Finite Group Databasebeta

← #11920183

Subgroups — #11920183

Order 1152.

466 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C42×C22⋊C9C211yesmaximal, characteristic
2C4⋊((C22⋊C9)⋊C4)C212yesmaximal
3((C22⋊C9)⋊C4)⋊C4C214yesmaximal
4#82074—31nomaximal
5C2×C4×C22⋊C9C2212yes—
6C2×C4×C22⋊C9C2211yescharacteristic
7C2×(C22⋊C9)⋊C4C2214yes—
8#63432—41nomaximal
9C22×C3×C42D311yescharacteristic
10C2×#870—31no—
11#5212—32no—
12#5210—34no—
13#4936—31no—
14#4933—34no—
15#4928—32no—
16C22×C22⋊C9C2311yescharacteristic
17C4×C22⋊C9—22no—
18C4×C22⋊C9Q812yes—
19(C22⋊C9)⋊C4—24no—
20C42×C9—41no—
21C4⋊Dic9—42no—
22Dic9⋊C4—44no—
23#2851—91noSylow
24C23×C3×C4C2×D312yes—
25C23×C3×C4C2×D311yescharacteristic
26C2×C3×C42—31no—
27C2×C3×C42—31no—
28C2×C3×C42—32no—
29C2×#217—34no—
30C2×C4⋊Dic3—32no—
31C2×C4⋊Dic3—32no—
32C2×Dic3⋊C4—34no—
33C2×Dic3⋊C4—34no—
34#870—61no—
35#870—62no—
36#870—61no—
37C3⋊#95—34no—
38C3⋊#95—34no—
39C3⋊#95—34no—
40C2×C22⋊C9C2×Q811yescharacteristic
41C2×C22⋊C9#4112yes—
42C2×C4×C9—41no—
43C2×C4×C9—42no—
44C2×Dic9—44no—
45C2×#125—91no—
46C22×C42D911yescharacteristic
47#389—92no—
48#387—94no—
49#385—94no—
50#382—91no—
51#380—92no—
52C24×C3C22×D311yescharacteristic
53C22×C3×C4—22no—
54C22×C3×C4—31no—
55C22×C3×C4—31no—
56C22×C3×C4—32no—
57C22×C3×C4—32no—
58C22×C3×C4—32no—
59C22×C3×C4—62no—
60C22×C3×C4Dic612yes—
61C22×Dic3—34no—
62C22×Dic3—34no—
63C3×C42—32no—
64C3×C42—31no—
65C3×C42—61no—
66C3×C42S411yescharacteristic
67#217—64no—
68#217—64no—
69C4⋊Dic3—62no—
70C4⋊Dic3—64no—
71C4⋊Dic3—62no—
72Dic3⋊C4—64no—
73Dic3⋊C4—68no—
74Dic3⋊C4—64no—
75C22×C9—41no—
76C22⋊C9#12511yescharacteristic, complemented
77C4×C9—42no—
78C4×C9—82no—
79Dic9—84no—
80C23×C4C2×D912yes—
81C23×C4C2×D911yescharacteristic
82#125—181no—
83#125—182no—
84#125—181no—
85C2×C4⋊C4—92no—
86C2×C4⋊C4—94no—
87C2×C4⋊C4—92no—
88C2×C4⋊C4—94no—
89C2×C22⋊C4—94no—
90C2×C42—31no—
91C2×C42—32no—
92C2×C42—31no—
93#95—94no—
94#95—94no—
95#95—94no—
96C23×C3—31no—
97C23×C3—32no—
98C23×C3—31no—
99C23×C3C2×Dic611yescharacteristic
100C23×C3#23512yes—
101C2×C3×C4—31no—
102C2×C3×C4—32no—
103C2×C3×C4—32no—
104C2×C3×C4—32no—
105C2×C3×C4—34no—
106C2×C3×C4—32no—
107C2×C3×C4—62no—
108C2×C3×C4—62no—
109C2×C3×C4—61no—
110C2×C3×C4—62no—
111C2×C3×C4C2×S412yes—
112C2×C3×C4C2×S411yescharacteristic
113C2×Dic3—64no—
114C2×Dic3—64no—
115C2×Dic3—64no—
116C2×Dic3—64no—
117C2×Dic3—64no—
118C2×Dic3—64no—
119C2×C9—41no—
120C2×C9—42no—
121C24C22×D911yescharacteristic
122C22×C4—22no—
123C22×C4—31no—
124C22×C4—31no—
125C22×C4—32no—
126C22×C4—32no—
127C22×C4—32no—
128C22×C4—62no—
129C22×C4—94no—
130C22×C4—94no—
131C22×C4Dic1812yes—
132C4⋊C4—184no—
133C4⋊C4—182no—
134C4⋊C4—188no—
135C4⋊C4—184no—
136C4⋊C4—184no—
137C4⋊C4—182no—
138C22⋊C4—184no—
139C22⋊C4—184no—
140C42—32no—
141C42—31no—
142C42—61no—
143C42(C22⋊C9)⋊C211yescharacteristic
144C22×C3—31no—
145C22×C3—32no—
146C22×C3—31no—
147C22×C3—31no—
148C22×C3—32no—
149C22×C3—32no—
150C22×C3—61no—
151C22×C3#87011yescharacteristic
152C22×C3C22×S411yescharacteristic
153C3×C4—22no—
154C3×C4—32no—
155C3×C4—62no—
156C3×C4A4⋊Q812yes—
157Dic3—124no—
158Dic3—124no—
159C9—41noSylow
160C23—31no—
161C23—32no—
162C23—31no—
163C23C2×Dic1811yescharacteristic
164C23#369712yes—
165C2×C4—31no—
166C2×C4—32no—
167C2×C4—32no—
168C2×C4—32no—
169C2×C4—34no—
170C2×C4—32no—
171C2×C4—62no—
172C2×C4—62no—
173C2×C4—61no—
174C2×C4—62no—
175C2×C4—184no—
176C2×C4—184no—
177C2×C4—184no—
178C2×C4—184no—
179C2×C4—184no—
180C2×C4—184no—
181C2×C4C2×(C22⋊C9)⋊C212yes—
182C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
183C2×C3—32no—
184C2×C3—31no—
185C2×C3—31no—
186C2×C3C2×A4⋊Q811yescharacteristic
187C2×C3#591212yes—
188C22—31no—
189C22—32no—
190C22—31no—
191C22—31no—
192C22—32no—
193C22—32no—
194C22—61no—
195C22#6343211yescharacteristic, complemented
196C22C22×(C22⋊C9)⋊C211yescharacteristic
197C4—22no—
198C4—32no—
199C4—62no—
200C4—364no—
201C4—364no—
202C4(C22⋊C9)⋊Q812yes—
203C3#8528411yescharacteristic
204C2—32no—
205C2—31no—
206C2—31no—
207C2C2×(C22⋊C9)⋊Q811yescharacteristic
208C2#1059308712yes—
subgroupG/H
centerC22C22×(C22⋊C9)⋊C2
commutator, cosocleC22×C22⋊C9C23
FrattiniC22×C3C22×S4
FittingC22×C3×C42D3
socle, prime radicalC24×C3C22×D3
hypercenterC42(C22⋊C9)⋊C2
hypocenterC22⋊C9#125
LCSG ▷ C22×C22⋊C9 ▷ C22⋊C9
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
76. C22⋊C9#125semidirect
195. C22#63432semidirect

Maximal subgroups

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

subgroupindex
C42×C22⋊C92
C4⋊((C22⋊C9)⋊C4)2
((C22⋊C9)⋊C4)⋊C42
#820743
#634324