Finite Group Databasebeta

← #3392⋊C9 #11919613

Subgroups — #3392⋊C9 #11919613

Order 1152.

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

normal subgroups only

This group has 200 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
2C4⋊(#41⋊C9)C211yesmaximal, characteristic
3C8×Q8⋊C9C211yesmaximal, characteristic, complemented
4C3×#3392C311yesmaximal, characteristic
5C2×#41⋊C9—21no—
6C4×Q8⋊C9—21no—
7C4×Q8⋊C9C2211yescharacteristic
8C9×#106—41nomaximal
9C3×#557C2×C311yescharacteristic
10C3×#550C2×C311yescharacteristic
11C3×#492—31no—
12C3×#461—31no—
13C3×#460—31no—
14C3×C8×Q8C2×C311yescharacteristic
15C3×C4×SD16—31no—
16#41⋊C9—41no—
17C2×Q8⋊C9D411yescharacteristic
18C2×C8×C9—41no—
19C9×C4⋊C4—41no—
20C9×C4⋊C4—41no—
21#3392C911yescharacteristic, complemented, Sylow
22C2×C3×#41—21no—
23C2×C3×SD16—32no—
24C2×C3×SD16—31no—
25C3×C4⋊Q8—31no—
26C3×#127—31no—
27C3×#125—61no—
28C3×#121—61no—
29C3×C4×Q8—21no—
30C3×C4×Q8—31no—
31C3×C4×Q8C22×C311yescharacteristic
32C3×C4×D4—31no—
33C3×#106A411yescharacteristic
34C3×C4⋊C8—31no—
35C3×#103—31no—
36C3×#102—31no—
37C3×C4×C8—31no—
38C2×C4×C9—41no—
39C2×C4×C9—81no—
40C2×C4×C9—81no—
41Q8⋊C9SD1611yescharacteristic, complemented
42C8×C9—42no—
43#557C2×C911yescharacteristic
44#550C2×C911yescharacteristic
45#492—31no—
46#461—31no—
47#460—31no—
48C8×Q8C2×C911yescharacteristic
49C4×SD16—31no—
50C3×#41—41no—
51C3×#41—121no—
52C2×C3×Q8—31no—
53C2×C3×Q8C3×D411yescharacteristic
54C2×C3×D4—31no—
55C2×C3×D4—61no—
56C2×C3×D4—61no—
57C22×C3×C4—61no—
58C3×SD16—62no—
59C3×SD16—122no—
60C2×C3×C8—31no—
61C2×C3×C8C2×A411yescharacteristic
62C3×C4⋊C4—31no—
63C3×C4⋊C4—61no—
64C3×C4⋊C4—61no—
65C3×C4⋊C4—61no—
66C3×C4⋊C4C2×A411yescharacteristic
67C3×C4⋊C4C2×A411yescharacteristic
68C3×C22⋊C4—61no—
69C3×C42—31no—
70C3×C42—61no—
71C22×C9—41no—
72C4×C9—41no—
73C4×C9—41no—
74C4×C9—161no—
75C4×C9—161no—
76C2×#41—21no—
77C2×SD16—32no—
78C2×SD16—31no—
79C4⋊Q8—31no—
80#127—31no—
81#125—61no—
82#121—61no—
83C4×Q8—21no—
84C4×Q8—31no—
85C4×Q8C22×C911yescharacteristic
86C4×D4—31no—
87#106C22⋊C911yescharacteristic
88C4⋊C8—31no—
89#103—31no—
90#102—31no—
91C4×C8—31no—
92C23×C3—61no—
93C3×Q8—31no—
94C3×Q8—61no—
95C3×Q8—61no—
96C3×Q8C3×SD1611yescharacteristic
97C3×D4—61no—
98C3×D4—61no—
99C3×D4—121no—
100C3×D4—121no—
101C3×D4—241no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—31no—
105C2×C3×C4—31no—
106C2×C3×C4—61no—
107C2×C3×C4—121no—
108C2×C3×C4—121no—
109C2×C3×C4C22×A411yescharacteristic
110C3×C8—61no—
111C3×C8#41⋊C312yes—
112C2×C9—41no—
113C2×C9—41no—
114C2×C9—41no—
115#41—41no—
116#41—121no—
117C2×Q8—31no—
118C2×Q8D4×C911yescharacteristic
119C2×D4—31no—
120C2×D4—61no—
121C2×D4—61no—
122C22×C4—61no—
123SD16—62no—
124SD16—122no—
125C2×C8—31no—
126C2×C8C2×C22⋊C911yescharacteristic
127C4⋊C4—31no—
128C4⋊C4—61no—
129C4⋊C4—61no—
130C4⋊C4—61no—
131C4⋊C4C2×C22⋊C911yescharacteristic
132C4⋊C4C2×C22⋊C911yescharacteristic
133C22⋊C4—61no—
134C42—31no—
135C42—61no—
136C22×C3—121no—
137C22×C3—121no—
138C22×C3—121no—
139C22×C3D4×A411yescharacteristic
140C3×C4—31no—
141C3×C4—31no—
142C3×C4—41no—
143C3×C4—41no—
144C3×C4—61no—
145C3×C4—121no—
146C3×C4C2×#41⋊C311yescharacteristic
147C3×C4#99411yescharacteristic
148C9—41noSylow
149C23—61no—
150Q8—31no—
151Q8—61no—
152Q8—61no—
153Q8C9×SD1611yescharacteristic
154D4—61no—
155D4—61no—
156D4—121no—
157D4—121no—
158D4—241no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—31no—
162C2×C4—31no—
163C2×C4—61no—
164C2×C4—121no—
165C2×C4—121no—
166C2×C4C22×C22⋊C911yescharacteristic
167C8—61no—
168C8#41⋊C912yescomplemented
169C2×C3—241no—
170C2×C3C4⋊(#41⋊C3)11yescharacteristic
171C2×C3A4×SD1611yescharacteristic
172C2×C3#577⋊C311yescharacteristic
173C22—121no—
174C22—121no—
175C22—121no—
176C22D4×C22⋊C911yescharacteristic
177C4—31no—
178C4—31no—
179C4—41no—
180C4—41no—
181C4—61no—
182C4—121no—
183C4C2×#41⋊C911yescharacteristic
184C4#6370011yescharacteristic
185C3#3392⋊C311yescharacteristic
186C2—241no—
187C2C4⋊(#41⋊C9)11yescharacteristic
188C2SD16×C22⋊C911yescharacteristic
189C2#577⋊C911yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutatorC4×Q8C22×C9
FrattiniC2×C3×C4C22×A4
FittingC3×#3392C3
prime radicalC3×#550C2×C3
cosocleC3×C4×Q8C22×C3
hypercenterC3×#106A4
hypocenterQ8C9×SD16
LCSG ▷ C4×Q8 ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#106

Complements

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

NH ≅ G/Ntype
1. #557⋊C9C2semidirect
3. C8×Q8⋊C9C2semidirect
21. #3392C9semidirect
41. Q8⋊C9SD16semidirect
168. C8#41⋊C9semidirect

Maximal subgroups

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

subgroupindex
#557⋊C92
C4⋊(#41⋊C9)2
C8×Q8⋊C92
C3×#33923
C9×#1064