Finite Group Databasebeta

← #20243772

Subgroups — #20243772

Order 6016.

332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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#15689890C211yesmaximal, characteristic, complemented
2#15689140C212yesmaximal, complemented
3#15689097C211yesmaximal, characteristic, complemented
4#15688883C212yesmaximal, complemented
5C47×#532C211yesmaximal, characteristic
6#13094031—24no—
7C2×#10625329—22no—
8C2×#10625329C2212yes—
9#13093983C2212yes—
10#13093951—24no—
11#13093939—22no—
12C2×#41×C47C2211yescharacteristic
13C2×#41×C47C2211yescharacteristic
14C4⋊Q8×C47C411yescharacteristic, complemented
15#127×C47C411yescharacteristic, complemented
16#124×C47C411yescharacteristic, complemented
17#124×C47C411yescharacteristic, complemented
18#121×C47—22no—
19C4×D4×C47—22no—
20C2×C42×C47C2211yescharacteristic
21#41×C47—22no—
22#41×C47—22no—
23#41×C47—22no—
24#41×C47—22no—
25C2×Q8×C47C2×C411yescharacteristic
26C2×Q8×C47C2×C411yescharacteristic
27C2×D4×C47—22no—
28C2×D4×C47—21no—
29C2×D4×C47C2×C411yescharacteristic
30C2×D4×C47C2×C411yescharacteristic
31C2×D4×C47D412yes—
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47D412yes—
35C22×C4×C47C2311yescharacteristic
36C4⋊C4×C47—22no—
37C22⋊C4×C47—22no—
38C22⋊C4×C47—22no—
39C42×C47—21no—
40C42×C47C2×C411yescharacteristic
41C42×C47C2×C411yescharacteristic
42C22⋊Dic47—22no—
43C4⋊Dic47—22no—
44C4×Dic47—22no—
45#10625329—24no—
46#10625329—22no—
47#10625329D414yescomplemented
48C2×C47⋊C8—24no—
49C2×C47⋊C8—22no—
50C23×C47—21no—
51C23×C47C22⋊C412yes—
52C23×C47C2×D411yescharacteristic
53Q8×C47—22no—
54Q8×C47—22no—
55D4×C47—24no—
56D4×C47—22no—
57D4×C47—22no—
58D4×C47—44no—
59D4×C47—42no—
60C2×C4×C47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—42no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47C22⋊C412yes—
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47#4112yes—
73C2×Dic47—42no—
74C47⋊C8—24no—
75C22×C47—22no—
76C22×C47—41no—
77C22×C47—42no—
78C22×C47—42no—
79C22×C47—41no—
80C22×C47C2×C22⋊C411yescharacteristic
81C22×C47#12112yes—
82C4×C47—22no—
83C4×C47—22no—
84C4×C47—41no—
85C4×C47—41no—
86C4×C47C4×D412yes—
87C4×C47#12011yescharacteristic
88C4×C47#12311yescharacteristic
89Dic47—82no—
90#1884—471nomaximal, Sylow
91C2×C47—22no—
92C2×C47—21no—
93C2×C47—42no—
94C2×C47—81no—
95C2×C47#38611yescharacteristic
96#568—471no—
97#532D4711yescharacteristic
98#421—472no—
99#410—471no—
100#339—472no—
101C47#188411yescharacteristic, complemented, Sylow
102C2×#41C2×D4711yescharacteristic
103C2×#41C2×D4711yescharacteristic
104#131—944no—
105C2×M16—472no—
106C2×M16—942no—
107C4⋊Q8Dic4711yescharacteristic, complemented
108#127Dic4711yescharacteristic, complemented
109#124Dic4711yescharacteristic, complemented
110#124Dic4711yescharacteristic, complemented
111#121—22no—
112C4×D4—22no—
113#117—472no—
114C2×C42C2×D4711yescharacteristic
115#104—944no—
116#99—942no—
117#41—22no—
118#41—22no—
119#41—22no—
120#41—22no—
121C2×Q8C2×Dic4711yescharacteristic
122C2×Q8C2×Dic4711yescharacteristic
123C2×D4—22no—
124C2×D4—21no—
125C2×D4C2×Dic4711yescharacteristic
126C2×D4C2×Dic4711yescharacteristic
127C2×D4C22⋊D4712yes—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4C22⋊D4712yes—
131C22×C4C22×D4711yescharacteristic
132M16—474no—
133M16—944no—
134M16—942no—
135C2×C8—944no—
136C2×C8—942no—
137C4⋊C4—22no—
138C4⋊C4—942no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—942no—
142C42—21no—
143C42—942no—
144C42C2×Dic4711yescharacteristic
145C42C2×Dic4711yescharacteristic
146C23—21no—
147C23C22⋊Dic4712yes—
148C23C2×C22⋊D4711yescharacteristic
149Q8—22no—
150Q8—22no—
151D4—24no—
152D4—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—1882no—
165C2×C4C22⋊Dic4712yes—
166C2×C4D4×D4712yes—
167C2×C4#1062535212yes—
168C2×C4C22×Dic4711yescharacteristic
169C2×C4C2×C22⋊D4711yescharacteristic
170C8—944no—
171C22—22no—
172C22—41no—
173C22—42no—
174C22—42no—
175C22—41no—
176C22C2×C22⋊Dic4711yescharacteristic
177C22#1309399612yes—
178C4—22no—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—3762no—
183C4D4×Dic4712yes—
184C4#1309399211yescharacteristic
185C4#1309400511yescharacteristic
186C2—21no—
187C2—22no—
188C2—42no—
189C2—81no—
190C2#1568900311yescharacteristic
subgroupG/H
centerC4#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#532C2
socleC2×C47#386
hypercenter#532D47
hypocenterC47#1884
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #15689890C2semidirect
2. #15689140C2semidirect
3. #15689097C2semidirect
4. #15688883C2semidirect
14. C4⋊Q8×C47C4semidirect
15. #127×C47C4semidirect
16. #124×C47C4semidirect
17. #124×C47C4semidirect
47. #10625329D4semidirect
101. C47#1884semidirect
107. C4⋊Q8Dic47semidirect
108. #127Dic47semidirect
109. #124Dic47semidirect
110. #124Dic47semidirect