Finite Group Databasebeta

← #11778804

Subgroups — #11778804

Order 1152.

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

normal subgroups only

This group has 606 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
1#10595971C211yesmaximal, characteristic
2C32×#400C211yesmaximal, characteristic
3#10592669C212yesmaximal
4#10589394C211yesmaximal, characteristic
5#10589318C212yesmaximal
6#69719—34nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9#64135—21no—
10#64133—21no—
11#64133C2212yes—
12#64099—22no—
13#64097—22no—
14C32×#95—21no—
15C32×#95—21no—
16C32×#95C2211yescharacteristic
17#63657C2212yes—
18#63637—22no—
19#63634—22no—
20#5500—34no—
21C3×#400D314yes—
22#4970—38no—
23#4528—34no—
24#4452—38no—
25C22×C32×C4—21no—
26C22×C32×C4—21no—
27C22×C32×C4D411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4C2311yescharacteristic
30C2×#634—21no—
31C2×#634D412yes—
32C32×C4⋊C4—22no—
33C32×C4⋊C4—22no—
34#3757—22no—
35C4⋊(C3⋊Dic3)—21no—
36C4⋊(C3⋊Dic3)—21no—
37C4⋊(C3⋊Dic3)—21no—
38C4⋊(C3⋊Dic3)D412yes—
39#3750—22no—
40#3750—22no—
41C4×C3⋊Dic3—22no—
42C2×C3⋊(C3⋊C8)—22no—
43#1617—91noSylow
44C2×C3×C4⋊C4C2×D314yes—
45C2×C3×C4⋊C4C2×D314yes—
46#926—64no—
47#924—38no—
48#924—64no—
49#890—68no—
50#888—68no—
51C3×#95—24no—
52C3×#95—24no—
53C3×#95C2×D314yes—
54#830—38no—
55#810—68no—
56#807—68no—
57C23×C32C2×D411yescharacteristic
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4—21no—
61C2×C32×C4—41no—
62C2×C32×C4—41no—
63C2×C32×C4—41no—
64C2×C32×C4—41no—
65C2×C32×C4—42no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4Q1612yes—
69C2×C32×C4C2×D412yes—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—22no—
72#634—42no—
73#634—81no—
74C3⋊(C3⋊C8)—42no—
75#544—91no—
76#484—92no—
77#400C3⋊D311yescharacteristic
78#328—92no—
79#324—91no—
80C22×C3×C4—24no—
81C22×C3×C4—24no—
82C22×C3×C4#6714yes—
83C22×C3×C4#6714yes—
84C22×C3×C4C22×D314yes—
85C2×Dic6—38no—
86C2×Dic6—64no—
87C3×C4⋊C4—28no—
88C3×C4⋊C4—28no—
89#217—68no—
90C4⋊Dic3—38no—
91C4⋊Dic3—64no—
92C4⋊Dic3—64no—
93C4⋊Dic3—64no—
94Dic3⋊C4—68no—
95Dic3⋊C4—68no—
96C4×Dic3—68no—
97C2×C3⋊C8—68no—
98C22×C32—21no—
99C22×C32—21no—
100C22×C32#12011yescharacteristic
101C22×C32C2×Q1611yescharacteristic
102C22×C32#13711yescharacteristic
103C32×C4—22no—
104C32×C4—22no—
105C32×C4—41no—
106C32×C4—81no—
107C32×C4—81no—
108C3⋊Dic3—42no—
109C3⋊Dic3—42no—
110C4⋊Q8—182no—
111#125—182no—
112C22⋊Q8—92no—
113C22⋊Q8—181no—
114#117—181no—
115C2×C4⋊C4C2×C3⋊D311yescharacteristic
116C2×C4⋊C4C2×C3⋊D311yescharacteristic
117#107—182no—
118#103—182no—
119C22⋊C8—92no—
120#95—21no—
121#95—21no—
122#95C2×C3⋊D311yescharacteristic
123C23×C3C2×#6714yes—
124C2×C3×C4—24no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—44no—
128C2×C3×C4—44no—
129C2×C3×C4—44no—
130C2×C3×C4—44no—
131C2×C3×C4—48no—
132C2×C3×C4—44no—
133C2×C3×C4—44no—
134C2×C3×C4#21618yes—
135C2×C3×C4D3×D418yes—
136C2×Dic3—68no—
137C2×Dic3—68no—
138Dic6—128no—
139Dic6—244no—
140C3⋊C8—128no—
141C2×C32—21no—
142C2×C32—21no—
143C2×C32#45111yescharacteristic
144C2×C32#45411yescharacteristic
145C2×C32#45811yescharacteristic
146C2×Q8—92no—
147C2×Q8—181no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4#63811yescharacteristic
151C22×C4#63811yescharacteristic
152C22×C4C22×C3⋊D311yescharacteristic
153C2×C8—182no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—92no—
157C4⋊C4—181no—
158C4⋊C4—181no—
159C4⋊C4—181no—
160C4⋊C4—182no—
161C4⋊C4—182no—
162C22⋊C4—182no—
163C42—182no—
164C22×C3—24no—
165C22×C3—24no—
166C22×C3#93714yes—
167C22×C3C2×#21614yes—
168C22×C3#95114yes—
169C3×C4—28no—
170C3×C4—28no—
171C3×C4—44no—
172C3×C4—84no—
173C3×C4—84no—
174Dic3—128no—
175Dic3—128no—
176C32#161711yescharacteristic, complemented, Sylow
177C23C2×#63811yescharacteristic
178Q8—362no—
179Q8—721no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—42no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—182no—
191C2×C4—182no—
192C2×C4#375612yes—
193C2×C4D4×C3⋊D312yes—
194C8—362no—
195C2×C3—24no—
196C2×C3—24no—
197C2×C3#505014yes—
198C2×C3#505314yes—
199C2×C3#506214yes—
200C22—21no—
201C22—21no—
202C22#6414611yescharacteristic
203C22C2×#375611yescharacteristic
204C22#6416011yescharacteristic
205C4—22no—
206C4—22no—
207C4—41no—
208C4—81no—
209C4—81no—
210C4—362no—
211C4—362no—
212C3#6971914yescomplemented
213C2—21no—
214C2—21no—
215C2#1059274911yescharacteristic
216C2#1059275211yescharacteristic
217C2#1059276111yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#400C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenter#400C3⋊D3
hypocenterC32#1617
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
176. C32#1617semidirect
212. C3#69719semidirect

Maximal subgroups

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

subgroupindex
#105959712
C32×#4002
#105926692
#105893942
#105893182
#697193