Finite Group Databasebeta

← #20253632

Subgroups — #20253632

Order 6016.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689728C211yesmaximal, characteristic, complemented
2#15689597C211yesmaximal, characteristic, complemented
3#15689448C212yesmaximal, complemented
4#15689424C212yesmaximal, complemented
5#15689319C212yesmaximal, complemented
6#15689259C212yesmaximal, complemented
7#15689236C212yesmaximal, complemented
8C4×D376C212yesmaximal, complemented
9C47×#433C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C2×D376C2212yes—
12C2×D376C2212yes—
13#13094021C2211yescharacteristic, complemented
14#13094016C2211yescharacteristic, complemented
15#13094009—22no—
16#13093998C2212yes—
17#13093997—22no—
18C4×D188C2212yes—
19C4×D188C2212yes—
20C4×D188C2212yescomplemented
21#13093986—22no—
22#13093983C2211yescharacteristic
23C22⋊C4×D47—22no—
24#13093958C2212yescomplemented
25#13093956C2212yescomplemented
26#13093946C2212yes—
27#13093946C2212yes—
28#13093946C2212yescomplemented
29#13093946C2212yescomplemented
30#117×C47C2211yescharacteristic
31C4⋊C8×C47C2212yescomplemented
32C22⋊C8×C47C2212yes—
33#97×C47C2211yescharacteristic, complemented
34C4×C8×C47C2211yescharacteristic, complemented
35C23×D47—21no—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—22no—
38C2×D188—21no—
39C2×D188—24no—
40C2×D188—22no—
41C2×D188C2312yes—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×C4×D47—22no—
45C2×C4×D47—22no—
46C2×C8×C47C2312yes—
47C2×C8×C47C2312yes—
48C4⋊C4×C47D412yes—
49C22⋊C4×C47D412yes—
50C42×C47C2311yescharacteristic
51C42×C47C2311yescharacteristic
52C22⋊Dic47—21no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57C4⋊Dic47C2312yes—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60C4×Dic47—21no—
61D376—24no—
62D376—24no—
63C23×C47C2×D411yescharacteristic
64C22×D47—22no—
65C22×D47—24no—
66C22×D47—22no—
67C22×D47—82no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D412yes—
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2411yescharacteristic
73C22⋊D47—82no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76D188—24no—
77D188—22no—
78D188—22no—
79D188—22no—
80D188—82no—
81D188#4114yes—
82C4×D47—82no—
83C4×D47—82no—
84C4×D47—82no—
85C8×C47—22no—
86C8×C47—22no—
87C22×C47—21no—
88C22×C47—22no—
89C22×C47C22×D411yescharacteristic
90C2×D47—24no—
91C2×D47—42no—
92C2×D47—42no—
93C2×D47—42no—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—84no—
97C4×C47—21no—
98C4×C47—22no—
99C4×C47—22no—
100C4×C47C2×#4112yes—
101Dic47—42no—
102Dic47—42no—
103#3122—471nomaximal, Sylow
104C2×C47—41no—
105C2×C47#52511yescharacteristic
106C2×C47#57612yes—
107D47—44no—
108D47—82no—
109#540—471no—
110#518—471no—
111#482—472no—
112#478—472no—
113#459—472no—
114#447—472no—
115#442—472no—
116C4×D8—472no—
117#433D4711yescharacteristic, complemented
118C47#312211yescharacteristic, complemented, Sylow
119C22×D4—471no—
120C2×D8—472no—
121C2×D8—472no—
122#127—471no—
123#125—471no—
124#123—942no—
125#121—472no—
126#121—942no—
127C4×D4—472no—
128C4×D4—472no—
129C4×D4—472no—
130C4×D4—942no—
131#117—471no—
132#117C2×D4711yescharacteristic
133C2×C22⋊C4—942no—
134#107—472no—
135#106—472no—
136C4⋊C8C2×D4712yescomplemented
137#102—472no—
138#102—472no—
139#102—472no—
140#102—472no—
141C22⋊C8C2×D4712yes—
142#97C2×D4711yescharacteristic, complemented
143C4×C8C2×D4711yescharacteristic, complemented
144C24—941no—
145C2×D4—472no—
146C2×D4—472no—
147C2×D4—944no—
148C2×D4—942no—
149C2×D4—941no—
150C2×D4—942no—
151C22×C4—942no—
152C22×C4—942no—
153C22×C4—942no—
154C22×C4C22×D4711yescharacteristic
155D8—944no—
156D8—944no—
157C2×C8C22×D4712yes—
158C2×C8C22×D4712yes—
159C4⋊C4—472no—
160C4⋊C4—472no—
161C4⋊C4—942no—
162C4⋊C4D18812yes—
163C22⋊C4—941no—
164C22⋊C4—942no—
165C22⋊C4—942no—
166C22⋊C4—942no—
167C22⋊C4—942no—
168C22⋊C4D18812yes—
169C42—941no—
170C42C22×D4711yescharacteristic
171C42C22×D4711yescharacteristic
172C23—944no—
173C23—942no—
174C23—942no—
175C23—3762no—
176C23C2×D18811yescharacteristic
177D4—474no—
178D4—944no—
179D4—942no—
180D4—942no—
181D4—942no—
182D4—3762no—
183D4—3762no—
184C2×C4—22no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—3762no—
188C2×C4—3762no—
189C2×C4—3762no—
190C2×C4C2×D18811yescharacteristic
191C2×C4C2×D18812yes—
192C2×C4C2×D18812yes—
193C2×C4C23×D4711yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—944no—
199C22—3764no—
200C22—1882no—
201C22—1882no—
202C22—1882no—
203C22—1882no—
204C22—1882no—
205C22C22×D18811yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—1882no—
210C4—1882no—
211C4#41×D4712yes—
212C2—41no—
213C2—3762no—
214C2—1884no—
215C2#1568963511yescharacteristic
216C2#1568992812yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#433C2
socleC22×C47C22×D4
hypercenter#433D47
hypocenterC47#3122
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #15689728C2semidirect
2. #15689597C2semidirect
3. #15689448C2semidirect
4. #15689424C2semidirect
5. #15689319C2semidirect
6. #15689259C2semidirect
7. #15689236C2semidirect
8. C4×D376C2semidirect
9. C47×#433C2semidirect
13. #13094021C22semidirect
14. #13094016C22semidirect
20. C4×D188C22semidirect
24. #13093958C22semidirect
25. #13093956C22semidirect
28. #13093946C22semidirect
29. #13093946C22semidirect
31. C4⋊C8×C47C22semidirect
33. #97×C47C22semidirect
34. C4×C8×C47C22semidirect
117. #433D47semidirect
118. C47#3122semidirect
136. C4⋊C8C2×D47semidirect
142. #97C2×D47semidirect
143. C4×C8C2×D47semidirect