Finite Group Databasebeta

← #20244613

Subgroups — #20244613

Order 6016.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#15689704C211yesmaximal, characteristic
2C2×#13093950C212yesmaximal, complemented
3#15689125C212yesmaximal, complemented
4#15688992C211yesmaximal, characteristic, complemented
5C47×#343C211yesmaximal, characteristic, complemented
6C2×#10625350C2212yes—
7#13094004—22no—
8#13093999—22no—
9#13093998—22no—
10C2×C4⋊Dic47C2211yescharacteristic
11C2×Dic47⋊C4—22no—
12C2×C4×Dic47C2211yescharacteristic
13#13093950—24no—
14#13093949—22no—
15#13093946—22no—
16C2×M16×C47C2212yes—
17C2×C4⋊C4×C47C2211yescharacteristic
18C22×C4×C47D412yes—
19C22×C4×C47C2311yescharacteristic
20C2×C22⋊D47—22no—
21C22×Dic47—21no—
22C22×Dic47—21no—
23#10625350—22no—
24#10625350—22no—
25#10625350—22no—
26#10625350—22no—
27C2×D188—22no—
28C2×D188D412yes—
29C2×C4×D47—22no—
30C2×Dic94D412yes—
31M16×C47—22no—
32M16×C47—22no—
33C2×C8×C47—22no—
34C4⋊C4×C47—22no—
35(C2×D47)⋊C4—24no—
36C4⋊Dic47—22no—
37C4⋊Dic47—22no—
38Dic47⋊C4—44no—
39C4×Dic47—21no—
40C4×Dic47D412yescomplemented
41C23×C47C2×D411yescharacteristic
42C22×D47—22no—
43C2×C4×C47—22no—
44C2×C4×C47—42no—
45C2×C4×C47C2×D411yescharacteristic
46C2×C4×C47C2×D412yes—
47C2×C4×C47#4112yes—
48C2×C4×C47#4111yescharacteristic
49C22⋊D47—42no—
50C22⋊D47—42no—
51C2×Dic47—22no—
52C2×Dic47—22no—
53C2×Dic47—22no—
54C2×Dic47—22no—
55C2×Dic47—42no—
56C2×Dic47—41no—
57D188—22no—
58D188—22no—
59D188—82no—
60C4×D47—42no—
61C4×D47—42no—
62Dic94—22no—
63Dic94—22no—
64C8×C47—42no—
65C22×C47—21no—
66C22×C47—21no—
67C22×C47#12011yescharacteristic
68C22×C47#12111yescharacteristic
69C22×C47#12411yescharacteristic
70C2×D47—42no—
71C2×D47—42no—
72C2×D47—42no—
73C4×C47—42no—
74C4×C47#12112yes—
75C4×C47#12312yes—
76Dic47—24no—
77Dic47—42no—
78Dic47—81no—
79#2039—471nomaximal, Sylow
80C2×C47—21no—
81C2×C47—21no—
82C2×C47#39411yescharacteristic
83C2×C47#45311yescharacteristic
84C2×C47#45611yescharacteristic
85D47—82no—
86#537—471no—
87C2×#104—472no—
88#417—472no—
89#384—471no—
90#343D4711yescharacteristic, complemented
91C47#203911yescharacteristic, complemented, Sylow
92C2×#41—472no—
93C2×M16C2×D4712yes—
94C22⋊Q8—942no—
95#121—942no—
96#121—942no—
97C2×C4⋊C4—471no—
98C2×C4⋊C4—942no—
99C2×C4⋊C4C2×D4711yescharacteristic
100C2×C42—471no—
101#104—944no—
102#103—942no—
103#102—942no—
104#41—942no—
105#41—942no—
106#41—942no—
107#41—942no—
108C2×Q8—472no—
109C2×D4—472no—
110C2×D4—942no—
111C2×D4—942no—
112C22×C4—941no—
113C22×C4—942no—
114C22×C4—941no—
115C22×C4D18812yes—
116C22×C4C22×D4711yescharacteristic
117M16—22no—
118M16—22no—
119C2×C8—22no—
120C4⋊C4—22no—
121C4⋊C4—942no—
122C4⋊C4—942no—
123C4⋊C4—1884no—
124C22⋊C4—944no—
125C42—472no—
126C42—941no—
127C23—942no—
128C23C2×D18811yescharacteristic
129Q8—942no—
130Q8—942no—
131D4—942no—
132D4—942no—
133D4—3762no—
134D4—1882no—
135D4—1882no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—942no—
139C2×C4—942no—
140C2×C4—942no—
141C2×C4—942no—
142C2×C4—1882no—
143C2×C4—1881no—
144C2×C4—1882no—
145C2×C4—1882no—
146C2×C4#1062535012yes—
147C2×C4D4×D4711yescharacteristic
148C2×C4D4×D4712yes—
149C2×C4#1062535411yescharacteristic
150C8—42no—
151C22—21no—
152C22—21no—
153C22—1882no—
154C22—1882no—
155C22—1882no—
156C22#1309399411yescharacteristic
157C22#1309399911yescharacteristic
158C22#1309401211yescharacteristic
159C4—42no—
160C4—944no—
161C4—3761no—
162C4—1882no—
163C4#1309399712yes—
164C4#1309400912yes—
165C2—21no—
166C2—21no—
167C2—3762no—
168C2#1568904111yescharacteristic
169C2#1568929311yescharacteristic
170C2#1568930811yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#343C2
socleC22×C47#120
hypercenter#343D47
hypocenterC47#2039
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#13093950C2semidirect
3. #15689125C2semidirect
4. #15688992C2semidirect
5. C47×#343C2semidirect
40. C4×Dic47D4semidirect
90. #343D47semidirect
91. C47#2039semidirect