Finite Group Databasebeta

← C47×#27018 #26066716

Subgroups — C47×#27018 #26066716

Order 12032.

706 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2454C211yesmaximal, characteristic
2C47×#2369C211yesmaximal, characteristic, complemented
3C47×#2067C211yesmaximal, characteristic
4C47×#2059C211yesmaximal, characteristic, complemented
5C47×#2057C211yesmaximal, characteristic, complemented
6C47×#2023C211yesmaximal, characteristic
7C47×#1989C211yesmaximal, characteristic, complemented
8C47×#1943C211yesmaximal, characteristic, complemented
9C47×#1926C211yesmaximal, characteristic
10C47×#1925C211yesmaximal, characteristic
11C47×#1921C211yesmaximal, characteristic, complemented
12C47×#1918C211yesmaximal, characteristic, complemented
13C47×#1917C211yesmaximal, characteristic, complemented
14C47×#1862C211yesmaximal, characteristic
15C47×#1762C211yesmaximal, characteristic
16C2×C4⋊Q8×C47C2211yescharacteristic
17C2×#125×C47C2211yescharacteristic
18C2×C4×D4×C47C2211yescharacteristic
19C2×#107×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#106×C47C2211yescharacteristic
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×#102×C47C2211yescharacteristic
25C2×#102×C47C2211yescharacteristic
26C2×#102×C47C2211yescharacteristic
27C2×#102×C47C2211yescharacteristic
28C2×#97×C47C2211yescharacteristic
29C47×#399—21no—
30C47×#396—21no—
31C47×#391—21no—
32C47×#391—21no—
33C47×#390C2211yescharacteristic
34C47×#390C2211yescharacteristic
35C47×#389—21no—
36C47×#389C2211yescharacteristic
37C47×#389C2211yescharacteristic
38C47×#389C2211yescharacteristic
39C47×#389C2211yescharacteristic
40C47×#385—21no—
41C47×#380—21no—
42C4×C4⋊C4×C47—21no—
43C4×C4⋊C4×C47C2211yescharacteristic
44C4×C4⋊C4×C47C2211yescharacteristic
45C4×C4⋊C4×C47C2211yescharacteristic
46C4×C4⋊C4×C47C2211yescharacteristic
47C47×#340C2211yescharacteristic
48C47×#340C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×Q8×C47—21no—
60C22×D4×C47C2311yescharacteristic
61C23×C4×C47—21no—
62C22×C8×C47C2311yescharacteristic
63C22×C8×C47C2311yescharacteristic
64C22×C8×C47C2311yescharacteristic
65C22×C8×C47C2311yescharacteristic
66C4⋊Q8×C47—22no—
67C4⋊Q8×C47—22no—
68#125×C47—22no—
69#125×C47—41no—
70C4×D4×C47—22no—
71C4×D4×C47—41no—
72C2×C4⋊C4×C47—21no—
73C2×C4⋊C4×C47—21no—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47D411yescharacteristic
80C2×C4⋊C4×C47D411yescharacteristic
81C2×C4⋊C4×C47C2311yescharacteristic
82C2×C4⋊C4×C47C2311yescharacteristic
83C2×C4⋊C4×C47C2311yescharacteristic
84C2×C4⋊C4×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2311yescharacteristic
86C2×C4⋊C4×C47C2311yescharacteristic
87C2×C4⋊C4×C47C2311yescharacteristic
88C2×C22⋊C4×C47—21no—
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C42×C47—21no—
94C2×C42×C47—21no—
95C2×C42×C47—21no—
96C2×C42×C47C2311yescharacteristic
97C2×C42×C47C2311yescharacteristic
98C2×C42×C47C2311yescharacteristic
99#107×C47—22no—
100#107×C47—22no—
101#107×C47—22no—
102#106×C47—41no—
103C4⋊C8×C47—41no—
104#102×C47—22no—
105#102×C47—22no—
106#102×C47—41no—
107#102×C47Q814yescomplemented
108#97×C47—41no—
109#95×C47—21no—
110#95×C47—21no—
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47D411yescharacteristic
117#95×C47D411yescharacteristic
118C24×C47—21no—
119C2×Q8×C47—24no—
120C2×Q8×C47—81no—
121C2×Q8×C47—81no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47C2×Q812yes—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—42no—
136C22×C4×C47—42no—
137C22×C4×C47—81no—
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2411yescharacteristic
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47C2×Q812yes—
157C4⋊C4×C47—24no—
158C4⋊C4×C47—22no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—41no—
170C4⋊C4×C47—42no—
171C4⋊C4×C47—42no—
172C4⋊C4×C47—81no—
173C4⋊C4×C47—81no—
174C4⋊C4×C47—81no—
175C4⋊C4×C47—81no—
176C4⋊C4×C47C2×Q812yes—
177C4⋊C4×C47#4112yes—
178C4⋊C4×C47#4112yes—
179C4⋊C4×C47#4112yes—
180C22⋊C4×C47—42no—
181C22⋊C4×C47—42no—
182C22⋊C4×C47—81no—
183C22⋊C4×C47—81no—
184C22⋊C4×C47—81no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47—42no—
192C42×C47—81no—
193C42×C47—81no—
194C23×C47—22no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47—41no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47C22×D411yescharacteristic
202Q8×C47—84no—
203D4×C47—22no—
204D4×C47—22no—
205D4×C47—41no—
206D4×C47—41no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—84no—
246C2×C4×C47#13712yes—
247C2×C4×C47C22×Q811yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47C2×#4111yescharacteristic
251C2×C4×C47H(5,𝔽2)11yescharacteristic
252C2×C4×C472−1+411yescharacteristic
253C8×C47—22no—
254C8×C47—41no—
255C8×C47—41no—
256C8×C47—41no—
257#27018C4711yesmaximal, characteristic, direct product factor, Sylow
258C22×C47—42no—
259C22×C47—42no—
260C22×C47—42no—
261C22×C47—81no—
262C22×C47—81no—
263C22×C47—81no—
264C22×C47—81no—
265C22×C47#52511yescharacteristic
266C22×C47#54611yescharacteristic
267C22×C47D4×Q811yescharacteristic
268C22×C47C2×#13711yescharacteristic
269C22×C47#57511yescharacteristic
270C22×C47#57611yescharacteristic
271C22×C47#57611yescharacteristic
272C4×C47—22no—
273C4×C47—41no—
274C4×C47—41no—
275C4×C47—41no—
276C4×C47—42no—
277C4×C47—42no—
278C4×C47—42no—
279C4×C47—41no—
280C4×C47—41no—
281C4×C47—42no—
282C4×C47—81no—
283C4×C47—81no—
284C4×C47—81no—
285C4×C47#53311yescharacteristic
286C4×C47#54211yescharacteristic
287C4×C47#55411yescharacteristic
288C4×C47#55611yescharacteristic
289#2454C2×C4711yescharacteristic
290#2369C2×C4711yescharacteristic, complemented
291#2067C2×C4711yescharacteristic
292#2059C2×C4711yescharacteristic, complemented
293#2057C2×C4711yescharacteristic, complemented
294#2023C2×C4711yescharacteristic
295#1989C2×C4711yescharacteristic, complemented
296#1943C2×C4711yescharacteristic, complemented
297#1926C2×C4711yescharacteristic
298#1925C2×C4711yescharacteristic
299#1921C2×C4711yescharacteristic, complemented
300#1918C2×C4711yescharacteristic, complemented
301#1917C2×C4711yescharacteristic, complemented
302#1862C2×C4711yescharacteristic
303#1762C2×C4711yescharacteristic
304C2×C47—82no—
305C2×C47#246511yescharacteristic
306C2×C47#311711yescharacteristic
307C2×C47#312211yescharacteristic
308C2×C47#331911yescharacteristic
309C2×C47#333311yescharacteristic
310C2×C47#338511yescharacteristic
311C2×C47#338911yescharacteristic
312C2×C4⋊Q8C22×C4711yescharacteristic
313C2×#125C22×C4711yescharacteristic
314C2×C4×D4C22×C4711yescharacteristic
315C2×#107C22×C4711yescharacteristic
316C2×#107C22×C4711yescharacteristic
317C2×#107C22×C4711yescharacteristic
318C2×#106C22×C4711yescharacteristic
319C2×C4⋊C8C22×C4711yescharacteristic
320C2×#102C22×C4711yescharacteristic
321C2×#102C22×C4711yescharacteristic
322C2×#102C22×C4711yescharacteristic
323C2×#102C22×C4711yescharacteristic
324C2×#97C22×C4711yescharacteristic
325#399—21no—
326#396—21no—
327#391—21no—
328#391—21no—
329#390C22×C4711yescharacteristic
330#390C22×C4711yescharacteristic
331#389—21no—
332#389C22×C4711yescharacteristic
333#389C22×C4711yescharacteristic
334#389C22×C4711yescharacteristic
335#389C22×C4711yescharacteristic
336#385—21no—
337#380—21no—
338C4×C4⋊C4—21no—
339C4×C4⋊C4C22×C4711yescharacteristic
340C4×C4⋊C4C22×C4711yescharacteristic
341C4×C4⋊C4C22×C4711yescharacteristic
342C4×C4⋊C4C22×C4711yescharacteristic
343#340C22×C4711yescharacteristic
344#340C22×C4711yescharacteristic
345#340C22×C4711yescharacteristic
346#340C22×C4711yescharacteristic
347#340C22×C4711yescharacteristic
348#340C22×C4711yescharacteristic
349#340C22×C4711yescharacteristic
350#340C22×C4711yescharacteristic
351#336C22×C4711yescharacteristic
352#336C22×C4711yescharacteristic
353#336C22×C4711yescharacteristic
354#336C22×C4711yescharacteristic
355C47#2701811yescharacteristic, direct product factor, Sylow
356C22×Q8—21no—
357C22×D4C23×C4711yescharacteristic
358C23×C4—21no—
359C22×C8C23×C4711yescharacteristic
360C22×C8C23×C4711yescharacteristic
361C22×C8C23×C4711yescharacteristic
362C22×C8C23×C4711yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365#125—22no—
366#125—41no—
367C4×D4—22no—
368C4×D4—41no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4D4×C4711yescharacteristic
377C2×C4⋊C4D4×C4711yescharacteristic
378C2×C4⋊C4C23×C4711yescharacteristic
379C2×C4⋊C4C23×C4711yescharacteristic
380C2×C4⋊C4C23×C4711yescharacteristic
381C2×C4⋊C4C23×C4711yescharacteristic
382C2×C4⋊C4C23×C4711yescharacteristic
383C2×C4⋊C4C23×C4711yescharacteristic
384C2×C4⋊C4C23×C4711yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C4711yescharacteristic
394C2×C42C23×C4711yescharacteristic
395C2×C42C23×C4711yescharacteristic
396#107—22no—
397#107—22no—
398#107—22no—
399#106—41no—
400C4⋊C8—41no—
401#102—22no—
402#102—22no—
403#102—41no—
404#102Q8×C4714yescomplemented
405#97—41no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95D4×C4711yescharacteristic
414#95D4×C4711yescharacteristic
415C24—21no—
416C2×Q8—24no—
417C2×Q8—81no—
418C2×Q8—81no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C2×Q8×C4712yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—81no—
435C22×C4C2×D4×C4711yescharacteristic
436C22×C4C2×D4×C4711yescharacteristic
437C22×C4C2×D4×C4711yescharacteristic
438C22×C4C2×D4×C4711yescharacteristic
439C22×C4C2×D4×C4711yescharacteristic
440C22×C4C2×D4×C4711yescharacteristic
441C22×C4C24×C4711yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8C2×Q8×C4712yes—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4C2×Q8×C4712yes—
474C4⋊C4#41×C4712yes—
475C4⋊C4#41×C4712yes—
476C4⋊C4#41×C4712yes—
477C22⋊C4—42no—
478C22⋊C4—42no—
479C22⋊C4—81no—
480C22⋊C4—81no—
481C22⋊C4—81no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—42no—
489C42—81no—
490C42—81no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23C22×D4×C4711yescharacteristic
499Q8—84no—
500D4—22no—
501D4—22no—
502D4—41no—
503D4—41no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—84no—
543C2×C4#137×C4712yes—
544C2×C4C22×Q8×C4711yescharacteristic
545C2×C4C2×#41×C4711yescharacteristic
546C2×C4C2×#41×C4711yescharacteristic
547C2×C4C2×#41×C4711yescharacteristic
548C2×C4H(5,𝔽2)×C4711yescharacteristic
549C2×C42−1+4×C4711yescharacteristic
550C8—22no—
551C8—41no—
552C8—41no—
553C8—41no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22C47×#52511yescharacteristic
562C22C47×#54611yescharacteristic
563C22D4×Q8×C4711yescharacteristic
564C22C2×#137×C4711yescharacteristic
565C22C47×#57511yescharacteristic
566C22C47×#57611yescharacteristic
567C22C47×#57611yescharacteristic
568C4—22no—
569C4—41no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C47×#53311yescharacteristic
582C4C47×#54211yescharacteristic
583C4C47×#55411yescharacteristic
584C4C47×#55611yescharacteristic
585C2—82no—
586C2C47×#246511yescharacteristic
587C2C47×#311711yescharacteristic
588C2C47×#312211yescharacteristic
589C2C47×#331911yescharacteristic
590C2C47×#333311yescharacteristic
591C2C47×#338511yescharacteristic
592C2C47×#338911yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C4⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2369C2semidirect
4. C47×#2059C2semidirect
5. C47×#2057C2semidirect
7. C47×#1989C2semidirect
8. C47×#1943C2semidirect
11. C47×#1921C2semidirect
12. C47×#1918C2semidirect
13. C47×#1917C2semidirect
107. #102×C47Q8semidirect
257. #27018C47direct (N × H)
290. #2369C2×C47semidirect
292. #2059C2×C47semidirect
293. #2057C2×C47semidirect
295. #1989C2×C47semidirect
296. #1943C2×C47semidirect
299. #1921C2×C47semidirect
300. #1918C2×C47semidirect
301. #1917C2×C47semidirect
355. C47#27018direct (N × H)
404. #102Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#24542
C47×#23692
C47×#20672
C47×#20592
C47×#20572
C47×#20232
C47×#19892
C47×#19432
C47×#19262
C47×#19252
C47×#19212
C47×#19182
C47×#19172
C47×#18622
C47×#17622
#2701847