Finite Group Databasebeta

← #20242322

Subgroups — #20242322

Order 6016.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689704C211yesmaximal, characteristic, complemented
2#15689257C212yesmaximal, complemented
3#15688856C212yesmaximal, complemented
4#15688849C211yesmaximal, characteristic, complemented
5C47×#394C211yesmaximal, characteristic, complemented
6C2×#10625350—21no—
7C2×#10625334—22no—
8#13094004—22no—
9#13093999—22no—
10#13093998—21no—
11#13093998C2212yes—
12#13093945—22no—
13C22⋊(C47⋊C8)C2212yes—
14C22×D4×C47C2211yescharacteristic
15C2×C4⋊C4×C47C2211yescharacteristic
16C2×C22⋊C4×C47—21no—
17C2×C22⋊C4×C47—21no—
18#95×C47C2211yescharacteristic
19C24×C47—21no—
20C2×D4×C47—22no—
21C2×D4×C47—42no—
22C22×C4×C47—21no—
23C22×C4×C47D411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47C2311yescharacteristic
26C2×C22⋊D47—22no—
27#10625350—42no—
28#10625350—42no—
29C2×D188—21no—
30C2×D188—21no—
31C2×D188D412yes—
32C2×C4×D47—22no—
33C2×Dic94—21no—
34C4⋊C4×C47—22no—
35C22⋊C4×C47—42no—
36C22⋊C4×C47—42no—
37#10625334—44no—
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—22no—
40C4⋊Dic47—21no—
41C4⋊Dic47D412yes—
42C2×C47⋊C8—22no—
43C23×C47—22no—
44C23×C47—41no—
45C23×C47—41no—
46C23×C47—41no—
47C23×C47—41no—
48C23×C47—41no—
49C23×C47—41no—
50C23×C47C2×D411yescharacteristic
51C22×D47—22no—
52D4×C47—24no—
53D4×C47—42no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47D812yescomplemented
63C2×C4×C47C2×D412yes—
64C22⋊D47—42no—
65C22⋊D47—42no—
66C2×Dic47—22no—
67D188—42no—
68D188—42no—
69D188—81no—
70C4×D47—44no—
71Dic94—42no—
72C47⋊C8—42no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—42no—
76C22×C47—42no—
77C22×C47—42no—
78C22×C47—81no—
79C22×C47—81no—
80C22×C47—81no—
81C22×C47—81no—
82C22×C47#12011yescharacteristic
83C22×C47C2×D811yescharacteristic
84C22×C47AGL(1,ℤ/8)11yescharacteristic
85C2×D47—42no—
86C2×D47—42no—
87C2×D47—42no—
88C4×C47—22no—
89C4×C47—22no—
90C4×C47—41no—
91C4×C47—81no—
92Dic47—42no—
93#1598—471nomaximal, Sylow
94C2×C47—21no—
95C2×C47—21no—
96C2×C47—82no—
97C2×C47#44711yescharacteristic
98C2×C47#45411yescharacteristic
99C2×C47B(4,𝔽2)11yescharacteristic
100D47—82no—
101#537—471no—
102#447—472no—
103#394D4711yescharacteristic, complemented
104#327—472no—
105#324—471no—
106C47#159811yescharacteristic, complemented, Sylow
107C2×#41—941no—
108C22×D4C2×D4711yescharacteristic
109C2×D8—942no—
110C22⋊Q8—942no—
111#121—472no—
112#121—942no—
113#121—941no—
114C2×C4⋊C4C2×D4711yescharacteristic
115C2×C22⋊C4—21no—
116C2×C22⋊C4—21no—
117#102—942no—
118C22⋊C8—472no—
119#95C2×D4711yescharacteristic
120C24—21no—
121#41—1882no—
122#41—1882no—
123C2×Q8—941no—
124C2×D4—22no—
125C2×D4—42no—
126C2×D4—472no—
127C2×D4—941no—
128C2×D4—941no—
129C2×D4—942no—
130C22×C4—21no—
131C22×C4—942no—
132C22×C4C22⋊D4711yescharacteristic
133C22×C4C22⋊D4711yescharacteristic
134C22×C4C22×D4711yescharacteristic
135D8—1884no—
136C2×C8—942no—
137C4⋊C4—22no—
138C4⋊C4—472no—
139C4⋊C4—941no—
140C22⋊C4—42no—
141C22⋊C4—42no—
142C22⋊C4—942no—
143C22⋊C4—942no—
144C23—22no—
145C23—41no—
146C23—41no—
147C23—41no—
148C23—41no—
149C23—41no—
150C23—41no—
151C23—942no—
152C23C2×C22⋊D4711yescharacteristic
153Q8—1882no—
154D4—24no—
155D4—42no—
156D4—3761no—
157D4—1882no—
158D4—1882no—
159D4—1882no—
160D4—1882no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—942no—
170C2×C4—1884no—
171C2×C4#1062533412yescomplemented
172C2×C4D4×D4712yes—
173C8—1882no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—81no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—1882no—
184C22—1882no—
185C22—1882no—
186C22#1309399211yescharacteristic
187C22C2×#1062533411yescharacteristic
188C22#1309404911yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—81no—
193C4—1882no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—3762no—
198C2#1568925611yescharacteristic
199C2#1568929511yescharacteristic
200C2#1568930911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#394C2
socleC22×C47#120
hypercenter#394D47
hypocenterC47#1598
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #15689704C2semidirect
2. #15689257C2semidirect
3. #15688856C2semidirect
4. #15688849C2semidirect
5. C47×#394C2semidirect
62. C2×C4×C47D8semidirect
103. #394D47semidirect
106. C47#1598semidirect
171. C2×C4#10625334semidirect