Finite Group Databasebeta

← #20242540

Subgroups — #20242540

Order 6016.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689776C211yesmaximal, characteristic
2#15689475C211yesmaximal, characteristic, complemented
3#15689414C211yesmaximal, characteristic, complemented
4#15689414C211yesmaximal, characteristic, complemented
5#15688850C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×#332C211yesmaximal, characteristic, complemented
8C2×#10625354—21no—
9#13094024C2211yescharacteristic
10#13094009—22no—
11#13094000—21no—
12#13093999—21no—
13C4×D188C2211yescharacteristic
14C4×D188C2211yescharacteristic
15C4⋊C4×D47—21no—
16#13093956—21no—
17#13093956—21no—
18#13093947—22no—
19#13093946—21no—
20#13093946—21no—
21C4×C47⋊C8C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26#10625354—42no—
27#10625354—42no—
28C2×D188—22no—
29C2×D188D411yescharacteristic
30C2×D188D411yescharacteristic
31C2×C4×D47—22no—
32C2×C4×D47—21no—
33C2×C4×D47—21no—
34C2×Dic94—21no—
35C2×C8×C47—21no—
36C2×C8×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47D412yes—
39C42×C47C2311yescharacteristic
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47D411yescharacteristic
46C4⋊Dic47D411yescharacteristic
47Dic47⋊C4—22no—
48C2×C47⋊C8—21no—
49C22×D47—21no—
50C22×D47—21no—
51Q8×C47—41no—
52Q8×C47—41no—
53C2×C4×C47—22no—
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—41no—
60D188—21no—
61D188—21no—
62D188—21no—
63D188—44no—
64D188SD1612yes—
65C4×D47—44no—
66C4×D47—41no—
67C4×D47—41no—
68C4×D47—41no—
69C4×D47—41no—
70Dic94—42no—
71C8×C47—41no—
72C8×C47—41no—
73C47⋊C8—41no—
74C22×C47#12011yescharacteristic
75C2×D47—22no—
76C2×D47—41no—
77C2×D47—41no—
78C2×D47—41no—
79C2×D47—41no—
80C2×D47—41no—
81C4×C47—21no—
82C4×C47—42no—
83C4×C47C2×SD1611yescharacteristic
84C4×C47#13511yescharacteristic
85C4×C47AGL(1,ℤ/8)11yescharacteristic
86C4×C47#13711yescharacteristic
87Dic47—41no—
88Dic47—41no—
89Dic47—81no—
90#1635—471nomaximal, Sylow
91C2×C47#45011yescharacteristic
92C2×C47#45211yescharacteristic
93C2×C47#45411yescharacteristic
94D47—42no—
95D47—81no—
96#547—471no—
97#487—471no—
98#476—471no—
99#476—471no—
100#332D4711yescharacteristic, complemented
101D4⋊C8—471no—
102D4⋊C8—471no—
103C47#163511yescharacteristic, complemented, Sylow
104C2×#41—941no—
105C4⋊Q8—471no—
106C4⋊Q8C2×D4711yescharacteristic
107#123—942no—
108C22⋊Q8—941no—
109#121—941no—
110C4×D4—471no—
111C4×D4—471no—
112C2×C4⋊C4—941no—
113#106—941no—
114#106—941no—
115C4⋊C8C2×D4711yescharacteristic
116C4⋊C8C2×D4711yescharacteristic
117#103—942no—
118#102—941no—
119#102—941no—
120C4×C8—471no—
121#41—1882no—
122#41—1882no—
123C2×Q8—21no—
124C2×Q8—941no—
125C2×D4—471no—
126C2×D4—471no—
127C2×D4—942no—
128C22×C4—942no—
129C22×C4—941no—
130C22×C4—941no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—941no—
134C4⋊C4—21no—
135C4⋊C4—471no—
136C4⋊C4—471no—
137C4⋊C4—942no—
138C4⋊C4—941no—
139C4⋊C4—941no—
140C4⋊C4D18812yes—
141C22⋊C4—942no—
142C22⋊C4—941no—
143C22⋊C4—941no—
144C42C22×D4711yescharacteristic
145C23—941no—
146C23—941no—
147Q8—41no—
148Q8—41no—
149Q8—1882no—
150D4—472no—
151D4—941no—
152D4—941no—
153D4—941no—
154D4—1884no—
155C2×C4—22no—
156C2×C4—941no—
157C2×C4—941no—
158C2×C4—1884no—
159C2×C4—1881no—
160C2×C4—1881no—
161C2×C4—1881no—
162C2×C4—1881no—
163C2×C4—1881no—
164C2×C4C2×D18811yescharacteristic
165C2×C4D4×D4711yescharacteristic
166C2×C4D4×D4711yescharacteristic
167C8—41no—
168C8—41no—
169C8—1881no—
170C22—942no—
171C22—1881no—
172C22—1881no—
173C22—1881no—
174C22—1881no—
175C22—1881no—
176C22#1309399411yescharacteristic
177C4—21no—
178C4—42no—
179C4—3761no—
180C4—1881no—
181C4—1881no—
182C4SD16×D4711yescharacteristic
183C4#1309404511yescharacteristic
184C4#1309404811yescharacteristic
185C4#1309405611yescharacteristic
186C2—3761no—
187C2—1882no—
188C2#1568927511yescharacteristic
189C2#1568928811yescharacteristic
190C2#1568929811yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#332C2
socleC22×C47#120
hypercenter#332D47
hypocenterC47#1635
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #15689475C2semidirect
3. #15689414C2semidirect
4. #15689414C2semidirect
5. #15688850C2semidirect
6. #15688850C2semidirect
7. C47×#332C2semidirect
100. #332D47semidirect
103. C47#1635semidirect