Finite Group Databasebeta

← #11781871

Subgroups — #11781871

Order 1152.

438 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 139 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×#498C211yesmaximal, characteristic
2#10592790C211yesmaximal, characteristic
3#10592789C211yesmaximal, characteristic
4#10592378C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic
6#10589412C211yesmaximal, characteristic
7#10589324C211yesmaximal, characteristic
8#71349—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—21no—
12C4×#634C2211yescharacteristic
13C32×#106—21no—
14C32×#106—21no—
15C32×C4×C8C2211yescharacteristic
16#63662—21no—
17#63642—21no—
18#63641—21no—
19#63637—21no—
20#63634—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#498D314yes—
25#5091—34no—
26#5090—34no—
27#4679—34no—
28#4547—34no—
29#4546—34no—
30#4458—34no—
31C2×C32×Q8—21no—
32C2×C32×Q8—21no—
33C2×#634D411yescharacteristic
34C2×C32×C8D411yescharacteristic
35C2×C32×C8D411yescharacteristic
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C42C2311yescharacteristic
41#3756—42no—
42C4⋊(C3⋊Dic3)D411yescharacteristic
43#3750—21no—
44C4×C3⋊Dic3—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48#1692—91noSylow
49C3×C4⋊Q8C2×D314yes—
50C3×C4⋊Q8C2×D314yes—
51C2×#216—64no—
52C4×Dic6—34no—
53C3×#106—24no—
54C3×#106—24no—
55C3×C4×C8C2×D314yes—
56#835—64no—
57#815—64no—
58Dic3⋊C8—64no—
59#810—64no—
60#807—64no—
61C4⋊(C3⋊C8)—34no—
62C4⋊(C3⋊C8)—34no—
63C4⋊(C3⋊C8)—34no—
64C32×Q8—41no—
65C32×Q8—41no—
66C32×Q8—81no—
67C2×C32×C4—41no—
68C2×C32×C4—41no—
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4#4111yescharacteristic
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—21no—
74#634—21no—
75#634—21no—
76C32×C8—21no—
77C32×C8Q1612yescomplemented
78C3⋊(C3⋊C8)—41no—
79C3⋊(C3⋊C8)—41no—
80C3⋊(C3⋊C8)—41no—
81#498C3⋊D311yescharacteristic
82#477—91no—
83#462—91no—
84#446—91no—
85#335—91no—
86#333—91no—
87#332—91no—
88C2×C3×Q8—24no—
89C2×C3×Q8—24no—
90C2×Dic6—34no—
91C2×C3×C8#6714yes—
92C2×C3×C8#6714yes—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4—24no—
97C3×C42C22×D314yes—
98#216—128no—
99C4⋊Dic3—34no—
100Dic3⋊C4—64no—
101C4×Dic3—64no—
102C2×C3⋊C8—64no—
103C2×C3⋊C8—64no—
104C2×C3⋊C8—64no—
105C22×C32#12111yescharacteristic
106C32×C4—21no—
107C32×C4—81no—
108C32×C4—81no—
109C32×C4C2×Q1611yescharacteristic
110C32×C4AGL(1,ℤ/8)11yescharacteristic
111C32×C4#13711yescharacteristic
112C32×C4#13711yescharacteristic
113C3⋊Dic3—41no—
114C3⋊Dic3—41no—
115C2×Q16—181no—
116C4⋊Q8C2×C3⋊D311yescharacteristic
117C4⋊Q8C2×C3⋊D311yescharacteristic
118C4×Q8—91no—
119#107—181no—
120#106—21no—
121#106—21no—
122C4⋊C8—91no—
123C4⋊C8—91no—
124C4⋊C8—91no—
125C4⋊C8—181no—
126#103—181no—
127#103—181no—
128#97—181no—
129C4×C8C2×C3⋊D311yescharacteristic
130C3×Q8—44no—
131C3×Q8—44no—
132C3×Q8—84no—
133C2×C3×C4—44no—
134C2×C3×C4—44no—
135C2×C3×C4D3×D414yes—
136C2×C3×C4#23714yes—
137C2×C3×C4C2×#6714yes—
138C2×Dic3—64no—
139C2×Dic3—64no—
140Dic6—64no—
141Dic6—64no—
142C3×C8—24no—
143C3×C8#21618yescomplemented
144C3⋊C8—124no—
145C3⋊C8—124no—
146C3⋊C8—124no—
147C2×C32#46211yescharacteristic
148C2×C32#46811yescharacteristic
149C2×C32#47111yescharacteristic
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—91no—
153Q16—362no—
154C2×C8—181no—
155C2×C8—181no—
156C2×C8—181no—
157C2×C8#63811yescharacteristic
158C2×C8#63811yescharacteristic
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—91no—
164C4⋊C4—181no—
165C42—181no—
166C42C22×C3⋊D311yescharacteristic
167C22×C3#93814yes—
168C3×C4—24no—
169C3×C4—84no—
170C3×C4—84no—
171C3×C4#91414yes—
172C3×C4#91514yes—
173C3×C4#94214yes—
174C3×C4C2×#21614yes—
175Dic3—124no—
176Dic3—124no—
177C32#169211yescharacteristic, complemented, Sylow
178Q8—41no—
179Q8—41no—
180Q8—81no—
181Q8—181no—
182Q8—181no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—181no—
186C2×C4—181no—
187C2×C4D4×C3⋊D311yescharacteristic
188C2×C4#383011yescharacteristic
189C2×C4C2×#63811yescharacteristic
190C8—21no—
191C8—361no—
192C8—361no—
193C8—361no—
194C8#375612yescomplemented
195C2×C3#509014yes—
196C2×C3#517414yes—
197C2×C3#517714yes—
198C22#6414711yescharacteristic
199C4—21no—
200C4—81no—
201C4—81no—
202C4—361no—
203C4—361no—
204C4#6412311yescharacteristic
205C4#6412411yescharacteristic
206C4#6415111yescharacteristic
207C4C2×#375611yescharacteristic
208C3#7134914yescomplemented
209C2#1059278911yescharacteristic
210C2#1059287311yescharacteristic
211C2#1059287611yescharacteristic
subgroupG/H
centerC22#64147
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#498C2
socle, prime radicalC22×C32#121
hypercenter#498C3⋊D3
hypocenterC32#1692
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
77. C32×C8Q16semidirect
143. C3×C8#216semidirect
177. C32#1692semidirect
194. C8#3756semidirect
208. C3#71349semidirect

Maximal subgroups

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

subgroupindex
C32×#4982
#105927902
#105927892
#105923782
#105894132
#105894122
#105893242
#713493