Finite Group Databasebeta

← #26216381

Subgroups — #26216381

Order 12032.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689606C211yesmaximal, characteristic
2C2×#15689181C211yesmaximal, characteristic, complemented
3#20245995C211yesmaximal, characteristic, complemented
4#20243476C211yesmaximal, characteristic, complemented
5#20243475C211yesmaximal, characteristic, complemented
6#20243401C211yesmaximal, characteristic, complemented
7#20243396C211yesmaximal, characteristic, complemented
8#20243391C211yesmaximal, characteristic, complemented
9#20243386C211yesmaximal, characteristic, complemented
10#20243328C211yesmaximal, characteristic
11#20243220C211yesmaximal, characteristic, complemented
12#20243215C211yesmaximal, characteristic, complemented
13#103×Dic47C211yesmaximal, characteristic, complemented
14#102×Dic47C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic
16#15689606—24no—
17#15689606C418yescomplemented
18C2×Q8×Dic47C2211yescharacteristic
19C2×Q8×Dic47C2211yescharacteristic
20C2×D4×Dic47—21no—
21C2×D4×Dic47—21no—
22C2×D4×Dic47C2211yescharacteristic
23C2×D4×Dic47C2211yescharacteristic
24C2×#13093983—21no—
25C2×#13093983C2211yescharacteristic
26C22×C4⋊Dic47—21no—
27C22×C4⋊Dic47C2211yescharacteristic
28#15689181—24no—
29C2×Dic47⋊C8C2211yescharacteristic
30C2×Dic47⋊C8C2211yescharacteristic
31C2×#13093948C2211yescharacteristic
32C2×#13093948C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093945C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×#13093934C2211yescharacteristic
37C2×C8×Dic47C2211yescharacteristic
38#15689017—21no—
39#15689011—21no—
40#15689008—21no—
41#15689006—21no—
42#15688992C2211yescharacteristic
43#15688988C2211yescharacteristic
44#15688983C2211yescharacteristic
45C4⋊C4×Dic47C2211yescharacteristic
46C4⋊C4×Dic47C2211yescharacteristic
47#15688886C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688886C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688885C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C22×#41×C47C2211yescharacteristic
56C2×#103×C47C2211yescharacteristic
57C2×#103×C47C2211yescharacteristic
58C2×#102×C47C2211yescharacteristic
59C2×#102×C47C2211yescharacteristic
60C2×C22⋊C8×C47C2211yescharacteristic
61C47×#380C2211yescharacteristic
62C23×Dic47—21no—
63C23×Dic47—21no—
64C23×Dic47—21no—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67Q8×Dic47—22no—
68Q8×Dic47—22no—
69Q8×Dic47C2×C414yes—
70Q8×Dic47C2×C414yes—
71D4×Dic47—28no—
72D4×Dic47—28no—
73D4×Dic47—22no—
74D4×Dic47—22no—
75D4×Dic47C2×C414yes—
76D4×Dic47C2×C414yes—
77#13093983—28no—
78#13093983C2×C414yes—
79#13093983D414yes—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—22no—
82C2×C4⋊Dic47—21no—
83C2×C4⋊Dic47—21no—
84C2×C4⋊Dic47—28no—
85C2×C4⋊Dic47C2×C414yes—
86C2×C4⋊Dic47D411yescharacteristic
87C2×C4⋊Dic47D411yescharacteristic
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C4⋊Dic47C2311yescharacteristic
90C2×C4⋊Dic47C2311yescharacteristic
91C2×C4⋊Dic47C2311yescharacteristic
92C2×Dic47⋊C4—21no—
93C2×Dic47⋊C4—21no—
94C2×C22⋊Dic47—21no—
95C2×C22⋊Dic47—21no—
96C2×C22⋊Dic47—21no—
97C2×C22⋊Dic47D411yescharacteristic
98C2×C22⋊Dic47D411yescharacteristic
99C2×C4×Dic47—21no—
100C2×C4×Dic47—21no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47—21no—
103C2×C4×Dic47C2311yescharacteristic
104C2×C4×Dic47C2311yescharacteristic
105Dic47⋊C8—22no—
106Dic47⋊C8—22no—
107#13093948—22no—
108#13093948—22no—
109#13093945—22no—
110#13093945—22no—
111C22⋊(C47⋊C8)—22no—
112#13093934—22no—
113C8×Dic47—22no—
114C47⋊#95—21no—
115C47⋊#95—21no—
116C47⋊#95—21no—
117C47⋊#95—21no—
118C47⋊#95—21no—
119C2×#41×C47—22no—
120C2×#41×C47—22no—
121C2×#41×C47—22no—
122C2×#41×C47—22no—
123C2×#41×C47—22no—
124C2×#41×C47C2×C414yes—
125C22×Q8×C47C2311yescharacteristic
126C22×D4×C47—21no—
127C22×D4×C47C2311yescharacteristic
128C23×C4×C47—21no—
129C23×C4×C47C2311yescharacteristic
130C22×C8×C47C2311yescharacteristic
131C22×C8×C47C2311yescharacteristic
132C2×C4⋊C4×C47C2311yescharacteristic
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C22⋊C4×C47—21no—
135#103×C47—22no—
136#103×C47—22no—
137#102×C47—22no—
138#102×C47—22no—
139C22⋊C8×C47—22no—
140#95×C47—21no—
141C24×C47—21no—
142C24×C47C2×D411yescharacteristic
143#41×C47—28no—
144#41×C47—28no—
145#41×C47—28no—
146#41×C47—28no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47C22×C412yes—
151C2×Q8×C47#4112yes—
152C2×Q8×C47#4112yes—
153C2×D4×C47—24no—
154C2×D4×C47—24no—
155C2×D4×C47—24no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47C22×C412yes—
160C2×D4×C47#4112yes—
161C2×D4×C47#4112yes—
162C22×C4×C47—24no—
163C22×C4×C47—24no—
164C22×C4×C47—21no—
165C22×C4×C47—24no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47C22×C412yes—
173C22×C4×C47C2×D411yescharacteristic
174C22×C4×C47C2×D412yes—
175C22×C4×C47C2411yescharacteristic
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—24no—
179C22×Dic47—24no—
180C22×Dic47—24no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—81no—
184C22×Dic47—81no—
185C22×Dic47—81no—
186C22×Dic47—81no—
187C22×Dic47—81no—
188C22×Dic47—81no—
189C22×Dic47C2×D411yescharacteristic
190C22×Dic47C2×D411yescharacteristic
191C22×Dic47C2×D411yescharacteristic
192C22×Dic47C2×D411yescharacteristic
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C22⋊C4×C47—81no—
204C22⋊Dic47—24no—
205C22⋊Dic47—24no—
206C22⋊Dic47—81no—
207C22⋊Dic47C22⋊C414yes—
208C22⋊Dic47C22⋊C414yes—
209C4⋊Dic47—24no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—24no—
213C4⋊Dic47—24no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47C22⋊C414yes—
219C4⋊Dic47C22⋊C414yes—
220C4⋊Dic47C22×C412yes—
221C4⋊Dic47C22×C412yes—
222Dic47⋊C4—81no—
223Dic47⋊C4—81no—
224C4×Dic47—24no—
225C4×Dic47—24no—
226C4×Dic47—81no—
227C4×Dic47—81no—
228C4×Dic47C22×C412yes—
229C4×Dic47C22×C412yes—
230C4×Dic47C2×D412yes—
231C4×Dic47C2×D412yes—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C23×C47—22no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47C2×C22⋊C412yes—
252C23×C47C22×D411yescharacteristic
253Q8×C47—22no—
254Q8×C47—22no—
255Q8×C47—22no—
256Q8×C47#11714yes—
257D4×C47—216no—
258D4×C47—22no—
259D4×C47—22no—
260D4×C47—22no—
261D4×C47#11714yes—
262C2×C4×C47—216no—
263C2×C4×C47—22no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47C2×C22⋊C412yes—
279C2×C4×C47C23×C411yescharacteristic
280C2×C4×C47C22×D411yescharacteristic
281C2×C4×C47C2×#4111yescharacteristic
282C2×C4×C47C2×#4111yescharacteristic
283C2×C4×C47C2×#4111yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×Dic47—21no—
286C2×Dic47—21no—
287C2×Dic47—21no—
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—21no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—41no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—84no—
306C2×Dic47—84no—
307C2×Dic47—84no—
308C2×Dic47C2×C22⋊C412yes—
309C2×Dic47C2×C22⋊C412yes—
310C2×Dic47C2×C22⋊C412yes—
311C2×Dic47C2×C22⋊C412yes—
312C8×C47—41no—
313C8×C47—41no—
314C47⋊C8—41no—
315C47⋊C8—41no—
316#20746—471nomaximal, Sylow
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—24no—
321C22×C47—41no—
322C22×C47—42no—
323C22×C47—41no—
324C22×C47—42no—
325C22×C47—41no—
326C22×C47—42no—
327C22×C47—41no—
328C22×C47—42no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47C22×C22⋊C411yescharacteristic
332C22×C47#52511yescharacteristic
333C22×C47#52511yescharacteristic
334C22×C47#57611yescharacteristic
335C22×C47#57711yescharacteristic
336C22×C47#57711yescharacteristic
337C22×C47#57811yescharacteristic
338C4×C47—22no—
339C4×C47—24no—
340C4×C47—81no—
341C4×C47—81no—
342C4×C47C2×#11711yescharacteristic
343C4×C47C2×#11711yescharacteristic
344C4×C47#52511yescharacteristic
345C4×C47#52511yescharacteristic
346Dic47—22no—
347Dic47—22no—
348Dic47—22no—
349Dic47—22no—
350Dic47—42no—
351Dic47—42no—
352Dic47—81no—
353Dic47—81no—
354C2×#520—471no—
355C2×#433—471no—
356#2314—471no—
357#1824—471no—
358#1823—471no—
359#1805—471no—
360#1804—471no—
361#1803—471no—
362#1802—471no—
363#1788—471no—
364#1788D4711yescharacteristic
365#1763—471no—
366#1762—471no—
367C4×#103—471no—
368C4×#102—471no—
369C2×C47—42no—
370C2×C47—44no—
371C2×C47#228011yescharacteristic
372C2×C47#289711yescharacteristic
373C2×C47#289811yescharacteristic
374C2×C47#311911yescharacteristic
375C2×C47#312011yescharacteristic
376C2×C47#312411yescharacteristic
377C2×C47#312511yescharacteristic
378C22×#41C2×D4711yescharacteristic
379#520—478no—
380#520—944no—
381C2×C4×Q8—471no—
382C2×C4×Q8—471no—
383C2×C4×D4—471no—
384C2×C4×D4—471no—
385C2×C4×D4—941no—
386C2×C4×D4—941no—
387C2×#117—471no—
388C2×#117—941no—
389C22×C4⋊C4—471no—
390C22×C4⋊C4—941no—
391#433—944no—
392C2×C4⋊C8—471no—
393C2×C4⋊C8—471no—
394C2×#103—471no—
395C2×#103—471no—
396C2×#103C2×D4711yescharacteristic
397C2×#103C2×D4711yescharacteristic
398C2×#102—471no—
399C2×#102—471no—
400C2×#102C2×D4711yescharacteristic
401C2×#102C2×D4711yescharacteristic
402C2×C22⋊C8—471no—
403C2×C22⋊C8C2×D4711yescharacteristic
404C2×#97—471no—
405C2×C4×C8—471no—
406#388—941no—
407#388—941no—
408#387—941no—
409#387—941no—
410#384—471no—
411#382—471no—
412#380—471no—
413#380C2×D4711yescharacteristic
414C4×C4⋊C4—471no—
415C4×C4⋊C4—471no—
416#340—471no—
417#340—471no—
418#340—471no—
419#340—471no—
420#340—471no—
421#340—471no—
422#340—471no—
423#340—471no—
424C47#2074611yescharacteristic, complemented, Sylow
425C2×#41—22no—
426C2×#41—22no—
427C2×#41—22no—
428C2×#41—22no—
429C2×#41—22no—
430C2×#41C4×D4714yes—
431C22×Q8C22×D4711yescharacteristic
432C22×D4—21no—
433C22×D4C22×D4711yescharacteristic
434C23×C4—21no—
435C23×C4—941no—
436C23×C4—941no—
437C23×C4—941no—
438C23×C4C22×D4711yescharacteristic
439C22×C8—471no—
440C22×C8—471no—
441C22×C8C22×D4711yescharacteristic
442C22×C8C22×D4711yescharacteristic
443C4×Q8—474no—
444C4×Q8—474no—
445C4×Q8—942no—
446C4×Q8—942no—
447C4×D4—474no—
448C4×D4—474no—
449C4×D4—942no—
450C4×D4—942no—
451C4×D4—948no—
452C4×D4—948no—
453#117—474no—
454#117—474no—
455#117—948no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4—471no—
458C2×C4⋊C4—474no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—471no—
463C2×C4⋊C4—948no—
464C2×C4⋊C4—941no—
465C2×C4⋊C4—941no—
466C2×C4⋊C4—941no—
467C2×C4⋊C4—942no—
468C2×C4⋊C4—941no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4C22×D4711yescharacteristic
471C2×C4⋊C4C22×D4711yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—471no—
474C2×C22⋊C4—471no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4—941no—
477C2×C22⋊C4—941no—
478C2×C42—471no—
479C2×C42—471no—
480C2×C42—941no—
481C2×C42—941no—
482C2×C42—941no—
483C2×C42—941no—
484C4⋊C8—942no—
485C4⋊C8—942no—
486#103—22no—
487#103—22no—
488#103—942no—
489#103—942no—
490#102—22no—
491#102—22no—
492#102—942no—
493#102—942no—
494C22⋊C8—22no—
495C22⋊C8—942no—
496#97—942no—
497C4×C8—942no—
498#95—21no—
499#95—941no—
500#95—941no—
501#95—941no—
502#95—941no—
503#95—941no—
504C24—21no—
505C24D4×D4711yescharacteristic
506#41—28no—
507#41—28no—
508#41—28no—
509#41—28no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8C2×C4×D4712yes—
514C2×Q8#1062535212yes—
515C2×Q8#1062535212yes—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4C2×C4×D4712yes—
523C2×D4#1062535212yes—
524C2×D4#1062535212yes—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—471no—
536C22×C4—471no—
537C22×C4—471no—
538C22×C4—471no—
539C22×C4—944no—
540C22×C4—944no—
541C22×C4—944no—
542C22×C4—941no—
543C22×C4—941no—
544C22×C4—941no—
545C22×C4—941no—
546C22×C4—3761no—
547C22×C4—3761no—
548C22×C4—3761no—
549C22×C4—3761no—
550C22×C4—3761no—
551C22×C4—3761no—
552C22×C4C2×C4×D4712yes—
553C22×C4D4×D4711yescharacteristic
554C22×C4D4×D4712yes—
555C22×C4C23×D4711yescharacteristic
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—941no—
563C2×C8—941no—
564C2×C8—941no—
565C2×C8—941no—
566C2×C8—941no—
567C2×C8—941no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—474no—
573C4⋊C4—474no—
574C4⋊C4—472no—
575C4⋊C4—472no—
576C4⋊C4—944no—
577C4⋊C4—944no—
578C4⋊C4—944no—
579C4⋊C4—941no—
580C4⋊C4—941no—
581C4⋊C4—941no—
582C4⋊C4—941no—
583C4⋊C4—941no—
584C4⋊C4—941no—
585C4⋊C4—3761no—
586C4⋊C4—3761no—
587C22⋊C4—81no—
588C22⋊C4—474no—
589C22⋊C4—474no—
590C22⋊C4—944no—
591C22⋊C4—944no—
592C22⋊C4—3761no—
593C42—472no—
594C42—472no—
595C42—472no—
596C42—472no—
597C42—944no—
598C42—944no—
599C42—3761no—
600C42—3761no—
601C23—22no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—22no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23C22⋊C4×D4712yes—
615C23C2×D4×D4711yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8#1309398014yes—
620D4—216no—
621D4—22no—
622D4—22no—
623D4—22no—
624D4#1309398014yes—
625C2×C4—216no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—472no—
642C2×C4—472no—
643C2×C4—472no—
644C2×C4—472no—
645C2×C4—941no—
646C2×C4—941no—
647C2×C4—941no—
648C2×C4—941no—
649C2×C4—941no—
650C2×C4—941no—
651C2×C4—941no—
652C2×C4—941no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—3764no—
656C2×C4—3764no—
657C2×C4—3764no—
658C2×C4—1881no—
659C2×C4—1881no—
660C2×C4—1881no—
661C2×C4—1881no—
662C2×C4—1881no—
663C2×C4—1881no—
664C2×C4—1881no—
665C2×C4—1881no—
666C2×C4—1881no—
667C2×C4—1881no—
668C2×C4C22⋊C4×D4712yes—
669C2×C4C22×C4×D4711yescharacteristic
670C2×C4C2×D4×D4711yescharacteristic
671C2×C4C2×#1062535211yescharacteristic
672C2×C4C2×#1062535211yescharacteristic
673C2×C4C2×#1062535211yescharacteristic
674C2×C4C2×#1062535211yescharacteristic
675C8—41no—
676C8—41no—
677C8—1881no—
678C8—1881no—
679C22—22no—
680C22—22no—
681C22—24no—
682C22—22no—
683C22—42no—
684C22—42no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—42no—
689C22—41no—
690C22—42no—
691C22—41no—
692C22—42no—
693C22C2×C22⋊C4×D4711yescharacteristic
694C22#1568962911yescharacteristic
695C22#1568962911yescharacteristic
696C22#1568992511yescharacteristic
697C22#1568993011yescharacteristic
698C22#1568993311yescharacteristic
699C22#1568993911yescharacteristic
700C4—22no—
701C4—24no—
702C4—81no—
703C4—81no—
704C4—942no—
705C4—942no—
706C4—942no—
707C4—942no—
708C4—3761no—
709C4—3761no—
710C4—1882no—
711C4—1882no—
712C4C2×#1309398011yescharacteristic
713C4C2×#1309398011yescharacteristic
714C4#1568962911yescharacteristic
715C4#1568962911yescharacteristic
716C2—42no—
717C2—44no—
718C2#2024576611yescharacteristic
719C2#2025191011yescharacteristic
720C2#2025191911yescharacteristic
721C2#2025358011yescharacteristic
722C2#2025359511yescharacteristic
723C2#2025365111yescharacteristic
724C2#2025366611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1788C2
socleC23×C47C22×D4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenter#1788D47
hypocenterC47#20746
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#15689181C2semidirect
3. #20245995C2semidirect
4. #20243476C2semidirect
5. #20243475C2semidirect
6. #20243401C2semidirect
7. #20243396C2semidirect
8. #20243391C2semidirect
9. #20243386C2semidirect
11. #20243220C2semidirect
12. #20243215C2semidirect
13. #103×Dic47C2semidirect
14. #102×Dic47C2semidirect
17. #15689606C4semidirect
424. C47#20746semidirect

Maximal subgroups

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

subgroupindex
C2×#156896062
C2×#156891812
#202459952
#202434762
#202434752
#202434012
#202433962
#202433912
#202433862
#202433282
#202432202
#202432152
#103×Dic472
#102×Dic472
C47×#17882
#2074647