Finite Group Databasebeta

← #11920101

Subgroups — #11920101

Order 1152.

344 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C2×Q8×C22⋊C9C211yesmaximal, characteristic
2#10589511C212yesmaximal
3#72133—31nomaximal
4Q8×C22⋊C9—22no—
5C2×C4×C22⋊C9C412yes—
6C2×C4×C22⋊C9C2211yescharacteristic
7(C22⋊C9)⋊C8—22no—
8#63394—41nomaximal
9C23×C3×Q8D311yescharacteristic
10C2×#836—32no—
11C2×#836—31no—
12C2×#836—31no—
13#5207—32no—
14C22×C22⋊C9C2×C411yescharacteristic
15C2×Q8×C9—41no—
16C4×C22⋊C9—22no—
17C4×C22⋊C9D412yes—
18#3667—42no—
19#1784—91noSylow
20C22×C3×Q8—22no—
21C22×C3×Q8—31no—
22C22×C3×Q8—31no—
23C22×C3×Q8—32no—
24C22×C3×Q8—62no—
25C23×C3×C4Dic312yes—
26C23×C3×C4C2×D311yescharacteristic
27C2×#208—32no—
28C2×#208—32no—
29#836—64no—
30#836—62no—
31#836—61no—
32#836—61no—
33#830—62no—
34#830—62no—
35C2×C22⋊C9—21no—
36C2×C22⋊C9C22⋊C411yescharacteristic
37Q8×C9—82no—
38C2×C4×C9—42no—
39C2×C4×C9—41no—
40C9⋊C8—82no—
41C23×Q8D911yescharacteristic
42C2×#101—92no—
43C2×#101—91no—
44C2×#101—91no—
45#407—92no—
46C24×C3C2×Dic311yescharacteristic
47C2×C3×Q8—34no—
48C2×C3×Q8—32no—
49C2×C3×Q8—31no—
50C2×C3×Q8—61no—
51C2×C3×Q8—62no—
52C2×C3×Q8—62no—
53C2×C3×Q8—62no—
54C2×C3×Q8—64no—
55C2×C3×Q8—64no—
56C2×C3×Q8S411yescharacteristic
57C22×C3×C4—22no—
58C22×C3×C4—31no—
59C22×C3×C4—32no—
60C22×C3×C4—32no—
61C22×C3×C4—31no—
62C22×C3×C4—32no—
63C22×C3×C4—62no—
64C22×C3×C4#6712yes—
65#208—62no—
66#208—62no—
67#208—62no—
68#208—62no—
69C2×C3⋊C8—62no—
70C2×C3⋊C8—62no—
71C22×C9—41no—
72C22⋊C9#10111yescharacteristic, complemented
73C4×C9—42no—
74C4×C9—82no—
75C22×Q8—22no—
76C22×Q8—31no—
77C22×Q8—31no—
78C22×Q8—32no—
79C22×Q8—62no—
80C23×C4Dic912yes—
81C23×C4C2×D911yescharacteristic
82C2×M16—92no—
83C2×M16—92no—
84#101—184no—
85#101—182no—
86#101—181no—
87#101—181no—
88C22⋊C8—182no—
89C22⋊C8—182no—
90C23×C3—21no—
91C23×C3—31no—
92C23×C3—31no—
93C23×C3—61no—
94C23×C3#21711yescharacteristic
95C3×Q8—22no—
96C3×Q8—64no—
97C3×Q8—64no—
98C3×Q8—62no—
99C2×C3×C4—31no—
100C2×C3×C4—32no—
101C2×C3×C4—32no—
102C2×C3×C4—32no—
103C2×C3×C4—34no—
104C2×C3×C4—32no—
105C2×C3×C4—62no—
106C2×C3×C4—62no—
107C2×C3×C4—61no—
108C2×C3×C4—62no—
109C2×C3×C4SL(2,ℤ/4)12yes—
110C2×C3×C4C2×S411yescharacteristic
111C3⋊C8—122no—
112C3⋊C8—122no—
113C2×C9—41no—
114C2×C9—81no—
115C24C2×Dic911yescharacteristic
116C2×Q8—34no—
117C2×Q8—32no—
118C2×Q8—31no—
119C2×Q8—61no—
120C2×Q8—62no—
121C2×Q8—62no—
122C2×Q8—62no—
123C2×Q8—64no—
124C2×Q8—64no—
125C2×Q8(C22⋊C9)⋊C211yescharacteristic
126C22×C4—22no—
127C22×C4—31no—
128C22×C4—32no—
129C22×C4—32no—
130C22×C4—31no—
131C22×C4—32no—
132C22×C4—62no—
133C22×C4#61112yes—
134M16—182no—
135M16—182no—
136M16—182no—
137M16—182no—
138C2×C8—182no—
139C2×C8—182no—
140C22×C3—31no—
141C22×C3—31no—
142C22×C3—32no—
143C22×C3—31no—
144C22×C3—61no—
145C22×C3—61no—
146C22×C3—61no—
147C22×C3#83611yescharacteristic
148C22×C3C2×SL(2,ℤ/4)11yescharacteristic
149C3×C4—22no—
150C3×C4—32no—
151C3×C4—62no—
152C3×C4GL(2,ℤ/4)12yes—
153C9—41noSylow
154C23—21no—
155C23—31no—
156C23—31no—
157C23—61no—
158C23#367611yescharacteristic
159Q8—22no—
160Q8—64no—
161Q8—64no—
162Q8—62no—
163C2×C4—31no—
164C2×C4—32no—
165C2×C4—32no—
166C2×C4—32no—
167C2×C4—34no—
168C2×C4—32no—
169C2×C4—62no—
170C2×C4—62no—
171C2×C4—61no—
172C2×C4—62no—
173C2×C4(C22⋊C9)⋊C412yes—
174C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
175C8—362no—
176C8—362no—
177C2×C3—21no—
178C2×C3—31no—
179C2×C3—31no—
180C2×C3—61no—
181C2×C3#543211yescharacteristic
182C22—31no—
183C22—31no—
184C22—32no—
185C22—31no—
186C22—61no—
187C22—61no—
188C22—61no—
189C22#6339411yescharacteristic, complemented
190C22C2×(C22⋊C9)⋊C411yescharacteristic
191C4—22no—
192C4—32no—
193C4—62no—
194C4#6369412yes—
195C3#7314611yescharacteristic
196C2—21no—
197C2—31no—
198C2—31no—
199C2—61no—
200C2#1058953411yescharacteristic
subgroupG/H
centerC2#10589534
commutatorC22×C22⋊C9C2×C4
FrattiniC2×C3×C4C2×S4
FittingC23×C3×Q8D3
socleC23×C3#217
prime radicalC24×C3C2×Dic3
cosocleC2×C4×C22⋊C9C22
hypercenterC2×Q8(C22⋊C9)⋊C2
hypocenterC22⋊C9#101
LCSG ▷ C22×C22⋊C9 ▷ C2×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
72. C22⋊C9#101semidirect
189. C22#63394semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊C92
#105895112
#721333
#633944