Finite Group Databasebeta

← #26236561

Subgroups — #26236561

Order 12032.

1118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689285C211yesmaximal, characteristic
2C2×#15689223C211yesmaximal, characteristic, complemented
3C2×#15689119C211yesmaximal, characteristic
4#20246413C211yesmaximal, characteristic, complemented
5#20244258C211yesmaximal, characteristic, complemented
6#20244081C211yesmaximal, characteristic, complemented
7#20244026C211yesmaximal, characteristic, complemented
8#20243809C211yesmaximal, characteristic, complemented
9#20243732C211yesmaximal, characteristic, complemented
10#20243722C211yesmaximal, characteristic, complemented
11#20243649C211yesmaximal, characteristic, complemented
12#20243585C211yesmaximal, characteristic, complemented
13#20243213C211yesmaximal, characteristic, complemented
14#20243166C211yesmaximal, characteristic, complemented
15C47×#2339C211yesmaximal, characteristic
16C22×#10625337C2211yescharacteristic
17C22×#10625335C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C2×#13094003C2211yescharacteristic
20C2×C4×Dic94C2211yescharacteristic
21C2×#13093983C2211yescharacteristic
22#15689285C418yescomplemented
23#15689223—24no—
24C2×#13093957C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26#15689119—24no—
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093947C2211yescharacteristic
31C2×#13093947C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×#13093945C2211yescharacteristic
34C2×#13093945C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×#13093935C2211yescharacteristic
37C2×#13093935C2211yescharacteristic
38#15689029C2211yescharacteristic
39#15689021C2211yescharacteristic
40#15689017—21no—
41#15689011—21no—
42#15689005—21no—
43C4×C4⋊Dic47C2211yescharacteristic
44#15688974—21no—
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51C22×#41×C47C2211yescharacteristic
52C2×C4×D4×C47C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C47×#391C2211yescharacteristic
55C47×#391C2211yescharacteristic
56C47×#386—21no—
57C47×#386—21no—
58C47×#381—21no—
59C47×#380C2211yescharacteristic
60C4×C22⋊C4×C47C2211yescharacteristic
61C2×#95×C47—21no—
62C22×Dic94C2311yescharacteristic
63C2×#10625337—41no—
64C2×#10625337—41no—
65C2×#10625337C2×C414yescomplemented
66C2×#10625335—22no—
67C2×#10625335—22no—
68C2×#10625335C2×C414yes—
69C22×C47⋊C8—22no—
70C22×C47⋊C8—22no—
71C22×C47⋊C8—41no—
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76#13094003—22no—
77#13094003C2×C414yescomplemented
78C4×Dic94—22no—
79C4×Dic94—41no—
80#13093983—22no—
81#13093983—41no—
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×Dic47⋊C4—21no—
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C2×C22⋊Dic47—21no—
89C2×C22⋊Dic47—21no—
90C2×C4×Dic47—21no—
91C2×C4×Dic47—21no—
92C2×C4×Dic47—21no—
93#13093957—22no—
94#13093955—41no—
95#13093948—22no—
96#13093948—22no—
97#13093948C2×C414yescomplemented
98#13093947—22no—
99#13093947—41no—
100#13093945—22no—
101#13093945C2×C414yes—
102#13093945D414yes—
103C22⋊(C47⋊C8)C2×C414yescomplemented
104#13093935—22no—
105#13093935—41no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C2×#41×C47—22no—
111C2×#41×C47—22no—
112C2×#41×C47—22no—
113C2×#41×C47—41no—
114C2×#41×C47—41no—
115C2×#41×C47C2×C414yes—
116C22×Q8×C47C2311yescharacteristic
117C22×D4×C47—21no—
118C22×D4×C47C2311yescharacteristic
119C23×C4×C47—21no—
120C23×C4×C47—21no—
121C23×C4×C47—21no—
122C23×C4×C47C2311yescharacteristic
123C4×D4×C47—22no—
124C4×D4×C47—22no—
125C4×D4×C47—41no—
126C4×D4×C47—41no—
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47D411yescharacteristic
133C2×C22⋊C4×C47D411yescharacteristic
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47D411yescharacteristic
142#95×C47D411yescharacteristic
143C24×C47—21no—
144C24×C47C2×D411yescharacteristic
145#41×C47—28no—
146#41×C47—44no—
147#41×C47—44no—
148#41×C47—44no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47C22×C412yes—
155C2×D4×C47—24no—
156C2×D4×C47—21no—
157C2×D4×C47—21no—
158C2×D4×C47—21no—
159C2×D4×C47—42no—
160C2×D4×C47—42no—
161C2×D4×C47C22×C412yes—
162C2×D4×C47C2×D412yes—
163C2×D4×C47#4112yes—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—24no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—42no—
173C22×C4×C47—42no—
174C22×C4×C47—42no—
175C22×C4×C47—42no—
176C22×C4×C47—42no—
177C22×C4×C47—42no—
178C22×C4×C47—81no—
179C22×C4×C47—81no—
180C22×C4×C47C22×C412yes—
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47#4112yes—
187C22×C4×C47C2411yescharacteristic
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—21no—
192C2×Dic94—21no—
193C2×Dic94—21no—
194C2×Dic94—21no—
195C2×Dic94—21no—
196C2×Dic94—21no—
197C2×Dic94C22×C412yes—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—21no—
200C4⋊C4×C47—21no—
201C4⋊C4×C47—21no—
202C22⋊C4×C47—41no—
203C22⋊C4×C47—41no—
204C22⋊C4×C47—42no—
205C22⋊C4×C47—42no—
206C22⋊C4×C47—81no—
207C42×C47—21no—
208C42×C47—21no—
209C42×C47—21no—
210C42×C47—21no—
211C22⋊Dic47—24no—
212C22⋊Dic47—42no—
213#10625337—44no—
214#10625335—28no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—21no—
218C4⋊Dic47—21no—
219C4⋊Dic47C22×C412yes—
220C4⋊Dic47C2×D412yes—
221Dic47⋊C4—24no—
222Dic47⋊C4—42no—
223Dic47⋊C4—42no—
224C4×Dic47—42no—
225C4×Dic47—42no—
226C4×Dic47—42no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—44no—
237C2×C47⋊C8C22×C412yes—
238C2×C47⋊C8C22×C412yes—
239C2×C47⋊C8C2×D412yes—
240C23×C47—22no—
241C23×C47—21no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47C4×D412yes—
254C23×C47C22×D411yescharacteristic
255Q8×C47—22no—
256Q8×C47—22no—
257Q8×C47—41no—
258Q8×C47—41no—
259D4×C47—22no—
260D4×C47—22no—
261D4×C47—22no—
262D4×C47—48no—
263D4×C47C4×D414yes—
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—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—48no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—84no—
293C2×C4×C47—84no—
294C2×C4×C47C4×D412yes—
295C2×C4×C47C23×C411yescharacteristic
296C2×C4×C47C22×D411yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47C2×#4111yescharacteristic
299C2×C4×C47H(5,𝔽2)11yescharacteristic
300C2×C4×C47H(5,𝔽2)11yescharacteristic
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313Dic94—22no—
314Dic94—22no—
315Dic94—41no—
316Dic94—41no—
317C47⋊C8—22no—
318C47⋊C8—22no—
319C47⋊C8—22no—
320C47⋊C8—41no—
321#22856—471nomaximal, Sylow
322C22×C47—22no—
323C22×C47—24no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—42no—
327C22×C47—42no—
328C22×C47—42no—
329C22×C47—41no—
330C22×C47—41no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47—41no—
334C22×C47—41no—
335C22×C47—42no—
336C22×C47C2×C4×D411yescharacteristic
337C22×C47D4211yescharacteristic
338C22×C47#54611yescharacteristic
339C22×C47#57511yescharacteristic
340C22×C47#57511yescharacteristic
341C22×C47#57711yescharacteristic
342C22×C47#57811yescharacteristic
343C4×C47—22no—
344C4×C47—42no—
345C4×C47—41no—
346C4×C47—41no—
347C4×C47—41no—
348C4×C47—41no—
349C4×C47—81no—
350C4×C47—81no—
351C4×C47C2×C4×D411yescharacteristic
352C4×C47#51811yescharacteristic
353C4×C47#54611yescharacteristic
354C4×C47#55111yescharacteristic
355Dic47—42no—
356Dic47—42no—
357Dic47—42no—
358Dic47—81no—
359C2×#452—471no—
360C2×#440—471no—
361C2×#416—471no—
362#2362—471no—
363#2339D4711yescharacteristic
364#1971—471no—
365#1935—471no—
366#1928—471no—
367#1892—471no—
368#1878—471no—
369#1877—471no—
370#1864—471no—
371#1854—471no—
372#1762—471no—
373#1752—471no—
374C2×C47—42no—
375C2×C47—44no—
376C2×C47#235811yescharacteristic
377C2×C47#294311yescharacteristic
378C2×C47#294711yescharacteristic
379C2×C47#326711yescharacteristic
380C2×C47#326911yescharacteristic
381C2×C47#331111yescharacteristic
382C2×C47#331511yescharacteristic
383C22×#41C2×D4711yescharacteristic
384C22×Q16—471no—
385C22×SD16—471no—
386C23×C8—471no—
387C2×C22⋊Q8—471no—
388C2×C4×Q8—471no—
389C2×C4×D4C2×D4711yescharacteristic
390C2×C4×D4C2×D4711yescharacteristic
391C2×#117—471no—
392#452—478no—
393#440—944no—
394C2×#107—471no—
395C2×#106—471no—
396#416—944no—
397C2×#103—471no—
398C2×#103—471no—
399C2×#103—471no—
400C2×#103—471no—
401C2×#103—471no—
402C2×#102—471no—
403C2×#102—471no—
404C2×#102—471no—
405C2×C22⋊C8—471no—
406C2×#97—471no—
407C2×#97—471no—
408#391—471no—
409#391C2×D4711yescharacteristic
410#391C2×D4711yescharacteristic
411#389—471no—
412#388—941no—
413#388—941no—
414#387—941no—
415#386—21no—
416#386—21no—
417#381—21no—
418#380C2×D4711yescharacteristic
419C4×C4⋊C4—471no—
420C4×C4⋊C4—941no—
421C4×C22⋊C4C2×D4711yescharacteristic
422C2×#95—21no—
423#340—471no—
424#340—471no—
425#340—471no—
426#340—471no—
427#336—471no—
428#336—471no—
429C47#2285611yescharacteristic, complemented, Sylow
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41C4×D4714yes—
436C22×Q8—471no—
437C22×Q8C22×D4711yescharacteristic
438C22×D4—21no—
439C22×D4C22×D4711yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—21no—
443C23×C4C22×D4711yescharacteristic
444C2×Q16—474no—
445C2×Q16—1881no—
446C2×Q16—1881no—
447C2×SD16—474no—
448C2×SD16—942no—
449C2×SD16—942no—
450C22×C8—471no—
451C22×C8—471no—
452C22×C8—471no—
453C22×C8—471no—
454C22×C8—942no—
455C22×C8—942no—
456C22×C8—1881no—
457C22⋊Q8—474no—
458C22⋊Q8—942no—
459C4×Q8—942no—
460C4×Q8—1881no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—41no—
464C4×D4—41no—
465#117—942no—
466#117—1881no—
467C2×C4⋊C4—471no—
468C2×C4⋊C4—471no—
469C2×C4⋊C4—471no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4C22×D4711yescharacteristic
474C2×C4⋊C4C22×D4711yescharacteristic
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—941no—
479C2×C22⋊C4—941no—
480C2×C22⋊C4C22⋊D4711yescharacteristic
481C2×C22⋊C4C22⋊D4711yescharacteristic
482C2×C42—941no—
483C2×C42—941no—
484C2×C42—941no—
485C2×C42C22×D4711yescharacteristic
486C2×C42C22×D4711yescharacteristic
487#107—942no—
488#106—1881no—
489#103—474no—
490#103—942no—
491#103—942no—
492#103—942no—
493#103—1881no—
494#102—474no—
495#102—474no—
496#102—942no—
497C22⋊C8—474no—
498#97—942no—
499#97—1881no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—941no—
506#95—941no—
507#95—941no—
508#95—941no—
509#95C22⋊D4711yescharacteristic
510#95C22⋊D4711yescharacteristic
511C24—21no—
512C24C2×C22⋊D4711yescharacteristic
513#41—28no—
514#41—44no—
515#41—44no—
516#41—44no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—472no—
523C2×Q8—941no—
524C2×Q8—941no—
525C2×Q8—941no—
526C2×Q8—941no—
527C2×Q8—941no—
528C2×Q8C2×C4×D4712yes—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4C2×C4×D4712yes—
536C2×D4D4×D4712yes—
537C2×D4#1062535212yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4C2×C4×D4712yes—
559C22×C4#1062535012yes—
560C22×C4C2×C22⋊D4711yescharacteristic
561C22×C4C2×C22⋊D4711yescharacteristic
562C22×C4C2×C22⋊D4711yescharacteristic
563C22×C4C2×C22⋊D4711yescharacteristic
564C22×C4C2×C22⋊D4711yescharacteristic
565C22×C4C23×D4711yescharacteristic
566Q16—1884no—
567SD16—948no—
568C2×C8—472no—
569C2×C8—472no—
570C2×C8—472no—
571C2×C8—941no—
572C2×C8—941no—
573C2×C8—941no—
574C2×C8—941no—
575C2×C8—941no—
576C2×C8—941no—
577C2×C8—941no—
578C2×C8—941no—
579C2×C8—941no—
580C2×C8—1884no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—472no—
586C4⋊C4—472no—
587C4⋊C4—944no—
588C4⋊C4—941no—
589C4⋊C4—941no—
590C4⋊C4—941no—
591C4⋊C4—941no—
592C4⋊C4—1882no—
593C4⋊C4—1882no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—81no—
599C22⋊C4—944no—
600C22⋊C4—1882no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—1882no—
606C42—1882no—
607C42—1882no—
608C23—22no—
609C23—21no—
610C23—22no—
611C23—21no—
612C23—22no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23C4×C22⋊D4712yes—
622C23C22×C22⋊D4711yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—41no—
626Q8—41no—
627Q8—942no—
628Q8—942no—
629Q8—1881no—
630Q8—1881no—
631D4—22no—
632D4—22no—
633D4—22no—
634D4—48no—
635D4(C22⋊D47)⋊C414yes—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—48no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—942no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—1881no—
670C2×C4—1881no—
671C2×C4—1881no—
672C2×C4—1881no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4C4×C22⋊D4712yes—
679C2×C4C22×C4×D4711yescharacteristic
680C2×C4C2×D4×D4711yescharacteristic
681C2×C4C2×#1062535211yescharacteristic
682C2×C4C2×#1062535011yescharacteristic
683C2×C4#1309406911yescharacteristic
684C2×C4#1309406911yescharacteristic
685C8—942no—
686C8—942no—
687C8—942no—
688C8—1881no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—41no—
697C22—42no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—41no—
702C22—42no—
703C22C2×C4×C22⋊D4711yescharacteristic
704C22D4×C22⋊D4711yescharacteristic
705C22#1568976711yescharacteristic
706C22#1568992111yescharacteristic
707C22#1568992111yescharacteristic
708C22#1568993411yescharacteristic
709C22#1568993811yescharacteristic
710C4—22no—
711C4—42no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—41no—
716C4—81no—
717C4—81no—
718C4—3761no—
719C4—1882no—
720C4—1882no—
721C4—1882no—
722C4C2×(C22⋊D47)⋊C411yescharacteristic
723C4#1568959611yescharacteristic
724C4#1568976311yescharacteristic
725C4#1568979911yescharacteristic
726C2—42no—
727C2—44no—
728C2#2024636711yescharacteristic
729C2#2025218611yescharacteristic
730C2#2025222711yescharacteristic
731C2#2025490911yescharacteristic
732C2#2025493911yescharacteristic
733C2#2025542411yescharacteristic
734C2#2025548411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2339C2
socleC23×C47C22×D4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenter#2339D47
hypocenterC47#22856
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#15689223C2semidirect
4. #20246413C2semidirect
5. #20244258C2semidirect
6. #20244081C2semidirect
7. #20244026C2semidirect
8. #20243809C2semidirect
9. #20243732C2semidirect
10. #20243722C2semidirect
11. #20243649C2semidirect
12. #20243585C2semidirect
13. #20243213C2semidirect
14. #20243166C2semidirect
22. #15689285C4semidirect
65. C2×#10625337C2×C4semidirect
77. #13094003C2×C4semidirect
97. #13093948C2×C4semidirect
103. C22⋊(C47⋊C8)C2×C4semidirect
429. C47#22856semidirect

Maximal subgroups

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

subgroupindex
C2×#156892852
C2×#156892232
C2×#156891192
#202464132
#202442582
#202440812
#202440262
#202438092
#202437322
#202437222
#202436492
#202435852
#202432132
#202431662
C47×#23392
#2285647