Finite Group Databasebeta

← #20253358

Subgroups — #20253358

Order 6016.

386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689694C211yesmaximal, characteristic
2#15689606C211yesmaximal, characteristic
3#15689465C212yesmaximal, complemented
4#15689465C212yesmaximal, complemented
5#15689459C212yesmaximal, complemented
6#15689454C212yesmaximal, complemented
7#15689165C211yesmaximal, characteristic, complemented
8#15689161C211yesmaximal, characteristic, complemented
9#15689133C211yesmaximal, characteristic, complemented
10C2×#13093949C211yesmaximal, characteristic, complemented
11C47×#408C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13#13094022—21no—
14#13094011—21no—
15#13094005—22no—
16#13094003C2212yes—
17#13094003C2212yes—
18Q8×Dic47—21no—
19D4×Dic47—22no—
20D4×Dic47—21no—
21#13093983C2211yescharacteristic
22#13093983C2212yes—
23#13093983C2211yescharacteristic
24C2×C4⋊Dic47C2211yescharacteristic
25C2×C4⋊Dic47C2212yes—
26#13093958C2211yescharacteristic
27#13093958C2211yescharacteristic
28#13093958C2212yes—
29#13093956C2211yescharacteristic
30#13093956C2211yescharacteristic
31#13093956C2212yes—
32#13093949C2212yes—
33#13093949C2212yes—
34#13093949C2212yes—
35#13093949C2212yes—
36C2×#41×C47C2211yescharacteristic
37C2×M16×C47C2211yescharacteristic
38C22×C8×C47C2211yescharacteristic
39C22⋊C8×C47C2212yes—
40C22⋊C8×C47C2212yes—
41#41×C47—22no—
42#41×C47—22no—
43C2×Q8×C47D411yescharacteristic
44C2×D4×C47D412yes—
45C2×D4×C47D411yescharacteristic
46C22×C4×C47C2312yes—
47C22×C4×C47C2311yescharacteristic
48C22×Dic47—21no—
49C22×Dic47—22no—
50C22×Dic47—21no—
51C2×Dic94—22no—
52C2×Dic94—22no—
53C2×Dic94—21no—
54C2×Dic94C2312yes—
55M16×C47—22no—
56C2×C8×C47—22no—
57C2×C8×C47C2311yescharacteristic
58C2×C8×C47C2311yescharacteristic
59C2×C8×C47C2312yes—
60C22⋊Dic47—22no—
61C22⋊Dic47—21no—
62C22⋊Dic47—21no—
63C22⋊Dic47—22no—
64C22⋊Dic47—22no—
65C4⋊Dic47—22no—
66C4⋊Dic47—21no—
67C4⋊Dic47C2312yes—
68C4⋊Dic47C2311yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70C4⋊Dic47C2311yescharacteristic
71C4⋊Dic47C2311yescharacteristic
72Dic47⋊C4—22no—
73Dic47⋊C4—22no—
74C4×Dic47—22no—
75C4×Dic47—21no—
76C4×Dic47—21no—
77C23×C47C2×D412yes—
78C23×C47C2×D411yescharacteristic
79Q8×C47—22no—
80D4×C47—24no—
81D4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47C2×D412yes—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47#4112yes—
87C2×C4×C47#4112yes—
88C2×C4×C47C2411yescharacteristic
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—22no—
93C2×Dic47—21no—
94C2×Dic47—22no—
95C2×Dic47—42no—
96C2×Dic47—81no—
97C2×Dic47—82no—
98Dic94—22no—
99Dic94—22no—
100Dic94—42no—
101C8×C47—21no—
102C8×C47—21no—
103C8×C47—22no—
104C22×C47—21no—
105C22×C47—21no—
106C22×C47—22no—
107C22×C47—22no—
108C22×C47—22no—
109C22×C47#12312yes—
110C22×C47C22×D411yescharacteristic
111C4×C47—22no—
112C4×C47#12312yes—
113C4×C47C2×#4111yescharacteristic
114C4×C47C2×#4111yescharacteristic
115Dic47—42no—
116Dic47—41no—
117Dic47—42no—
118Dic47—41no—
119Dic47—41no—
120Dic47—41no—
121#3097—471nomaximal, Sylow
122C2×C47—22no—
123C2×C47—42no—
124C2×C47C2×#12311yescharacteristic
125C2×C47#57711yescharacteristic
126C2×C47#57811yescharacteristic
127#536—471no—
128#520—471no—
129#485—472no—
130#485—472no—
131#484—472no—
132#483—472no—
133#428—471no—
134#427—471no—
135#419—471no—
136C2×#103—471no—
137#408D4711yescharacteristic
138C47#309711yescharacteristic, complemented, Sylow
139C2×#41C2×D4711yescharacteristic
140C22×Q8—471no—
141C2×M16C2×D4711yescharacteristic
142C22×C8C2×D4711yescharacteristic
143C4⋊Q8—941no—
144#124—941no—
145#123—942no—
146C22⋊Q8—472no—
147C22⋊Q8—472no—
148C4×Q8—941no—
149C4×D4—942no—
150C4×D4—941no—
151#117—471no—
152#117—472no—
153#117—471no—
154C2×C4⋊C4—471no—
155C2×C4⋊C4—472no—
156#107—471no—
157#107—471no—
158#107—472no—
159#106—471no—
160#106—471no—
161#106—472no—
162#103—472no—
163#103—472no—
164#103—472no—
165#103—472no—
166C22⋊C8C2×D4712yes—
167C22⋊C8C2×D4712yes—
168#41—22no—
169#41—22no—
170C2×Q8—472no—
171C2×Q8—941no—
172C2×Q8—942no—
173C2×Q8—942no—
174C2×Q8D18811yescharacteristic
175C2×D4D18812yes—
176C2×D4D18811yescharacteristic
177C22×C4—942no—
178C22×C4—941no—
179C22×C4—941no—
180C22×C4C22×D4712yes—
181C22×C4C22×D4711yescharacteristic
182M16—22no—
183C2×C8—22no—
184C2×C8C22×D4711yescharacteristic
185C2×C8C22×D4712yes—
186C2×C8C22×D4711yescharacteristic
187C4⋊C4—472no—
188C4⋊C4—471no—
189C4⋊C4—471no—
190C4⋊C4—471no—
191C4⋊C4—471no—
192C4⋊C4—942no—
193C4⋊C4—942no—
194C4⋊C4—942no—
195C4⋊C4—941no—
196C22⋊C4—942no—
197C22⋊C4—941no—
198C22⋊C4—941no—
199C22⋊C4—942no—
200C22⋊C4—942no—
201C42—942no—
202C42—941no—
203C42—941no—
204C23C2×D18812yes—
205C23C2×D18811yescharacteristic
206Q8—22no—
207Q8—942no—
208Q8—942no—
209Q8—1882no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—941no—
217C2×C4—942no—
218C2×C4—941no—
219C2×C4—942no—
220C2×C4—3761no—
221C2×C4—3762no—
222C2×C4—1882no—
223C2×C4C2×D18812yes—
224C2×C4C2×D18811yescharacteristic
225C2×C4#1062535212yes—
226C2×C4#1062535212yes—
227C2×C4C23×D4711yescharacteristic
228C8—21no—
229C8—21no—
230C8—22no—
231C22—21no—
232C22—21no—
233C22—22no—
234C22—22no—
235C22—22no—
236C22#1309400812yes—
237C22C22×D18811yescharacteristic
238C4—22no—
239C4—1882no—
240C4—1882no—
241C4—1881no—
242C4—1881no—
243C4—1881no—
244C4—1881no—
245C4#1309400812yes—
246C4C2×#1062535211yescharacteristic
247C4C2×#1062535211yescharacteristic
248C2—22no—
249C2—42no—
250C2C2×#1309400811yescharacteristic
251C2#1568993511yescharacteristic
252C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#408C2
socleC22×C47C22×D4
hypercenter#408D47
hypocenterC47#3097
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
3. #15689465C2semidirect
4. #15689465C2semidirect
5. #15689459C2semidirect
6. #15689454C2semidirect
7. #15689165C2semidirect
8. #15689161C2semidirect
9. #15689133C2semidirect
10. C2×#13093949C2semidirect
138. C47#3097semidirect