Finite Group Databasebeta

← #20255109

Subgroups — #20255109

Order 6016.

484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#13094043C212yesmaximal, complemented
2#15689777C212yesmaximal, complemented
3#15689503C211yesmaximal, characteristic, complemented
4#15689365C212yesmaximal, complemented
5#15689328C212yesmaximal, complemented
6#15689286C214yesmaximal, complemented
7C8×D188C211yesmaximal, characteristic, complemented
8C4×D8×C47C211yesmaximal, characteristic, complemented
9C2×#10625352C2214yes—
10#13094043—28no—
11C2×Dic188C2212yes—
12C2×Dic188C2212yes—
13C2×#10625335C2214yes—
14C2×C8×D47C2212yes—
15#13094024C2212yes—
16#13094008—24no—
17#13094004C2214yes—
18#13093998—22no—
19C4×D188C2211yescharacteristic
20C2×C4⋊Dic47—22no—
21C4⋊(C47⋊C8)C2211yescharacteristic
22#13093947C2214yes—
23(C2×D47)⋊C8C2212yes—
24C2×D8×C47C2211yescharacteristic
25C4×D4×C47C2212yes—
26#107×C47C2211yescharacteristic
27#102×C47C2212yes—
28C4×C8×C47C2211yescharacteristic
29C2×D4×C47C2312yes—
30C22×C4×C47—22no—
31C2×C22⋊D47—24no—
32C22×Dic47—24no—
33#10625352—28no—
34#10625352—44no—
35C2×D188D411yescharacteristic
36C2×C4×D47C2312yes—
37C2×Dic94C2314yes—
38D8×C47D414yescomplemented
39C2×C8×C47C2311yescharacteristic
40C2×C8×C47C2311yescharacteristic
41C4⋊C4×C47C2312yes—
42C22⋊C4×C47—22no—
43C42×C47C2311yescharacteristic
44#10625335—28no—
45(C2×D47)⋊C4—24no—
46(C2×D47)⋊C4D412yes—
47C4⋊Dic47—22no—
48C4⋊Dic47—22no—
49C4⋊Dic47—24no—
50C4⋊Dic47D411yescharacteristic
51C2×C47⋊C8C2312yes—
52Dic188—24no—
53Dic188—42no—
54C8×D47—24no—
55C23×C47—22no—
56C22×D47C2×D412yes—
57D4×C47—22no—
58D4×C47C2×D414yes—
59C2×C4×C47—22no—
60C2×C4×C47—44no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2411yescharacteristic
64C22⋊D47—48no—
65C2×Dic47—24no—
66C2×Dic47—48no—
67C2×Dic47C2×D412yes—
68D188—22no—
69C4×D47—22no—
70C4×D47—22no—
71Dic94—24no—
72Dic94—24no—
73C8×C47—21no—
74C8×C47C2×D412yes—
75C47⋊C8—22no—
76C22×C47—24no—
77C22×C47—42no—
78C22×C47—42no—
79C22×C47C22×D411yescharacteristic
80C2×D47—22no—
81C2×D47—22no—
82C2×D47—22no—
83C4×C47—21no—
84C4×C47—42no—
85C4×C47#13512yescomplemented
86C4×C47C22×D411yescharacteristic
87C4×C47H(5,𝔽2)11yescharacteristic
88Dic47—22no—
89Dic47—44no—
90#3283—471nomaximal, Sylow
91C2×C47—44no—
92C2×C47D4211yescharacteristic
93C2×C47C2×#13511yescharacteristic
94C2×C47#57811yescharacteristic
95D47—42no—
96C2×#135—472no—
97#547—472no—
98#494—471no—
99#467—472no—
100#461—472no—
101#452—474no—
102C4×D8D4711yescharacteristic, complemented
103C8×D4—471no—
104C47#328311yescharacteristic, complemented, Sylow
105C2×#41—474no—
106#135—948no—
107C2×Q16—472no—
108C2×Q16—472no—
109C2×SD16—474no—
110C2×D8C2×D4711yescharacteristic
111C22×C8—472no—
112C4⋊Q8—472no—
113#123—944no—
114C22⋊Q8—474no—
115#121—942no—
116C4×D4—471no—
117C4×D4C2×D4712yes—
118C2×C4⋊C4—942no—
119#107C2×D4711yescharacteristic
120C4⋊C8—471no—
121#103—474no—
122#102C2×D4712yes—
123C22⋊C8—472no—
124C4×C8C2×D4711yescharacteristic
125#41—948no—
126#41—1884no—
127C2×Q8—474no—
128C2×D4—471no—
129C2×D4—944no—
130C2×D4C22×D4712yes—
131C22×C4—22no—
132C22×C4—472no—
133C22×C4—944no—
134Q16—944no—
135Q16—1882no—
136SD16—948no—
137D8D18814yescomplemented
138C2×C8—472no—
139C2×C8—944no—
140C2×C8C22×D4711yescharacteristic
141C2×C8C22×D4711yescharacteristic
142C4⋊C4—471no—
143C4⋊C4—944no—
144C4⋊C4—942no—
145C4⋊C4—942no—
146C4⋊C4C22×D4712yes—
147C22⋊C4—22no—
148C22⋊C4—472no—
149C22⋊C4—944no—
150C42C22×D4711yescharacteristic
151C23—22no—
152C23—472no—
153Q8—944no—
154Q8—944no—
155D4—22no—
156D4—942no—
157D4—1888no—
158D4C2×D18814yes—
159C2×C4—22no—
160C2×C4—44no—
161C2×C4—472no—
162C2×C4—942no—
163C2×C4—942no—
164C2×C4—944no—
165C2×C4—1888no—
166C2×C4D4×D4711yescharacteristic
167C2×C4D4×D4711yescharacteristic
168C2×C4C23×D4711yescharacteristic
169C8—21no—
170C8—942no—
171C8C2×D18812yes—
172C22—24no—
173C22—42no—
174C22—42no—
175C22—942no—
176C22—942no—
177C22—942no—
178C22C2×D4×D4711yescharacteristic
179C4—21no—
180C4—42no—
181C4—942no—
182C4—1884no—
183C4#1309404312yescomplemented
184C4C22×D18811yescharacteristic
185C4#1309407011yescharacteristic
186C2—44no—
187C2—1882no—
188C2D4×D18811yescharacteristic
189C2C2×#1309404311yescharacteristic
190C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×D8×C47C2
socleC22×C47C22×D4
hypercenterC4×D8D47
hypocenterC47#3283
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#13094043C2semidirect
2. #15689777C2semidirect
3. #15689503C2semidirect
4. #15689365C2semidirect
5. #15689328C2semidirect
6. #15689286C2semidirect
7. C8×D188C2semidirect
8. C4×D8×C47C2semidirect
38. D8×C47D4semidirect
85. C4×C47#135semidirect
102. C4×D8D47semidirect
104. C47#3283semidirect
137. D8D188semidirect
183. C4#13094043semidirect