Finite Group Databasebeta

← #20244597

Subgroups — #20244597

Order 6016.

326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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#15689687C211yesmaximal, characteristic
2#15689165C211yesmaximal, characteristic, complemented
3#15689124C211yesmaximal, characteristic, complemented
4C2×#13093940C211yesmaximal, characteristic, complemented
5#15689025C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10#13094020—21no—
11#13094013—21no—
12#13093998—21no—
13#13093998—21no—
14#13093992—22no—
15#13093983C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×(C2×D47)⋊C4—22no—
18#13093958—21no—
19#13093956—21no—
20#13093948—21no—
21#13093945—21no—
22#13093940—22no—
23C2×#41×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25C2×C42×C47C2211yescharacteristic
26#104×C47—22no—
27C23×D47D412yes—
28#41×C47—21no—
29#41×C47—21no—
30#41×C47—21no—
31#41×C47—21no—
32C2×Q8×C47D411yescharacteristic
33C2×D4×C47—21no—
34C2×D4×C47D411yescharacteristic
35C22×C4×C47—21no—
36C22×C4×C47—21no—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—22no—
39C2×C22⋊D47—22no—
40C22×Dic47—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188—21no—
47M16×C47—21no—
48M16×C47D412yescomplemented
49C2×C8×C47—21no—
50C42×C47—21no—
51C42×C47—21no—
52C22⋊Dic47—21no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—44no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47D411yescharacteristic
59C4⋊Dic47D411yescharacteristic
60C4×Dic47—21no—
61#10625329—21no—
62#10625329—21no—
63C2×C47⋊C8—21no—
64C23×C47—21no—
65C23×C47C2×D411yescharacteristic
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—22no—
69C22×D47—42no—
70C22×D47—42no—
71Q8×C47—21no—
72Q8×C47—21no—
73D4×C47—21no—
74D4×C47—21no—
75D4×C47—41no—
76D4×C47—41no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47#4111yescharacteristic
87C2×C4×C47#4111yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C22⋊D47—82no—
90C22⋊D47—82no—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—42no—
94C2×Dic47—41no—
95D188—41no—
96D188—41no—
97D188—41no—
98D188—41no—
99C8×C47—22no—
100C47⋊C8—41no—
101C22×C47—21no—
102C22×C47—21no—
103C22×C47—41no—
104C22×C47—41no—
105C22×C47—41no—
106C22×C47#12011yescharacteristic
107C22×C47#12111yescharacteristic
108C22×C47#12311yescharacteristic
109C2×D47—44no—
110C2×D47—42no—
111C2×D47—42no—
112C2×D47—42no—
113C2×D47—82no—
114C4×C47—42no—
115C4×C47—41no—
116C4×C47#12111yescharacteristic
117C4×C47#12111yescharacteristic
118C4×C47#12311yescharacteristic
119C4×C47#12411yescharacteristic
120Dic47—41no—
121Dic47—41no—
122Dic47—81no—
123#2037—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47—81no—
127C2×C47#39411yescharacteristic
128C2×C47#45311yescharacteristic
129C2×C47#45511yescharacteristic
130D47—82no—
131#535—471no—
132#428—471no—
133C2×#104D4711yescharacteristic, complemented
134#417—471no—
135C2×#100—471no—
136#390—471no—
137#339—471no—
138C47#203711yescharacteristic, complemented, Sylow
139C2×#41C2×D4711yescharacteristic
140C22×D4—471no—
141C2×M16—471no—
142C2×M16C2×D4711yescharacteristic
143#127—941no—
144#124—941no—
145#121—941no—
146#121—941no—
147#120—942no—
148#117—471no—
149C2×C4⋊C4—471no—
150C2×C22⋊C4—942no—
151C2×C42C2×D4711yescharacteristic
152#107—941no—
153#106—941no—
154#104—22no—
155#103—941no—
156#102—941no—
157#100—942no—
158C24—472no—
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163C2×Q8D18811yescharacteristic
164C2×D4—21no—
165C2×D4—942no—
166C2×D4—942no—
167C2×D4—941no—
168C2×D4—941no—
169C2×D4—941no—
170C2×D4—941no—
171C2×D4—941no—
172C2×D4—941no—
173C2×D4D18811yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178M16—21no—
179M16—941no—
180M16—941no—
181M16C22⋊D4712yescomplemented
182C2×C8—21no—
183C2×C8—941no—
184C4⋊C4—471no—
185C4⋊C4—471no—
186C4⋊C4—941no—
187C4⋊C4—941no—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—941no—
191C22⋊C4—1884no—
192C42—21no—
193C42—21no—
194C42—941no—
195C23—21no—
196C23—942no—
197C23—942no—
198C23—942no—
199C23—1882no—
200C23—1882no—
201C23D4×D4711yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—3762no—
209D4—3762no—
210D4—1881no—
211D4—1881no—
212D4—1881no—
213D4—1881no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—941no—
221C2×C4—941no—
222C2×C4—1882no—
223C2×C4—1881no—
224C2×C4C2×D18811yescharacteristic
225C2×C4#1062535011yescharacteristic
226C2×C4D4×D4711yescharacteristic
227C2×C4#1062535211yescharacteristic
228C2×C4#1062535211yescharacteristic
229C2×C4C2×C22⋊D4711yescharacteristic
230C8—22no—
231C8—1881no—
232C22—21no—
233C22—21no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—3762no—
238C22—1884no—
239C22—1882no—
240C22—1882no—
241C22—1882no—
242C22#1309399411yescharacteristic
243C22#1309399511yescharacteristic
244C22#1309400611yescharacteristic
245C4—42no—
246C4—41no—
247C4—3761no—
248C4—1881no—
249C4—1881no—
250C4#1309399611yescharacteristic
251C4#1309399811yescharacteristic
252C4#1309400811yescharacteristic
253C4#1309401011yescharacteristic
254C2—21no—
255C2—21no—
256C2—81no—
257C2—3762no—
258C2#1568903911yescharacteristic
259C2#1568929211yescharacteristic
260C2#1568930211yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC22×C47#120
hypercenterC2×#104D47
hypocenterC47#2037
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #15689165C2semidirect
3. #15689124C2semidirect
4. C2×#13093940C2semidirect
5. #15689025C2semidirect
6. #15688883C2semidirect
7. C2×#104×C47C2semidirect
48. M16×C47D4semidirect
133. C2×#104D47semidirect
138. C47#2037semidirect
181. M16C22⋊D47semidirect