Finite Group Databasebeta

← #26232680

Subgroups — #26232680

Order 12032.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689813C211yesmaximal, characteristic
2C2×#15689201C211yesmaximal, characteristic
3#20244352C211yesmaximal, characteristic, complemented
4#20244345C211yesmaximal, characteristic, complemented
5#20243819C211yesmaximal, characteristic, complemented
6#20243819C211yesmaximal, characteristic, complemented
7#20243700C211yesmaximal, characteristic, complemented
8#20243695C211yesmaximal, characteristic, complemented
9#20243480C211yesmaximal, characteristic, complemented
10#20243476C211yesmaximal, characteristic, complemented
11#20243400C211yesmaximal, characteristic, complemented
12C4×#13093947C211yesmaximal, characteristic, complemented
13#20243109C211yesmaximal, characteristic, complemented
14#20243107C211yesmaximal, characteristic, complemented
15C47×#2352C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18#15689813—24no—
19#15689813C418yescomplemented
20C2×#13094017—21no—
21C2×#13094016C2211yescharacteristic
22C2×#13094014—21no—
23C2×#13094005—21no—
24C2×#13094003C2211yescharacteristic
25C2×#13094003C2211yescharacteristic
26C2×C4×Dic94C2211yescharacteristic
27C2×#13093983C2211yescharacteristic
28C2×#13093980—21no—
29C22×C4⋊Dic47C2211yescharacteristic
30#15689201—24no—
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×#13093947C2211yescharacteristic
33C2×#13093947C2211yescharacteristic
34C2×#13093947C2211yescharacteristic
35C2×#13093947C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×C22⋊(C47⋊C8)C2211yescharacteristic
38C2×C4×C47⋊C8C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×C4×D4×C47C2211yescharacteristic
52C2×#117×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C47×#388—21no—
55C47×#387—21no—
56C47×#386—21no—
57C47×#382C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C4×C22⋊C4×C47—21no—
62C22×Dic94C2311yescharacteristic
63C23×Dic47—21no—
64C2×#10625329—22no—
65C2×#10625329—22no—
66C2×#10625329—22no—
67C2×#10625329—22no—
68C2×#10625329—41no—
69C2×#10625329—41no—
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74#13094017—28no—
75#13094016—22no—
76#13094016C2×C414yescomplemented
77#13094014—28no—
78#13094005—28no—
79#13094003—22no—
80#13094003—22no—
81#13094003C2×C414yes—
82#13094003C2×C414yescomplemented
83C4×Dic94—22no—
84C4×Dic94C2×C414yescomplemented
85#13093983—22no—
86#13093983C2×C414yes—
87#13093980—28no—
88C2×C4⋊Dic47—22no—
89C2×C4⋊Dic47—21no—
90C2×C4⋊Dic47C2×C414yescomplemented
91C2×C4⋊Dic47C2311yescharacteristic
92C2×C4⋊Dic47C2311yescharacteristic
93C2×C4⋊Dic47C2311yescharacteristic
94C2×Dic47⋊C4—21no—
95C2×Dic47⋊C4—21no—
96C2×Dic47⋊C4—21no—
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×C22⋊Dic47—21no—
100C2×C22⋊Dic47—21no—
101C2×C22⋊Dic47—21no—
102C2×C4×Dic47—21no—
103C2×C4×Dic47—21no—
104C4⋊(C47⋊C8)—22no—
105#13093947—22no—
106#13093947—22no—
107#13093947—41no—
108#13093947—41no—
109C22⋊(C47⋊C8)—22no—
110C22⋊(C47⋊C8)—22no—
111C4×C47⋊C8—22no—
112C22×D4×C47D411yescharacteristic
113C23×C4×C47—21no—
114C23×C4×C47C2311yescharacteristic
115C23×C4×C47C2311yescharacteristic
116C4×D4×C47C2×C414yes—
117C4×D4×C47D414yes—
118#117×C47—22no—
119#117×C47—41no—
120C2×C4⋊C4×C47—22no—
121C2×C4⋊C4×C47—21no—
122C2×C4⋊C4×C47—41no—
123C2×C4⋊C4×C47D411yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C22⋊C4×C47D411yescharacteristic
133C2×C42×C47—21no—
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C2×D4×C47—41no—
144C2×D4×C47—41no—
145C2×D4×C47C22⋊C414yes—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
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—42no—
159C22×C4×C47—42no—
160C22×C4×C47—81no—
161C22×C4×C47C22×C412yes—
162C22×C4×C47C22×C412yes—
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47C2×D411yescharacteristic
166C22×C4×C47C2×D411yescharacteristic
167C22×C4×C47C2×D412yes—
168C22×C4×C47C2×D412yes—
169C22×C4×C47C2411yescharacteristic
170C22×Dic47—24no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—42no—
176C22×Dic47—42no—
177C2×Dic94—21no—
178C2×Dic94—21no—
179C2×Dic94—21no—
180C2×Dic94—21no—
181C2×Dic94—21no—
182C2×Dic94C22×C412yes—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—42no—
191C4⋊C4×C47C22⋊C414yes—
192C4⋊C4×C47#4112yes—
193C22⋊C4×C47—42no—
194C22⋊C4×C47—42no—
195C22⋊C4×C47—81no—
196C22⋊C4×C47C22⋊C414yes—
197C22⋊C4×C47C22⋊C414yes—
198C42×C47—42no—
199C42×C47—81no—
200C42×C47C22×C412yes—
201C42×C47C2×D412yes—
202C22⋊Dic47—24no—
203C22⋊Dic47—24no—
204C22⋊Dic47—24no—
205C4⋊Dic47—24no—
206C4⋊Dic47—21no—
207C4⋊Dic47—21no—
208C4⋊Dic47—21no—
209C4⋊Dic47C22×C412yes—
210C4⋊Dic47C22×C412yes—
211C4⋊Dic47C22×C412yes—
212Dic47⋊C4—24no—
213Dic47⋊C4—24no—
214Dic47⋊C4—24no—
215Dic47⋊C4—24no—
216Dic47⋊C4—24no—
217C4×Dic47—24no—
218C4×Dic47—24no—
219#10625329—44no—
220#10625329—44no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8#4112yes—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47C2×C22⋊C412yes—
246C23×C47C2×C22⋊C412yes—
247C23×C47C22×D411yescharacteristic
248D4×C47—44no—
249C2×C4×C47—21no—
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—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
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×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—84no—
278C2×C4×C47C2×C22⋊C412yes—
279C2×C4×C47C2×C22⋊C412yes—
280C2×C4×C47C2×C22⋊C412yes—
281C2×C4×C47C2×C22⋊C412yes—
282C2×C4×C47C23×C411yescharacteristic
283C2×C4×C47C22×D411yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47C2×#4111yescharacteristic
286C2×C4×C47H(5,𝔽2)11yescharacteristic
287C2×C4×C472−1+411yescharacteristic
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—48no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301Dic94—22no—
302Dic94—22no—
303Dic94—41no—
304Dic94—41no—
305C47⋊C8—22no—
306C47⋊C8—41no—
307C47⋊C8—41no—
308C47⋊C8—41no—
309#22499—471nomaximal, Sylow
310C22×C47—22no—
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—22no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—41no—
319C22×C47—41no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47C22×C22⋊C411yescharacteristic
325C22×C47#54611yescharacteristic
326C22×C47#54711yescharacteristic
327C22×C47#57511yescharacteristic
328C22×C47#57511yescharacteristic
329C22×C47#57711yescharacteristic
330C22×C47#57811yescharacteristic
331C4×C47—22no—
332C4×C47—22no—
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—42no—
336C4×C47—81no—
337C4×C47—81no—
338C4×C47—81no—
339C4×C47C4×#4111yescharacteristic
340C4×C47#52011yescharacteristic
341C4×C47#54611yescharacteristic
342C4×C47#54711yescharacteristic
343Dic47—42no—
344Dic47—42no—
345Dic47—42no—
346Dic47—42no—
347C2×#552—471no—
348C2×#436—471no—
349#2352D4711yescharacteristic
350#1991—471no—
351#1989—471no—
352#1894—471no—
353#1894—471no—
354#1873—471no—
355#1872—471no—
356#1825—471no—
357#1824—471no—
358#1805—471no—
359C4×#103—471no—
360#1736—471no—
361#1736—471no—
362C2×C47—42no—
363C2×C47—42no—
364C2×C47#233911yescharacteristic
365C2×C47#289611yescharacteristic
366C2×C47#289811yescharacteristic
367C2×C47#332311yescharacteristic
368C2×C47#332711yescharacteristic
369C2×C47#335111yescharacteristic
370C2×C47#335211yescharacteristic
371C22×M16—471no—
372C22×M16—471no—
373#552—478no—
374#552—944no—
375C2×#126—941no—
376C2×#125—471no—
377C2×#125—941no—
378C2×#123—941no—
379C2×C22⋊Q8—471no—
380C2×C22⋊Q8—471no—
381C2×C4×Q8—471no—
382C2×C4×D4C2×D4711yescharacteristic
383C2×#117—471no—
384C2×#117—941no—
385C2×#117C2×D4711yescharacteristic
386C22×C4⋊C4—471no—
387C22×C4⋊C4C2×D4711yescharacteristic
388#436—944no—
389C2×C4⋊C8—471no—
390C2×#103—471no—
391C2×#103—471no—
392C2×#103—471no—
393C2×#103—471no—
394C2×C22⋊C8—471no—
395C2×C22⋊C8—471no—
396C2×C4×C8—471no—
397#388—21no—
398#387—21no—
399#386—21no—
400#382C2×D4711yescharacteristic
401#380C2×D4711yescharacteristic
402#380C2×D4711yescharacteristic
403C4×C4⋊C4C2×D4711yescharacteristic
404C4×C22⋊C4—21no—
405#340—471no—
406#340—471no—
407#340—471no—
408#340—471no—
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340—471no—
416#340—471no—
417C47#2249911yescharacteristic, complemented, Sylow
418C22×Q8—471no—
419C22×D4C22⋊D4711yescharacteristic
420C23×C4—21no—
421C23×C4—941no—
422C23×C4C22×D4711yescharacteristic
423C23×C4C22×D4711yescharacteristic
424C2×M16—942no—
425C2×M16—942no—
426C2×M16—942no—
427C2×M16—942no—
428C2×M16—1881no—
429C2×M16—1881no—
430C22×C8—471no—
431C22×C8—471no—
432C22×C8—471no—
433C22×C8—471no—
434#126—948no—
435#125—474no—
436#125—948no—
437#125—942no—
438#123—948no—
439C22⋊Q8—474no—
440C22⋊Q8—474no—
441C22⋊Q8—942no—
442C22⋊Q8—942no—
443C4×Q8—474no—
444C4×Q8—942no—
445C4×D4C4×D4714yes—
446C4×D4D18814yes—
447#117—22no—
448#117—41no—
449#117—474no—
450#117—942no—
451#117—948no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—474no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—471no—
459C2×C4⋊C4—942no—
460C2×C4⋊C4—941no—
461C2×C4⋊C4—941no—
462C2×C4⋊C4—941no—
463C2×C4⋊C4—941no—
464C2×C4⋊C4—941no—
465C2×C4⋊C4—941no—
466C2×C4⋊C4C22⋊D4711yescharacteristic
467C2×C4⋊C4C22×D4711yescharacteristic
468C2×C4⋊C4C22×D4711yescharacteristic
469C2×C4⋊C4C22×D4711yescharacteristic
470C2×C4⋊C4C22×D4711yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4—941no—
477C2×C22⋊C4C22⋊D4711yescharacteristic
478C2×C22⋊C4C22⋊D4711yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—941no—
482C2×C42—941no—
483C2×C42C22×D4711yescharacteristic
484C4⋊C8—942no—
485#103—942no—
486#103—942no—
487#103—1881no—
488#103—1881no—
489C22⋊C8—942no—
490C22⋊C8—942no—
491C4×C8—942no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24C2×C22⋊D4711yescharacteristic
498C24C2×C22⋊D4711yescharacteristic
499C2×Q8—472no—
500C2×Q8—941no—
501C2×Q8—941no—
502C2×Q8—941no—
503C2×Q8—941no—
504C2×Q8—941no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4(C2×D47)⋊C414yes—
508C22×C4—21no—
509C22×C4—21no—
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—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—944no—
524C22×C4—941no—
525C22×C4—941no—
526C22×C4—941no—
527C22×C4—941no—
528C22×C4—1882no—
529C22×C4—1882no—
530C22×C4C2×C4×D4712yes—
531C22×C4C2×C4×D4712yes—
532C22×C4C2×D18812yes—
533C22×C4C2×D18812yes—
534C22×C4C2×C22⋊D4711yescharacteristic
535C22×C4C2×C22⋊D4711yescharacteristic
536C22×C4C2×C22⋊D4711yescharacteristic
537C22×C4C2×C22⋊D4711yescharacteristic
538C22×C4C23×D4711yescharacteristic
539M16—1884no—
540M16—1884no—
541C2×C8—472no—
542C2×C8—941no—
543C2×C8—941no—
544C2×C8—941no—
545C2×C8—941no—
546C2×C8—941no—
547C2×C8—941no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—941no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—472no—
562C4⋊C4—472no—
563C4⋊C4—472no—
564C4⋊C4—944no—
565C4⋊C4—944no—
566C4⋊C4—944no—
567C4⋊C4—944no—
568C4⋊C4—944no—
569C4⋊C4—944no—
570C4⋊C4—941no—
571C4⋊C4—941no—
572C4⋊C4—941no—
573C4⋊C4(C2×D47)⋊C414yes—
574C4⋊C4#1062535212yes—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C22⋊C4—944no—
579C22⋊C4—944no—
580C22⋊C4—944no—
581C22⋊C4(C2×D47)⋊C414yes—
582C22⋊C4(C2×D47)⋊C414yes—
583C42—42no—
584C42—81no—
585C42—944no—
586C42—944no—
587C42C2×C4×D4712yes—
588C42C2×D18812yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×(C2×D47)⋊C412yes—
602C23C2×(C2×D47)⋊C412yes—
603C23C22×C22⋊D4711yescharacteristic
604Q8—942no—
605Q8—942no—
606Q8—1881no—
607Q8—1881no—
608D4—44no—
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—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
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—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—942no—
639C2×C4—942no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—1888no—
643C2×C4—1881no—
644C2×C4—1881no—
645C2×C4—1881no—
646C2×C4—1881no—
647C2×C4—1881no—
648C2×C4—1881no—
649C2×C4—1881no—
650C2×C4—1881no—
651C2×C4C2×(C2×D47)⋊C412yes—
652C2×C4C2×(C2×D47)⋊C412yes—
653C2×C4C2×(C2×D47)⋊C412yes—
654C2×C4C2×(C2×D47)⋊C412yes—
655C2×C4C22×C4×D4711yescharacteristic
656C2×C4C22×D18811yescharacteristic
657C2×C4#41×D4711yescharacteristic
658C2×C4C2×#1062535211yescharacteristic
659C2×C4#1309406911yescharacteristic
660C2×C4#1309407111yescharacteristic
661C8—942no—
662C8—1881no—
663C8—1881no—
664C8—1881no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×(C2×D47)⋊C411yescharacteristic
680C22#1568976711yescharacteristic
681C22#1568977211yescharacteristic
682C22#1568992111yescharacteristic
683C22#1568992111yescharacteristic
684C22#1568993411yescharacteristic
685C22#1568993811yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—1882no—
695C4—1882no—
696C4—1882no—
697C4—1882no—
698C4C4×#1062535211yescharacteristic
699C4#1568960211yescharacteristic
700C4#1568976811yescharacteristic
701C4#1568977711yescharacteristic
702C2—42no—
703C2—42no—
704C2#2024621311yescharacteristic
705C2#2025190511yescharacteristic
706C2#2025191811yescharacteristic
707C2#2025560411yescharacteristic
708C2#2025565611yescharacteristic
709C2#2025594211yescharacteristic
710C2#2025595711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2352C2
socleC23×C47C22×D4
prime radicalC22×D4×C47D4
cosocleC22×C4×C47C24
hypercenter#2352D47
hypocenterC47#22499
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. #20244352C2semidirect
4. #20244345C2semidirect
5. #20243819C2semidirect
6. #20243819C2semidirect
7. #20243700C2semidirect
8. #20243695C2semidirect
9. #20243480C2semidirect
10. #20243476C2semidirect
11. #20243400C2semidirect
12. C4×#13093947C2semidirect
13. #20243109C2semidirect
14. #20243107C2semidirect
19. #15689813C4semidirect
76. #13094016C2×C4semidirect
82. #13094003C2×C4semidirect
84. C4×Dic94C2×C4semidirect
90. C2×C4⋊Dic47C2×C4semidirect
417. C47#22499semidirect

Maximal subgroups

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

subgroupindex
C2×#156898132
C2×#156892012
#202443522
#202443452
#202438192
#202437002
#202436952
#202434802
#202434762
#202434002
C4×#130939472
#202431092
#202431072
C47×#23522
#2249947