Finite Group Databasebeta

← C47×#22784 #26062482

Subgroups — C47×#22784 #26062482

Order 12032.

740 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2943C211yesmaximal, characteristic
2C47×#2925C211yesmaximal, characteristic, complemented
3C47×#2906C211yesmaximal, characteristic, complemented
4C47×#1938C211yesmaximal, characteristic, complemented
5C47×#1937C211yesmaximal, characteristic, complemented
6C47×#1922C211yesmaximal, characteristic, complemented
7C47×#1922C211yesmaximal, characteristic, complemented
8C47×#1876C211yesmaximal, characteristic
9C47×#1876C211yesmaximal, characteristic
10C47×#1838C211yesmaximal, characteristic, complemented
11C47×#1806C211yesmaximal, characteristic, complemented
12C47×#1806C211yesmaximal, characteristic, complemented
13C47×#1771C211yesmaximal, characteristic, complemented
14C47×#1765C211yesmaximal, characteristic, complemented
15C47×#1764C211yesmaximal, characteristic, complemented
16C2×#135×C47C2211yescharacteristic
17C2×#131×C47C2211yescharacteristic
18C2×#131×C47C2211yescharacteristic
19C4×#41×C47C2211yescharacteristic
20C4×#41×C47C2211yescharacteristic
21C47×#442C411yescharacteristic, complemented
22C47×#442C411yescharacteristic, complemented
23C47×#441C411yescharacteristic, complemented
24C47×#441C411yescharacteristic, complemented
25C47×#440C411yescharacteristic, complemented
26C47×#440C411yescharacteristic, complemented
27C47×#440C411yescharacteristic, complemented
28C47×#440C411yescharacteristic, complemented
29C47×#433—21no—
30C47×#433—21no—
31C47×#432—21no—
32C47×#431—21no—
33C47×#427C2211yescharacteristic
34C47×#424—21no—
35C47×#424—21no—
36C47×#424C2211yescharacteristic
37C47×#424C2211yescharacteristic
38C47×#423—21no—
39C47×#423C2211yescharacteristic
40C47×#423C2211yescharacteristic
41C2×C4⋊C8×C47—21no—
42C2×C4⋊C8×C47C2211yescharacteristic
43C2×#104×C47C2211yescharacteristic
44C2×#104×C47C2211yescharacteristic
45C2×#104×C47C2211yescharacteristic
46C2×#104×C47C2211yescharacteristic
47C47×#416C2211yescharacteristic
48C47×#416C2211yescharacteristic
49C47×#408C2211yescharacteristic
50C47×#408C2211yescharacteristic
51C47×#405C2211yescharacteristic
52C47×#405C2211yescharacteristic
53C2×#97×C47C2211yescharacteristic
54C2×#97×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C47×#341C2211yescharacteristic
58C47×#341C2211yescharacteristic
59C47×#341C2211yescharacteristic
60C47×#341C2211yescharacteristic
61C47×#339C2211yescharacteristic
62C47×#339C2211yescharacteristic
63C47×#339C2211yescharacteristic
64C47×#339C2211yescharacteristic
65C47×#336C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C2×#41×C47C2311yescharacteristic
68C2×#41×C47C2311yescharacteristic
69#135×C47—22no—
70#135×C47—22no—
71C2×Q16×C47C2×C411yescharacteristic
72C2×SD16×C47C2×C411yescharacteristic
73C2×SD16×C47C2×C411yescharacteristic
74C2×D8×C47C2×C411yescharacteristic
75#131×C47—22no—
76#131×C47—22no—
77#131×C47—41no—
78#131×C47—41no—
79C2×M16×C47—21no—
80C2×M16×C47—21no—
81C2×M16×C47C2311yescharacteristic
82C2×M16×C47C2311yescharacteristic
83C2×M16×C47C2311yescharacteristic
84C2×M16×C47C2311yescharacteristic
85C22×C8×C47—21no—
86C22×C8×C47—21no—
87C22×C8×C47C2311yescharacteristic
88C22×C8×C47C2311yescharacteristic
89C22×C8×C47C2311yescharacteristic
90C22×C8×C47C2311yescharacteristic
91C4×Q8×C47C2×C411yescharacteristic
92C4×Q8×C47C2×C411yescharacteristic
93C4×Q8×C47C2×C411yescharacteristic
94C4×Q8×C47C2×C411yescharacteristic
95C4×D4×C47—21no—
96C4×D4×C47—21no—
97C4×D4×C47—21no—
98C4×D4×C47—21no—
99C4×D4×C47C2×C411yescharacteristic
100C4×D4×C47C2×C411yescharacteristic
101C4×D4×C47C2×C411yescharacteristic
102C4×D4×C47C2×C411yescharacteristic
103#117×C47—21no—
104#117×C47—21no—
105#117×C47C2311yescharacteristic
106#117×C47C2311yescharacteristic
107C2×C4⋊C4×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47—21no—
110C2×C42×C47C2311yescharacteristic
111C2×C42×C47C2311yescharacteristic
112C2×C42×C47C2311yescharacteristic
113#107×C47C2×C411yescharacteristic
114#107×C47C2×C411yescharacteristic
115#106×C47C2×C411yescharacteristic
116#106×C47C2×C411yescharacteristic
117C4⋊C8×C47—21no—
118C4⋊C8×C47—21no—
119C4⋊C8×C47—21no—
120C4⋊C8×C47—21no—
121C4⋊C8×C47—21no—
122C4⋊C8×C47—21no—
123C4⋊C8×C47—21no—
124C4⋊C8×C47—21no—
125C4⋊C8×C47D411yescharacteristic
126C4⋊C8×C47D411yescharacteristic
127C4⋊C8×C47D411yescharacteristic
128C4⋊C8×C47D411yescharacteristic
129#104×C47—22no—
130#104×C47—22no—
131#104×C47—41no—
132#104×C47—41no—
133#103×C47C2×C411yescharacteristic
134#103×C47C2×C411yescharacteristic
135#103×C47C2×C411yescharacteristic
136#103×C47C2×C411yescharacteristic
137#102×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140#102×C47C2×C411yescharacteristic
141C22⋊C8×C47—21no—
142C22⋊C8×C47—21no—
143C22⋊C8×C47—21no—
144C22⋊C8×C47—21no—
145#97×C47—21no—
146#97×C47—21no—
147#97×C47—41no—
148#97×C47C2×C411yescharacteristic
149#97×C47C2×C411yescharacteristic
150#97×C47C2×C411yescharacteristic
151#97×C47C2×C411yescharacteristic
152C4×C8×C47—21no—
153C4×C8×C47—21no—
154C4×C8×C47—41no—
155#95×C47—21no—
156#41×C47—21no—
157#41×C47—21no—
158#41×C47—21no—
159#41×C47—21no—
160#41×C47—21no—
161#41×C47—21no—
162#41×C47#4112yes—
163#41×C47#4112yes—
164C2×Q8×C47C22×C411yescharacteristic
165C2×Q8×C47C22×C411yescharacteristic
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47C22×C411yescharacteristic
169C2×D4×C47C22×C411yescharacteristic
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47#4111yescharacteristic
179C22×C4×C47#4111yescharacteristic
180C22×C4×C47C2411yescharacteristic
181Q16×C47—22no—
182SD16×C47—22no—
183SD16×C47—22no—
184D8×C47—22no—
185M16×C47—21no—
186M16×C47—21no—
187M16×C47—21no—
188M16×C47—21no—
189M16×C47—21no—
190M16×C47—21no—
191M16×C47—21no—
192M16×C47—21no—
193M16×C47—42no—
194M16×C47—42no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—42no—
208C2×C8×C47—42no—
209C2×C8×C47C22×C411yescharacteristic
210C2×C8×C47C22×C411yescharacteristic
211C2×C8×C47C22×C411yescharacteristic
212C2×C8×C47C22×C411yescharacteristic
213C2×C8×C47C2×D411yescharacteristic
214C2×C8×C47C2×D411yescharacteristic
215C2×C8×C47C2×D411yescharacteristic
216C2×C8×C47C2×D411yescharacteristic
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—42no—
222C4⋊C4×C47C22×C411yescharacteristic
223C4⋊C4×C47C22×C411yescharacteristic
224C4⋊C4×C47C22×C411yescharacteristic
225C4⋊C4×C47C22×C411yescharacteristic
226C22⋊C4×C47—21no—
227C22⋊C4×C47—21no—
228C22⋊C4×C47—21no—
229C22⋊C4×C47—21no—
230C22⋊C4×C47—21no—
231C22⋊C4×C47—21no—
232C42×C47—21no—
233C42×C47—21no—
234C42×C47—21no—
235C42×C47—21no—
236C42×C47—21no—
237C42×C47—21no—
238C42×C47—21no—
239C42×C47—21no—
240C42×C47—21no—
241C42×C47—21no—
242C42×C47C22×C411yescharacteristic
243C42×C47C22×C411yescharacteristic
244C42×C47C2×D411yescharacteristic
245C42×C47C2×D411yescharacteristic
246C23×C47—21no—
247C23×C47—21no—
248C23×C47C2×#4111yescharacteristic
249Q8×C47—21no—
250Q8×C47—21no—
251Q8×C47—21no—
252Q8×C47#11712yes—
253D4×C47—22no—
254D4×C47—22no—
255D4×C47—21no—
256D4×C47—21no—
257D4×C47—21no—
258D4×C47—41no—
259D4×C47—41no—
260D4×C47#11712yes—
261C2×C4×C47—21no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—42no—
273C2×C4×C47—42no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—81no—
282C2×C4×C47—81no—
283C2×C4×C47C4×D411yescharacteristic
284C2×C4×C47C4×D411yescharacteristic
285C2×C4×C47C4×D411yescharacteristic
286C2×C4×C47C4×D411yescharacteristic
287C2×C4×C47C23×C411yescharacteristic
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C2×#4111yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47H(5,𝔽2)11yescharacteristic
292C2×C4×C472−1+411yescharacteristic
293C8×C47—21no—
294C8×C47—21no—
295C8×C47—21no—
296C8×C47—21no—
297C8×C47—21no—
298C8×C47—21no—
299C8×C47—21no—
300C8×C47—21no—
301C8×C47—41no—
302C8×C47—41no—
303C8×C47—41no—
304C8×C47—41no—
305#22784C4711yesmaximal, characteristic, direct product factor, Sylow
306C22×C47—21no—
307C22×C47—21no—
308C22×C47—22no—
309C22×C47—41no—
310C22×C47—41no—
311C22×C47—41no—
312C22×C47—41no—
313C22×C47—41no—
314C22×C47C2×C4×D411yescharacteristic
315C22×C47#55211yescharacteristic
316C22×C47#55311yescharacteristic
317C4×C47—22no—
318C4×C47—21no—
319C4×C47—21no—
320C4×C47—21no—
321C4×C47—21no—
322C4×C47—42no—
323C4×C47—41no—
324C4×C47—41no—
325C4×C47—41no—
326C4×C47—41no—
327C4×C47—41no—
328C4×C47—81no—
329C4×C47C2×#11711yescharacteristic
330C4×C47#52011yescharacteristic
331C4×C47#54611yescharacteristic
332C4×C47#54811yescharacteristic
333#2943C2×C4711yescharacteristic
334#2925C2×C4711yescharacteristic, complemented
335#2906C2×C4711yescharacteristic, complemented
336#1938C2×C4711yescharacteristic, complemented
337#1937C2×C4711yescharacteristic, complemented
338#1922C2×C4711yescharacteristic, complemented
339#1922C2×C4711yescharacteristic, complemented
340#1876C2×C4711yescharacteristic
341#1876C2×C4711yescharacteristic
342#1838C2×C4711yescharacteristic, complemented
343#1806C2×C4711yescharacteristic, complemented
344#1806C2×C4711yescharacteristic, complemented
345#1771C2×C4711yescharacteristic, complemented
346#1765C2×C4711yescharacteristic, complemented
347#1764C2×C4711yescharacteristic, complemented
348C2×C47—21no—
349C2×C47—21no—
350C2×C47—42no—
351C2×C47—81no—
352C2×C47#235211yescharacteristic
353C2×C47#295511yescharacteristic
354C2×C47#295611yescharacteristic
355C2×#135C22×C4711yescharacteristic
356C2×#131C22×C4711yescharacteristic
357C2×#131C22×C4711yescharacteristic
358C4×#41C22×C4711yescharacteristic
359C4×#41C22×C4711yescharacteristic
360#442C4×C4711yescharacteristic, complemented
361#442C4×C4711yescharacteristic, complemented
362#441C4×C4711yescharacteristic, complemented
363#441C4×C4711yescharacteristic, complemented
364#440C4×C4711yescharacteristic, complemented
365#440C4×C4711yescharacteristic, complemented
366#440C4×C4711yescharacteristic, complemented
367#440C4×C4711yescharacteristic, complemented
368#433—21no—
369#433—21no—
370#432—21no—
371#431—21no—
372#427C22×C4711yescharacteristic
373#424—21no—
374#424—21no—
375#424C22×C4711yescharacteristic
376#424C22×C4711yescharacteristic
377#423—21no—
378#423C22×C4711yescharacteristic
379#423C22×C4711yescharacteristic
380C2×C4⋊C8—21no—
381C2×C4⋊C8C22×C4711yescharacteristic
382C2×#104C22×C4711yescharacteristic
383C2×#104C22×C4711yescharacteristic
384C2×#104C22×C4711yescharacteristic
385C2×#104C22×C4711yescharacteristic
386#416C22×C4711yescharacteristic
387#416C22×C4711yescharacteristic
388#408C22×C4711yescharacteristic
389#408C22×C4711yescharacteristic
390#405C22×C4711yescharacteristic
391#405C22×C4711yescharacteristic
392C2×#97C22×C4711yescharacteristic
393C2×#97C22×C4711yescharacteristic
394C2×C4×C8C22×C4711yescharacteristic
395C4×C4⋊C4C22×C4711yescharacteristic
396#341C22×C4711yescharacteristic
397#341C22×C4711yescharacteristic
398#341C22×C4711yescharacteristic
399#341C22×C4711yescharacteristic
400#339C22×C4711yescharacteristic
401#339C22×C4711yescharacteristic
402#339C22×C4711yescharacteristic
403#339C22×C4711yescharacteristic
404#336C22×C4711yescharacteristic
405#336C22×C4711yescharacteristic
406C47#2278411yescharacteristic, direct product factor, Sylow
407C2×#41C23×C4711yescharacteristic
408C2×#41C23×C4711yescharacteristic
409#135—22no—
410#135—22no—
411C2×Q16C2×C4×C4711yescharacteristic
412C2×SD16C2×C4×C4711yescharacteristic
413C2×SD16C2×C4×C4711yescharacteristic
414C2×D8C2×C4×C4711yescharacteristic
415#131—22no—
416#131—22no—
417#131—41no—
418#131—41no—
419C2×M16—21no—
420C2×M16—21no—
421C2×M16C23×C4711yescharacteristic
422C2×M16C23×C4711yescharacteristic
423C2×M16C23×C4711yescharacteristic
424C2×M16C23×C4711yescharacteristic
425C22×C8—21no—
426C22×C8—21no—
427C22×C8C23×C4711yescharacteristic
428C22×C8C23×C4711yescharacteristic
429C22×C8C23×C4711yescharacteristic
430C22×C8C23×C4711yescharacteristic
431C4×Q8C2×C4×C4711yescharacteristic
432C4×Q8C2×C4×C4711yescharacteristic
433C4×Q8C2×C4×C4711yescharacteristic
434C4×Q8C2×C4×C4711yescharacteristic
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4C2×C4×C4711yescharacteristic
440C4×D4C2×C4×C4711yescharacteristic
441C4×D4C2×C4×C4711yescharacteristic
442C4×D4C2×C4×C4711yescharacteristic
443#117—21no—
444#117—21no—
445#117C23×C4711yescharacteristic
446#117C23×C4711yescharacteristic
447C2×C4⋊C4—21no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42C23×C4711yescharacteristic
451C2×C42C23×C4711yescharacteristic
452C2×C42C23×C4711yescharacteristic
453#107C2×C4×C4711yescharacteristic
454#107C2×C4×C4711yescharacteristic
455#106C2×C4×C4711yescharacteristic
456#106C2×C4×C4711yescharacteristic
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—21no—
462C4⋊C8—21no—
463C4⋊C8—21no—
464C4⋊C8—21no—
465C4⋊C8D4×C4711yescharacteristic
466C4⋊C8D4×C4711yescharacteristic
467C4⋊C8D4×C4711yescharacteristic
468C4⋊C8D4×C4711yescharacteristic
469#104—22no—
470#104—22no—
471#104—41no—
472#104—41no—
473#103C2×C4×C4711yescharacteristic
474#103C2×C4×C4711yescharacteristic
475#103C2×C4×C4711yescharacteristic
476#103C2×C4×C4711yescharacteristic
477#102C2×C4×C4711yescharacteristic
478#102C2×C4×C4711yescharacteristic
479#102C2×C4×C4711yescharacteristic
480#102C2×C4×C4711yescharacteristic
481C22⋊C8—21no—
482C22⋊C8—21no—
483C22⋊C8—21no—
484C22⋊C8—21no—
485#97—21no—
486#97—21no—
487#97—41no—
488#97C2×C4×C4711yescharacteristic
489#97C2×C4×C4711yescharacteristic
490#97C2×C4×C4711yescharacteristic
491#97C2×C4×C4711yescharacteristic
492C4×C8—21no—
493C4×C8—21no—
494C4×C8—41no—
495#95—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41—21no—
502#41#41×C4712yes—
503#41#41×C4712yes—
504C2×Q8C22×C4×C4711yescharacteristic
505C2×Q8C22×C4×C4711yescharacteristic
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C22×C4×C4711yescharacteristic
509C2×D4C22×C4×C4711yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4#41×C4711yescharacteristic
519C22×C4#41×C4711yescharacteristic
520C22×C4C24×C4711yescharacteristic
521Q16—22no—
522SD16—22no—
523SD16—22no—
524D8—22no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—42no—
534M16—42no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—42no—
548C2×C8—42no—
549C2×C8C22×C4×C4711yescharacteristic
550C2×C8C22×C4×C4711yescharacteristic
551C2×C8C22×C4×C4711yescharacteristic
552C2×C8C22×C4×C4711yescharacteristic
553C2×C8C2×D4×C4711yescharacteristic
554C2×C8C2×D4×C4711yescharacteristic
555C2×C8C2×D4×C4711yescharacteristic
556C2×C8C2×D4×C4711yescharacteristic
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—42no—
562C4⋊C4C22×C4×C4711yescharacteristic
563C4⋊C4C22×C4×C4711yescharacteristic
564C4⋊C4C22×C4×C4711yescharacteristic
565C4⋊C4C22×C4×C4711yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42C22×C4×C4711yescharacteristic
583C42C22×C4×C4711yescharacteristic
584C42C2×D4×C4711yescharacteristic
585C42C2×D4×C4711yescharacteristic
586C23—21no—
587C23—21no—
588C23C2×#41×C4711yescharacteristic
589Q8—21no—
590Q8—21no—
591Q8—21no—
592Q8#117×C4712yes—
593D4—22no—
594D4—22no—
595D4—21no—
596D4—21no—
597D4—21no—
598D4—41no—
599D4—41no—
600D4#117×C4712yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4C4×D4×C4711yescharacteristic
624C2×C4C4×D4×C4711yescharacteristic
625C2×C4C4×D4×C4711yescharacteristic
626C2×C4C4×D4×C4711yescharacteristic
627C2×C4C23×C4×C4711yescharacteristic
628C2×C4C22×D4×C4711yescharacteristic
629C2×C4C2×#41×C4711yescharacteristic
630C2×C4C2×#41×C4711yescharacteristic
631C2×C4H(5,𝔽2)×C4711yescharacteristic
632C2×C42−1+4×C4711yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—21no—
640C8—21no—
641C8—41no—
642C8—41no—
643C8—41no—
644C8—41no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22C2×C4×D4×C4711yescharacteristic
654C22C47×#55211yescharacteristic
655C22C47×#55311yescharacteristic
656C4—22no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—81no—
668C4C2×#117×C4711yescharacteristic
669C4C47×#52011yescharacteristic
670C4C47×#54611yescharacteristic
671C4C47×#54811yescharacteristic
672C2—21no—
673C2—21no—
674C2—42no—
675C2—81no—
676C2C47×#235211yescharacteristic
677C2C47×#295511yescharacteristic
678C2C47×#295611yescharacteristic
subgroupG/H
centerC2×C4×C47C22×D4
commutatorC2×C4C23×C4×C47
Frattini, cosocleC22×C4C24×C47
socleC22×C47C2×C4×D4
prime radicalC2×#135×C47C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ C2×C4⋊C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2925C2semidirect
3. C47×#2906C2semidirect
4. C47×#1938C2semidirect
5. C47×#1937C2semidirect
6. C47×#1922C2semidirect
7. C47×#1922C2semidirect
10. C47×#1838C2semidirect
11. C47×#1806C2semidirect
12. C47×#1806C2semidirect
13. C47×#1771C2semidirect
14. C47×#1765C2semidirect
15. C47×#1764C2semidirect
21. C47×#442C4semidirect
22. C47×#442C4semidirect
23. C47×#441C4semidirect
24. C47×#441C4semidirect
25. C47×#440C4semidirect
26. C47×#440C4semidirect
27. C47×#440C4semidirect
28. C47×#440C4semidirect
305. #22784C47direct (N × H)
334. #2925C2×C47semidirect
335. #2906C2×C47semidirect
336. #1938C2×C47semidirect
337. #1937C2×C47semidirect
338. #1922C2×C47semidirect
339. #1922C2×C47semidirect
342. #1838C2×C47semidirect
343. #1806C2×C47semidirect
344. #1806C2×C47semidirect
345. #1771C2×C47semidirect
346. #1765C2×C47semidirect
347. #1764C2×C47semidirect
360. #442C4×C47semidirect
361. #442C4×C47semidirect
362. #441C4×C47semidirect
363. #441C4×C47semidirect
364. #440C4×C47semidirect
365. #440C4×C47semidirect
366. #440C4×C47semidirect
367. #440C4×C47semidirect
406. C47#22784direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#29432
C47×#29252
C47×#29062
C47×#19382
C47×#19372
C47×#19222
C47×#18762
C47×#18382
C47×#18062
C47×#17712
C47×#17652
C47×#17642
#2278447