Finite Group Databasebeta

← #11799828

Subgroups — #11799828

Order 1152.

426 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 105 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#10592856C211yesmaximal, characteristic
2#10592579C211yesmaximal, characteristic, complemented
3C32×#357C211yesmaximal, characteristic, complemented
4#10589428C211yesmaximal, characteristic, complemented
5#10589373C211yesmaximal, characteristic, complemented
6#10589370C211yesmaximal, characteristic, complemented
7#10589356C211yesmaximal, characteristic, complemented
8#69201—34nomaximal
9C2×C32×D8C2211yescharacteristic
10#64147—21no—
11C2×C8×C3⋊D3C2211yescharacteristic
12#64101—21no—
13C2×C32×C16C2211yescharacteristic
14C32×#107C2211yescharacteristic
15#63659—21no—
16#63645C2211yescharacteristic
17#63645C2211yescharacteristic
18C2×C3⋊(C3⋊C16)C2211yescharacteristic
19#63635—21no—
20#5157—34no—
21#4880—34no—
22C3×#357D314yescomplemented
23#4562—34no—
24(C2×D3)⋊C16—34no—
25#4504—34no—
26#4490—34no—
27C2×C32×D4—21no—
28C2×#638—41no—
29C2×C4×C3⋊D3D411yescharacteristic
30C32×D8—21no—
31C32×D8—21no—
32C2×C32×C8C2311yescharacteristic
33C32×C4⋊C4—21no—
34#3757—41no—
35#3752—41no—
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)—21no—
38C4×C3⋊Dic3—41no—
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40C8×C3⋊D3—21no—
41C8×C3⋊D3—21no—
42C32×C16—21no—
43C3⋊(C3⋊C16)—21no—
44#2234—91noSylow
45C2×C3×D8C2×D314yes—
46#938—64no—
47C2×D3×C8—34no—
48#892—64no—
49C2×C3×C16C2×D314yes—
50C3×#107C2×D314yes—
51#832—64no—
52#818—34no—
53#818—34no—
54C2×C3⋊C16—34no—
55#808—64no—
56C23×C32—41no—
57C22×C3⋊D3D811yescharacteristic
58C32×D4—41no—
59C32×D4—41no—
60C2×C32×C4—41no—
61C2×C32×C4C2×D411yescharacteristic
62#638—82no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3D811yescharacteristic
66C4×C3⋊D3—21no—
67C4×C3⋊D3—21no—
68C32×C8#4111yescharacteristic
69C32×C8#4111yescharacteristic
70C3⋊(C3⋊C8)—21no—
71#466—91no—
72#427—91no—
73#367—91no—
74#366—91no—
75#357—91no—
76#357C3⋊D311yescharacteristic, complemented
77C22⋊C16—91no—
78C2×C3×D4—24no—
79C2×#67—124no—
80C2×C4×D3—34no—
81C3×D8—24no—
82C3×D8—24no—
83C2×C3×C8C22×D314yes—
84C3×C4⋊C4—24no—
85#217—124no—
86(C2×D3)⋊C4—124no—
87C4⋊Dic3—64no—
88C4⋊Dic3—64no—
89C4×Dic3—124no—
90C2×C3⋊C8—34no—
91D3×C8—64no—
92D3×C8—64no—
93C3×C16—24no—
94C3⋊C16—64no—
95C22×C32—81no—
96C22×C32—81no—
97C22×C32—81no—
98C22×C32C2×D811yescharacteristic
99C2×C3⋊D3—21no—
100C2×C3⋊D3—21no—
101C2×C3⋊D3—21no—
102C32×C4—81no—
103C32×C4#12311yescharacteristic
104C32×C4#13711yescharacteristic
105C3⋊Dic3—21no—
106C3⋊Dic3—81no—
107C3⋊Dic3—81no—
108C2×D8C2×C3⋊D311yescharacteristic
109C22×C8—91no—
110#121—181no—
111#117—181no—
112C2×C16—91no—
113C2×C16C2×C3⋊D311yescharacteristic
114#107—91no—
115#107—91no—
116#107C2×C3⋊D311yescharacteristic
117#106—181no—
118#102—181no—
119C23×C3—44no—
120C22×D3—34no—
121C3×D4—44no—
122C3×D4—44no—
123C2×C3×C4—44no—
124C2×C3×C4D3×D414yes—
125#67—248no—
126C2×Dic3—34no—
127C2×Dic3—124no—
128C2×Dic3—124no—
129C4×D3—64no—
130C4×D3—64no—
131C3×C8#23514yes—
132C3×C8#23714yes—
133C3⋊C8—64no—
134C2×C32—161no—
135C2×C32#48011yescharacteristic
136C2×C32#50811yescharacteristic
137C2×C32#50911yescharacteristic
138C3⋊D3—41no—
139C2×D4—21no—
140C2×D4—361no—
141C22×C4—91no—
142D8—21no—
143D8—21no—
144C2×C8—91no—
145C2×C8—181no—
146C2×C8—181no—
147C2×C8C22×C3⋊D311yescharacteristic
148C4⋊C4—21no—
149C4⋊C4—181no—
150C4⋊C4—181no—
151C22⋊C4—361no—
152C22⋊C4—361no—
153C42—361no—
154C16—21no—
155C16—181no—
156C22×C3—84no—
157C22×C3—84no—
158C22×C3—84no—
159C22×C3D3×D814yes—
160C2×D3—64no—
161C2×D3—64no—
162C2×D3—64no—
163C3×C4—84no—
164C3×C4#88314yes—
165C3×C4#91514yes—
166Dic3—64no—
167Dic3—244no—
168Dic3—244no—
169C32#223411yescharacteristic, complemented, Sylow
170C23—41no—
171C23—91no—
172D4—41no—
173D4—41no—
174D4—722no—
175C2×C4—41no—
176C2×C4—91no—
177C2×C4—181no—
178C2×C4—181no—
179C2×C4—361no—
180C2×C4—361no—
181C2×C4D4×C3⋊D311yescharacteristic
182C8—181no—
183C8#382811yescharacteristic
184C8#383011yescharacteristic
185C2×C3—164no—
186C2×C3#477414yes—
187C2×C3#491214yes—
188C2×C3#491414yes—
189D3—124no—
190C22—81no—
191C22—81no—
192C22—81no—
193C22—181no—
194C22—181no—
195C22—181no—
196C22D8×C3⋊D311yescharacteristic
197C4—81no—
198C4—181no—
199C4—721no—
200C4—721no—
201C4#6409211yescharacteristic
202C4#6412411yescharacteristic
203C3#6920114yescomplemented
204C2—161no—
205C2—361no—
206C2#1059247311yescharacteristic
207C2#1059261111yescharacteristic
208C2#1059261311yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#357C2
socleC22×C32C2×D8
prime radical#10592856C2
hypercenter#357C3⋊D3
hypocenterC32#2234
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. #10592579C2semidirect
3. C32×#357C2semidirect
4. #10589428C2semidirect
5. #10589373C2semidirect
6. #10589370C2semidirect
7. #10589356C2semidirect
22. C3×#357D3semidirect
76. #357C3⋊D3semidirect
169. C32#2234semidirect
203. C3#69201semidirect

Maximal subgroups

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

subgroupindex
#105928562
#105925792
C32×#3572
#105894282
#105893732
#105893702
#105893562
#692013