Finite Group Databasebeta

← C4×#15689354 #26222763

Subgroups — C4×#15689354 #26222763

Order 12032.

1138 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689354C211yesmaximal, characteristic
2C2×C4×#10625336C211yesmaximal, characteristic, complemented
3C22×C4×C47⋊C8C211yesmaximal, characteristic, complemented
4C4×#13093998C211yesmaximal, characteristic
5#20244245C211yesmaximal, characteristic, complemented
6#20244113C211yesmaximal, characteristic, complemented
7#20244070C211yesmaximal, characteristic, complemented
8#20244067C211yesmaximal, characteristic, complemented
9#20243814C211yesmaximal, characteristic
10#20243812C211yesmaximal, characteristic, complemented
11#20243411C211yesmaximal, characteristic, complemented
12C4×#13093955C211yesmaximal, characteristic, complemented
13C4×#13093948C211yesmaximal, characteristic, complemented
14C4×#13093944C211yesmaximal, characteristic, complemented
15C4×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C23×C47⋊C8C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C2×#13093998C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21C2×C4×C22⋊D47—21no—
22#15689354C418yesdirect product factor
23C4×#10625336—24no—
24C2×#13093955C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093955C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093944C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32C2×#13093944C2211yescharacteristic
33C2×C4×C47⋊C8—24no—
34C2×C4×C47⋊C8C2211yescharacteristic
35C2×C4×C47⋊C8C2211yescharacteristic
36C2×C4×C47⋊C8C2211yescharacteristic
37C2×C4×C47⋊C8C2211yescharacteristic
38#15689025C2211yescharacteristic
39#15689021C2211yescharacteristic
40#15689014—21no—
41#15689002—21no—
42#15688983C2211yescharacteristic
43C4×C4⋊Dic47C2211yescharacteristic
44C4×(C2×D47)⋊C4—21no—
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×C22⋊Q8×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C22×C42×C47C2211yescharacteristic
54C47×#391C2211yescharacteristic
55C47×#389C2211yescharacteristic
56C47×#387—21no—
57C47×#385—21no—
58C47×#380C2211yescharacteristic
59C4×C4⋊C4×C47—21no—
60C4×C4⋊C4×C47C2211yescharacteristic
61C4×C22⋊C4×C47—21no—
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C22×C4×D47—21no—
65C2×#10625336—22no—
66C2×#10625336—22no—
67C2×#10625336C2×C414yescomplemented
68C22×C47⋊C8—22no—
69C22×C47⋊C8—22no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—22no—
72C22×C47⋊C8—22no—
73C22×C47⋊C8C2×C414yescomplemented
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78#13093998—22no—
79#13093998C2×C414yes—
80C4×D188—22no—
81C4×D188—22no—
82C4×C22⋊D47—44no—
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×C4⋊Dic47C2311yescharacteristic
86C2×Dic47⋊C4—21no—
87C2×C22⋊Dic47—21no—
88C2×(C2×D47)⋊C4—21no—
89C2×(C2×D47)⋊C4—21no—
90C2×(C2×D47)⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×C4×Dic47—21no—
93#13093955—22no—
94#13093955—22no—
95#13093955C2×C414yescomplemented
96#13093948—22no—
97#13093948—22no—
98#13093948C2×C414yescomplemented
99#13093944—22no—
100#13093944—22no—
101#13093944C2×C414yescomplemented
102C4×C47⋊C8—22no—
103C4×C47⋊C8—22no—
104C4×C47⋊C8—22no—
105C4×C47⋊C8D414yescomplemented
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C22×Q8×C47C2311yescharacteristic
110C23×C4×C47D411yescharacteristic
111C23×C4×C47D411yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C22⋊Q8×C47—22no—
114C22⋊Q8×C47C2×C414yescomplemented
115C4×Q8×C47—22no—
116C4×Q8×C47—22no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C42×C47—22no—
126C2×C42×C47—22no—
127C2×C42×C47—21no—
128C2×C42×C47—21no—
129C2×C42×C47D411yescharacteristic
130C2×C42×C47D411yescharacteristic
131C2×C42×C47C2311yescharacteristic
132C2×C42×C47C2311yescharacteristic
133#95×C47—21no—
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138C24×C47C2×D411yescharacteristic
139C23×D47—21no—
140C2×Q8×C47—21no—
141C2×Q8×C47—21no—
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47C22×C412yes—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47SD1614yescomplemented
160C22×C4×C47C22×C412yes—
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×D411yescharacteristic
166C22×C4×C47#4112yes—
167C22×C4×C47C2411yescharacteristic
168C2×C22⋊D47—24no—
169C2×C22⋊D47—42no—
170C2×C22⋊D47—42no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C2×D188—21no—
175C2×D188—21no—
176C2×D188—21no—
177C2×D188—21no—
178C2×D188—21no—
179C2×D188C22×C412yes—
180C2×C4×D47—42no—
181C2×C4×D47—42no—
182C2×C4×D47—42no—
183C4⋊C4×C47—24no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—42no—
190C4⋊C4×C47—42no—
191C4⋊C4×C47C22×C412yes—
192C22⋊C4×C47—24no—
193C22⋊C4×C47—42no—
194C42×C47—22no—
195C42×C47—22no—
196C42×C47—21no—
197C42×C47—21no—
198C42×C47—42no—
199C42×C47—42no—
200C42×C47C2×D412yes—
201C42×C47#4112yes—
202C22⋊Dic47—42no—
203#10625336—28no—
204(C2×D47)⋊C4—24no—
205(C2×D47)⋊C4—42no—
206(C2×D47)⋊C4—42no—
207(C2×D47)⋊C4—42no—
208C4⋊Dic47—21no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47C22×C412yes—
214Dic47⋊C4—42no—
215C4×Dic47—42no—
216C2×C47⋊C8—28no—
217C2×C47⋊C8—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—28no—
224C2×C47⋊C8C22×C412yes—
225C2×C47⋊C8C22×C412yes—
226C2×C47⋊C8C2×D412yes—
227C2×C47⋊C8C2×D412yes—
228C2×C47⋊C8#4112yes—
229C2×C47⋊C8#4112yes—
230C23×C47—21no—
231C23×C47—21no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47C4×D412yes—
235C23×C47C2×SD1612yes—
236C23×C47#13512yes—
237C23×C47C22×D411yescharacteristic
238C22×D47—22no—
239C22×D47—41no—
240C22×D47—41no—
241C22×D47—41no—
242C22×D47—41no—
243C22×D47—41no—
244C22×D47—41no—
245Q8×C47—22no—
246Q8×C47—22no—
247Q8×C47—41no—
248Q8×C47—41no—
249C2×C4×C47—28no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—28no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47C4×D412yes—
276C2×C4×C47#12112yes—
277C2×C4×C47#12112yes—
278C2×C4×C47C2×SD1612yes—
279C2×C4×C47C2×SD1612yes—
280C2×C4×C47#13512yes—
281C2×C4×C47#13512yes—
282C2×C4×C47C23×C411yescharacteristic
283C2×C4×C47C22×D411yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47C2×#4111yescharacteristic
287C2×C4×C47C2×#4111yescharacteristic
288C22⋊D47—48no—
289C2×Dic47—22no—
290C2×Dic47—41no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298D188—22no—
299D188—22no—
300D188—41no—
301D188—41no—
302C4×D47—84no—
303C47⋊C8—22no—
304C47⋊C8—22no—
305C47⋊C8—22no—
306C47⋊C8C4×D414yescomplemented
307C4×#465—471nomaximal, Sylow
308C22×C47—22no—
309C22×C47—22no—
310C22×C47—22no—
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—22no—
314C22×C47C4×SD1614yescomplemented
315C22×C47C2×C4×D411yescharacteristic
316C22×C47C2×#12111yescharacteristic
317C22×C47#53211yescharacteristic
318C22×C47C22×SD1611yescharacteristic
319C22×C47C2×#13511yescharacteristic
320C22×C47C2×#13511yescharacteristic
321C22×C47C2×#13511yescharacteristic
322C2×D47—42no—
323C2×D47—42no—
324C2×D47—42no—
325C2×D47—81no—
326C2×D47—81no—
327C2×D47—81no—
328C2×D47—81no—
329C4×C47—22no—
330C4×C47—22no—
331C4×C47—22no—
332C4×C47—22no—
333C4×C47—42no—
334C4×C47—42no—
335C4×C47—81no—
336C4×C47—81no—
337C4×C47#46514yescomplemented
338C4×C47C2×C4×D411yescharacteristic
339C4×C47C4×#4111yescharacteristic
340C4×C47#52511yescharacteristic
341C4×C47#52911yescharacteristic
342Dic47—42no—
343Dic47—81no—
344Dic47—81no—
345C2×#465—471no—
346C2×C4×SD16—471no—
347C22×C4×C8—471no—
348C4×C22⋊Q8D4711yescharacteristic, complemented
349C4×#121—471no—
350#1968—471no—
351#1941—471no—
352#1934—471no—
353#1933—471no—
354#1893—471no—
355#1892—471no—
356#1807—471no—
357C4×#106—471no—
358C4×#103—471no—
359C4×#102—471no—
360C2×C47—24no—
361C2×C47C4×#12111yescharacteristic
362C2×C47C2×C4×SD1611yescharacteristic
363C2×C47C4×#13511yescharacteristic
364C2×C47C2×#46511yescharacteristic
365C2×C47#305011yescharacteristic
366C2×C47#316711yescharacteristic
367C2×C47#316811yescharacteristic
368D47—82no—
369C22×SD16—471no—
370C23×C8—471no—
371C23×C8—471no—
372C2×C22⋊Q8C2×D4711yescharacteristic
373C2×#121—471no—
374C2×C4×Q8C2×D4711yescharacteristic
375C2×C4×D4—471no—
376C2×C4×D4—941no—
377C22×C42C2×D4711yescharacteristic
378#465—478no—
379C4×SD16—944no—
380C2×#106—471no—
381C2×#106—471no—
382C2×#106—471no—
383C2×#103—471no—
384C2×#103—471no—
385C2×#103—471no—
386C2×#102—471no—
387C2×#102—471no—
388C2×#102—471no—
389C2×C4×C8—471no—
390C2×C4×C8—471no—
391C2×C4×C8—471no—
392C2×C4×C8—471no—
393C2×C4×C8—944no—
394#391C2×D4711yescharacteristic
395#390—471no—
396#389—471no—
397#389C2×D4711yescharacteristic
398#388—941no—
399#387—21no—
400#386—941no—
401#385—21no—
402#380—471no—
403#380C2×D4711yescharacteristic
404C4×C4⋊C4—21no—
405C4×C4⋊C4—471no—
406C4×C4⋊C4C2×D4711yescharacteristic
407C4×C22⋊C4—21no—
408C4×C22⋊C4—941no—
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415C47C4×#46511yescharacteristic, complemented, Sylow
416C22×Q8C22×D4711yescharacteristic
417C22×D4—471no—
418C22×D4—941no—
419C23×C4—941no—
420C23×C4C22⋊D4711yescharacteristic
421C23×C4C22⋊D4711yescharacteristic
422C23×C4C22×D4711yescharacteristic
423C2×SD16—474no—
424C2×SD16—942no—
425C2×SD16—942no—
426C22×C8—471no—
427C22×C8—474no—
428C22×C8—471no—
429C22×C8—471no—
430C22×C8—471no—
431C22×C8—942no—
432C22×C8—942no—
433C22×C8—942no—
434C22×C8—942no—
435C22×C8—942no—
436C22⋊Q8—22no—
437C22⋊Q8C4×D4714yescomplemented
438#121—474no—
439#121—942no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×D4—942no—
443C4×D4—942no—
444C4×D4—1884no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—471no—
449C2×C4⋊C4—471no—
450C2×C4⋊C4—471no—
451C2×C4⋊C4—941no—
452C2×C4⋊C4C22×D4711yescharacteristic
453C2×C4⋊C4C22×D4711yescharacteristic
454C2×C4⋊C4C22×D4711yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—941no—
458C2×C22⋊C4—941no—
459C2×C22⋊C4—941no—
460C2×C22⋊C4—941no—
461C2×C22⋊C4—941no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—941no—
467C2×C42C22⋊D4711yescharacteristic
468C2×C42C22⋊D4711yescharacteristic
469C2×C42C22×D4711yescharacteristic
470C2×C42C22×D4711yescharacteristic
471#106—474no—
472#106—942no—
473#106—942no—
474#103—474no—
475#103—942no—
476#103—942no—
477#102—474no—
478#102—942no—
479#102—942no—
480C4×C8—474no—
481C4×C8—942no—
482C4×C8—942no—
483C4×C8—942no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—941no—
490#95—941no—
491#95—941no—
492C24—941no—
493C24C2×C22⋊D4711yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×C4×D4712yes—
500C2×D4—472no—
501C2×D4—944no—
502C2×D4—941no—
503C2×D4—941no—
504C2×D4—941no—
505C2×D4—941no—
506C2×D4—941no—
507C2×D4—1882no—
508C2×D4—1882no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—941no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—1882no—
526C22×C4—1882no—
527C22×C4—1882no—
528C22×C4#1062533614yescomplemented
529C22×C4C2×C4×D4712yes—
530C22×C4#1062535012yes—
531C22×C4C2×C22⋊D4711yescharacteristic
532C22×C4C2×C22⋊D4711yescharacteristic
533C22×C4C2×C22⋊D4711yescharacteristic
534C22×C4C2×C22⋊D4711yescharacteristic
535C22×C4C2×C22⋊D4711yescharacteristic
536C22×C4C23×D4711yescharacteristic
537SD16—948no—
538C2×C8—472no—
539C2×C8—472no—
540C2×C8—472no—
541C2×C8—472no—
542C2×C8—472no—
543C2×C8—472no—
544C2×C8—948no—
545C2×C8—948no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—472no—
561C4⋊C4—941no—
562C4⋊C4—941no—
563C4⋊C4—941no—
564C4⋊C4—941no—
565C4⋊C4—941no—
566C4⋊C4—1882no—
567C4⋊C4C2×C4×D4712yes—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—944no—
571C22⋊C4—1882no—
572C22⋊C4—1882no—
573C22⋊C4—1882no—
574C22⋊C4—1882no—
575C42—22no—
576C42—22no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—1882no—
582C42D4×D4712yes—
583C42#1062535212yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—942no—
589C23—1881no—
590C23—1881no—
591C23—1881no—
592C23—1881no—
593C23—1881no—
594C23—1881no—
595C23C4×C22⋊D4712yes—
596C23C2×#1062533612yes—
597C23#1309404412yes—
598C23C22×C22⋊D4711yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—942no—
604D4—942no—
605D4—1888no—
606D4—1881no—
607D4—1881no—
608C2×C4—28no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—942no—
635C2×C4—3764no—
636C2×C4—1881no—
637C2×C4—1881no—
638C2×C4—1881no—
639C2×C4—1881no—
640C2×C4—1881no—
641C2×C4—1881no—
642C2×C4—1881no—
643C2×C4—1881no—
644C2×C4C4×C22⋊D4712yes—
645C2×C4#1309399612yes—
646C2×C4#1309399612yes—
647C2×C4C2×#1062533612yes—
648C2×C4C2×#1062533612yes—
649C2×C4#1309404412yes—
650C2×C4#1309404412yes—
651C2×C4C22×C4×D4711yescharacteristic
652C2×C4C2×D4×D4711yescharacteristic
653C2×C4#41×D4711yescharacteristic
654C2×C4#41×D4711yescharacteristic
655C2×C4C2×#1062535211yescharacteristic
656C2×C4C2×#1062535011yescharacteristic
657C8—474no—
658C8—942no—
659C8—942no—
660C8—942no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—3761no—
668C22—3761no—
669C22—3761no—
670C22—3761no—
671C22—1882no—
672C22—1882no—
673C22—1882no—
674C22C4×#1062533614yescomplemented
675C22C2×C4×C22⋊D4711yescharacteristic
676C22C2×#1309399611yescharacteristic
677C22#1568966911yescharacteristic
678C22C22×#1062533611yescharacteristic
679C22C2×#1309404411yescharacteristic
680C22C2×#1309404411yescharacteristic
681C22C2×#1309404411yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—42no—
687C4—42no—
688C4—81no—
689C4—81no—
690C4—3761no—
691C4—3761no—
692C4—1882no—
693C4#1568935414yesdirect product factor
694C4C4×D4×D4711yescharacteristic
695C4C4×#1062535211yescharacteristic
696C4#1568963211yescharacteristic
697C4#1568965311yescharacteristic
698C2—24no—
699C2—3762no—
700C2C4×#1309399611yescharacteristic
701C2C2×C4×#1062533611yescharacteristic
702C2C4×#1309404411yescharacteristic
703C2C2×#1568935411yescharacteristic
704C2#2025296611yescharacteristic
705C2#2025394811yescharacteristic
706C2#2025395211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×C22⋊Q8×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenterC4×C22⋊Q8D47
hypocenterC47C4×#465
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10625336C2semidirect
3. C22×C4×C47⋊C8C2semidirect
5. #20244245C2semidirect
6. #20244113C2semidirect
7. #20244070C2semidirect
8. #20244067C2semidirect
10. #20243812C2semidirect
11. #20243411C2semidirect
12. C4×#13093955C2semidirect
13. C4×#13093948C2semidirect
14. C4×#13093944C2semidirect
15. C4×C22⋊Q8×C47C2semidirect
22. #15689354C4direct (N × H)
67. C2×#10625336C2×C4semidirect
73. C22×C47⋊C8C2×C4semidirect
95. #13093955C2×C4semidirect
98. #13093948C2×C4semidirect
101. #13093944C2×C4semidirect
105. C4×C47⋊C8D4semidirect
114. C22⋊Q8×C47C2×C4semidirect
159. C22×C4×C47SD16semidirect
306. C47⋊C8C4×D4semidirect
314. C22×C47C4×SD16semidirect
337. C4×C47#465semidirect
348. C4×C22⋊Q8D47semidirect
415. C47C4×#465semidirect
437. C22⋊Q8C4×D47semidirect
528. C22×C4#10625336semidirect
674. C22C4×#10625336semidirect
693. C4#15689354direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156893542
C2×C4×#106253362
C22×C4×C47⋊C82
C4×#130939982
#202442452
#202441132
#202440702
#202440672
#202438142
#202438122
#202434112
C4×#130939552
C4×#130939482
C4×#130939442
C4×C22⋊Q8×C472
C4×#46547