Finite Group Databasebeta

← #25148802

Subgroups — #25148802

Order 11008.

1194 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
1C2×#14583453C211yesmaximal, characteristic, complemented
2C2×#14583127C211yesmaximal, characteristic
3C2×#14583125C211yesmaximal, characteristic
4#19142925C211yesmaximal, characteristic
5#19135927C211yesmaximal, characteristic, complemented
6#19135840C211yesmaximal, characteristic, complemented
7#19135729C211yesmaximal, characteristic, complemented
8#19135676C211yesmaximal, characteristic, complemented
9#19135017C211yesmaximal, characteristic, complemented
10#19135015C211yesmaximal, characteristic, complemented
11#19134953C211yesmaximal, characteristic, complemented
12#19134866C211yesmaximal, characteristic, complemented
13#19134863C211yesmaximal, characteristic, complemented
14#336×D43C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583453—24no—
20#14583453—24no—
21C2×#13063324C2211yescharacteristic
22C2×#13063323C2211yescharacteristic
23C2×#13063315—21no—
24C2×#13063307—21no—
25C2×#13063305C2211yescharacteristic
26C2×#13063303—21no—
27C2×#13063301C2211yescharacteristic
28C2×#13063296C2211yescharacteristic
29C2×C4×Dic86—21no—
30C2×C4×Dic86C2211yescharacteristic
31C2×#13063282—21no—
32C2×C42×D43C2211yescharacteristic
33#14583127—24no—
34#14583125—24no—
35C2×#13063257C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43#14582802C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582793—21no—
47#14582792—21no—
48#14582775—21no—
49#14582756C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C43×#390C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C4×D43D411yescharacteristic
67C22×C4×D43D411yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43—22no—
77C2×C8×D43—22no—
78C2×C8×D43—41no—
79C2×C8×D43—41no—
80#13063324—22no—
81#13063324—22no—
82#13063323—22no—
83#13063323—22no—
84#13063315—28no—
85#13063307—44no—
86#13063305—22no—
87#13063305D414yes—
88#13063303—28no—
89#13063301—22no—
90#13063301D414yes—
91#13063296—22no—
92#13063296—22no—
93C4×Dic86—28no—
94C4×Dic86—22no—
95C4×Dic86—22no—
96#13063282—28no—
97C2×C4⋊Dic43—21no—
98C2×C4⋊Dic43—21no—
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43D411yescharacteristic
116C2×C4×Dic43D411yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118C42×D43—22no—
119C42×D43—22no—
120#13063257—22no—
121#13063256—22no—
122#13063250—22no—
123#13063250—22no—
124#13063249—22no—
125#13063249—22no—
126#13063248—41no—
127#13063246—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×Q8×C43C2311yescharacteristic
132C22×D4×C43C2311yescharacteristic
133C2×SD16×C43—22no—
134C2×SD16×C43—22no—
135C2×SD16×C43—41no—
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C4×Q8×C43—22no—
139C4×Q8×C43—22no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C42×C43—21no—
146C2×C42×C43C2311yescharacteristic
147#103×C43—41no—
148#102×C43—22no—
149C24×C43—21no—
150C23×D43C2×D411yescharacteristic
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43C2×D412yes—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2411yescharacteristic
169C2×C22⋊D43—42no—
170C2×C22⋊D43—42no—
171C2×C22⋊D43—42no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—21no—
176C22×Dic43C2×D411yescharacteristic
177C22×Dic43C2×D411yescharacteristic
178C22×Dic43C2×D411yescharacteristic
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—22no—
184C2×C4×D43—22no—
185C2×C4×D43—22no—
186C2×C4×D43—22no—
187C2×C4×D43—41no—
188C2×C4×D43SD1614yescomplemented
189C2×C4×D43C2×D412yes—
190C2×C4×D43C2×D412yes—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—24no—
196C2×Dic86—21no—
197C2×Dic86—42no—
198C2×Dic86—42no—
199C2×Dic86C2×D412yes—
200SD16×C43—44no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43#4112yes—
207C4⋊C4×C43—24no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43C2×D412yes—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C42×C43—24no—
215C42×C43—21no—
216C42×C43—21no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220#10621883—44no—
221(C2×D43)⋊C4—24no—
222(C2×D43)⋊C4—24no—
223(C2×D43)⋊C4—42no—
224C4⋊Dic43—21no—
225C4⋊Dic43—24no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—42no—
231C4⋊Dic43C2×D412yes—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4—24no—
235Dic43⋊C4—24no—
236Dic43⋊C4—24no—
237Dic43⋊C4—42no—
238C4×Dic43—24no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—22no—
242C4×Dic43—22no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8#4112yes—
249C8×D43—44no—
250C8×D43—44no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43C22×D411yescharacteristic
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43#12012yes—
264C22×D43C2×SD1612yes—
265C22×D43#13712yes—
266Q8×C43—22no—
267Q8×C43—22no—
268Q8×C43—41no—
269Q8×C43—41no—
270D4×C43—41no—
271D4×C43—41no—
272D4×C43—41no—
273D4×C43—41no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43C2×SD1612yes—
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C2×C4×C432−1+411yescharacteristic
295C22⋊D43—84no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43#12012yes—
315C2×Dic43C2×SD1612yes—
316C2×Dic43#13512yes—
317C4×D43—28no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—44no—
323Dic86—22no—
324Dic86—22no—
325Dic86—48no—
326Dic86—41no—
327Dic86—41no—
328C8×C43—22no—
329C8×C43—41no—
330C43⋊C8—22no—
331C43⋊C8—41no—
332#25497—431nomaximal, Sylow
333C22×C43—81no—
334C22×C43—81no—
335C22×C43—81no—
336C22×C43—81no—
337C22×C43—81no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43C2×#12011yescharacteristic
341C22×C43#53211yescharacteristic
342C22×C43#53711yescharacteristic
343C22×C43C22×SD1611yescharacteristic
344C22×C43C2×#13511yescharacteristic
345C22×C43C2×#13711yescharacteristic
346C22×C43#57511yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43#44814yes—
354C4×C43—22no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—41no—
358C4×C43—81no—
359C4×C43#54611yescharacteristic
360C4×C43#54611yescharacteristic
361C4×C43#54711yescharacteristic
362C4×C43#54711yescharacteristic
363Dic43—22no—
364Dic43—22no—
365Dic43—22no—
366Dic43—42no—
367Dic43—42no—
368Dic43—81no—
369Dic43—81no—
370C2×#533—431no—
371C2×#465—431no—
372C2×#465—431no—
373#2854—431no—
374#2058—431no—
375#2043—431no—
376#2023—431no—
377#2013—431no—
378#1892—431no—
379#1892—431no—
380#1880—431no—
381#1880D4311yescharacteristic, complemented
382#1865—431no—
383#1865—431no—
384C2×#336—431no—
385C2×C43—161no—
386C2×C43#243011yescharacteristic
387C2×C43C2×#44811yescharacteristic
388C2×C43#300211yescharacteristic
389C2×C43#316711yescharacteristic
390C2×C43#318111yescharacteristic
391C2×C43#324611yescharacteristic
392C2×C43#324811yescharacteristic
393D43—24no—
394C22×SD16—431no—
395C22×SD16C2×D4311yescharacteristic
396C23×C8—431no—
397C23×C8—431no—
398#533—864no—
399#533—864no—
400C2×C4⋊Q8—431no—
401C2×C4⋊Q8—431no—
402C2×#125—861no—
403C2×#123—861no—
404C2×C22⋊Q8—431no—
405C2×C22⋊Q8—431no—
406C2×C22⋊Q8—861no—
407C2×#121—431no—
408C2×C4×Q8—431no—
409C2×C4×Q8—861no—
410C2×C4×Q8C2×D4311yescharacteristic
411C2×#117—861no—
412C22×C42—431no—
413#465—864no—
414#465—864no—
415C2×#106—431no—
416C2×#106—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103—431no—
422C2×#103C2×D4311yescharacteristic
423C2×#102—431no—
424C2×#102C2×D4311yescharacteristic
425#390—431no—
426#390C2×D4311yescharacteristic
427#389—431no—
428#389—431no—
429#388—861no—
430#388—861no—
431#386—861no—
432#380—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#340C2×D4311yescharacteristic
437#336—431no—
438#336—431no—
439#336—431no—
440#336C2×D4311yescharacteristic
441C43#2549711yescharacteristic, complemented, Sylow
442C22×Q8—431no—
443C22×Q8—861no—
444C22×Q8C22×D4311yescharacteristic
445C22×D4—861no—
446C22×D4C22×D4311yescharacteristic
447C23×C4—431no—
448C23×C4—431no—
449C23×C4—431no—
450C2×SD16—22no—
451C2×SD16—22no—
452C2×SD16—41no—
453C2×SD16—862no—
454C2×SD16—862no—
455C2×SD16—1721no—
456C22×C8—431no—
457C22×C8—431no—
458C22×C8—862no—
459C22×C8—862no—
460C22×C8—862no—
461C22×C8—862no—
462C22×C8—1721no—
463C22×C8—1721no—
464C22×C8C22×D4311yescharacteristic
465C22×C8C22×D4311yescharacteristic
466C4⋊Q8—862no—
467C4⋊Q8—862no—
468C4⋊Q8—862no—
469C4⋊Q8—862no—
470#125—868no—
471#123—1724no—
472C22⋊Q8—434no—
473C22⋊Q8—434no—
474C22⋊Q8—862no—
475C22⋊Q8—868no—
476C22⋊Q8—862no—
477#121—862no—
478#121—862no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×Q8—868no—
484#117—868no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C42—21no—
508C2×C42—431no—
509C2×C42—431no—
510C2×C42—431no—
511C2×C42—862no—
512C2×C42—862no—
513C2×C42—861no—
514C2×C42C22×D4311yescharacteristic
515#106—862no—
516#106—862no—
517#103—41no—
518#103—862no—
519#103—862no—
520#103—862no—
521#103—862no—
522#103—1721no—
523#102—22no—
524#102—862no—
525#95—861no—
526#95—861no—
527#95—861no—
528C24—21no—
529C24—431no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—432no—
536C2×Q8—864no—
537C2×Q8—861no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—1722no—
543C2×Q8—1722no—
544C2×Q8D4×D4312yes—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—1722no—
552C2×D4—1722no—
553C2×D4—1722no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—431no—
558C22×C4—431no—
559C22×C4—431no—
560C22×C4—434no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—862no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—1721no—
576C22×C4D4×D4311yescharacteristic
577C22×C4D4×D4311yescharacteristic
578C22×C4C23×D4311yescharacteristic
579SD16—44no—
580SD16—1724no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—432no—
587C2×C8—861no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—1724no—
593C2×C8—1724no—
594C2×C8#1062189812yes—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—432no—
600C4⋊C4—864no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—1722no—
612C4⋊C4—1722no—
613C4⋊C4D4×D4312yes—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—864no—
617C22⋊C4—864no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C42—24no—
623C42—21no—
624C42—21no—
625C42—862no—
626C42—862no—
627C42—864no—
628C42—861no—
629C42—861no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—432no—
638C23—432no—
639C23—432no—
640C23—861no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23C2×D4×D4311yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—862no—
650Q8—862no—
651Q8—1728no—
652Q8—1721no—
653Q8—1721no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—3444no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—432no—
674C2×C4—432no—
675C2×C4—432no—
676C2×C4—868no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—861no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—1724no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4SD16×D4312yes—
701C2×C4C2×D4×D4311yescharacteristic
702C2×C4C2×D4×D4311yescharacteristic
703C2×C4#41×D4311yescharacteristic
704C2×C4C2×#1062189811yescharacteristic
705C2×C4#1306337011yescharacteristic
706C2×C4#1306337211yescharacteristic
707C8—22no—
708C8—41no—
709C8—862no—
710C8—1721no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—434no—
719C22—862no—
720C22—862no—
721C22—862no—
722C22—862no—
723C22—862no—
724C22—862no—
725C22#120×D4311yescharacteristic
726C22#1458344611yescharacteristic
727C22#1458347811yescharacteristic
728C22C2×SD16×D4311yescharacteristic
729C22#135×D4311yescharacteristic
730C22#137×D4311yescharacteristic
731C22#1458369511yescharacteristic
732C4—22no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—81no—
737C4—862no—
738C4—862no—
739C4—862no—
740C4—3441no—
741C4—3441no—
742C4—1722no—
743C4—1722no—
744C4#1458353911yescharacteristic
745C4#1458354611yescharacteristic
746C4#1458354711yescharacteristic
747C4#1458355411yescharacteristic
748C2—161no—
749C2—864no—
750C2#1913820211yescharacteristic
751C2#448×D4311yescharacteristic
752C2#1914381011yescharacteristic
753C2#1914515111yescharacteristic
754C2#1914530011yescharacteristic
755C2#1914590911yescharacteristic
756C2#1914592911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1880D43
hypocenterC43#25497
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×#14583453C2semidirect
5. #19135927C2semidirect
6. #19135840C2semidirect
7. #19135729C2semidirect
8. #19135676C2semidirect
9. #19135017C2semidirect
10. #19135015C2semidirect
11. #19134953C2semidirect
12. #19134866C2semidirect
13. #19134863C2semidirect
14. #336×D43C2semidirect
15. C43×#1880C2semidirect
188. C2×C4×D43SD16semidirect
381. #1880D43semidirect
441. C43#25497semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
C2×#145831272
C2×#145831252
#191429252
#191359272
#191358402
#191357292
#191356762
#191350172
#191350152
#191349532
#191348662
#191348632
#336×D432
C43×#18802
#2549743