Finite Group Databasebeta

← #3363⋊C9 #11919603

Subgroups — #3363⋊C9 #11919603

Order 1152.

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

normal subgroups only

This group has 182 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
2#557⋊C9C211yesmaximal, characteristic
3C8×Q8⋊C9C211yesmaximal, characteristic
4C3×#3363C311yesmaximal, characteristic
5C4×Q8⋊C9—21no—
6C4×Q8⋊C9—21no—
7C4×Q8⋊C9C2211yescharacteristic
8C9×#103—41nomaximal
9C3×Q82C2×C311yescharacteristic
10C3×#557C2×C311yescharacteristic
11C3×#487—31no—
12C3×#477—31no—
13C3×#462—31no—
14C3×C8×Q8C2×C311yescharacteristic
15C3×C4×Q16—31no—
16C2×Q8×C9—41no—
17C2×Q8⋊C9D411yescharacteristic
18C2×C8×C9—41no—
19C9×C4⋊C4—41no—
20#3363C911yescharacteristic, complemented, Sylow
21C2×C3×Q16—31no—
22C3×C4⋊Q8—31no—
23C3×C4⋊Q8—31no—
24C3×C4⋊Q8—61no—
25C3×#125—61no—
26C3×C4×Q8—21no—
27C3×C4×Q8—21no—
28C3×C4×Q8—31no—
29C3×C4×Q8—31no—
30C3×C4×Q8C22×C311yescharacteristic
31C3×#107—31no—
32C3×C4⋊C8—31no—
33C3×#103—32no—
34C3×#103—31no—
35C3×#103A411yescharacteristic
36C3×C4×C8—31no—
37Q8×C9—42no—
38Q8×C9—81no—
39C2×C4×C9—41no—
40C2×C4×C9—81no—
41C2×C4×C9—81no—
42Q8⋊C9Q1611yescharacteristic, complemented
43C8×C9—81no—
44Q82C2×C911yescharacteristic
45#557C2×C911yescharacteristic
46#487—31no—
47#477—31no—
48#462—31no—
49C8×Q8C2×C911yescharacteristic
50C4×Q16—31no—
51C2×C3×Q8—31no—
52C2×C3×Q8—61no—
53C2×C3×Q8C3×D411yescharacteristic
54C2×C3×Q8C2×A411yescharacteristic
55C3×Q16—62no—
56C2×C3×C8—31no—
57C2×C3×C8C2×A411yescharacteristic
58C3×C4⋊C4—31no—
59C3×C4⋊C4—31no—
60C3×C4⋊C4—61no—
61C3×C4⋊C4—61no—
62C3×C4⋊C4—61no—
63C3×C4⋊C4—61no—
64C3×C4⋊C4—61no—
65C3×C4⋊C4C2×A411yescharacteristic
66C3×C42—31no—
67C3×C42—61no—
68C3×C42—61no—
69C22×C9—41no—
70C4×C9—41no—
71C4×C9—41no—
72C4×C9—82no—
73C4×C9—161no—
74C2×Q16—31no—
75C4⋊Q8—31no—
76C4⋊Q8—31no—
77C4⋊Q8—61no—
78#125—61no—
79C4×Q8—21no—
80C4×Q8—21no—
81C4×Q8—31no—
82C4×Q8—31no—
83C4×Q8C22×C911yescharacteristic
84#107—31no—
85C4⋊C8—31no—
86#103—32no—
87#103—31no—
88#103C22⋊C911yescharacteristic
89C4×C8—31no—
90C3×Q8—21no—
91C3×Q8—31no—
92C3×Q8—61no—
93C3×Q8—61no—
94C3×Q8—241no—
95C3×Q8C3×Q1611yescharacteristic
96C3×Q8#41⋊C312yes—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×C3×C4—31no—
100C2×C3×C4—31no—
101C2×C3×C4—61no—
102C2×C3×C4—61no—
103C2×C3×C4C22×A411yescharacteristic
104C3×C8—21no—
105C3×C8—61no—
106C2×C9—41no—
107C2×C9—41no—
108C2×C9—41no—
109C2×Q8—31no—
110C2×Q8—61no—
111C2×Q8D4×C911yescharacteristic
112C2×Q8C2×C22⋊C911yescharacteristic
113Q16—62no—
114C2×C8—31no—
115C2×C8C2×C22⋊C911yescharacteristic
116C4⋊C4—31no—
117C4⋊C4—31no—
118C4⋊C4—61no—
119C4⋊C4—61no—
120C4⋊C4—61no—
121C4⋊C4—61no—
122C4⋊C4—61no—
123C4⋊C4C2×C22⋊C911yescharacteristic
124C42—31no—
125C42—61no—
126C42—61no—
127C22×C3D4×A411yescharacteristic
128C3×C4—22no—
129C3×C4—31no—
130C3×C4—31no—
131C3×C4—41no—
132C3×C4—61no—
133C3×C4—121no—
134C3×C4—121no—
135C3×C4C2×#41⋊C311yescharacteristic
136C3×C42−1+4⋊C311yescharacteristic
137C9—41noSylow
138Q8—21no—
139Q8—31no—
140Q8—61no—
141Q8—61no—
142Q8—241no—
143Q8C9×Q1611yescharacteristic
144Q8#41⋊C912yes—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—31no—
148C2×C4—31no—
149C2×C4—61no—
150C2×C4—61no—
151C2×C4C22×C22⋊C911yescharacteristic
152C8—21no—
153C8—61no—
154C2×C3#548⋊C311yescharacteristic
155C2×C3A4×Q1611yescharacteristic
156C2×C3#577⋊C311yescharacteristic
157C22D4×C22⋊C911yescharacteristic
158C4—22no—
159C4—31no—
160C4—31no—
161C4—41no—
162C4—61no—
163C4—121no—
164C4—121no—
165C4C2×#41⋊C911yescharacteristic
166C42−1+4⋊C911yescharacteristic
167C3#3363⋊C311yescharacteristic
168C2#548⋊C911yescharacteristic
169C2Q16×C22⋊C911yescharacteristic
170C2#577⋊C911yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C3D4×A4
commutatorC4×Q8C22×C9
FrattiniC2×C3×C4C22×A4
FittingC3×#3363C3
cosocleC3×C4×Q8C22×C3
hypercenterC3×#103A4
hypocenterQ8C9×Q16
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
20. #3363C9semidirect
42. Q8⋊C9Q16semidirect

Maximal subgroups

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

subgroupindex
Q8×Q8⋊C92
#557⋊C92
C8×Q8⋊C92
C3×#33633
C9×#1034