Finite Group Databasebeta

← #11781985

Subgroups — #11781985

Order 1152.

462 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 129 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×#476C211yesmaximal, characteristic
2#10592777C211yesmaximal, characteristic, complemented
3#10592711C211yesmaximal, characteristic
4#10592707C211yesmaximal, characteristic
5#10589412C211yesmaximal, characteristic, complemented
6#10589347C211yesmaximal, characteristic, complemented
7#10589346C211yesmaximal, characteristic, complemented
8#71137—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4×D4C2211yescharacteristic
11C2×#3748—21no—
12#64078C2211yescharacteristic
13C32×#106—21no—
14C32×C4⋊C8C2211yescharacteristic
15C32×#102—21no—
16#63659—21no—
17#63657—21no—
18#63635—21no—
19#63634—21no—
20#63634—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#476D314yes—
25#5078—34no—
26#5012—34no—
27#5008—34no—
28#4546—34no—
29#4481—34no—
30#4480—34no—
31C2×C32×Q8—21no—
32C2×C32×D4D411yescharacteristic
33C22×C32×C4—21no—
34C2×#634—21no—
35C2×C32×C8—21no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4D411yescharacteristic
39C32×C22⋊C4—21no—
40C32×C42C2311yescharacteristic
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43#3748—42no—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48#1695—91noSylow
49C3×C4⋊Q8C2×D314yes—
50C3×C4×D4C2×D314yes—
51C2×#208—64no—
52#869—34no—
53C3×#106—24no—
54C3×C4⋊C8C2×D314yes—
55C3×#102—24no—
56#832—64no—
57#830—64no—
58#808—64no—
59#807—64no—
60#807—64no—
61C4⋊(C3⋊C8)—34no—
62C4⋊(C3⋊C8)—34no—
63C4×C3⋊C8—34no—
64C23×C32—21no—
65C32×Q8—81no—
66C32×D4—21no—
67C32×D4—21no—
68C2×C32×C4—21no—
69C2×C32×C4—41no—
70C2×C32×C4—41no—
71C2×C32×C4—41no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C3⋊Dic3—41no—
76#634—81no—
77C32×C8—41no—
78C3⋊(C3⋊C8)—21no—
79C3⋊(C3⋊C8)—41no—
80C3⋊(C3⋊C8)—41no—
81C3⋊(C3⋊C8)SD1612yes—
82#500—91no—
83#476—91no—
84#476C3⋊D311yescharacteristic
85#436—91no—
86#334—91no—
87#333—91no—
88#333—91no—
89C2×C3×Q8—24no—
90C2×C3×D4#6714yes—
91C22×C3×C4—24no—
92C2×Dic6—64no—
93C2×C3×C8—24no—
94C3×C4⋊C4—24no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4#6714yes—
97C3×C22⋊C4—24no—
98C3×C42C22×D314yes—
99C4⋊Dic3—64no—
100C4⋊Dic3—64no—
101#208—128no—
102C2×C3⋊C8—34no—
103C2×C3⋊C8—34no—
104C2×C3⋊C8—64no—
105C2×C3⋊C8—64no—
106C22×C32—41no—
107C22×C32—41no—
108C22×C32—41no—
109C22×C32#12111yescharacteristic
110C32×C4—21no—
111C32×C4—41no—
112C32×C4—81no—
113C32×C4C2×SD1611yescharacteristic
114C32×C4#13711yescharacteristic
115C32×C4#13711yescharacteristic
116C32×C4#13711yescharacteristic
117C3⋊Dic3—81no—
118C2×M16—181no—
119C4⋊Q8—91no—
120C4⋊Q8C2×C3⋊D311yescharacteristic
121C4×D4C2×C3⋊D311yescharacteristic
122#107—181no—
123#107—181no—
124#106—21no—
125#106—181no—
126C4⋊C8—91no—
127C4⋊C8—91no—
128C4⋊C8C2×C3⋊D311yescharacteristic
129#102—21no—
130#102—181no—
131C22⋊C8—181no—
132C4×C8—91no—
133C23×C3—24no—
134C3×Q8—84no—
135C3×D4—24no—
136C3×D4—24no—
137C2×C3×C4—24no—
138C2×C3×C4—44no—
139C2×C3×C4—44no—
140C2×C3×C4—44no—
141C2×C3×C4D3×D414yes—
142C2×C3×C4#23714yes—
143C2×C3×C4C2×#6714yes—
144C2×Dic3—124no—
145Dic6—244no—
146C3×C8—44no—
147C3⋊C8—38no—
148C3⋊C8—64no—
149C3⋊C8—124no—
150C3⋊C8—124no—
151C2×C32—81no—
152C2×C32#46111yescharacteristic
153C2×C32#47011yescharacteristic
154C2×C32#47211yescharacteristic
155C2×Q8—21no—
156C2×Q8—181no—
157C2×D4#63811yescharacteristic
158C22×C4—21no—
159M16—362no—
160C2×C8—21no—
161C2×C8—91no—
162C2×C8—91no—
163C2×C8—181no—
164C2×C8—181no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—181no—
168C4⋊C4—181no—
169C4⋊C4#63811yescharacteristic
170C22⋊C4—21no—
171C42C22×C3⋊D311yescharacteristic
172C22×C3—44no—
173C22×C3—44no—
174C22×C3—44no—
175C22×C3#93914yes—
176C3×C4—24no—
177C3×C4—44no—
178C3×C4—84no—
179C3×C4D3×SD1614yes—
180C3×C4#91514yes—
181C3×C4#94214yes—
182C3×C4#95114yes—
183Dic3—244no—
184C32#169511yescharacteristic, complemented, Sylow
185C23—21no—
186Q8—81no—
187Q8—721no—
188D4—21no—
189D4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—361no—
195C2×C4D4×C3⋊D311yescharacteristic
196C2×C4#383011yescharacteristic
197C2×C4C2×#63811yescharacteristic
198C8—41no—
199C8—92no—
200C8—181no—
201C8—361no—
202C8—361no—
203C2×C3—84no—
204C2×C3#505214yes—
205C2×C3#516214yes—
206C2×C3#519914yes—
207C22—41no—
208C22—41no—
209C22—41no—
210C22#6414811yescharacteristic
211C4—21no—
212C4—41no—
213C4—81no—
214C4—721no—
215C4SD16×C3⋊D311yescharacteristic
216C4#6412411yescharacteristic
217C4#6415111yescharacteristic
218C4#6416011yescharacteristic
219C3#7113714yescomplemented
220C2—81no—
221C2#1059275111yescharacteristic
222C2#1059286111yescharacteristic
223C2#1059289811yescharacteristic
subgroupG/H
centerC22#64148
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#476C2
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenter#476C3⋊D3
hypocenterC32#1695
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #10592777C2semidirect
5. #10589412C2semidirect
6. #10589347C2semidirect
7. #10589346C2semidirect
184. C32#1695semidirect
219. C3#71137semidirect

Maximal subgroups

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

subgroupindex
C32×#4762
#105927772
#105927112
#105927072
#105894122
#105893472
#105893462
#711373