Finite Group Databasebeta

← #11794275

Subgroups — #11794275

Order 1152.

690 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 181 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×#382C211yesmaximal, characteristic
3#10592663C212yesmaximal
4#10589396C211yesmaximal, characteristic
5#10589389C212yesmaximal
6#69543—34nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×C32×C42C2211yescharacteristic
10#64135C2212yes—
11#64133—22no—
12C2×#3748C2212yes—
13#64099—22no—
14#64097—22no—
15C32×#95—22no—
16#63635—22no—
17#63634—22no—
18#5500—34no—
19C3×#382D314yes—
20#4964—38no—
21#4530—34no—
22#4523—38no—
23C22×C32×C4—21no—
24C22×C32×C4—21no—
25C22×C32×C4D412yes—
26C22×C32×C4C2311yescharacteristic
27C2×#634—22no—
28C32×C4⋊C4—22no—
29C32×C4⋊C4—22no—
30C32×C42—21no—
31C32×C42Q812yescomplemented
32#3757—22no—
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)D412yes—
35C4⋊(C3⋊Dic3)D412yes—
36#3750—24no—
37C4×C3⋊Dic3—22no—
38#3748—22no—
39#3748Q814yescomplemented
40C2×C3⋊(C3⋊C8)—22no—
41#2061—91noSylow
42C2×C3×C4⋊C4C2×D314yes—
43C2×C3×C4⋊C4C2×D314yes—
44C2×C3×C42C2×D314yes—
45#926—38no—
46#924—68no—
47C2×#208—38no—
48#890—68no—
49#888—68no—
50C3×#95—28no—
51#808—68no—
52#807—68no—
53C23×C32C2×D411yescharacteristic
54C2×C32×C4—22no—
55C2×C32×C4—22no—
56C2×C32×C4—41no—
57C2×C32×C4—41no—
58C2×C32×C4—42no—
59C2×C32×C4—42no—
60C2×C32×C4—41no—
61C2×C32×C4C2×D412yes—
62C2×C32×C4C2×Q811yescharacteristic
63C2×C32×C4C2×Q812yes—
64C2×C32×C4#4111yescharacteristic
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—22no—
67#634—82no—
68C3⋊(C3⋊C8)—24no—
69#544—91no—
70#428—92no—
71#382C3⋊D311yescharacteristic
72#343—91no—
73#339—92no—
74C22×C3×C4—24no—
75C22×C3×C4—24no—
76C22×C3×C4#6718yes—
77C22×C3×C4C22×D314yes—
78C2×Dic6—68no—
79C3×C4⋊C4—28no—
80C3×C4⋊C4—28no—
81C3×C42—24no—
82C3×C42Dic618yescomplemented
83#217—68no—
84C4⋊Dic3—38no—
85C4⋊Dic3—38no—
86C4⋊Dic3—68no—
87Dic3⋊C4—616no—
88C4×Dic3—68no—
89#208—316no—
90#208—68no—
91C2×C3⋊C8—68no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32#12011yescharacteristic
95C22×C32C22⋊Q811yescharacteristic
96C22×C32C4⋊Q811yescharacteristic
97C32×C4—42no—
98C32×C4—42no—
99C32×C4—81no—
100C32×C4C22⋊Q812yes—
101C32×C4C4⋊Q812yes—
102C3⋊Dic3—42no—
103C3⋊Dic3—42no—
104C2×M16—92no—
105C4⋊Q8—182no—
106#125—182no—
107C22⋊Q8—182no—
108#117—92no—
109C2×C4⋊C4C2×C3⋊D311yescharacteristic
110C2×C4⋊C4C2×C3⋊D311yescharacteristic
111C2×C42C2×C3⋊D311yescharacteristic
112#107—182no—
113#106—182no—
114#95—22no—
115C23×C3C2×#6714yes—
116C2×C3×C4—28no—
117C2×C3×C4—28no—
118C2×C3×C4—44no—
119C2×C3×C4—44no—
120C2×C3×C4—48no—
121C2×C3×C4—48no—
122C2×C3×C4—44no—
123C2×C3×C4C2×Dic614yes—
124C2×C3×C4#23514yes—
125C2×C3×C4D3×D418yes—
126C2×C3×C4D3×Q818yes—
127C2×Dic3—68no—
128C2×Dic3—68no—
129Dic6—248no—
130C3⋊C8—616no—
131C2×C32—21no—
132C2×C32—21no—
133C2×C32#39511yescharacteristic
134C2×C32#45411yescharacteristic
135C2×C32#45511yescharacteristic
136C2×Q8—182no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4#63812yes—
140C22×C4C22×C3⋊D311yescharacteristic
141M16—94no—
142M16—182no—
143C2×C8—182no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C4⋊C4—92no—
147C4⋊C4—92no—
148C4⋊C4—182no—
149C4⋊C4—184no—
150C22⋊C4—182no—
151C42—21no—
152C42—182no—
153C42#63412yescomplemented
154C22×C3—24no—
155C22×C3—24no—
156C22×C3#92414yes—
157C22×C3#93714yes—
158C22×C3#94414yes—
159C3×C4—48no—
160C3×C4—48no—
161C3×C4—84no—
162C3×C4#88818yes—
163C3×C4#89618yes—
164Dic3—128no—
165Dic3—128no—
166C32#206111yescharacteristic, complemented, Sylow
167C23C2×#63811yescharacteristic
168Q8—722no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—41no—
176C2×C4—182no—
177C2×C4—182no—
178C2×C4C2×#63411yescharacteristic
179C2×C4#382811yescharacteristic
180C2×C4D4×C3⋊D312yes—
181C2×C4Q8×C3⋊D312yes—
182C8—184no—
183C2×C3—24no—
184C2×C3—24no—
185C2×C3#497914yes—
186C2×C3#506114yes—
187C2×C3#506214yes—
188C22—21no—
189C22—21no—
190C22#6413311yescharacteristic
191C22#6414611yescharacteristic
192C22#6415311yescharacteristic
193C4—42no—
194C4—42no—
195C4—81no—
196C4—362no—
197C4—362no—
198C4#6409712yes—
199C4#6410512yes—
200C3#6954314yescomplemented
201C2—21no—
202C2—21no—
203C2#1059267811yescharacteristic
204C2#1059276011yescharacteristic
205C2#1059276111yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#382C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenter#382C3⋊D3
hypocenterC32#2061
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
31. C32×C42Q8semidirect
39. #3748Q8semidirect
82. C3×C42Dic6semidirect
153. C42#634semidirect
166. C32#2061semidirect
200. C3#69543semidirect

Maximal subgroups

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

subgroupindex
#105959712
C32×#3822
#105926632
#105893962
#105893892
#695433