Finite Group Databasebeta

← #20254025

Subgroups — #20254025

Order 6016.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689745C211yesmaximal, characteristic, complemented
2#15689738C211yesmaximal, characteristic, complemented
3#15689527C211yesmaximal, characteristic, complemented
4#15689504C211yesmaximal, characteristic, complemented
5#15689484C211yesmaximal, characteristic, complemented
6#15689481C211yesmaximal, characteristic, complemented
7#15689370C211yesmaximal, characteristic, complemented
8#15689366C211yesmaximal, characteristic, complemented
9#15689363C211yesmaximal, characteristic, complemented
10#15689358C211yesmaximal, characteristic
11#15689225C211yesmaximal, characteristic, complemented
12C4×#10625337C211yesmaximal, characteristic, complemented
13C4×#10625334C211yesmaximal, characteristic, complemented
14#15689080C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×#10625337C2211yescharacteristic
17C2×#10625325C2211yescharacteristic
18C2×#10625334C2211yescharacteristic
19C2×#10625324C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic
21#13094023C2211yescharacteristic
22#13094023C2211yescharacteristic
23#13094018—21no—
24#13094017—21no—
25#13094013C2211yescharacteristic
26#13094012—21no—
27#13094011C2211yescharacteristic
28#13094010—21no—
29#13094009—21no—
30#13094007—21no—
31#13094004C2211yescharacteristic
32#13094003—21no—
33#13094002—21no—
34#13094000C2211yescharacteristic
35#13093999C2211yescharacteristic
36#13093995C2211yescharacteristic
37C4×Dic94C2211yescharacteristic
38C4×D188C2211yescharacteristic
39#13093981C2211yescharacteristic
40#13093958C2211yescharacteristic
41#13093957C2211yescharacteristic
42#13093957C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093948C2211yescharacteristic
45#13093947C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093934C2211yescharacteristic
50C4×C47⋊C8C2211yescharacteristic
51C8×Dic47C2211yescharacteristic
52C2×SD16×C47C2211yescharacteristic
53C4×Q8×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic
55#107×C47C2211yescharacteristic
56#103×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58#97×C47C2211yescharacteristic
59C2×Q8×C47C2311yescharacteristic
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×D188—21no—
64C2×D188C2311yescharacteristic
65C2×C4×D47—21no—
66C2×C4×D47C2311yescharacteristic
67C2×Dic94—21no—
68C2×Dic94—21no—
69C2×Dic94C2311yescharacteristic
70SD16×C47—22no—
71C2×C8×C47C2311yescharacteristic
72C2×C8×C47C2311yescharacteristic
73C4⋊C4×C47—21no—
74C4⋊C4×C47C2311yescharacteristic
75C4⋊C4×C47C2311yescharacteristic
76C22⋊C4×C47—21no—
77C42×C47—21no—
78C42×C47C2311yescharacteristic
79C22⋊Dic47—21no—
80C22⋊Dic47—21no—
81C22⋊Dic47—21no—
82#10625337—22no—
83#10625334—22no—
84(C2×D47)⋊C4—21no—
85(C2×D47)⋊C4—21no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4D411yescharacteristic
91(C2×D47)⋊C4D411yescharacteristic
92C4⋊Dic47—21no—
93C4⋊Dic47C2311yescharacteristic
94C4⋊Dic47C2311yescharacteristic
95Dic47⋊C4—21no—
96Dic47⋊C4—21no—
97Dic47⋊C4—21no—
98Dic47⋊C4—21no—
99Dic47⋊C4D411yescharacteristic
100Dic47⋊C4D411yescharacteristic
101C4×Dic47—21no—
102C4×Dic47C2311yescharacteristic
103C2×C47⋊C8C2311yescharacteristic
104C2×C47⋊C8C2311yescharacteristic
105#10625325—22no—
106#10625324—22no—
107C8×D47—22no—
108C23×C47—21no—
109C22×D47—21no—
110C22×D47C2×D411yescharacteristic
111Q8×C47—21no—
112Q8×C47—21no—
113D4×C47—21no—
114D4×C47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—81no—
119C2×C4×C47C2×D411yescharacteristic
120C2×C4×C47C2×D411yescharacteristic
121C2×C4×C47C2411yescharacteristic
122C22⋊D47—81no—
123C2×Dic47—21no—
124C2×Dic47—21no—
125C2×Dic47—21no—
126C2×Dic47C2×D411yescharacteristic
127C2×Dic47C2×D411yescharacteristic
128C2×Dic47C2×D411yescharacteristic
129D188—21no—
130D188—21no—
131D188—81no—
132C4×D47—21no—
133C4×D47—21no—
134C4×D47—81no—
135Dic94—21no—
136Dic94—21no—
137Dic94—81no—
138Dic94—81no—
139C8×C47—21no—
140C8×C47#4112yes—
141C47⋊C8—21no—
142C47⋊C8#4112yes—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47C22×D411yescharacteristic
147C2×D47—21no—
148C2×D47—21no—
149C2×D47—21no—
150C2×D47—41no—
151C2×D47—41no—
152C2×D47—41no—
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47—41no—
158C4×C47C2×#4111yescharacteristic
159C4×C47C2×#4111yescharacteristic
160Dic47—21no—
161Dic47—21no—
162Dic47—21no—
163Dic47—41no—
164Dic47—41no—
165Dic47—41no—
166#3175—471nomaximal, Sylow
167C2×C47—81no—
168C2×C47#53211yescharacteristic
169C2×C47#57611yescharacteristic
170C2×C47#57811yescharacteristic
171D47—41no—
172D47—81no—
173#542—471no—
174#542—471no—
175#500—471no—
176#495—471no—
177#489—471no—
178#489—471no—
179#468—471no—
180#468—471no—
181#467—471no—
182#466—471no—
183#440—471no—
184#440D4711yescharacteristic, complemented
185C4×Q16—471no—
186C4×D8—471no—
187#405—471no—
188C47#317511yescharacteristic, complemented, Sylow
189C2×Q16—471no—
190C2×SD16—471no—
191C2×SD16C2×D4711yescharacteristic
192C2×D8—471no—
193C2×M16—471no—
194C22×C8—471no—
195C4⋊Q8—471no—
196C4⋊Q8—471no—
197#126—941no—
198#126—941no—
199#124—471no—
200#124—471no—
201#124—941no—
202#124—941no—
203#123—941no—
204#123—941no—
205C22⋊Q8—471no—
206C22⋊Q8—471no—
207C22⋊Q8—941no—
208C22⋊Q8—941no—
209#121—471no—
210#121—471no—
211C4×Q8—471no—
212C4×Q8C2×D4711yescharacteristic
213C4×D4—471no—
214C4×D4C2×D4711yescharacteristic
215#117—471no—
216#107—471no—
217#107—471no—
218#107—471no—
219#107C2×D4711yescharacteristic
220#103—471no—
221#103—471no—
222#103—471no—
223#103C2×D4711yescharacteristic
224#102—471no—
225#102—471no—
226#102—471no—
227#102C2×D4711yescharacteristic
228#97—471no—
229#97C2×D4711yescharacteristic
230C4×C8—471no—
231C4×C8—471no—
232C2×Q8—471no—
233C2×Q8—941no—
234C2×Q8—941no—
235C2×Q8C22×D4711yescharacteristic
236C2×D4—471no—
237C2×D4—941no—
238C2×D4—941no—
239C2×D4C22×D4711yescharacteristic
240C22×C4—21no—
241C22×C4—471no—
242C22×C4—941no—
243Q16—942no—
244SD16—22no—
245SD16—942no—
246D8—942no—
247M16—942no—
248C2×C8—471no—
249C2×C8—471no—
250C2×C8—942no—
251C2×C8C22×D4711yescharacteristic
252C2×C8C22×D4711yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—471no—
255C4⋊C4—471no—
256C4⋊C4—471no—
257C4⋊C4—471no—
258C4⋊C4—941no—
259C4⋊C4—941no—
260C4⋊C4—941no—
261C4⋊C4—941no—
262C4⋊C4—941no—
263C4⋊C4C22×D4711yescharacteristic
264C4⋊C4C22×D4711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—471no—
267C22⋊C4—471no—
268C22⋊C4—941no—
269C22⋊C4—941no—
270C22⋊C4—941no—
271C22⋊C4—941no—
272C22⋊C4—941no—
273C22⋊C4—941no—
274C22⋊C4—941no—
275C22⋊C4—941no—
276C22⋊C4—941no—
277C42—21no—
278C42—471no—
279C42—941no—
280C42C22×D4711yescharacteristic
281C23—21no—
282C23—471no—
283C23—941no—
284Q8—21no—
285Q8—21no—
286Q8—941no—
287Q8—941no—
288Q8—3761no—
289Q8—3761no—
290D4—21no—
291D4—21no—
292D4—941no—
293D4—941no—
294D4—3761no—
295D4—3761no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—471no—
301C2×C4—471no—
302C2×C4—471no—
303C2×C4—941no—
304C2×C4—941no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—3761no—
309C2×C4D4×D4711yescharacteristic
310C2×C4D4×D4711yescharacteristic
311C2×C4C23×D4711yescharacteristic
312C8—21no—
313C8—472no—
314C8—941no—
315C8#1062535012yes—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—941no—
320C22—941no—
321C22—941no—
322C22—1881no—
323C22—1881no—
324C22—1881no—
325C22C2×D4×D4711yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—941no—
332C4—941no—
333C4—941no—
334C4—1881no—
335C4—1881no—
336C4—1881no—
337C4#41×D4711yescharacteristic
338C4C2×#1062535011yescharacteristic
339C2—81no—
340C2—3761no—
341C2—1881no—
342C2#1568967011yescharacteristic
343C2#1568992711yescharacteristic
344C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3175
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #15689745C2semidirect
2. #15689738C2semidirect
3. #15689527C2semidirect
4. #15689504C2semidirect
5. #15689484C2semidirect
6. #15689481C2semidirect
7. #15689370C2semidirect
8. #15689366C2semidirect
9. #15689363C2semidirect
11. #15689225C2semidirect
12. C4×#10625337C2semidirect
13. C4×#10625334C2semidirect
14. #15689080C2semidirect
15. C47×#440C2semidirect
184. #440D47semidirect
188. C47#3175semidirect