Finite Group Databasebeta

← C2×C47×#1854 #26060540

Subgroups — C2×C47×#1854 #26060540

Order 12032.

1662 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C47C211yesmaximal, characteristic
2C22×#107×C47C211yesmaximal, characteristic, complemented
3C22×#106×C47C211yesmaximal, characteristic, complemented
4C22×C22⋊C8×C47C211yesmaximal, characteristic
5C2×C47×#380C211yesmaximal, characteristic
6C47×#1854C218yesmaximal, direct product factor
7C2×C47×#340C211yesmaximal, characteristic, complemented
8C2×C47×#340C211yesmaximal, characteristic, complemented
9C24×C4×C47C2211yescharacteristic
10C23×C8×C47C2211yescharacteristic
11C23×C8×C47C2211yescharacteristic
12C2×#117×C47—22no—
13C2×#117×C47—24no—
14C2×#117×C47—24no—
15C2×#117×C47C2214yes—
16C22×C4⋊C4×C47C2211yescharacteristic
17C22×C4⋊C4×C47C2211yescharacteristic
18C22×C4⋊C4×C47C2211yescharacteristic
19C22×C4⋊C4×C47C2211yescharacteristic
20C22×C22⋊C4×C47—21no—
21C22×C22⋊C4×C47—21no—
22C22×C42×C47—21no—
23C2×#107×C47—24no—
24C2×#107×C47C2214yescomplemented
25C2×#106×C47—24no—
26C2×#106×C47C2214yescomplemented
27C2×C22⋊C8×C47C418yescomplemented
28C2×C22⋊C8×C47C2214yes—
29C47×#380—22no—
30C47×#380C2214yes—
31C2×#95×C47—21no—
32C47×#340C2214yescomplemented
33C47×#340C2214yescomplemented
34C25×C47D411yescharacteristic
35C23×C4×C47—22no—
36C23×C4×C47—22no—
37C23×C4×C47—22no—
38C23×C4×C47—22no—
39C23×C4×C47—21no—
40C23×C4×C47—21no—
41C23×C4×C47—21no—
42C23×C4×C47—21no—
43C23×C4×C47C2×C414yes—
44C23×C4×C47D412yes—
45C23×C4×C47D411yescharacteristic
46C23×C4×C47Q814yes—
47C23×C4×C47C2312yes—
48C23×C4×C47C2311yescharacteristic
49C22×C8×C47—22no—
50C22×C8×C47—22no—
51C22×C8×C47—22no—
52C22×C8×C47—22no—
53C22×C8×C47C2×C414yes—
54C22×C8×C47C2×C414yes—
55C22×C8×C47C2312yes—
56C22×C8×C47C2312yes—
57#117×C47—216no—
58#117×C47—28no—
59#117×C47—28no—
60C2×C4⋊C4×C47—21no—
61C2×C4⋊C4×C47—21no—
62C2×C4⋊C4×C47—22no—
63C2×C4⋊C4×C47—22no—
64C2×C4⋊C4×C47—22no—
65C2×C4⋊C4×C47—22no—
66C2×C4⋊C4×C47—22no—
67C2×C4⋊C4×C47—22no—
68C2×C4⋊C4×C47—21no—
69C2×C4⋊C4×C47—21no—
70C2×C4⋊C4×C47D414yes—
71C2×C4⋊C4×C47D414yes—
72C2×C4⋊C4×C47C2312yes—
73C2×C4⋊C4×C47C2312yes—
74C2×C4⋊C4×C47C2312yes—
75C2×C4⋊C4×C47C2312yes—
76C2×C22⋊C4×C47—28no—
77C2×C22⋊C4×C47—24no—
78C2×C22⋊C4×C47—24no—
79C2×C22⋊C4×C47—44no—
80C2×C42×C47—28no—
81C2×C42×C47—24no—
82#107×C47—28no—
83#106×C47—28no—
84C22⋊C8×C47C2×C4116yescomplemented
85#95×C47—24no—
86C24×C47—22no—
87C24×C47—22no—
88C24×C47—22no—
89C24×C47—22no—
90C24×C47—22no—
91C24×C47—22no—
92C24×C47C4⋊C414yes—
93C24×C47C2×D412yes—
94C24×C47C2×D411yescharacteristic
95C22×C4×C47—22no—
96C22×C4×C47—22no—
97C22×C4×C47—28no—
98C22×C4×C47—28no—
99C22×C4×C47—24no—
100C22×C4×C47—28no—
101C22×C4×C47—28no—
102C22×C4×C47—24no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—24no—
108C22×C4×C47—24no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—42no—
114C22×C4×C47—42no—
115C22×C4×C47—42no—
116C22×C4×C47—42no—
117C22×C4×C47—42no—
118C22×C4×C47—42no—
119C22×C4×C47—42no—
120C22×C4×C47—42no—
121C22×C4×C47—42no—
122C22×C4×C47—42no—
123C22×C4×C47C4⋊C414yes—
124C22×C4×C47C4⋊C418yes—
125C22×C4×C47C22×C414yes—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C2×D412yes—
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D412yes—
130C22×C4×C47C2×D412yes—
131C22×C4×C47C2×Q814yes—
132C22×C4×C47C2×Q812yes—
133C22×C4×C47#4112yes—
134C22×C4×C47#4112yes—
135C22×C4×C47C2411yescharacteristic
136C2×C8×C47—28no—
137C2×C8×C47—28no—
138C2×C8×C47—22no—
139C2×C8×C47—22no—
140C2×C8×C47—22no—
141C2×C8×C47—22no—
142C2×C8×C47C22×C414yes—
143C2×C8×C47C22×C414yes—
144C4⋊C4×C47—24no—
145C4⋊C4×C47—24no—
146C4⋊C4×C47—22no—
147C4⋊C4×C47—22no—
148C4⋊C4×C47—22no—
149C4⋊C4×C47—22no—
150C4⋊C4×C47—22no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—42no—
153C4⋊C4×C47—42no—
154C4⋊C4×C47C2×D414yes—
155C4⋊C4×C47C2×D414yes—
156C22⋊C4×C47—216no—
157C22⋊C4×C47—48no—
158C42×C47—216no—
159C23×C47—22no—
160C23×C47—22no—
161C23×C47—22no—
162C23×C47—22no—
163C23×C47—22no—
164C23×C47—22no—
165C23×C47—28no—
166C23×C47—28no—
167C23×C47—28no—
168C23×C47—44no—
169C23×C47—44no—
170C23×C47—44no—
171C23×C47—44no—
172C23×C47C2×C4⋊C414yes—
173C23×C47C2×C4⋊C412yes—
174C23×C47#12012yes—
175C23×C47#12312yes—
176C23×C47#13512yes—
177C23×C47#13512yes—
178C23×C47AGL(1,ℤ/8)12yes—
179C23×C47#13712yes—
180C23×C47C22×D411yescharacteristic
181C2×C4×C47—22no—
182C2×C4×C47—22no—
183C2×C4×C47—28no—
184C2×C4×C47—24no—
185C2×C4×C47—24no—
186C2×C4×C47—24no—
187C2×C4×C47—24no—
188C2×C4×C47—216no—
189C2×C4×C47—24no—
190C2×C4×C47—24no—
191C2×C4×C47—42no—
192C2×C4×C47—42no—
193C2×C4×C47—42no—
194C2×C4×C47—42no—
195C2×C4×C47—48no—
196C2×C4×C47—48no—
197C2×C4×C47—42no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—84no—
204C2×C4×C47—84no—
205C2×C4×C47C2×C4⋊C414yes—
206C2×C4×C47C2×C4⋊C412yes—
207C2×C4×C47C4×D414yes—
208C2×C4×C47C4×D414yes—
209C2×C4×C47#12012yes—
210C2×C4×C47C22⋊Q814yes—
211C2×C4×C47C22⋊Q814yes—
212C2×C4×C47#12312yes—
213C2×C4×C47C23×C411yescharacteristic
214C2×C4×C47C22×D411yescharacteristic
215C2×C4×C47C22×D411yescharacteristic
216C2×C4×C47C22×Q811yescharacteristic
217C2×C4×C47C2×#4111yescharacteristic
218C2×C4×C47C2×#4111yescharacteristic
219C8×C47—24no—
220C8×C47—24no—
221C2×#1854C4711yesmaximal, characteristic, direct product factor, Sylow
222C22×C47—24no—
223C22×C47—24no—
224C22×C47—24no—
225C22×C47—42no—
226C22×C47—42no—
227C22×C47—416no—
228C22×C47—42no—
229C22×C47—42no—
230C22×C47#38514yes—
231C22×C47#42714yes—
232C22×C47#42814yes—
233C22×C47#44914yes—
234C22×C47#45214yes—
235C22×C47#48214yes—
236C22×C47#48514yes—
237C22×C47C22×C4⋊C411yescharacteristic
238C22×C47C2×#12011yescharacteristic
239C22×C47C2×#12311yescharacteristic
240C22×C47C2×#13511yescharacteristic
241C22×C47C2×#13511yescharacteristic
242C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
243C22×C47C2×#13711yescharacteristic
244C4×C47—24no—
245C4×C47—44no—
246C4×C47—44no—
247C4×C47—82no—
248C4×C47—82no—
249C4×C47#38514yes—
250C4×C47C2×C4×D411yescharacteristic
251C4×C47C2×C4×D411yescharacteristic
252C4×C47C2×C22⋊Q811yescharacteristic
253C4×C47C2×C22⋊Q811yescharacteristic
254C22×#117C2×C4711yescharacteristic
255C22×#107C2×C4711yescharacteristic, complemented
256C22×#106C2×C4711yescharacteristic, complemented
257C22×C22⋊C8C2×C4711yescharacteristic
258C2×#380C2×C4711yescharacteristic
259#1854C2×C4718yesdirect product factor
260C2×#340C2×C4711yescharacteristic, complemented
261C2×#340C2×C4711yescharacteristic, complemented
262C2×C47—44no—
263C2×C47#185418yesdirect product factor
264C2×C47C2×#38511yescharacteristic
265C2×C47C2×#42711yescharacteristic
266C2×C47C2×#42811yescharacteristic
267C2×C47C2×#44911yescharacteristic
268C2×C47C2×#45211yescharacteristic
269C2×C47C2×#48211yescharacteristic
270C2×C47C2×#48511yescharacteristic
271C24×C4C22×C4711yescharacteristic
272C23×C8C22×C4711yescharacteristic
273C23×C8C22×C4711yescharacteristic
274C2×#117—22no—
275C2×#117—24no—
276C2×#117—24no—
277C2×#117C22×C4714yes—
278C22×C4⋊C4C22×C4711yescharacteristic
279C22×C4⋊C4C22×C4711yescharacteristic
280C22×C4⋊C4C22×C4711yescharacteristic
281C22×C4⋊C4C22×C4711yescharacteristic
282C22×C22⋊C4—21no—
283C22×C22⋊C4—21no—
284C22×C42—21no—
285C2×#107—24no—
286C2×#107C22×C4714yescomplemented
287C2×#106—24no—
288C2×#106C22×C4714yescomplemented
289C2×C22⋊C8C4×C4718yescomplemented
290C2×C22⋊C8C22×C4714yes—
291#380—22no—
292#380C22×C4714yes—
293C2×#95—21no—
294#340C22×C4714yescomplemented
295#340C22×C4714yescomplemented
296C47C2×#185411yescharacteristic, direct product factor, Sylow
297C25D4×C4711yescharacteristic
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4C2×C4×C4714yes—
307C23×C4D4×C4712yes—
308C23×C4D4×C4711yescharacteristic
309C23×C4Q8×C4714yes—
310C23×C4C23×C4712yes—
311C23×C4C23×C4711yescharacteristic
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8C2×C4×C4714yes—
317C22×C8C2×C4×C4714yes—
318C22×C8C23×C4712yes—
319C22×C8C23×C4712yes—
320#117—216no—
321#117—28no—
322#117—28no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4D4×C4714yes—
334C2×C4⋊C4D4×C4714yes—
335C2×C4⋊C4C23×C4712yes—
336C2×C4⋊C4C23×C4712yes—
337C2×C4⋊C4C23×C4712yes—
338C2×C4⋊C4C23×C4712yes—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—44no—
343C2×C42—28no—
344C2×C42—24no—
345#107—28no—
346#106—28no—
347C22⋊C8C2×C4×C47116yescomplemented
348#95—24no—
349C24—22no—
350C24—22no—
351C24—22no—
352C24—22no—
353C24—22no—
354C24—22no—
355C24C4⋊C4×C4714yes—
356C24C2×D4×C4712yes—
357C24C2×D4×C4711yescharacteristic
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—28no—
361C22×C4—28no—
362C22×C4—24no—
363C22×C4—28no—
364C22×C4—28no—
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4C4⋊C4×C4714yes—
387C22×C4C4⋊C4×C4718yes—
388C22×C4C22×C4×C4714yes—
389C22×C4C22×C4×C4712yes—
390C22×C4C2×D4×C4712yes—
391C22×C4C2×D4×C4711yescharacteristic
392C22×C4C2×D4×C4712yes—
393C22×C4C2×D4×C4712yes—
394C22×C4C2×Q8×C4714yes—
395C22×C4C2×Q8×C4712yes—
396C22×C4#41×C4712yes—
397C22×C4#41×C4712yes—
398C22×C4C24×C4711yescharacteristic
399C2×C8—28no—
400C2×C8—28no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8C22×C4×C4714yes—
406C2×C8C22×C4×C4714yes—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—42no—
416C4⋊C4—42no—
417C4⋊C4C2×D4×C4714yes—
418C4⋊C4C2×D4×C4714yes—
419C22⋊C4—216no—
420C22⋊C4—48no—
421C42—216no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—28no—
429C23—28no—
430C23—28no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23C2×C4⋊C4×C4714yes—
436C23C2×C4⋊C4×C4712yes—
437C23#120×C4712yes—
438C23#123×C4712yes—
439C23#135×C4712yes—
440C23#135×C4712yes—
441C23AGL(1,ℤ/8)×C4712yes—
442C23#137×C4712yes—
443C23C22×D4×C4711yescharacteristic
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—28no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—216no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—48no—
455C2×C4—48no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—84no—
467C2×C4—84no—
468C2×C4C2×C4⋊C4×C4714yes—
469C2×C4C2×C4⋊C4×C4712yes—
470C2×C4C4×D4×C4714yes—
471C2×C4C4×D4×C4714yes—
472C2×C4#120×C4712yes—
473C2×C4C22⋊Q8×C4714yes—
474C2×C4C22⋊Q8×C4714yes—
475C2×C4#123×C4712yes—
476C2×C4C23×C4×C4711yescharacteristic
477C2×C4C22×D4×C4711yescharacteristic
478C2×C4C22×D4×C4711yescharacteristic
479C2×C4C22×Q8×C4711yescharacteristic
480C2×C4C2×#41×C4711yescharacteristic
481C2×C4C2×#41×C4711yescharacteristic
482C8—24no—
483C8—24no—
484C22—24no—
485C22—24no—
486C22—24no—
487C22—42no—
488C22—42no—
489C22—416no—
490C22—42no—
491C22—42no—
492C22C47×#38514yes—
493C22C47×#42714yes—
494C22C47×#42814yes—
495C22C47×#44914yes—
496C22C47×#45214yes—
497C22C47×#48214yes—
498C22C47×#48514yes—
499C22C22×C4⋊C4×C4711yescharacteristic
500C22C2×#120×C4711yescharacteristic
501C22C2×#123×C4711yescharacteristic
502C22C2×#135×C4711yescharacteristic
503C22C2×#135×C4711yescharacteristic
504C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
505C22C2×#137×C4711yescharacteristic
506C4—24no—
507C4—44no—
508C4—44no—
509C4—82no—
510C4—82no—
511C4C47×#38514yes—
512C4C2×C4×D4×C4711yescharacteristic
513C4C2×C4×D4×C4711yescharacteristic
514C4C2×C22⋊Q8×C4711yescharacteristic
515C4C2×C22⋊Q8×C4711yescharacteristic
516C2—44no—
517C2C47×#185418yesdirect product factor
518C2C2×C47×#38511yescharacteristic
519C2C2×C47×#42711yescharacteristic
520C2C2×C47×#42811yescharacteristic
521C2C2×C47×#44911yescharacteristic
522C2C2×C47×#45211yescharacteristic
523C2C2×C47×#48211yescharacteristic
524C2C2×C47×#48511yescharacteristic
subgroupG/H
center, socleC24×C47C2×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
prime radicalC25×C47D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#107×C47C2semidirect
3. C22×#106×C47C2semidirect
6. C47×#1854C2direct (N × H)
7. C2×C47×#340C2semidirect
8. C2×C47×#340C2semidirect
24. C2×#107×C47C22semidirect
26. C2×#106×C47C22semidirect
27. C2×C22⋊C8×C47C4semidirect
32. C47×#340C22semidirect
33. C47×#340C22semidirect
84. C22⋊C8×C47C2×C4semidirect
221. C2×#1854C47direct (N × H)
255. C22×#107C2×C47semidirect
256. C22×#106C2×C47semidirect
259. #1854C2×C47direct (N × H)
260. C2×#340C2×C47semidirect
261. C2×#340C2×C47semidirect
263. C2×C47#1854direct (N × H)
286. C2×#107C22×C47semidirect
288. C2×#106C22×C47semidirect
289. C2×C22⋊C8C4×C47semidirect
294. #340C22×C47semidirect
295. #340C22×C47semidirect
296. C47C2×#1854direct (N × H)
347. C22⋊C8C2×C4×C47semidirect
517. C2C47×#1854direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#117×C472
C22×#107×C472
C22×#106×C472
C22×C22⋊C8×C472
C2×C47×#3802
C47×#18542
C2×C47×#3402
C2×#185447