Finite Group Databasebeta

← #11772783

Subgroups — #11772783

Order 1152.

159 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 159 conjugacy classes of subgroups — too many to draw. Only its 32 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#10588775C211yesmaximal, characteristic
2C9×#333C211yesmaximal, characteristic, complemented
3#10588225C211yesmaximal, characteristic, complemented
4#67463—31nomaximal
5#63713C411yescharacteristic
6C9×C4⋊Q8C2211yescharacteristic
7#63505—21no—
8C9×C4⋊C8—21no—
9#63394—21no—
10#63394C411yescharacteristic
11#63364—21no—
12#5095—31no—
13C3×#333D311yescharacteristic
14#4548—31no—
15C2×Q8×C9C2×C411yescharacteristic
16C2×Q8×C9D411yescharacteristic
17#3701—41no—
18Q8×D9—41no—
19#3697—21no—
20#3697—41no—
21C2×C8×C9—41no—
22C9×C4⋊C4—41no—
23C42×C9D411yescharacteristic
24#3675—41no—
25#3674—41no—
26#3667—21no—
27#3667—41no—
28#1405—91noSylow
29#1007—31no—
30C3×C4⋊Q8C2×D311yescharacteristic
31#942—61no—
32C3×C4⋊C8—21no—
33#836—31no—
34#836—61no—
35#805—61no—
36Q8×C9—41no—
37Q8×C9—41no—
38C2×C4×C9—21no—
39C2×C4×C9—21no—
40C2×C4×C9—21no—
41C2×C4×C9C22⋊C411yescharacteristic
42#611—41no—
43D36—21no—
44D36—41no—
45C4×D9—41no—
46C4×D9—42no—
47Dic18—21no—
48Dic18—41no—
49C8×C9—81no—
50C9⋊C8—41no—
51C9⋊C8—81no—
52#456—91no—
53#356—91no—
54#333D911yescharacteristic, complemented
55C2×C3×Q8C4×D311yescharacteristic
56C2×C3×Q8D1211yescharacteristic
57#239—121no—
58D3×Q8—121no—
59#235—61no—
60#235—121no—
61C2×C3×C8—41no—
62C3×C4⋊C4—41no—
63C3×C42#6711yescharacteristic
64#216—121no—
65#215—121no—
66#208—61no—
67#208—121no—
68C22×C9#9911yescharacteristic
69C2×D9—41no—
70C4×C9—21no—
71C4×C9—21no—
72C4×C9—21no—
73C4×C9—41no—
74C4×C9—41no—
75Dic9—41no—
762−1+4—91no—
77#137—181no—
78C4⋊Q8C2×D911yescharacteristic
79C4⋊C8—21no—
80#104—181no—
81#101—91no—
82#101—181no—
83C3×Q8—41no—
84C3×Q8—41no—
85C2×C3×C4—21no—
86C2×C3×C4—21no—
87C2×C3×C4—21no—
88C2×C3×C4(C2×D3)⋊C411yescharacteristic
89#67—121no—
90D12—61no—
91D12—121no—
92C4×D3—121no—
93C4×D3—122no—
94Dic6—61no—
95Dic6—121no—
96C3×C8—81no—
97C3⋊C8—121no—
98C3⋊C8—241no—
99C2×C9—21no—
100C2×C9AΣL(1,𝔽16)11yescharacteristic
101D9—81no—
102#41—181no—
103#41—361no—
104#41—361no—
105C2×Q8—361no—
106C2×Q8C4×D911yescharacteristic
107C2×Q8D3611yescharacteristic
108Q16—361no—
109SD16—361no—
110M16—181no—
111M16—361no—
112C2×C8—41no—
113C4⋊C4—41no—
114C42#61111yescharacteristic
115C22×C3#80611yescharacteristic
116C2×D3—121no—
117C3×C4—21no—
118C3×C4—21no—
119C3×C4—21no—
120C3×C4—41no—
121C3×C4—41no—
122Dic3—121no—
123C9#140511yescharacteristic, complemented, Sylow
124Q8—41no—
125Q8—41no—
126Q8—181no—
127Q8—361no—
128D4—181no—
129D4—361no—
130D4—361no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—361no—
135C2×C4—362no—
136C2×C4(C2×D9)⋊C411yescharacteristic
137C8—81no—
138C8—361no—
139C8—721no—
140C2×C3—21no—
141C2×C3#447511yescharacteristic
142D3—241no—
143C22—361no—
144C22#6336511yescharacteristic
145C4—21no—
146C4—21no—
147C4—21no—
148C4—41no—
149C4—41no—
150C4—361no—
151C3#6746311yescharacteristic
152C2—21no—
153C2—721no—
154C2#1058815311yescharacteristic
subgroupG/H
centerC2#10588153
commutatorC2×Q8×C9C2×C4
FrattiniC3×C4⋊Q8C2×D3
FittingC9×#333C2
socleC2×C3#4475
prime radical#63713C4
cosocleC9×C4⋊Q8C22
hypercenter#333D9
hypocenterC9#1405
LCSG ▷ C2×Q8×C9 ▷ C2×C4×C9 ▷ C22×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #333

Complements

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

NH ≅ G/Ntype
2. C9×#333C2semidirect
3. #10588225C2semidirect
54. #333D9semidirect
123. C9#1405semidirect

Maximal subgroups

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

subgroupindex
#105887752
C9×#3332
#105882252
#674633