Finite Group Databasebeta

← #25107897

Subgroups — #25107897

Order 11008.

1024 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137290C211yesmaximal, characteristic, complemented
2#19137187C211yesmaximal, characteristic, complemented
3#19135472C211yesmaximal, characteristic, complemented
4#19135451C211yesmaximal, characteristic, complemented
5#19135287C211yesmaximal, characteristic, complemented
6#19135280C211yesmaximal, characteristic, complemented
7#19135231C211yesmaximal, characteristic, complemented
8#19135224C211yesmaximal, characteristic, complemented
9#19134945C211yesmaximal, characteristic, complemented
10#19134931C211yesmaximal, characteristic, complemented
11#19134913C211yesmaximal, characteristic, complemented
12#19134790C211yesmaximal, characteristic, complemented
13#19134535C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C2×C43×#449C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18C22×C4⋊Dic43C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582806C2211yescharacteristic
32#14582802—21no—
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582792—21no—
38#14582779—21no—
39#14582779—21no—
40#14582779—21no—
41#14582774—21no—
42#14582759—21no—
43#14582759—21no—
44#14582759C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×#121×C43C2211yescharacteristic
56C43×#449C418yescomplemented
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64D4×Dic43—41no—
65D4×Dic43—41no—
66#13063284—41no—
67#13063284—41no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—41no—
71C2×C4⋊Dic43—41no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43D411yescharacteristic
87C2×C22⋊Dic43D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063257—41no—
92#13063257—41no—
93#13063249—41no—
94#13063249—41no—
95#13063246—41no—
96#13063246—41no—
97#13063246—41no—
98#13063246—41no—
99C22⋊(C43⋊C8)—22no—
100#13063235—41no—
101C8×Dic43—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C2×#41×C43—22no—
110C2×#41×C43—41no—
111C2×#41×C43—41no—
112C2×#41×C43—41no—
113C2×#41×C43—41no—
114C2×#41×C43C2×C414yescomplemented
115C22×Q8×C43C2311yescharacteristic
116C22×D4×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43C2311yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43—21no—
121C23×C4×C43C2311yescharacteristic
122C2×SD16×C43—41no—
123C2×SD16×C43—41no—
124C2×SD16×C43C2×C414yescomplemented
125C2×D8×C43—41no—
126C2×D8×C43—41no—
127C2×D8×C43C2×C414yescomplemented
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130#121×C43—22no—
131#121×C43C2×C414yes—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134#103×C43C2×C414yescomplemented
135#102×C43C2×C414yescomplemented
136C22⋊C8×C43C2×C414yescomplemented
137C24×C43—21no—
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140#41×C43—44no—
141#41×C43—44no—
142#41×C43—44no—
143#41×C43—44no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C22×C412yes—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—24no—
153C2×D4×C43—24no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43C22×C412yes—
167C2×D4×C43C22×C412yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—24no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—42no—
176C22×C4×C43—42no—
177C22×C4×C43C22×C412yes—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43#4112yes—
180C22×C4×C43C2411yescharacteristic
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—42no—
186C22×Dic43—42no—
187C22×Dic43—81no—
188C22×Dic43—81no—
189C22×Dic43—81no—
190C22×Dic43—81no—
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195SD16×C43—44no—
196D8×C43—44no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43C22×C412yes—
202C2×C8×C43C22×C412yes—
203C4⋊C4×C43—21no—
204C4⋊C4×C43C22×C412yes—
205C22⋊C4×C43—24no—
206C22⋊Dic43—41no—
207C22⋊Dic43—41no—
208C22⋊Dic43—42no—
209C22⋊Dic43—81no—
210C22⋊Dic43—81no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213C22⋊Dic43—81no—
214C22⋊Dic43—81no—
215C22⋊Dic43—81no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—41no—
225C4⋊Dic43—41no—
226C4⋊Dic43—42no—
227C4⋊Dic43—81no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—81no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43C4×D412yes—
260C23×C43C22×D411yescharacteristic
261Q8×C43—22no—
262Q8×C43—22no—
263Q8×C43—41no—
264Q8×C43—41no—
265D4×C43—22no—
266D4×C43—22no—
267D4×C43—22no—
268D4×C43—22no—
269D4×C43—48no—
270D4×C43—41no—
271D4×C43—41no—
272D4×C43—41no—
273D4×C43—41no—
274D4×C43—84no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—48no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43C4×D412yes—
289C2×C4×C43C23×C411yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—84no—
320C2×Dic43—84no—
321C8×C43—22no—
322C8×C43—22no—
323C43⋊C8—41no—
324C43⋊C8—41no—
325#22053—431nomaximal, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43C2×C4×D411yescharacteristic
348C22×C43#53411yescharacteristic
349C22×C43#53511yescharacteristic
350C22×C43#57611yescharacteristic
351C22×C43#57711yescharacteristic
352C22×C43#57711yescharacteristic
353C22×C43#57711yescharacteristic
354C4×C43—22no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43#51811yescharacteristic
358C4×C43#51811yescharacteristic
359C4×C43#53811yescharacteristic
360C4×C43#53811yescharacteristic
361Dic43—41no—
362Dic43—41no—
363Dic43—41no—
364Dic43—41no—
365Dic43—81no—
366Dic43—81no—
367Dic43—81no—
368Dic43—81no—
369C2×#449D4311yescharacteristic
370#2324—431no—
371#2311—431no—
372#1972—431no—
373#1968—431no—
374#1935—431no—
375#1934—431no—
376#1927—431no—
377#1926—431no—
378#1879—431no—
379#1877—431no—
380#1874—431no—
381#1853—431no—
382#1788—431no—
383#1750—431no—
384C2×C43—42no—
385C2×C43—82no—
386C2×C43—82no—
387C2×C43#232111yescharacteristic
388C2×C43#294611yescharacteristic
389C2×C43#295211yescharacteristic
390C2×C43#319811yescharacteristic
391C2×C43#320411yescharacteristic
392C2×C43#322111yescharacteristic
393C2×C43#322411yescharacteristic
394C22×#41C2×D4311yescharacteristic
395C22×SD16C2×D4311yescharacteristic
396C22×D8C2×D4311yescharacteristic
397C2×#121C2×D4311yescharacteristic
398C2×C4×D4—431no—
399C2×#117—431no—
400C22×C4⋊C4—431no—
401#449Dic4318yescomplemented
402C2×#106—431no—
403C2×#106—431no—
404C2×#103—431no—
405C2×#103—431no—
406C2×#103C2×D4311yescharacteristic
407C2×#102—431no—
408C2×#102—431no—
409C2×#102—431no—
410C2×#102—431no—
411C2×#102C2×D4311yescharacteristic
412C2×C22⋊C8—431no—
413C2×C22⋊C8C2×D4311yescharacteristic
414C2×#97—431no—
415C2×C4×C8—431no—
416#391—431no—
417#391—431no—
418#390—431no—
419#390—431no—
420#390—431no—
421#390—861no—
422#389—431no—
423#388—861no—
424#386—861no—
425#386—861no—
426#386—861no—
427#385—861no—
428#380—431no—
429#380—861no—
430#380—861no—
431C4×C4⋊C4—431no—
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#336—431no—
437#336—431no—
438C43#2205311yescharacteristic, complemented, Sylow
439C2×#41—22no—
440C2×#41—41no—
441C2×#41—41no—
442C2×#41—41no—
443C2×#41—41no—
444C2×#41C2×Dic4314yescomplemented
445C22×Q8C22×D4311yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22×D4311yescharacteristic
449C22×D4C22×D4311yescharacteristic
450C23×C4—21no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4C22×D4311yescharacteristic
454C2×SD16—41no—
455C2×SD16—41no—
456C2×SD16C2×Dic4314yescomplemented
457C2×D8—41no—
458C2×D8—41no—
459C2×D8C2×Dic4314yescomplemented
460C22×C8—431no—
461C22×C8—431no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464#121—22no—
465#121C2×Dic4314yes—
466C4×D4—1721no—
467C4×D4—1721no—
468#117—1721no—
469#117—1721no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—1721no—
479C2×C4⋊C4—1721no—
480C2×C4⋊C4C22×D4311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—431no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C22⋊C4—861no—
487C2×C22⋊C4—861no—
488C2×C22⋊C4—861no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C42—431no—
493C2×C42—431no—
494C2×C42—861no—
495#106—1721no—
496#106—1721no—
497#103—1721no—
498#103—1721no—
499#103C2×Dic4314yescomplemented
500#102—1721no—
501#102—1721no—
502#102—1721no—
503#102—1721no—
504#102C2×Dic4314yescomplemented
505C22⋊C8—862no—
506C22⋊C8C2×Dic4314yescomplemented
507#97—1721no—
508C4×C8—1721no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95—861no—
513#95—861no—
514#95—861no—
515#95—861no—
516C24—21no—
517C24—21no—
518C24D4×D4311yescharacteristic
519#41—44no—
520#41—44no—
521#41—44no—
522#41—44no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8C22×Dic4312yes—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—81no—
544C2×D4—81no—
545C2×D4C22×Dic4312yes—
546C2×D4C22×Dic4312yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—431no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—3441no—
565C22×C4—3441no—
566C22×C4—3441no—
567C22×C4—3441no—
568C22×C4—1722no—
569C22×C4—1722no—
570C22×C4D4×D4311yescharacteristic
571C22×C4#1062190012yes—
572C22×C4C22×Dic4312yes—
573C22×C4C23×D4311yescharacteristic
574SD16—44no—
575D8—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8C22×Dic4312yes—
587C2×C8C22×Dic4312yes—
588C4⋊C4—21no—
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—3441no—
598C4⋊C4—1721no—
599C4⋊C4—1721no—
600C4⋊C4—1722no—
601C4⋊C4C22×Dic4312yes—
602C22⋊C4—24no—
603C22⋊C4—3441no—
604C22⋊C4—3441no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—3441no—
608C22⋊C4—3441no—
609C22⋊C4—3441no—
610C22⋊C4—1721no—
611C22⋊C4—1721no—
612C22⋊C4—1722no—
613C42—861no—
614C42—861no—
615C42—861no—
616C42—861no—
617C42—3441no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—22no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23D4×Dic4312yes—
639C23C2×D4×D4311yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—41no—
643Q8—41no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—48no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—84no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—48no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—3444no—
680C2×C4—3444no—
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—1721no—
692C2×C4—1721no—
693C2×C4D4×Dic4312yes—
694C2×C4C23×Dic4311yescharacteristic
695C2×C4C2×#1062190011yescharacteristic
696C2×C4#1306337011yescharacteristic
697C2×C4#1306337011yescharacteristic
698C2×C4#1306337011yescharacteristic
699C2×C4#1306337011yescharacteristic
700C8—22no—
701C8—22no—
702C8—1721no—
703C8—1721no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22C2×D4×Dic4311yescharacteristic
726C22#1458345911yescharacteristic
727C22#1458346411yescharacteristic
728C22#1458370311yescharacteristic
729C22#1458370611yescharacteristic
730C22#1458370611yescharacteristic
731C22#1458370911yescharacteristic
732C4—22no—
733C4—42no—
734C4—42no—
735C4—3441no—
736C4—3441no—
737C4—3441no—
738C4—3441no—
739C4—1721no—
740C4—1721no—
741C4—1721no—
742C4—1721no—
743C4#1458337411yescharacteristic
744C4#1458337411yescharacteristic
745C4#1458348411yescharacteristic
746C4#1458348411yescharacteristic
747C2—42no—
748C2—82no—
749C2—82no—
750C2#1913725611yescharacteristic
751C2#1914342811yescharacteristic
752C2#1914347911yescharacteristic
753C2#1914544611yescharacteristic
754C2#1914550411yescharacteristic
755C2#1914565411yescharacteristic
756C2#1914568711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#449C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#449D43
hypocenterC43#22053
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. #19137290C2semidirect
2. #19137187C2semidirect
3. #19135472C2semidirect
4. #19135451C2semidirect
5. #19135287C2semidirect
6. #19135280C2semidirect
7. #19135231C2semidirect
8. #19135224C2semidirect
9. #19134945C2semidirect
10. #19134931C2semidirect
11. #19134913C2semidirect
12. #19134790C2semidirect
13. #19134535C2semidirect
14. #19134363C2semidirect
56. C43×#449C4semidirect
114. C2×#41×C43C2×C4semidirect
124. C2×SD16×C43C2×C4semidirect
127. C2×D8×C43C2×C4semidirect
134. #103×C43C2×C4semidirect
135. #102×C43C2×C4semidirect
136. C22⋊C8×C43C2×C4semidirect
401. #449Dic43semidirect
438. C43#22053semidirect
444. C2×#41C2×Dic43semidirect
456. C2×SD16C2×Dic43semidirect
459. C2×D8C2×Dic43semidirect
499. #103C2×Dic43semidirect
504. #102C2×Dic43semidirect
506. C22⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191372902
#191371872
#191354722
#191354512
#191352872
#191352802
#191352312
#191352242
#191349452
#191349312
#191349132
#191347902
#191345352
#191343632
C2×C43×#4492
#2205343