Finite Group Databasebeta

← #20251979

Subgroups — #20251979

Order 6016.

476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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×#13094030C211yesmaximal, characteristic
2#15689604C212yesmaximal
3#15689163C212yesmaximal, complemented
4#15689162C214yesmaximal, complemented
5#15689161C211yesmaximal, characteristic, complemented
6#15689158C212yesmaximal, complemented
7#106×D47C212yesmaximal, complemented
8C2×#106×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2211yescharacteristic
10#13094030C418yescomplemented
11C2×#10625329C2211yescharacteristic
12C2×#10625324C2212yes—
13C2×C8×D47C2212yes—
14#13093989—22no—
15#13093986—22no—
16C4×C22⋊D47—24no—
17#13093983C2212yes—
18#13093982C2214yes—
19C4⋊C4×D47C2214yes—
20#13093958C2212yes—
21#13093957C2214yes—
22#13093956C2211yescharacteristic
23#13093956C2211yescharacteristic
24#13093955C2214yes—
25C22×C8×C47C2211yescharacteristic
26C2×C4⋊C4×C47C2212yes—
27#106×C47C2212yes—
28#106×C47C2212yes—
29C22×C4×C47—22no—
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47D412yes—
32#10625350C2×C414yes—
33#10625350Q814yes—
34C2×D188D411yescharacteristic
35C2×C4×D47—24no—
36C2×C4×D47C2312yes—
37C2×Dic94D411yescharacteristic
38C2×C8×C47C2×C414yescomplemented
39C2×C8×C47C2311yescharacteristic
40C2×C8×C47C2311yescharacteristic
41C4⋊C4×C47—22no—
42C4⋊C4×C47C2314yes—
43C22⋊Dic47—22no—
44(C2×D47)⋊C4—24no—
45C4⋊Dic47C2312yes—
46C4⋊Dic47C2312yes—
47Dic47⋊C4—24no—
48C4×Dic47—22no—
49C4×Dic47—24no—
50#10625329C2×C414yescomplemented
51C2×C47⋊C8C2312yes—
52#10625324C2×C418yescomplemented
53C8×D47C2×C418yescomplemented
54C23×C47C2×D411yescharacteristic
55C22×D47C2×D412yes—
56C2×C4×C47—24no—
57C2×C4×C47—82no—
58C2×C4×C47C22×C412yes—
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×Q812yes—
61C2×C4×C47C2411yescharacteristic
62C22⋊D47C4⋊C418yes—
63C2×Dic47—22no—
64C2×Dic47—22no—
65C2×Dic47C2×D412yes—
66D188C4⋊C414yes—
67C4×D47—84no—
68C4×D47C22×C414yes—
69C4×D47C2×Q814yes—
70Dic94C4⋊C414yes—
71C8×C47C22×C412yes—
72C8×C47C22×C412yes—
73C47⋊C8C22×C414yes—
74C22×C47—22no—
75C22×C47C2×C4⋊C412yes—
76C22×C47C22×D411yescharacteristic
77C2×D47—24no—
78C2×D47C2×C4⋊C414yes—
79C4×C47—44no—
80C4×C47C2×C4⋊C412yes—
81C4×C47C23×C411yescharacteristic
82C4×C47C22×Q811yescharacteristic
83Dic47—42no—
84Dic47—42no—
85Dic47C2×C4⋊C414yes—
86#2912—471nomaximal, Sylow
87C2×C47—22no—
88C2×C47C22×C4⋊C411yescharacteristic
89C2×C47#57712yes—
90D47—24no—
91C2×#131—471no—
92#520—472no—
93#428—472no—
94#428—474no—
95#427—471no—
96#427—472no—
97C2×#106—472no—
98C2×#106D4711yescharacteristic, complemented
99C47#291211yescharacteristic, complemented, Sylow
100C2×#41—471no—
101#131—478no—
102C2×M16—471no—
103C2×M16—472no—
104C22×C8—472no—
105C22×C8C2×D4711yescharacteristic
106C4×Q8—942no—
107C4×D4—942no—
108C4×D4—944no—
109#117—472no—
110#117—474no—
111C2×C4⋊C4—474no—
112C2×C4⋊C4C2×D4712yes—
113#107—472no—
114#107—474no—
115#106—471no—
116#106—471no—
117#106—474no—
118#106C2×D4712yes—
119#106C2×D4712yes—
120#41—474no—
121#41—474no—
122C2×Q8—471no—
123C2×D4—472no—
124C2×D4—471no—
125C22×C4—22no—
126C22×C4—472no—
127C22×C4—944no—
128C22×C4C22×D4711yescharacteristic
129M16—474no—
130M16—478no—
131C2×C8—472no—
132C2×C8—478no—
133C2×C8C4×D4714yescomplemented
134C2×C8C22×D4711yescharacteristic
135C2×C8C22×D4711yescharacteristic
136C4⋊C4—22no—
137C4⋊C4—472no—
138C4⋊C4—472no—
139C4⋊C4—944no—
140C4⋊C4C22×D4714yes—
141C22⋊C4—944no—
142C22⋊C4—942no—
143C42—944no—
144C42—942no—
145C23—472no—
146C23D4×D4711yescharacteristic
147Q8—474no—
148D4—478no—
149D4—474no—
150C2×C4—24no—
151C2×C4—82no—
152C2×C4—472no—
153C2×C4—474no—
154C2×C4—474no—
155C2×C4—942no—
156C2×C4—942no—
157C2×C4—3764no—
158C2×C4C2×C4×D4712yes—
159C2×C4D4×D4711yescharacteristic
160C2×C4Q8×D4712yes—
161C2×C4C23×D4711yescharacteristic
162C8—474no—
163C8C2×C4×D4712yes—
164C8C2×C4×D4712yes—
165C22—22no—
166C22—474no—
167C22—944no—
168C22C4⋊C4×D4712yes—
169C22C2×D4×D4711yescharacteristic
170C4—44no—
171C4—474no—
172C4—1882no—
173C4—1882no—
174C4C4⋊C4×D4712yes—
175C4C22×C4×D4711yescharacteristic
176C4C2×Q8×D4711yescharacteristic
177C2—22no—
178C2—944no—
179C2C2×C4⋊C4×D4711yescharacteristic
180C2#1568992912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC2×#106×C47C2
socleC22×C47C22×D4
hypercenterC2×#106D47
hypocenterC47#2912
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #15689163C2semidirect
4. #15689162C2semidirect
5. #15689161C2semidirect
6. #15689158C2semidirect
7. #106×D47C2semidirect
8. C2×#106×C47C2semidirect
10. #13094030C4semidirect
38. C2×C8×C47C2×C4semidirect
50. #10625329C2×C4semidirect
52. #10625324C2×C4semidirect
53. C8×D47C2×C4semidirect
98. C2×#106D47semidirect
99. C47#2912semidirect
133. C2×C8C4×D47semidirect