Finite Group Databasebeta

← #20254892

Subgroups — #20254892

Order 6016.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D47C211yesmaximal, characteristic, complemented
2Q8×C22⋊D47C211yesmaximal, characteristic, complemented
3#15689761C211yesmaximal, characteristic
4#15689516C211yesmaximal, characteristic, complemented
5#15689369C211yesmaximal, characteristic, complemented
6#15689361C211yesmaximal, characteristic, complemented
7#15689347C211yesmaximal, characteristic, complemented
8#15689326C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689277C211yesmaximal, characteristic, complemented
11#15689272C211yesmaximal, characteristic, complemented
12#15689262C211yesmaximal, characteristic, complemented
13#15689224C211yesmaximal, characteristic, complemented
14#15689192C211yesmaximal, characteristic, complemented
15C2×#137×C47C211yesmaximal, characteristic, complemented
16C2×Q8×D47C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625336C2211yescharacteristic
22C2×#10625336C2211yescharacteristic
23SD16×D47—24no—
24C2×C8×D47C2211yescharacteristic
25#13094022—21no—
26#13094022C2211yescharacteristic, complemented
27#13094013C2211yescharacteristic
28#13094007—21no—
29#13094003—21no—
30#13094003C2211yescharacteristic, complemented
31#13094000—21no—
32#13094000C2211yescharacteristic
33#13094000C2211yescharacteristic
34#13093998C2211yescharacteristic
35#13093996—21no—
36#13093992—21no—
37Q8×Dic47C2211yescharacteristic, complemented
38D4×Dic47C2211yescharacteristic
39C4×C22⋊D47—21no—
40C4×C22⋊D47C2211yescharacteristic
41C2×(C2×D47)⋊C4—21no—
42#13093958C2211yescharacteristic, complemented
43Dic47⋊C8C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093948C2211yescharacteristic, complemented
47#13093948C2211yescharacteristic, complemented
48#13093946C2211yescharacteristic
49#13093945C2211yescharacteristic
50C22⋊(C47⋊C8)C2211yescharacteristic, complemented
51(C2×D47)⋊C8C2211yescharacteristic
52#13093934C2211yescharacteristic, complemented
53C2×#41×C47C2211yescharacteristic
54C22×Q8×C47C2211yescharacteristic, complemented
55#137×C47—24no—
56C2×Q16×C47C2211yescharacteristic, complemented
57C2×Q16×C47C2211yescharacteristic, complemented
58C2×SD16×C47C2211yescharacteristic
59C2×SD16×C47C2211yescharacteristic
60C2×M16×C47C2211yescharacteristic, complemented
61C23×D47—21no—
62#41×C47—22no—
63#41×C47—41no—
64C2×Q8×C47—21no—
65C2×Q8×C47—22no—
66C2×Q8×C47—41no—
67C2×Q8×C47C2311yescharacteristic
68C2×Q8×C47C2311yescharacteristic
69C2×Q8×C47C2311yescharacteristic
70C2×D4×C47—21no—
71C2×D4×C47C2311yescharacteristic
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47C2311yescharacteristic
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47D411yescharacteristic
78C22×Dic47—21no—
79Q8×D47—22no—
80Q8×D47—41no—
81D4×D47—22no—
82D4×D47—41no—
83C2×D188C2311yescharacteristic
84C2×C4×D47—21no—
85C2×C4×D47C2311yescharacteristic
86C2×Dic94—21no—
87C2×Dic94C2311yescharacteristic
88Q16×C47—22no—
89Q16×C47—22no—
90SD16×C47—22no—
91SD16×C47D414yescomplemented
92M16×C47—22no—
93C2×C8×C47C2311yescharacteristic
94C2×C8×C47C2311yescharacteristic
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47D411yescharacteristic
98#10625337—41no—
99#10625336—22no—
100#10625336—41no—
101#10625335—22no—
102(C2×D47)⋊C4—21no—
103(C2×D47)⋊C4—21no—
104(C2×D47)⋊C4—21no—
105(C2×D47)⋊C4—21no—
106(C2×D47)⋊C4—21no—
107(C2×D47)⋊C4D411yescharacteristic
108C4⋊Dic47—21no—
109C4⋊Dic47C2311yescharacteristic
110C4⋊Dic47C2311yescharacteristic
111Dic47⋊C4—21no—
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114Dic47⋊C4—21no—
115Dic47⋊C4—21no—
116Dic47⋊C4D411yescharacteristic
117C4×Dic47—21no—
118C4×Dic47C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120C2×C47⋊C8C2311yescharacteristic
121#10625325—22no—
122C8×D47—22no—
123C23×C47—21no—
124C23×C47C2×D411yescharacteristic
125C22×D47—21no—
126C22×D47—42no—
127C22×D47—42no—
128C22×D47—81no—
129C22×D47C2×D411yescharacteristic
130Q8×C47—21no—
131Q8×C47—21no—
132Q8×C47—21no—
133Q8×C47—21no—
134Q8×C47—21no—
135Q8×C47—42no—
136Q8×C47C2×D412yes—
137D4×C47—21no—
138D4×C47—42no—
139D4×C47C2×D412yes—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47—21no—
143C2×C4×C47—21no—
144C2×C4×C47—21no—
145C2×C4×C47—42no—
146C2×C4×C47—42no—
147C2×C4×C47C2×D411yescharacteristic
148C2×C4×C47C2411yescharacteristic
149C22⋊D47—22no—
150C22⋊D47—42no—
151C22⋊D47—81no—
152C2×Dic47—21no—
153C2×Dic47—21no—
154C2×Dic47—21no—
155C2×Dic47—81no—
156C2×Dic47C2×D411yescharacteristic
157C2×Dic47C2×D411yescharacteristic
158C2×Dic47C2×D411yescharacteristic
159D188—21no—
160D188—21no—
161C4×D47—21no—
162C4×D47—21no—
163C4×D47—42no—
164Dic94—21no—
165Dic94—21no—
166Dic94—42no—
167C8×C47—21no—
168C8×C47C2×D412yes—
169C47⋊C8—21no—
170C47⋊C8—21no—
171C22×C47—22no—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—21no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47C22×D411yescharacteristic
178C2×D47—21no—
179C2×D47—21no—
180C2×D47—41no—
181C2×D47—41no—
182C2×D47—41no—
183C2×D47—84no—
184C2×D47#13712yescomplemented
185C4×C47—22no—
186C4×C47—21no—
187C4×C47—41no—
188C4×C47—41no—
189C4×C47C22×D411yescharacteristic
190C4×C47H(5,𝔽2)11yescharacteristic
191Dic47—21no—
192Dic47—21no—
193Dic47—21no—
194Dic47—41no—
195Dic47—41no—
196Dic47—41no—
197#3266—471nomaximal, Sylow
198C2×C47—42no—
199C2×C47—41no—
200C2×C47D4211yescharacteristic
201C2×C47C2×#13711yescharacteristic
202C2×C47#57711yescharacteristic
203D47—22no—
204D47—81no—
205C2×#137D4711yescharacteristic, complemented
206C22×SD16—471no—
207D4×Q8—471no—
208#546—471no—
209#497—471no—
210#468—471no—
211#467—471no—
212#464—471no—
213#461—471no—
214#452—471no—
215#451—471no—
216#450—471no—
217#448—471no—
218#440—471no—
219#435—471no—
220C47#326611yescharacteristic, complemented, Sylow
221C2×#41C2×D4711yescharacteristic
222C22×Q8—471no—
223C22×Q8C2×D4711yescharacteristic, complemented
224C22×D4—471no—
225#137—24no—
226C2×Q16—471no—
227C2×Q16C2×D4711yescharacteristic, complemented
228C2×Q16C2×D4711yescharacteristic, complemented
229C2×SD16—471no—
230C2×SD16—471no—
231C2×SD16—471no—
232C2×SD16—471no—
233C2×SD16—944no—
234C2×SD16C2×D4711yescharacteristic
235C2×SD16C2×D4711yescharacteristic
236C2×M16C2×D4711yescharacteristic, complemented
237C22×C8—471no—
238C4⋊Q8—471no—
239C4⋊Q8—941no—
240#124—471no—
241#123—941no—
242C22⋊Q8—471no—
243C22⋊Q8—471no—
244C22⋊Q8—471no—
245C22⋊Q8—941no—
246C22⋊Q8—941no—
247#121—471no—
248#121—941no—
249#120—941no—
250C4×Q8—471no—
251C4×D4—471no—
252C4×D4—471no—
253C4×D4—941no—
254C2×C22⋊C4—941no—
255#107—471no—
256C4⋊C8—471no—
257#103—471no—
258#103—471no—
259#103—471no—
260#103—471no—
261#102—471no—
262#102—471no—
263C22⋊C8—471no—
264C22⋊C8—471no—
265#97—471no—
266C24—941no—
267#41—22no—
268#41—41no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—471no—
273C2×Q8—941no—
274C2×Q8—942no—
275C2×Q8—1881no—
276C2×Q8C22×D4711yescharacteristic
277C2×Q8C22×D4711yescharacteristic
278C2×Q8C22×D4711yescharacteristic
279C2×D4—21no—
280C2×D4—471no—
281C2×D4—471no—
282C2×D4—941no—
283C2×D4—942no—
284C2×D4—941no—
285C2×D4—1881no—
286C2×D4C22×D4711yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—471no—
290C22×C4—941no—
291C22×C4—941no—
292C22×C4C22×D4711yescharacteristic
293Q16—22no—
294Q16—22no—
295Q16—1881no—
296SD16—22no—
297SD16—942no—
298SD16—942no—
299SD16—942no—
300SD16—1881no—
301SD16C22⋊D4714yescomplemented
302M16—22no—
303C2×C8—471no—
304C2×C8—471no—
305C2×C8—942no—
306C2×C8C22×D4711yescharacteristic
307C2×C8C22×D4711yescharacteristic
308C4⋊C4—471no—
309C4⋊C4—471no—
310C4⋊C4—471no—
311C4⋊C4—941no—
312C4⋊C4—941no—
313C4⋊C4—941no—
314C4⋊C4—941no—
315C4⋊C4—941no—
316C4⋊C4—941no—
317C22⋊C4—471no—
318C22⋊C4—471no—
319C22⋊C4—941no—
320C22⋊C4—941no—
321C22⋊C4—941no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C42—471no—
327C42—941no—
328C23—21no—
329C23—471no—
330C23—941no—
331C23—3761no—
332C23—1882no—
333C23—1882no—
334C23D4×D4711yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—941no—
342Q8—941no—
343Q8—1882no—
344Q8C2×C22⋊D4712yes—
345D4—21no—
346D4—42no—
347D4—942no—
348D4—941no—
349D4—941no—
350D4—3761no—
351D4—1882no—
352D4C2×C22⋊D4712yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—471no—
361C2×C4—471no—
362C2×C4—471no—
363C2×C4—941no—
364C2×C4—941no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—3761no—
369C2×C4—1882no—
370C2×C4D4×D4711yescharacteristic
371C2×C4C23×D4711yescharacteristic
372C8—21no—
373C8—941no—
374C8—941no—
375C8C2×C22⋊D4712yes—
376C22—21no—
377C22—22no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—472no—
383C22—941no—
384C22—941no—
385C22—3764no—
386C22—1881no—
387C22—1881no—
388C22—1881no—
389C22C2×D4×D4711yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—941no—
395C4—941no—
396C4—941no—
397C4—1881no—
398C4—1881no—
399C4—1881no—
400C4C22×C22⋊D4711yescharacteristic
401C4#1309406911yescharacteristic
402C2—41no—
403C2—42no—
404C2—942no—
405C2—3761no—
406C2D4×C22⋊D4711yescharacteristic
407C2#137×D4711yescharacteristic
408C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#137×C47C2
socleC22×C47C22×D4
hypercenterC2×#137D47
hypocenterC47#3266
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D47C2semidirect
2. Q8×C22⋊D47C2semidirect
4. #15689516C2semidirect
5. #15689369C2semidirect
6. #15689361C2semidirect
7. #15689347C2semidirect
8. #15689326C2semidirect
9. #15689285C2semidirect
10. #15689277C2semidirect
11. #15689272C2semidirect
12. #15689262C2semidirect
13. #15689224C2semidirect
14. #15689192C2semidirect
15. C2×#137×C47C2semidirect
18. C2×#10625337C22semidirect
26. #13094022C22semidirect
30. #13094003C22semidirect
37. Q8×Dic47C22semidirect
42. #13093958C22semidirect
43. Dic47⋊C8C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
46. #13093948C22semidirect
47. #13093948C22semidirect
50. C22⋊(C47⋊C8)C22semidirect
52. #13093934C22semidirect
54. C22×Q8×C47C22semidirect
56. C2×Q16×C47C22semidirect
57. C2×Q16×C47C22semidirect
60. C2×M16×C47C22semidirect
91. SD16×C47D4semidirect
184. C2×D47#137semidirect
205. C2×#137D47semidirect
220. C47#3266semidirect
223. C22×Q8C2×D47semidirect
227. C2×Q16C2×D47semidirect
228. C2×Q16C2×D47semidirect
236. C2×M16C2×D47semidirect
301. SD16C22⋊D47semidirect