Finite Group Databasebeta

← C4×#15689321 #26222472

Subgroups — C4×#15689321 #26222472

Order 12032.

1152 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689321C211yesmaximal, characteristic
2C2×C4×#10625336C211yesmaximal, characteristic, complemented
3C4×#13094020C211yesmaximal, characteristic
4C4×Q8×Dic47C211yesmaximal, characteristic, complemented
5#20244313C211yesmaximal, characteristic
6#20244148C211yesmaximal, characteristic, complemented
7#20244018C211yesmaximal, characteristic, complemented
8#20244014C211yesmaximal, characteristic, complemented
9#20243745C211yesmaximal, characteristic, complemented
10#20243741C211yesmaximal, characteristic, complemented
11#20243391C211yesmaximal, characteristic, complemented
12C4×Dic47⋊C8C211yesmaximal, characteristic, complemented
13C4×#13093946C211yesmaximal, characteristic, complemented
14C4×#13093945C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C2×#13094020C2211yescharacteristic
18C2×Q8×Dic47C2211yescharacteristic
19C2×Q8×Dic47C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21C2×C4×C22⋊D47—21no—
22C2×C4×C22⋊D47—21no—
23#15689321C418yesdirect product factor
24C4×#10625336—24no—
25C2×#13093955C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×Dic47⋊C8C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093946C2211yescharacteristic
30C2×#13093946C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35#15689026C2211yescharacteristic
36#15689024C2211yescharacteristic
37#15689023—21no—
38#15689023—21no—
39#15688992C2211yescharacteristic
40C4⋊C4×Dic47—21no—
41C4⋊C4×Dic47—21no—
42C4⋊C4×Dic47C2211yescharacteristic
43C4⋊C4×Dic47C2211yescharacteristic
44C4×C4⋊Dic47—21no—
45C4×C4⋊Dic47C2211yescharacteristic
46C42×Dic47—21no—
47C42×Dic47C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C22×SD16×C47C2211yescharacteristic
55C2×C4×Q8×C47C2211yescharacteristic
56C2×C4×D4×C47C2211yescharacteristic
57C4×SD16×C47—24no—
58C2×#106×C47C2211yescharacteristic
59C2×#103×C47C2211yescharacteristic
60C2×#102×C47C2211yescharacteristic
61C2×C4×C8×C47C2211yescharacteristic
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C22×C22⋊D47—21no—
65C22×C4×D47—21no—
66C2×#10625336—22no—
67C2×#10625336—22no—
68C2×#10625336C2×C414yescomplemented
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71#13094020—22no—
72#13094020C2×C414yes—
73Q8×Dic47—22no—
74Q8×Dic47—22no—
75Q8×Dic47—22no—
76Q8×Dic47C2×C414yescomplemented
77C4×D188—22no—
78C4×D188—22no—
79C4×C22⋊D47—44no—
80C4×C22⋊D47—44no—
81C2×C4⋊Dic47—21no—
82C2×C4⋊Dic47—21no—
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×C4⋊Dic47C2311yescharacteristic
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C2×C22⋊Dic47—21no—
89C2×C22⋊Dic47—21no—
90C2×(C2×D47)⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×(C2×D47)⋊C4—21no—
93C2×C4×Dic47—21no—
94C2×C4×Dic47—21no—
95C2×C4×Dic47—21no—
96C2×C4×Dic47—21no—
97C2×C4×Dic47—21no—
98C2×C4×Dic47D411yescharacteristic
99C2×C4×Dic47D411yescharacteristic
100C2×C4×Dic47D411yescharacteristic
101C2×C4×Dic47D411yescharacteristic
102C2×C4×Dic47C2311yescharacteristic
103C2×C4×Dic47C2311yescharacteristic
104#13093955—22no—
105Dic47⋊C8—22no—
106Dic47⋊C8C2×C414yescomplemented
107#13093948—22no—
108#13093946—22no—
109#13093946C2×C414yescomplemented
110#13093945—22no—
111#13093945C2×C414yescomplemented
112#13093944—22no—
113C4×C47⋊C8—22no—
114C47⋊#95—21no—
115C47⋊#95—21no—
116C47⋊#95—21no—
117C22×Q8×C47C2311yescharacteristic
118C22×D4×C47C2311yescharacteristic
119C23×C4×C47—21no—
120C2×SD16×C47—22no—
121C2×SD16×C47—22no—
122C2×SD16×C47C2×C414yescomplemented
123C22×C8×C47C2311yescharacteristic
124C22×C8×C47C2311yescharacteristic
125C4×Q8×C47—22no—
126C4×Q8×C47D414yescomplemented
127C4×D4×C47—22no—
128C4×D4×C47—22no—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C22⋊C4×C47—21no—
133C2×C42×C47—21no—
134C2×C42×C47C2311yescharacteristic
135#106×C47—22no—
136#103×C47—22no—
137#102×C47—22no—
138C4×C8×C47—22no—
139C24×C47—21no—
140C23×D47—21no—
141C2×Q8×C47—21no—
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47C22×C412yes—
145C2×Q8×C47C2×D412yes—
146C2×Q8×C47#4112yes—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47C22×C412yes—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—42no—
157C22×C4×C47—42no—
158C22×C4×C47—42no—
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2411yescharacteristic
162C2×C22⋊D47—24no—
163C2×C22⋊D47—24no—
164C2×C22⋊D47—42no—
165C2×C22⋊D47—42no—
166C2×C22⋊D47—42no—
167C2×C22⋊D47—42no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47C2×D411yescharacteristic
172C22×Dic47C2×D411yescharacteristic
173C22×Dic47C2×D411yescharacteristic
174C22×Dic47C2×D411yescharacteristic
175C2×D188—21no—
176C2×D188—21no—
177C2×D188—21no—
178C2×D188—21no—
179C2×D188—21no—
180C2×D188C22×C412yes—
181C2×C4×D47—42no—
182C2×C4×D47—42no—
183C2×C4×D47—42no—
184SD16×C47—28no—
185C2×C8×C47—21no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47C22×C412yes—
191C4⋊C4×C47—24no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47C2×D412yes—
196C22⋊C4×C47—42no—
197C42×C47—24no—
198C42×C47C2×D412yes—
199C42×C47#4112yes—
200C22⋊Dic47—42no—
201C22⋊Dic47—42no—
202#10625336—28no—
203(C2×D47)⋊C4—42no—
204(C2×D47)⋊C4—42no—
205(C2×D47)⋊C4—42no—
206C4⋊Dic47—24no—
207C4⋊Dic47—21no—
208C4⋊Dic47—21no—
209C4⋊Dic47—24no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47C22×C412yes—
213C4⋊Dic47#4112yes—
214Dic47⋊C4—42no—
215Dic47⋊C4—42no—
216C4×Dic47—24no—
217C4×Dic47—22no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220C4×Dic47—24no—
221C4×Dic47—22no—
222C4×Dic47—41no—
223C4×Dic47—42no—
224C4×Dic47—42no—
225C4×Dic47—42no—
226C4×Dic47SD1614yescomplemented
227C4×Dic47C22×C412yes—
228C4×Dic47#4112yes—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8C22×C412yes—
235C23×C47—22no—
236C23×C47—41no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47—41no—
242C23×C47C22×D411yescharacteristic
243C22×D47—22no—
244C22×D47—41no—
245C22×D47—41no—
246C22×D47—41no—
247C22×D47—41no—
248C22×D47—41no—
249C22×D47—41no—
250Q8×C47—22no—
251Q8×C47—22no—
252Q8×C47—22no—
253Q8×C47C4×D414yescomplemented
254D4×C47—22no—
255D4×C47—22no—
256D4×C47—41no—
257D4×C47—41no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—22no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—84no—
270C2×C4×C47#12112yes—
271C2×C4×C47#12112yes—
272C2×C4×C47C2×SD1612yes—
273C2×C4×C47AGL(1,ℤ/8)12yes—
274C2×C4×C47C23×C411yescharacteristic
275C2×C4×C47C22×D411yescharacteristic
276C2×C4×C47C2×#4111yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C2×C4×C47C2×#4111yescharacteristic
279C2×C4×C47C2×#4111yescharacteristic
280C22⋊D47—48no—
281C22⋊D47—48no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—21no—
286C2×Dic47—22no—
287C2×Dic47—21no—
288C2×Dic47—22no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47C4×D412yes—
299C2×Dic47C4×D412yes—
300C2×Dic47C2×SD1612yes—
301C2×Dic47C2×SD1612yes—
302C2×Dic47#13512yes—
303D188—22no—
304D188—22no—
305D188—41no—
306D188—41no—
307C4×D47—84no—
308C8×C47—22no—
309C8×C47—41no—
310C47⋊C8—22no—
311C47⋊C8—41no—
312C4×#460—471nomaximal, Sylow
313C22×C47—42no—
314C22×C47—42no—
315C22×C47—42no—
316C22×C47—81no—
317C22×C47—81no—
318C22×C47—81no—
319C22×C47—81no—
320C22×C47C2×C4×D411yescharacteristic
321C22×C47C2×#12111yescharacteristic
322C22×C47#52511yescharacteristic
323C22×C47C22×SD1611yescharacteristic
324C22×C47C2×#13511yescharacteristic
325C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C47#57511yescharacteristic
327C2×D47—42no—
328C2×D47—42no—
329C2×D47—42no—
330C2×D47—81no—
331C2×D47—81no—
332C2×D47—81no—
333C2×D47—81no—
334C4×C47—22no—
335C4×C47—24no—
336C4×C47—42no—
337C4×C47—81no—
338C4×C47#46014yescomplemented
339C4×C47C2×C4×D411yescharacteristic
340C4×C47C4×#4111yescharacteristic
341C4×C47#52911yescharacteristic
342C4×C47#53211yescharacteristic
343Dic47—22no—
344Dic47—22no—
345Dic47—41no—
346Dic47—42no—
347Dic47—42no—
348Dic47—81no—
349Dic47C4×SD1614yescomplemented
350C2×#460—471no—
351C2×C4×SD16—471no—
352C2×C4×SD16D4711yescharacteristic, complemented
353C4×#127—471no—
354C42×Q8—471no—
355#1982—471no—
356#1948—471no—
357#1926—471no—
358#1926—471no—
359#1880—471no—
360#1880—471no—
361#1803—471no—
362C4×C4⋊C8—471no—
363C4×#102—471no—
364C4×#102—471no—
365C2×C47—82no—
366C2×C47C4×#12111yescharacteristic
367C2×C47C2×C4×SD1611yescharacteristic
368C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
369C2×C47C2×#46011yescharacteristic
370C2×C47#303511yescharacteristic
371C2×C47#310311yescharacteristic
372C2×C47#310611yescharacteristic
373D47—82no—
374C22×SD16—471no—
375C22×SD16C2×D4711yescharacteristic
376C2×#127—471no—
377C2×C4×Q8—471no—
378C2×C4×Q8—471no—
379C2×C4×Q8C2×D4711yescharacteristic
380C2×C4×D4—471no—
381C2×C4×D4—941no—
382C2×C4×D4—941no—
383C2×C4×D4C2×D4711yescharacteristic
384#460—478no—
385C4×SD16—24no—
386C4×SD16—944no—
387C2×#106—471no—
388C2×#106C2×D4711yescharacteristic
389C2×C4⋊C8—471no—
390C2×C4⋊C8—471no—
391C2×#103—471no—
392C2×#103C2×D4711yescharacteristic
393C2×#102—471no—
394C2×#102—471no—
395C2×#102—471no—
396C2×#102—471no—
397C2×#102—471no—
398C2×#102C2×D4711yescharacteristic
399C2×C4×C8—471no—
400C2×C4×C8C2×D4711yescharacteristic
401#390—471no—
402#390—471no—
403#390—941no—
404#390—941no—
405#384—471no—
406C4×C4⋊C4—471no—
407C4×C4⋊C4—471no—
408C4×C4⋊C4—471no—
409C4×C4⋊C4—941no—
410C4×C4⋊C4—941no—
411C4×C4⋊C4—941no—
412C43—471no—
413C43—941no—
414#340—471no—
415#340—471no—
416#340—471no—
417#340—471no—
418#336—471no—
419#336—471no—
420C47C4×#46011yescharacteristic, complemented, Sylow
421C22×Q8C22×D4711yescharacteristic
422C22×D4—471no—
423C22×D4—941no—
424C22×D4—941no—
425C22×D4C22×D4711yescharacteristic
426C23×C4—21no—
427C23×C4—941no—
428C2×SD16—22no—
429C2×SD16—22no—
430C2×SD16—474no—
431C2×SD16—942no—
432C2×SD16—942no—
433C2×SD16C4×D4714yescomplemented
434C22×C8—471no—
435C22×C8—471no—
436C22×C8C22×D4711yescharacteristic
437C22×C8C22×D4711yescharacteristic
438#127—474no—
439#127—942no—
440C4×Q8—22no—
441C4×Q8—474no—
442C4×Q8—942no—
443C4×Q8—942no—
444C4×Q8—942no—
445C4×Q8C22⋊D4714yescomplemented
446C4×D4—22no—
447C4×D4—22no—
448C4×D4—942no—
449C4×D4—942no—
450C4×D4—1884no—
451C4×D4—1884no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—471no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—941no—
457C2×C4⋊C4—941no—
458C2×C4⋊C4—941no—
459C2×C4⋊C4—941no—
460C2×C4⋊C4C22×D4711yescharacteristic
461C2×C4⋊C4C22×D4711yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—941no—
464C2×C22⋊C4—941no—
465C2×C22⋊C4—941no—
466C2×C22⋊C4—941no—
467C2×C22⋊C4—941no—
468C2×C42—21no—
469C2×C42—471no—
470C2×C42—471no—
471C2×C42—471no—
472C2×C42—471no—
473C2×C42—471no—
474C2×C42—471no—
475C2×C42—941no—
476C2×C42—941no—
477C2×C42—941no—
478C2×C42—941no—
479C2×C42—941no—
480C2×C42C22×D4711yescharacteristic
481#106—22no—
482#106—942no—
483C4⋊C8—474no—
484C4⋊C8—942no—
485#103—22no—
486#103—942no—
487#102—22no—
488#102—474no—
489#102—474no—
490#102—942no—
491#102—942no—
492#102—942no—
493C4×C8—22no—
494C4×C8—942no—
495#95—941no—
496#95—941no—
497#95—941no—
498C24—21no—
499C24—941no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C2×C4×D4712yes—
504C2×Q8#1062535012yes—
505C2×Q8C2×C22⋊D4712yes—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—472no—
512C2×D4—944no—
513C2×D4—944no—
514C2×D4—941no—
515C2×D4—941no—
516C2×D4—941no—
517C2×D4—941no—
518C2×D4—941no—
519C2×D4—1882no—
520C2×D4—1882no—
521C2×D4—1882no—
522C2×D4—1882no—
523C2×D4C2×C4×D4712yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—471no—
531C22×C4—471no—
532C22×C4—471no—
533C22×C4—471no—
534C22×C4—941no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—1882no—
538C22×C4—1882no—
539C22×C4—1882no—
540C22×C4D4×D4711yescharacteristic
541C22×C4D4×D4711yescharacteristic
542C22×C4C23×D4711yescharacteristic
543SD16—28no—
544SD16—948no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—472no—
551C2×C8—941no—
552C2×C8—941no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8—941no—
556C2×C8C2×C4×D4712yes—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—472no—
562C4⋊C4—472no—
563C4⋊C4—944no—
564C4⋊C4—944no—
565C4⋊C4—941no—
566C4⋊C4—941no—
567C4⋊C4—941no—
568C4⋊C4—941no—
569C4⋊C4—1882no—
570C4⋊C4—1882no—
571C4⋊C4C2×C22⋊D4712yes—
572C22⋊C4—42no—
573C22⋊C4—1882no—
574C22⋊C4—1882no—
575C22⋊C4—1882no—
576C22⋊C4—1882no—
577C22⋊C4—1882no—
578C42—24no—
579C42—474no—
580C42—472no—
581C42—472no—
582C42—942no—
583C42—944no—
584C42—944no—
585C42—942no—
586C42—941no—
587C42—941no—
588C42—1881no—
589C42—1882no—
590C42—1882no—
591C42—1882no—
592C42#1062535212yes—
593C42C2×C22⋊D4712yes—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—942no—
602C23—1881no—
603C23—1881no—
604C23—1881no—
605C23—1881no—
606C23—1881no—
607C23—1881no—
608C23C2×D4×D4711yescharacteristic
609Q8—22no—
610Q8—22no—
611Q8—22no—
612Q8C4×C22⋊D4714yescomplemented
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—942no—
618D4—942no—
619D4—1888no—
620D4—1888no—
621D4—1881no—
622D4—1881no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—472no—
636C2×C4—472no—
637C2×C4—472no—
638C2×C4—472no—
639C2×C4—472no—
640C2×C4—941no—
641C2×C4—941no—
642C2×C4—941no—
643C2×C4—941no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—941no—
647C2×C4—941no—
648C2×C4—941no—
649C2×C4—3764no—
650C2×C4—1881no—
651C2×C4—1881no—
652C2×C4—1881no—
653C2×C4—1881no—
654C2×C4—1881no—
655C2×C4—1881no—
656C2×C4—1881no—
657C2×C4#1309399612yes—
658C2×C4#1309399612yes—
659C2×C4SD16×D4712yes—
660C2×C4#1309405112yes—
661C2×C4C22×C4×D4711yescharacteristic
662C2×C4C22×C22⋊D4711yescharacteristic
663C2×C4#41×D4711yescharacteristic
664C2×C4#41×D4711yescharacteristic
665C2×C4C2×#1062535211yescharacteristic
666C2×C4C2×#1062535011yescharacteristic
667C8—22no—
668C8—41no—
669C8—942no—
670C8—1881no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—3761no—
679C22—3761no—
680C22—3761no—
681C22—3761no—
682C22—1882no—
683C22—1882no—
684C22—1882no—
685C22C4×D4×D4711yescharacteristic
686C22C2×#1309399611yescharacteristic
687C22#1568963211yescharacteristic
688C22C2×SD16×D4711yescharacteristic
689C22#135×D4711yescharacteristic
690C22C2×#1309405111yescharacteristic
691C22#1568992011yescharacteristic
692C4—24no—
693C4—22no—
694C4—42no—
695C4—81no—
696C4—474no—
697C4—942no—
698C4—942no—
699C4—3761no—
700C4—1881no—
701C4—1882no—
702C4—1882no—
703C4#1568932114yesdirect product factor
704C4C2×C4×C22⋊D4711yescharacteristic
705C4C4×#1062535211yescharacteristic
706C4#1568965311yescharacteristic
707C4#1568966911yescharacteristic
708C2—82no—
709C2—3762no—
710C2C4×#1309399611yescharacteristic
711C2C4×SD16×D4711yescharacteristic
712C2C4×#1309405111yescharacteristic
713C2C2×#1568932111yescharacteristic
714C2#2025283911yescharacteristic
715C2#2025341711yescharacteristic
716C2#2025344611yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
prime radicalC2×#13094020C22
cosocleC22×C4×C47C24
hypercenterC2×C4×SD16D47
hypocenterC47C4×#460
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625336C2semidirect
4. C4×Q8×Dic47C2semidirect
6. #20244148C2semidirect
7. #20244018C2semidirect
8. #20244014C2semidirect
9. #20243745C2semidirect
10. #20243741C2semidirect
11. #20243391C2semidirect
12. C4×Dic47⋊C8C2semidirect
13. C4×#13093946C2semidirect
14. C4×#13093945C2semidirect
15. C2×C4×SD16×C47C2semidirect
23. #15689321C4direct (N × H)
68. C2×#10625336C2×C4semidirect
76. Q8×Dic47C2×C4semidirect
106. Dic47⋊C8C2×C4semidirect
109. #13093946C2×C4semidirect
111. #13093945C2×C4semidirect
122. C2×SD16×C47C2×C4semidirect
126. C4×Q8×C47D4semidirect
226. C4×Dic47SD16semidirect
253. Q8×C47C4×D4semidirect
338. C4×C47#460semidirect
349. Dic47C4×SD16semidirect
352. C2×C4×SD16D47semidirect
420. C47C4×#460semidirect
433. C2×SD16C4×D47semidirect
445. C4×Q8C22⋊D47semidirect
612. Q8C4×C22⋊D47semidirect
703. C4#15689321direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156893212
C2×C4×#106253362
C4×#130940202
C4×Q8×Dic472
#202443132
#202441482
#202440182
#202440142
#202437452
#202437412
#202433912
C4×Dic47⋊C82
C4×#130939462
C4×#130939452
C2×C4×SD16×C472
C4×#46047