Finite Group Databasebeta

← #20243759

Subgroups — #20243759

Order 6016.

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

normal subgroups only

This group has 334 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
1#15689606C211yesmaximal, characteristic
2C2×#13093951C211yesmaximal, characteristic
3#15689132C211yesmaximal, characteristic, complemented
4#15689030C211yesmaximal, characteristic, complemented
5#15688891C211yesmaximal, characteristic, complemented
6#15688884C211yesmaximal, characteristic, complemented
7C2×#137×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9Q8×Dic47—21no—
10D4×Dic47—21no—
11D4×Dic47—22no—
12#13093983—21no—
13#13093983C2211yescharacteristic
14C2×C4⋊Dic47—21no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4×Dic47C2211yescharacteristic
17#13093951—22no—
18#13093948—21no—
19#13093948—21no—
20C47⋊#95—22no—
21C2×#41×C47C2211yescharacteristic
22C22×Q8×C47C2211yescharacteristic
23#137×C47—22no—
24#137×C47C414yescomplemented
25C2×Q16×C47—21no—
26C2×SD16×C47—21no—
27C2×M16×C47C2211yescharacteristic
28#41×C47—21no—
29#41×C47—21no—
30#41×C47C2×C412yes—
31#41×C47D412yes—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47—21no—
36C2×Q8×C47—21no—
37C2×Q8×C47C2×C412yescomplemented
38C2×Q8×C47D411yescharacteristic
39C2×D4×C47—21no—
40C2×D4×C47D411yescharacteristic
41C22×C4×C47—21no—
42C22×C4×C47—21no—
43C22×C4×C47C2311yescharacteristic
44C22×Dic47—21no—
45C22×Dic47—22no—
46C22×Dic47D412yes—
47Q16×C47—24no—
48SD16×C47—24no—
49M16×C47—21no—
50M16×C47C2×C412yescomplemented
51C2×C8×C47—21no—
52C22⋊Dic47—22no—
53C22⋊Dic47—21no—
54C4⋊Dic47—22no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47D411yescharacteristic
58C4⋊Dic47D411yescharacteristic
59C4×Dic47—22no—
60C4×Dic47—21no—
61C4×Dic47—21no—
62C4×Dic47—21no—
63#10625329—21no—
64#10625329—21no—
65C2×C47⋊C8—21no—
66C23×C47—21no—
67C23×C47C2×D411yescharacteristic
68Q8×C47—21no—
69Q8×C47—22no—
70Q8×C47—22no—
71Q8×C47—41no—
72Q8×C47—41no—
73Q8×C47C22⋊C412yes—
74D4×C47—22no—
75D4×C47—22no—
76D4×C47—21no—
77D4×C47C22⋊C412yes—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47C22×C411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C2×C4×C47#4111yescharacteristic
90C2×Dic47—22no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—21no—
94C2×Dic47—41no—
95C2×Dic47—41no—
96C2×Dic47—42no—
97C2×Dic47—82no—
98C8×C47—22no—
99C47⋊C8—41no—
100C22×C47—21no—
101C22×C47—21no—
102C22×C47—22no—
103C22×C47—41no—
104C22×C47—41no—
105C22×C47C4×D411yescharacteristic
106C22×C47#12011yescharacteristic
107C22×C47#12111yescharacteristic
108C4×C47—22no—
109C4×C47—42no—
110C4×C47C2×C22⋊C411yescharacteristic
111C4×C47C4×D411yescharacteristic
112C4×C47#12111yescharacteristic
113C4×C47#12311yescharacteristic
114Dic47—42no—
115Dic47—42no—
116Dic47—41no—
117Dic47—41no—
118#1882—471nomaximal, Sylow
119C2×C47—21no—
120C2×C47—21no—
121C2×C47—42no—
122C2×C47#38611yescharacteristic
123C2×C47#45511yescharacteristic
124C2×C47#45611yescharacteristic
125C2×#137D4711yescharacteristic
126#520—471no—
127C2×#104—471no—
128#419—471no—
129#391—471no—
130#343—471no—
131#339—471no—
132C47#188211yescharacteristic, complemented, Sylow
133C2×#41C2×D4711yescharacteristic
134C22×Q8C2×D4711yescharacteristic
135#137—22no—
136#137Dic4714yescomplemented
137C2×Q16—21no—
138C2×SD16—21no—
139C2×M16—471no—
140C2×M16C2×D4711yescharacteristic
141C4×Q8—941no—
142C4×D4—942no—
143C4×D4—941no—
144#117—471no—
145#117—941no—
146C2×C4⋊C4—471no—
147C2×C4⋊C4—941no—
148C2×C42—471no—
149#104—942no—
150#103—941no—
151#103—941no—
152#95—942no—
153#41—21no—
154#41—21no—
155#41C2×Dic4712yes—
156#41C22⋊D4712yes—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8C2×Dic4712yescomplemented
163C2×Q8C22⋊D4711yescharacteristic
164C2×D4—21no—
165C2×D4C22⋊D4711yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—472no—
169C22×C4—942no—
170C22×C4—941no—
171C22×C4C22×D4711yescharacteristic
172Q16—24no—
173SD16—24no—
174M16—21no—
175M16—941no—
176M16—941no—
177M16C2×Dic4712yescomplemented
178C2×C8—21no—
179C2×C8—941no—
180C4⋊C4—471no—
181C4⋊C4—471no—
182C4⋊C4—942no—
183C4⋊C4—941no—
184C4⋊C4—941no—
185C22⋊C4—942no—
186C22⋊C4—941no—
187C42—942no—
188C42—941no—
189C42—941no—
190C42—941no—
191C23—21no—
192C23D4×D4711yescharacteristic
193Q8—21no—
194Q8—22no—
195Q8—22no—
196Q8—41no—
197Q8—41no—
198Q8C22⋊Dic4712yes—
199D4—22no—
200D4—22no—
201D4—21no—
202D4C22⋊Dic4712yes—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—942no—
210C2×C4—941no—
211C2×C4—941no—
212C2×C4—942no—
213C2×C4—3762no—
214C2×C4—1881no—
215C2×C4—1881no—
216C2×C4—1882no—
217C2×C4D4×D4711yescharacteristic
218C2×C4#1062535211yescharacteristic
219C2×C4#1062535211yescharacteristic
220C2×C4C22×Dic4711yescharacteristic
221C2×C4C2×C22⋊D4711yescharacteristic
222C2×C4C2×C22⋊D4711yescharacteristic
223C8—22no—
224C8—1881no—
225C22—21no—
226C22—21no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22D4×Dic4711yescharacteristic
231C22#1309399211yescharacteristic
232C22#1309399611yescharacteristic
233C4—22no—
234C4—42no—
235C4—1882no—
236C4—1881no—
237C4—1882no—
238C4—1881no—
239C4C2×C22⋊Dic4711yescharacteristic
240C4D4×Dic4711yescharacteristic
241C4#1309399611yescharacteristic
242C4#1309400511yescharacteristic
243C2—21no—
244C2—21no—
245C2—42no—
246C2#1568900311yescharacteristic
247C2#1568929911yescharacteristic
248C2#1568930411yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#137×C47C2
socleC22×C47#120
hypercenterC2×#137D47
hypocenterC47#1882
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
3. #15689132C2semidirect
4. #15689030C2semidirect
5. #15688891C2semidirect
6. #15688884C2semidirect
24. #137×C47C4semidirect
37. C2×Q8×C47C2×C4semidirect
50. M16×C47C2×C4semidirect
132. C47#1882semidirect
136. #137Dic47semidirect
162. C2×Q8C2×Dic47semidirect
177. M16C2×Dic47semidirect