Finite Group Databasebeta

← #25098613

Subgroups — #25098613

Order 11008.

1748 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147928C211yesmaximal, characteristic
2#19147796C211yesmaximal, characteristic, complemented
3C2×#14582872C211yesmaximal, characteristic, complemented
4C2×#14582872C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic, complemented
6#19135136C218yesmaximal, complemented
7#19134327C211yesmaximal, characteristic, complemented
8C43×#1740C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621898C2211yescharacteristic
11#14583480—22no—
12#14583475—21no—
13#14583475C412yescomplemented
14#14583468—21no—
15#14583468C412yescomplemented
16#14583461C2214yes—
17#14583449—22no—
18#14583411—22no—
19#14583411C414yescomplemented
20#14583380—22no—
21#14583379—22no—
22#14583376—21no—
23#14583373—21no—
24#14583372C2214yes—
25C4×#10621898—22no—
26#14583367—22no—
27C2×#13063284C2211yescharacteristic
28C2×#13063284C2211yescharacteristic
29#117×D43—22no—
30#14582872—22no—
31#14582872—22no—
32#14582872—22no—
33#14582872—22no—
34#14582872—22no—
35#14582872—22no—
36C2×#13063239C2214yes—
37C2×#13063239C2214yes—
38C2×#13063239C2214yes—
39#14582665C2214yes—
40C2×#117×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C43×#342C2214yes—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C2×#10621898—21no—
53C2×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621898—21no—
56C2×#10621898—21no—
57C2×#10621898—21no—
58C2×#10621898—21no—
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898—21no—
62C2×#10621898—21no—
63C2×#10621898—21no—
64C2×#10621898C2×C412yes—
65C2×#10621898C2×C412yes—
66C2×#10621898D412yes—
67C2×#10621898D412yes—
68C22×Dic86C2×C411yescharacteristic, complemented
69C22×Dic86D411yescharacteristic
70C22×D172C2×C411yescharacteristic, complemented
71C22×D172D411yescharacteristic
72C22×C22⋊D43C2312yes—
73C22×C22⋊D43C2312yes—
74C22×C4×D43C2×C412yescomplemented
75C22×C4×D43D412yes—
76#13063325—22no—
77#13063322—22no—
78#13063313—22no—
79#13063313—22no—
80#13063309—24no—
81#13063309C2×C418yescomplemented
82#13063305—24no—
83#13063305—24no—
84#13063300—24no—
85#13063300—24no—
86#13063299—28no—
87#13063295—24no—
88#13063295C2×C418yescomplemented
89C4×Dic86—24no—
90#13063290—24no—
91C4×D172—24no—
92C4×D172—28no—
93#13063287—24no—
94C4×C22⋊D43—28no—
95(C22⋊D43)⋊C4—28no—
96#13063284—21no—
97#13063284—21no—
98#13063284—21no—
99#13063284—21no—
100#13063284—21no—
101#13063284—21no—
102#13063284D412yescomplemented
103#13063284D412yescomplemented
104#13063283—24no—
105#13063282—24no—
106#13063281—24no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43—21no—
109C4⋊C4×D43—24no—
110C2×C22⋊Dic43C2312yes—
111C2×C22⋊Dic43C2312yes—
112C22⋊C4×D43—24no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C42×D43—24no—
116#13063239—28no—
117#13063239—28no—
118#13063239—28no—
119C23×C4×C43C2311yescharacteristic
120#117×C43—21no—
121#117×C43—21no—
122#117×C43—21no—
123#117×C43—21no—
124#117×C43—21no—
125#117×C43—21no—
126#117×C43—21no—
127#117×C43—21no—
128#117×C43C2×C412yescomplemented
129#117×C43C2×C412yescomplemented
130#117×C43D412yescomplemented
131#117×C43D412yescomplemented
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C22⋊C4×C43C2312yes—
136C2×C22⋊C4×C43C2312yes—
137C2×C22⋊C4×C43C2312yes—
138C2×C42×C43—21no—
139C2×C42×C43—21no—
140C2×C42×C43—21no—
141C24×C43C2411yescharacteristic
142C23×D43C22×C412yes—
143C23×D43C2×D412yes—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43#4111yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43#4111yescharacteristic
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43C22×C414yes—
172C2×C22⋊D43C2×D414yes—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43C22×C412yes—
176C22×Dic43C2×D412yes—
177#10621898—22no—
178#10621898—22no—
179#10621898—22no—
180#10621898—22no—
181#10621898—22no—
182#10621898—22no—
183#10621898—22no—
184#10621898—22no—
185#10621898—22no—
186#10621898—22no—
187#10621898—22no—
188#10621898—22no—
189#10621898—22no—
190#10621898—22no—
191#10621898—22no—
192#10621898—22no—
193#10621898—41no—
194#10621898—41no—
195#10621898—41no—
196#10621898—41no—
197#10621898—41no—
198#10621898—41no—
199#10621898—41no—
200#10621898—41no—
201#10621898—41no—
202#10621898—41no—
203#10621898—41no—
204#10621898—41no—
205#10621898—41no—
206#10621898—41no—
207#10621898—41no—
208#10621898—41no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—28no—
220C2×D172C22⋊C412yes—
221C2×D172C22⋊C412yes—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—22no—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—22no—
232C2×C4×D43—28no—
233C2×C4×D43C22⋊C414yes—
234C2×C4×D43C22⋊C414yes—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—21no—
245C2×Dic86C22⋊C412yes—
246C2×Dic86C22⋊C412yes—
247C4⋊C4×C43—22no—
248C4⋊C4×C43—22no—
249C4⋊C4×C43—22no—
250C4⋊C4×C43—22no—
251C4⋊C4×C43—41no—
252C4⋊C4×C43—41no—
253C22⋊C4×C43—22no—
254C22⋊C4×C43—22no—
255C22⋊C4×C43—22no—
256C22⋊C4×C43—22no—
257C22⋊C4×C43C22×C414yes—
258C22⋊C4×C43C2×D414yes—
259C42×C43—22no—
260C42×C43—22no—
261C42×C43—22no—
262C42×C43—22no—
263C42×C43—41no—
264C42×C43—41no—
265C22⋊Dic43—22no—
266C22⋊Dic43—22no—
267C22⋊Dic43—22no—
268C22⋊Dic43C2×D414yes—
269(C2×D43)⋊C4—28no—
270(C2×D43)⋊C4—28no—
271(C2×D43)⋊C4—28no—
272C4⋊Dic43—22no—
273C4⋊Dic43—22no—
274C4⋊Dic43—28no—
275C4⋊Dic43—41no—
276C4⋊Dic43—41no—
277Dic43⋊C4—28no—
278C4×Dic43—28no—
279C4×Dic43—22no—
280C4×Dic43—22no—
281C4×Dic43—41no—
282C4×Dic43—41no—
283C23×C43—81no—
284C23×C43C23×C411yescharacteristic
285C23×C43C22×D411yescharacteristic
286C23×C43C22×D411yescharacteristic
287C23×C43C22×D411yescharacteristic
288C23×C43C22×D411yescharacteristic
289C23×C43C2×#4111yescharacteristic
290C23×C43C2×#4111yescharacteristic
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—82no—
297C22×D43—82no—
298C22×D43C2×C22⋊C414yes—
299C2×C4×C43—24no—
300C2×C4×C43—24no—
301C2×C4×C43—42no—
302C2×C4×C43—82no—
303C2×C4×C43—82no—
304C2×C4×C43—82no—
305C2×C4×C43C2×C22⋊C411yescharacteristic
306C2×C4×C43C2×C22⋊C411yescharacteristic
307C2×C4×C43C2×C22⋊C411yescharacteristic
308C2×C4×C43C2×C22⋊C411yescharacteristic
309C2×C4×C43C4×D411yescharacteristic
310C2×C4×C43C4×D411yescharacteristic
311C2×C4×C43C4×D411yescharacteristic
312C2×C4×C43C4×D411yescharacteristic
313C2×C4×C43C4×D411yescharacteristic
314C2×C4×C43C4×D411yescharacteristic
315C2×C4×C43C4×D411yescharacteristic
316C2×C4×C43C4×D411yescharacteristic
317C2×C4×C43#12011yescharacteristic
318C2×C4×C43#12011yescharacteristic
319C2×C4×C43#12011yescharacteristic
320C2×C4×C43#12011yescharacteristic
321C2×C4×C43#12111yescharacteristic
322C2×C4×C43#12111yescharacteristic
323C2×C4×C43#12111yescharacteristic
324C2×C4×C43#12111yescharacteristic
325C2×C4×C43#12111yescharacteristic
326C2×C4×C43#12111yescharacteristic
327C2×C4×C43#12111yescharacteristic
328C2×C4×C43#12111yescharacteristic
329C2×C4×C43#12311yescharacteristic
330C2×C4×C43#12311yescharacteristic
331C2×C4×C43#12311yescharacteristic
332C2×C4×C43#12311yescharacteristic
333C22⋊D43—24no—
334C22⋊D43—24no—
335C22⋊D43—24no—
336C22⋊D43—24no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C22⋊D43—42no—
340C22⋊D43—42no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—24no—
347C2×Dic43—42no—
348C2×Dic43—82no—
349C2×Dic43—82no—
350C2×Dic43C2×C22⋊C414yes—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—22no—
355D172—41no—
356D172—41no—
357D172—41no—
358D172—41no—
359D172—88no—
360C4×D43—24no—
361C4×D43—24no—
362C4×D43—24no—
363C4×D43—24no—
364C4×D43—42no—
365C4×D43—42no—
366C4×D43—42no—
367C4×D43—42no—
368C4×D43—88no—
369Dic86—22no—
370Dic86—22no—
371Dic86—22no—
372Dic86—22no—
373Dic86—41no—
374Dic86—41no—
375Dic86—41no—
376Dic86—41no—
377#21014—431nomaximal, Sylow
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43C22×C22⋊C411yescharacteristic
386C22×C43C2×C4×D411yescharacteristic
387C22×C43C2×C4×D411yescharacteristic
388C22×C43C2×#12011yescharacteristic
389C22×C43C2×#12111yescharacteristic
390C22×C43C2×#12111yescharacteristic
391C22×C43C2×#12311yescharacteristic
392C2×D43—24no—
393C2×D43—44no—
394C2×D43—44no—
395C2×D43—44no—
396C2×D43—42no—
397C2×D43—82no—
398C2×D43—82no—
399C2×D43—82no—
400C4×C43—44no—
401C4×C43—44no—
402C4×C43—82no—
403C4×C43#38611yescharacteristic
404C4×C43#38611yescharacteristic
405C4×C43#38611yescharacteristic
406C4×C43#38611yescharacteristic
407C4×C43#38611yescharacteristic
408C4×C43#38611yescharacteristic
409C4×C43#38611yescharacteristic
410C4×C43#38611yescharacteristic
411Dic43—24no—
412Dic43—44no—
413Dic43—42no—
414Dic43—82no—
415#3449—431no—
416#3428—431no—
417C2×#410—431no—
418C2×#410—431no—
419C2×#410—431no—
420#1913—438no—
421#1740—431no—
422#1740D4311yescharacteristic, complemented
423C2×C43—21no—
424C2×C43—21no—
425C2×C43—21no—
426C2×C43—21no—
427C2×C43—21no—
428C2×C43—21no—
429C2×C43—21no—
430C2×C43C2×#38611yescharacteristic
431D43—44no—
432D43—82no—
433C22×#41—431no—
434C22×#41—431no—
435#537—862no—
436#536—432no—
437#536—861no—
438#535—432no—
439#535—861no—
440#534—434no—
441#532—862no—
442#525—434no—
443#525—862no—
444#520—862no—
445#520—862no—
446#519—861no—
447#518—434no—
448#518—861no—
449C4×#41—862no—
450C4×#41—862no—
451C2×#117—431no—
452C2×#117—431no—
453C2×#117—862no—
454C2×#117C2×D4311yescharacteristic
455C2×#117C2×D4311yescharacteristic
456C2×#117C2×D4311yescharacteristic
457#410—862no—
458#410—862no—
459#410—862no—
460#410—862no—
461#410—862no—
462#410—862no—
463C2×#99—434no—
464C2×#99—434no—
465C2×#99—434no—
466#342—434no—
467#342C2×D4314yes—
468C43#2101411yescharacteristic, complemented, Sylow
469C2×#41—432no—
470C2×#41—432no—
471C2×#41—432no—
472C2×#41—432no—
473C2×#41—861no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41—861no—
477C2×#41—861no—
478C2×#41—861no—
479C2×#41—861no—
480C2×#41—861no—
481C2×#41—861no—
482C2×#41—861no—
483C2×#41—861no—
484C2×#41—861no—
485C2×#41—861no—
486C2×#41—861no—
487C2×#41—861no—
488C2×#41—861no—
489C2×#41—861no—
490C2×#41—861no—
491C2×#41—861no—
492C2×#41—861no—
493C22×Q8—431no—
494C22×Q8—431no—
495C22×D4—432no—
496C22×D4—432no—
497C22×D4—431no—
498C22×D4—431no—
499C23×C4—432no—
500C23×C4—432no—
501C23×C4C22×D4311yescharacteristic
502C4⋊Q8—862no—
503#127—862no—
504#124—862no—
505#124—862no—
506#123—438no—
507#123—864no—
508C22⋊Q8—864no—
509C22⋊Q8—864no—
510#121—864no—
511#121—864no—
512#121—868no—
513#120—438no—
514#120—864no—
515C4×Q8—864no—
516C4×Q8—864no—
517C4×D4—868no—
518C4×D4—864no—
519C4×D4—868no—
520C4×D4—864no—
521C4×D4—868no—
522#117—21no—
523#117—21no—
524#117—21no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—21no—
529#117—21no—
530#117—432no—
531#117—432no—
532#117—864no—
533#117—864no—
534#117—864no—
535#117—861no—
536#117—861no—
537#117—861no—
538#117—861no—
539#117—861no—
540#117—861no—
541#117C4×D4312yescomplemented
542#117C4×D4312yescomplemented
543#117D17212yescomplemented
544#117D17212yescomplemented
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—864no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C22⋊C4—432no—
552C2×C22⋊C4—432no—
553C2×C22⋊C4—864no—
554C2×C22⋊C4C22×D4312yes—
555C2×C22⋊C4C22×D4312yes—
556C2×C22⋊C4C22×D4312yes—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—21no—
560C2×C42—864no—
561C2×C42—861no—
562C2×C42—861no—
563#99—868no—
564#99—868no—
565#99—868no—
566C24—432no—
567C24—432no—
568C24C23×D4311yescharacteristic
569#41—862no—
570#41—862no—
571#41—862no—
572#41—862no—
573#41—862no—
574#41—862no—
575#41—862no—
576#41—862no—
577#41—862no—
578#41—862no—
579#41—862no—
580#41—862no—
581#41—862no—
582#41—862no—
583#41—862no—
584#41—862no—
585#41—1721no—
586#41—1721no—
587#41—1721no—
588#41—1721no—
589#41—1721no—
590#41—1721no—
591#41—1721no—
592#41—1721no—
593#41—1721no—
594#41—1721no—
595#41—1721no—
596#41—1721no—
597#41—1721no—
598#41—1721no—
599#41—1721no—
600#41—1721no—
601C2×Q8—432no—
602C2×Q8—432no—
603C2×Q8—861no—
604C2×Q8—861no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×Q8—861no—
612C2×Q8—861no—
613C2×D4—434no—
614C2×D4—434no—
615C2×D4—432no—
616C2×D4—432no—
617C2×D4—868no—
618C2×D4—862no—
619C2×D4—862no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—862no—
626C2×D4—862no—
627C2×D4—862no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4—861no—
632C2×D4—861no—
633C2×D4—861no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—432no—
642C22×C4—434no—
643C22×C4—434no—
644C22×C4—432no—
645C22×C4—868no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—862no—
657C22×C4—862no—
658C22×C4C2×C4×D4311yescharacteristic
659C22×C4C2×C4×D4311yescharacteristic
660C22×C4C2×D17211yescharacteristic
661C22×C4C2×D17211yescharacteristic
662C22×C4#1062189811yescharacteristic
663C22×C4#1062189811yescharacteristic
664C22×C4D4×D4311yescharacteristic
665C22×C4D4×D4311yescharacteristic
666C22×C4D4×D4311yescharacteristic
667C22×C4D4×D4311yescharacteristic
668C22×C4D4×D4311yescharacteristic
669C22×C4D4×D4311yescharacteristic
670C22×C4#1062190211yescharacteristic
671C22×C4#1062190211yescharacteristic
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—868no—
679C4⋊C4—868no—
680C4⋊C4—862no—
681C4⋊C4—862no—
682C4⋊C4—1721no—
683C4⋊C4—1721no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—434no—
689C22⋊C4—868no—
690C22⋊C4—868no—
691C22⋊C4—868no—
692C22⋊C4—862no—
693C22⋊C4—862no—
694C22⋊C4—862no—
695C22⋊C4C2×C4×D4314yes—
696C22⋊C4C2×D17214yes—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—41no—
702C42—41no—
703C42—868no—
704C42—862no—
705C42—862no—
706C42—1721no—
707C42—1721no—
708C23—81no—
709C23—434no—
710C23—862no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—3442no—
716C23—3442no—
717C23C22×C4×D4311yescharacteristic
718C23C2×D4×D4311yescharacteristic
719C23C2×D4×D4311yescharacteristic
720C23C2×D4×D4311yescharacteristic
721C23C22×D17211yescharacteristic
722C23C2×#1062189811yescharacteristic
723C23C2×#1062190211yescharacteristic
724Q8—862no—
725Q8—862no—
726Q8—862no—
727Q8—862no—
728Q8—1721no—
729Q8—1721no—
730Q8—1721no—
731Q8—1721no—
732D4—864no—
733D4—864no—
734D4—864no—
735D4—864no—
736D4—862no—
737D4—862no—
738D4—862no—
739D4—862no—
740D4—3448no—
741D4—1722no—
742D4—1722no—
743D4—1722no—
744D4—1722no—
745D4—1721no—
746D4—1721no—
747D4—1721no—
748D4—1721no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—42no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4—82no—
755C2×C4—434no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—864no—
759C2×C4—864no—
760C2×C4—864no—
761C2×C4—864no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—864no—
766C2×C4—3448no—
767C2×C4—3442no—
768C2×C4—3442no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4—1722no—
774C2×C4C22⋊C4×D4311yescharacteristic
775C2×C4C22⋊C4×D4311yescharacteristic
776C2×C4C22⋊C4×D4311yescharacteristic
777C2×C4C22⋊C4×D4311yescharacteristic
778C2×C4#1306328711yescharacteristic
779C2×C4#1306328711yescharacteristic
780C2×C4#1306328711yescharacteristic
781C2×C4#1306328711yescharacteristic
782C2×C4C4×D17211yescharacteristic
783C2×C4C4×D17211yescharacteristic
784C2×C4C4×D17211yescharacteristic
785C2×C4C4×D17211yescharacteristic
786C2×C4#1306329511yescharacteristic
787C2×C4#1306329511yescharacteristic
788C2×C4#1306329511yescharacteristic
789C2×C4#1306329511yescharacteristic
790C2×C4#1306329811yescharacteristic
791C2×C4#1306329811yescharacteristic
792C2×C4#1306329811yescharacteristic
793C2×C4#1306329811yescharacteristic
794C2×C4#1306330011yescharacteristic
795C2×C4#1306330011yescharacteristic
796C2×C4#1306330011yescharacteristic
797C2×C4#1306330011yescharacteristic
798C2×C4#1306331011yescharacteristic
799C2×C4#1306331011yescharacteristic
800C2×C4#1306331011yescharacteristic
801C2×C4#1306331011yescharacteristic
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—864no—
810C22—3442no—
811C22—3442no—
812C22—3442no—
813C22—1724no—
814C22—1724no—
815C22—1724no—
816C22—1722no—
817C22C2×C22⋊C4×D4311yescharacteristic
818C22C2×#1306328711yescharacteristic
819C22C2×C4×D17211yescharacteristic
820C22C2×#1306329511yescharacteristic
821C22C2×#1306329811yescharacteristic
822C22C2×#1306330011yescharacteristic
823C22C2×#1306331011yescharacteristic
824C4—44no—
825C4—44no—
826C4—82no—
827C4—864no—
828C4—3442no—
829C4—1724no—
830C4—1722no—
831C4#1458277711yescharacteristic
832C4#1458277711yescharacteristic
833C4#1458277711yescharacteristic
834C4#1458277711yescharacteristic
835C4#1458277711yescharacteristic
836C4#1458277711yescharacteristic
837C4#1458277711yescharacteristic
838C4#1458277711yescharacteristic
839C2—21no—
840C2—21no—
841C2—21no—
842C2—21no—
843C2—21no—
844C2—21no—
845C2—21no—
846C2—3442no—
847C2—1724no—
848C2C2×#1458277711yescharacteristic
subgroupG/H
centerC4#14582777
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1740C2
socleC2×C43C2×#386
prime radical#19147928C2
cosocleC24×C43C24
hypercenter#1740D43
hypocenterC43#21014
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. #19147796C2semidirect
3. C2×#14582872C2semidirect
4. C2×#14582872C2semidirect
5. C2×#14582872C2semidirect
6. #19135136C2semidirect
7. #19134327C2semidirect
8. C43×#1740C2semidirect
13. #14583475C4semidirect
15. #14583468C4semidirect
19. #14583411C4semidirect
68. C22×Dic86C2×C4semidirect
70. C22×D172C2×C4semidirect
74. C22×C4×D43C2×C4semidirect
81. #13063309C2×C4semidirect
88. #13063295C2×C4semidirect
102. #13063284D4semidirect
103. #13063284D4semidirect
128. #117×C43C2×C4semidirect
129. #117×C43C2×C4semidirect
130. #117×C43D4semidirect
131. #117×C43D4semidirect
422. #1740D43semidirect
468. C43#21014semidirect
541. #117C4×D43semidirect
542. #117C4×D43semidirect
543. #117D172semidirect
544. #117D172semidirect

Maximal subgroups

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

subgroupindex
#191479282
#191477962
C2×#145828722
#191351362
#191343272
C43×#17402
#2101443