Finite Group Databasebeta

← #25124109

Subgroups — #25124109

Order 11008.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14582941C211yesmaximal, characteristic, complemented
3C2×#14582901C211yesmaximal, characteristic, complemented
4C2×#14582901C211yesmaximal, characteristic, complemented
5C2×#14582759C211yesmaximal, characteristic, complemented
6#19135799C212yesmaximal, complemented
7#19135792C212yesmaximal, complemented
8#19135785C212yesmaximal, complemented
9#19135778C212yesmaximal, complemented
10#19134315C211yesmaximal, characteristic, complemented
11C2×C43×#407C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13#14583410—24no—
14#14583410—24no—
15C2×#13063308—21no—
16C2×#13063304C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063294—21no—
21C2×C4×C22⋊D43—21no—
22C2×C4×C22⋊D43—21no—
23C2×#13063284C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43—21no—
27#14582941—24no—
28C2×#13063259C2212yescomplemented
29C2×#13063257C2212yescomplemented
30#14582901—24no—
31#14582901—24no—
32C2×#13063250C2212yescomplemented
33C2×#13063250C2212yescomplemented
34C2×#13063247C2212yescomplemented
35C2×#13063247C2212yescomplemented
36#14582759—21no—
37#14582759—21no—
38#14582759C2212yes—
39#14582759C2212yes—
40C2×C43⋊#95—21no—
41#14582662C2212yescomplemented
42#14582662C2212yescomplemented
43C24×C4×C43C2211yescharacteristic
44C22×M16×C43C2211yescharacteristic
45C22×M16×C43C2211yescharacteristic
46C43×#407—24no—
47C2×C22⋊C8×C43C2212yes—
48C2×C22⋊C8×C43C2212yes—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898—22no—
52C2×#10621898—22no—
53C2×#10621898—22no—
54C2×#10621898D414yes—
55C22×Dic86C2311yescharacteristic
56C22×D172C2311yescharacteristic
57C22×C22⋊D43—21no—
58C22×C22⋊D43—21no—
59C22×C22⋊D43—21no—
60C23×Dic43—21no—
61C23×Dic43—21no—
62C22×C4×D43—21no—
63#13063308—28no—
64#13063304—22no—
65#13063304—22no—
66#13063304—22no—
67#13063304—22no—
68#13063299—22no—
69#13063299—22no—
70#13063299—22no—
71#13063299—22no—
72#13063294—28no—
73C4×C22⋊D43—28no—
74C4×C22⋊D43—28no—
75#13063284—22no—
76#13063284D414yes—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—22no—
80C2×C4⋊Dic43—22no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2312yes—
84C2×C4⋊Dic43C2312yes—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—22no—
93C2×C22⋊Dic43—22no—
94C2×C22⋊Dic43—44no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×C4×Dic43—21no—
98#13063259—24no—
99#13063257—24no—
100#13063250—24no—
101#13063250—24no—
102#13063247—24no—
103#13063247—24no—
104C43⋊#95—22no—
105C43⋊#95—22no—
106C25×C43D411yescharacteristic
107C23×C4×C43—22no—
108C23×C4×C43—22no—
109C23×C4×C43—22no—
110C23×C4×C43—22no—
111C23×C4×C43—22no—
112C23×C4×C43—22no—
113C23×C4×C43D411yescharacteristic
114C23×C4×C43D411yescharacteristic
115C23×C4×C43D411yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C23×C4×C43C2311yescharacteristic
119C2×M16×C43—22no—
120C2×M16×C43—22no—
121C2×M16×C43—22no—
122C2×M16×C43—22no—
123C2×M16×C43—22no—
124C2×M16×C43D414yescomplemented
125C22×C8×C43C2312yes—
126C22×C8×C43C2312yes—
127C22⋊C8×C43—24no—
128C22⋊C8×C43—24no—
129C24×C43—22no—
130C24×C43—22no—
131C24×C43—22no—
132C24×C43—22no—
133C24×C43—22no—
134C24×C43—41no—
135C24×C43—41no—
136C24×C43C2×D411yescharacteristic
137C24×C43C2×D411yescharacteristic
138C24×C43C2×D411yescharacteristic
139C23×D43—21no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
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×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—44no—
162C22×C4×C43—44no—
163C22×C4×C43—44no—
164C22×C4×C43—44no—
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2×D412yes—
167C22×C4×C43C2×D412yes—
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43#4112yes—
172C22×C4×C43#4112yes—
173C22×C4×C43#4112yes—
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—24no—
176C2×C22⋊D43—24no—
177C2×C22⋊D43—24no—
178C2×C22⋊D43—42no—
179C2×C22⋊D43—42no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—42no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43—42no—
192C22×Dic43—42no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195#10621898—28no—
196#10621898—28no—
197#10621898—44no—
198#10621898—44no—
199C2×D172—21no—
200C2×D172—21no—
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172C2×D412yes—
205C2×C4×D43—24no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86C2×D412yes—
214M16×C43—28no—
215M16×C43—44no—
216C2×C8×C43—22no—
217C2×C8×C43—22no—
218C2×C8×C43—22no—
219C2×C8×C43—22no—
220C2×C8×C43—22no—
221C2×C8×C43C2×D414yes—
222C22⋊Dic43—24no—
223C22⋊Dic43—24no—
224C22⋊Dic43—24no—
225C22⋊Dic43—44no—
226C22⋊Dic43—44no—
227(C2×D43)⋊C4—24no—
228(C2×D43)⋊C4—24no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—22no—
232C4⋊Dic43—22no—
233C4⋊Dic43—22no—
234C4⋊Dic43—22no—
235C4⋊Dic43—42no—
236C4⋊Dic43—42no—
237C4⋊Dic43C2×D412yes—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241C4×Dic43—24no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—28no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—44no—
260C23×C43—44no—
261C23×C43—44no—
262C23×C43—44no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43#12012yes—
266C23×C43#12112yes—
267C23×C43#12312yes—
268C23×C43AGL(1,ℤ/8)12yes—
269C23×C43#13712yes—
270C23×C43C22×D411yescharacteristic
271C22×D43—22no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—44no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—44no—
294C2×C4×C43—44no—
295C2×C4×C43#12012yes—
296C2×C4×C43#12114yes—
297C2×C4×C43#12114yes—
298C2×C4×C43#12112yes—
299C2×C4×C43#12314yes—
300C2×C4×C43#12312yes—
301C2×C4×C43#12414yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C22⋊D43—48no—
309C22⋊D43—48no—
310C22⋊D43—48no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—84no—
327C2×Dic43—84no—
328D172—22no—
329D172—22no—
330D172—41no—
331D172—41no—
332C4×D43—48no—
333Dic86—22no—
334Dic86—22no—
335Dic86—41no—
336Dic86—41no—
337C8×C43—24no—
338C8×C43—42no—
339#23482—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—416no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43#39414yes—
362C22×C43C2×#12011yescharacteristic
363C22×C43C2×#12111yescharacteristic
364C22×C43C2×#12311yescharacteristic
365C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C43C2×#13711yescharacteristic
367C22×C43#57511yescharacteristic
368C22×C43#57511yescharacteristic
369C2×D43—42no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—81no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43#39414yes—
379C4×C43C2×#12111yescharacteristic
380C4×C43C2×#12111yescharacteristic
381C4×C43C2×#12311yescharacteristic
382C4×C43C2×#12411yescharacteristic
383Dic43—42no—
384Dic43—42no—
385Dic43—42no—
386Dic43—82no—
387Dic43—82no—
388C2×#525—431no—
389C2×#428—431no—
390C2×#417—431no—
391C2×#417—431no—
392C2×#407D4311yescharacteristic, complemented
393C2×#380—431no—
394#2036—432no—
395#2035—432no—
396#2034—432no—
397#2033—432no—
398#1736—431no—
399C2×C43—24no—
400C2×C43—42no—
401C2×C43—42no—
402C2×C43C2×#39411yescharacteristic
403C2×C43#300611yescharacteristic
404C2×C43#300711yescharacteristic
405C2×C43#305511yescharacteristic
406C2×C43#305611yescharacteristic
407C2×C43#309211yescharacteristic
408C2×C43#309311yescharacteristic
409D43—82no—
410C22×#41—431no—
411C24×C4C2×D4311yescharacteristic
412C22×M16C2×D4311yescharacteristic
413C22×M16C2×D4311yescharacteristic
414#525—864no—
415#525—864no—
416C2×#123—861no—
417C2×C22⋊Q8—431no—
418C2×C22⋊Q8—431no—
419C2×#121—431no—
420C2×#121—431no—
421C2×#120—861no—
422C2×C4×D4—861no—
423C2×C4×D4—861no—
424C2×#117—431no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427C22×C22⋊C4—861no—
428#428—864no—
429C2×#107—432no—
430C2×#106—432no—
431#417—864no—
432#417—864no—
433C2×#103—432no—
434C2×#103—432no—
435C2×#102—432no—
436C2×#102—432no—
437#407—24no—
438C2×C22⋊C8C2×D4312yes—
439C2×C22⋊C8C2×D4312yes—
440#380—432no—
441#380—432no—
442#380—861no—
443#380—861no—
444C2×#95—861no—
445#340—432no—
446#340—432no—
447C43#2348211yescharacteristic, complemented, Sylow
448C25D17211yescharacteristic
449C2×#41—434no—
450C2×#41—862no—
451C2×#41—862no—
452C2×#41—862no—
453C2×#41—862no—
454C2×#41—862no—
455C22×Q8—431no—
456C22×D4—431no—
457C22×D4—861no—
458C22×D4—861no—
459C22×D4—861no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4—861no—
469C23×C4D17211yescharacteristic
470C23×C4D17211yescharacteristic
471C23×C4D17211yescharacteristic
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C23×C4C22×D4311yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16C22⋊D4314yescomplemented
481C22×C8C22×D4312yes—
482C22×C8C22×D4312yes—
483#123—868no—
484C22⋊Q8—862no—
485C22⋊Q8—862no—
486C22⋊Q8—862no—
487C22⋊Q8—862no—
488#121—862no—
489#121—862no—
490#121—862no—
491#121—862no—
492#120—868no—
493C4×D4—868no—
494C4×D4—868no—
495#117—434no—
496#117—862no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—432no—
500C2×C4⋊C4—432no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—862no—
505C2×C4⋊C4—862no—
506C2×C4⋊C4—862no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—862no—
515C2×C22⋊C4—862no—
516C2×C22⋊C4—1724no—
517C2×C42—861no—
518#107—864no—
519#106—864no—
520#103—864no—
521#103—864no—
522#102—864no—
523#102—864no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—862no—
527#95—862no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—41no—
534C24—41no—
535C24—861no—
536C24C2×D17211yescharacteristic
537C24C2×D17211yescharacteristic
538C24C2×D17211yescharacteristic
539#41—868no—
540#41—868no—
541#41—1724no—
542#41—1724no—
543C2×Q8—432no—
544C2×Q8—861no—
545C2×Q8—861no—
546C2×Q8—861no—
547C2×Q8—861no—
548C2×Q8—861no—
549C2×D4—432no—
550C2×D4—864no—
551C2×D4—864no—
552C2×D4—864no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—1722no—
559C2×D4—1722no—
560C2×D4—1722no—
561C2×D4—1722no—
562C2×D4—1722no—
563C2×D4—1722no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—864no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—1722no—
596C22×C4—1722no—
597C22×C4—1722no—
598C22×C4—1722no—
599C22×C4—1722no—
600C22×C4—1722no—
601C22×C4—1722no—
602C22×C4—1722no—
603C22×C4C2×D17211yescharacteristic
604C22×C4C2×D17211yescharacteristic
605C22×C4C2×D17211yescharacteristic
606C22×C4#1062189812yes—
607C22×C4D4×D4312yes—
608C22×C4D4×D4312yes—
609C22×C4#1062190012yes—
610C22×C4#1062190012yes—
611C22×C4C2×C22⋊D4312yes—
612C22×C4C23×D4311yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×C22⋊D4314yes—
621C4⋊C4—432no—
622C4⋊C4—432no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—862no—
628C4⋊C4—862no—
629C4⋊C4—862no—
630C4⋊C4—862no—
631C4⋊C4—1722no—
632C4⋊C4—1722no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C22⋊C4—1724no—
639C22⋊C4—1724no—
640C42—864no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—862no—
665C23—1721no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23#1306329512yes—
672C23#1306329912yes—
673C23#1306330912yes—
674C23#1306335312yes—
675C23#1306335812yes—
676C23C22×D17211yescharacteristic
677Q8—862no—
678Q8—862no—
679Q8—1721no—
680Q8—1721no—
681D4—862no—
682D4—862no—
683D4—1728no—
684D4—1728no—
685D4—1728no—
686D4—1721no—
687D4—1721no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—3444no—
709C2×C4—3444no—
710C2×C4—1722no—
711C2×C4—1722no—
712C2×C4—1722no—
713C2×C4—1722no—
714C2×C4—1722no—
715C2×C4—1722no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1728no—
723C2×C4#1306329512yes—
724C2×C4#1306329614yes—
725C2×C4#1306329714yes—
726C2×C4#1306329912yes—
727C2×C4#1306330714yes—
728C2×C4#1306330912yes—
729C2×C4#1306331114yes—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C2×D4×D4311yescharacteristic
732C2×C4C22×C22⋊D4311yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4C2×#1062190011yescharacteristic
735C2×C4C2×#1062189811yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—3441no—
760C22—3441no—
761C22—3441no—
762C22—3441no—
763C22—1722no—
764C22—1722no—
765C22—1722no—
766C22#1458281514yes—
767C22C2×#1306329511yescharacteristic
768C22C2×#1306329911yescharacteristic
769C22C2×#1306330911yescharacteristic
770C22C2×#1306335311yescharacteristic
771C22C2×#1306335811yescharacteristic
772C22#1458369911yescharacteristic
773C22#1458369911yescharacteristic
774C4—41no—
775C4—41no—
776C4—3442no—
777C4—3442no—
778C4—1722no—
779C4—1722no—
780C4—1722no—
781C4#1458281514yes—
782C4C2×#1306329611yescharacteristic
783C4C2×#1306329711yescharacteristic
784C4C2×#1306330711yescharacteristic
785C4C2×#1306331111yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—3442no—
790C2C2×#1458281511yescharacteristic
791C2#1914384911yescharacteristic
792C2#1914385711yescharacteristic
793C2#1914421411yescharacteristic
794C2#1914422511yescharacteristic
795C2#1914452011yescharacteristic
796C2#1914452811yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC23×C43C22×D4
prime radicalC2×#14583410C2
hypercenterC2×#407D43
hypocenterC43#23482
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#14582941C2semidirect
3. C2×#14582901C2semidirect
4. C2×#14582901C2semidirect
5. C2×#14582759C2semidirect
6. #19135799C2semidirect
7. #19135792C2semidirect
8. #19135785C2semidirect
9. #19135778C2semidirect
10. #19134315C2semidirect
11. C2×C43×#407C2semidirect
28. C2×#13063259C22semidirect
29. C2×#13063257C22semidirect
32. C2×#13063250C22semidirect
33. C2×#13063250C22semidirect
34. C2×#13063247C22semidirect
35. C2×#13063247C22semidirect
41. #14582662C22semidirect
42. #14582662C22semidirect
124. C2×M16×C43D4semidirect
392. C2×#407D43semidirect
447. C43#23482semidirect
480. C2×M16C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145829412
C2×#145829012
C2×#145827592
#191357992
#191357922
#191357852
#191357782
#191343152
C2×C43×#4072
#2348243