Finite Group Databasebeta

← #20243731

Subgroups — #20243731

Order 6016.

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

normal subgroups only

This group has 338 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
1C2×Q8×Dic47C211yesmaximal, characteristic
2C2×#13093948C211yesmaximal, characteristic
3C2×#13093948C211yesmaximal, characteristic
4#15689030C211yesmaximal, characteristic
5#15688886C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C22×Q16×C47C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9Q8×Dic47—22no—
10Q8×Dic47—22no—
11C2×C4⋊Dic47—21no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4×Dic47—21no—
15C2×C4×Dic47C2211yescharacteristic
16#13093948—22no—
17#13093948—22no—
18C47⋊#95—21no—
19C47⋊#95—21no—
20C22×Q8×C47C2211yescharacteristic
21C22×Q8×C47C2211yescharacteristic
22C2×Q16×C47—22no—
23C2×Q16×C47—22no—
24C2×Q16×C47C414yescomplemented
25C22×C8×C47C2211yescharacteristic
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47C2×C412yes—
35C2×Q8×C47C2×C412yes—
36C2×Q8×C47D412yes—
37C2×Q8×C47D412yes—
38C22×C4×C47—21no—
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—21no—
42C22×Dic47—21no—
43C22×Dic47D411yescharacteristic
44C22×Dic47D411yescharacteristic
45Q16×C47—28no—
46C2×C8×C47—21no—
47C2×C8×C47—21no—
48C2×C8×C47C2×C412yes—
49C4⋊Dic47—24no—
50C4⋊Dic47—21no—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C4⋊Dic47D412yes—
54C4×Dic47—24no—
55C4×Dic47—21no—
56C4×Dic47—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C2×C47⋊C8—21no—
60C23×C47C2×D411yescharacteristic
61Q8×C47—22no—
62Q8×C47—22no—
63Q8×C47—22no—
64Q8×C47—22no—
65Q8×C47—22no—
66Q8×C47—41no—
67Q8×C47—41no—
68Q8×C47C22⋊C414yes—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47C22×C411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47#4111yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—41no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C2×Dic47—41no—
91C2×Dic47—41no—
92C2×Dic47Q1612yescomplemented
93C8×C47—22no—
94C47⋊C8—41no—
95C22×C47C4×D411yescharacteristic
96C22×C47#12011yescharacteristic
97C22×C47#12111yescharacteristic
98C22×C47C2×Q1611yescharacteristic
99C22×C47#13511yescharacteristic
100C22×C47#13711yescharacteristic
101C22×C47#13711yescharacteristic
102C4×C47—24no—
103C4×C47—42no—
104C4×C47C2×C22⋊C411yescharacteristic
105C4×C47C4×D411yescharacteristic
106C4×C47#12111yescharacteristic
107C4×C47#12311yescharacteristic
108Dic47—22no—
109Dic47—41no—
110Dic47—42no—
111Dic47—81no—
112#1878—471nomaximal, Sylow
113C2×C47#38611yescharacteristic
114C2×C47C4×Q1611yescharacteristic
115C2×C47#44111yescharacteristic
116C2×C47#45111yescharacteristic
117C2×C47#45211yescharacteristic
118C2×C47#46211yescharacteristic
119C2×C47#46411yescharacteristic
120C22×Q16D4711yescharacteristic
121C2×C4×Q8—471no—
122C2×#103—471no—
123C2×#103—471no—
124#391—471no—
125#340—471no—
126#336—471no—
127C47#187811yescharacteristic, complemented, Sylow
128C22×Q8C2×D4711yescharacteristic
129C22×Q8C2×D4711yescharacteristic
130C2×Q16—22no—
131C2×Q16—22no—
132C2×Q16Dic4714yescomplemented
133C22×C8—471no—
134C22×C8C2×D4711yescharacteristic
135C4×Q8—942no—
136C4×Q8—942no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—941no—
140C2×C42—471no—
141C2×C42—941no—
142#103—942no—
143#103—942no—
144#95—941no—
145#95—941no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8C2×Dic4712yes—
155C2×Q8C2×Dic4712yes—
156C2×Q8C22⋊D4712yes—
157C2×Q8C22⋊D4712yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—471no—
161C22×C4—471no—
162C22×C4—941no—
163C22×C4—941no—
164C22×C4C22×D4711yescharacteristic
165Q16—28no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—941no—
169C2×C8—941no—
170C2×C8—941no—
171C2×C8C2×Dic4712yes—
172C4⋊C4—472no—
173C4⋊C4—944no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C4⋊C4—941no—
177C42—944no—
178C42—941no—
179C42—941no—
180C23D4×D4711yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—22no—
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8C22⋊Dic4714yes—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—472no—
196C2×C4—941no—
197C2×C4—941no—
198C2×C4—942no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—1881no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4—1881no—
207C2×C4D4×D4711yescharacteristic
208C2×C4#1062535211yescharacteristic
209C2×C4#1062535211yescharacteristic
210C2×C4C22×Dic4711yescharacteristic
211C2×C4C2×C22⋊D4711yescharacteristic
212C2×C4C2×C22⋊D4711yescharacteristic
213C8—22no—
214C8—1881no—
215C22D4×Dic4711yescharacteristic
216C22#1309399211yescharacteristic
217C22#1309399611yescharacteristic
218C22Q16×D4711yescharacteristic
219C22#1309404711yescharacteristic
220C22#1309405611yescharacteristic
221C22#1309405611yescharacteristic
222C4—24no—
223C4—42no—
224C4—942no—
225C4—3761no—
226C4—1881no—
227C4—1882no—
228C4C2×C22⋊Dic4711yescharacteristic
229C4D4×Dic4711yescharacteristic
230C4#1309399611yescharacteristic
231C4#1309400511yescharacteristic
232C2#1568900311yescharacteristic
233C2Q16×Dic4711yescharacteristic
234C2#1568923011yescharacteristic
235C2#1568927711yescharacteristic
236C2#1568928411yescharacteristic
237C2#1568933111yescharacteristic
238C2#1568934711yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC22×Q16×C47C2
socleC23×C47C2×D4
hypercenterC22×Q16D47
hypocenterC47#1878
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
24. C2×Q16×C47C4semidirect
92. C2×Dic47Q16semidirect
127. C47#1878semidirect
132. C2×Q16Dic47semidirect