Finite Group Databasebeta

← C47×#10404 #26050102

Subgroups — C47×#10404 #26050102

Order 12032.

602 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2639C211yesmaximal, characteristic
2C47×#1874C211yesmaximal, characteristic
3C47×#1872C211yesmaximal, characteristic, complemented
4C2×C47×#328C211yesmaximal, characteristic, complemented
5C2×C47×#327C211yesmaximal, characteristic
6C47×#1442C211yesmaximal, characteristic, complemented
7C47×#1280C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C47C2211yescharacteristic
9C2×#121×C47C2211yescharacteristic
10C22×C4⋊C4×C47C2211yescharacteristic
11C2×#103×C47—21no—
12C2×#102×C47—21no—
13C2×C22⋊C8×C47C2211yescharacteristic
14C2×C22⋊C8×C47C2211yescharacteristic
15C47×#400—21no—
16C47×#397—21no—
17C47×#394—21no—
18C47×#393—21no—
19C47×#386—21no—
20C47×#386—21no—
21C2×#95×C47—21no—
22C2×#95×C47—21no—
23C2×#95×C47C2211yescharacteristic
24C2×#95×C47C2211yescharacteristic
25C47×#340—21no—
26C47×#340—21no—
27C47×#328—22no—
28C47×#327—22no—
29C22×Q8×C47D411yescharacteristic
30C22×D4×C47—21no—
31C22×D4×C47D411yescharacteristic
32C23×C4×C47—21no—
33C23×C4×C47—21no—
34C23×C4×C47D411yescharacteristic
35C23×C4×C47D411yescharacteristic
36C23×C4×C47C2311yescharacteristic
37C22×C8×C47—21no—
38C22×C8×C47—21no—
39C22⋊Q8×C47—21no—
40C22⋊Q8×C47—21no—
41C22⋊Q8×C47—21no—
42C22⋊Q8×C47—21no—
43#121×C47—21no—
44#121×C47—21no—
45#121×C47—21no—
46#121×C47—21no—
47C2×C4⋊C4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—42no—
51C2×C4⋊C4×C47D411yescharacteristic
52C2×C4⋊C4×C47D411yescharacteristic
53C2×C22⋊C4×C47—21no—
54C2×C22⋊C4×C47—21no—
55C2×C22⋊C4×C47—21no—
56C2×C22⋊C4×C47—21no—
57C2×C22⋊C4×C47—21no—
58C2×C22⋊C4×C47—21no—
59#103×C47—42no—
60#102×C47—42no—
61C22⋊C8×C47—21no—
62C22⋊C8×C47—21no—
63C22⋊C8×C47—21no—
64C22⋊C8×C47—21no—
65#95×C47—21no—
66#95×C47—21no—
67#95×C47—21no—
68#95×C47—21no—
69#95×C47—21no—
70#95×C47—21no—
71#95×C47—21no—
72#95×C47—42no—
73#95×C47—42no—
74#95×C47D412yes—
75C24×C47—21no—
76C24×C47C2×D411yescharacteristic
77C2×Q8×C47—21no—
78C2×Q8×C47—21no—
79C2×Q8×C47—41no—
80C2×Q8×C47—41no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47—41no—
84C2×D4×C47—41no—
85C2×D4×C47—41no—
86C2×D4×C47—41no—
87C2×D4×C47—41no—
88C2×D4×C47—41no—
89C2×D4×C47—41no—
90C2×D4×C47—41no—
91C22×C4×C47—22no—
92C22×C4×C47—21no—
93C22×C4×C47—21no—
94C22×C4×C47—21no—
95C22×C4×C47—21no—
96C22×C4×C47—21no—
97C22×C4×C47—22no—
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47—21no—
102C22×C4×C47—41no—
103C22×C4×C47—41no—
104C22×C4×C47—41no—
105C22×C4×C47—41no—
106C22×C4×C47—41no—
107C22×C4×C47—41no—
108C22×C4×C47—41no—
109C22×C4×C47—41no—
110C22×C4×C47—41no—
111C22×C4×C47—41no—
112C22×C4×C47—41no—
113C22×C4×C47—41no—
114C22×C4×C47—41no—
115C22×C4×C47—41no—
116C22×C4×C47—41no—
117C22×C4×C47—41no—
118C22×C4×C47—41no—
119C22×C4×C47—41no—
120C22×C4×C47C2×D411yescharacteristic
121C22×C4×C47C2×D411yescharacteristic
122C22×C4×C47C2×D411yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C22×C4×C47#4111yescharacteristic
126C2×C8×C47—41no—
127C2×C8×C47—41no—
128C2×C8×C47—41no—
129C2×C8×C47—41no—
130C2×C8×C47—41no—
131C2×C8×C47—41no—
132C4⋊C4×C47—22no—
133C4⋊C4×C47—22no—
134C4⋊C4×C47—21no—
135C4⋊C4×C47—21no—
136C4⋊C4×C47—21no—
137C4⋊C4×C47—21no—
138C4⋊C4×C47—41no—
139C4⋊C4×C47—41no—
140C4⋊C4×C47—41no—
141C4⋊C4×C47—41no—
142C22⋊C4×C47—41no—
143C22⋊C4×C47—41no—
144C22⋊C4×C47—41no—
145C22⋊C4×C47—41no—
146C22⋊C4×C47—81no—
147C22⋊C4×C47—81no—
148C22⋊C4×C47—81no—
149C22⋊C4×C47—81no—
150C23×C47—21no—
151C23×C47—21no—
152C23×C47—21no—
153C23×C47—21no—
154C23×C47—41no—
155C23×C47—41no—
156C23×C47—41no—
157C23×C47—41no—
158C23×C47—41no—
159C23×C47—41no—
160C23×C47—41no—
161C23×C47#12011yescharacteristic
162C23×C47#12111yescharacteristic
163C23×C47#12411yescharacteristic
164C23×C47#13511yescharacteristic
165C23×C47#13511yescharacteristic
166C23×C47AGL(1,ℤ/8)11yescharacteristic
167C23×C47#13711yescharacteristic
168Q8×C47—42no—
169Q8×C47—81no—
170D4×C47—42no—
171D4×C47—81no—
172D4×C47—81no—
173D4×C47—81no—
174D4×C47—81no—
175D4×C47—81no—
176C2×C4×C47—21no—
177C2×C4×C47—21no—
178C2×C4×C47—21no—
179C2×C4×C47—21no—
180C2×C4×C47—41no—
181C2×C4×C47—41no—
182C2×C4×C47—41no—
183C2×C4×C47—41no—
184C2×C4×C47—42no—
185C2×C4×C47—42no—
186C2×C4×C47—42no—
187C2×C4×C47—42no—
188C2×C4×C47—42no—
189C2×C4×C47—42no—
190C2×C4×C47—41no—
191C2×C4×C47—41no—
192C2×C4×C47—41no—
193C2×C4×C47—41no—
194C2×C4×C47—41no—
195C2×C4×C47—41no—
196C2×C4×C47—41no—
197C2×C4×C47—41no—
198C2×C4×C47—41no—
199C2×C4×C47—41no—
200C2×C4×C47—41no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47—42no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47—42no—
207C2×C4×C47—81no—
208C2×C4×C47—81no—
209C2×C4×C47—81no—
210C2×C4×C47—81no—
211C2×C4×C47—81no—
212C2×C4×C47—81no—
213C2×C4×C47—81no—
214C2×C4×C47—81no—
215C2×C4×C47—81no—
216C2×C4×C47—81no—
217C2×C4×C47#12111yescharacteristic
218C2×C4×C47#12111yescharacteristic
219C2×C4×C47#12311yescharacteristic
220C2×C4×C47#12311yescharacteristic
221C8×C47—81no—
222C8×C47—81no—
223#10404C4711yesmaximal, characteristic, direct product factor, Sylow
224C22×C47—21no—
225C22×C47—21no—
226C22×C47—21no—
227C22×C47—21no—
228C22×C47—21no—
229C22×C47—21no—
230C22×C47—21no—
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—21no—
234C22×C47—21no—
235C22×C47—21no—
236C22×C47—81no—
237C22×C47—81no—
238C22×C47—81no—
239C22×C47—81no—
240C22×C47—81no—
241C22×C47—81no—
242C22×C47—81no—
243C22×C47#39411yescharacteristic
244C22×C47#44911yescharacteristic
245C22×C47#45211yescharacteristic
246C22×C47#45411yescharacteristic
247C22×C47#45511yescharacteristic
248C22×C47B(4,𝔽2)11yescharacteristic
249C22×C47#45811yescharacteristic
250C22×C47#46311yescharacteristic
251C22×C47#46411yescharacteristic
252C22×C47#48811yescharacteristic
253C22×C47#48911yescharacteristic
254C4×C47—21no—
255C4×C47—21no—
256C4×C47—21no—
257C4×C47—21no—
258C4×C47—82no—
259C4×C47—82no—
260C4×C47—81no—
261C4×C47—81no—
262C4×C47—81no—
263C4×C47—81no—
264C4×C47—81no—
265#2639C2×C4711yescharacteristic
266#1874C2×C4711yescharacteristic
267#1872C2×C4711yescharacteristic, complemented
268C2×#328C2×C4711yescharacteristic, complemented
269C2×#327C2×C4711yescharacteristic
270#1442C2×C4711yescharacteristic, complemented
271#1280C2×C4711yescharacteristic, complemented
272C2×C47—21no—
273C2×C47—21no—
274C2×C47—21no—
275C2×C47—21no—
276C2×C47—161no—
277C2×C47#159711yescharacteristic
278C2×C47#160611yescharacteristic
279C2×C47#161211yescharacteristic
280C2×C47#161511yescharacteristic
281C2×C47#204011yescharacteristic
282C2×C47#204211yescharacteristic
283C2×C47#204411yescharacteristic
284C2×C22⋊Q8C22×C4711yescharacteristic
285C2×#121C22×C4711yescharacteristic
286C22×C4⋊C4C22×C4711yescharacteristic
287C2×#103—21no—
288C2×#102—21no—
289C2×C22⋊C8C22×C4711yescharacteristic
290C2×C22⋊C8C22×C4711yescharacteristic
291#400—21no—
292#397—21no—
293#394—21no—
294#393—21no—
295#386—21no—
296#386—21no—
297C2×#95—21no—
298C2×#95—21no—
299C2×#95C22×C4711yescharacteristic
300C2×#95C22×C4711yescharacteristic
301#340—21no—
302#340—21no—
303#328—22no—
304#327—22no—
305C47#1040411yescharacteristic, direct product factor, Sylow
306C22×Q8D4×C4711yescharacteristic
307C22×D4—21no—
308C22×D4D4×C4711yescharacteristic
309C23×C4—21no—
310C23×C4—21no—
311C23×C4D4×C4711yescharacteristic
312C23×C4D4×C4711yescharacteristic
313C23×C4C23×C4711yescharacteristic
314C22×C8—21no—
315C22×C8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320#121—21no—
321#121—21no—
322#121—21no—
323#121—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4D4×C4711yescharacteristic
329C2×C4⋊C4D4×C4711yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336#103—42no—
337#102—42no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—42no—
350#95—42no—
351#95D4×C4712yes—
352C24—21no—
353C24C2×D4×C4711yescharacteristic
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4C2×D4×C4711yescharacteristic
398C22×C4C2×D4×C4711yescharacteristic
399C22×C4C2×D4×C4711yescharacteristic
400C22×C4#41×C4711yescharacteristic
401C22×C4#41×C4711yescharacteristic
402C22×C4#41×C4711yescharacteristic
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—41no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23#120×C4711yescharacteristic
439C23#121×C4711yescharacteristic
440C23#124×C4711yescharacteristic
441C23#135×C4711yescharacteristic
442C23#135×C4711yescharacteristic
443C23AGL(1,ℤ/8)×C4711yescharacteristic
444C23#137×C4711yescharacteristic
445Q8—42no—
446Q8—81no—
447D4—42no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4#121×C4711yescharacteristic
495C2×C4#121×C4711yescharacteristic
496C2×C4#123×C4711yescharacteristic
497C2×C4#123×C4711yescharacteristic
498C8—81no—
499C8—81no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22C47×#39411yescharacteristic
520C22C47×#44911yescharacteristic
521C22C47×#45211yescharacteristic
522C22C47×#45411yescharacteristic
523C22C47×#45511yescharacteristic
524C22C47×B(4,𝔽2)11yescharacteristic
525C22C47×#45811yescharacteristic
526C22C47×#46311yescharacteristic
527C22C47×#46411yescharacteristic
528C22C47×#48811yescharacteristic
529C22C47×#48911yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—82no—
539C4—81no—
540C4—81no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—161no—
546C2C47×#159711yescharacteristic
547C2C47×#160611yescharacteristic
548C2C47×#161211yescharacteristic
549C2C47×#161511yescharacteristic
550C2C47×#204011yescharacteristic
551C2C47×#204211yescharacteristic
552C2C47×#204411yescharacteristic
subgroupG/H
center, socleC23×C47#120
commutator, Frattini, cosocleC23×C4C23×C47
prime radicalC2×#121×C47C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1872C2semidirect
4. C2×C47×#328C2semidirect
6. C47×#1442C2semidirect
7. C47×#1280C2semidirect
223. #10404C47direct (N × H)
267. #1872C2×C47semidirect
268. C2×#328C2×C47semidirect
270. #1442C2×C47semidirect
271. #1280C2×C47semidirect
305. C47#10404direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#26392
C47×#18742
C47×#18722
C2×C47×#3282
C2×C47×#3272
C47×#14422
C47×#12802
#1040447