Finite Group Databasebeta

← #26221415

Subgroups — #26221415

Order 12032.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689746C211yesmaximal, characteristic
2C2×#15689181C211yesmaximal, characteristic, complemented
3#20245745C211yesmaximal, characteristic, complemented
4#20244338C211yesmaximal, characteristic, complemented
5#20244334C211yesmaximal, characteristic, complemented
6#20244317C211yesmaximal, characteristic, complemented
7#20244317C211yesmaximal, characteristic, complemented
8#20243708C211yesmaximal, characteristic
9#20243705C211yesmaximal, characteristic
10#20243701C211yesmaximal, characteristic, complemented
11#20243220C211yesmaximal, characteristic, complemented
12#20243212C211yesmaximal, characteristic, complemented
13#103×Dic47C211yesmaximal, characteristic, complemented
14#20243202C211yesmaximal, characteristic, complemented
15C47×#1872C211yesmaximal, characteristic, complemented
16#15689746—24no—
17#15689746C418yescomplemented
18C2×#13094023C2211yescharacteristic
19C2×#13094019—21no—
20C2×#13094013C2211yescharacteristic
21C2×#13094010—21no—
22C2×#13094006—21no—
23C2×#13094004—21no—
24C2×#13093998C2211yescharacteristic
25C2×Q8×Dic47C2211yescharacteristic
26C2×#13093986C2211yescharacteristic
27C2×#13093983C2211yescharacteristic
28C2×#13093983C2211yescharacteristic
29#15689181—24no—
30C2×Dic47⋊C8C2211yescharacteristic
31C2×Dic47⋊C8C2211yescharacteristic
32C2×#13093948C2211yescharacteristic
33C2×#13093948C2211yescharacteristic
34C2×#13093946C2211yescharacteristic
35C2×#13093946C2211yescharacteristic
36C2×#13093944C2211yescharacteristic
37C2×#13093944C2211yescharacteristic
38C2×C22⋊(C47⋊C8)C2211yescharacteristic
39C2×#13093934C2211yescharacteristic
40C2×C8×Dic47C2211yescharacteristic
41C4⋊C4×Dic47—21no—
42C4⋊C4×Dic47—21no—
43C4⋊C4×Dic47C2211yescharacteristic
44C4⋊C4×Dic47C2211yescharacteristic
45C4⋊C4×Dic47C2211yescharacteristic
46C4⋊C4×Dic47C2211yescharacteristic
47C4×C22⋊Dic47—21no—
48C4×C22⋊Dic47—21no—
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C2×C22⋊Q8×C47C2211yescharacteristic
56C22×C4⋊C4×C47C2211yescharacteristic
57C2×#103×C47C2211yescharacteristic
58C2×#103×C47C2211yescharacteristic
59C2×C22⋊C8×C47C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×Dic94—21no—
63C22×D188C2311yescharacteristic
64C22×C22⋊D47—21no—
65C22×C4×D47—21no—
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13094023—22no—
69#13094023C2×C414yescomplemented
70#13094019—28no—
71#13094013—22no—
72#13094013C2×C414yescomplemented
73#13094010—28no—
74#13094006—28no—
75#13094004—28no—
76#13093998—22no—
77#13093998C2×C414yes—
78Q8×Dic47—22no—
79Q8×Dic47C2×C414yescomplemented
80#13093986—22no—
81#13093986C2×C414yescomplemented
82#13093983—22no—
83#13093983—22no—
84#13093983C2×C414yes—
85#13093983D414yes—
86C2×C4⋊Dic47—21no—
87C2×C4⋊Dic47D411yescharacteristic
88C2×C4⋊Dic47D411yescharacteristic
89C2×C4⋊Dic47C2311yescharacteristic
90C2×C4⋊Dic47C2311yescharacteristic
91C2×C4⋊Dic47C2311yescharacteristic
92C2×Dic47⋊C4—21no—
93C2×C22⋊Dic47—21no—
94C2×C22⋊Dic47D411yescharacteristic
95C2×C22⋊Dic47D411yescharacteristic
96C2×(C2×D47)⋊C4—21no—
97C2×(C2×D47)⋊C4—21no—
98C2×(C2×D47)⋊C4—21no—
99C2×(C2×D47)⋊C4—21no—
100C2×C4×Dic47—21no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47—21no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47C2311yescharacteristic
107C2×C4×Dic47C2311yescharacteristic
108Dic47⋊C8—22no—
109Dic47⋊C8—22no—
110#13093948—22no—
111#13093948—22no—
112#13093946—22no—
113#13093946—22no—
114#13093944—22no—
115#13093944—22no—
116C22⋊(C47⋊C8)—22no—
117#13093934—22no—
118C8×Dic47—22no—
119C47⋊#95—21no—
120C47⋊#95—21no—
121C47⋊#95—21no—
122C47⋊#95—21no—
123C22×Q8×C47C2311yescharacteristic
124C23×C4×C47—21no—
125C23×C4×C47C2311yescharacteristic
126C22×C8×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22⋊Q8×C47—22no—
129C22⋊Q8×C47C2×C414yes—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—22no—
133C2×C4⋊C4×C47—22no—
134C2×C4⋊C4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2311yescharacteristic
136C2×C4⋊C4×C47C2311yescharacteristic
137C2×C22⋊C4×C47—21no—
138#103×C47—22no—
139#103×C47—22no—
140C22⋊C8×C47—22no—
141C24×C47C2×D411yescharacteristic
142C23×D47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47C22×C412yes—
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—24no—
158C22×C4×C47—81no—
159C22×C4×C47—81no—
160C22×C4×C47C22×C412yes—
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D412yes—
163C22×C4×C47C2411yescharacteristic
164C2×C22⋊D47—24no—
165C2×C22⋊D47—81no—
166C2×C22⋊D47—81no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47C2×D411yescharacteristic
171C22×Dic47C2×D411yescharacteristic
172C22×Dic47C2×D411yescharacteristic
173C22×Dic47C2×D411yescharacteristic
174C2×D188—21no—
175C2×D188—21no—
176C2×D188—21no—
177C2×D188—21no—
178C2×D188—21no—
179C2×D188C22×C412yes—
180C2×C4×D47—24no—
181C2×C4×D47—81no—
182C2×C4×D47—81no—
183C2×Dic94—24no—
184C2×Dic94—81no—
185C2×Dic94—81no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C4⋊C4×C47—24no—
193C4⋊C4×C47—24no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47C22×C412yes—
198C4⋊C4×C47#4112yes—
199C4⋊C4×C47#4112yes—
200C22⋊C4×C47—24no—
201C22⋊Dic47—24no—
202C22⋊Dic47C22⋊C414yes—
203C22⋊Dic47C22⋊C414yes—
204(C2×D47)⋊C4—24no—
205(C2×D47)⋊C4—24no—
206(C2×D47)⋊C4—24no—
207(C2×D47)⋊C4—24no—
208C4⋊Dic47—21no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—24no—
212C4⋊Dic47C22⋊C414yes—
213C4⋊Dic47C22⋊C414yes—
214C4⋊Dic47C22×C412yes—
215C4⋊Dic47#4112yes—
216C4⋊Dic47#4112yes—
217Dic47⋊C4—24no—
218C4×Dic47—24no—
219C4×Dic47—24no—
220C4×Dic47—81no—
221C4×Dic47—81no—
222C4×Dic47—81no—
223C4×Dic47—81no—
224C4×Dic47C22×C412yes—
225C4×Dic47C22×C412yes—
226C4×Dic47C2×D412yes—
227C4×Dic47C2×D412yes—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47C2×C22⋊C412yes—
241C23×C47C22×D411yescharacteristic
242C22×D47—22no—
243C22×D47—41no—
244C22×D47—41no—
245C22×D47—41no—
246C22×D47—41no—
247C22×D47—41no—
248C22×D47—41no—
249Q8×C47—22no—
250Q8×C47—22no—
251Q8×C47—41no—
252Q8×C47—41no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
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—41no—
264C2×C4×C47—41no—
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—84no—
272C2×C4×C47C2×C22⋊C412yes—
273C2×C4×C47C23×C411yescharacteristic
274C2×C4×C47C22×D411yescharacteristic
275C2×C4×C47C2×#4111yescharacteristic
276C2×C4×C47C2×#4111yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C2×C4×C47C2×#4111yescharacteristic
279C22⋊D47—84no—
280C2×Dic47—21no—
281C2×Dic47—21no—
282C2×Dic47—21no—
283C2×Dic47—21no—
284C2×Dic47—21no—
285C2×Dic47—21no—
286C2×Dic47—21no—
287C2×Dic47—21no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—22no—
291C2×Dic47—41no—
292C2×Dic47—41no—
293C2×Dic47—41no—
294C2×Dic47—41no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47C2×C22⋊C412yes—
298C2×Dic47C2×C22⋊C412yes—
299C2×Dic47C2×C22⋊C412yes—
300C2×Dic47C2×C22⋊C412yes—
301D188—22no—
302D188—22no—
303D188—41no—
304D188—41no—
305C4×D47—84no—
306Dic94—84no—
307C8×C47—41no—
308C8×C47—41no—
309C47⋊C8—41no—
310C47⋊C8—41no—
311#21397—471nomaximal, Sylow
312C22×C47—22no—
313C22×C47—22no—
314C22×C47—22no—
315C22×C47—41no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—41no—
319C22×C47C22×C22⋊C411yescharacteristic
320C22×C47#52511yescharacteristic
321C22×C47#52511yescharacteristic
322C22×C47#57611yescharacteristic
323C22×C47#57711yescharacteristic
324C22×C47#57711yescharacteristic
325C22×C47#57811yescharacteristic
326C2×D47—42no—
327C2×D47—42no—
328C2×D47—42no—
329C2×D47—81no—
330C2×D47—81no—
331C2×D47—81no—
332C2×D47—81no—
333C4×C47—22no—
334C4×C47—42no—
335C4×C47—42no—
336C4×C47—42no—
337C4×C47—42no—
338C4×C47C4×#4111yescharacteristic
339C4×C47C4×#4111yescharacteristic
340C4×C47#53211yescharacteristic
341C4×C47#53211yescharacteristic
342Dic47—22no—
343Dic47—22no—
344Dic47—22no—
345Dic47—22no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349C2×#542—471no—
350C2×#433—471no—
351#2274—471no—
352#1988—471no—
353#1987—471no—
354#1983—471no—
355#1983—471no—
356#1875—471no—
357#1874—471no—
358#1873—471no—
359#1872D4711yescharacteristic, complemented
360#1763—471no—
361#1762—471no—
362C4×#103—471no—
363C4×#102—471no—
364C2×C47—42no—
365C2×C47#229711yescharacteristic
366C2×C47#289711yescharacteristic
367C2×C47#289811yescharacteristic
368C2×C47#311811yescharacteristic
369C2×C47#312111yescharacteristic
370C2×C47#312411yescharacteristic
371C2×C47#312511yescharacteristic
372D47—82no—
373#542—478no—
374#542—944no—
375C2×C4⋊Q8—471no—
376C2×#126—941no—
377C2×#124—471no—
378C2×#124—941no—
379C2×#123—941no—
380C2×C22⋊Q8—941no—
381C2×C22⋊Q8C2×D4711yescharacteristic
382C2×#121—471no—
383C2×C4×Q8—471no—
384C2×C4×D4—471no—
385C2×#117—471no—
386C2×#117—471no—
387C22×C4⋊C4C2×D4711yescharacteristic
388#433—944no—
389C2×C4⋊C8—471no—
390C2×C4⋊C8—471no—
391C2×#103—471no—
392C2×#103—471no—
393C2×#103C2×D4711yescharacteristic
394C2×#103C2×D4711yescharacteristic
395C2×#102—471no—
396C2×#102—471no—
397C2×#102—471no—
398C2×#102—471no—
399C2×C22⋊C8—471no—
400C2×C22⋊C8C2×D4711yescharacteristic
401C2×#97—471no—
402C2×C4×C8—471no—
403C4×C4⋊C4—471no—
404C4×C4⋊C4—471no—
405C4×C4⋊C4—471no—
406C4×C4⋊C4—471no—
407C4×C4⋊C4—941no—
408C4×C4⋊C4—941no—
409C4×C22⋊C4—941no—
410C4×C22⋊C4—941no—
411#340—471no—
412#340—471no—
413#340—471no—
414#340—471no—
415#340—471no—
416#340—471no—
417#340C2×D4711yescharacteristic
418#340C2×D4711yescharacteristic
419C47#2139711yescharacteristic, complemented, Sylow
420C22×Q8—941no—
421C22×Q8C22×D4711yescharacteristic
422C22×D4—471no—
423C22×D4—941no—
424C23×C4—21no—
425C23×C4—941no—
426C23×C4C22×D4711yescharacteristic
427C22×C8—471no—
428C22×C8—471no—
429C22×C8C22×D4711yescharacteristic
430C22×C8C22×D4711yescharacteristic
431C4⋊Q8—474no—
432C4⋊Q8—942no—
433#126—948no—
434#124—474no—
435#124—942no—
436#124—948no—
437#123—948no—
438C22⋊Q8—22no—
439C22⋊Q8—948no—
440C22⋊Q8C4×D4714yes—
441#121—474no—
442#121—942no—
443C4×Q8—474no—
444C4×Q8—942no—
445C4×D4—474no—
446C4×D4—942no—
447#117—474no—
448#117—474no—
449#117—942no—
450#117—942no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—471no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—941no—
461C2×C4⋊C4—941no—
462C2×C4⋊C4C22×D4711yescharacteristic
463C2×C4⋊C4C22×D4711yescharacteristic
464C2×C4⋊C4C22×D4711yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—471no—
467C2×C22⋊C4—471no—
468C2×C22⋊C4—941no—
469C2×C22⋊C4—941no—
470C2×C22⋊C4—941no—
471C2×C22⋊C4—941no—
472C2×C22⋊C4—941no—
473C2×C42—471no—
474C2×C42—471no—
475C2×C42—941no—
476C2×C42—941no—
477C2×C42—941no—
478C2×C42—941no—
479C2×C42—941no—
480C2×C42—941no—
481C4⋊C8—942no—
482C4⋊C8—942no—
483#103—22no—
484#103—22no—
485#103—942no—
486#103—942no—
487#102—942no—
488#102—942no—
489#102—942no—
490#102—942no—
491C22⋊C8—22no—
492C22⋊C8—942no—
493#97—942no—
494C4×C8—942no—
495#95—941no—
496#95—941no—
497#95—941no—
498#95—941no—
499C24—941no—
500C24D4×D4711yescharacteristic
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—944no—
507C2×Q8—3761no—
508C2×Q8—3761no—
509C2×Q8C2×C4×D4712yes—
510C2×D4—472no—
511C2×D4—944no—
512C2×D4—941no—
513C2×D4—941no—
514C2×D4—941no—
515C2×D4—941no—
516C2×D4—941no—
517C2×D4—3761no—
518C2×D4—3761no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—471no—
531C22×C4—471no—
532C22×C4—471no—
533C22×C4—471no—
534C22×C4—944no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—3761no—
539C22×C4—3761no—
540C22×C4C2×C4×D4712yes—
541C22×C4D4×D4711yescharacteristic
542C22×C4D4×D4712yes—
543C22×C4C23×D4711yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—941no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8—941no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—474no—
562C4⋊C4—474no—
563C4⋊C4—472no—
564C4⋊C4—472no—
565C4⋊C4—472no—
566C4⋊C4—944no—
567C4⋊C4—944no—
568C4⋊C4—941no—
569C4⋊C4—941no—
570C4⋊C4—941no—
571C4⋊C4C2×C4×D4712yes—
572C4⋊C4#1062535212yes—
573C4⋊C4#1062535212yes—
574C22⋊C4—24no—
575C22⋊C4—474no—
576C22⋊C4—474no—
577C22⋊C4—944no—
578C22⋊C4—944no—
579C22⋊C4—944no—
580C22⋊C4—944no—
581C22⋊C4—944no—
582C42—472no—
583C42—472no—
584C42—472no—
585C42—472no—
586C42—944no—
587C42—944no—
588C42—3761no—
589C42—3761no—
590C42—3761no—
591C42—3761no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—942no—
599C23—1881no—
600C23—1881no—
601C23—1881no—
602C23—1881no—
603C23—1881no—
604C23—1881no—
605C23C22⋊C4×D4712yes—
606C23C2×D4×D4711yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—3764no—
612D4—942no—
613D4—942no—
614D4—3764no—
615D4—1881no—
616D4—1881no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
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—84no—
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—941no—
645C2×C4—941no—
646C2×C4—941no—
647C2×C4—941no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—3764no—
652C2×C4—1881no—
653C2×C4—1881no—
654C2×C4—1881no—
655C2×C4—1881no—
656C2×C4—1881no—
657C2×C4—1881no—
658C2×C4C22⋊C4×D4712yes—
659C2×C4C22×C4×D4711yescharacteristic
660C2×C4C2×D4×D4711yescharacteristic
661C2×C4#41×D4711yescharacteristic
662C2×C4#41×D4711yescharacteristic
663C2×C4C2×#1062535211yescharacteristic
664C2×C4C2×#1062535211yescharacteristic
665C8—41no—
666C8—41no—
667C8—1881no—
668C8—1881no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—3761no—
677C22—3761no—
678C22—3761no—
679C22—3761no—
680C22—1882no—
681C22—1882no—
682C22—1882no—
683C22C2×C22⋊C4×D4711yescharacteristic
684C22#1568962911yescharacteristic
685C22#1568963111yescharacteristic
686C22#1568992711yescharacteristic
687C22#1568992911yescharacteristic
688C22#1568993211yescharacteristic
689C22#1568993611yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—942no—
696C4—942no—
697C4—942no—
698C4—942no—
699C4—1882no—
700C4—1882no—
701C4—1882no—
702C4C4×#1062535211yescharacteristic
703C4C4×#1062535211yescharacteristic
704C4#1568966811yescharacteristic
705C4#1568966811yescharacteristic
706C2—42no—
707C2—3762no—
708C2#2024587311yescharacteristic
709C2#2025191211yescharacteristic
710C2#2025191611yescharacteristic
711C2#2025357311yescharacteristic
712C2#2025361811yescharacteristic
713C2#2025365311yescharacteristic
714C2#2025366011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1872C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenter#1872D47
hypocenterC47#21397
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#15689181C2semidirect
3. #20245745C2semidirect
4. #20244338C2semidirect
5. #20244334C2semidirect
6. #20244317C2semidirect
7. #20244317C2semidirect
10. #20243701C2semidirect
11. #20243220C2semidirect
12. #20243212C2semidirect
13. #103×Dic47C2semidirect
14. #20243202C2semidirect
15. C47×#1872C2semidirect
17. #15689746C4semidirect
69. #13094023C2×C4semidirect
72. #13094013C2×C4semidirect
79. Q8×Dic47C2×C4semidirect
81. #13093986C2×C4semidirect
359. #1872D47semidirect
419. C47#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#156897462
C2×#156891812
#202457452
#202443382
#202443342
#202443172
#202437082
#202437052
#202437012
#202432202
#202432122
#103×Dic472
#202432022
C47×#18722
#2139747