Finite Group Databasebeta

← #20246366

Subgroups — #20246366

Order 6016.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13093994C211yesmaximal, characteristic
2C2×C4×D188C211yesmaximal, characteristic, complemented
3C2×#13093986C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D47C211yesmaximal, characteristic, complemented
6#15689023C211yesmaximal, characteristic, complemented
7#15689016C211yesmaximal, characteristic, complemented
8#15689001C211yesmaximal, characteristic, complemented
9#15689001C211yesmaximal, characteristic, complemented
10#15688999C211yesmaximal, characteristic, complemented
11#15688997C211yesmaximal, characteristic, complemented
12#15688994C211yesmaximal, characteristic, complemented
13C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
14#15688970C211yesmaximal, characteristic, complemented
15C47×#388C211yesmaximal, characteristic, complemented
16C24×D47C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C22×D188C2211yescharacteristic
19C22×C22⋊D47C2211yescharacteristic
20C22×C4×D47C2211yescharacteristic
21C22×C4×D47C2211yescharacteristic
22C22×C4×D47C2211yescharacteristic
23C22×C4×D47C2211yescharacteristic
24C22×C4×D47C2211yescharacteristic, complemented
25#13093994C418yescomplemented
26C4×D188—24no—
27#13093986—24no—
28C2×C4⋊Dic47C2211yescharacteristic, complemented
29C2×Dic47⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic47C2211yescharacteristic
31C2×C22⋊Dic47C2211yescharacteristic
32C2×(C2×D47)⋊C4C2211yescharacteristic
33C2×(C2×D47)⋊C4C2211yescharacteristic
34C2×(C2×D47)⋊C4C2211yescharacteristic
35C2×(C2×D47)⋊C4C2211yescharacteristic
36C2×(C2×D47)⋊C4C2211yescharacteristic
37C2×(C2×D47)⋊C4C2211yescharacteristic
38C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
41C22⋊C4×D47—24no—
42C22⋊C4×D47—24no—
43C2×C4×Dic47C2211yescharacteristic, complemented
44C2×C4×Dic47C2211yescharacteristic, complemented
45C47⋊#95C2211yescharacteristic, complemented
46C47⋊#95C2211yescharacteristic, complemented
47C47⋊#95C2211yescharacteristic, complemented
48C47⋊#95C2211yescharacteristic, complemented
49C2×C4⋊C4×C47C2211yescharacteristic, complemented
50C2×C22⋊C4×C47C2211yescharacteristic
51C2×C22⋊C4×C47C2211yescharacteristic
52C2×C22⋊C4×C47C2211yescharacteristic
53C2×C42×C47C2211yescharacteristic, complemented
54#95×C47C2211yescharacteristic, complemented
55#95×C47C2211yescharacteristic, complemented
56C24×C47C2311yescharacteristic
57C23×D47—22no—
58C23×D47—22no—
59C23×D47—22no—
60C23×D47—22no—
61C23×D47—41no—
62C23×D47—41no—
63C23×D47C2×C414yescomplemented
64C23×D47C2311yescharacteristic
65C23×D47C2311yescharacteristic
66C23×D47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C22×C4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C22×C4×C47C2311yescharacteristic
71C22×C4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C2×C22⋊D47—41no—
74C2×C22⋊D47—41no—
75C2×C22⋊D47C2×C414yescomplemented
76C22×Dic47C2311yescharacteristic
77C22×Dic47C2311yescharacteristic
78C22×Dic47C2311yescharacteristic
79C22×Dic47C2311yescharacteristic
80C22×Dic47C2311yescharacteristic
81C2×D188—22no—
82C2×D188—22no—
83C2×D188—22no—
84C2×D188—22no—
85C2×D188C2×C414yescomplemented
86C2×D188C2×C414yescomplemented
87C2×C4×D47—22no—
88C2×C4×D47—22no—
89C2×C4×D47—22no—
90C2×C4×D47—22no—
91C2×C4×D47—22no—
92C2×C4×D47—22no—
93C2×C4×D47—22no—
94C2×C4×D47—22no—
95C2×C4×D47—22no—
96C2×C4×D47—22no—
97C2×C4×D47—41no—
98C2×C4×D47—41no—
99C2×C4×D47—41no—
100C2×C4×D47—41no—
101C2×C4×D47—41no—
102C4⋊C4×C47—22no—
103C22⋊C4×C47—22no—
104C22⋊C4×C47—22no—
105C22⋊C4×C47C2×C414yescomplemented
106C42×C47—22no—
107C22⋊Dic47—22no—
108C22⋊Dic47—22no—
109(C2×D47)⋊C4—22no—
110(C2×D47)⋊C4—22no—
111(C2×D47)⋊C4—22no—
112(C2×D47)⋊C4—22no—
113(C2×D47)⋊C4—41no—
114(C2×D47)⋊C4C2×C414yescomplemented
115(C2×D47)⋊C4C2×C414yescomplemented
116(C2×D47)⋊C4D414yescomplemented
117(C2×D47)⋊C4D414yescomplemented
118C4⋊Dic47—22no—
119Dic47⋊C4—41no—
120C4×Dic47—22no—
121C4×Dic47—41no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47C22×C412yes—
129C23×C47C2411yescharacteristic
130C22×D47—21no—
131C22×D47—21no—
132C22×D47—21no—
133C22×D47—21no—
134C22×D47—21no—
135C22×D47—21no—
136C22×D47—21no—
137C22×D47—21no—
138C22×D47—21no—
139C22×D47—21no—
140C22×D47—21no—
141C22×D47—21no—
142C22×D47—21no—
143C22×D47—21no—
144C22×D47—28no—
145C22×D47—28no—
146C22×D47—44no—
147C22×D47—44no—
148C22×D47—44no—
149C22×D47—44no—
150C22×D47—44no—
151C22×D47C22×C412yes—
152C22×D47C22×C412yes—
153C22×D47C22×C412yes—
154C22×D47C2×D412yes—
155C22×D47C2×D412yes—
156C22×D47#4112yes—
157C22×D47#4112yes—
158C2×C4×C47—21no—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—21no—
165C2×C4×C47—21no—
166C2×C4×C47—21no—
167C2×C4×C47—21no—
168C2×C4×C47—21no—
169C2×C4×C47—21no—
170C2×C4×C47—21no—
171C2×C4×C47—21no—
172C2×C4×C47C22×C412yes—
173C2×C4×C47C22×C412yes—
174C2×C4×C47C2×D412yes—
175C2×C4×C47C2×D412yes—
176C22⋊D47—44no—
177C2×Dic47—21no—
178C2×Dic47—21no—
179C2×Dic47—21no—
180C2×Dic47—21no—
181C2×Dic47—21no—
182C2×Dic47—21no—
183C2×Dic47—21no—
184C2×Dic47—21no—
185C2×Dic47—21no—
186C2×Dic47—21no—
187C2×Dic47—21no—
188C2×Dic47—21no—
189C2×Dic47C22×C412yes—
190C2×Dic47C2×D412yes—
191C2×Dic47C2×D412yes—
192D188—28no—
193D188—28no—
194C4×D47—44no—
195C4×D47—44no—
196C4×D47—44no—
197C4×D47—44no—
198C4×D47—44no—
199C22×C47—22no—
200C22×C47—22no—
201C22×C47—22no—
202C22×C47—41no—
203C22×C47—41no—
204C22×C47—41no—
205C22×C47—41no—
206C22×C47C23×C411yescharacteristic
207C22×C47C22×D411yescharacteristic
208C22×C47C22×D411yescharacteristic
209C22×C47C2×#4111yescharacteristic
210C22×C47C2×#4111yescharacteristic
211C22×C47H(5,𝔽2)11yescharacteristic
212C22×C47H(5,𝔽2)11yescharacteristic
213C2×D47—22no—
214C2×D47—22no—
215C2×D47—22no—
216C2×D47—22no—
217C2×D47—22no—
218C2×D47—22no—
219C2×D47—22no—
220C2×D47—22no—
221C2×D47—22no—
222C2×D47—22no—
223C2×D47—22no—
224C2×D47—22no—
225C2×D47—22no—
226C2×D47—22no—
227C2×D47—22no—
228C2×D47—416no—
229C2×D47—41no—
230C2×D47—41no—
231C2×D47—41no—
232C2×D47—41no—
233C2×D47C4×D414yescomplemented
234C2×D47C4×D414yescomplemented
235C4×C47—22no—
236C4×C47—22no—
237C4×C47—22no—
238C4×C47—22no—
239C4×C47—41no—
240C4×C47—41no—
241Dic47—22no—
242Dic47—22no—
243Dic47—22no—
244Dic47—41no—
245Dic47—41no—
246#2358—471nomaximal, Sylow
247C2×C47—42no—
248C2×C47C2×C4×D411yescharacteristic
249C2×C47C2×C4×D411yescharacteristic
250C2×C47#51811yescharacteristic
251C2×C47D4211yescharacteristic
252C2×C47#54611yescharacteristic
253C2×C47#54611yescharacteristic
254C2×C47#55111yescharacteristic
255D47—24no—
256D47—24no—
257D47—42no—
258C2×#120—471no—
259C2×C4×D4—471no—
260C2×C4×D4—471no—
261C22×C22⋊C4—471no—
262C22×C22⋊C4—471no—
263#390—471no—
264#388—471no—
265#388D4711yescharacteristic, complemented
266#386—471no—
267#386—471no—
268#386—471no—
269#385—471no—
270#385—471no—
271C4×C22⋊C4—471no—
272C4×C22⋊C4—471no—
273C47#235811yescharacteristic, complemented, Sylow
274C25—471no—
275C22×D4—471no—
276C22×D4—471no—
277C22×D4—471no—
278C23×C4—471no—
279C23×C4—471no—
280C23×C4—471no—
281C23×C4—471no—
282C23×C4—471no—
283#120—478no—
284C4×D4—944no—
285C4×D4—944no—
286C2×C4⋊C4—471no—
287C2×C4⋊C4—471no—
288C2×C4⋊C4C2×D4711yescharacteristic, complemented
289C2×C22⋊C4—471no—
290C2×C22⋊C4—471no—
291C2×C22⋊C4—471no—
292C2×C22⋊C4—471no—
293C2×C22⋊C4—471no—
294C2×C22⋊C4—471no—
295C2×C22⋊C4—471no—
296C2×C22⋊C4—471no—
297C2×C22⋊C4—471no—
298C2×C22⋊C4—471no—
299C2×C22⋊C4—471no—
300C2×C22⋊C4—944no—
301C2×C22⋊C4—944no—
302C2×C22⋊C4C2×D4711yescharacteristic
303C2×C22⋊C4C2×D4711yescharacteristic
304C2×C22⋊C4C2×D4711yescharacteristic
305C2×C42—471no—
306C2×C42—471no—
307C2×C42C2×D4711yescharacteristic, complemented
308#95—471no—
309#95—471no—
310#95—471no—
311#95—471no—
312#95C2×D4711yescharacteristic, complemented
313#95C2×D4711yescharacteristic, complemented
314C24—471no—
315C24—471no—
316C24—471no—
317C24—474no—
318C24—942no—
319C24—942no—
320C24—942no—
321C24—942no—
322C24—1881no—
323C24—1881no—
324C24C22×D4711yescharacteristic
325C2×D4—474no—
326C2×D4—474no—
327C2×D4—474no—
328C2×D4—942no—
329C2×D4—942no—
330C2×D4—942no—
331C2×D4—942no—
332C2×D4—1881no—
333C2×D4—1881no—
334C22×C4—471no—
335C22×C4—471no—
336C22×C4—471no—
337C22×C4—471no—
338C22×C4—471no—
339C22×C4—942no—
340C22×C4—942no—
341C22×C4—942no—
342C22×C4—942no—
343C22×C4—942no—
344C22×C4—942no—
345C22×C4—942no—
346C22×C4—942no—
347C22×C4—942no—
348C22×C4—942no—
349C22×C4—1881no—
350C22×C4—1881no—
351C22×C4—1881no—
352C22×C4—1881no—
353C22×C4—1881no—
354C22×C4C22×D4711yescharacteristic
355C22×C4C22×D4711yescharacteristic
356C22×C4C22×D4711yescharacteristic
357C22×C4C22×D4711yescharacteristic
358C22×C4C22×D4711yescharacteristic
359C22×C4C22×D4711yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—942no—
362C4⋊C4—1881no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—474no—
366C22⋊C4—474no—
367C22⋊C4—474no—
368C22⋊C4—474no—
369C22⋊C4—942no—
370C22⋊C4—942no—
371C22⋊C4—942no—
372C22⋊C4—942no—
373C22⋊C4—942no—
374C22⋊C4—942no—
375C22⋊C4—1881no—
376C22⋊C4C4×D4714yescomplemented
377C42—22no—
378C42—942no—
379C42—1881no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—472no—
387C23—472no—
388C23—472no—
389C23—472no—
390C23—472no—
391C23—472no—
392C23—472no—
393C23—948no—
394C23—948no—
395C23—941no—
396C23—941no—
397C23—941no—
398C23—941no—
399C23—941no—
400C23—941no—
401C23—941no—
402C23—941no—
403C23—941no—
404C23—941no—
405C23—941no—
406C23—941no—
407C23—941no—
408C23—941no—
409C23—1884no—
410C23—1884no—
411C23—1884no—
412C23—1884no—
413C23—1884no—
414C23C2×C4×D4712yes—
415C23C23×D4711yescharacteristic
416D4—948no—
417D4—948no—
418D4—1884no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—472no—
434C2×C4—472no—
435C2×C4—472no—
436C2×C4—941no—
437C2×C4—941no—
438C2×C4—941no—
439C2×C4—941no—
440C2×C4—941no—
441C2×C4—941no—
442C2×C4—941no—
443C2×C4—941no—
444C2×C4—941no—
445C2×C4—941no—
446C2×C4—941no—
447C2×C4—941no—
448C2×C4—1884no—
449C2×C4—1884no—
450C2×C4—1884no—
451C2×C4—1884no—
452C2×C4—1884no—
453C2×C4C2×C4×D4712yes—
454C2×C4C2×C4×D4712yes—
455C2×C4D4×D4712yes—
456C2×C4D4×D4712yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—474no—
465C22—474no—
466C22—942no—
467C22—942no—
468C22—942no—
469C22—942no—
470C22—942no—
471C22—942no—
472C22—942no—
473C22—942no—
474C22—942no—
475C22—942no—
476C22—942no—
477C22—942no—
478C22—942no—
479C22—942no—
480C22—942no—
481C22—18816no—
482C22—1881no—
483C22—1881no—
484C22—1881no—
485C22—1881no—
486C22C22×C4×D4711yescharacteristic
487C22C2×D4×D4711yescharacteristic
488C22C2×D4×D4711yescharacteristic
489C22#41×D4711yescharacteristic
490C22#41×D4711yescharacteristic
491C22#1309407011yescharacteristic
492C22#1309407011yescharacteristic
493C4—22no—
494C4—22no—
495C4—22no—
496C4—22no—
497C4—41no—
498C4—41no—
499C4—942no—
500C4—942no—
501C4—942no—
502C4—1881no—
503C4—1881no—
504C2—42no—
505C2—944no—
506C2—944no—
507C2—1882no—
508C2C4×D4×D4711yescharacteristic
509C2C4×D4×D4711yescharacteristic
510C2#1568959711yescharacteristic
511C2#1568975711yescharacteristic
512C2#1568976511yescharacteristic
513C2#1568976611yescharacteristic
514C2#1568979811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#388C2
socleC23×C47C24
hypercenter#388D47
hypocenterC47#2358
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×C4×D188C2semidirect
3. C2×#13093986C2semidirect
4. C2×C22⋊C4×D47C2semidirect
5. C2×C22⋊C4×D47C2semidirect
6. #15689023C2semidirect
7. #15689016C2semidirect
8. #15689001C2semidirect
9. #15689001C2semidirect
10. #15688999C2semidirect
11. #15688997C2semidirect
12. #15688994C2semidirect
13. C4×(C2×D47)⋊C4C2semidirect
14. #15688970C2semidirect
15. C47×#388C2semidirect
24. C22×C4×D47C22semidirect
25. #13093994C4semidirect
28. C2×C4⋊Dic47C22semidirect
29. C2×Dic47⋊C4C22semidirect
38. C2×(C2×D47)⋊C4C22semidirect
39. C2×(C2×D47)⋊C4C22semidirect
40. C2×(C2×D47)⋊C4C22semidirect
43. C2×C4×Dic47C22semidirect
44. C2×C4×Dic47C22semidirect
45. C47⋊#95C22semidirect
46. C47⋊#95C22semidirect
47. C47⋊#95C22semidirect
48. C47⋊#95C22semidirect
49. C2×C4⋊C4×C47C22semidirect
53. C2×C42×C47C22semidirect
54. #95×C47C22semidirect
55. #95×C47C22semidirect
63. C23×D47C2×C4semidirect
75. C2×C22⋊D47C2×C4semidirect
85. C2×D188C2×C4semidirect
86. C2×D188C2×C4semidirect
105. C22⋊C4×C47C2×C4semidirect
114. (C2×D47)⋊C4C2×C4semidirect
115. (C2×D47)⋊C4C2×C4semidirect
116. (C2×D47)⋊C4D4semidirect
117. (C2×D47)⋊C4D4semidirect
233. C2×D47C4×D4semidirect
234. C2×D47C4×D4semidirect
265. #388D47semidirect
273. C47#2358semidirect
288. C2×C4⋊C4C2×D47semidirect
307. C2×C42C2×D47semidirect
312. #95C2×D47semidirect
313. #95C2×D47semidirect
376. C22⋊C4C4×D47semidirect