Finite Group Databasebeta

← #20256000

Subgroups — #20256000

Order 6016.

342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689847C211yesmaximal, characteristic
2#15689833C211yesmaximal, characteristic
3#15689519C211yesmaximal, characteristic, complemented
4#15689463C212yesmaximal, complemented
5#15689455C212yesmaximal, complemented
6#15689419C211yesmaximal, characteristic, complemented
7#15689380C212yesmaximal, complemented
8C4×#10625337C211yesmaximal, characteristic, complemented
9#15689200C211yesmaximal, characteristic
10#15689162C212yesmaximal, complemented
11C47×#475C211yesmaximal, characteristic, complemented
12C2×#10625337C2211yescharacteristic
13C2×#10625324C2212yes—
14#13094024C2211yescharacteristic
15#13094019—22no—
16#13094016—21no—
17#13094013—21no—
18#13094004C2212yes—
19#13094002—22no—
20#13094000C2212yes—
21Q8×Dic47—21no—
22C4×Dic94C2211yescharacteristic
23C4×D188—21no—
24C4×D188C2211yescharacteristic
25#13093982C2212yes—
26C4⋊C4×D47C2212yes—
27#13093958C2212yes—
28#13093957C2211yescharacteristic
29#13093955C2212yes—
30#13093955C2212yes—
31#13093949C2212yes—
32#13093948C2211yescharacteristic
33#13093947C2211yescharacteristic
34(C2×D47)⋊C8C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×D188D411yescharacteristic
44C2×C4×D47—22no—
45C2×C4×D47C2312yes—
46C2×Dic94—21no—
47C2×Dic94C2311yescharacteristic
48C2×C8×C47C2312yes—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C4⋊C4×C47C2312yes—
52C4⋊C4×C47C2311yescharacteristic
53C42×C47—21no—
54C42×C47C2311yescharacteristic
55#10625337—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4D412yes—
60C4⋊Dic47—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47D411yescharacteristic
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2312yes—
65Dic47⋊C4—21no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68C4×Dic47—21no—
69C4×Dic47—22no—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72#10625324—24no—
73C22×D47C2×D412yes—
74Q8×C47—21no—
75Q8×C47—21no—
76Q8×C47—42no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47C2×D412yes—
87D188—22no—
88C4×D47—22no—
89C4×D47—22no—
90C4×D47—82no—
91Dic94—21no—
92Dic94—21no—
93Dic94—81no—
94C8×C47—22no—
95C47⋊C8—21no—
96C47⋊C8#4112yes—
97C22×C47C22×D411yescharacteristic
98C2×D47—22no—
99C2×D47—22no—
100C2×D47—22no—
101C4×C47—21no—
102C4×C47—41no—
103C4×C47—42no—
104C4×C47—41no—
105C4×C47#13712yes—
106C4×C47C2×#4111yescharacteristic
107C4×C472−1+411yescharacteristic
108Dic47—22no—
109Dic47—41no—
110Dic47—42no—
111Dic47—41no—
112#3356—471nomaximal, Sylow
113C2×C47#54711yescharacteristic
114C2×C47C2×#13711yescharacteristic
115C2×C47#57711yescharacteristic
116D47—42no—
117#556—471no—
118#554—471no—
119#498—471no—
120#485—472no—
121#483—472no—
122#477—471no—
123#475D4711yescharacteristic, complemented
124#470—472no—
125C4×Q16—471no—
126#436—471no—
127#428—472no—
128C47#335611yescharacteristic, complemented, Sylow
129C2×Q16—471no—
130C2×M16—472no—
131C4⋊Q8—471no—
132C4⋊Q8C2×D4711yescharacteristic
133#126—942no—
134#125—941no—
135#124—941no—
136C22⋊Q8—472no—
137C22⋊Q8—472no—
138C22⋊Q8—942no—
139C4×Q8—471no—
140C4×Q8—941no—
141C4×Q8C2×D4711yescharacteristic
142C4×D4—471no—
143C4×D4—941no—
144#117—472no—
145C2×C4⋊C4—472no—
146#107—472no—
147#107—471no—
148#106—472no—
149#106—472no—
150#106C2×D4712yes—
151C4⋊C8C2×D4711yescharacteristic
152#103—471no—
153#103—472no—
154#103—471no—
155#103C2×D4712yes—
156C22⋊C8—472no—
157C4×C8—471no—
158C2×Q8—21no—
159C2×Q8—471no—
160C2×Q8—941no—
161C2×Q8C22×D4711yescharacteristic
162C2×D4—471no—
163C22×C4—472no—
164C22×C4—942no—
165Q16—942no—
166M16—944no—
167C2×C8—471no—
168C2×C8—471no—
169C2×C8C22×D4712yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—471no—
173C4⋊C4—472no—
174C4⋊C4—471no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—941no—
179C4⋊C4—941no—
180C4⋊C4C22×D4711yescharacteristic
181C4⋊C4C22×D4712yes—
182C22⋊C4—472no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C42—21no—
187C42—942no—
188C42—941no—
189C42C22×D4711yescharacteristic
190C23—472no—
191Q8—21no—
192Q8—21no—
193Q8—42no—
194Q8—941no—
195Q8—941no—
196Q8—3761no—
197D4—942no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—472no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—941no—
205C2×C4—941no—
206C2×C4—942no—
207C2×C4—3762no—
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—22no—
212C8—472no—
213C8—941no—
214C22—942no—
215C22—942no—
216C22—942no—
217C22C2×D4×D4711yescharacteristic
218C4—21no—
219C4—41no—
220C4—42no—
221C4—41no—
222C4—942no—
223C4—1881no—
224C4—1882no—
225C4—1881no—
226C4#1309405312yes—
227C4#41×D4711yescharacteristic
228C4#1309407211yescharacteristic
229C2—1882no—
230C2#1568977511yescharacteristic
231C2C2×#1309405311yescharacteristic
232C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3356
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #15689519C2semidirect
4. #15689463C2semidirect
5. #15689455C2semidirect
6. #15689419C2semidirect
7. #15689380C2semidirect
8. C4×#10625337C2semidirect
10. #15689162C2semidirect
11. C47×#475C2semidirect
123. #475D47semidirect
128. C47#3356semidirect