Finite Group Databasebeta

← C47×#25995 #26065693

Subgroups — C47×#25995 #26065693

Order 12032.

702 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2439C211yesmaximal, characteristic
2C47×#2346C211yesmaximal, characteristic
3C47×#2101C211yesmaximal, characteristic, complemented
4C47×#2088C211yesmaximal, characteristic, complemented
5C47×#2086C211yesmaximal, characteristic, complemented
6C47×#2057C211yesmaximal, characteristic, complemented
7C47×#1987C211yesmaximal, characteristic, complemented
8C47×#1949C211yesmaximal, characteristic, complemented
9C47×#1921C211yesmaximal, 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×C4⋊Q8×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×#396—21no—
28C47×#393—21no—
29C47×#391—21no—
30C47×#389C2211yescharacteristic
31C47×#389C2211yescharacteristic
32C47×#389C2211yescharacteristic
33C47×#389C2211yescharacteristic
34C47×#388—21no—
35C47×#388—21no—
36C47×#387—21no—
37C47×#382—21no—
38C47×#382C2211yescharacteristic
39C47×#380C2211yescharacteristic
40C47×#380C2211yescharacteristic
41C4×C4⋊C4×C47C2211yescharacteristic
42C4×C4⋊C4×C47C2211yescharacteristic
43C4×C22⋊C4×C47C2211yescharacteristic
44C47×#376—21no—
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
59C22×Q8×C47—21no—
60C23×C4×C47C2311yescharacteristic
61C22×C8×C47—22no—
62C22×C8×C47—22no—
63C22×C8×C47—41no—
64C22×C8×C47C2311yescharacteristic
65C22×C8×C47C2311yescharacteristic
66C22×C8×C47C2311yescharacteristic
67C22×C8×C47C2311yescharacteristic
68C4⋊Q8×C47—22no—
69C4⋊Q8×C47—41no—
70#117×C47—22no—
71#117×C47—22no—
72#117×C47—41no—
73#117×C47Q814yescomplemented
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×C47C2311yescharacteristic
80C2×C4⋊C4×C47C2311yescharacteristic
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×C22⋊C4×C47—21no—
88C2×C22⋊C4×C47—21no—
89C2×C22⋊C4×C47—21no—
90C2×C22⋊C4×C47—21no—
91C2×C22⋊C4×C47D411yescharacteristic
92C2×C22⋊C4×C47D411yescharacteristic
93C2×C42×C47—21no—
94C2×C42×C47—21no—
95C2×C42×C47—21no—
96C2×C42×C47—21no—
97C2×C42×C47C2311yescharacteristic
98C2×C42×C47C2311yescharacteristic
99#107×C47—22no—
100#107×C47—22no—
101#107×C47—41no—
102#106×C47—41no—
103C4⋊C8×C47—22no—
104C4⋊C8×C47—41no—
105C22⋊C8×C47—22no—
106#95×C47—21no—
107#95×C47—21no—
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
119C2×Q8×C47—42no—
120C2×Q8×C47—42no—
121C2×Q8×C47—81no—
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×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×Q812yes—
140C22×C4×C47#4112yes—
141C22×C4×C47C2411yescharacteristic
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—21no—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—44no—
154C2×C8×C47#4112yes—
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—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—42no—
169C4⋊C4×C47—42no—
170C4⋊C4×C47—81no—
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—42no—
189C42×C47—42no—
190C23×C47—21no—
191C23×C47—21no—
192C23×C47—21no—
193C23×C47—21no—
194C23×C47—21no—
195C23×C47—21no—
196C23×C47C22⋊Q812yes—
197C23×C47C22×D411yescharacteristic
198Q8×C47—84no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
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—21no—
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×C47—41no—
240C2×C4×C47C22⋊Q812yes—
241C2×C4×C47#13512yes—
242C2×C4×C47C22×Q811yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47H(5,𝔽2)11yescharacteristic
247C2×C4×C472−1+411yescharacteristic
248C8×C47—22no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47—41no—
252#25995C4711yesmaximal, characteristic, direct product factor, Sylow
253C22×C47—22no—
254C22×C47—22no—
255C22×C47—22no—
256C22×C47—41no—
257C22×C47—41no—
258C22×C47—41no—
259C22×C47—41no—
260C22×C47C2×C22⋊Q811yescharacteristic
261C22×C47#54611yescharacteristic
262C22×C47#54711yescharacteristic
263C22×C47C2×#13511yescharacteristic
264C22×C47#57511yescharacteristic
265C22×C47#57611yescharacteristic
266C22×C47#57811yescharacteristic
267C4×C47—22no—
268C4×C47—22no—
269C4×C47—42no—
270C4×C47—42no—
271C4×C47—41no—
272C4×C47—41no—
273C4×C47—41no—
274C4×C47—42no—
275C4×C47—81no—
276C4×C47—81no—
277C4×C47—81no—
278C4×C47—81no—
279C4×C47—81no—
280C4×C47#53311yescharacteristic
281C4×C47#54411yescharacteristic
282C4×C47#55111yescharacteristic
283C4×C47#55211yescharacteristic
284#2439C2×C4711yescharacteristic
285#2346C2×C4711yescharacteristic
286#2101C2×C4711yescharacteristic, complemented
287#2088C2×C4711yescharacteristic, complemented
288#2086C2×C4711yescharacteristic, complemented
289#2057C2×C4711yescharacteristic, complemented
290#1987C2×C4711yescharacteristic, complemented
291#1949C2×C4711yescharacteristic, complemented
292#1921C2×C4711yescharacteristic, complemented
293#1918C2×C4711yescharacteristic, complemented
294#1854C2×C4711yescharacteristic
295#1850C2×C4711yescharacteristic
296#1825C2×C4711yescharacteristic
297#1808C2×C4711yescharacteristic
298#1735C2×C4711yescharacteristic
299C2×C47—42no—
300C2×C47#243811yescharacteristic
301C2×C47#307611yescharacteristic
302C2×C47#308311yescharacteristic
303C2×C47#330011yescharacteristic
304C2×C47#331911yescharacteristic
305C2×C47#334111yescharacteristic
306C2×C47#334911yescharacteristic
307C23×C8C22×C4711yescharacteristic
308C2×C4⋊Q8C22×C4711yescharacteristic
309C2×#117C22×C4711yescharacteristic
310C2×#117C22×C4711yescharacteristic
311C2×#107C22×C4711yescharacteristic
312C2×#107C22×C4711yescharacteristic
313C2×#107C22×C4711yescharacteristic
314C2×#106C22×C4711yescharacteristic
315C2×C4⋊C8C22×C4711yescharacteristic
316C2×C4⋊C8C22×C4711yescharacteristic
317C2×C22⋊C8C22×C4711yescharacteristic
318#396—21no—
319#393—21no—
320#391—21no—
321#389C22×C4711yescharacteristic
322#389C22×C4711yescharacteristic
323#389C22×C4711yescharacteristic
324#389C22×C4711yescharacteristic
325#388—21no—
326#388—21no—
327#387—21no—
328#382—21no—
329#382C22×C4711yescharacteristic
330#380C22×C4711yescharacteristic
331#380C22×C4711yescharacteristic
332C4×C4⋊C4C22×C4711yescharacteristic
333C4×C4⋊C4C22×C4711yescharacteristic
334C4×C22⋊C4C22×C4711yescharacteristic
335#376—21no—
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#340C22×C4711yescharacteristic
348#336C22×C4711yescharacteristic
349#336C22×C4711yescharacteristic
350C47#2599511yescharacteristic, direct product factor, Sylow
351C22×Q8—21no—
352C23×C4C23×C4711yescharacteristic
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—41no—
356C22×C8C23×C4711yescharacteristic
357C22×C8C23×C4711yescharacteristic
358C22×C8C23×C4711yescharacteristic
359C22×C8C23×C4711yescharacteristic
360C4⋊Q8—22no—
361C4⋊Q8—41no—
362#117—22no—
363#117—22no—
364#117—41no—
365#117Q8×C4714yescomplemented
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4C23×C4711yescharacteristic
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×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4D4×C4711yescharacteristic
384C2×C22⋊C4D4×C4711yescharacteristic
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C4711yescharacteristic
390C2×C42C23×C4711yescharacteristic
391#107—22no—
392#107—22no—
393#107—41no—
394#106—41no—
395C4⋊C8—22no—
396C4⋊C8—41no—
397C22⋊C8—22no—
398#95—21no—
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#95—21no—
408#95D4×C4711yescharacteristic
409#95D4×C4711yescharacteristic
410C24C2×D4×C4711yescharacteristic
411C2×Q8—42no—
412C2×Q8—42no—
413C2×Q8—81no—
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×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4C2×D4×C4711yescharacteristic
427C22×C4C2×D4×C4711yescharacteristic
428C22×C4C2×D4×C4711yescharacteristic
429C22×C4C2×D4×C4711yescharacteristic
430C22×C4C2×D4×C4711yescharacteristic
431C22×C4C2×Q8×C4712yes—
432C22×C4#41×C4712yes—
433C22×C4C24×C4711yescharacteristic
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—44no—
446C2×C8#41×C4712yes—
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—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4C2×Q8×C4712yes—
466C4⋊C4C2×Q8×C4712yes—
467C4⋊C4#41×C4712yes—
468C22⋊C4—24no—
469C22⋊C4—22no—
470C22⋊C4—41no—
471C22⋊C4—42no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C42—24no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—42no—
480C42—42no—
481C42—42no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23C22⋊Q8×C4712yes—
489C23C22×D4×C4711yescharacteristic
490Q8—84no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
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×C4—41no—
531C2×C4—41no—
532C2×C4C22⋊Q8×C4712yes—
533C2×C4#135×C4712yes—
534C2×C4C22×Q8×C4711yescharacteristic
535C2×C4C2×#41×C4711yescharacteristic
536C2×C4C2×#41×C4711yescharacteristic
537C2×C4C2×#41×C4711yescharacteristic
538C2×C4H(5,𝔽2)×C4711yescharacteristic
539C2×C42−1+4×C4711yescharacteristic
540C8—22no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22C2×C22⋊Q8×C4711yescharacteristic
552C22C47×#54611yescharacteristic
553C22C47×#54711yescharacteristic
554C22C2×#135×C4711yescharacteristic
555C22C47×#57511yescharacteristic
556C22C47×#57611yescharacteristic
557C22C47×#57811yescharacteristic
558C4—22no—
559C4—22no—
560C4—41no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C47×#53311yescharacteristic
572C4C47×#54411yescharacteristic
573C4C47×#55111yescharacteristic
574C4C47×#55211yescharacteristic
575C2—42no—
576C2C47×#243811yescharacteristic
577C2C47×#307611yescharacteristic
578C2C47×#308311yescharacteristic
579C2C47×#330011yescharacteristic
580C2C47×#331911yescharacteristic
581C2C47×#334111yescharacteristic
582C2C47×#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×#2101C2semidirect
4. C47×#2088C2semidirect
5. C47×#2086C2semidirect
6. C47×#2057C2semidirect
7. C47×#1987C2semidirect
8. C47×#1949C2semidirect
9. C47×#1921C2semidirect
10. C47×#1918C2semidirect
73. #117×C47Q8semidirect
252. #25995C47direct (N × H)
286. #2101C2×C47semidirect
287. #2088C2×C47semidirect
288. #2086C2×C47semidirect
289. #2057C2×C47semidirect
290. #1987C2×C47semidirect
291. #1949C2×C47semidirect
292. #1921C2×C47semidirect
293. #1918C2×C47semidirect
350. C47#25995direct (N × H)
365. #117Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#24392
C47×#23462
C47×#21012
C47×#20882
C47×#20862
C47×#20572
C47×#19872
C47×#19492
C47×#19212
C47×#19182
C47×#18542
C47×#18502
C47×#18252
C47×#18082
C47×#17352
#2599547