Finite Group Databasebeta

← #3362⋊C9 #11919601

Subgroups — #3362⋊C9 #11919601

Order 1152.

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

normal subgroups only

This group has 203 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
1Q8×Q8⋊C9C211yesmaximal, characteristic, complemented
2C4⋊(#41⋊C9)C211yesmaximal, characteristic
3C8×Q8⋊C9C211yesmaximal, characteristic, complemented
4C3×#3362C311yesmaximal, characteristic
5C2×#41⋊C9—21no—
6C4×Q8⋊C9—21no—
7C4×Q8⋊C9C2211yescharacteristic
8C9×#103—41nomaximal
9C3×Q82C2×C311yescharacteristic
10C3×#550C2×C311yescharacteristic
11C3×#486—31no—
12C3×#476—31no—
13C3×#460—31no—
14C3×C8×Q8C2×C311yescharacteristic
15C3×C4×SD16—31no—
16C2×Q8×C9—41no—
17#41⋊C9—41no—
18C2×Q8⋊C9D411yescharacteristic
19C2×C8×C9—41no—
20C9×C4⋊C4—41no—
21#3362C911yescharacteristic, complemented, Sylow
22C2×C3×#41—21no—
23C2×C3×SD16—31no—
24C3×C4⋊Q8—31no—
25C3×C4⋊Q8—61no—
26C3×#127—31no—
27C3×#121—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×#103A411yescharacteristic
35C3×#102—32no—
36C3×#102—31no—
37C3×C4×C8—31no—
38Q8×C9—42no—
39Q8×C9—81no—
40C2×C4×C9—41no—
41C2×C4×C9—81no—
42C2×C4×C9—81no—
43Q8⋊C9SD1611yescharacteristic, complemented
44C8×C9—81no—
45Q82C2×C911yescharacteristic
46#550C2×C911yescharacteristic
47#486—31no—
48#476—31no—
49#460—31no—
50C8×Q8C2×C911yescharacteristic
51C4×SD16—31no—
52C3×#41—41no—
53C3×#41—121no—
54C2×C3×Q8—61no—
55C2×C3×Q8C3×D411yescharacteristic
56C2×C3×Q8C2×A411yescharacteristic
57C2×C3×D4—31no—
58C2×C3×D4—61no—
59C2×C3×D4—61no—
60C22×C3×C4—61no—
61C3×SD16—62no—
62C2×C3×C8—31no—
63C2×C3×C8C2×A411yescharacteristic
64C3×C4⋊C4—31no—
65C3×C4⋊C4—31no—
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—
73C4×C9—41no—
74C4×C9—41no—
75C4×C9—82no—
76C4×C9—161no—
77C2×#41—21no—
78C2×SD16—31no—
79C4⋊Q8—31no—
80C4⋊Q8—61no—
81#127—31no—
82#121—61no—
83C4×Q8—21no—
84C4×Q8—31no—
85C4×Q8C22×C911yescharacteristic
86C4×D4—31no—
87#106—31no—
88C4⋊C8—31no—
89#103C22⋊C911yescharacteristic
90#102—32no—
91#102—31no—
92C4×C8—31no—
93C23×C3—61no—
94C3×Q8—21no—
95C3×Q8—31no—
96C3×Q8—241no—
97C3×Q8C3×SD1611yescharacteristic
98C3×Q8#41⋊C312yes—
99C3×D4—61no—
100C3×D4—61no—
101C3×D4—121no—
102C3×D4—121no—
103C3×D4—241no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—31no—
107C2×C3×C4—31no—
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—
117#41—41no—
118#41—121no—
119C2×Q8—61no—
120C2×Q8D4×C911yescharacteristic
121C2×Q8C2×C22⋊C911yescharacteristic
122C2×D4—31no—
123C2×D4—61no—
124C2×D4—61no—
125C22×C4—61no—
126SD16—62no—
127C2×C8—31no—
128C2×C8C2×C22⋊C911yescharacteristic
129C4⋊C4—31no—
130C4⋊C4—31no—
131C4⋊C4—61no—
132C4⋊C4—61no—
133C4⋊C4C2×C22⋊C911yescharacteristic
134C22⋊C4—61no—
135C42—31no—
136C42—61no—
137C22×C3—121no—
138C22×C3—121no—
139C22×C3—121no—
140C22×C3D4×A411yescharacteristic
141C3×C4—22no—
142C3×C4—31no—
143C3×C4—31no—
144C3×C4—41no—
145C3×C4—61no—
146C3×C4—121no—
147C3×C4C2×#41⋊C311yescharacteristic
148C3×C42−1+4⋊C311yescharacteristic
149C9—41noSylow
150C23—61no—
151Q8—21no—
152Q8—31no—
153Q8—241no—
154Q8C9×SD1611yescharacteristic
155Q8#41⋊C912yescomplemented
156D4—61no—
157D4—61no—
158D4—121no—
159D4—121no—
160D4—241no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—31no—
164C2×C4—31no—
165C2×C4—61no—
166C2×C4—121no—
167C2×C4—121no—
168C2×C4C22×C22⋊C911yescharacteristic
169C8—21no—
170C8—61no—
171C2×C3—241no—
172C2×C3#548⋊C311yescharacteristic
173C2×C3A4×SD1611yescharacteristic
174C2×C3#576⋊C311yescharacteristic
175C22—121no—
176C22—121no—
177C22—121no—
178C22D4×C22⋊C911yescharacteristic
179C4—22no—
180C4—31no—
181C4—31no—
182C4—41no—
183C4—61no—
184C4—121no—
185C4C2×#41⋊C911yescharacteristic
186C42−1+4⋊C911yescharacteristic
187C3#3362⋊C311yescharacteristic
188C2—241no—
189C2#548⋊C911yescharacteristic
190C2SD16×C22⋊C911yescharacteristic
191C2#576⋊C911yescharacteristic
subgroupG/H
center, socleC22×C3D4×A4
commutatorC4×Q8C22×C9
FrattiniC2×C3×C4C22×A4
FittingC3×#3362C3
prime radicalC3×#550C2×C3
cosocleC3×C4×Q8C22×C3
hypercenterC3×#103A4
hypocenterQ8C9×SD16
LCSG ▷ C4×Q8 ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#103

Complements

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

NH ≅ G/Ntype
1. Q8×Q8⋊C9C2semidirect
3. C8×Q8⋊C9C2semidirect
21. #3362C9semidirect
43. Q8⋊C9SD16semidirect
155. Q8#41⋊C9semidirect

Maximal subgroups

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

subgroupindex
Q8×Q8⋊C92
C4⋊(#41⋊C9)2
C8×Q8⋊C92
C3×#33623
C9×#1034