Finite Group Databasebeta

← #3504⋊C9 #11919757

Subgroups — #3504⋊C9 #11919757

Order 1152.

439 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 439 conjugacy classes of subgroups — too many to draw. Only its 101 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#557⋊C9C214yesmaximal, complemented
2#520⋊C9C212yesmaximal
3C4×#41⋊C9C211yesmaximal, characteristic
4C3×#3504C311yesmaximal, characteristic
5C2×#41⋊C9C2211yescharacteristic
6C9×#125—41nomaximal
7C4×Q8⋊C9C2212yes—
8C4×Q8⋊C9C2214yes—
9C3×#557C2×C314yes—
10C3×#554—34no—
11C3×#544—32no—
12C3×#533—31no—
13C2×C3×#125—31no—
14C3×#520C2×C312yes—
15C3×C4×#41C2×C311yescharacteristic
16#41⋊C9Q812yescomplemented
17C2×Q8⋊C9C2311yescharacteristic
18C9×C4⋊C4—42no—
19C9×C4⋊C4—44no—
20C42×C9—41no—
21#3504C911yescharacteristic, complemented, Sylow
22C2×C3×#41C22×C311yescharacteristic
23C3×C4⋊Q8—34no—
24C3×C4⋊Q8—32no—
25C3×#125—34no—
26C3×#125—34no—
27C3×#125—32no—
28C3×#125—31no—
29C3×#125A411yescharacteristic
30C3×C22⋊Q8—38no—
31C3×C22⋊Q8—34no—
32C3×C4×Q8—34no—
33C3×C4×Q8C22×C312yes—
34C3×C4×Q8C22×C314yes—
35C3×C4×D4—32no—
36C3×C4×D4—34no—
37C3×#117—32no—
38C3×#117—31no—
39C2×C3×C4⋊C4—34no—
40C2×C3×C4⋊C4—32no—
41C2×C3×C42—31no—
42C2×C4×C9—41no—
43C2×C4×C9—42no—
44C2×C4×C9—44no—
45Q8⋊C9C2×Q811yescharacteristic
46#557C2×C914yes—
47#554—34no—
48#544—32no—
49#533—31no—
50C2×#125—31no—
51#520C2×C912yes—
52C4×#41C2×C911yescharacteristic
53C3×#41—32no—
54C3×#41C3×Q812yes—
55C2×C3×Q8—34no—
56C2×C3×Q8C23×C311yescharacteristic
57C2×C3×D4—31no—
58C22×C3×C4—31no—
59C22×C3×C4—34no—
60C22×C3×C4—32no—
61C3×C4⋊C4—34no—
62C3×C4⋊C4—32no—
63C3×C4⋊C4—38no—
64C3×C4⋊C4—34no—
65C3×C4⋊C4—32no—
66C3×C4⋊C4—34no—
67C3×C4⋊C4C2×A412yes—
68C3×C4⋊C4C2×A414yes—
69C3×C22⋊C4—32no—
70C3×C22⋊C4—34no—
71C3×C42—31no—
72C3×C42—32no—
73C3×C42—34no—
74C3×C42C2×A411yescharacteristic
75C22×C9—41no—
76C4×C9—42no—
77C4×C9—82no—
78C4×C9—84no—
79C2×#41C22×C911yescharacteristic
80C4⋊Q8—34no—
81C4⋊Q8—32no—
82#125—34no—
83#125—34no—
84#125—32no—
85#125—31no—
86#125C22⋊C911yescharacteristic
87C22⋊Q8—38no—
88C22⋊Q8—34no—
89C4×Q8—34no—
90C4×Q8C22×C912yes—
91C4×Q8C22×C914yes—
92C4×D4—32no—
93C4×D4—34no—
94#117—32no—
95#117—31no—
96C2×C4⋊C4—34no—
97C2×C4⋊C4—32no—
98C2×C42—31no—
99C23×C3—31no—
100C3×Q8—31no—
101C3×Q8—124no—
102C3×Q8C2×C3×Q811yescharacteristic
103C3×D4—32no—
104C3×D4—32no—
105C2×C3×C4—31no—
106C2×C3×C4—32no—
107C2×C3×C4—32no—
108C2×C3×C4—32no—
109C2×C3×C4—34no—
110C2×C3×C4—122no—
111C2×C3×C4—124no—
112C2×C3×C4C22×A412yes—
113C2×C3×C4C22×A414yes—
114C2×C3×C4C22×A411yescharacteristic
115C2×C9—41no—
116C2×C9—42no—
117#41—32no—
118#41Q8×C912yes—
119C2×Q8—34no—
120C2×Q8C23×C911yescharacteristic
121C2×D4—31no—
122C22×C4—31no—
123C22×C4—34no—
124C22×C4—32no—
125C4⋊C4—34no—
126C4⋊C4—32no—
127C4⋊C4—38no—
128C4⋊C4—34no—
129C4⋊C4—32no—
130C4⋊C4—34no—
131C4⋊C4C2×C22⋊C912yes—
132C4⋊C4C2×C22⋊C914yes—
133C22⋊C4—32no—
134C22⋊C4—34no—
135C42—31no—
136C42—32no—
137C42—34no—
138C42C2×C22⋊C911yescharacteristic
139C22×C3—32no—
140C22×C3—62no—
141C22×C3C23×A411yescharacteristic
142C3×C4—22no—
143C3×C4—24no—
144C3×C4—31no—
145C3×C4—31no—
146C3×C4—64no—
147C3×C4—62no—
148C3×C4Q8×A412yes—
149C9—41noSylow
150C23—31no—
151Q8—31no—
152Q8—124no—
153Q8C2×Q8×C911yescharacteristic
154D4—32no—
155D4—32no—
156C2×C4—31no—
157C2×C4—32no—
158C2×C4—32no—
159C2×C4—32no—
160C2×C4—34no—
161C2×C4—122no—
162C2×C4—124no—
163C2×C4C22×C22⋊C912yes—
164C2×C4C22×C22⋊C914yes—
165C2×C4C22×C22⋊C911yescharacteristic
166C2×C3—62no—
167C2×C3C2×Q8×A411yescharacteristic
168C2×C3#594512yes—
169C22—32no—
170C22—62no—
171C22C23×C22⋊C911yescharacteristic
172C4—22no—
173C4—24no—
174C4—31no—
175C4—31no—
176C4—64no—
177C4—62no—
178C4Q8×C22⋊C912yes—
179C3#3504⋊C311yescharacteristic
180C2—62no—
181C2C2×Q8×C22⋊C911yescharacteristic
182C2#1059312012yes—
subgroupG/H
center, Frattini, socleC22×C3C23×A4
commutatorC2×Q8C23×C9
FittingC3×#3504C3
prime radicalC2×C3×#41C22×C3
cosocleC2×C3×Q8C23×C3
hypercenterC3×#125A4
hypocenterQ8C2×Q8×C9
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C3×#125

Complements

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

NH ≅ G/Ntype
1. #557⋊C9C2semidirect
16. #41⋊C9Q8semidirect
21. #3504C9semidirect

Maximal subgroups

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

subgroupindex
#557⋊C92
#520⋊C92
C4×#41⋊C92
C3×#35043
C9×#1254