Finite Group Databasebeta

← #11799452

Subgroups — #11799452

Order 1152.

432 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C32×#473C211yesmaximal, characteristic, complemented
2C2×#63655C211yesmaximal, characteristic, complemented
3#10592841C211yesmaximal, characteristic
4#10592839C211yesmaximal, characteristic, complemented
5#10589431C211yesmaximal, characteristic, complemented
6#10589361C211yesmaximal, characteristic, complemented
7#10589359C211yesmaximal, characteristic, complemented
8#71097—34nomaximal
9C32×#137—21no—
10C2×C32×Q16C2211yescharacteristic
11C32×#131C2211yescharacteristic
12#64158—21no—
13C2×#3745C2211yescharacteristic
14C32×#108C2211yescharacteristic
15C32×#101—21no—
16#63655—21no—
17#63655—21no—
18#63650—21no—
19#63646C2211yescharacteristic
20#63639—21no—
21#63639C2211yescharacteristic
22C2×C3⋊(C3⋊C16)—21no—
23C2×C3⋊(C3⋊C16)C2211yescharacteristic
24C3×#473D314yescomplemented
25C2×#828—34no—
26#5142—34no—
27#5140—34no—
28#4565—34no—
29#4495—34no—
30#4493—34no—
31C32×#41D411yescharacteristic
32C2×C32×Q8—21no—
33C2×C4⋊(C3⋊D3)—21no—
34C32×Q16—21no—
35C32×Q16—21no—
36C32×Q16—41no—
37C32×SD16—41no—
38C32×M16—21no—
39C32×M16—21no—
40C32×M16D411yescharacteristic
41C2×C32×C8—21no—
42C2×C32×C8C2311yescharacteristic
43#3755—41no—
44#3753—41no—
45#3748—21no—
46#3745—21no—
47#3745—21no—
48C3⋊(C3⋊C16)—21no—
49C3⋊(C3⋊C16)D411yescharacteristic
50C3⋊(C3⋊C16)D411yescharacteristic
51#2223—91noSylow
52C3×#137—24no—
53C2×C3×Q16C2×D314yes—
54C3×#131C2×D314yes—
55#949—64no—
56C2×D24—34no—
57C3×#108C2×D314yes—
58C3×#101—24no—
59#828—64no—
60#828—64no—
61#823—64no—
62#819—34no—
63#812—34no—
64#812—64no—
65C2×C3⋊C16—34no—
66C2×C3⋊C16—64no—
67C22×C3⋊D3—41no—
68C32×Q8—41no—
69C32×Q8—41no—
70C32×Q8D811yescharacteristic
71C32×D4—21no—
72C32×D4D811yescharacteristic
73C2×C32×C4—21no—
74C2×C32×C4—41no—
75C2×C32×C4C2×D411yescharacteristic
76C4⋊(C3⋊D3)—41no—
77C4⋊(C3⋊D3)—41no—
78C32×C8—21no—
79C32×C8—41no—
80C32×C8C2×D411yescharacteristic
81C32×C8#4111yescharacteristic
82C3⋊(C3⋊C8)—41no—
83C2×SD32—91no—
84#504—91no—
85#473C3⋊D311yescharacteristic, complemented
86#472—91no—
87#368—91no—
88#362—91no—
89#361—91no—
90C3×#41#6714yes—
91C2×C3×Q8—24no—
92C2×D12—64no—
93C3×Q16—24no—
94C3×Q16—24no—
95C3×Q16—44no—
96C3×SD16—44no—
97C3×M16—24no—
98C3×M16—24no—
99C3×M16#6714yes—
100C2×C3×C8—24no—
101C2×C3×C8C22×D314yes—
102#215—124no—
103#213—124no—
104#208—64no—
105D24—64no—
106D24—64no—
107C3⋊C16—34no—
108C3⋊C16—34no—
109C3⋊C16—64no—
110C22×C32—21no—
111C22×C32#13511yescharacteristic
112C2×C3⋊D3—81no—
113C2×C3⋊D3—161no—
114C32×C4—21no—
115C32×C4—81no—
116C32×C4#12111yescharacteristic
117C32×C4C2×D811yescharacteristic
118#137—21no—
119AGL(1,ℤ/8)—181no—
120C2×Q16C2×C3⋊D311yescharacteristic
121C2×D8—91no—
122#131C2×C3⋊D311yescharacteristic
123SD32—181no—
124SD32—181no—
125M32—91no—
126M32—181no—
127C2×C16—91no—
128C2×C16—181no—
129#108—91no—
130#108C2×C3⋊D311yescharacteristic
131#101—21no—
132#100—181no—
133C22×D3—124no—
134C3×Q8—44no—
135C3×Q8—44no—
136C3×Q8#21314yes—
137C3×D4—24no—
138C3×D4#21314yes—
139C2×C3×C4—24no—
140C2×C3×C4—44no—
141C2×C3×C4C2×#6714yes—
142D12—124no—
143D12—124no—
144C3×C8—24no—
145C3×C8—44no—
146C3×C8D3×D414yes—
147C3×C8#23714yes—
148C3⋊C8—124no—
149C2×C32—21no—
150C2×C32—41no—
151C2×C32#46611yescharacteristic
152C3⋊D3—161no—
153#41#63811yescharacteristic
154C2×Q8—21no—
155C2×D4—181no—
156Q16—21no—
157Q16—21no—
158Q16—41no—
159SD16—41no—
160SD16—361no—
161D8—181no—
162D8—181no—
163D8—361no—
164M16—21no—
165M16—21no—
166M16—181no—
167M16#63811yescharacteristic
168C2×C8—21no—
169C2×C8C22×C3⋊D311yescharacteristic
170C16—91no—
171C16—91no—
172C16—181no—
173C22×C3—24no—
174C22×C3#95014yes—
175C2×D3—244no—
176C2×D3—484no—
177C3×C4—24no—
178C3×C4—84no—
179C3×C4C2×#21314yes—
180C3×C4#93914yes—
181C32#222311yescharacteristic, complemented, Sylow
182C23—361no—
183Q8—41no—
184Q8—41no—
185Q8#375311yescharacteristic
186D4—21no—
187D4—361no—
188D4—361no—
189D4#375311yescharacteristic
190C2×C4—21no—
191C2×C4—41no—
192C2×C4C2×#63811yescharacteristic
193C8—21no—
194C8—41no—
195C8—361no—
196C8D4×C3⋊D311yescharacteristic
197C8#383011yescharacteristic
198C2×C3—24no—
199C2×C3—44no—
200C2×C3#503814yes—
201D3—484no—
202C22—21no—
203C22—721no—
204C22—1441no—
205C22#6415911yescharacteristic
206C4—21no—
207C4—81no—
208C4C2×#375311yescharacteristic
209C4#6414811yescharacteristic
210C3#7109714yescomplemented
211C2—21no—
212C2—41no—
213C2—1441no—
214C2#1059273711yescharacteristic
subgroupG/H
centerC2#10592737
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#473C2
socleC2×C32#466
prime radical#10592841C2
hypercenter#473C3⋊D3
hypocenterC32#2223
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
1. C32×#473C2semidirect
2. C2×#63655C2semidirect
4. #10592839C2semidirect
5. #10589431C2semidirect
6. #10589361C2semidirect
7. #10589359C2semidirect
24. C3×#473D3semidirect
85. #473C3⋊D3semidirect
181. C32#2223semidirect
210. C3#71097semidirect

Maximal subgroups

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

subgroupindex
C32×#4732
C2×#636552
#105928412
#105928392
#105894312
#105893612
#105893592
#710973