Finite Group Databasebeta

← #20242461

Subgroups — #20242461

Order 6016.

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

normal subgroups only

This group has 236 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#15689834C211yesmaximal, characteristic, complemented
2#15689497C211yesmaximal, characteristic, complemented
3#15689324C211yesmaximal, characteristic, complemented
4#15689319C211yesmaximal, characteristic
5#15688853C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×#333C211yesmaximal, characteristic, complemented
8C2×#10625325—21no—
9C2×#10625336—22no—
10C2×D376—21no—
11#13094021C2211yescharacteristic
12#13094015—21no—
13#13094004—21no—
14#13094000—22no—
15C4×Dic94C2211yescharacteristic
16C4×D188C2211yescharacteristic
17#13093986—21no—
18C4⋊C4×D47—21no—
19#13093946—21no—
20#13093946—21no—
21C4×C47⋊C8C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C2×Q8×C47D412yes—
26C2×D188—21no—
27C2×D188—21no—
28C2×D188—21no—
29C2×D188D411yescharacteristic
30C2×C4×D47—21no—
31C2×C4×D47—22no—
32C2×Dic94D411yescharacteristic
33C2×C8×C47—21no—
34C2×C8×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C42×C47C2311yescharacteristic
38#10625336—44no—
39(C2×D47)⋊C4—22no—
40(C2×D47)⋊C4—21no—
41C4⋊Dic47—22no—
42C4⋊Dic47D411yescharacteristic
43C4⋊Dic47D411yescharacteristic
44Dic47⋊C4—22no—
45Dic47⋊C4—21no—
46C4×Dic47—21no—
47C2×C47⋊C8—21no—
48D376—42no—
49#10625325—42no—
50C22×D47—21no—
51C22×D47—41no—
52Q8×C47—42no—
53C2×C4×C47—22no—
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—21no—
60D188—21no—
61D188—42no—
62D188—41no—
63D188—41no—
64D188—41no—
65D188—41no—
66D188SD1612yescomplemented
67C4×D47—41no—
68C4×D47—41no—
69C4×D47—82no—
70Dic94—21no—
71Dic94—21no—
72C8×C47—41no—
73C8×C47—41no—
74C47⋊C8—22no—
75C22×C47#12011yescharacteristic
76C2×D47—22no—
77C2×D47—41no—
78C2×D47—41no—
79C2×D47—81no—
80C2×D47—81no—
81C2×D47—81no—
82C4×C47—21no—
83C4×C47—42no—
84C4×C47C2×SD1611yescharacteristic
85C4×C47#13511yescharacteristic
86C4×C47AGL(1,ℤ/8)11yescharacteristic
87C4×C47#13711yescharacteristic
88Dic47—41no—
89Dic47—41no—
90Dic47—41no—
91#1622—471nomaximal, Sylow
92C2×C47#44811yescharacteristic
93C2×C47#44911yescharacteristic
94C2×C47#45311yescharacteristic
95D47—42no—
96D47—161no—
97#554—471no—
98#492—471no—
99#460—471no—
100#459—471no—
101#333D4711yescharacteristic, complemented
102Q8⋊C8—471no—
103D4⋊C8—471no—
104C47#162211yescharacteristic, complemented, Sylow
105C2×SD16—941no—
106C2×SD16—942no—
107C2×D8—941no—
108C4⋊Q8C2×D4711yescharacteristic
109#127—471no—
110#125—941no—
111C22⋊Q8—941no—
112C22⋊Q8—942no—
113C4×Q8—471no—
114C4×D4—471no—
115C4×D4—941no—
116C2×C4⋊C4—941no—
117C4⋊C8C2×D4711yescharacteristic
118C4⋊C8C2×D4711yescharacteristic
119#102—941no—
120#102—941no—
121C4×C8—471no—
122C2×Q8—471no—
123C2×Q8D18812yes—
124C2×D4—471no—
125C2×D4—941no—
126C2×D4—941no—
127C2×D4—941no—
128C22×C4—942no—
129C22×C4—941no—
130SD16—1882no—
131SD16—1884no—
132D8—1882no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—941no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—471no—
139C4⋊C4—471no—
140C4⋊C4—942no—
141C4⋊C4—942no—
142C4⋊C4—941no—
143C22⋊C4—942no—
144C22⋊C4—941no—
145C42—941no—
146C42C22×D4711yescharacteristic
147C23—941no—
148C23—1881no—
149Q8—42no—
150Q8—941no—
151Q8—941no—
152D4—472no—
153D4—941no—
154D4—1882no—
155D4—1881no—
156D4—1881no—
157D4—1881no—
158D4—1881no—
159C2×C4—22no—
160C2×C4—941no—
161C2×C4—941no—
162C2×C4—941no—
163C2×C4—3762no—
164C2×C4—1881no—
165C2×C4—1881no—
166C2×C4C2×D18811yescharacteristic
167C2×C4D4×D4711yescharacteristic
168C2×C4D4×D4711yescharacteristic
169C8—41no—
170C8—41no—
171C8—942no—
172C22—942no—
173C22—3761no—
174C22—3761no—
175C22—3761no—
176C22—1881no—
177C22—1881no—
178C22#1309399411yescharacteristic
179C4—21no—
180C4—42no—
181C4—1881no—
182C4—1881no—
183C4—1881no—
184C4SD16×D4711yescharacteristic
185C4#1309404711yescharacteristic
186C4#1309405111yescharacteristic
187C4#1309405611yescharacteristic
188C2—1882no—
189C2—7521no—
190C2#1568926311yescharacteristic
191C2#1568927111yescharacteristic
192C2#1568929311yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#333C2
socleC22×C47#120
hypercenter#333D47
hypocenterC47#1622
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #15689834C2semidirect
2. #15689497C2semidirect
3. #15689324C2semidirect
5. #15688853C2semidirect
6. #15688850C2semidirect
7. C47×#333C2semidirect
66. D188SD16semidirect
101. #333D47semidirect
104. C47#1622semidirect