Finite Group Databasebeta

← #25140305

Subgroups — #25140305

Order 11008.

1006 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583241C211yesmaximal, characteristic, complemented
2C2×#14582901C211yesmaximal, characteristic, complemented
3#19137940C211yesmaximal, characteristic
4#19137524C211yesmaximal, characteristic, complemented
5#19136115C211yesmaximal, characteristic, complemented
6#19136015C211yesmaximal, characteristic, complemented
7#19135792C211yesmaximal, characteristic, complemented
8#19135785C211yesmaximal, characteristic, complemented
9#19135230C211yesmaximal, characteristic, complemented
10#19135223C211yesmaximal, characteristic, complemented
11#19134915C211yesmaximal, characteristic, complemented
12#19134790C211yesmaximal, characteristic, complemented
13#19134628C211yesmaximal, characteristic, complemented
14#19134536C211yesmaximal, characteristic, complemented
15C43×#1870C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21#14583241—24no—
22C2×#13063259C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063257C2211yescharacteristic
26#14582901—24no—
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35#14582814—21no—
36#14582807—21no—
37#14582805C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582792—21no—
40#14582785—21no—
41#14582779—21no—
42#14582775—21no—
43#14582770—21no—
44#14582765C2211yescharacteristic
45#14582759C2211yescharacteristic
46#14582759C2211yescharacteristic
47#14582759C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49C22⋊C4×Dic43—21no—
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C22×Dic86C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C23×Dic43—21no—
72C22×C4×D43—21no—
73#13063304—22no—
74#13063304—41no—
75#13063299—22no—
76#13063299—41no—
77#13063284—22no—
78#13063284—41no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—41no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43—21no—
99#13063259—22no—
100#13063257—22no—
101#13063257—41no—
102#13063257—41no—
103#13063250—22no—
104#13063250—22no—
105#13063250—41no—
106#13063250D414yescomplemented
107#13063247—22no—
108#13063247—22no—
109#13063247—22no—
110#13063247—41no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×D4×C43D411yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C2×M16×C43—22no—
123C2×M16×C43—22no—
124C2×M16×C43—41no—
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C2×C4⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C22⋊C8×C43—22no—
136C22⋊C8×C43—22no—
137C22⋊C8×C43—41no—
138C24×C43C2×D411yescharacteristic
139C24×C43C2×D411yescharacteristic
140C23×D43—21no—
141C2×D4×C43—22no—
142C2×D4×C43—41no—
143C2×D4×C43—41no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4112yes—
159C22×C4×C43#4112yes—
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—42no—
162C2×C22⋊D43—42no—
163C2×C22⋊D43—42no—
164C2×C22⋊D43—42no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43—81no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—42no—
175C22×Dic43—42no—
176C22×Dic43—81no—
177#10621898—28no—
178#10621898—44no—
179#10621898—44no—
180#10621898—44no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172#4112yes—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86C2×D412yes—
196M16×C43—44no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43C2×D412yes—
209C4⋊C4×C43—22no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—22no—
212C42×C43—21no—
213C42×C43—21no—
214C22⋊Dic43—42no—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C22⋊Dic43—81no—
218C22⋊Dic43—81no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—81no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—42no—
234C4⋊Dic43C2×D412yes—
235Dic43⋊C4—42no—
236C4×Dic43—42no—
237C4×Dic43—81no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43#12312yes—
252C23×C43C22×D411yescharacteristic
253C22×D43—22no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260D4×C43—44no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43#12312yes—
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C22⋊D43—48no—
288C22⋊D43—84no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—84no—
311D172—22no—
312D172—22no—
313D172—41no—
314D172—41no—
315C4×D43—48no—
316Dic86—22no—
317Dic86—22no—
318Dic86—41no—
319Dic86—41no—
320C8×C43—22no—
321C8×C43—41no—
322C8×C43—41no—
323C8×C43—41no—
324#24891—431nomaximal, Sylow
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43C2×#12311yescharacteristic
340C22×C43D4211yescharacteristic
341C22×C43#54611yescharacteristic
342C22×C43#57511yescharacteristic
343C22×C43#57511yescharacteristic
344C22×C43#57711yescharacteristic
345C22×C43#57711yescharacteristic
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—81no—
350C2×D43—81no—
351C2×D43—81no—
352C2×D43—81no—
353C4×C43—22no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43#52511yescharacteristic
358C4×C43#53811yescharacteristic
359C4×C43#54611yescharacteristic
360C4×C43#55111yescharacteristic
361Dic43—42no—
362Dic43—42no—
363Dic43—81no—
364Dic43—81no—
365Dic43—81no—
366Dic43—81no—
367Dic43—81no—
368C2×#485—431no—
369C2×#417—431no—
370#2407—431no—
371#2352—431no—
372#2092—431no—
373#2074—431no—
374#2035—431no—
375#2034—431no—
376#1927—431no—
377#1926—431no—
378#1875—431no—
379#1870D4311yescharacteristic, complemented
380#1853—431no—
381#1809—431no—
382#1788—431no—
383C2×C43—42no—
384C2×C43—81no—
385C2×C43#241811yescharacteristic
386C2×C43#309311yescharacteristic
387C2×C43#309911yescharacteristic
388C2×C43#327111yescharacteristic
389C2×C43#327511yescharacteristic
390C2×C43#330711yescharacteristic
391C2×C43#332311yescharacteristic
392D43—82no—
393C22×#41—431no—
394C22×M16C2×D4311yescharacteristic
395C2×C22⋊Q8—431no—
396C2×#121—431no—
397C2×C4×D4C2×D4311yescharacteristic
398C2×#117—431no—
399C22×C4⋊C4—431no—
400#485—864no—
401C2×#107—431no—
402C2×#106—431no—
403C2×#106—431no—
404C2×#106—431no—
405#417—864no—
406C2×#103—431no—
407C2×#103—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#102—431no—
411C2×#102—431no—
412C2×#102—431no—
413C2×#102—431no—
414C2×C22⋊C8C2×D4311yescharacteristic
415C2×C22⋊C8C2×D4311yescharacteristic
416C2×C22⋊C8C2×D4311yescharacteristic
417#394—861no—
418#392—861no—
419#391—431no—
420#390—431no—
421#388—861no—
422#387—861no—
423#386—861no—
424#386—861no—
425#385—861no—
426#382—431no—
427#380—431no—
428#380—431no—
429#380—431no—
430C4×C4⋊C4—431no—
431C4×C22⋊C4—861no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#336C2×D4311yescharacteristic
437#336C2×D4311yescharacteristic
438C43#2489111yescharacteristic, complemented, Sylow
439C2×#41—862no—
440C2×#41—862no—
441C2×#41—862no—
442C2×#41—862no—
443C2×#41—1721no—
444C2×#41—1721no—
445C22×Q8—431no—
446C22×D4—431no—
447C22×D4—861no—
448C22×D4—861no—
449C22×D4D17211yescharacteristic
450C23×C4—861no—
451C23×C4—861no—
452C23×C4C22×D4311yescharacteristic
453C23×C4C22×D4311yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459C22×C8C22×D4311yescharacteristic
460C22×C8C22×D4311yescharacteristic
461C22⋊Q8—862no—
462C22⋊Q8—1721no—
463#121—862no—
464#121—1721no—
465C4×D4—22no—
466C4×D4—22no—
467#117—862no—
468#117—1721no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—862no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—1721no—
479C2×C4⋊C4D17211yescharacteristic
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4D17211yescharacteristic
489C2×C22⋊C4D17211yescharacteristic
490C2×C42—861no—
491C2×C42—861no—
492C2×C42C22×D4311yescharacteristic
493#107—862no—
494#106—862no—
495#106—1721no—
496#106—1721no—
497#103—434no—
498#103—862no—
499#103—862no—
500#103—1721no—
501#102—862no—
502#102—862no—
503#102—862no—
504#102—1721no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—41no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—861no—
517C24C2×D17211yescharacteristic
518C24C2×D17211yescharacteristic
519#41—868no—
520#41—1724no—
521#41—1724no—
522#41—1724no—
523C2×Q8—432no—
524C2×Q8—861no—
525C2×Q8—861no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×D4—22no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—432no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C2×D4—861no—
537C2×D4—861no—
538C2×D4—3441no—
539C2×D4—1722no—
540C2×D4—1722no—
541C2×D4—1722no—
542C2×D4—1722no—
543C2×D4—1722no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—3441no—
562C22×C4—1722no—
563C22×C4—1722no—
564C22×C4—1722no—
565C22×C4—1722no—
566C22×C4—1722no—
567C22×C4C2×D17211yescharacteristic
568C22×C4C2×D17211yescharacteristic
569C22×C4C2×D17211yescharacteristic
570C22×C4C2×D17211yescharacteristic
571C22×C4#1062190012yes—
572C22×C4#1062190012yes—
573C22×C4C23×D4311yescharacteristic
574M16—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8D4×D4312yes—
587C4⋊C4—22no—
588C4⋊C4—432no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—861no—
595C4⋊C4—861no—
596C4⋊C4—861no—
597C4⋊C4—861no—
598C4⋊C4—861no—
599C4⋊C4—861no—
600C4⋊C4—1722no—
601C4⋊C4—1722no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C22⋊C4—1722no—
610C22⋊C4—1722no—
611C22⋊C4—1722no—
612C42—21no—
613C42—21no—
614C42—3441no—
615C42—1722no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—862no—
630C23—1721no—
631C23—1721no—
632C23—1721no—
633C23—1721no—
634C23—1721no—
635C23—1721no—
636C23#1306330912yes—
637C23C22×D17211yescharacteristic
638Q8—862no—
639Q8—862no—
640Q8—1721no—
641Q8—1721no—
642D4—44no—
643D4—862no—
644D4—862no—
645D4—3444no—
646D4—1728no—
647D4—1721no—
648D4—1721no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—3444no—
671C2×C4—1728no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4#1306330912yes—
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4#41×D4311yescharacteristic
694C2×C4C2×#1062190011yescharacteristic
695C2×C4C2×#1062190011yescharacteristic
696C2×C4#1306337011yescharacteristic
697C2×C4#1306337111yescharacteristic
698C8—22no—
699C8—41no—
700C8—41no—
701C8—41no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—3441no—
717C22—3441no—
718C22—3441no—
719C22—3441no—
720C22—1722no—
721C22—1722no—
722C22—1722no—
723C22C2×#1306330911yescharacteristic
724C22D4×D17211yescharacteristic
725C22#1458354411yescharacteristic
726C22#1458369911yescharacteristic
727C22#1458369911yescharacteristic
728C22#1458371111yescharacteristic
729C22#1458371111yescharacteristic
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—3441no—
735C4—3441no—
736C4—3441no—
737C4—3441no—
738C4—3441no—
739C4—1722no—
740C4—1722no—
741C4#1458340911yescharacteristic
742C4#1458348611yescharacteristic
743C4#1458353611yescharacteristic
744C4#1458357211yescharacteristic
745C2—42no—
746C2—81no—
747C2—3442no—
748C2#1913805511yescharacteristic
749C2#1914452811yescharacteristic
750C2#1914458611yescharacteristic
751C2#1914618511yescharacteristic
752C2#1914623111yescharacteristic
753C2#1914657311yescharacteristic
754C2#1914681311yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1870C2
socleC23×C43C22×D4
prime radical#19137940C2
hypercenter#1870D43
hypocenterC43#24891
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#14583241C2semidirect
2. C2×#14582901C2semidirect
4. #19137524C2semidirect
5. #19136115C2semidirect
6. #19136015C2semidirect
7. #19135792C2semidirect
8. #19135785C2semidirect
9. #19135230C2semidirect
10. #19135223C2semidirect
11. #19134915C2semidirect
12. #19134790C2semidirect
13. #19134628C2semidirect
14. #19134536C2semidirect
15. C43×#1870C2semidirect
106. #13063250D4semidirect
379. #1870D43semidirect
438. C43#24891semidirect

Maximal subgroups

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

subgroupindex
C2×#145832412
C2×#145829012
#191379402
#191375242
#191361152
#191360152
#191357922
#191357852
#191352302
#191352232
#191349152
#191347902
#191346282
#191345362
C43×#18702
#2489143