Finite Group Databasebeta

← #20255265

Subgroups — #20255265

Order 6016.

388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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#15689830C211yesmaximal, characteristic
2D4×Dic94C211yesmaximal, characteristic
3#15689474C211yesmaximal, characteristic, complemented
4#15689459C212yesmaximal, complemented
5#15689419C211yesmaximal, characteristic, complemented
6#15689364C212yesmaximal, complemented
7#15689334C211yesmaximal, characteristic, complemented
8#15689281C212yesmaximal, complemented
9C4×Dic188C211yesmaximal, characteristic, complemented
10C2×#13093949C212yesmaximal, complemented
11C8×D4×C47C211yesmaximal, characteristic
12C22×Dic94C2212yes—
13C2×Dic188C2211yescharacteristic
14C2×Dic188C2212yes—
15#13094024C2211yescharacteristic
16#13094024C2211yescharacteristic
17#13094023—21no—
18#13094015—21no—
19#13094003C2212yes—
20#13094003C2212yes—
21#13094001—22no—
22#13094001—22no—
23C4×Dic94C2211yescharacteristic
24C4×Dic94C2211yescharacteristic
25D4×Dic47—21no—
26D4×Dic47—21no—
27C2×C4⋊Dic47C2212yes—
28#13093958C2211yescharacteristic
29#13093958C2212yes—
30#13093949C2212yes—
31#13093949C2212yes—
32#13093949C2211yescharacteristic
33#13093949C2211yescharacteristic
34#13093949C2212yes—
35#13093949C2212yes—
36C22×C8×C47C2212yes—
37C4×D4×C47C2211yescharacteristic
38C4⋊C8×C47C2211yescharacteristic
39C22⋊C8×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×D4×C47D411yescharacteristic
42C22×C4×C47C2312yes—
43C22×Dic47—22no—
44C22×Dic47—22no—
45C2×Dic94—24no—
46C2×Dic94—22no—
47C2×Dic94—21no—
48C2×Dic94—42no—
49C2×Dic94C2312yes—
50C2×Dic94C2311yescharacteristic
51C2×Dic94C2311yescharacteristic
52C2×C8×C47—42no—
53C2×C8×C47C2312yes—
54C2×C8×C47C2311yescharacteristic
55C2×C8×C47C2311yescharacteristic
56C4⋊C4×C47D411yescharacteristic
57C22⋊C4×C47D412yes—
58C42×C47C2311yescharacteristic
59C22⋊Dic47—22no—
60C22⋊Dic47—22no—
61C4⋊Dic47—22no—
62C4⋊Dic47—21no—
63C4⋊Dic47—21no—
64C4⋊Dic47—21no—
65C4⋊Dic47C2311yescharacteristic
66C4⋊Dic47C2312yes—
67C4⋊Dic47C2311yescharacteristic
68Dic47⋊C4—21no—
69Dic47⋊C4—21no—
70Dic47⋊C4—22no—
71Dic47⋊C4—22no—
72C4×Dic47—21no—
73C4×Dic47—21no—
74Dic188—22no—
75Dic188—42no—
76C23×C47C2×D412yes—
77D4×C47Q1614yescomplemented
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2411yescharacteristic
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—44no—
91C2×Dic47—82no—
92Dic94—21no—
93Dic94—21no—
94Dic94—22no—
95Dic94—21no—
96Dic94—22no—
97Dic94—44no—
98Dic94—81no—
99Dic94#4112yes—
100C8×C47—21no—
101C8×C47—22no—
102C8×C47—21no—
103C22×C47—22no—
104C22×C47—22no—
105C22×C47C2×Q1614yes—
106C22×C47C22×D411yescharacteristic
107C4×C47—22no—
108C4×C47—21no—
109C4×C47C2×Q1612yes—
110C4×C47C2×#4111yescharacteristic
111C4×C47H(5,𝔽2)11yescharacteristic
112Dic47—22no—
113Dic47—42no—
114Dic47—41no—
115Dic47—42no—
116Dic47—41no—
117Dic47—41no—
118#3299—471nomaximal, Sylow
119C2×C47—24no—
120C2×C47#54611yescharacteristic
121C2×C47C22×Q1611yescharacteristic
122C2×C47#57711yescharacteristic
123#554—471no—
124D4×Q8—471no—
125#487—471no—
126#484—472no—
127#477—471no—
128#467—472no—
129#462—471no—
130#451—472no—
131C4×Q16—471no—
132C8×D4D4711yescharacteristic
133C2×#103—472no—
134C47#329911yescharacteristic, complemented, Sylow
135C22×Q8—472no—
136C2×Q16—471no—
137C2×Q16—472no—
138C22×C8C2×D4712yes—
139C4⋊Q8—471no—
140C4⋊Q8—471no—
141C4⋊Q8—941no—
142#125—941no—
143C22⋊Q8—472no—
144C22⋊Q8—472no—
145C22⋊Q8—942no—
146C22⋊Q8—942no—
147C4×Q8—471no—
148C4×Q8—471no—
149C4×D4—941no—
150C4×D4—941no—
151C4×D4C2×D4711yescharacteristic
152C2×C4⋊C4—472no—
153#107—471no—
154#107—472no—
155C4⋊C8C2×D4711yescharacteristic
156#103—471no—
157#103—472no—
158#103—472no—
159#103—472no—
160#103—471no—
161#103—472no—
162C22⋊C8C2×D4712yes—
163C4×C8C2×D4711yescharacteristic
164C2×Q8—471no—
165C2×Q8—472no—
166C2×Q8—471no—
167C2×Q8—944no—
168C2×Q8—941no—
169C2×Q8—942no—
170C2×Q8—1882no—
171C2×D4D18811yescharacteristic
172C22×C4—942no—
173C22×C4—942no—
174C22×C4C22×D4712yes—
175Q16—942no—
176Q16—1882no—
177C2×C8—42no—
178C2×C8C22×D4711yescharacteristic
179C2×C8C22×D4711yescharacteristic
180C2×C8C22×D4712yes—
181C4⋊C4—471no—
182C4⋊C4—472no—
183C4⋊C4—471no—
184C4⋊C4—941no—
185C4⋊C4—941no—
186C4⋊C4—942no—
187C4⋊C4—942no—
188C4⋊C4—942no—
189C4⋊C4—941no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4D18811yescharacteristic
193C22⋊C4—942no—
194C22⋊C4—942no—
195C22⋊C4D18812yes—
196C42—941no—
197C42—941no—
198C42C22×D4711yescharacteristic
199C23C2×D18812yes—
200Q8—472no—
201Q8—941no—
202Q8—941no—
203Q8—942no—
204Q8—941no—
205Q8—942no—
206Q8—3761no—
207Q8—1884no—
208D4Dic18814yescomplemented
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—941no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4—941no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—3762no—
218C2×C4—1884no—
219C2×C4C2×D18811yescharacteristic
220C2×C4C2×D18812yes—
221C2×C4C2×D18811yescharacteristic
222C2×C4C23×D4711yescharacteristic
223C8—21no—
224C8—21no—
225C8—22no—
226C22—22no—
227C22—22no—
228C22C2×Dic18814yes—
229C22C22×D18811yescharacteristic
230C4—22no—
231C4—21no—
232C4—942no—
233C4—1882no—
234C4—1881no—
235C4—1881no—
236C4—1882no—
237C4—1881no—
238C4C2×Dic18812yes—
239C4#41×D4711yescharacteristic
240C4#1309406911yescharacteristic
241C2—24no—
242C2#1568976811yescharacteristic
243C2C22×Dic18811yescharacteristic
244C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC8×D4×C47C2
socleC22×C47C22×D4
hypercenterC8×D4D47
hypocenterC47#3299
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
3. #15689474C2semidirect
4. #15689459C2semidirect
5. #15689419C2semidirect
6. #15689364C2semidirect
7. #15689334C2semidirect
8. #15689281C2semidirect
9. C4×Dic188C2semidirect
10. C2×#13093949C2semidirect
77. D4×C47Q16semidirect
134. C47#3299semidirect
208. D4Dic188semidirect