Finite Group Databasebeta

← #20243874

Subgroups — #20243874

Order 6016.

346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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×#13094052C211yesmaximal, characteristic
2#15689597C211yesmaximal, characteristic, complemented
3#15689139C211yesmaximal, characteristic, complemented
4#15689129C211yesmaximal, characteristic, complemented
5#15689096C211yesmaximal, characteristic, complemented
6#15688880C211yesmaximal, characteristic, complemented
7C47×#344C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C22×D188C2211yescharacteristic
10#13094052—22no—
11#13094052—22no—
12C2×#10625325C412yescomplemented
13C2×D376C412yescomplemented
14C4×D188—22no—
15#13093986—22no—
16#13093983C2211yescharacteristic
17#13093983C2211yescharacteristic
18C22⋊C4×D47—22no—
19#13093950—22no—
20#13093946—22no—
21#13093938—22no—
22C2×M16×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24#117×C47C2211yescharacteristic
25C23×D47—21no—
26C22×C4×C47C2311yescharacteristic
27C2×C22⋊D47—21no—
28#10625350—21no—
29#10625350—21no—
30#10625350—21no—
31#10625350—21no—
32C2×D188—21no—
33C2×D188—21no—
34C2×D188—21no—
35C2×D188C2×C412yes—
36C2×D188C2×C411yescharacteristic, complemented
37C2×D188D412yes—
38C2×D188D412yes—
39C2×C4×D47—21no—
40C2×C4×D47—24no—
41C2×Dic94C2×C411yescharacteristic, complemented
42M16×C47—21no—
43M16×C47—21no—
44M16×C47—21no—
45M16×C47—21no—
46C2×C8×C47—21no—
47C2×C8×C47C2×C412yescomplemented
48C4⋊C4×C47—21no—
49C22⋊C4×C47D412yes—
50C42×C47—21no—
51C22⋊Dic47—21no—
52C22⋊Dic47—21no—
53(C2×D47)⋊C4—24no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4×Dic47—21no—
57C4×Dic47D412yes—
58D376—24no—
59#10625325—24no—
60C23×C47C2×D411yescharacteristic
61C22×D47—22no—
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—21no—
65C22×D47—82no—
66C2×C4×C47—22no—
67C2×C4×C47C22×C411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×C4×C47#4111yescharacteristic
73C22⋊D47—41no—
74C22⋊D47—41no—
75C2×Dic47—21no—
76C2×Dic47—22no—
77C2×Dic47—41no—
78D188—21no—
79D188—22no—
80D188—21no—
81D188—22no—
82D188—22no—
83D188C22⋊C414yes—
84C4×D47—41no—
85C4×D47—41no—
86C4×D47—84no—
87Dic94—21no—
88Dic94—21no—
89C8×C47—22no—
90C8×C47—41no—
91C22×C47—41no—
92C22×C47C4×D411yescharacteristic
93C22×C47#12011yescharacteristic
94C22×C47#12111yescharacteristic
95C2×D47—24no—
96C2×D47—44no—
97C2×D47—41no—
98C2×D47—82no—
99C2×D47—82no—
100C2×D47—81no—
101C4×C47—42no—
102C4×C47C2×C22⋊C411yescharacteristic
103C4×C47C4×D411yescharacteristic
104C4×C47#12111yescharacteristic
105C4×C47#12311yescharacteristic
106Dic47—42no—
107Dic47—41no—
108Dic47—81no—
109#1904—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—21no—
113C2×C47#38611yescharacteristic
114D47—44no—
115D47—81no—
116C2×AGL(1,ℤ/8)—471no—
117#518—471no—
118#421—471no—
119#418—471no—
120#410—471no—
121#344D4711yescharacteristic, complemented
122H(3,ℤ/4)—471no—
123C47#190411yescharacteristic, complemented, Sylow
124C2×#41—471no—
125C22×D4—471no—
126AGL(1,ℤ/8)—942no—
127AGL(1,ℤ/8)—942no—
128C2×SD16—472no—
129C2×D8—472no—
130C2×M16C2×D4711yescharacteristic
131C2×M16C2×D4711yescharacteristic
132C4×D4—942no—
133C4×D4—942no—
134#117—471no—
135#117—471no—
136#117C2×D4711yescharacteristic
137C2×C22⋊C4—942no—
138#104—942no—
139#102—942no—
140#99—942no—
141C24—941no—
142#41—941no—
143#41—941no—
144#41—941no—
145#41—941no—
146C2×Q8—471no—
147C2×D4—472no—
148C2×D4—471no—
149C2×D4—472no—
150C2×D4—472no—
151C2×D4—941no—
152C2×D4—941no—
153C2×D4—941no—
154C2×D4—941no—
155C22×C4—944no—
156C22×C4—941no—
157C22×C4C22×D4711yescharacteristic
158SD16—944no—
159D8—944no—
160M16—21no—
161M16—21no—
162M16—21no—
163M16—21no—
164C2×C8—21no—
165C2×C8C4×D4712yescomplemented
166C4⋊C4—21no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C22⋊C4—944no—
170C22⋊C4—941no—
171C22⋊C4—941no—
172C22⋊C4D18812yes—
173C42—21no—
174C42—472no—
175C42—941no—
176C23—942no—
177C23—942no—
178C23—942no—
179C23—941no—
180C23—3762no—
181C23C2×D18811yescharacteristic
182Q8—941no—
183Q8—941no—
184D4—474no—
185D4—941no—
186D4—942no—
187D4—941no—
188D4—942no—
189D4—942no—
190D4—1881no—
191D4—1881no—
192C2×C4—22no—
193C2×C4—941no—
194C2×C4—942no—
195C2×C4—3764no—
196C2×C4—1881no—
197C2×C4—1881no—
198C2×C4—1881no—
199C2×C4C2×C4×D4711yescharacteristic
200C2×C4#1062535011yescharacteristic
201C2×C4D4×D4711yescharacteristic
202C2×C4D4×D4711yescharacteristic
203C2×C4D4×D4711yescharacteristic
204C2×C4#1062535411yescharacteristic
205C8—22no—
206C8—41no—
207C22—41no—
208C22—944no—
209C22—3761no—
210C22—3762no—
211C22—3762no—
212C22—1884no—
213C22—1881no—
214C22C4×D18811yescharacteristic
215C22#1309399411yescharacteristic
216C22#1309399911yescharacteristic
217C4—42no—
218C4—3761no—
219C4—1882no—
220C4—1881no—
221C4C22⋊C4×D4711yescharacteristic
222C4#1309398611yescharacteristic
223C4#1309399711yescharacteristic
224C4#1309400911yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—3761no—
229C2—1884no—
230C2#1568900111yescharacteristic
subgroupG/H
centerC2#15689001
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#344C2
socleC2×C47#386
hypercenter#344D47
hypocenterC47#1904
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #15689597C2semidirect
3. #15689139C2semidirect
4. #15689129C2semidirect
5. #15689096C2semidirect
6. #15688880C2semidirect
7. C47×#344C2semidirect
12. C2×#10625325C4semidirect
13. C2×D376C4semidirect
36. C2×D188C2×C4semidirect
41. C2×Dic94C2×C4semidirect
47. C2×C8×C47C2×C4semidirect
121. #344D47semidirect
123. C47#1904semidirect
165. C2×C8C4×D47semidirect