Finite Group Databasebeta

← #20256399

Subgroups — #20256399

Order 6016.

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

normal subgroups only

This group has 384 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
1#15689859C211yesmaximal, characteristic, complemented
2#15689858C211yesmaximal, characteristic, complemented
3#15689504C212yesmaximal, complemented
4#15689499C211yesmaximal, characteristic
5#15689340C212yesmaximal, complemented
6#15689337C212yesmaximal, complemented
7#15689324C211yesmaximal, characteristic, complemented
8#15689247C211yesmaximal, characteristic, complemented
9C4×#10625337C211yesmaximal, characteristic, complemented
10#15689203C212yesmaximal, complemented
11C47×#460C211yesmaximal, characteristic, complemented
12C2×#10625337C2211yescharacteristic
13C2×#10625325C2212yes—
14C2×#10625334C2212yes—
15C2×#10625334C2212yes—
16#13094021C2211yescharacteristic
17#13094013C2212yes—
18#13094012—21no—
19#13094011—21no—
20#13094011C2212yes—
21#13094009—22no—
22#13094005—22no—
23C4×Dic94C2211yescharacteristic
24C4×Dic94C2211yescharacteristic
25C4×D188—21no—
26D4×Dic47—21no—
27D4×Dic47C2212yes—
28#13093986C2212yes—
29#13093957C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093948C2211yescharacteristic
32#13093947C2211yescharacteristic
33#13093946C2212yes—
34C4×C47⋊C8C2211yescharacteristic
35C8×Dic47C2212yes—
36C2×SD16×C47C2212yes—
37#127×C47C2211yescharacteristic
38C4×Q8×C47C2211yescharacteristic
39C4⋊C8×C47C2211yescharacteristic
40#102×C47C2212yes—
41C2×Q8×C47C2311yescharacteristic
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47C2312yes—
45C22×Dic47—22no—
46C2×D188—21no—
47C2×D188—21no—
48C2×D188C2312yes—
49C2×C4×D47—22no—
50C2×Dic94D411yescharacteristic
51C2×Dic94C2311yescharacteristic
52SD16×C47—42no—
53C2×C8×C47C2312yes—
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2311yescharacteristic
56C42×C47—21no—
57C42×C47C2311yescharacteristic
58C22⋊Dic47—22no—
59C22⋊Dic47—22no—
60C22⋊Dic47—22no—
61#10625337—22no—
62#10625334—24no—
63#10625334—42no—
64(C2×D47)⋊C4—22no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—22no—
67C4⋊Dic47D411yescharacteristic
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—21no—
70Dic47⋊C4D412yes—
71C4×Dic47—21no—
72C4×Dic47C2312yes—
73C2×C47⋊C8C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75#10625325—42no—
76C23×C47—22no—
77C22×D47—22no—
78Q8×C47—21no—
79Q8×C47—21no—
80D4×C47—22no—
81D4×C47—22no—
82D4×C47—42no—
83D4×C47—81no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2411yescharacteristic
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—82no—
92C2×Dic47C2×D412yes—
93C2×Dic47C2×D412yes—
94D188—22no—
95D188—22no—
96D188—42no—
97D188—81no—
98C4×D47—82no—
99Dic94—22no—
100Dic94—21no—
101Dic94—21no—
102C8×C47—22no—
103C47⋊C8—21no—
104C47⋊C8#4112yes—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47—42no—
108C22×C47C22×D411yescharacteristic
109C2×D47—42no—
110C2×D47—42no—
111C2×D47—42no—
112C4×C47—21no—
113C4×C47—41no—
114C4×C47—41no—
115C4×C47#13512yes—
116C4×C47C2×#4111yescharacteristic
117C4×C47H(5,𝔽2)11yescharacteristic
118Dic47—22no—
119Dic47—22no—
120Dic47—41no—
121Dic47—41no—
122#3396—471nomaximal, Sylow
123C2×C47—82no—
124C2×C47#55011yescharacteristic
125C2×C47C2×#13511yescharacteristic
126C2×C47#57611yescharacteristic
127D47—82no—
128#559—471no—
129#559—471no—
130#495—472no—
131#493—471no—
132#463—472no—
133#463—472no—
134#460—471no—
135#460D4711yescharacteristic, complemented
136C8×Q8—471no—
137C4×Q16—471no—
138C4×D8—472no—
139C47#339611yescharacteristic, complemented, Sylow
140C2×Q16—471no—
141C2×SD16—472no—
142C2×SD16C2×D4712yes—
143C2×D8—472no—
144C2×D8—472no—
145#127—471no—
146#127C2×D4711yescharacteristic
147#124—472no—
148#124—472no—
149#124—941no—
150#124—941no—
151#123—942no—
152#123—942no—
153C4×Q8—471no—
154C4×Q8—471no—
155C4×Q8C2×D4711yescharacteristic
156C4×D4—472no—
157C4×D4—472no—
158C4×D4—941no—
159C4×D4—941no—
160#107—471no—
161C4⋊C8—472no—
162C4⋊C8C2×D4711yescharacteristic
163#103—471no—
164#103—471no—
165#102—472no—
166#102C2×D4712yes—
167C4×C8—472no—
168C4×C8—471no—
169C2×Q8—471no—
170C2×Q8—471no—
171C2×Q8C22×D4711yescharacteristic
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—472no—
175C2×D4—941no—
176C2×D4—941no—
177C2×D4C22×D4712yes—
178C22×C4—942no—
179C22×C4—942no—
180Q16—942no—
181SD16—42no—
182SD16—1882no—
183D8—944no—
184D8—1882no—
185C2×C8—471no—
186C2×C8—471no—
187C2×C8C22×D4712yes—
188C4⋊C4—21no—
189C4⋊C4—472no—
190C4⋊C4—471no—
191C4⋊C4—471no—
192C4⋊C4—941no—
193C4⋊C4C22×D4711yescharacteristic
194C22⋊C4—942no—
195C22⋊C4—942no—
196C22⋊C4—942no—
197C22⋊C4—942no—
198C22⋊C4—942no—
199C22⋊C4—942no—
200C42—21no—
201C42—472no—
202C42—941no—
203C42C22×D4711yescharacteristic
204C23—22no—
205C23—942no—
206Q8—21no—
207Q8—21no—
208Q8—942no—
209Q8—941no—
210Q8—941no—
211D4—22no—
212D4—22no—
213D4—42no—
214D4—81no—
215D4—942no—
216D4—942no—
217D4—3761no—
218D4—1882no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—472no—
222C2×C4—472no—
223C2×C4—941no—
224C2×C4—941no—
225C2×C4—3762no—
226C2×C4—3762no—
227C2×C4D4×D4711yescharacteristic
228C2×C4D4×D4711yescharacteristic
229C2×C4C23×D4711yescharacteristic
230C8—22no—
231C8—472no—
232C8—941no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—1882no—
237C22—1882no—
238C22—1882no—
239C22C2×D4×D4711yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—942no—
244C4—942no—
245C4—1881no—
246C4—1881no—
247C4#1309404512yes—
248C4#41×D4711yescharacteristic
249C4#1309406911yescharacteristic
250C2—82no—
251C2—3762no—
252C2#1568979111yescharacteristic
253C2C2×#1309404511yescharacteristic
254C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3396
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #15689859C2semidirect
2. #15689858C2semidirect
3. #15689504C2semidirect
5. #15689340C2semidirect
6. #15689337C2semidirect
7. #15689324C2semidirect
8. #15689247C2semidirect
9. C4×#10625337C2semidirect
10. #15689203C2semidirect
11. C47×#460C2semidirect
135. #460D47semidirect
139. C47#3396semidirect