Finite Group Databasebeta

← #20243356

Subgroups — #20243356

Order 6016.

588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13094070C211yesmaximal, characteristic
2#15689141C212yesmaximal, complemented
3#15689127C212yesmaximal, complemented
4#15689107C211yesmaximal, characteristic, complemented
5C47×#410C211yesmaximal, characteristic, complemented
6#13094070—24no—
7#13094070—24no—
8C2×#10625354—21no—
9C2×#10625350C412yescomplemented
10C2×#10625350C2211yescharacteristic
11C22×D188C412yescomplemented
12C22×D188C2211yescharacteristic
13C2×D4×D47—22no—
14C2×D4×D47—21no—
15C2×#10625329C2212yescomplemented
16#13093952—24no—
17#13093944—24no—
18#13093943—21no—
19#13093941—21no—
20C2×#41×C47C2211yescharacteristic
21#117×C47C2212yescomplemented
22#99×C47—22no—
23C23×D47—22no—
24C23×D47—21no—
25#41×C47—22no—
26#41×C47—22no—
27C2×Q8×C47D411yescharacteristic
28C2×D4×C47D412yes—
29C2×D4×C47D411yescharacteristic
30C22×C4×C47C2×C412yes—
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47—22no—
33C2×C22⋊D47—21no—
34#10625354—28no—
35D4×D47—216no—
36D4×D47—28no—
37#10625350—22no—
38#10625350—24no—
39#10625350—24no—
40#10625350D414yes—
41C2×D188—22no—
42C2×D188—21no—
43C2×D188—22no—
44C2×D188—24no—
45C2×D188—24no—
46C2×D188C2×C411yescharacteristic
47C2×D188C2×C412yes—
48C2×D188D414yes—
49C2×C4×D47—22no—
50C2×C4×D47—21no—
51C2×Dic94C2×C411yescharacteristic
52C4⋊C4×C47—22no—
53C22⋊C4×C47—22no—
54C42×C47—22no—
55#10625329—22no—
56#10625329—22no—
57C2×C47⋊C8—22no—
58C23×C47C22⋊C412yes—
59C23×C47C2×D411yescharacteristic
60C22×D47—22no—
61C22×D47—21no—
62C22×D47—28no—
63C22×D47—24no—
64C22×D47—82no—
65C22×D47—84no—
66Q8×C47—22no—
67D4×C47—24no—
68D4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—42no—
72C2×C4×C47C22⋊C412yes—
73C2×C4×C47C22×C411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D412yes—
77C22⋊D47—28no—
78C22⋊D47—24no—
79C2×Dic47—21no—
80D188—28no—
81D188—21no—
82D188—22no—
83D188—24no—
84D188C22⋊C412yes—
85D188C22⋊C414yes—
86C4×D47—28no—
87C4×D47—24no—
88Dic94—21no—
89Dic94C22⋊C412yes—
90C47⋊C8—42no—
91C22×C47—22no—
92C22×C47—41no—
93C22×C47—42no—
94C22×C47C2×C22⋊C411yescharacteristic
95C22×C47#12012yes—
96C2×D47—24no—
97C2×D47—22no—
98C2×D47—44no—
99C2×D47—42no—
100C2×D47—84no—
101C2×D47—88no—
102C4×C47—22no—
103C4×C47—82no—
104C4×C47C2×C22⋊C411yescharacteristic
105C4×C47C2×C22⋊C411yescharacteristic
106C4×C47#12012yes—
107Dic47—22no—
108#1795—471nomaximal, Sylow
109C2×C47—22no—
110C2×C47—21no—
111C2×C47—42no—
112C2×C47#37911yescharacteristic
113D47—44no—
114D47—42no—
115C2×H(5,𝔽2)—471no—
116#421—472no—
117#418—472no—
118#413—471no—
119#410D4711yescharacteristic, complemented
120C47#179511yescharacteristic, complemented, Sylow
121H(5,𝔽2)—944no—
122H(5,𝔽2)—944no—
123C2×#41—472no—
124C2×#41—471no—
125C2×#41—941no—
126C2×#41C2×D4711yescharacteristic
127C22×D4—472no—
128C22×D4—471no—
129C22×D4—941no—
130C22×D4—942no—
131C2×M16—472no—
132#117C2×D4712yescomplemented
133#104—944no—
134#102—944no—
135#101—941no—
136#100—941no—
137#99—22no—
138C24—942no—
139C24—941no—
140#41—22no—
141#41—22no—
142#41—474no—
143#41—944no—
144#41—944no—
145#41—948no—
146#41—942no—
147C2×Q8—471no—
148C2×Q8D18811yescharacteristic
149C2×D4—472no—
150C2×D4—471no—
151C2×D4—474no—
152C2×D4—944no—
153C2×D4—944no—
154C2×D4—9416no—
155C2×D4—948no—
156C2×D4—942no—
157C2×D4—941no—
158C2×D4—942no—
159C2×D4—941no—
160C2×D4—942no—
161C2×D4D18811yescharacteristic
162C2×D4C22⋊D4712yes—
163C22×C4—942no—
164C22×C4—941no—
165C22×C4C4×D4712yes—
166C22×C4C22×D4711yescharacteristic
167M16—942no—
168M16—942no—
169C2×C8—942no—
170C4⋊C4—22no—
171C22⋊C4—22no—
172C42—22no—
173C23—948no—
174C23—944no—
175C23—942no—
176C23—941no—
177C23—3762no—
178C23—3764no—
179C23(C2×D47)⋊C412yes—
180C23C2×C22⋊D4711yescharacteristic
181Q8—22no—
182Q8—472no—
183Q8—941no—
184D4—24no—
185D4—22no—
186D4—474no—
187D4—472no—
188D4—948no—
189D4—948no—
190D4—944no—
191D4—941no—
192D4—942no—
193D4—944no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—948no—
198C2×C4—941no—
199C2×C4—944no—
200C2×C4(C2×D47)⋊C412yes—
201C2×C4C2×C4×D4711yescharacteristic
202C2×C4C2×D18811yescharacteristic
203C2×C4D4×D4712yes—
204C2×C4D4×D4712yes—
205C8—1882no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22—944no—
210C22—942no—
211C22—3764no—
212C22—3768no—
213C22—1884no—
214C22—1882no—
215C22C2×(C2×D47)⋊C411yescharacteristic
216C22#1309399212yes—
217C4—22no—
218C4—82no—
219C4—942no—
220C4C22⋊C4×D4711yescharacteristic
221C4C22⋊C4×D4711yescharacteristic
222C4#1309399412yes—
223C2—22no—
224C2—21no—
225C2—42no—
226C2—1884no—
227C2—1882no—
228C2#1568897811yescharacteristic
subgroupG/H
centerC2#15688978
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#410C2
socleC2×C47#379
hypercenter#410D47
hypocenterC47#1795
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #15689141C2semidirect
3. #15689127C2semidirect
4. #15689107C2semidirect
5. C47×#410C2semidirect
9. C2×#10625350C4semidirect
11. C22×D188C4semidirect
15. C2×#10625329C22semidirect
21. #117×C47C22semidirect
119. #410D47semidirect
120. C47#1795semidirect
132. #117C2×D47semidirect