Finite Group Databasebeta

← C47×#22588 #26062286

Subgroups — C47×#22588 #26062286

Order 12032.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2924C211yesmaximal, characteristic, complemented
2C47×#2896C211yesmaximal, characteristic
3C47×#2880C211yesmaximal, characteristic
4C47×#1938C211yesmaximal, characteristic, complemented
5C47×#1937C211yesmaximal, characteristic, complemented
6C47×#1929C211yesmaximal, characteristic, complemented
7C47×#1929C211yesmaximal, characteristic, complemented
8C47×#1866C211yesmaximal, characteristic, complemented
9C47×#1866C211yesmaximal, characteristic, complemented
10C47×#1826C211yesmaximal, characteristic, complemented
11C47×#1811C211yesmaximal, characteristic, complemented
12C47×#1789C211yesmaximal, characteristic
13C47×#1765C211yesmaximal, characteristic, complemented
14C47×#1764C211yesmaximal, characteristic, complemented
15C47×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C2×#131×C47C2211yescharacteristic
18C2×#131×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic
20C2×#117×C47C2211yescharacteristic
21C47×#433—21no—
22C47×#433—21no—
23C47×#432—21no—
24C47×#431—21no—
25C2×#108×C47C2211yescharacteristic, complemented
26C2×#108×C47C2211yescharacteristic, complemented
27C47×#424C2211yescharacteristic, complemented
28C47×#424C2211yescharacteristic, complemented
29C2×#104×C47C2211yescharacteristic
30C2×#104×C47C2211yescharacteristic
31C2×#104×C47C2211yescharacteristic
32C2×#104×C47C2211yescharacteristic
33C47×#419C411yescharacteristic, complemented
34C47×#419C411yescharacteristic, complemented
35C47×#418C411yescharacteristic, complemented
36C47×#418C411yescharacteristic, complemented
37C47×#417C411yescharacteristic, complemented
38C47×#417C411yescharacteristic, complemented
39C47×#417C411yescharacteristic, complemented
40C47×#417C411yescharacteristic, complemented
41C47×#416C2211yescharacteristic
42C47×#416C2211yescharacteristic
43C47×#416C2211yescharacteristic
44C47×#416C2211yescharacteristic
45C47×#408—21no—
46C47×#408—21no—
47C47×#408C2211yescharacteristic
48C47×#408C2211yescharacteristic
49C47×#407—21no—
50C47×#407C2211yescharacteristic
51C47×#407C2211yescharacteristic
52C2×C22⋊C8×C47—21no—
53C2×C22⋊C8×C47C2211yescharacteristic
54C47×#405C2211yescharacteristic, complemented
55C47×#405C2211yescharacteristic, complemented
56C2×#97×C47C2211yescharacteristic, complemented
57C2×C4×C8×C47C2211yescharacteristic, complemented
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#341C2211yescharacteristic, complemented
60C47×#341C2211yescharacteristic, complemented
61C47×#339C2211yescharacteristic, complemented
62C47×#339C2211yescharacteristic, complemented
63C47×#339C2211yescharacteristic, complemented
64C47×#339C2211yescharacteristic, complemented
65C47×#336C2211yescharacteristic, complemented
66C47×#336C2211yescharacteristic, complemented
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C2×#41×C47—22no—
70C2×#41×C47—22no—
71C2×#41×C47—41no—
72C2×#41×C47—41no—
73C2×#41×C47C2×C411yescharacteristic
74C2×#41×C47C2×C411yescharacteristic
75C2×#41×C47C2311yescharacteristic
76C2×#41×C47C2311yescharacteristic
77C22×Q8×C47C2×C411yescharacteristic
78C22×D4×C47—21no—
79C22×D4×C47C2×C411yescharacteristic
80C23×C4×C47—21no—
81C23×C4×C47C2311yescharacteristic
82#131×C47—22no—
83#131×C47—22no—
84#131×C47—41no—
85#131×C47—41no—
86C2×M16×C47—21no—
87C2×M16×C47—21no—
88C2×M16×C47—41no—
89C2×M16×C47—41no—
90C2×M16×C47C2×C411yescharacteristic
91C2×M16×C47C2×C411yescharacteristic
92C2×M16×C47C2×C411yescharacteristic
93C2×M16×C47C2×C411yescharacteristic
94C2×M16×C47C2311yescharacteristic
95C2×M16×C47C2311yescharacteristic
96C2×M16×C47C2311yescharacteristic
97C2×M16×C47C2311yescharacteristic
98C22×C8×C47—21no—
99C22×C8×C47—21no—
100C22×C8×C47C2311yescharacteristic
101C22×C8×C47C2311yescharacteristic
102C22×C8×C47C2311yescharacteristic
103C22×C8×C47C2311yescharacteristic
104#117×C47—21no—
105#117×C47—21no—
106#117×C47C2×C411yescharacteristic
107#117×C47C2×C411yescharacteristic
108#117×C47C2311yescharacteristic
109#117×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2×C411yescharacteristic
111C2×C4⋊C4×C47C2×C411yescharacteristic
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C42×C47—21no—
115C2×C42×C47C2311yescharacteristic
116C2×C42×C47C2311yescharacteristic
117#108×C47—41no—
118#108×C47—41no—
119C4⋊C8×C47—21no—
120C4⋊C8×C47—21no—
121C4⋊C8×C47—21no—
122C4⋊C8×C47—21no—
123#104×C47—22no—
124#104×C47—22no—
125#104×C47—41no—
126#104×C47—41no—
127#103×C47C2×C411yescharacteristic
128#103×C47C2×C411yescharacteristic
129#103×C47C2×C411yescharacteristic
130#103×C47C2×C411yescharacteristic
131#103×C47C2×C411yescharacteristic
132#103×C47C2×C411yescharacteristic
133#103×C47C2×C411yescharacteristic
134#103×C47C2×C411yescharacteristic
135#102×C47C2×C411yescharacteristic
136#102×C47C2×C411yescharacteristic
137#102×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140#102×C47C2×C411yescharacteristic
141#102×C47C2×C411yescharacteristic
142#102×C47C2×C411yescharacteristic
143C22⋊C8×C47—21no—
144C22⋊C8×C47—21no—
145C22⋊C8×C47—21no—
146C22⋊C8×C47—21no—
147C22⋊C8×C47—21no—
148C22⋊C8×C47—21no—
149C22⋊C8×C47—21no—
150C22⋊C8×C47—21no—
151C22⋊C8×C47D411yescharacteristic
152C22⋊C8×C47D411yescharacteristic
153C22⋊C8×C47D411yescharacteristic
154C22⋊C8×C47D411yescharacteristic
155#97×C47—21no—
156#97×C47—21no—
157#97×C47—41no—
158C4×C8×C47—21no—
159C4×C8×C47—21no—
160C4×C8×C47—41no—
161#95×C47—21no—
162C24×C47—21no—
163C24×C47#4111yescharacteristic
164#41×C47—21no—
165#41×C47—21no—
166#41×C47—22no—
167#41×C47—22no—
168#41×C47—21no—
169#41×C47—21no—
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—42no—
173#41×C47—42no—
174#41×C47—41no—
175#41×C47—41no—
176#41×C47—42no—
177#41×C47—42no—
178#41×C47#4112yes—
179#41×C47#4112yes—
180C2×Q8×C47—21no—
181C2×Q8×C47—22no—
182C2×Q8×C47—41no—
183C2×Q8×C47C22×C411yescharacteristic
184C2×Q8×C47C22×C411yescharacteristic
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—41no—
192C2×D4×C47—42no—
193C2×D4×C47—42no—
194C2×D4×C47C22×C411yescharacteristic
195C2×D4×C47C22×C411yescharacteristic
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—21no—
205C22×C4×C47—21no—
206C22×C4×C47—21no—
207C22×C4×C47—21no—
208C22×C4×C47—21no—
209C22×C4×C47—42no—
210C22×C4×C47—42no—
211C22×C4×C47C22×C411yescharacteristic
212C22×C4×C47C22×C411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47#4111yescharacteristic
216C22×C4×C47C2411yescharacteristic
217M16×C47—21no—
218M16×C47—21no—
219M16×C47—21no—
220M16×C47—21no—
221M16×C47—21no—
222M16×C47—21no—
223M16×C47—21no—
224M16×C47—21no—
225M16×C47—41no—
226M16×C47—41no—
227M16×C47—41no—
228M16×C47—41no—
229M16×C47—42no—
230M16×C47—42no—
231C2×C8×C47—21no—
232C2×C8×C47—21no—
233C2×C8×C47—21no—
234C2×C8×C47—21no—
235C2×C8×C47—21no—
236C2×C8×C47—21no—
237C2×C8×C47—21no—
238C2×C8×C47—21no—
239C2×C8×C47—21no—
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—42no—
244C2×C8×C47—42no—
245C2×C8×C47C22×C411yescharacteristic
246C2×C8×C47C22×C411yescharacteristic
247C2×C8×C47C22×C411yescharacteristic
248C2×C8×C47C22×C411yescharacteristic
249C2×C8×C47C2×D411yescharacteristic
250C2×C8×C47C2×D411yescharacteristic
251C2×C8×C47C2×D411yescharacteristic
252C2×C8×C47C2×D411yescharacteristic
253C4⋊C4×C47—21no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47C22×C411yescharacteristic
256C4⋊C4×C47C22×C411yescharacteristic
257C4⋊C4×C47C22×C411yescharacteristic
258C4⋊C4×C47C22×C411yescharacteristic
259C22⋊C4×C47—21no—
260C22⋊C4×C47—21no—
261C22⋊C4×C47—21no—
262C22⋊C4×C47—21no—
263C22⋊C4×C47—42no—
264C42×C47—21no—
265C42×C47—21no—
266C42×C47—21no—
267C42×C47—21no—
268C42×C47—21no—
269C42×C47—21no—
270C42×C47—21no—
271C42×C47—21no—
272C23×C47—21no—
273C23×C47—21no—
274C23×C47—21no—
275C23×C47—21no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—42no—
279C23×C47—42no—
280C23×C47—81no—
281C23×C47C4×D411yescharacteristic
282C23×C47C4×D411yescharacteristic
283C23×C47C2×#4111yescharacteristic
284Q8×C47—21no—
285Q8×C47—21no—
286Q8×C47—21no—
287Q8×C47—42no—
288Q8×C47#11712yes—
289D4×C47—22no—
290D4×C47—22no—
291D4×C47—21no—
292D4×C47—21no—
293D4×C47—21no—
294D4×C47—42no—
295D4×C47—42no—
296D4×C47—42no—
297D4×C47—41no—
298D4×C47—41no—
299D4×C47#11712yes—
300C2×C4×C47—21no—
301C2×C4×C47—21no—
302C2×C4×C47—21no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—21no—
312C2×C4×C47—21no—
313C2×C4×C47—22no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—41no—
323C2×C4×C47—42no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—41no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47—41no—
330C2×C4×C47—81no—
331C2×C4×C47C4×D411yescharacteristic
332C2×C4×C47C4×D411yescharacteristic
333C2×C4×C47C23×C411yescharacteristic
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C2×#4111yescharacteristic
336C2×C4×C47C2×#4111yescharacteristic
337C2×C4×C47H(5,𝔽2)11yescharacteristic
338C2×C4×C47H(5,𝔽2)11yescharacteristic
339C8×C47—21no—
340C8×C47—21no—
341C8×C47—21no—
342C8×C47—21no—
343C8×C47—21no—
344C8×C47—21no—
345C8×C47—21no—
346C8×C47—21no—
347C8×C47—41no—
348C8×C47—41no—
349C8×C47—41no—
350C8×C47—41no—
351#22588C4711yesmaximal, characteristic, direct product factor, Sylow
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—22no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47—41no—
364C22×C47—41no—
365C22×C47—41no—
366C22×C47—81no—
367C22×C47—81no—
368C22×C47—84no—
369C22×C47C2×C4×D411yescharacteristic
370C22×C47#55111yescharacteristic
371C22×C47#55111yescharacteristic
372C4×C47—21no—
373C4×C47—21no—
374C4×C47—22no—
375C4×C47—42no—
376C4×C47—41no—
377C4×C47—41no—
378C4×C47—41no—
379C4×C47—41no—
380C4×C47—41no—
381C4×C47—81no—
382C4×C47C2×#11711yescharacteristic
383C4×C47#51811yescharacteristic
384C4×C47#54611yescharacteristic
385C4×C47#54611yescharacteristic
386#2924C2×C4711yescharacteristic, complemented
387#2896C2×C4711yescharacteristic
388#2880C2×C4711yescharacteristic
389#1938C2×C4711yescharacteristic, complemented
390#1937C2×C4711yescharacteristic, complemented
391#1929C2×C4711yescharacteristic, complemented
392#1929C2×C4711yescharacteristic, complemented
393#1866C2×C4711yescharacteristic, complemented
394#1866C2×C4711yescharacteristic, complemented
395#1826C2×C4711yescharacteristic, complemented
396#1811C2×C4711yescharacteristic, complemented
397#1789C2×C4711yescharacteristic
398#1765C2×C4711yescharacteristic, complemented
399#1764C2×C4711yescharacteristic, complemented
400#1753C2×C4711yescharacteristic, complemented
401C2×C47—21no—
402C2×C47—21no—
403C2×C47—41no—
404C2×C47—41no—
405C2×C47—42no—
406C2×C47—81no—
407C2×C47#234211yescharacteristic
408C2×C47#295511yescharacteristic
409C2×C47#295611yescharacteristic
410C22×#41C22×C4711yescharacteristic
411C2×#131C22×C4711yescharacteristic
412C2×#131C22×C4711yescharacteristic
413C22×M16C22×C4711yescharacteristic
414C2×#117C22×C4711yescharacteristic
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108C22×C4711yescharacteristic, complemented
420C2×#108C22×C4711yescharacteristic, complemented
421#424C22×C4711yescharacteristic, complemented
422#424C22×C4711yescharacteristic, complemented
423C2×#104C22×C4711yescharacteristic
424C2×#104C22×C4711yescharacteristic
425C2×#104C22×C4711yescharacteristic
426C2×#104C22×C4711yescharacteristic
427#419C4×C4711yescharacteristic, complemented
428#419C4×C4711yescharacteristic, complemented
429#418C4×C4711yescharacteristic, complemented
430#418C4×C4711yescharacteristic, complemented
431#417C4×C4711yescharacteristic, complemented
432#417C4×C4711yescharacteristic, complemented
433#417C4×C4711yescharacteristic, complemented
434#417C4×C4711yescharacteristic, complemented
435#416C22×C4711yescharacteristic
436#416C22×C4711yescharacteristic
437#416C22×C4711yescharacteristic
438#416C22×C4711yescharacteristic
439#408—21no—
440#408—21no—
441#408C22×C4711yescharacteristic
442#408C22×C4711yescharacteristic
443#407—21no—
444#407C22×C4711yescharacteristic
445#407C22×C4711yescharacteristic
446C2×C22⋊C8—21no—
447C2×C22⋊C8C22×C4711yescharacteristic
448#405C22×C4711yescharacteristic, complemented
449#405C22×C4711yescharacteristic, complemented
450C2×#97C22×C4711yescharacteristic, complemented
451C2×C4×C8C22×C4711yescharacteristic, complemented
452C4×C22⋊C4C22×C4711yescharacteristic
453#341C22×C4711yescharacteristic, complemented
454#341C22×C4711yescharacteristic, complemented
455#339C22×C4711yescharacteristic, complemented
456#339C22×C4711yescharacteristic, complemented
457#339C22×C4711yescharacteristic, complemented
458#339C22×C4711yescharacteristic, complemented
459#336C22×C4711yescharacteristic, complemented
460#336C22×C4711yescharacteristic, complemented
461C47#2258811yescharacteristic, direct product factor, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×C4×C4711yescharacteristic
469C2×#41C2×C4×C4711yescharacteristic
470C2×#41C23×C4711yescharacteristic
471C2×#41C23×C4711yescharacteristic
472C22×Q8C2×C4×C4711yescharacteristic
473C22×D4—21no—
474C22×D4C2×C4×C4711yescharacteristic
475C23×C4—21no—
476C23×C4C23×C4711yescharacteristic
477#131—22no—
478#131—22no—
479#131—41no—
480#131—41no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—41no—
484C2×M16—41no—
485C2×M16C2×C4×C4711yescharacteristic
486C2×M16C2×C4×C4711yescharacteristic
487C2×M16C2×C4×C4711yescharacteristic
488C2×M16C2×C4×C4711yescharacteristic
489C2×M16C23×C4711yescharacteristic
490C2×M16C23×C4711yescharacteristic
491C2×M16C23×C4711yescharacteristic
492C2×M16C23×C4711yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8C23×C4711yescharacteristic
496C22×C8C23×C4711yescharacteristic
497C22×C8C23×C4711yescharacteristic
498C22×C8C23×C4711yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×C4×C4711yescharacteristic
502#117C2×C4×C4711yescharacteristic
503#117C23×C4711yescharacteristic
504#117C23×C4711yescharacteristic
505C2×C4⋊C4C2×C4×C4711yescharacteristic
506C2×C4⋊C4C2×C4×C4711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42—21no—
510C2×C42C23×C4711yescharacteristic
511C2×C42C23×C4711yescharacteristic
512#108—41no—
513#108—41no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—22no—
519#104—22no—
520#104—41no—
521#104—41no—
522#103C2×C4×C4711yescharacteristic
523#103C2×C4×C4711yescharacteristic
524#103C2×C4×C4711yescharacteristic
525#103C2×C4×C4711yescharacteristic
526#103C2×C4×C4711yescharacteristic
527#103C2×C4×C4711yescharacteristic
528#103C2×C4×C4711yescharacteristic
529#103C2×C4×C4711yescharacteristic
530#102C2×C4×C4711yescharacteristic
531#102C2×C4×C4711yescharacteristic
532#102C2×C4×C4711yescharacteristic
533#102C2×C4×C4711yescharacteristic
534#102C2×C4×C4711yescharacteristic
535#102C2×C4×C4711yescharacteristic
536#102C2×C4×C4711yescharacteristic
537#102C2×C4×C4711yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546C22⋊C8D4×C4711yescharacteristic
547C22⋊C8D4×C4711yescharacteristic
548C22⋊C8D4×C4711yescharacteristic
549C22⋊C8D4×C4711yescharacteristic
550#97—21no—
551#97—21no—
552#97—41no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—41no—
556#95—21no—
557C24—21no—
558C24#41×C4711yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#41×C4712yes—
574#41#41×C4712yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×C4×C4711yescharacteristic
579C2×Q8C22×C4×C4711yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×C4×C4711yescharacteristic
590C2×D4C22×C4×C4711yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C22×C4×C4711yescharacteristic
607C22×C4C22×C4×C4711yescharacteristic
608C22×C4C2×D4×C4711yescharacteristic
609C22×C4C2×D4×C4711yescharacteristic
610C22×C4#41×C4711yescharacteristic
611C22×C4C24×C4711yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—42no—
625M16—42no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8C22×C4×C4711yescharacteristic
641C2×C8C22×C4×C4711yescharacteristic
642C2×C8C22×C4×C4711yescharacteristic
643C2×C8C22×C4×C4711yescharacteristic
644C2×C8C2×D4×C4711yescharacteristic
645C2×C8C2×D4×C4711yescharacteristic
646C2×C8C2×D4×C4711yescharacteristic
647C2×C8C2×D4×C4711yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×C4×C4711yescharacteristic
651C4⋊C4C22×C4×C4711yescharacteristic
652C4⋊C4C22×C4×C4711yescharacteristic
653C4⋊C4C22×C4×C4711yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×D4×C4711yescharacteristic
677C23C4×D4×C4711yescharacteristic
678C23C2×#41×C4711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#117×C4712yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#117×C4712yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4C4×D4×C4711yescharacteristic
727C2×C4C4×D4×C4711yescharacteristic
728C2×C4C23×C4×C4711yescharacteristic
729C2×C4C22×D4×C4711yescharacteristic
730C2×C4C2×#41×C4711yescharacteristic
731C2×C4C2×#41×C4711yescharacteristic
732C2×C4H(5,𝔽2)×C4711yescharacteristic
733C2×C4H(5,𝔽2)×C4711yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—22no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×D4×C4711yescharacteristic
764C22C47×#55111yescharacteristic
765C22C47×#55111yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4C2×#117×C4711yescharacteristic
777C4C47×#51811yescharacteristic
778C4C47×#54611yescharacteristic
779C4C47×#54611yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2C47×#234211yescharacteristic
787C2C47×#295511yescharacteristic
788C2C47×#295611yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC22×C47C2×C4×D4
prime radicalC22×#41×C47C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×C22⋊C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2924C2semidirect
4. C47×#1938C2semidirect
5. C47×#1937C2semidirect
6. C47×#1929C2semidirect
7. C47×#1929C2semidirect
8. C47×#1866C2semidirect
9. C47×#1866C2semidirect
10. C47×#1826C2semidirect
11. C47×#1811C2semidirect
13. C47×#1765C2semidirect
14. C47×#1764C2semidirect
15. C47×#1753C2semidirect
25. C2×#108×C47C22semidirect
26. C2×#108×C47C22semidirect
27. C47×#424C22semidirect
28. C47×#424C22semidirect
33. C47×#419C4semidirect
34. C47×#419C4semidirect
35. C47×#418C4semidirect
36. C47×#418C4semidirect
37. C47×#417C4semidirect
38. C47×#417C4semidirect
39. C47×#417C4semidirect
40. C47×#417C4semidirect
54. C47×#405C22semidirect
55. C47×#405C22semidirect
56. C2×#97×C47C22semidirect
57. C2×C4×C8×C47C22semidirect
59. C47×#341C22semidirect
60. C47×#341C22semidirect
61. C47×#339C22semidirect
62. C47×#339C22semidirect
63. C47×#339C22semidirect
64. C47×#339C22semidirect
65. C47×#336C22semidirect
66. C47×#336C22semidirect
351. #22588C47direct (N × H)
386. #2924C2×C47semidirect
389. #1938C2×C47semidirect
390. #1937C2×C47semidirect
391. #1929C2×C47semidirect
392. #1929C2×C47semidirect
393. #1866C2×C47semidirect
394. #1866C2×C47semidirect
395. #1826C2×C47semidirect
396. #1811C2×C47semidirect
398. #1765C2×C47semidirect
399. #1764C2×C47semidirect
400. #1753C2×C47semidirect
419. C2×#108C22×C47semidirect
420. C2×#108C22×C47semidirect
421. #424C22×C47semidirect
422. #424C22×C47semidirect
427. #419C4×C47semidirect
428. #419C4×C47semidirect
429. #418C4×C47semidirect
430. #418C4×C47semidirect
431. #417C4×C47semidirect
432. #417C4×C47semidirect
433. #417C4×C47semidirect
434. #417C4×C47semidirect
448. #405C22×C47semidirect
449. #405C22×C47semidirect
450. C2×#97C22×C47semidirect
451. C2×C4×C8C22×C47semidirect
453. #341C22×C47semidirect
454. #341C22×C47semidirect
455. #339C22×C47semidirect
456. #339C22×C47semidirect
457. #339C22×C47semidirect
458. #339C22×C47semidirect
459. #336C22×C47semidirect
460. #336C22×C47semidirect
461. C47#22588direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#29242
C47×#28962
C47×#28802
C47×#19382
C47×#19372
C47×#19292
C47×#18662
C47×#18262
C47×#18112
C47×#17892
C47×#17652
C47×#17642
C47×#17532
#2258847