Finite Group Databasebeta

← C2×C47×#3518 #26102489

Subgroups — C2×C47×#3518 #26102489

Order 12032.

7118 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3518C2132yesmaximal, direct product factor
2C2×Q82×C47C211yesmaximal, characteristic, complemented
3C2×C47×#556C216yesmaximal, complemented
4C2×C47×#556C213yesmaximal, complemented
5C2×C47×#555C213yesmaximal, complemented
6C2×D4×Q8×C47C211yesmaximal, characteristic, complemented
7C2×C47×#548C212yesmaximal, complemented
8C2×C47×#542C216yesmaximal, complemented
9C2×C47×#533C213yesmaximal, complemented
10C2×C47×#529C213yesmaximal, complemented
11C2×C47×#519C212yesmaximal, complemented
12C2×C4×#41×C47C211yesmaximal, characteristic, complemented
13C22×#41×C47C2211yescharacteristic
14C23×Q8×C47C2212yes—
15Q82×C47C22116yescomplemented
16C47×#556C22196yescomplemented
17C47×#556C22148yescomplemented
18C47×#555C22148yescomplemented
19D4×Q8×C47C22116yescomplemented
20C47×#548C22132yescomplemented
21C47×#542C22196yescomplemented
22C47×#533C22148yescomplemented
23C2×C4⋊Q8×C47C2213yes—
24C2×C4⋊Q8×C47C2213yes—
25C2×C4⋊Q8×C47C2216yes—
26C47×#529C22148yescomplemented
27C2×#126×C47C2216yes—
28C2×#126×C47C22112yes—
29C2×#125×C47C2213yes—
30C2×#124×C47C2211yescharacteristic
31C2×#124×C47C2216yes—
32C2×#124×C47C22112yes—
33C2×#123×C47C2216yes—
34C2×C22⋊Q8×C47C2213yes—
35C2×C22⋊Q8×C47C2216yes—
36C2×C22⋊Q8×C47C2216yes—
37C2×C22⋊Q8×C47C2216yes—
38C2×#121×C47C2213yes—
39C2×#121×C47C2216yes—
40C47×#519C22132yescomplemented
41C4×#41×C47C22116yescomplemented
42C2×C4×Q8×C47C2211yescharacteristic
43C2×C4×Q8×C47C2211yescharacteristic
44C2×C4×Q8×C47C2216yes—
45C2×C4×Q8×C47C2212yes—
46C2×C4×Q8×C47C2216yes—
47C2×C4×Q8×C47C2213yes—
48C2×C4×Q8×C47C2216yes—
49C2×C4×D4×C47C2213yes—
50C2×C4×D4×C47C2213yes—
51C2×C4×D4×C47C2216yes—
52C2×C4×D4×C47C2213yes—
53C2×#117×C47C2213yes—
54C2×#117×C47C2216yes—
55C2×#117×C47C2216yes—
56C2×#117×C47C2216yes—
57C22×C42×C47C2213yes—
58C2×#41×C47—28no—
59C2×#41×C47C2318yes—
60C22×Q8×C47—216no—
61C22×Q8×C47C2311yescharacteristic
62C22×Q8×C47C2316yes—
63C22×Q8×C47C23116yes—
64C22×Q8×C47C2316yes—
65C22×Q8×C47C2311yescharacteristic
66C22×D4×C47C2311yescharacteristic
67C22×D4×C47C2313yes—
68C22×D4×C47C2316yes—
69C23×C4×C47C2313yes—
70C23×C4×C47C2313yes—
71C23×C4×C47C2316yes—
72C23×C4×C47C2313yes—
73C4⋊Q8×C47C23124yes—
74C4⋊Q8×C47C23124yes—
75C4⋊Q8×C47C23148yes—
76#126×C47C23148yes—
77#126×C47C23196yes—
78#125×C47C23124yes—
79#124×C47C2318yes—
80#124×C47C23148yes—
81#124×C47C23196yes—
82#123×C47C23148yes—
83C22⋊Q8×C47C23124yes—
84C22⋊Q8×C47C23148yes—
85C22⋊Q8×C47C23148yes—
86C22⋊Q8×C47C23148yes—
87#121×C47C23124yes—
88#121×C47C23148yes—
89C4×Q8×C47C2318yes—
90C4×Q8×C47C2318yes—
91C4×Q8×C47C23148yes—
92C4×Q8×C47C23116yes—
93C4×Q8×C47C23148yes—
94C4×Q8×C47C23124yes—
95C4×Q8×C47C23148yes—
96C4×D4×C47C23124yes—
97C4×D4×C47C23124yes—
98C4×D4×C47C23148yes—
99C4×D4×C47C23124yes—
100#117×C47C23124yes—
101#117×C47C23148yes—
102#117×C47C23148yes—
103#117×C47C23148yes—
104C2×C4⋊C4×C47C2313yes—
105C2×C4⋊C4×C47C2313yes—
106C2×C4⋊C4×C47C2313yes—
107C2×C4⋊C4×C47C2313yes—
108C2×C4⋊C4×C47C2316yes—
109C2×C4⋊C4×C47C2316yes—
110C2×C4⋊C4×C47C2316yes—
111C2×C4⋊C4×C47C2316yes—
112C2×C4⋊C4×C47C2316yes—
113C2×C4⋊C4×C47C2316yes—
114C2×C22⋊C4×C47C2316yes—
115C2×C22⋊C4×C47C2312yes—
116C2×C22⋊C4×C47C2316yes—
117C2×C22⋊C4×C47C23112yes—
118C2×C22⋊C4×C47C2312yes—
119C2×C22⋊C4×C47C2316yes—
120C2×C22⋊C4×C47C2316yes—
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2313yes—
123C2×C42×C47C2313yes—
124C2×C42×C47C2313yes—
125C2×C42×C47C23124yes—
126C2×C42×C47C23112yes—
127C2×C42×C47C2316yes—
128C24×C47C2412yes—
129C24×C47C2413yes—
130#41×C47—232no—
131C2×Q8×C47—264no—
132C2×Q8×C47—224no—
133C2×Q8×C47—24no—
134C2×Q8×C47—412no—
135C2×Q8×C47#4118yes—
136C2×Q8×C47C2414yes—
137C2×Q8×C47C24124yes—
138C2×Q8×C47C24124yes—
139C2×Q8×C47C2414yes—
140C2×D4×C47—212no—
141C2×D4×C47—24no—
142C2×D4×C47—412no—
143C2×D4×C47C2414yes—
144C2×D4×C47C24112yes—
145C2×D4×C47C24124yes—
146C22×C4×C47—224no—
147C22×C4×C47—212no—
148C22×C4×C47—212no—
149C22×C4×C47—46no—
150C22×C4×C47C24112yes—
151C22×C4×C47C24112yes—
152C22×C4×C47C24124yes—
153C22×C4×C47C2413yes—
154C22×C4×C47C2411yescharacteristic
155C22×C4×C47C2411yescharacteristic
156C22×C4×C47C2412yes—
157C22×C4×C47C2416yes—
158C22×C4×C47C2416yes—
159C22×C4×C47C2413yes—
160C22×C4×C47C24112yes—
161C22×C4×C47C2413yes—
162C22×C4×C47C2411yescharacteristic
163C4⋊C4×C47C24112yes—
164C4⋊C4×C47C24112yes—
165C4⋊C4×C47C24112yes—
166C4⋊C4×C47C24112yes—
167C4⋊C4×C47C24124yes—
168C4⋊C4×C47C24124yes—
169C4⋊C4×C47C24124yes—
170C4⋊C4×C47C24124yes—
171C4⋊C4×C47C24124yes—
172C4⋊C4×C47C24124yes—
173C22⋊C4×C47C24124yes—
174C22⋊C4×C47C2418yes—
175C22⋊C4×C47C24124yes—
176C22⋊C4×C47C24148yes—
177C22⋊C4×C47C2418yes—
178C22⋊C4×C47C24124yes—
179C22⋊C4×C47C24124yes—
180C42×C47C2414yes—
181C42×C47C24112yes—
182C42×C47C24112yes—
183C42×C47C24112yes—
184C42×C47C24148yes—
185C42×C47C24124yes—
186C23×C47—24no—
187C23×C47—26no—
188C23×C47—26no—
189C23×C47—24no—
190C23×C47—26no—
191C23×C47—24no—
192C23×C47C2514yes—
193C23×C47C2516yes—
194C23×C47C2511yescharacteristic
195Q8×C47—248no—
196Q8×C47—28no—
197Q8×C47—424no—
198Q8×C47C2×#41116yes—
199D4×C47—224no—
200D4×C47—28no—
201D4×C47—424no—
202C2×C4×C47—22no—
203C2×C4×C47—212no—
204C2×C4×C47—26no—
205C2×C4×C47—24no—
206C2×C4×C47—22no—
207C2×C4×C47—26no—
208C2×C4×C47—212no—
209C2×C4×C47—248no—
210C2×C4×C47—224no—
211C2×C4×C47—224no—
212C2×C4×C47—412no—
213C2×C4×C47C2×#41112yes—
214C2×C4×C472−1+414yes—
215C2×C4×C47C2516yes—
216C2×C4×C47C2512yes—
217C2×C4×C47C2512yes—
218C2×C4×C47C2514yes—
219C2×C4×C47C25112yes—
220C2×C4×C47C25112yes—
221C2×C4×C47C2516yes—
222C2×C4×C47C2516yes—
223C2×C4×C47C2512yes—
224C2×#3518C4711yesmaximal, characteristic, direct product factor, Sylow
225C22×C47—24no—
226C22×C47—26no—
227C22×C47—26no—
228C22×C47—24no—
229C22×C47—26no—
230C22×C47—24no—
231C22×C47—48no—
232C22×C47—412no—
233C22×C47C22×#4112yes—
234C22×C47C2×2−1+412yes—
235C22×C47#58512yes—
236C22×C47C2611yescharacteristic
237C4×C47—22no—
238C4×C47—212no—
239C4×C47—26no—
240C4×C47—24no—
241C4×C47—22no—
242C4×C47—26no—
243C4×C47—212no—
244C4×C47C22×#41112yes—
245C4×C47C2×2−1+414yes—
246#3518C2×C47132yesdirect product factor
247C2×Q82C2×C4711yescharacteristic, complemented
248C2×#556C2×C4716yescomplemented
249C2×#556C2×C4713yescomplemented
250C2×#555C2×C4713yescomplemented
251C2×D4×Q8C2×C4711yescharacteristic, complemented
252C2×#548C2×C4712yescomplemented
253C2×#542C2×C4716yescomplemented
254C2×#533C2×C4713yescomplemented
255C2×#529C2×C4713yescomplemented
256C2×#519C2×C4712yescomplemented
257C2×C4×#41C2×C4711yescharacteristic, complemented
258C2×C47—44no—
259C2×C47—46no—
260C2×C47#351814yesdirect product factor
261C2×C47C23×#4111yescharacteristic
262C2×C47C22×2−1+411yescharacteristic
263C2×C47C2×#58511yescharacteristic
264C22×#41C22×C4711yescharacteristic
265C23×Q8C22×C4712yes—
266Q82C22×C47116yescomplemented
267#556C22×C47196yescomplemented
268#556C22×C47148yescomplemented
269#555C22×C47148yescomplemented
270D4×Q8C22×C47116yescomplemented
271#548C22×C47132yescomplemented
272#542C22×C47196yescomplemented
273#533C22×C47148yescomplemented
274C2×C4⋊Q8C22×C4713yes—
275C2×C4⋊Q8C22×C4713yes—
276C2×C4⋊Q8C22×C4716yes—
277#529C22×C47148yescomplemented
278C2×#126C22×C4716yes—
279C2×#126C22×C47112yes—
280C2×#125C22×C4713yes—
281C2×#124C22×C4711yescharacteristic
282C2×#124C22×C4716yes—
283C2×#124C22×C47112yes—
284C2×#123C22×C4716yes—
285C2×C22⋊Q8C22×C4713yes—
286C2×C22⋊Q8C22×C4716yes—
287C2×C22⋊Q8C22×C4716yes—
288C2×C22⋊Q8C22×C4716yes—
289C2×#121C22×C4713yes—
290C2×#121C22×C4716yes—
291#519C22×C47132yescomplemented
292C4×#41C22×C47116yescomplemented
293C2×C4×Q8C22×C4711yescharacteristic
294C2×C4×Q8C22×C4711yescharacteristic
295C2×C4×Q8C22×C4716yes—
296C2×C4×Q8C22×C4712yes—
297C2×C4×Q8C22×C4716yes—
298C2×C4×Q8C22×C4713yes—
299C2×C4×Q8C22×C4716yes—
300C2×C4×D4C22×C4713yes—
301C2×C4×D4C22×C4713yes—
302C2×C4×D4C22×C4716yes—
303C2×C4×D4C22×C4713yes—
304C2×#117C22×C4713yes—
305C2×#117C22×C4716yes—
306C2×#117C22×C4716yes—
307C2×#117C22×C4716yes—
308C22×C42C22×C4713yes—
309C47C2×#351811yescharacteristic, direct product factor, Sylow
310C2×#41—28no—
311C2×#41C23×C4718yes—
312C22×Q8—216no—
313C22×Q8C23×C4711yescharacteristic
314C22×Q8C23×C4716yes—
315C22×Q8C23×C47116yes—
316C22×Q8C23×C4716yes—
317C22×Q8C23×C4711yescharacteristic
318C22×D4C23×C4711yescharacteristic
319C22×D4C23×C4713yes—
320C22×D4C23×C4716yes—
321C23×C4C23×C4716yes—
322C23×C4C23×C4713yes—
323C23×C4C23×C4713yes—
324C23×C4C23×C4713yes—
325C4⋊Q8C23×C47124yes—
326C4⋊Q8C23×C47124yes—
327C4⋊Q8C23×C47148yes—
328#126C23×C47148yes—
329#126C23×C47196yes—
330#125C23×C47124yes—
331#124C23×C4718yes—
332#124C23×C47148yes—
333#124C23×C47196yes—
334#123C23×C47148yes—
335C22⋊Q8C23×C47124yes—
336C22⋊Q8C23×C47148yes—
337C22⋊Q8C23×C47148yes—
338C22⋊Q8C23×C47148yes—
339#121C23×C47124yes—
340#121C23×C47148yes—
341C4×Q8C23×C4718yes—
342C4×Q8C23×C4718yes—
343C4×Q8C23×C47148yes—
344C4×Q8C23×C47116yes—
345C4×Q8C23×C47148yes—
346C4×Q8C23×C47124yes—
347C4×Q8C23×C47148yes—
348C4×D4C23×C47124yes—
349C4×D4C23×C47124yes—
350C4×D4C23×C47148yes—
351C4×D4C23×C47124yes—
352#117C23×C47124yes—
353#117C23×C47148yes—
354#117C23×C47148yes—
355#117C23×C47148yes—
356C2×C4⋊C4C23×C4713yes—
357C2×C4⋊C4C23×C4713yes—
358C2×C4⋊C4C23×C4713yes—
359C2×C4⋊C4C23×C4713yes—
360C2×C4⋊C4C23×C4716yes—
361C2×C4⋊C4C23×C4716yes—
362C2×C4⋊C4C23×C4716yes—
363C2×C4⋊C4C23×C4716yes—
364C2×C4⋊C4C23×C4716yes—
365C2×C4⋊C4C23×C4716yes—
366C2×C22⋊C4C23×C4716yes—
367C2×C22⋊C4C23×C4712yes—
368C2×C22⋊C4C23×C4716yes—
369C2×C22⋊C4C23×C47112yes—
370C2×C22⋊C4C23×C4712yes—
371C2×C22⋊C4C23×C4716yes—
372C2×C22⋊C4C23×C4716yes—
373C2×C42C23×C4713yes—
374C2×C42C23×C47112yes—
375C2×C42C23×C4713yes—
376C2×C42C23×C4716yes—
377C2×C42C23×C4713yes—
378C2×C42C23×C47124yes—
379C2×C42C23×C4711yescharacteristic
380C24C24×C4712yes—
381C24C24×C4713yes—
382#41—232no—
383C2×Q8—264no—
384C2×Q8—224no—
385C2×Q8—24no—
386C2×Q8—412no—
387C2×Q8#41×C4718yes—
388C2×Q8C24×C4714yes—
389C2×Q8C24×C47124yes—
390C2×Q8C24×C47124yes—
391C2×Q8C24×C4714yes—
392C2×D4—212no—
393C2×D4—24no—
394C2×D4—412no—
395C2×D4C24×C4714yes—
396C2×D4C24×C47112yes—
397C2×D4C24×C47124yes—
398C22×C4—224no—
399C22×C4—212no—
400C22×C4—212no—
401C22×C4—46no—
402C22×C4C24×C4713yes—
403C22×C4C24×C4711yescharacteristic
404C22×C4C24×C4711yescharacteristic
405C22×C4C24×C4712yes—
406C22×C4C24×C4716yes—
407C22×C4C24×C4716yes—
408C22×C4C24×C4713yes—
409C22×C4C24×C47112yes—
410C22×C4C24×C47112yes—
411C22×C4C24×C47124yes—
412C22×C4C24×C47112yes—
413C22×C4C24×C4713yes—
414C22×C4C24×C4711yescharacteristic
415C4⋊C4C24×C47112yes—
416C4⋊C4C24×C47112yes—
417C4⋊C4C24×C47112yes—
418C4⋊C4C24×C47112yes—
419C4⋊C4C24×C47124yes—
420C4⋊C4C24×C47124yes—
421C4⋊C4C24×C47124yes—
422C4⋊C4C24×C47124yes—
423C4⋊C4C24×C47124yes—
424C4⋊C4C24×C47124yes—
425C22⋊C4C24×C47124yes—
426C22⋊C4C24×C4718yes—
427C22⋊C4C24×C47124yes—
428C22⋊C4C24×C47148yes—
429C22⋊C4C24×C4718yes—
430C22⋊C4C24×C47124yes—
431C22⋊C4C24×C47124yes—
432C42C24×C4714yes—
433C42C24×C47112yes—
434C42C24×C47112yes—
435C42C24×C47112yes—
436C42C24×C47148yes—
437C42C24×C47124yes—
438C23—24no—
439C23—26no—
440C23—26no—
441C23—24no—
442C23—26no—
443C23—24no—
444C23C25×C4714yes—
445C23C25×C4716yes—
446C23C25×C4711yescharacteristic
447Q8—248no—
448Q8—28no—
449Q8—424no—
450Q8C2×#41×C47116yes—
451D4—224no—
452D4—28no—
453D4—424no—
454C2×C4—22no—
455C2×C4—212no—
456C2×C4—26no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—26no—
460C2×C4—212no—
461C2×C4—248no—
462C2×C4—224no—
463C2×C4—224no—
464C2×C4—412no—
465C2×C4C2×#41×C47112yes—
466C2×C42−1+4×C4714yes—
467C2×C4C25×C4716yes—
468C2×C4C25×C4712yes—
469C2×C4C25×C4712yes—
470C2×C4C25×C4714yes—
471C2×C4C25×C47112yes—
472C2×C4C25×C47112yes—
473C2×C4C25×C4716yes—
474C2×C4C25×C4716yes—
475C2×C4C25×C4712yes—
476C22—24no—
477C22—26no—
478C22—26no—
479C22—24no—
480C22—26no—
481C22—24no—
482C22—48no—
483C22—412no—
484C22C22×#41×C4712yes—
485C22C2×2−1+4×C4712yes—
486C22C47×#58512yes—
487C22C26×C4711yescharacteristic
488C4—22no—
489C4—212no—
490C4—26no—
491C4—24no—
492C4—22no—
493C4—26no—
494C4—212no—
495C4C22×#41×C47112yes—
496C4C2×2−1+4×C4714yes—
497C2—44no—
498C2—46no—
499C2C47×#351814yesdirect product factor
500C2C23×#41×C4711yescharacteristic
501C2C22×2−1+4×C4711yescharacteristic
502C2C2×C47×#58511yescharacteristic
subgroupG/H
center, socleC23×C47C25
commutator, Frattini, cosocleC22C26×C47
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3518C2direct (N × H)
2. C2×Q82×C47C2semidirect
3. C2×C47×#556C2semidirect
4. C2×C47×#556C2semidirect
5. C2×C47×#555C2semidirect
6. C2×D4×Q8×C47C2semidirect
7. C2×C47×#548C2semidirect
8. C2×C47×#542C2semidirect
9. C2×C47×#533C2semidirect
10. C2×C47×#529C2semidirect
11. C2×C47×#519C2semidirect
12. C2×C4×#41×C47C2semidirect
15. Q82×C47C22semidirect
16. C47×#556C22semidirect
17. C47×#556C22semidirect
18. C47×#555C22semidirect
19. D4×Q8×C47C22semidirect
20. C47×#548C22semidirect
21. C47×#542C22semidirect
22. C47×#533C22semidirect
26. C47×#529C22semidirect
40. C47×#519C22semidirect
41. C4×#41×C47C22semidirect
224. C2×#3518C47direct (N × H)
246. #3518C2×C47direct (N × H)
247. C2×Q82C2×C47semidirect
248. C2×#556C2×C47semidirect
249. C2×#556C2×C47semidirect
250. C2×#555C2×C47semidirect
251. C2×D4×Q8C2×C47semidirect
252. C2×#548C2×C47semidirect
253. C2×#542C2×C47semidirect
254. C2×#533C2×C47semidirect
255. C2×#529C2×C47semidirect
256. C2×#519C2×C47semidirect
257. C2×C4×#41C2×C47semidirect
260. C2×C47#3518direct (N × H)
266. Q82C22×C47semidirect
267. #556C22×C47semidirect
268. #556C22×C47semidirect
269. #555C22×C47semidirect
270. D4×Q8C22×C47semidirect
271. #548C22×C47semidirect
272. #542C22×C47semidirect
273. #533C22×C47semidirect
277. #529C22×C47semidirect
291. #519C22×C47semidirect
292. C4×#41C22×C47semidirect
309. C47C2×#3518direct (N × H)
499. C2C47×#3518direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C47×#35182
C2×Q82×C472
C2×C47×#5562
C2×C47×#5552
C2×D4×Q8×C472
C2×C47×#5482
C2×C47×#5422
C2×C47×#5332
C2×C47×#5292
C2×C47×#5192
C2×C4×#41×C472
C2×#351847