Finite Group Databasebeta

← #11799834

Subgroups — #11799834

Order 1152.

426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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×#427C211yesmaximal, characteristic, complemented
2#10592814C211yesmaximal, characteristic
3#10589415C211yesmaximal, characteristic, complemented
4#10589357C211yesmaximal, characteristic, complemented
5#10589357C211yesmaximal, characteristic, complemented
6#10589356C211yesmaximal, characteristic, complemented
7#10589355C211yesmaximal, characteristic, complemented
8#70653—34nomaximal
9C22×C32×C8C2211yescharacteristic
10C32×#117—21no—
11#64139—21no—
12C2×#3745C2211yescharacteristic
13C32×#107C2211yescharacteristic
14C32×#107C2211yescharacteristic
15C32×#106—21no—
16#63648—21no—
17#63645C2211yescharacteristic
18C2×C3⋊(C3⋊C16)C2211yescharacteristic
19C2×C3⋊(C3⋊C16)C2211yescharacteristic
20C3×#427D314yescomplemented
21#5115—34no—
22#4549—34no—
23#4491—34no—
24#4491—34no—
25#4490—34no—
26#4489—34no—
27C22×C32×C4D411yescharacteristic
28C2×#638—41no—
29C2×C4⋊(C3⋊D3)—21no—
30C2×C32×C8—21no—
31C2×C32×C8—21no—
32C2×C32×C8D411yescharacteristic
33C2×C32×C8C2311yescharacteristic
34C32×C4⋊C4—21no—
35C32×C4⋊C4—21no—
36C32×C22⋊C4—41no—
37C32×C42—41no—
38#3752—41no—
39C4⋊(C3⋊Dic3)—21no—
40#3745—21no—
41#3745—21no—
42C3⋊(C3⋊C16)—21no—
43C3⋊(C3⋊C16)—21no—
44#2234—91noSylow
45C22×C3×C8C2×D314yes—
46C3×#117—24no—
47#930—64no—
48C2×D24—34no—
49C3×#107C2×D314yes—
50C3×#107C2×D314yes—
51C3×#106—24no—
52#821—64no—
53#818—34no—
54C2×C3⋊C16—34no—
55C2×C3⋊C16—34no—
56C23×C32D811yescharacteristic
57C22×C3⋊D3—41no—
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—41no—
61C2×C32×C4—41no—
62C2×C32×C4D811yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64#638—82no—
65C2×C3⋊Dic3—41no—
66C4⋊(C3⋊D3)—41no—
67C4⋊(C3⋊D3)—41no—
68C32×C8—21no—
69C32×C8#4111yescharacteristic
70C32×C8#4111yescharacteristic
71#466—91no—
72#427C3⋊D311yescharacteristic, complemented
73#367—91no—
74#366—91no—
75#357—91no—
76#357—91no—
77C22⋊C16—91no—
78C22×C3×C4#6714yes—
79C2×#67—124no—
80C2×D12—64no—
81C2×C3×C8—24no—
82C2×C3×C8—24no—
83C2×C3×C8#6714yes—
84C2×C3×C8C22×D314yes—
85C3×C4⋊C4—24no—
86C3×C4⋊C4—24no—
87C3×C22⋊C4—44no—
88C3×C42—44no—
89(C2×D3)⋊C4—124no—
90C4⋊Dic3—64no—
91D24—64no—
92D24—64no—
93C3⋊C16—64no—
94C3⋊C16—64no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32—21no—
98C22×C32C2×D811yescharacteristic
99C2×C3⋊D3—81no—
100C2×C3⋊D3—81no—
101C2×C3⋊D3—81no—
102C32×C4—21no—
103C32×C4—81no—
104C32×C4—81no—
105C32×C4#12311yescharacteristic
106C32×C4#13711yescharacteristic
107C3⋊Dic3—81no—
108C2×D8—91no—
109C22×C8C2×C3⋊D311yescharacteristic
110#121—181no—
111#117—21no—
112C2×C16—91no—
113C2×C16—91no—
114#107—91no—
115#107C2×C3⋊D311yescharacteristic
116#107C2×C3⋊D311yescharacteristic
117#106—21no—
118#102—181no—
119C23×C3#21314yes—
120C22×D3—124no—
121C2×C3×C4—24no—
122C2×C3×C4—24no—
123C2×C3×C4—44no—
124C2×C3×C4—44no—
125C2×C3×C4#21314yes—
126C2×C3×C4C2×#6714yes—
127#67—248no—
128C2×Dic3—124no—
129D12—124no—
130D12—124no—
131C3×C8—24no—
132C3×C8#23514yes—
133C3×C8#23514yes—
134C2×C32—41no—
135C2×C32#48011yescharacteristic
136C2×C32#50811yescharacteristic
137C2×C32#50911yescharacteristic
138C3⋊D3—161no—
139C2×D4—181no—
140C2×D4—361no—
141C22×C4#63811yescharacteristic
142D8—181no—
143D8—181no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8#63811yescharacteristic
147C2×C8C22×C3⋊D311yescharacteristic
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—181no—
151C22⋊C4—41no—
152C22⋊C4—361no—
153C42—41no—
154C16—181no—
155C16—181no—
156C22×C3—24no—
157C22×C3—24no—
158C22×C3—24no—
159C22×C3C2×#21314yes—
160C2×D3—244no—
161C2×D3—244no—
162C2×D3—244no—
163C3×C4—24no—
164C3×C4—84no—
165C3×C4—84no—
166C3×C4#92914yes—
167C3×C4#94214yes—
168Dic3—244no—
169C32#223411yescharacteristic, complemented, Sylow
170C23—361no—
171C23#375311yescharacteristic
172D4—361no—
173D4—361no—
174D4—722no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—361no—
180C2×C4#375311yescharacteristic
181C2×C4C2×#63811yescharacteristic
182C8—21no—
183C8#382811yescharacteristic
184C8#382811yescharacteristic
185C2×C3—44no—
186C2×C3#496714yes—
187C2×C3#519314yes—
188C2×C3#519414yes—
189D3—484no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—721no—
194C22—721no—
195C22—721no—
196C22C2×#375311yescharacteristic
197C4—21no—
198C4—81no—
199C4—81no—
200C4—721no—
201C4#6413811yescharacteristic
202C4#6415111yescharacteristic
203C3#7065314yescomplemented
204C2—41no—
205C2—1441no—
206C2#1059266611yescharacteristic
207C2#1059289211yescharacteristic
208C2#1059289311yescharacteristic
subgroupG/H
centerC22C2×#3753
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#427C2
socleC22×C32C2×D8
prime radical#10592814C2
hypercenter#427C3⋊D3
hypocenterC32#2234
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
1. C32×#427C2semidirect
3. #10589415C2semidirect
4. #10589357C2semidirect
5. #10589357C2semidirect
6. #10589356C2semidirect
7. #10589355C2semidirect
20. C3×#427D3semidirect
72. #427C3⋊D3semidirect
169. C32#2234semidirect
203. C3#70653semidirect

Maximal subgroups

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

subgroupindex
C32×#4272
#105928142
#105894152
#105893572
#105893562
#105893552
#706533