Finite Group Databasebeta

← C47×#25997 #26065695

Subgroups — C47×#25997 #26065695

Order 12032.

694 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2441C211yesmaximal, characteristic
2C47×#2347C211yesmaximal, characteristic
3C47×#2100C211yesmaximal, characteristic, complemented
4C47×#2087C211yesmaximal, characteristic, complemented
5C47×#2086C211yesmaximal, characteristic, complemented
6C47×#2059C211yesmaximal, characteristic, complemented
7C47×#1989C211yesmaximal, characteristic, complemented
8C47×#1947C211yesmaximal, characteristic, complemented
9C47×#1919C211yesmaximal, characteristic, complemented
10C47×#1918C211yesmaximal, characteristic, complemented
11C47×#1854C211yesmaximal, characteristic
12C47×#1850C211yesmaximal, characteristic
13C47×#1825C211yesmaximal, characteristic
14C47×#1808C211yesmaximal, characteristic
15C47×#1735C211yesmaximal, characteristic
16C23×C8×C47C2211yescharacteristic
17C2×#125×C47C2211yescharacteristic
18C2×#117×C47C2211yescharacteristic
19C2×#117×C47C2211yescharacteristic
20C2×#107×C47C2211yescharacteristic
21C2×#107×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#106×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C2×C4⋊C8×C47C2211yescharacteristic
26C2×C22⋊C8×C47C2211yescharacteristic
27C47×#399—21no—
28C47×#396—21no—
29C47×#389—21no—
30C47×#389C2211yescharacteristic
31C47×#389C2211yescharacteristic
32C47×#389C2211yescharacteristic
33C47×#389C2211yescharacteristic
34C47×#388—21no—
35C47×#388—21no—
36C47×#387—21no—
37C47×#384C2211yescharacteristic
38C47×#383—21no—
39C47×#380C2211yescharacteristic
40C47×#380C2211yescharacteristic
41C4×C4⋊C4×C47—21no—
42C4×C4⋊C4×C47C2211yescharacteristic
43C4×C4⋊C4×C47C2211yescharacteristic
44C4×C22⋊C4×C47C2211yescharacteristic
45C47×#340C2211yescharacteristic
46C47×#340C2211yescharacteristic
47C47×#340C2211yescharacteristic
48C47×#340C2211yescharacteristic
49C47×#340C2211yescharacteristic
50C47×#340C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C23×C4×C47C2311yescharacteristic
60C22×C8×C47—22no—
61C22×C8×C47—22no—
62C22×C8×C47—41no—
63C22×C8×C47C2311yescharacteristic
64C22×C8×C47C2311yescharacteristic
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67#125×C47—22no—
68#125×C47—41no—
69#117×C47—22no—
70#117×C47—22no—
71#117×C47—41no—
72#117×C47Q814yes—
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×C47—21no—
80C2×C4⋊C4×C47—21no—
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×C4⋊C4×C47C2311yescharacteristic
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47—21no—
92C2×C22⋊C4×C47—21no—
93C2×C22⋊C4×C47D411yescharacteristic
94C2×C22⋊C4×C47D411yescharacteristic
95C2×C42×C47—21no—
96C2×C42×C47—21no—
97C2×C42×C47—21no—
98C2×C42×C47—21no—
99C2×C42×C47C2311yescharacteristic
100C2×C42×C47C2311yescharacteristic
101#107×C47—22no—
102#107×C47—41no—
103#107×C47—41no—
104#106×C47—22no—
105C4⋊C8×C47—22no—
106C4⋊C8×C47—41no—
107C22⋊C8×C47—22no—
108#95×C47—21no—
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×C47C2×D411yescharacteristic
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×Q812yes—
137C22×C4×C47#4112yes—
138C22×C4×C47C2411yescharacteristic
139C2×C8×C47—21no—
140C2×C8×C47—21no—
141C2×C8×C47—21no—
142C2×C8×C47—21no—
143C2×C8×C47—21no—
144C2×C8×C47—21no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—44no—
151C2×C8×C47#4112yes—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
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—42no—
166C4⋊C4×C47—42no—
167C4⋊C4×C47—42no—
168C4⋊C4×C47—42no—
169C4⋊C4×C47—42no—
170C4⋊C4×C47—42no—
171C4⋊C4×C47—81no—
172C4⋊C4×C47—81no—
173C4⋊C4×C47C2×Q812yes—
174C4⋊C4×C47C2×Q812yes—
175C4⋊C4×C47#4112yes—
176C22⋊C4×C47—24no—
177C22⋊C4×C47—22no—
178C22⋊C4×C47—41no—
179C22⋊C4×C47—42no—
180C22⋊C4×C47—81no—
181C22⋊C4×C47—81no—
182C42×C47—24no—
183C42×C47—21no—
184C42×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—42no—
188C42×C47—81no—
189C42×C47—81no—
190C23×C47—21no—
191C23×C47—21no—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47C22⋊Q812yes—
197C23×C47C22×D411yescharacteristic
198C2×C4×C47—21no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—22no—
211C2×C4×C47—21no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
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×C47C22⋊Q812yes—
240C2×C4×C47#13512yes—
241C2×C4×C47C22×Q811yescharacteristic
242C2×C4×C47C2×#4111yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47H(5,𝔽2)11yescharacteristic
246C2×C4×C472−1+411yescharacteristic
247C8×C47—22no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251#25997C4711yesmaximal, characteristic, direct product factor, Sylow
252C22×C47—22no—
253C22×C47—22no—
254C22×C47—22no—
255C22×C47—41no—
256C22×C47—41no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47C2×C22⋊Q811yescharacteristic
260C22×C47#54611yescharacteristic
261C22×C47#54711yescharacteristic
262C22×C47C2×#13511yescharacteristic
263C22×C47#57511yescharacteristic
264C22×C47#57611yescharacteristic
265C22×C47#57811yescharacteristic
266C4×C47—22no—
267C4×C47—22no—
268C4×C47—42no—
269C4×C47—42no—
270C4×C47—41no—
271C4×C47—41no—
272C4×C47—42no—
273C4×C47—41no—
274C4×C47—81no—
275C4×C47—81no—
276C4×C47—81no—
277C4×C47—81no—
278C4×C47—81no—
279C4×C47#53311yescharacteristic
280C4×C47#54411yescharacteristic
281C4×C47#55111yescharacteristic
282C4×C47#55211yescharacteristic
283#2441C2×C4711yescharacteristic
284#2347C2×C4711yescharacteristic
285#2100C2×C4711yescharacteristic, complemented
286#2087C2×C4711yescharacteristic, complemented
287#2086C2×C4711yescharacteristic, complemented
288#2059C2×C4711yescharacteristic, complemented
289#1989C2×C4711yescharacteristic, complemented
290#1947C2×C4711yescharacteristic, complemented
291#1919C2×C4711yescharacteristic, complemented
292#1918C2×C4711yescharacteristic, complemented
293#1854C2×C4711yescharacteristic
294#1850C2×C4711yescharacteristic
295#1825C2×C4711yescharacteristic
296#1808C2×C4711yescharacteristic
297#1735C2×C4711yescharacteristic
298C2×C47—42no—
299C2×C47#243811yescharacteristic
300C2×C47#307611yescharacteristic
301C2×C47#308311yescharacteristic
302C2×C47#330211yescharacteristic
303C2×C47#330911yescharacteristic
304C2×C47#333911yescharacteristic
305C2×C47#334911yescharacteristic
306C23×C8C22×C4711yescharacteristic
307C2×#125C22×C4711yescharacteristic
308C2×#117C22×C4711yescharacteristic
309C2×#117C22×C4711yescharacteristic
310C2×#107C22×C4711yescharacteristic
311C2×#107C22×C4711yescharacteristic
312C2×#107C22×C4711yescharacteristic
313C2×#106C22×C4711yescharacteristic
314C2×C4⋊C8C22×C4711yescharacteristic
315C2×C4⋊C8C22×C4711yescharacteristic
316C2×C22⋊C8C22×C4711yescharacteristic
317#399—21no—
318#396—21no—
319#389—21no—
320#389C22×C4711yescharacteristic
321#389C22×C4711yescharacteristic
322#389C22×C4711yescharacteristic
323#389C22×C4711yescharacteristic
324#388—21no—
325#388—21no—
326#387—21no—
327#384C22×C4711yescharacteristic
328#383—21no—
329#380C22×C4711yescharacteristic
330#380C22×C4711yescharacteristic
331C4×C4⋊C4—21no—
332C4×C4⋊C4C22×C4711yescharacteristic
333C4×C4⋊C4C22×C4711yescharacteristic
334C4×C22⋊C4C22×C4711yescharacteristic
335#340C22×C4711yescharacteristic
336#340C22×C4711yescharacteristic
337#340C22×C4711yescharacteristic
338#340C22×C4711yescharacteristic
339#340C22×C4711yescharacteristic
340#340C22×C4711yescharacteristic
341#340C22×C4711yescharacteristic
342#340C22×C4711yescharacteristic
343#340C22×C4711yescharacteristic
344#340C22×C4711yescharacteristic
345#340C22×C4711yescharacteristic
346#340C22×C4711yescharacteristic
347#336C22×C4711yescharacteristic
348#336C22×C4711yescharacteristic
349C47#2599711yescharacteristic, direct product factor, Sylow
350C23×C4C23×C4711yescharacteristic
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—41no—
354C22×C8C23×C4711yescharacteristic
355C22×C8C23×C4711yescharacteristic
356C22×C8C23×C4711yescharacteristic
357C22×C8C23×C4711yescharacteristic
358#125—22no—
359#125—41no—
360#117—22no—
361#117—22no—
362#117—41no—
363#117Q8×C4714yes—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4C23×C4711yescharacteristic
373C2×C4⋊C4C23×C4711yescharacteristic
374C2×C4⋊C4C23×C4711yescharacteristic
375C2×C4⋊C4C23×C4711yescharacteristic
376C2×C4⋊C4C23×C4711yescharacteristic
377C2×C4⋊C4C23×C4711yescharacteristic
378C2×C4⋊C4C23×C4711yescharacteristic
379C2×C4⋊C4C23×C4711yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4D4×C4711yescharacteristic
385C2×C22⋊C4D4×C4711yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C23×C4711yescharacteristic
391C2×C42C23×C4711yescharacteristic
392#107—22no—
393#107—41no—
394#107—41no—
395#106—22no—
396C4⋊C8—22no—
397C4⋊C8—41no—
398C22⋊C8—22no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95D4×C4711yescharacteristic
408#95D4×C4711yescharacteristic
409C24C2×D4×C4711yescharacteristic
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4C2×D4×C4711yescharacteristic
423C22×C4C2×D4×C4711yescharacteristic
424C22×C4C2×D4×C4711yescharacteristic
425C22×C4C2×D4×C4711yescharacteristic
426C22×C4C2×D4×C4711yescharacteristic
427C22×C4C2×Q8×C4712yes—
428C22×C4#41×C4712yes—
429C22×C4C24×C4711yescharacteristic
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—44no—
442C2×C8#41×C4712yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4C2×Q8×C4712yes—
465C4⋊C4C2×Q8×C4712yes—
466C4⋊C4#41×C4712yes—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—41no—
470C22⋊C4—42no—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C42—24no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42—81no—
480C42—81no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23C22⋊Q8×C4712yes—
488C23C22×D4×C4711yescharacteristic
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4C22⋊Q8×C4712yes—
531C2×C4#135×C4712yes—
532C2×C4C22×Q8×C4711yescharacteristic
533C2×C4C2×#41×C4711yescharacteristic
534C2×C4C2×#41×C4711yescharacteristic
535C2×C4C2×#41×C4711yescharacteristic
536C2×C4H(5,𝔽2)×C4711yescharacteristic
537C2×C42−1+4×C4711yescharacteristic
538C8—22no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22C2×C22⋊Q8×C4711yescharacteristic
550C22C47×#54611yescharacteristic
551C22C47×#54711yescharacteristic
552C22C2×#135×C4711yescharacteristic
553C22C47×#57511yescharacteristic
554C22C47×#57611yescharacteristic
555C22C47×#57811yescharacteristic
556C4—22no—
557C4—22no—
558C4—41no—
559C4—42no—
560C4—41no—
561C4—42no—
562C4—42no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4C47×#53311yescharacteristic
570C4C47×#54411yescharacteristic
571C4C47×#55111yescharacteristic
572C4C47×#55211yescharacteristic
573C2—42no—
574C2C47×#243811yescharacteristic
575C2C47×#307611yescharacteristic
576C2C47×#308311yescharacteristic
577C2C47×#330211yescharacteristic
578C2C47×#330911yescharacteristic
579C2C47×#333911yescharacteristic
580C2C47×#334911yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC24×C47C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#2100C2semidirect
4. C47×#2087C2semidirect
5. C47×#2086C2semidirect
6. C47×#2059C2semidirect
7. C47×#1989C2semidirect
8. C47×#1947C2semidirect
9. C47×#1919C2semidirect
10. C47×#1918C2semidirect
251. #25997C47direct (N × H)
285. #2100C2×C47semidirect
286. #2087C2×C47semidirect
287. #2086C2×C47semidirect
288. #2059C2×C47semidirect
289. #1989C2×C47semidirect
290. #1947C2×C47semidirect
291. #1919C2×C47semidirect
292. #1918C2×C47semidirect
349. C47#25997direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#24412
C47×#23472
C47×#21002
C47×#20872
C47×#20862
C47×#20592
C47×#19892
C47×#19472
C47×#19192
C47×#19182
C47×#18542
C47×#18502
C47×#18252
C47×#18082
C47×#17352
#2599747