Finite Group Databasebeta

← #11794274

Subgroups — #11794274

Order 1152.

345 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 345 conjugacy classes of subgroups — too many to draw. Only its 100 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#10589602C211yesmaximal, characteristic
2C9×#382C211yesmaximal, characteristic
3#10588644C212yesmaximal
4#10588207C211yesmaximal, characteristic
5#10588201C212yesmaximal
6#69543—31nomaximal
7C2×C9×C4⋊C4C2211yescharacteristic
8C2×C9×C4⋊C4C2211yescharacteristic
9C2×C42×C9C2211yescharacteristic
10#63488C2212yes—
11#63486—22no—
12C2×#3667C2212yes—
13#63452—22no—
14#63450—22no—
15C9×#95—22no—
16#63367—22no—
17#63366—22no—
18#5500—31no—
19C3×#382D311yescharacteristic
20#4964—32no—
21#4530—31no—
22#4523—32no—
23C22×C4×C9—21no—
24C22×C4×C9—21no—
25C22×C4×C9D412yes—
26C22×C4×C9C2311yescharacteristic
27C2×Dic18—22no—
28C9×C4⋊C4—22no—
29C9×C4⋊C4—22no—
30C42×C9—21no—
31C42×C9Q812yescomplemented
32#3676—22no—
33C4⋊Dic9—22no—
34C4⋊Dic9D412yes—
35C4⋊Dic9D412yes—
36Dic9⋊C4—24no—
37C4×Dic9—22no—
38#3667—22no—
39#3667Q814yescomplemented
40C2×C9⋊C8—22no—
41#2061—91noSylow
42C2×C3×C4⋊C4C2×D311yescharacteristic
43C2×C3×C4⋊C4C2×D311yescharacteristic
44C2×C3×C42C2×D311yescharacteristic
45#926—32no—
46#924—62no—
47C2×#208—32no—
48#890—62no—
49#888—62no—
50C3×#95—22no—
51#808—62no—
52#807—62no—
53C23×C9C2×D411yescharacteristic
54C2×C4×C9—22no—
55C2×C4×C9—22no—
56C2×C4×C9—41no—
57C2×C4×C9—41no—
58C2×C4×C9—42no—
59C2×C4×C9—42no—
60C2×C4×C9—41no—
61C2×C4×C9C2×D412yes—
62C2×C4×C9C2×Q811yescharacteristic
63C2×C4×C9C2×Q812yes—
64C2×C4×C9#4111yescharacteristic
65C2×Dic9—22no—
66C2×Dic9—22no—
67Dic18—82no—
68C9⋊C8—24no—
69#544—91no—
70#428—92no—
71#382D911yescharacteristic
72#343—91no—
73#339—92no—
74C22×C3×C4—21no—
75C22×C3×C4—21no—
76C22×C3×C4#6712yes—
77C22×C3×C4C22×D311yescharacteristic
78C2×Dic6—62no—
79C3×C4⋊C4—22no—
80C3×C4⋊C4—22no—
81C3×C42—21no—
82C3×C42Dic612yes—
83#217—62no—
84C4⋊Dic3—32no—
85C4⋊Dic3—32no—
86C4⋊Dic3—62no—
87Dic3⋊C4—64no—
88C4×Dic3—62no—
89#208—34no—
90#208—62no—
91C2×C3⋊C8—62no—
92C22×C9—21no—
93C22×C9—21no—
94C22×C9#12011yescharacteristic
95C22×C9C22⋊Q811yescharacteristic
96C22×C9C4⋊Q811yescharacteristic
97C4×C9—42no—
98C4×C9—42no—
99C4×C9—81no—
100C4×C9C22⋊Q812yes—
101C4×C9C4⋊Q812yes—
102Dic9—42no—
103Dic9—42no—
104C2×M16—92no—
105C4⋊Q8—182no—
106#125—182no—
107C22⋊Q8—182no—
108#117—92no—
109C2×C4⋊C4C2×D911yescharacteristic
110C2×C4⋊C4C2×D911yescharacteristic
111C2×C42C2×D911yescharacteristic
112#107—182no—
113#106—182no—
114#95—22no—
115C23×C3C2×#6711yescharacteristic
116C2×C3×C4—22no—
117C2×C3×C4—22no—
118C2×C3×C4—41no—
119C2×C3×C4—41no—
120C2×C3×C4—42no—
121C2×C3×C4—42no—
122C2×C3×C4—41no—
123C2×C3×C4C2×Dic611yescharacteristic
124C2×C3×C4#23511yescharacteristic
125C2×C3×C4D3×D412yes—
126C2×C3×C4D3×Q812yes—
127C2×Dic3—62no—
128C2×Dic3—62no—
129Dic6—242no—
130C3⋊C8—64no—
131C2×C9—21no—
132C2×C9—21no—
133C2×C9#39511yescharacteristic
134C2×C9#45411yescharacteristic
135C2×C9#45511yescharacteristic
136C2×Q8—182no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4#61112yes—
140C22×C4C22×D911yescharacteristic
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—
153C42Dic1812yescomplemented
154C22×C3—21no—
155C22×C3—21no—
156C22×C3#92411yescharacteristic
157C22×C3#93711yescharacteristic
158C22×C3#94411yescharacteristic
159C3×C4—42no—
160C3×C4—42no—
161C3×C4—81no—
162C3×C4#88812yes—
163C3×C4#89612yes—
164Dic3—122no—
165Dic3—122no—
166C9#206111yescharacteristic, complemented, Sylow
167C23C2×#61111yescharacteristic
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×Dic1811yescharacteristic
179C2×C4#369711yescharacteristic
180C2×C4D4×D912yes—
181C2×C4Q8×D912yes—
182C8—184no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3#497911yescharacteristic
186C2×C3#506111yescharacteristic
187C2×C3#506211yescharacteristic
188C22—21no—
189C22—21no—
190C22#6348611yescharacteristic
191C22#6349911yescharacteristic
192C22#6350611yescharacteristic
193C4—42no—
194C4—42no—
195C4—81no—
196C4—362no—
197C4—362no—
198C4#6345012yes—
199C4#6345812yes—
200C3#6954311yescharacteristic
201C2—21no—
202C2—21no—
203C2#1058865911yescharacteristic
204C2#1058874111yescharacteristic
205C2#1058874211yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#382C2
socleC22×C3#937
prime radicalC23×C3C2×#67
hypercenter#382D9
hypocenterC9#2061
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
31. C42×C9Q8semidirect
39. #3667Q8semidirect
153. C42Dic18semidirect
166. C9#2061semidirect

Maximal subgroups

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

subgroupindex
#105896022
C9×#3822
#105886442
#105882072
#105882012
#695433