Finite Group Databasebeta

← #20243449

Subgroups — #20243449

Order 6016.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#13094030C211yesmaximal, characteristic
2C2×#13093958C211yesmaximal, characteristic, complemented
3#15689125C212yesmaximal
4#15688891C212yesmaximal, complemented
5C2×#108×C47C211yesmaximal, characteristic, complemented
6C2×#10625350C2211yescharacteristic
7#13094030—22no—
8#13094030C414yescomplemented
9C2×#10625329C2211yescharacteristic
10C2×#10625324—21no—
11C2×C8×D47—21no—
12C2×C4⋊Dic47C2212yes—
13#13093958—21no—
14#13093958—21no—
15#13093949—22no—
16#13093946—22no—
17C2×M16×C47C2212yes—
18C22×C8×C47C2211yescharacteristic
19#108×C47—22no—
20C22×C4×C47C2311yescharacteristic
21C2×C22⋊D47—21no—
22C22×Dic47—22no—
23#10625350—21no—
24#10625350—21no—
25#10625350C2×C412yes—
26#10625350Q812yes—
27C2×D188D411yescharacteristic
28C2×C4×D47—21no—
29C2×Dic94D411yescharacteristic
30M16×C47—22no—
31M16×C47—22no—
32C2×C8×C47—22no—
33C2×C8×C47C2×C412yes—
34C2×C8×C47D411yescharacteristic
35C2×C8×C47D411yescharacteristic
36C2×C8×C47D412yes—
37C4⋊Dic47—22no—
38C4⋊Dic47—22no—
39#10625329—21no—
40#10625329C2×C412yes—
41C2×C47⋊C8—21no—
42#10625324—24no—
43C8×D47—24no—
44C23×C47#4111yescharacteristic
45C22×D47—21no—
46C2×C4×C47C22×C411yescharacteristic
47C2×C4×C47C2×D411yescharacteristic
48C2×C4×C47C2×D411yescharacteristic
49C2×C4×C47C2×D411yescharacteristic
50C2×C4×C47C2×Q811yescharacteristic
51C2×C4×C47#4111yescharacteristic
52C22⋊D47—22no—
53C22⋊D47—22no—
54C2×Dic47—21no—
55C2×Dic47—42no—
56C2×Dic47—82no—
57D188—21no—
58D188C4⋊C412yes—
59C4×D47—22no—
60C4×D47—22no—
61Dic94—21no—
62Dic94C4⋊C412yes—
63C8×C47—42no—
64C8×C47C22⋊C412yes—
65C8×C47C22⋊C412yes—
66C47⋊C8—22no—
67C22×C47—21no—
68C22×C47—21no—
69C22×C47#11711yescharacteristic
70C22×C47#12111yescharacteristic
71C22×C47C22⋊Q811yescharacteristic
72C2×D47—22no—
73C2×D47—41no—
74C2×D47—41no—
75C4×C47C2×C22⋊C411yescharacteristic
76C4×C47C2×C4⋊C411yescharacteristic
77C4×C47#12111yescharacteristic
78C4×C47C22⋊Q811yescharacteristic
79Dic47—22no—
80Dic47—82no—
81#1816—471nomaximal, Sylow
82C2×C47—21no—
83C2×C47—21no—
84C2×C47#38011yescharacteristic
85C2×C47#47211yescharacteristic
86C2×C47#47311yescharacteristic
87D47—42no—
88C2×#131—471no—
89C2×#108D4711yescharacteristic, complemented
90C2×#107—471no—
91#417—472no—
92#343—472no—
93C47#181611yescharacteristic, complemented, Sylow
94C2×#41—471no—
95#131—474no—
96#131—942no—
97C2×M16—471no—
98C2×M16—941no—
99C2×M16C2×D4712yes—
100C22×C8—941no—
101C22×C8C2×D4711yescharacteristic
102C2×C4⋊C4—472no—
103#108—22no—
104#107—941no—
105#107—941no—
106#103—942no—
107#102—942no—
108#41—472no—
109#41—472no—
110#41—941no—
111#41—941no—
112C2×Q8—471no—
113C2×D4—471no—
114C2×D4—941no—
115C22×C4—941no—
116C22×C4—942no—
117C22×C4C22×D4711yescharacteristic
118M16—22no—
119M16—22no—
120M16—472no—
121M16—941no—
122M16—944no—
123C2×C8—22no—
124C2×C8—941no—
125C2×C8—944no—
126C2×C8C4×D4712yes—
127C2×C8D18811yescharacteristic
128C2×C8D18811yescharacteristic
129C2×C8C22⋊D4712yes—
130C4⋊C4—942no—
131C4⋊C4—942no—
132C23—941no—
133C23#1062535411yescharacteristic
134Q8—472no—
135Q8—941no—
136D4—472no—
137D4—942no—
138D4—942no—
139D4—941no—
140C2×C4—941no—
141C2×C4—942no—
142C2×C4—942no—
143C2×C4—3762no—
144C2×C4—1882no—
145C2×C4C2×C4×D4711yescharacteristic
146C2×C4C2×D18811yescharacteristic
147C2×C4D4×D4711yescharacteristic
148C2×C4#1062535211yescharacteristic
149C2×C4Q8×D4711yescharacteristic
150C2×C4C2×C22⋊D4711yescharacteristic
151C8—42no—
152C8—942no—
153C8(C2×D47)⋊C412yes—
154C8(C2×D47)⋊C412yes—
155C22—21no—
156C22—21no—
157C22—942no—
158C22—1881no—
159C22—1881no—
160C22#1309398211yescharacteristic
161C22#1309399911yescharacteristic
162C22#1309400011yescharacteristic
163C4—942no—
164C4—3762no—
165C4C2×(C2×D47)⋊C411yescharacteristic
166C4C4⋊C4×D4711yescharacteristic
167C4#1309399511yescharacteristic
168C4#1309400411yescharacteristic
169C2—21no—
170C2—21no—
171C2—1882no—
172C2#1568898011yescharacteristic
173C2#1568939411yescharacteristic
174C2#1568939911yescharacteristic
subgroupG/H
centerC22#13093999
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#108×C47C2
socleC22×C47#121
hypercenterC2×#108D47
hypocenterC47#1816
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. C2×#13093958C2semidirect
4. #15688891C2semidirect
5. C2×#108×C47C2semidirect
8. #13094030C4semidirect
89. C2×#108D47semidirect
93. C47#1816semidirect