Finite Group Databasebeta

← #20243630

Subgroups — #20243630

Order 6016.

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

normal subgroups only

This group has 262 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
1#15689890C211yesmaximal, characteristic
2#15689172C211yesmaximal, characteristic, complemented
3#15689147C211yesmaximal, characteristic, complemented
4#15689140C211yesmaximal, characteristic
5#15688895C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic
8#13094031—22no—
9#13094031—22no—
10C2×#10625329—22no—
11C2×#10625329C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14#13093983C2211yescharacteristic
15#13093960—22no—
16C4⋊(C47⋊C8)—22no—
17#13093951—22no—
18C2×#41×C47C2211yescharacteristic
19C2×M16×C47C2211yescharacteristic
20C2×C42×C47C2211yescharacteristic
21#104×C47C412yescomplemented
22#104×C47C412yescomplemented
23#41×C47—21no—
24#41×C47—21no—
25#41×C47C2×C412yes—
26#41×C47D412yes—
27C2×Q8×C47Q811yescharacteristic
28C2×D4×C47—21no—
29C2×D4×C47Q811yescharacteristic
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47C2311yescharacteristic
33M16×C47—21no—
34M16×C47C2×C412yes—
35C2×C8×C47—21no—
36C42×C47—21no—
37C42×C47C2×C411yescharacteristic
38C42×C47C2×C411yescharacteristic
39C22⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4×Dic47—21no—
42#10625329—24no—
43#10625329—21no—
44#10625329—21no—
45#10625329—21no—
46#10625329—21no—
47#10625329—21no—
48#10625329D412yes—
49C2×C47⋊C8—24no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8D412yes—
53C23×C47—21no—
54C23×C47#4111yescharacteristic
55Q8×C47—21no—
56Q8×C47C4⋊C412yes—
57D4×C47—22no—
58D4×C47—22no—
59D4×C47—21no—
60D4×C47C4⋊C412yes—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—21no—
66C2×C4×C47—42no—
67C2×C4×C47C22×C411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×Q811yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C2×Dic47—41no—
74C8×C47—22no—
75C47⋊C8—22no—
76C47⋊C8—22no—
77C47⋊C8—41no—
78C22×C47—22no—
79C22×C47—41no—
80C22×C47—81no—
81C22×C47C4×D411yescharacteristic
82C22×C47C22⋊Q811yescharacteristic
83C22×C47#12311yescharacteristic
84C4×C47—22no—
85C4×C47—22no—
86C4×C47—41no—
87C4×C47C2×C4⋊C411yescharacteristic
88C4×C47C4×D411yescharacteristic
89C4×C47#12011yescharacteristic
90C4×C47C22⋊Q811yescharacteristic
91Dic47—81no—
92#1861—471nomaximal, Sylow
93C2×C47—21no—
94C2×C47—21no—
95C2×C47—21no—
96C2×C47—42no—
97C2×C47#38511yescharacteristic
98#568—471no—
99#430—471no—
100#423—471no—
101#421—471no—
102C2×#104D4711yescharacteristic
103#344—471no—
104#339—471no—
105C47#186111yescharacteristic, complemented, Sylow
106C2×#41C2×D4711yescharacteristic
107#131—942no—
108#131—942no—
109C2×M16—471no—
110C2×M16—471no—
111C2×M16—471no—
112C2×M16—942no—
113C2×M16C2×D4711yescharacteristic
114#117—471no—
115C2×C42C2×D4711yescharacteristic
116#108—942no—
117C4⋊C8—942no—
118#104—942no—
119#104Dic4712yescomplemented
120#104Dic4712yescomplemented
121#41—21no—
122#41—21no—
123#41D18812yes—
124#41C2×Dic4712yes—
125C2×Q8Dic9411yescharacteristic
126C2×D4—21no—
127C2×D4Dic9411yescharacteristic
128C22×C4—21no—
129C22×C4—21no—
130C22×C4C22×D4711yescharacteristic
131M16—21no—
132M16—472no—
133M16—944no—
134M16—941no—
135M16—941no—
136M16—941no—
137M16—941no—
138M16—941no—
139M16C2×Dic4712yes—
140C2×C8—21no—
141C2×C8—472no—
142C2×C8—944no—
143C2×C8—941no—
144C2×C8—941no—
145C4⋊C4—941no—
146C22⋊C4—941no—
147C42—21no—
148C42—941no—
149C42C2×Dic4711yescharacteristic
150C42C2×Dic4711yescharacteristic
151C23—21no—
152C23#1062535211yescharacteristic
153Q8—21no—
154Q8C4⋊Dic4712yes—
155D4—22no—
156D4—22no—
157D4—21no—
158D4C4⋊Dic4712yes—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—1881no—
166C2×C4C2×Dic9411yescharacteristic
167C2×C4C2×D18811yescharacteristic
168C2×C4D4×D4711yescharacteristic
169C2×C4D4×D4711yescharacteristic
170C2×C4#1062535211yescharacteristic
171C2×C4C22×Dic4711yescharacteristic
172C8—22no—
173C8—942no—
174C8—942no—
175C8—1881no—
176C22—22no—
177C22—41no—
178C22—81no—
179C22D4×Dic4711yescharacteristic
180C22#1309400111yescharacteristic
181C22#1309400811yescharacteristic
182C4—22no—
183C4—22no—
184C4—41no—
185C4—3761no—
186C4C2×C4⋊Dic4711yescharacteristic
187C4D4×Dic4711yescharacteristic
188C4#1309399411yescharacteristic
189C4#1309400111yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—42no—
194C2#1568899811yescharacteristic
subgroupG/H
centerC4#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC2×C47#385
hypercenterC2×#104D47
hypocenterC47#1861
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #15689172C2semidirect
3. #15689147C2semidirect
5. #15688895C2semidirect
6. #15688883C2semidirect
21. #104×C47C4semidirect
22. #104×C47C4semidirect
105. C47#1861semidirect
119. #104Dic47semidirect
120. #104Dic47semidirect