Finite Group Databasebeta

← #20242624

Subgroups — #20242624

Order 6016.

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

normal subgroups only

This group has 240 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#15689526C211yesmaximal, characteristic, complemented
3#15689404C211yesmaximal, characteristic, complemented
4#15689329C211yesmaximal, characteristic, complemented
5#15688850C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×#332C211yesmaximal, characteristic, complemented
8C2×#10625354—21no—
9C2×#10625325—21no—
10#13094024C2211yescharacteristic
11#13094009—22no—
12#13094000—21no—
13#13093999—21no—
14C4×D188C2211yescharacteristic
15C4×D188C2211yescharacteristic
16C4⋊C4×D47—21no—
17#13093958—21no—
18#13093957—22no—
19#13093949—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—
49#10625325—42no—
50C22×D47—21no—
51C22×D47—21no—
52Q8×C47—41no—
53Q8×C47—41no—
54C2×C4×C47—22no—
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×Dic47—21no—
59C2×Dic47—21no—
60C2×Dic47—41no—
61D188—21no—
62D188—21no—
63D188—21no—
64D188—44no—
65D188D812yes—
66C4×D47—44no—
67C4×D47—41no—
68C4×D47—41no—
69C4×D47—41no—
70C4×D47—41no—
71Dic94—41no—
72Dic94—41no—
73C8×C47—41no—
74C8×C47—41no—
75C47⋊C8—22no—
76C22×C47#12011yescharacteristic
77C2×D47—22no—
78C2×D47—41no—
79C2×D47—41no—
80C2×D47—41no—
81C2×D47—41no—
82C2×D47—41no—
83C4×C47—21no—
84C4×C47—42no—
85C4×C47C2×D811yescharacteristic
86C4×C47#13511yescharacteristic
87C4×C47AGL(1,ℤ/8)11yescharacteristic
88C4×C47#13711yescharacteristic
89Dic47—41no—
90Dic47—41no—
91Dic47—81no—
92#1647—471nomaximal, Sylow
93C2×C47#44711yescharacteristic
94C2×C47#45211yescharacteristic
95C2×C47#45611yescharacteristic
96D47—42no—
97D47—81no—
98#547—471no—
99#500—471no—
100#474—471no—
101#461—471no—
102#332D4711yescharacteristic, complemented
103D4⋊C8—471no—
104D4⋊C8—471no—
105C47#164711yescharacteristic, complemented, Sylow
106C2×#41—941no—
107C2×SD16—941no—
108C4⋊Q8—471no—
109C4⋊Q8C2×D4711yescharacteristic
110#123—942no—
111C22⋊Q8—941no—
112#121—941no—
113C4×D4—471no—
114C4×D4—471no—
115C2×C4⋊C4—941no—
116#107—941no—
117#107—942no—
118C4⋊C8C2×D4711yescharacteristic
119C4⋊C8C2×D4711yescharacteristic
120#103—941no—
121#102—941no—
122C4×C8—471no—
123#41—1882no—
124#41—1882no—
125C2×Q8—21no—
126C2×Q8—941no—
127C2×D4—471no—
128C2×D4—471no—
129C2×D4—942no—
130C22×C4—942no—
131C22×C4—941no—
132C22×C4—941no—
133SD16—1882no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—941no—
137C4⋊C4—21no—
138C4⋊C4—471no—
139C4⋊C4—471no—
140C4⋊C4—942no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4D18812yes—
144C22⋊C4—942no—
145C22⋊C4—941no—
146C22⋊C4—941no—
147C42C22×D4711yescharacteristic
148C23—941no—
149C23—941no—
150Q8—41no—
151Q8—41no—
152Q8—1881no—
153Q8—1881no—
154D4—472no—
155D4—941no—
156D4—941no—
157D4—941no—
158D4—1884no—
159C2×C4—22no—
160C2×C4—941no—
161C2×C4—941no—
162C2×C4—1884no—
163C2×C4—1881no—
164C2×C4—1881no—
165C2×C4—1881no—
166C2×C4—1881no—
167C2×C4—1881no—
168C2×C4C2×D18811yescharacteristic
169C2×C4D4×D4711yescharacteristic
170C2×C4D4×D4711yescharacteristic
171C8—41no—
172C8—41no—
173C8—942no—
174C22—942no—
175C22—1881no—
176C22—1881no—
177C22—1881no—
178C22—1881no—
179C22—1881no—
180C22#1309399411yescharacteristic
181C4—21no—
182C4—42no—
183C4—3761no—
184C4—1881no—
185C4—1881no—
186C4D8×D4711yescharacteristic
187C4#1309404511yescharacteristic
188C4#1309405111yescharacteristic
189C4#1309405611yescharacteristic
190C2—3761no—
191C2—1882no—
192C2#1568925811yescharacteristic
193C2#1568928811yescharacteristic
194C2#1568930811yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#332C2
socleC22×C47#120
hypercenter#332D47
hypocenterC47#1647
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. #15689526C2semidirect
3. #15689404C2semidirect
4. #15689329C2semidirect
5. #15688850C2semidirect
6. #15688850C2semidirect
7. C47×#332C2semidirect
102. #332D47semidirect
105. C47#1647semidirect