Finite Group Databasebeta

← #20244677

Subgroups — #20244677

Order 6016.

282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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×#13093959C211yesmaximal, characteristic, complemented
2#15689124C211yesmaximal, characteristic, complemented
3C2×#13093945C211yesmaximal, characteristic, complemented
4C2×#13093941C211yesmaximal, characteristic, complemented
5#15689090C211yesmaximal, characteristic, complemented
6#15688891C211yesmaximal, characteristic, complemented
7C2×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12#13093959—22no—
13#13093948—21no—
14#13093945—21no—
15#13093945—22no—
16#13093941—22no—
17C22⋊(C47⋊C8)—22no—
18C2×#41×C47C2211yescharacteristic
19C22×D4×C47C2211yescharacteristic
20AGL(1,ℤ/8)×C47—22no—
21AGL(1,ℤ/8)×C47—22no—
22C2×SD16×C47—21no—
23C2×D8×C47—21no—
24C2×M16×C47C2211yescharacteristic
25C24×C47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30C2×Q8×C47D411yescharacteristic
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47—21no—
36C2×D4×C47—21no—
37C2×D4×C47D411yescharacteristic
38C2×D4×C47D412yes—
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41C22×Dic47—21no—
42SD16×C47—24no—
43D8×C47—24no—
44M16×C47—21no—
45M16×C47D412yes—
46C2×C8×C47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49#10625329—21no—
50#10625329—21no—
51#10625329—21no—
52#10625329—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8D412yes—
58C23×C47—21no—
59C23×C47—22no—
60C23×C47—41no—
61C23×C47—41no—
62C23×C47—81no—
63C23×C47—81no—
64C23×C47#4111yescharacteristic
65Q8×C47—21no—
66Q8×C47—21no—
67D4×C47—21no—
68D4×C47—22no—
69D4×C47—22no—
70D4×C47—21no—
71D4×C47—41no—
72D4×C47—41no—
73D4×C47—41no—
74D4×C47—41no—
75C2×C4×C47—21no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C2×C4×C47#4111yescharacteristic
84C2×Dic47—41no—
85C2×Dic47—81no—
86C8×C47—22no—
87C47⋊C8—22no—
88C47⋊C8—41no—
89C47⋊C8—41no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47—41no—
93C22×C47—42no—
94C22×C47—41no—
95C22×C47—41no—
96C22×C47—82no—
97C22×C47—82no—
98C22×C47—81no—
99C22×C47—81no—
100C22×C47#12111yescharacteristic
101C22×C47#12311yescharacteristic
102C22×C47#12411yescharacteristic
103C4×C47—41no—
104C4×C47#12011yescharacteristic
105C4×C47#12111yescharacteristic
106C4×C47#12111yescharacteristic
107C4×C47#12311yescharacteristic
108Dic47—81no—
109#2051—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—81no—
113C2×C47—82no—
114C2×C47#39411yescharacteristic
115C2×C47#47111yescharacteristic
116C2×C47#47211yescharacteristic
117C2×AGL(1,ℤ/8)D4711yescharacteristic
118C2×#108—471no—
119#417—471no—
120C2×#102—471no—
121C2×#100—471no—
122#408—471no—
123#343—471no—
124C47#205111yescharacteristic, complemented, Sylow
125C2×#41C2×D4711yescharacteristic
126C22×D4C2×D4711yescharacteristic
127AGL(1,ℤ/8)—22no—
128AGL(1,ℤ/8)—22no—
129C2×SD16—21no—
130C2×D8—21no—
131C2×M16—471no—
132C2×M16—471no—
133C2×M16C2×D4711yescharacteristic
134C22×C8—471no—
135C2×C4⋊C4—471no—
136#108—942no—
137#103—941no—
138#102—942no—
139#102—941no—
140#100—942no—
141C22⋊C8—942no—
142C24—21no—
143#41—21no—
144#41—21no—
145#41—21no—
146#41—21no—
147C2×Q8C22⋊D4711yescharacteristic
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4C22⋊D4712yes—
155C2×D4C22⋊D4711yescharacteristic
156C22×C4—21no—
157C22×C4—941no—
158C22×C4C22×D4711yescharacteristic
159SD16—24no—
160D8—24no—
161M16—21no—
162M16—941no—
163M16—941no—
164M16—941no—
165M16—941no—
166M16C22⋊D4712yes—
167C2×C8—21no—
168C2×C8—472no—
169C2×C8—941no—
170C2×C8—941no—
171C2×C8—941no—
172C2×C8—941no—
173C4⋊C4—941no—
174C4⋊C4—941no—
175C23—21no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—81no—
180C23—81no—
181C23#1062535211yescharacteristic
182Q8—21no—
183Q8—21no—
184D4—21no—
185D4—22no—
186D4—22no—
187D4—21no—
188D4—41no—
189D4—41no—
190D4—41no—
191D4—41no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—3761no—
196C2×C4—1881no—
197C2×C4D4×D4711yescharacteristic
198C2×C4#1062535211yescharacteristic
199C2×C4#1062535211yescharacteristic
200C2×C4C2×C22⋊D4711yescharacteristic
201C2×C4C2×C22⋊D4711yescharacteristic
202C2×C4C2×C22⋊D4711yescharacteristic
203C8—22no—
204C8—942no—
205C8—1881no—
206C8—1881no—
207C22—21no—
208C22—21no—
209C22—41no—
210C22—42no—
211C22—41no—
212C22—41no—
213C22—82no—
214C22—82no—
215C22—81no—
216C22—81no—
217C22#1309399611yescharacteristic
218C22#1309400511yescharacteristic
219C22#1309401111yescharacteristic
220C4—41no—
221C4—3761no—
222C4#1309399311yescharacteristic
223C4#1309399511yescharacteristic
224C4#1309399611yescharacteristic
225C4#1309400511yescharacteristic
226C2—21no—
227C2—21no—
228C2—81no—
229C2—82no—
230C2#1568903711yescharacteristic
231C2#1568938411yescharacteristic
232C2#1568939111yescharacteristic
subgroupG/H
centerC22#13093996
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×AGL(1,ℤ/8)×C47C2
socleC22×C47#121
hypercenterC2×AGL(1,ℤ/8)D47
hypocenterC47#2051
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#13093959C2semidirect
2. #15689124C2semidirect
3. C2×#13093945C2semidirect
4. C2×#13093941C2semidirect
5. #15689090C2semidirect
6. #15688891C2semidirect
124. C47#2051semidirect