Finite Group Databasebeta

← #11858685

Subgroups — #11858685

Order 1152.

698 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 187 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#10596647C211yesmaximal, characteristic
2#10595443C212yesmaximal
3#10593331C213yesmaximal, complemented
4#10593330C216yesmaximal, complemented
5C2×#63733C213yesmaximal, complemented
6#41×C3⋊D3C2211yescharacteristic
7#64289C412yes—
8#64287C416yes—
9#64283C2213yes—
10C2×#3787C2213yes—
11C3×#948—22no—
12C2×#3712C2216yes—
13#63818C2216yes—
14#63817—26no—
15#63733C2211yescharacteristic
16#63733C2216yes—
17#63733C2213yes—
18#63733C2216yes—
19#5750—62no—
20C32×#41D411yescharacteristic
21#3832C2×C411yescharacteristic
22Q8×C3⋊D3Q811yescharacteristic
23#3830C2×C413yes—
24D4×C3⋊D3Q813yes—
25#3828D413yes—
26C2×C4×C3⋊D3C2313yes—
27#3792C2×C416yes—
28C2×#622C2×C416yes—
29#3788C2×C416yes—
30#3787C2×C416yes—
31#3787C2311yescharacteristic
32#3787C2313yes—
33C3×#208—26no—
34C2×C3×C3⋊C8—26no—
35#3712—26no—
36#3712C2316yes—
37#3712C2312yes—
38#3710—26no—
39#2916—91nomaximal, Sylow
40D3×#41—62no—
41C3×#131—62no—
42#948—22no—
43#907—66no—
44D3×M16—66no—
45#901—66no—
46C2×ΓL(1,𝔽25)—66no—
47C22×C3⋊D3C2×Q813yes—
48C32×Q8C4⋊C411yescharacteristic
49C32×D4C4⋊C413yes—
50C2×C32×C4C2×D413yes—
51#638C4⋊C416yes—
52C2×C3⋊Dic3C22×C413yes—
53C4⋊(C3⋊D3)C4⋊C413yes—
54C4×C3⋊D3C22×C413yes—
55C4×C3⋊D3C2×D413yes—
56C4×C3⋊D3C2×Q813yes—
57C4×C3⋊D3C2411yescharacteristic
58#634C4⋊C413yes—
59#622C22×C412yes—
60#622C22×C416yes—
61C3×C3⋊C8—26no—
62C3×C3⋊C8—22no—
63#568—92no—
64C2×#131—91no—
65#430—96no—
66C2×#108—93no—
67C2×#108—93no—
68C3×#41—22no—
69#239—62no—
70D3×Q8—62no—
71#237—66no—
72D3×D4—66no—
73#235—66no—
74C2×C4×D3—66no—
75C3×M16—66no—
76C2×C3×C8—66no—
77#208—26no—
78C2×C3⋊C8—26no—
79ΓL(1,𝔽25)—62no—
80ΓL(1,𝔽25)—66no—
81ΓL(1,𝔽25)—66no—
82ΓL(1,𝔽25)—66no—
83D3×C8—612no—
84C22×C32C2×C4⋊C413yes—
85C2×C3⋊D3—43no—
86C2×C3⋊D3C2×C4⋊C413yes—
87C2×C3⋊D3C22×Q811yescharacteristic
88C32×C4C2×C4⋊C413yes—
89C32×C4C22×D411yescharacteristic
90C3⋊Dic3C2×C4⋊C413yes—
91C3⋊Dic3C23×C411yescharacteristic
92C2×#41—91no—
93#131—62no—
94#131—96no—
95#131—92no—
96#131—186no—
97C2×M16—96no—
98C2×M16—93no—
99C2×M16—96no—
100C22×C8—93no—
101#108—91no—
102#108—93no—
103#108—96no—
104#108—96no—
105C22×D3—66no—
106C3×Q8—22no—
107C3×D4—26no—
108C2×C3×C4—26no—
109#67—612no—
110C2×Dic3—66no—
111D12—66no—
112C4×D3—66no—
113C4×D3—66no—
114C4×D3—66no—
115C4×D3—62no—
116Dic6—66no—
117C3×C8—66no—
118C3×C8—62no—
119C3⋊C8—26no—
120C3⋊C8—22no—
121C2×C32—23no—
122C2×C32C22×C4⋊C411yescharacteristic
123C3⋊D3—21no—
124C3⋊D3—23no—
125#41—91no—
126#41—93no—
127#41—93no—
128#41GO+(4,𝔽2)11yescharacteristic
129C2×Q8—91no—
130C2×D4—93no—
131C22×C4—93no—
132M16—66no—
133M16—92no—
134M16—96no—
135M16—96no—
136M16—96no—
137M16—186no—
138C2×C8—66no—
139C2×C8—91no—
140C2×C8—93no—
141C2×C8—96no—
142C2×C8—96no—
143C2×C8—186no—
144C22×C3—26no—
145C2×D3—62no—
146C2×D3—66no—
147C2×D3—246no—
148C3×C4—22no—
149C3×C4—26no—
150Dic3—66no—
151Dic3—62no—
152C32#291611yescharacteristic, complemented, Sylow
153C23—93no—
154Q8—93no—
155Q8#377311yescharacteristic
156D4—96no—
157D4—93no—
158D4#377313yes—
159C2×C4—93no—
160C2×C4—91no—
161C2×C4—93no—
162C2×C4—93no—
163C2×C4—93no—
164C2×C4C2×GO+(4,𝔽2)13yes—
165C8—62no—
166C8—66no—
167C8—92no—
168C8—96no—
169C2×C3—22no—
170C2×C3—46no—
171D3—122no—
172D3—126no—
173C22—91no—
174C22—93no—
175C22—363no—
176C22C2×#377313yes—
177C4—91no—
178C4—93no—
179C4C2×#377313yes—
180C4C22×GO+(4,𝔽2)11yescharacteristic
181C3—22no—
182C2—23no—
183C2—181no—
184C2—183no—
185C2C22×#377311yescharacteristic
subgroupG/H
center, FrattiniC4C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×#41D4
socleC2×C32C22×C4⋊C4
prime radical#41×C3⋊D3C22
cosocleC4×C3⋊D3C24
hypercenter#41GO+(4,𝔽2)
hypocenterC32#2916
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
3. #10593331C2semidirect
4. #10593330C2semidirect
5. C2×#63733C2semidirect
152. C32#2916semidirect

Maximal subgroups

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

subgroupindex
#105966472
#105954432
#105933312
#105933302
C2×#637332
#29169