Finite Group Databasebeta

← #20255564

Subgroups — #20255564

Order 6016.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689823C211yesmaximal, characteristic
2Q8×D188C211yesmaximal, characteristic, complemented
3#15689492C211yesmaximal, characteristic, complemented
4#15689466C211yesmaximal, characteristic, complemented
5#15689460C211yesmaximal, characteristic, complemented
6#15689430C211yesmaximal, characteristic, complemented
7#15689368C211yesmaximal, characteristic, complemented
8#15689351C211yesmaximal, characteristic, complemented
9#15689328C211yesmaximal, characteristic, complemented
10#15689260C211yesmaximal, characteristic, complemented
11#15689260C211yesmaximal, characteristic, complemented
12#15689196C211yesmaximal, characteristic, complemented
13#15689130C211yesmaximal, characteristic, complemented
14#103×D47C211yesmaximal, characteristic, complemented
15C47×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×Q8×D47C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625324C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094024—21no—
23#13094024C2211yescharacteristic
24#13094017—21no—
25#13094016C2211yescharacteristic
26#13094007—21no—
27#13094004—21no—
28#13094004—21no—
29#13094004C2211yescharacteristic
30#13094004C2211yescharacteristic
31#13093997—21no—
32#13093995C2211yescharacteristic
33#13093995C2211yescharacteristic
34C4×D188—21no—
35C4×D188C2211yescharacteristic
36C4×C22⋊D47—21no—
37#13093982C2211yescharacteristic
38C4⋊C4×D47C2211yescharacteristic
39#13093957C2211yescharacteristic
40#13093955C2211yescharacteristic
41C4⋊(C47⋊C8)C2211yescharacteristic
42#13093949C2211yescharacteristic
43#13093949C2211yescharacteristic
44#13093949C2211yescharacteristic
45#13093949C2211yescharacteristic
46#13093948C2211yescharacteristic
47#13093948C2211yescharacteristic
48#13093947C2211yescharacteristic
49#13093947C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic
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×C22⋊D47—21no—
64Q8×D47—22no—
65Q8×D47—22no—
66Q8×D47—41no—
67Q8×D47—41no—
68C2×D188D411yescharacteristic
69C2×C4×D47—21no—
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47C2311yescharacteristic
73C2×C4×D47C2311yescharacteristic
74C2×Dic94—21no—
75C2×Dic94—21no—
76C2×Dic94C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78SD16×C47—22no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C22⋊C4×C47—21no—
85C42×C47—21no—
86C42×C47C2311yescharacteristic
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89#10625335—41no—
90#10625335—41no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4D411yescharacteristic
95(C2×D47)⋊C4D411yescharacteristic
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47D411yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C4×Dic47—21no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109#10625324—41no—
110C8×D47—41no—
111C23×C47—21no—
112C22×D47C2×D411yescharacteristic
113C22×D47C2×D411yescharacteristic
114Q8×C47—21no—
115Q8×C47#4112yes—
116D4×C47—21no—
117D4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—81no—
122C2×C4×C47C2×D411yescharacteristic
123C2×C4×C47C2×D411yescharacteristic
124C2×C4×C47C2411yescharacteristic
125C22⋊D47—42no—
126C22⋊D47—81no—
127C2×Dic47—21no—
128C2×Dic47—21no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47C2×D411yescharacteristic
132C2×Dic47C2×D411yescharacteristic
133D188—22no—
134C4×D47—21no—
135C4×D47—21no—
136C4×D47—21no—
137C4×D47—21no—
138C4×D47—42no—
139C4×D47—42no—
140C4×D47—81no—
141Dic94—21no—
142Dic94—21no—
143Dic94—21no—
144Dic94—21no—
145Dic94—42no—
146Dic94—42no—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—41no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47C22×D411yescharacteristic
155C2×D47—21no—
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—21no—
160C2×D47#13712yes—
161C4×C47—22no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—41no—
165C4×C47—41no—
166C4×C47C2×#4111yescharacteristic
167C4×C47H(5,𝔽2)11yescharacteristic
168Dic47—21no—
169Dic47—21no—
170Dic47—41no—
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3320—471nomaximal, Sylow
175C2×C47—81no—
176C2×C47#54611yescharacteristic
177C2×C47C2×#13711yescharacteristic
178C2×C47#57711yescharacteristic
179D47—22no—
180D47—41no—
181#553—471no—
182D4×Q8—471no—
183#491—471no—
184#485—471no—
185#484—471no—
186#479—471no—
187#468—471no—
188#465—471no—
189#461—471no—
190#448—471no—
191#448—471no—
192#440D4711yescharacteristic, complemented
193#435—471no—
194#419—471no—
195C2×#103—471no—
196C47#332011yescharacteristic, complemented, Sylow
197C22×Q8—471no—
198C22×Q8—471no—
199C2×SD16—471no—
200C2×SD16—471no—
201C2×SD16C2×D4711yescharacteristic
202C2×M16—471no—
203C22×C8—471no—
204C4⋊Q8—471no—
205C4⋊Q8—941no—
206#126—941no—
207#125—471no—
208#123—941no—
209C22⋊Q8—471no—
210C22⋊Q8—471no—
211C22⋊Q8—941no—
212C22⋊Q8—941no—
213#121—471no—
214#121—471no—
215#121—941no—
216C4×Q8C2×D4711yescharacteristic
217C4×D4—471no—
218C4×D4—941no—
219C4×D4—941no—
220C4×D4C2×D4711yescharacteristic
221#117—471no—
222C2×C4⋊C4—471no—
223#107—471no—
224#107C2×D4711yescharacteristic
225#106—471no—
226C4⋊C8—471no—
227#103—471no—
228#103—471no—
229#103—471no—
230#103—471no—
231#103—471no—
232#103—471no—
233#103—471no—
234#103—471no—
235#103C2×D4711yescharacteristic
236#102C2×D4711yescharacteristic
237C22⋊C8—471no—
238C22⋊C8—471no—
239#97C2×D4711yescharacteristic
240C2×Q8—471no—
241C2×Q8—471no—
242C2×Q8—941no—
243C2×Q8—941no—
244C2×Q8—942no—
245C2×Q8—942no—
246C2×Q8—1881no—
247C2×Q8—1881no—
248C2×Q8C22×D4711yescharacteristic
249C2×D4—471no—
250C2×D4—941no—
251C2×D4—941no—
252C2×D4C22×D4711yescharacteristic
253C22×C4—21no—
254C22×C4—471no—
255C22×C4—471no—
256C22×C4—941no—
257C22×C4—941no—
258C22×C4—941no—
259SD16—22no—
260SD16—1881no—
261SD16—1881no—
262M16—1881no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—1881no—
266C2×C8C22×D4711yescharacteristic
267C2×C8C22×D4711yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—471no—
270C4⋊C4—471no—
271C4⋊C4—471no—
272C4⋊C4—941no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4C22×D4711yescharacteristic
280C4⋊C4C22×D4711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—471no—
283C22⋊C4—471no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C42—21no—
290C42—941no—
291C42C22×D4711yescharacteristic
292C23—21no—
293C23—471no—
294C23—471no—
295Q8—21no—
296Q8—941no—
297Q8—941no—
298Q8—941no—
299Q8—941no—
300Q8—1882no—
301Q8—1882no—
302Q8#1062535012yes—
303D4—21no—
304D4—21no—
305D4—942no—
306D4—3761no—
307D4—1882no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—471no—
313C2×C4—471no—
314C2×C4—941no—
315C2×C4—941no—
316C2×C4—941no—
317C2×C4—941no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—3761no—
323C2×C4—1882no—
324C2×C4—1882no—
325C2×C4D4×D4711yescharacteristic
326C2×C4D4×D4711yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—21no—
329C8—21no—
330C8—941no—
331C8—941no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—472no—
336C22—941no—
337C22—941no—
338C22—941no—
339C22—941no—
340C22—941no—
341C22C2×D4×D4711yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—941no—
348C4—941no—
349C4—1881no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4C2×#1062535011yescharacteristic
354C4#1309407011yescharacteristic
355C2—81no—
356C2—942no—
357C2—1881no—
358C2#1568976911yescharacteristic
359C2#137×D4711yescharacteristic
360C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#440C2
socleC22×C47C22×D4
hypercenter#440D47
hypocenterC47#3320
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
2. Q8×D188C2semidirect
3. #15689492C2semidirect
4. #15689466C2semidirect
5. #15689460C2semidirect
6. #15689430C2semidirect
7. #15689368C2semidirect
8. #15689351C2semidirect
9. #15689328C2semidirect
10. #15689260C2semidirect
11. #15689260C2semidirect
12. #15689196C2semidirect
13. #15689130C2semidirect
14. #103×D47C2semidirect
15. C47×#440C2semidirect
192. #440D47semidirect
196. C47#3320semidirect