Finite Group Databasebeta

← #11781874

Subgroups — #11781874

Order 1152.

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

normal subgroups only

This group has 438 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×#462C211yesmaximal, characteristic
2#10592779C211yesmaximal, characteristic
3#10592723C211yesmaximal, characteristic
4#10592720C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic
6#10589347C211yesmaximal, characteristic
7#10589345C211yesmaximal, characteristic
8#71056—34nomaximal
9C2×C32×Q16—21no—
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12#64078C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C32×#103—21no—
15#63662—21no—
16#63635—21no—
17#63635—21no—
18#63634—21no—
19C4⋊(C3⋊(C3⋊C8))—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22#63630—21no—
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#462D314yes—
25#5080—34no—
26#5024—34no—
27#5021—34no—
28#4547—34no—
29#4481—34no—
30#4479—34no—
31C2×C32×Q8—21no—
32C2×C32×Q8D411yescharacteristic
33C2×#634—21no—
34C32×Q16—42no—
35C2×C32×C8—21no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4D411yescharacteristic
40C32×C42—21no—
41C32×C42C2311yescharacteristic
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48#1692—91noSylow
49C2×C3×Q16—24no—
50C3×C4⋊Q8C2×D314yes—
51C3×C4×Q8C2×D314yes—
52#869—34no—
53C3×C4⋊C8C2×D314yes—
54C3×#103—24no—
55#835—64no—
56#808—64no—
57#808—64no—
58#807—64no—
59C4⋊(C3⋊C8)—34no—
60C4⋊(C3⋊C8)—34no—
61C4⋊(C3⋊C8)—64no—
62#803—64no—
63C4×C3⋊C8—34no—
64C32×Q8—21no—
65C32×Q8—21no—
66C32×Q8—41no—
67C32×Q8—41no—
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4—41no—
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4#4111yescharacteristic
74C2×C3⋊Dic3—41no—
75#634—81no—
76C32×C8—41no—
77C3⋊(C3⋊C8)—21no—
78C3⋊(C3⋊C8)—41no—
79C3⋊(C3⋊C8)—41no—
80C3⋊(C3⋊C8)Q1612yescomplemented
81#498—91no—
82#477—91no—
83#462C3⋊D311yescharacteristic
84#446—91no—
85#335—91no—
86#333—91no—
87#332—91no—
88C2×C3×Q8—24no—
89C2×C3×Q8#6714yes—
90C2×Dic6—64no—
91C3×Q16—48no—
92C2×C3×C8—24no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4#6714yes—
97C3×C42—24no—
98C3×C42C22×D314yes—
99C4⋊Dic3—64no—
100C4⋊Dic3—64no—
101C2×C3⋊C8—34no—
102C2×C3⋊C8—34no—
103C2×C3⋊C8—64no—
104C2×C3⋊C8—64no—
105C22×C32#12111yescharacteristic
106C32×C4—21no—
107C32×C4—41no—
108C32×C4—41no—
109C32×C4—81no—
110C32×C4C2×Q1611yescharacteristic
111C32×C4AGL(1,ℤ/8)11yescharacteristic
112C32×C4#13711yescharacteristic
113C32×C4#13711yescharacteristic
114C3⋊Dic3—81no—
115C2×Q16—21no—
116C4⋊Q8—91no—
117C4⋊Q8C2×C3⋊D311yescharacteristic
118C4×Q8C2×C3⋊D311yescharacteristic
119#107—181no—
120#106—181no—
121#106—181no—
122C4⋊C8—91no—
123C4⋊C8—91no—
124C4⋊C8—181no—
125C4⋊C8C2×C3⋊D311yescharacteristic
126#103—21no—
127#103—181no—
128#97—181no—
129C4×C8—91no—
130C3×Q8—24no—
131C3×Q8—24no—
132C3×Q8—44no—
133C3×Q8—44no—
134C2×C3×C4—24no—
135C2×C3×C4—24no—
136C2×C3×C4—44no—
137C2×C3×C4D3×D414yes—
138C2×C3×C4#23714yes—
139C2×C3×C4C2×#6714yes—
140C2×Dic3—124no—
141Dic6—244no—
142C3×C8—44no—
143C3⋊C8—38no—
144C3⋊C8—64no—
145C3⋊C8—124no—
146C3⋊C8—124no—
147C2×C32#46211yescharacteristic
148C2×C32#46811yescharacteristic
149C2×C32#47111yescharacteristic
150C2×Q8—21no—
151C2×Q8—181no—
152C2×Q8#63811yescharacteristic
153Q16—42no—
154C2×C8—21no—
155C2×C8—91no—
156C2×C8—91no—
157C2×C8—181no—
158C2×C8—181no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—181no—
163C4⋊C4—181no—
164C4⋊C4#63811yescharacteristic
165C42—21no—
166C42C22×C3⋊D311yescharacteristic
167C22×C3#93914yes—
168C3×C4—24no—
169C3×C4—44no—
170C3×C4—44no—
171C3×C4—84no—
172C3×C4D3×Q1614yes—
173C3×C4#91814yes—
174C3×C4#93214yes—
175C3×C4#95114yes—
176Dic3—244no—
177C32#169211yescharacteristic, complemented, Sylow
178Q8—21no—
179Q8—21no—
180Q8—41no—
181Q8—41no—
182Q8—721no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—361no—
187C2×C4D4×C3⋊D311yescharacteristic
188C2×C4#383011yescharacteristic
189C2×C4C2×#63811yescharacteristic
190C8—41no—
191C8—92no—
192C8—181no—
193C8—361no—
194C8—361no—
195C2×C3#504214yes—
196C2×C3#518214yes—
197C2×C3#520314yes—
198C22#6414811yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—721no—
204C4Q16×C3⋊D311yescharacteristic
205C4#6412711yescharacteristic
206C4#6414111yescharacteristic
207C4#6416011yescharacteristic
208C3#7105614yescomplemented
209C2#1059274111yescharacteristic
210C2#1059288111yescharacteristic
211C2#1059290211yescharacteristic
subgroupG/H
centerC22#64148
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#462C2
socle, prime radicalC22×C32#121
hypercenter#462C3⋊D3
hypocenterC32#1692
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
80. C3⋊(C3⋊C8)Q16semidirect
177. C32#1692semidirect
208. C3#71056semidirect

Maximal subgroups

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

subgroupindex
C32×#4622
#105927792
#105927232
#105927202
#105894132
#105893472
#105893452
#710563