6927114yescomplemented
211C2—21no—
212C2—361no—
213C2—1441no—
214C2#1059247411yescharacteristic
subgroupG/H
centerC2#10592474
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#362C2
socleC2×C32#466
prime radical#10592596C2
hypercenter#362C3⋊D3
hypocenterC32#2223
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
1. #10592891C2semidirect
2. C2×#63655C2semidirect
3. #10592606C2semidirect
5. C32×#362C2semidirect
6. #10589382C2semidirect
7. #10589359C2semidirect
28. C3×#362D3semidirect
88. #362C3⋊D3semidirect
181. C32#2223semidirect
210. C3#69271semidirect

Maximal subgroups

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

subgroupindex
#105928912
C2×#636552
#105926062
#105925962
C32×#3622
#105893822
#105893592
#692713