Finite Group Databasebeta

← #20255559

Subgroups — #20255559

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#15689819C211yesmaximal, characteristic
2#15689491C211yesmaximal, characteristic, complemented
3#15689461C211yesmaximal, characteristic, complemented
4#15689456C211yesmaximal, characteristic, complemented
5#15689430C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689325C211yesmaximal, characteristic, complemented
9#15689262C211yesmaximal, characteristic, complemented
10#15689262C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689132C211yesmaximal, characteristic, complemented
14C2×#13093948C211yesmaximal, characteristic, complemented
15D4×Q8×C47C211yesmaximal, characteristic, complemented
16C2×#10625336C2211yescharacteristic
17C2×#10625336C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20C22×C47⋊C8C2211yescharacteristic
21#13094019—21no—
22#13094016C2211yescharacteristic
23#13094006—21no—
24#13093998C2211yescharacteristic
25#13093998C2211yescharacteristic
26#13093996—21no—
27C4×D188C2211yescharacteristic
28(C22⋊D47)⋊C4—21no—
29#13093983C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic
31#13093957C2211yescharacteristic
32#13093957C2211yescharacteristic
33#13093955C2211yescharacteristic
34C4⋊(C47⋊C8)C2211yescharacteristic
35#13093948C2211yescharacteristic
36#13093948C2211yescharacteristic
37#13093948C2211yescharacteristic
38#13093948C2211yescharacteristic
39#13093948C2211yescharacteristic
40#13093948C2211yescharacteristic
41#13093948C2211yescharacteristic
42#13093948C2211yescharacteristic
43#13093948C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47#13093935C2211yescharacteristic
48C22×Q8×C47C2211yescharacteristic
49C22×Q8×C47C2211yescharacteristic
50C4⋊Q8×C47—21no—
51C4⋊Q8×C47C2211yescharacteristic
52C22⋊Q8×C47—21no—
53C22⋊Q8×C47—21no—
54C22⋊Q8×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56C4×Q8×C47C2211yescharacteristic
57C4×D4×C47—21no—
58C4×D4×C47C2211yescharacteristic
59C2×Q8×C47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47—22no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47—41no—
65C2×Q8×C47C2311yescharacteristic
66C2×Q8×C47C2311yescharacteristic
67C2×Q8×C47C2311yescharacteristic
68C2×D4×C47D411yescharacteristic
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C2×C22⋊D47—21no—
74C2×C22⋊D47—21no—
75C22×Dic47—21no—
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47D411yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47D411yescharacteristic
88C22⋊C4×C47D411yescharacteristic
89C42×C47—21no—
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92#10625336—22no—
93#10625336—41no—
94#10625336—41no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114Q8×C47—21no—
115Q8×C47—21no—
116Q8×C47—21no—
117Q8×C47—21no—
118Q8×C47—21no—
119Q8×C47—42no—
120Q8×C47—42no—
121Q8×C47#4112yes—
122D4×C47—22no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—42no—
132C2×C4×C47—42no—
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2411yescharacteristic
138C22⋊D47—42no—
139C22⋊D47—81no—
140C2×Dic47—21no—
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—81no—
144D188—21no—
145D188—21no—
146C4×D47—81no—
147C47⋊C8—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47#13712yes—
157C22×C47C22×D411yescharacteristic
158C2×D47—41no—
159C2×D47—41no—
160C2×D47—41no—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—22no—
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47H(5,𝔽2)11yescharacteristic
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174#3320—471nomaximal, Sylow
175C2×C47—22no—
176C2×C47—41no—
177C2×C47#54611yescharacteristic
178C2×C47C2×#13711yescharacteristic
179C2×C47#57711yescharacteristic
180D47—81no—
181#553—471no—
182D4×Q8D4711yescharacteristic, complemented
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#440—471no—
193#435—471no—
194#419—471no—
195C2×#103—471no—
196C47#332011yescharacteristic, complemented, Sylow
197C22×Q8C2×D4711yescharacteristic
198C22×Q8C2×D4711yescharacteristic
199C2×SD16—471no—
200C2×SD16—471no—
201C2×SD16—471no—
202C2×M16—471no—
203C22×C8—471no—
204C4⋊Q8—21no—
205C4⋊Q8C2×D4711yescharacteristic
206#126—941no—
207#125—471no—
208#123—941no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D4711yescharacteristic
212C22⋊Q8C2×D4711yescharacteristic
213#121—471no—
214#121—471no—
215#121—941no—
216C4×Q8C2×D4711yescharacteristic
217C4×D4—21no—
218C4×D4—471no—
219C4×D4—941no—
220C4×D4C2×D4711yescharacteristic
221#117—471no—
222C2×C4⋊C4—471no—
223#107—471no—
224#107—471no—
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#103—471no—
236#102—471no—
237C22⋊C8—471no—
238C22⋊C8—471no—
239#97—471no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C22×D4711yescharacteristic
247C2×Q8C22×D4711yescharacteristic
248C2×Q8C22×D4711yescharacteristic
249C2×D4—471no—
250C2×D4—941no—
251C2×D4—941no—
252C2×D4C22⋊D4711yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4C22×D4711yescharacteristic
258C22×C4C22×D4711yescharacteristic
259SD16—942no—
260SD16—1881no—
261SD16—1881no—
262M16—1881no—
263C2×C8—471no—
264C2×C8—471no—
265C2×C8—471no—
266C2×C8—471no—
267C2×C8—1881no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4C22⋊D4711yescharacteristic
280C4⋊C4C22×D4711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4C22⋊D4711yescharacteristic
288C22⋊C4C22⋊D4711yescharacteristic
289C42—21no—
290C42—941no—
291C42C22×D4711yescharacteristic
292C23—941no—
293C23C2×C22⋊D4711yescharacteristic
294C23C2×C22⋊D4711yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—42no—
302Q8#1062535212yes—
303D4—22no—
304D4—941no—
305D4—941no—
306D4—3761no—
307D4—1882no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—941no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—3761no—
322C2×C4—3761no—
323C2×C4C2×C22⋊D4711yescharacteristic
324C2×C4C2×C22⋊D4711yescharacteristic
325C2×C4C2×C22⋊D4711yescharacteristic
326C2×C4C2×C22⋊D4711yescharacteristic
327C2×C4C23×D4711yescharacteristic
328C8—941no—
329C8—941no—
330C8—941no—
331C8—941no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—1881no—
338C22—1881no—
339C22—1881no—
340C22#1309405512yes—
341C22C22×C22⋊D4711yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—1881no—
351C4—1881no—
352C4—1881no—
353C4C2×#1062535211yescharacteristic
354C4#1309406911yescharacteristic
355C2—22no—
356C2—41no—
357C2—3761no—
358C2#1568976711yescharacteristic
359C2C2×#1309405511yescharacteristic
360C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD4×Q8×C47C2
socleC22×C47C22×D4
hypercenterD4×Q8D47
hypocenterC47#3320
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #15689491C2semidirect
3. #15689461C2semidirect
4. #15689456C2semidirect
5. #15689430C2semidirect
6. #15689371C2semidirect
7. #15689354C2semidirect
8. #15689325C2semidirect
9. #15689262C2semidirect
10. #15689262C2semidirect
11. #15689221C2semidirect
12. #15689195C2semidirect
13. #15689132C2semidirect
14. C2×#13093948C2semidirect
15. D4×Q8×C47C2semidirect
182. D4×Q8D47semidirect
196. C47#3320semidirect