Finite Group Databasebeta

← #3359⋊C9 #11919599

Subgroups — #3359⋊C9 #11919599

Order 1152.

205 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 205 conjugacy classes of subgroups — too many to draw. Only its 49 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⋊C9C211yesmaximal, characteristic, complemented
2D4×Q8⋊C9C211yesmaximal, characteristic
3C8×Q8⋊C9C211yesmaximal, characteristic, complemented
4C3×#3359C311yesmaximal, characteristic
5C22×Q8⋊C9—21no—
6C4×Q8⋊C9—21no—
7C4×Q8⋊C9C2211yescharacteristic
8C9×#102—41nomaximal
9C3×#557C2×C311yescharacteristic
10C3×D4×Q8C2×C311yescharacteristic
11C3×#487—31no—
12C3×#475—31no—
13C3×#461—31no—
14C3×C8×Q8C2×C311yescharacteristic
15C3×C4×SD16—31no—
16C2×D4×C9—41no—
17C2×Q8⋊C9—41no—
18C2×Q8⋊C9D411yescharacteristic
19C2×C8×C9—41no—
20C9×C4⋊C4—41no—
21#3359C911yescharacteristic, complemented, Sylow
22C22×C3×Q8—21no—
23C2×C3×SD16—31no—
24C3×C4⋊Q8—31no—
25C3×C4⋊Q8—31no—
26C3×#125—61no—
27C3×C22⋊Q8—61no—
28C3×C4×Q8—21no—
29C3×C4×Q8—31no—
30C3×C4×Q8C22×C311yescharacteristic
31C3×C4×D4—31no—
32C3×#106—31no—
33C3×C4⋊C8—31no—
34C3×#103—32no—
35C3×#103—31no—
36C3×#102A411yescharacteristic
37C3×C4×C8—31no—
38C23×C9—81no—
39D4×C9—42no—
40D4×C9—81no—
41C2×C4×C9—41no—
42C2×C4×C9—81no—
43Q8⋊C9SD1611yescharacteristic, complemented
44C8×C9—81no—
45#557C2×C911yescharacteristic, complemented
46D4×Q8C2×C911yescharacteristic
47#487—31no—
48#475—31no—
49#461—31no—
50C8×Q8C2×C911yescharacteristic, complemented
51C4×SD16—31no—
52C2×C3×Q8—31no—
53C2×C3×Q8—41no—
54C2×C3×Q8—61no—
55C2×C3×Q8—121no—
56C2×C3×Q8C3×D411yescharacteristic
57C2×C3×D4C2×A411yescharacteristic
58C22×C3×C4—61no—
59C3×SD16—62no—
60C2×C3×C8—31no—
61C2×C3×C8C2×A411yescharacteristic
62C3×C4⋊C4—31no—
63C3×C4⋊C4—31no—
64C3×C4⋊C4—61no—
65C3×C4⋊C4—61no—
66C3×C4⋊C4—61no—
67C3×C4⋊C4—61no—
68C3×C4⋊C4C2×A411yescharacteristic
69C3×C22⋊C4—61no—
70C3×C42—31no—
71C3×C42—61no—
72C22×C9—41no—
73C22×C9—82no—
74C22×C9—161no—
75C22×C9—161no—
76C4×C9—41no—
77C4×C9—41no—
78C4×C9—161no—
79C22×Q8—21no—
80C2×SD16—31no—
81C4⋊Q8—31no—
82C4⋊Q8—31no—
83#125—61no—
84C22⋊Q8—61no—
85C4×Q8—21no—
86C4×Q8—31no—
87C4×Q8C22×C911yescharacteristic
88C4×D4—31no—
89#106—31no—
90C4⋊C8—31no—
91#103—32no—
92#103—31no—
93#102C22⋊C911yescharacteristic
94C4×C8—31no—
95C23×C3—21no—
96C3×Q8—31no—
97C3×Q8—61no—
98C3×Q8—61no—
99C3×Q8—121no—
100C3×Q8—121no—
101C3×Q8C3×SD1611yescharacteristic
102C3×D4—21no—
103C3×D4#41⋊C312yes—
104C2×C3×C4—21no—
105C2×C3×C4—31no—
106C2×C3×C4—31no—
107C2×C3×C4—61no—
108C2×C3×C4—61no—
109C2×C3×C4—121no—
110C2×C3×C4—121no—
111C2×C3×C4C22×A411yescharacteristic
112C3×C8—21no—
113C3×C8—61no—
114C2×C9—41no—
115C2×C9—41no—
116C2×C9—41no—
117C2×C9—162no—
118C2×Q8—31no—
119C2×Q8—41no—
120C2×Q8—61no—
121C2×Q8—121no—
122C2×Q8D4×C911yescharacteristic
123C2×D4C2×C22⋊C911yescharacteristic
124C22×C4—61no—
125SD16—62no—
126C2×C8—31no—
127C2×C8C2×C22⋊C911yescharacteristic
128C4⋊C4—31no—
129C4⋊C4—31no—
130C4⋊C4—61no—
131C4⋊C4—61no—
132C4⋊C4—61no—
133C4⋊C4—61no—
134C4⋊C4C2×C22⋊C911yescharacteristic
135C22⋊C4—61no—
136C42—31no—
137C42—61no—
138C22×C3—22no—
139C22×C3—41no—
140C22×C3—41no—
141C22×C3D4×A411yescharacteristic
142C3×C4—31no—
143C3×C4—31no—
144C3×C4—41no—
145C3×C4—61no—
146C3×C4—121no—
147C3×C4—121no—
148C3×C4C2×#41⋊C311yescharacteristic
149C3×C42−1+4⋊C311yescharacteristic
150C9—41noSylow
151C23—21no—
152Q8—31no—
153Q8—61no—
154Q8—61no—
155Q8—121no—
156Q8—121no—
157Q8C9×SD1611yescharacteristic
158D4—21no—
159D4#41⋊C912yes—
160C2×C4—21no—
161C2×C4—31no—
162C2×C4—31no—
163C2×C4—61no—
164C2×C4—61no—
165C2×C4—121no—
166C2×C4—121no—
167C2×C4C22×C22⋊C911yescharacteristic
168C8—21no—
169C8—61no—
170C2×C3—42no—
171C2×C3#548⋊C311yescharacteristic
172C2×C3A4×SD1611yescharacteristic
173C2×C3#578⋊C311yescharacteristic
174C22—22no—
175C22—41no—
176C22—41no—
177C22D4×C22⋊C911yescharacteristic
178C4—31no—
179C4—31no—
180C4—41no—
181C4—61no—
182C4—121no—
183C4—121no—
184C4C2×#41⋊C911yescharacteristic
185C42−1+4⋊C911yescharacteristic
186C3#3359⋊C311yescharacteristic
187C2—42no—
188C2#548⋊C911yescharacteristic
189C2SD16×C22⋊C911yescharacteristic
190C2#578⋊C911yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutatorC4×Q8C22×C9
FrattiniC2×C3×C4C22×A4
FittingC3×#3359C3
prime radicalC2×C3×D4C2×A4
cosocleC3×C4×Q8C22×C3
hypercenterC3×#102A4
hypocenterQ8C9×SD16
LCSG ▷ C4×Q8 ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#102

Complements

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

NH ≅ G/Ntype
1. #557⋊C9C2semidirect
3. C8×Q8⋊C9C2semidirect
21. #3359C9semidirect
43. Q8⋊C9SD16semidirect
45. #557C2×C9semidirect
50. C8×Q8C2×C9semidirect

Maximal subgroups

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

subgroupindex
#557⋊C92
D4×Q8⋊C92
C8×Q8⋊C92
C3×#33593
C9×#1024