Finite Group Databasebeta

← #2868⋊C9 #11919515

Subgroups — #2868⋊C9 #11919515

Order 1152.

258 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 36 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#384⋊C9C212yesmaximal
2C4×C42⋊C9C211yesmaximal, characteristic
3C3×#2868C311yesmaximal, characteristic
4Q8×C22⋊C9—41nomaximal
5C2×C42⋊C9C2211yescharacteristic
6C2×C3×C4⋊Q8—31no—
7C2×C3×C4⋊Q8—31no—
8C3×#384—32no—
9C3×#384C2×C312yes—
10C3×C43C2×C311yescharacteristic
11C4×C22⋊C9—41no—
12C4×C22⋊C9—42no—
13C42⋊C9Q811yescharacteristic, complemented
14#2868C911yescharacteristic, complemented, Sylow
15C22×C3×Q8—31no—
16C22×C3×Q8A411yescharacteristic
17C3×C4⋊Q8—62no—
18C3×C4⋊Q8—62no—
19C3×C4⋊Q8—62no—
20C3×C4⋊Q8—62no—
21C2×C3×C4⋊C4—32no—
22C2×C3×C4⋊C4—32no—
23C2×C3×C4⋊C4—32no—
24C2×C3×C4⋊C4—32no—
25C2×C3×C42—31no—
26C2×C3×C42—31no—
27C2×C3×C42C22×C311yescharacteristic
28C2×C22⋊C9—41no—
29Q8×C9—161no—
30C2×C4⋊Q8—31no—
31C2×C4⋊Q8—31no—
32#384—32no—
33#384C2×C912yes—
34C43C2×C911yescharacteristic
35C2×C3×Q8—61no—
36C2×C3×Q8—61no—
37C2×C3×Q8—61no—
38C2×C3×Q8—62no—
39C2×C3×Q8—61no—
40C2×C3×Q8—62no—
41C22×C3×C4—31no—
42C22×C3×C4—31no—
43C22×C3×C4—32no—
44C22×C3×C4C2×A411yescharacteristic
45C22×C3×C4C2×A412yes—
46C3×C4⋊C4—64no—
47C3×C4⋊C4—64no—
48C3×C4⋊C4—64no—
49C3×C4⋊C4—64no—
50C3×C42—31no—
51C3×C42—34no—
52C3×C42—32no—
53C3×C42—32no—
54C3×C42C3×Q811yescharacteristic
55C22⋊C9—41no—
56C4×C9—162no—
57C4×C9—161no—
58C22×Q8—31no—
59C22×Q8C22⋊C911yescharacteristic
60C4⋊Q8—62no—
61C4⋊Q8—62no—
62C4⋊Q8—62no—
63C4⋊Q8—62no—
64C2×C4⋊C4—32no—
65C2×C4⋊C4—32no—
66C2×C4⋊C4—32no—
67C2×C4⋊C4—32no—
68C2×C42—31no—
69C2×C42—31no—
70C2×C42C22×C911yescharacteristic
71C23×C3C22×A411yescharacteristic
72C3×Q8—41no—
73C3×Q8—121no—
74C3×Q8—121no—
75C3×Q8—122no—
76C3×Q8—121no—
77C2×C3×C4—32no—
78C2×C3×C4—32no—
79C2×C3×C4—32no—
80C2×C3×C4—34no—
81C2×C3×C4—31no—
82C2×C3×C4—31no—
83C2×C3×C4—31no—
84C2×C3×C4—31no—
85C2×C3×C4—62no—
86C2×C3×C4—62no—
87C2×C3×C4—64no—
88C2×C9—161no—
89C2×Q8—61no—
90C2×Q8—61no—
91C2×Q8—61no—
92C2×Q8—62no—
93C2×Q8—61no—
94C2×Q8—62no—
95C22×C4—31no—
96C22×C4—31no—
97C22×C4—32no—
98C22×C4C2×C22⋊C911yescharacteristic
99C22×C4C2×C22⋊C912yes—
100C4⋊C4—64no—
101C4⋊C4—64no—
102C4⋊C4—64no—
103C4⋊C4—64no—
104C42—31no—
105C42—32no—
106C42—32no—
107C42—34no—
108C42Q8×C911yescharacteristic, complemented
109C22×C3—31no—
110C22×C3—31no—
111C22×C3Q8×A411yescharacteristic
112C3×C4—34no—
113C3×C4—32no—
114C3×C4—32no—
115C3×C4—31no—
116C3×C4—42no—
117C3×C4—122no—
118C3×C4#127⋊C311yescharacteristic
119C9—161noSylow
120C23C22×C22⋊C911yescharacteristic
121Q8—41no—
122Q8—121no—
123Q8—121no—
124Q8—122no—
125Q8—121no—
126C2×C4—32no—
127C2×C4—32no—
128C2×C4—32no—
129C2×C4—34no—
130C2×C4—31no—
131C2×C4—31no—
132C2×C4—31no—
133C2×C4—31no—
134C2×C4—62no—
135C2×C4—62no—
136C2×C4—64no—
137C2×C3—31no—
138C2×C3—31no—
139C2×C3C2×#127⋊C311yescharacteristic
140C22—31no—
141C22—31no—
142C22Q8×C22⋊C911yescharacteristic
143C4—32no—
144C4—32no—
145C4—34no—
146C4—31no—
147C4—42no—
148C4—122no—
149C4#127⋊C911yescharacteristic
150C3#2868⋊C311yescharacteristic
151C2—31no—
152C2—31no—
153C2C2×#127⋊C911yescharacteristic
subgroupG/H
centerC2×C3C2×#127⋊C3
commutatorC2×C42C22×C9
Frattini, socle, prime radicalC23×C3C22×A4
FittingC3×#2868C3
cosocleC2×C3×C42C22×C3
hypercenterC3×C4#127⋊C3
hypocenterC42Q8×C9
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
13. C42⋊C9Q8semidirect
14. #2868C9semidirect
108. C42Q8×C9semidirect

Maximal subgroups

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

subgroupindex
#384⋊C92
C4×C42⋊C92
C3×#28683
Q8×C22⋊C94