Finite Group Databasebeta

← #26122502

Subgroups — #26122502

Order 12032.

1246 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688996C211yesmaximal, characteristic
2#20245741C211yesmaximal, characteristic
3C2×#15688890C211yesmaximal, characteristic
4C2×#15688889C211yesmaximal, characteristic
5C2×#15688889C211yesmaximal, characteristic
6#20241611C211yesmaximal, characteristic
7C47×C22⋊#95C211yesmaximal, characteristic
8C22×Dic47⋊C4—21no—
9C22×C22⋊Dic47C2211yescharacteristic
10C22×C22⋊Dic47C2211yescharacteristic
11C22×C22⋊Dic47C2211yescharacteristic
12C22×C22⋊Dic47C2211yescharacteristic
13#15688996—22no—
14#15688996C414yescomplemented
15C22⋊C4×Dic47—21no—
16C22⋊C4×Dic47—21no—
17C22⋊C4×Dic47—22no—
18C4×C22⋊Dic47—22no—
19C2×C47⋊#95—21no—
20C2×C47⋊#95—22no—
21#15688890C414yescomplemented
22#15688889—22no—
23#15688889C414yescomplemented
24C24×C4×C47C2211yescharacteristic
25C22×C22⋊C4×C47C2211yescharacteristic
26C22×C22⋊C4×C47C2211yescharacteristic
27C2×#95×C47—22no—
28C23×Dic47—21no—
29C23×Dic47—21no—
30C23×Dic47D411yescharacteristic
31C23×Dic47D411yescharacteristic
32C23×Dic47D412yes—
33C2×Dic47⋊C4—24no—
34C2×Dic47⋊C4—44no—
35C2×C22⋊Dic47—21no—
36C2×C22⋊Dic47—21no—
37C2×C22⋊Dic47—21no—
38C2×C22⋊Dic47—21no—
39C2×C22⋊Dic47—21no—
40C2×C22⋊Dic47—21no—
41C2×C22⋊Dic47—21no—
42C2×C22⋊Dic47—21no—
43C2×C22⋊Dic47—21no—
44C2×C22⋊Dic47—21no—
45C2×C22⋊Dic47—21no—
46C2×C22⋊Dic47—21no—
47C2×C22⋊Dic47—21no—
48C2×C22⋊Dic47—21no—
49C2×C22⋊Dic47—21no—
50C2×C22⋊Dic47—21no—
51C2×C22⋊Dic47C2×C412yes—
52C2×C22⋊Dic47C2×C412yes—
53C2×C22⋊Dic47C2×C412yes—
54C2×C22⋊Dic47C2×C412yes—
55C2×C22⋊Dic47C2×C412yes—
56C2×C22⋊Dic47C2×C412yes—
57C2×C22⋊Dic47D412yes—
58C2×C22⋊Dic47Q812yes—
59C2×C4×Dic47—22no—
60C2×C4×Dic47—22no—
61C47⋊#95—22no—
62C47⋊#95—22no—
63C47⋊#95—24no—
64C47⋊#95—44no—
65C25×C47C2311yescharacteristic
66C23×C4×C47—21no—
67C23×C4×C47—21no—
68C23×C4×C47—21no—
69C23×C4×C47—21no—
70C23×C4×C47—21no—
71C23×C4×C47—21no—
72C23×C4×C47—21no—
73C23×C4×C47—44no—
74C23×C4×C47C2×C412yes—
75C23×C4×C47D412yes—
76C2×C22⋊C4×C47—21no—
77C2×C22⋊C4×C47—21no—
78C2×C22⋊C4×C47—21no—
79C2×C22⋊C4×C47—21no—
80C2×C22⋊C4×C47—21no—
81C2×C22⋊C4×C47—21no—
82C2×C22⋊C4×C47—21no—
83C2×C22⋊C4×C47—21no—
84C2×C22⋊C4×C47—21no—
85C2×C22⋊C4×C47C2×C412yes—
86C2×C22⋊C4×C47C2×C412yes—
87C2×C22⋊C4×C47Q812yes—
88#95×C47—44no—
89C24×C47—42no—
90C24×C47—42no—
91C24×C47C22×C411yescharacteristic
92C24×C47C22×C411yescharacteristic
93C24×C47C22×C411yescharacteristic
94C24×C47C2×D411yescharacteristic
95C24×C47C2×D411yescharacteristic
96C24×C47C2×D411yescharacteristic
97C24×C47C2×D411yescharacteristic
98C24×C47C2×Q811yescharacteristic
99C24×C47C2×Q811yescharacteristic
100C24×C47#4111yescharacteristic
101C24×C47#4111yescharacteristic
102C24×C47#4111yescharacteristic
103C24×C47#4111yescharacteristic
104C24×C47#4111yescharacteristic
105C24×C47#4111yescharacteristic
106C22×C4×C47—24no—
107C22×C4×C47—24no—
108C22×C4×C47—24no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—44no—
116C22×C4×C47—44no—
117C22×C4×C47—44no—
118C22×C4×C47—44no—
119C22×C4×C47—42no—
120C22×C4×C47—42no—
121C22×C4×C47—42no—
122C22×C4×C47—41no—
123C22×C4×C47—41no—
124C22×C4×C47—41no—
125C22×C4×C47—41no—
126C22×C4×C47—42no—
127C22×C4×C47—42no—
128C22×C4×C47—42no—
129C22×C4×C47—42no—
130C22×C4×C47—41no—
131C22×C4×C47—41no—
132C22×C4×C47C4⋊C414yescomplemented
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—21no—
138C22×Dic47—21no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—42no—
144C22×Dic47—42no—
145C22×Dic47—42no—
146C22×Dic47—42no—
147C22×Dic47—42no—
148C22×Dic47—42no—
149C22×Dic47—42no—
150C22×Dic47—42no—
151C22×Dic47—41no—
152C22×Dic47—41no—
153C22×Dic47C22⋊C412yes—
154C22×Dic47C22⋊C412yes—
155C22×Dic47C4⋊C414yescomplemented
156C22⋊C4×C47—22no—
157C22⋊C4×C47—22no—
158C22⋊C4×C47—22no—
159C22⋊C4×C47—22no—
160C22⋊C4×C47—22no—
161C22⋊C4×C47—22no—
162C22⋊C4×C47—41no—
163C22⋊C4×C47—41no—
164C22⋊Dic47—22no—
165C22⋊Dic47—22no—
166C22⋊Dic47—22no—
167C22⋊Dic47—22no—
168C22⋊Dic47—22no—
169C22⋊Dic47—22no—
170C22⋊Dic47—22no—
171C22⋊Dic47—22no—
172C22⋊Dic47—22no—
173C22⋊Dic47—22no—
174C22⋊Dic47—22no—
175C22⋊Dic47—22no—
176C22⋊Dic47—22no—
177C22⋊Dic47—41no—
178C22⋊Dic47—41no—
179C22⋊Dic47C4214yescomplemented
180Dic47⋊C4—48no—
181C4×Dic47—82no—
182C4×Dic47—82no—
183C23×C47—22no—
184C23×C47—22no—
185C23×C47—22no—
186C23×C47—22no—
187C23×C47—22no—
188C23×C47—22no—
189C23×C47—41no—
190C23×C47—41no—
191C23×C47—41no—
192C23×C47—41no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—42no—
198C23×C47—42no—
199C23×C47—42no—
200C23×C47—41no—
201C23×C47—42no—
202C23×C47—42no—
203C23×C47—41no—
204C23×C47—42no—
205C23×C47C2×C4211yescharacteristic
206C23×C47C2×C22⋊C411yescharacteristic
207C23×C47C2×C4⋊C411yescharacteristic
208C23×C47C2×C4⋊C411yescharacteristic
209C23×C47#11711yescharacteristic
210C23×C47#11711yescharacteristic
211C23×C47#11711yescharacteristic
212C23×C47C4×D411yescharacteristic
213C23×C47C4×D411yescharacteristic
214C23×C47C4×D411yescharacteristic
215C23×C47C4×D411yescharacteristic
216C23×C47C4×D411yescharacteristic
217C23×C47C4×D411yescharacteristic
218C23×C47C4×D411yescharacteristic
219C23×C47C4×D411yescharacteristic
220C23×C47C4×Q811yescharacteristic
221C23×C47C4×Q811yescharacteristic
222C23×C47C4×Q811yescharacteristic
223C23×C47C4×Q811yescharacteristic
224C23×C47#12011yescharacteristic
225C23×C47#12111yescharacteristic
226C23×C47#12111yescharacteristic
227C23×C47C22⋊Q811yescharacteristic
228C23×C47C22⋊Q811yescharacteristic
229C23×C47C22⋊Q811yescharacteristic
230C23×C47C22⋊Q811yescharacteristic
231C23×C47#12311yescharacteristic
232C23×C47#12311yescharacteristic
233C23×C47#12311yescharacteristic
234C23×C47#12411yescharacteristic
235C23×C47#12511yescharacteristic
236C23×C47#12511yescharacteristic
237C23×C47#12611yescharacteristic
238C23×C47#12611yescharacteristic
239C23×C47C4⋊Q811yescharacteristic
240C2×C4×C47—24no—
241C2×C4×C47—24no—
242C2×C4×C47—24no—
243C2×C4×C47—24no—
244C2×C4×C47—42no—
245C2×C4×C47—44no—
246C2×C4×C47—44no—
247C2×C4×C47—42no—
248C2×C4×C47—42no—
249C2×C4×C47—44no—
250C2×C4×C47—42no—
251C2×C4×C47—42no—
252C2×C4×C47—44no—
253C2×C4×C47—42no—
254C2×C4×C47—44no—
255C2×C4×C47—44no—
256C2×C4×C47—42no—
257C2×C4×C47—82no—
258C2×C4×C47—82no—
259C2×C4×C47—81no—
260C2×C4×C47—81no—
261C2×Dic47—24no—
262C2×Dic47—24no—
263C2×Dic47—22no—
264C2×Dic47—22no—
265C2×Dic47—42no—
266C2×Dic47—44no—
267C2×Dic47—44no—
268C2×Dic47—42no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47—44no—
276C2×Dic47—44no—
277C2×Dic47—42no—
278C2×Dic47—82no—
279C2×Dic47—81no—
280C2×Dic47—81no—
281C2×Dic47—82no—
282C2×Dic47—81no—
283C2×Dic47—81no—
284#10918—471nomaximal, Sylow
285C22×C47—22no—
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—22no—
289C22×C47—22no—
290C22×C47—22no—
291C22×C47—22no—
292C22×C47—22no—
293C22×C47—22no—
294C22×C47—22no—
295C22×C47—22no—
296C22×C47—22no—
297C22×C47—21no—
298C22×C47—21no—
299C22×C47—21no—
300C22×C47—21no—
301C22×C47—21no—
302C22×C47—21no—
303C22×C47—21no—
304C22×C47—21no—
305C22×C47—21no—
306C22×C47—21no—
307C22×C47—21no—
308C22×C47—21no—
309C22×C47—41no—
310C22×C47—41no—
311C22×C47—41no—
312C22×C47—41no—
313C22×C47—41no—
314C22×C47—41no—
315C22×C47—41no—
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×C47—41no—
325C22×C47C4×C22⋊C411yescharacteristic
326C22×C47C4×C4⋊C411yescharacteristic
327C22×C47C4×C4⋊C411yescharacteristic
328C22×C47#38511yescharacteristic
329C22×C47#38511yescharacteristic
330C22×C47#38611yescharacteristic
331C22×C47#38711yescharacteristic
332C22×C47#38711yescharacteristic
333C22×C47#38711yescharacteristic
334C22×C47#38711yescharacteristic
335C22×C47#38811yescharacteristic
336C22×C47#38811yescharacteristic
337C22×C47#38911yescharacteristic
338C22×C47#38911yescharacteristic
339C22×C47#39111yescharacteristic
340C22×C47B(4,𝔽2)12yes—
341C22×C47#45812yes—
342C4×C47—44no—
343C4×C47—44no—
344C4×C47—82no—
345Dic47—44no—
346Dic47—44no—
347Dic47—42no—
348Dic47—42no—
349Dic47—82no—
350C2×#385—471no—
351#2273—471no—
352C2×#342—471no—
353C2×#342—471no—
354C2×#342—471no—
355C22⋊#95—471no—
356C22⋊#95D4711yescharacteristic
357C2×C47—21no—
358C2×C47—21no—
359C2×C47—21no—
360C2×C47—21no—
361C2×C47—21no—
362C2×C47—21no—
363C2×C47—21no—
364C2×C47—21no—
365C2×C47—21no—
366C2×C47—21no—
367C2×C47—21no—
368C2×C47—21no—
369C2×C47#143611yescharacteristic
370C2×C47#186712yes—
371C2×C47#186712yes—
372C2×C47#188911yescharacteristic
373C2×C47#189011yescharacteristic
374C24×C4C2×D4711yescharacteristic
375C22×C4⋊C4—941no—
376C22×C22⋊C4—471no—
377C22×C22⋊C4—471no—
378C22×C22⋊C4—471no—
379C22×C22⋊C4—471no—
380C22×C22⋊C4C2×D4711yescharacteristic
381C22×C22⋊C4C2×D4711yescharacteristic
382#385—474no—
383#385—942no—
384C4×C22⋊C4—941no—
385C4×C22⋊C4—941no—
386C4×C22⋊C4—942no—
387C4×C22⋊C4—942no—
388C2×#95—22no—
389C2×#95—941no—
390C2×#95—942no—
391#342—474no—
392#342—474no—
393#342—942no—
394C47#1091811yescharacteristic, complemented, Sylow
395C25C22×D4711yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—21no—
402C23×C4—21no—
403C23×C4—44no—
404C23×C4—471no—
405C23×C4—471no—
406C23×C4—472no—
407C23×C4—941no—
408C23×C4—941no—
409C23×C4C4×D4712yes—
410C23×C4C22⋊D4712yes—
411C2×C4⋊C4—944no—
412C2×C4⋊C4—1884no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—472no—
423C2×C22⋊C4—472no—
424C2×C22⋊C4—472no—
425C2×C22⋊C4—472no—
426C2×C22⋊C4—472no—
427C2×C22⋊C4—472no—
428C2×C22⋊C4—472no—
429C2×C22⋊C4—472no—
430C2×C22⋊C4—941no—
431C2×C22⋊C4—941no—
432C2×C22⋊C4—941no—
433C2×C22⋊C4—941no—
434C2×C22⋊C4—941no—
435C2×C22⋊C4—941no—
436C2×C22⋊C4—941no—
437C2×C22⋊C4—941no—
438C2×C22⋊C4—941no—
439C2×C22⋊C4—941no—
440C2×C22⋊C4—941no—
441C2×C22⋊C4—941no—
442C2×C22⋊C4—941no—
443C2×C22⋊C4—941no—
444C2×C22⋊C4—941no—
445C2×C22⋊C4—941no—
446C2×C22⋊C4Dic9412yes—
447C2×C22⋊C4C4×D4712yes—
448C2×C22⋊C4C4×D4712yes—
449C2×C42—942no—
450C2×C42—942no—
451#95—44no—
452#95—944no—
453#95—942no—
454#95—942no—
455#95—1884no—
456C24—42no—
457C24—42no—
458C24C2×Dic9411yescharacteristic
459C24C2×C4×D4711yescharacteristic
460C24C2×C4×D4711yescharacteristic
461C24C2×C4×D4711yescharacteristic
462C24#1062535011yescharacteristic
463C24#1062535011yescharacteristic
464C24D4×D4711yescharacteristic
465C24D4×D4711yescharacteristic
466C24D4×D4711yescharacteristic
467C24#1062535211yescharacteristic
468C24#1062535211yescharacteristic
469C24#1062535211yescharacteristic
470C24Q8×D4711yescharacteristic
471C24#1062535411yescharacteristic
472C24C2×C22⋊D4711yescharacteristic
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—44no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—472no—
500C22×C4—472no—
501C22×C4—474no—
502C22×C4—941no—
503C22×C4—941no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—941no—
510C22×C4—941no—
511C22×C4—942no—
512C22×C4—1882no—
513C22×C4—1882no—
514C22×C4—1881no—
515C22×C4—1881no—
516C22×C4—1882no—
517C22×C4—1882no—
518C22×C4—1882no—
519C22×C4—1882no—
520C22×C4—1882no—
521C22×C4—1882no—
522C22×C4Dic47⋊C414yescomplemented
523C4⋊C4—1888no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—474no—
533C22⋊C4—942no—
534C22⋊C4—942no—
535C22⋊C4—942no—
536C22⋊C4—942no—
537C22⋊C4—942no—
538C22⋊C4—942no—
539C22⋊C4—942no—
540C22⋊C4—942no—
541C22⋊C4—942no—
542C22⋊C4—942no—
543C22⋊C4—942no—
544C22⋊C4—942no—
545C22⋊C4—942no—
546C22⋊C4—1881no—
547C22⋊C4—1881no—
548C42—3762no—
549C42—3762no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—42no—
561C23—41no—
562C23—42no—
563C23—42no—
564C23—41no—
565C23—42no—
566C23—41no—
567C23—41no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23C42×D4711yescharacteristic
573C23C22⋊C4×D4711yescharacteristic
574C23C4⋊C4×D4711yescharacteristic
575C23C2×Dic47⋊C411yescharacteristic
576C23#1309398011yescharacteristic
577C23#1309398111yescharacteristic
578C23#1309398211yescharacteristic
579C23(C22⋊D47)⋊C411yescharacteristic
580C23(C22⋊D47)⋊C411yescharacteristic
581C23(C22⋊D47)⋊C411yescharacteristic
582C23(C22⋊D47)⋊C411yescharacteristic
583C23C4×C22⋊D4711yescharacteristic
584C23C4×C22⋊D4711yescharacteristic
585C23#1309398611yescharacteristic
586C23#1309398611yescharacteristic
587C23#1309398911yescharacteristic
588C23#1309398911yescharacteristic
589C23C4×Dic9411yescharacteristic
590C23C4×Dic9411yescharacteristic
591C23#1309399211yescharacteristic
592C23#1309399511yescharacteristic
593C23#1309399711yescharacteristic
594C23#1309400011yescharacteristic
595C23#1309400111yescharacteristic
596C23#1309400111yescharacteristic
597C23#1309400211yescharacteristic
598C23#1309400511yescharacteristic
599C23#1309400611yescharacteristic
600C23#1309400911yescharacteristic
601C23#1309401011yescharacteristic
602C23#1309401411yescharacteristic
603C23#1309401511yescharacteristic
604C23#1309401711yescharacteristic
605C23#1309401911yescharacteristic
606C23#1309402311yescharacteristic
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—44no—
620C2×C4—42no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—42no—
624C2×C4—82no—
625C2×C4—81no—
626C2×C4—81no—
627C2×C4—82no—
628C2×C4—944no—
629C2×C4—944no—
630C2×C4—942no—
631C2×C4—942no—
632C2×C4—3761no—
633C2×C4—3761no—
634C2×C4—3762no—
635C2×C4—3761no—
636C2×C4—3761no—
637C2×C4—3762no—
638C2×C4—1884no—
639C2×C4—1882no—
640C2×C4—1882no—
641C2×C4—1882no—
642C2×C4—1884no—
643C2×C4—1884no—
644C2×C4—1882no—
645C2×C4—1882no—
646C2×C4—1882no—
647C2×C4—1882no—
648C2×C4—1882no—
649C2×C4—1882no—
650C2×C4—1884no—
651C22—21no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22#1568897011yescharacteristic
692C22#1568897411yescharacteristic
693C22C4×Dic47⋊C411yescharacteristic
694C22#1568899411yescharacteristic
695C22#1568899511yescharacteristic
696C22#1568899911yescharacteristic
697C22#1568900411yescharacteristic
698C22#1568900511yescharacteristic
699C22#1568900611yescharacteristic
700C22#1568901011yescharacteristic
701C22#1568901111yescharacteristic
702C22#1568901211yescharacteristic
703C22#1568901911yescharacteristic
704C22#1568902011yescharacteristic
705C22#1568902711yescharacteristic
706C22#1568930912yes—
707C22#1568931212yes—
708C4—44no—
709C4—44no—
710C4—82no—
711C4—3762no—
712C4—1884no—
713C4—1882no—
714C4—1882no—
715C4—1884no—
716C2—21no—
717C2—21no—
718C2—21no—
719C2—21no—
720C2—21no—
721C2—21no—
722C2—21no—
723C2—21no—
724C2—21no—
725C2—21no—
726C2—21no—
727C2—21no—
728C2#2024161911yescharacteristic
729C2#2024366712yes—
730C2#2024366812yes—
731C2#2024379311yescharacteristic
732C2#2024379811yescharacteristic
subgroupG/H
centerC23#13093992
commutatorC23×C47C2×C42
FrattiniC25C22×D47
FittingC47×C22⋊#95C2
socleC23×C47#120
prime radical, cosocleC25×C47C23
hypercenterC22⋊#95D47
hypocenterC47#10918
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
14. #15688996C4semidirect
21. #15688890C4semidirect
23. #15688889C4semidirect
132. C22×C4×C47C4⋊C4semidirect
155. C22×Dic47C4⋊C4semidirect
179. C22⋊Dic47C42semidirect
394. C47#10918semidirect
522. C22×C4Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156889962
#202457412
C2×#156888902
C2×#156888892
#202416112
C47×C22⋊#952
#1091847