Finite Group Databasebeta

← #11781370

Subgroups — #11781370

Order 1152.

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

normal subgroups only

This group has 450 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×#487C211yesmaximal, characteristic
2#10592793C211yesmaximal, characteristic
3#10592789C211yesmaximal, characteristic
4C8×#634C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic
6#10589413C211yesmaximal, characteristic
7#10589323C211yesmaximal, characteristic
8#71240—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—21no—
12C4×#634C2211yescharacteristic
13C32×#103—21no—
14C32×#103—21no—
15C32×C4×C8C2211yescharacteristic
16#63662—21no—
17#63641—21no—
18C8×C3⋊Dic3—21no—
19#63637—21no—
20#63635—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#487D314yes—
25#5094—34no—
26#5090—34no—
27C8×Dic6—34no—
28#4547—34no—
29#4547—34no—
30#4457—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#1680—91noSylow
49C3×C4⋊Q8C2×D314yes—
50C3×C4⋊Q8C2×D314yes—
51C2×#216—64no—
52C4×Dic6—34no—
53C3×#103—24no—
54C3×#103—24no—
55C3×C4×C8C2×D314yes—
56#835—64no—
57Dic3⋊C8—64no—
58C8×Dic3—64no—
59#810—64no—
60#808—64no—
61C4⋊(C3⋊C8)—34no—
62C4⋊(C3⋊C8)—34no—
63C4⋊(C3⋊C8)—34no—
64C32×Q8—41no—
65C32×Q8—41no—
66C32×Q8—41no—
67C32×Q8—41no—
68C2×C32×C4—41no—
69C2×C32×C4—41no—
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4#4111yescharacteristic
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3—21no—
75#634—21no—
76#634SD1612yes—
77C32×C8—21no—
78C32×C8—21no—
79C3⋊(C3⋊C8)—41no—
80C3⋊(C3⋊C8)—41no—
81C3⋊(C3⋊C8)—41no—
82#487C3⋊D311yescharacteristic
83#475—91no—
84#462—91no—
85C8×Q8—91no—
86#334—91no—
87#332—91no—
88#332—91no—
89C2×C3×Q8—24no—
90C2×C3×Q8—24no—
91C2×Dic6—34no—
92C2×C3×C8#6714yes—
93C2×C3×C8#6714yes—
94C3×C4⋊C4—24no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4—24no—
97C3×C4⋊C4—24no—
98C3×C42C22×D314yes—
99#216—128no—
100C4⋊Dic3—34no—
101Dic3⋊C4—64no—
102C4×Dic3—64no—
103C2×C3⋊C8—64no—
104C2×C3⋊C8—64no—
105C2×C3⋊C8—64no—
106C22×C32#12111yescharacteristic
107C32×C4—21no—
108C32×C4—81no—
109C32×C4—81no—
110C32×C4C2×SD1611yescharacteristic
111C32×C4#13511yescharacteristic
112C32×C4#13511yescharacteristic
113C32×C4#13711yescharacteristic
114C3⋊Dic3—22no—
115C3⋊Dic3—41no—
116C2×Q16—181no—
117C4⋊Q8C2×C3⋊D311yescharacteristic
118C4⋊Q8C2×C3⋊D311yescharacteristic
119C4×Q8—91no—
120#106—181no—
121C4⋊C8—91no—
122C4⋊C8—91no—
123C4⋊C8—91no—
124C4⋊C8—181no—
125#103—21no—
126#103—21no—
127#103—181no—
128#103—181no—
129C4×C8—181no—
130C4×C8C2×C3⋊D311yescharacteristic
131C3×Q8—44no—
132C3×Q8—44no—
133C3×Q8—44no—
134C3×Q8—44no—
135C2×C3×C4—44no—
136C2×C3×C4—44no—
137C2×C3×C4D3×D414yes—
138C2×C3×C4#23714yes—
139C2×C3×C4C2×#6714yes—
140C2×Dic3—64no—
141C2×Dic3—64no—
142Dic6—38no—
143Dic6—64no—
144C3×C8—24no—
145C3×C8—24no—
146C3⋊C8—124no—
147C3⋊C8—124no—
148C3⋊C8—124no—
149C2×C32#46411yescharacteristic
150C2×C32#46511yescharacteristic
151C2×C32#47311yescharacteristic
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—91no—
155Q16—362no—
156C2×C8—181no—
157C2×C8—181no—
158C2×C8—181no—
159C2×C8#63811yescharacteristic
160C2×C8#63811yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—91no—
166C4⋊C4—181no—
167C42—181no—
168C42C22×C3⋊D311yescharacteristic
169C22×C3#93814yes—
170C3×C4—24no—
171C3×C4—84no—
172C3×C4—84no—
173C3×C4D3×SD1614yes—
174C3×C4#91614yes—
175C3×C4#95014yes—
176C3×C4#95114yes—
177Dic3—68no—
178Dic3—124no—
179C32#168011yescharacteristic, complemented, Sylow
180Q8—41no—
181Q8—41no—
182Q8—41no—
183Q8—41no—
184Q8—92no—
185Q8—181no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—181no—
189C2×C4—181no—
190C2×C4D4×C3⋊D311yescharacteristic
191C2×C4#383011yescharacteristic
192C2×C4C2×#63811yescharacteristic
193C8—21no—
194C8—21no—
195C8—361no—
196C8—361no—
197C8—361no—
198C2×C3#505414yes—
199C2×C3#517114yes—
200C2×C3#519214yes—
201C22#6414711yescharacteristic
202C4—21no—
203C4—81no—
204C4—81no—
205C4—182no—
206C4—361no—
207C4SD16×C3⋊D311yescharacteristic
208C4#6412511yescharacteristic
209C4#6415911yescharacteristic
210C4#6416011yescharacteristic
211C3#7124014yescomplemented
212C2#1059275311yescharacteristic
213C2#1059287011yescharacteristic
214C2#1059289111yescharacteristic
subgroupG/H
centerC22#64147
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#487C2
socle, prime radicalC22×C32#121
hypercenter#487C3⋊D3
hypocenterC32#1680
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
179. C32#1680semidirect
211. C3#71240semidirect

Maximal subgroups

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

subgroupindex
C32×#4872
#105927932
#105927892
C8×#6342
#105894132
#105893232
#712403