Finite Group Databasebeta

← #20254697

Subgroups — #20254697

Order 6016.

436 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689674C211yesmaximal, characteristic, complemented
2#15689670C211yesmaximal, characteristic, complemented
3#15689402C212yesmaximal, complemented
4#15689400C211yesmaximal, characteristic, complemented
5#15689360C212yesmaximal, complemented
6#15689358C212yesmaximal, complemented
7#15689319C211yesmaximal, characteristic, complemented
8#15689318C211yesmaximal, characteristic, complemented
9#15689317C212yesmaximal, complemented
10C4⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#474C211yesmaximal, characteristic, complemented
12C2×#10625354—21no—
13C2×#10625350—21no—
14C2×D376C2212yes—
15C2×#10625334C2212yes—
16C2×C8×D47C2212yes—
17#13094023C2211yescharacteristic
18#13094021C2211yescharacteristic
19#13094020C2211yescharacteristic
20#13094013—21no—
21#13094010—21no—
22#13093999—21no—
23#13093999C2212yes—
24#13093999C2211yescharacteristic
25#13093997—21no—
26#13093995C2211yescharacteristic
27C4×D188C2211yescharacteristic
28#13093986—21no—
29#13093986C2212yes—
30C4×C22⋊D47—21no—
31C42×D47C2211yescharacteristic
32#13093957C2212yes—
33C4⋊(C47⋊C8)C2211yescharacteristic
34Dic47⋊C8C2212yes—
35#13093946C2212yes—
36#13093944C2212yes—
37#13093944C2212yes—
38C4⋊Q8×C47C2211yescharacteristic
39C4×D4×C47C2211yescharacteristic
40#107×C47C2212yes—
41C4⋊C8×C47C2211yescharacteristic
42#102×C47C2212yes—
43C2×Q8×C47—21no—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C2×C22⋊D47—21no—
47C2×C22⋊D47—21no—
48C2×C22⋊D47—21no—
49#10625354—44no—
50#10625350—44no—
51C2×D188—21no—
52C2×D188—22no—
53C2×D188—21no—
54C2×D188—21no—
55C2×D188C2311yescharacteristic
56C2×D188C2312yes—
57C2×C4×D47—21no—
58C2×C4×D47—22no—
59C2×C4×D47D411yescharacteristic
60C2×C4×D47D411yescharacteristic
61C2×C4×D47C2311yescharacteristic
62C2×Dic94—21no—
63C2×C8×C47C2312yes—
64C4⋊C4×C47—21no—
65C4⋊C4×C47C2311yescharacteristic
66C4⋊C4×C47C2312yes—
67C22⋊C4×C47—21no—
68C42×C47C2311yescharacteristic
69C22⋊Dic47—21no—
70#10625334—42no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—21no—
73(C2×D47)⋊C4—22no—
74(C2×D47)⋊C4—22no—
75C4⋊Dic47C2311yescharacteristic
76Dic47⋊C4—21no—
77C4×Dic47D411yescharacteristic
78C4×Dic47D411yescharacteristic
79C4×Dic47C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81D376—42no—
82C8×D47—42no—
83C23×C47—21no—
84C22×D47—22no—
85C22×D47—21no—
86C22×D47C2×D411yescharacteristic
87Q8×C47—42no—
88D4×C47—21no—
89D4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—22no—
92C2×C4×C47—42no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2411yescharacteristic
96C22⋊D47—42no—
97C22⋊D47—42no—
98C22⋊D47—42no—
99C2×Dic47—21no—
100C2×Dic47C2×D411yescharacteristic
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103D188—21no—
104D188—22no—
105D188—21no—
106D188—22no—
107D188—42no—
108D188—42no—
109D188—44no—
110D188—42no—
111C4×D47—21no—
112C4×D47—21no—
113C4×D47—41no—
114C4×D47—42no—
115C4×D47—44no—
116C4×D47D814yescomplemented
117Dic94—42no—
118C8×C47—22no—
119C47⋊C8—22no—
120C22×C47—41no—
121C22×C47—41no—
122C22×C47—41no—
123C22×C47C22×D411yescharacteristic
124C2×D47—21no—
125C2×D47—21no—
126C2×D47—41no—
127C2×D47—42no—
128C2×D47—42no—
129C2×D47—41no—
130C2×D47—42no—
131C2×D47—41no—
132C2×D47C2×D812yes—
133C4×C47—21no—
134C4×C47—41no—
135C4×C47—42no—
136C4×C47C2×D812yes—
137C4×C47H(5,𝔽2)11yescharacteristic
138C4×C472−1+411yescharacteristic
139Dic47—21no—
140Dic47—21no—
141Dic47—41no—
142Dic47C2×D812yes—
143#3245—471nomaximal, Sylow
144C2×C47—81no—
145C2×C47#53711yescharacteristic
146C2×C47C22×D811yescharacteristic
147C2×C47#57511yescharacteristic
148D47—22no—
149D47—82no—
150D47—81no—
151#532—471no—
152#532—471no—
153#474—471no—
154#474—472no—
155#474D4711yescharacteristic, complemented
156#466—472no—
157#466—472no—
158#459—471no—
159#459—471no—
160#459—472no—
161C2×C4⋊C8—471no—
162C47#324511yescharacteristic, complemented, Sylow
163C2×#41—941no—
164C2×#41—941no—
165C2×D8—472no—
166C2×D8—472no—
167C22×C8—472no—
168C4⋊Q8—471no—
169C4⋊Q8C2×D4711yescharacteristic
170#127—471no—
171#127—471no—
172#124—941no—
173#124—941no—
174#121—471no—
175#121—471no—
176#121—472no—
177#121—941no—
178#121—941no—
179C4×D4—472no—
180C4×D4—471no—
181C4×D4—941no—
182C4×D4—941no—
183C4×D4C2×D4711yescharacteristic
184C2×C42—471no—
185#107—472no—
186#107C2×D4712yes—
187C4⋊C8—472no—
188C4⋊C8—471no—
189C4⋊C8C2×D4711yescharacteristic
190#102—472no—
191#102—472no—
192#102—472no—
193#102C2×D4712yes—
194#41—1884no—
195#41—1884no—
196C2×Q8—21no—
197C2×Q8—941no—
198C2×D4—471no—
199C2×D4—472no—
200C2×D4—941no—
201C2×D4—942no—
202C2×D4—941no—
203C2×D4—941no—
204C2×D4—941no—
205C2×D4—941no—
206C2×D4—941no—
207C2×D4C22×D4711yescharacteristic
208C22×C4—21no—
209C22×C4—471no—
210C22×C4—471no—
211C22×C4—471no—
212C22×C4—942no—
213C22×C4—941no—
214D8—1882no—
215D8—1882no—
216C2×C8—472no—
217C2×C8—1882no—
218C2×C8C22×D4712yes—
219C4⋊C4—21no—
220C4⋊C4—471no—
221C4⋊C4—941no—
222C4⋊C4C22×D4711yescharacteristic
223C4⋊C4C22×D4712yes—
224C22⋊C4—21no—
225C22⋊C4—942no—
226C22⋊C4—941no—
227C22⋊C4—942no—
228C22⋊C4—941no—
229C22⋊C4—941no—
230C42—471no—
231C42—471no—
232C42—471no—
233C42C22×D4711yescharacteristic
234C23—21no—
235C23—471no—
236C23—942no—
237C23—941no—
238Q8—42no—
239Q8—1882no—
240D4—21no—
241D4—21no—
242D4—941no—
243D4—942no—
244D4—941no—
245D4—942no—
246D4—1882no—
247D4—1882no—
248D4—1884no—
249D4—1882no—
250D4—1882no—
251D4—1882no—
252D4—1882no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—471no—
257C2×C4—474no—
258C2×C4—471no—
259C2×C4—471no—
260C2×C4—941no—
261C2×C4—941no—
262C2×C4—941no—
263C2×C4—1881no—
264C2×C4—1884no—
265C2×C4—1882no—
266C2×C4D4×D4711yescharacteristic
267C2×C4D4×D4711yescharacteristic
268C2×C4C23×D4711yescharacteristic
269C8—22no—
270C8—942no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—472no—
275C22—941no—
276C22—941no—
277C22—1882no—
278C22—1881no—
279C22—1882no—
280C22—1881no—
281C22—1881no—
282C22—1882no—
283C22C2×D4×D4711yescharacteristic
284C4—21no—
285C4—41no—
286C4—42no—
287C4—472no—
288C4—941no—
289C4—941no—
290C4—1881no—
291C4D8×D4712yes—
292C4#1309407011yescharacteristic
293C4#1309407211yescharacteristic
294C2—81no—
295C2—942no—
296C2—3762no—
297C2—3761no—
298C2#1568970311yescharacteristic
299C2C2×D8×D4711yescharacteristic
300C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#474C2
socleC22×C47C22×D4
hypercenter#474D47
hypocenterC47#3245
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #15689674C2semidirect
2. #15689670C2semidirect
3. #15689402C2semidirect
4. #15689400C2semidirect
5. #15689360C2semidirect
6. #15689358C2semidirect
7. #15689319C2semidirect
8. #15689318C2semidirect
9. #15689317C2semidirect
10. C4⋊C8×D47C2semidirect
11. C47×#474C2semidirect
116. C4×D47D8semidirect
155. #474D47semidirect
162. C47#3245semidirect