Finite Group Databasebeta

← #25101628

Subgroups — #25101628

Order 11008.

1164 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2C4×M16×D43C211yesmaximal, characteristic, complemented
3#19136987C211yesmaximal, characteristic, complemented
4#19135537C212yesmaximal, complemented
5#19135512C212yesmaximal, complemented
6#19134896C212yesmaximal, complemented
7#19134894C212yesmaximal, complemented
8#19134408C211yesmaximal, characteristic, complemented
9#19134406C211yesmaximal, characteristic, complemented
10#19134405C211yesmaximal, characteristic, complemented
11C43×#1759C211yesmaximal, characteristic, complemented
12C2×M16×D43C2212yes—
13#14583453C411yescharacteristic, complemented
14#14583453C411yescharacteristic, complemented
15#14583452C2211yescharacteristic
16#14583446C411yescharacteristic, complemented
17#14583446C411yescharacteristic, complemented
18#14583445C2211yescharacteristic
19#14583436C411yescharacteristic, complemented
20#14583436C411yescharacteristic, complemented
21#14583431C411yescharacteristic, complemented
22#14583431C411yescharacteristic, complemented
23#14583429—21no—
24#14583429—21no—
25#14583427—21no—
26#14583427—21no—
27#14583411C2211yescharacteristic
28#14583408—21no—
29#14583408—21no—
30#14583406C2211yescharacteristic
31C4×#10621898—21no—
32C4×#10621898—21no—
33C4×#10621898C2211yescharacteristic
34C2×C42×D43C2211yescharacteristic
35C2×#13063253C2212yes—
36C2×#13063252C2212yes—
37C2×#13063251C2212yes—
38C4×#10621877C2211yescharacteristic
39#14582851—21no—
40M16×Dic43C2212yes—
41C4×#10621872—21no—
42#97×D43—21no—
43C4×C8×D43—21no—
44#14582766—21no—
45#14582763—21no—
46#14582761—21no—
47#14582758—21no—
48C4×Dic43⋊C4C2212yes—
49C4×(C2×D43)⋊C4C2212yes—
50#14582745C2211yescharacteristic
51#14582660C2212yes—
52#14582659C2212yes—
53#14582658C2212yes—
54C4×#41×C43C2211yescharacteristic
55C2×#104×C43C2212yes—
56C4×M16×C43C2211yescharacteristic
57C43×#376C2211yescharacteristic
58C43×#339C2212yes—
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2311yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621877C2312yes—
66C2×#10621872—22no—
67M16×D43—24no—
68M16×D43—24no—
69C2×C8×D43—22no—
70#13063324C2×C411yescharacteristic
71#13063324C2×C411yescharacteristic
72#13063323C2×C411yescharacteristic
73#13063321C2×C411yescharacteristic
74#13063320—21no—
75#13063320—21no—
76#13063318—21no—
77#13063318—21no—
78#13063316C2×C411yescharacteristic
79#13063316C2×C411yescharacteristic
80#13063315—21no—
81#13063315—21no—
82#13063314C2×C411yescharacteristic
83#13063312C2×C411yescharacteristic
84#13063311—21no—
85#13063311—21no—
86#13063310—21no—
87#13063310—21no—
88#13063309—21no—
89#13063307—21no—
90#13063307—21no—
91#13063306—21no—
92#13063305C2×C411yescharacteristic
93#13063305C2×C411yescharacteristic
94#13063303—21no—
95#13063303—21no—
96#13063302—21no—
97#13063302—21no—
98#13063301C2×C411yescharacteristic
99#13063301C2×C411yescharacteristic
100#13063300C2×C411yescharacteristic
101#13063300C2×C411yescharacteristic
102#13063298—21no—
103#13063298—21no—
104#13063297—21no—
105#13063297—21no—
106#13063296C2×C411yescharacteristic
107#13063296C2×C411yescharacteristic
108#13063295—21no—
109#13063293—21no—
110C4×Dic86—21no—
111C4×Dic86—21no—
112C4×Dic86—21no—
113C4×Dic86—21no—
114C4×Dic86C2×C411yescharacteristic
115C4×Dic86C2×C411yescharacteristic
116C4×D172—21no—
117C4×D172—21no—
118C4×D172—21no—
119C4×D172—21no—
120C4×D172C2×C411yescharacteristic
121C4×D172C2×C411yescharacteristic
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129C4×C22⋊D43—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132#13063284—21no—
133#13063284—21no—
134#13063284C2311yescharacteristic
135#13063282—21no—
136#13063282—21no—
137#13063282—21no—
138#13063282—21no—
139#13063282—21no—
140C2×Dic43⋊C4—22no—
141C2×(C2×D43)⋊C4—22no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2312yes—
145C2×C4×Dic43C2311yescharacteristic
146C42×D43—21no—
147C42×D43C2×C411yescharacteristic
148C42×D43C2×C411yescharacteristic
149C42×D43C2×C411yescharacteristic
150C42×D43C2×C411yescharacteristic
151C42×D43D411yescharacteristic
152C42×D43D411yescharacteristic
153C42×D43D411yescharacteristic
154C42×D43D411yescharacteristic
155#13063253—24no—
156#13063252—24no—
157#13063251—24no—
158#13063236—21no—
159#13063235—22no—
160C4×C43⋊C8—21no—
161C8×Dic43—22no—
162C43⋊#95—21no—
163C43⋊#95—21no—
164C43⋊#95—22no—
165C43⋊#95—22no—
166C2×#41×C43C2311yescharacteristic
167C2×M16×C43C2312yes—
168C4×Q8×C43C2×C411yescharacteristic
169C4×Q8×C43C2×C411yescharacteristic
170C4×D4×C43—21no—
171C4×D4×C43—21no—
172C4×D4×C43C2×C411yescharacteristic
173C4×D4×C43C2×C411yescharacteristic
174#117×C43—21no—
175#117×C43C2311yescharacteristic
176C2×C42×C43—21no—
177C2×C42×C43C2312yes—
178C2×C42×C43C2311yescharacteristic
179#104×C43—24no—
180#97×C43—21no—
181C4×C8×C43—21no—
182#95×C43—21no—
183#95×C43—21no—
184C23×D43C2×D411yescharacteristic
185#41×C43—22no—
186#41×C43—22no—
187C2×Q8×C43C22×C411yescharacteristic
188C2×D4×C43—21no—
189C2×D4×C43C22×C411yescharacteristic
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—22no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—21no—
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C22×Dic43—22no—
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206#10621898—22no—
207#10621898—22no—
208#10621898—44no—
209#10621898—44no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172C22×C411yescharacteristic
213C2×C4×D43—22no—
214C2×C4×D43—22no—
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—42no—
219C2×C4×D43—42no—
220C2×C4×D43C22⋊C411yescharacteristic
221C2×C4×D43C22⋊C411yescharacteristic
222C2×C4×D43C22⋊C411yescharacteristic
223C2×C4×D43C22⋊C411yescharacteristic
224C2×C4×D43C22⋊C411yescharacteristic
225C2×C4×D43C22⋊C411yescharacteristic
226C2×C4×D43C22⋊C411yescharacteristic
227C2×C4×D43C22⋊C411yescharacteristic
228C2×C4×D43C22×C411yescharacteristic
229C2×C4×D43C22×C411yescharacteristic
230C2×C4×D43C2×D411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86C22×C411yescharacteristic
235M16×C43—22no—
236M16×C43#4114yescomplemented
237C2×C8×C43—22no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43C22×C411yescharacteristic
241C4⋊C4×C43C22×C411yescharacteristic
242C22⋊C4×C43—21no—
243C22⋊C4×C43—21no—
244C22⋊C4×C43—21no—
245C42×C43—21no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—22no—
249C42×C43—22no—
250C42×C43C22×C411yescharacteristic
251C42×C43C22×C411yescharacteristic
252C42×C43C2×D411yescharacteristic
253C42×C43C2×D411yescharacteristic
254C22⋊Dic43—21no—
255C22⋊Dic43—21no—
256C22⋊Dic43—21no—
257C22⋊Dic43—21no—
258C22⋊Dic43—21no—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—21no—
261(C2×D43)⋊C4—21no—
262(C2×D43)⋊C4—21no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—44no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—21no—
274C4⋊Dic43C22×C411yescharacteristic
275C4⋊Dic43C22×C411yescharacteristic
276Dic43⋊C4—21no—
277Dic43⋊C4—21no—
278Dic43⋊C4—21no—
279Dic43⋊C4—21no—
280Dic43⋊C4—21no—
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285Dic43⋊C4—21no—
286Dic43⋊C4—44no—
287C4×Dic43—21no—
288C4×Dic43—21no—
289C4×Dic43—21no—
290C4×Dic43—22no—
291C4×Dic43—22no—
292C4×Dic43C22⋊C411yescharacteristic
293C4×Dic43C22⋊C411yescharacteristic
294C4×Dic43C22⋊C411yescharacteristic
295C4×Dic43C22⋊C411yescharacteristic
296C4×Dic43C22⋊C411yescharacteristic
297C4×Dic43C22⋊C411yescharacteristic
298C4×Dic43C22⋊C411yescharacteristic
299C4×Dic43C22⋊C411yescharacteristic
300C4×Dic43C22×C411yescharacteristic
301C4×Dic43C22×C411yescharacteristic
302C4×Dic43C2×D411yescharacteristic
303C4×Dic43C2×D411yescharacteristic
304#10621877—22no—
305#10621877#4114yescomplemented
306C2×C43⋊C8—22no—
307#10621872—28no—
308C8×D43—28no—
309C23×C43—21no—
310C23×C43C22×D411yescharacteristic
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—21no—
314C22×D43—41no—
315C22×D43C2×C22⋊C411yescharacteristic
316C22×D43C2×C22⋊C411yescharacteristic
317Q8×C43—21no—
318Q8×C43—21no—
319D4×C43—21no—
320D4×C43—21no—
321D4×C43—42no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43—42no—
333C2×C4×C43C2×C22⋊C411yescharacteristic
334C2×C4×C43C2×C22⋊C411yescharacteristic
335C2×C4×C43C2×C22⋊C411yescharacteristic
336C2×C4×C43C2×C22⋊C411yescharacteristic
337C2×C4×C43C23×C411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C2×#4112yes—
340C2×C4×C43C2×#4112yes—
341C22⋊D43—42no—
342C22⋊D43—42no—
343C22⋊D43—42no—
344C22⋊D43—42no—
345C22⋊D43—42no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—41no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43C2×C22⋊C411yescharacteristic
356C2×Dic43C2×C22⋊C411yescharacteristic
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361D172—21no—
362D172—21no—
363D172—42no—
364D172—42no—
365C4×D43—22no—
366C4×D43—22no—
367C4×D43—21no—
368C4×D43—21no—
369C4×D43—21no—
370C4×D43—21no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—41no—
376C4×D43—41no—
377C4×D43—41no—
378C4×D43—41no—
379C4×D43—42no—
380C4×D43—42no—
381C4×D43—42no—
382Dic86—21no—
383Dic86—21no—
384Dic86—42no—
385Dic86—42no—
386C8×C43—24no—
387C43⋊C8—24no—
388#21383—431nomaximal, Sylow
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43C22×C22⋊C411yescharacteristic
395C22×C43#53212yes—
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—21no—
399C2×D43—21no—
400C2×D43—21no—
401C2×D43—44no—
402C2×D43—41no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43#42112yes—
406C4×C43—21no—
407C4×C43—21no—
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—41no—
411C4×C43—41no—
412C4×C43—41no—
413C4×C43—82no—
414C4×C43C4×#4111yescharacteristic
415C4×C43C4×#4111yescharacteristic
416C4×C43#52512yes—
417Dic43—21no—
418Dic43—21no—
419Dic43—21no—
420Dic43—21no—
421Dic43—21no—
422Dic43—41no—
423Dic43—41no—
424Dic43—41no—
425Dic43—82no—
426Dic43#42112yes—
427#3444—431no—
428C2×C4×M16—431no—
429#2283—431no—
430#1986—432no—
431#1980—432no—
432#1871—432no—
433#1871—432no—
434#1759—431no—
435#1759—431no—
436#1759—431no—
437#1759D4311yescharacteristic, complemented
438C2×C43—22no—
439C2×C43—81no—
440C2×C43#229711yescharacteristic
441C2×C43C2×#42111yescharacteristic
442C2×C43C2×#42111yescharacteristic
443D43—22no—
444D43—41no—
445D43—81no—
446C22×M16—432no—
447#533—431no—
448#533—431no—
449#533—431no—
450#532—431no—
451#532—431no—
452#532—431no—
453#529—431no—
454#529—431no—
455#529—431no—
456#529—431no—
457#529—861no—
458#529—861no—
459#529—861no—
460#529—861no—
461#525—431no—
462#525—431no—
463#525—861no—
464#525—861no—
465C4×#41—431no—
466C4×#41—861no—
467C4×#41—861no—
468C4×#41C2×D4311yescharacteristic
469C22×C42—431no—
470C2×#104—432no—
471C2×#104—432no—
472C2×#104—432no—
473C2×#104C2×D4312yes—
474C4×M16—432no—
475C4×M16—431no—
476C4×M16—861no—
477C4×M16—861no—
478C4×M16C2×D4311yescharacteristic
479C2×#97—861no—
480C2×C4×C8—861no—
481#383—861no—
482#382—861no—
483#381—861no—
484#380—861no—
485C4×C4⋊C4—432no—
486C4×C22⋊C4—432no—
487#376—431no—
488#376C2×D4311yescharacteristic
489#339—432no—
490#339—432no—
491#339—432no—
492#339C2×D4312yes—
493C43#2138311yescharacteristic, complemented, Sylow
494C2×#41—431no—
495C2×#41—861no—
496C2×#41—861no—
497C2×#41C22×D4311yescharacteristic
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—431no—
501C2×M16—432no—
502C2×M16—862no—
503C2×M16—864no—
504C2×M16—864no—
505C2×M16C22×D4312yes—
506C22×C8—862no—
507C4⋊Q8—431no—
508C4⋊Q8—431no—
509C4⋊Q8—431no—
510#127—431no—
511#126—861no—
512#126—861no—
513#126—861no—
514#126—861no—
515#125—431no—
516#125—431no—
517#125—861no—
518#125—861no—
519#124—431no—
520#124—431no—
521#124—861no—
522#124—861no—
523#123—861no—
524#123—861no—
525#123—861no—
526#123—861no—
527#123—861no—
528#123—861no—
529C22⋊Q8—431no—
530C22⋊Q8—431no—
531C22⋊Q8—431no—
532C22⋊Q8—431no—
533C22⋊Q8—861no—
534C22⋊Q8—861no—
535C22⋊Q8—861no—
536C22⋊Q8—861no—
537#121—431no—
538#121—431no—
539#121—431no—
540#121—431no—
541#121—861no—
542#121—861no—
543#121—861no—
544#121—861no—
545#120—861no—
546#120—861no—
547C4×Q8—431no—
548C4×Q8—431no—
549C4×Q8—861no—
550C4×Q8—861no—
551C4×Q8—861no—
552C4×Q8—861no—
553C4×Q8C4×D4311yescharacteristic
554C4×Q8C4×D4311yescharacteristic
555C4×D4—21no—
556C4×D4—21no—
557C4×D4—431no—
558C4×D4—431no—
559C4×D4—861no—
560C4×D4—861no—
561C4×D4—861no—
562C4×D4—861no—
563C4×D4—861no—
564C4×D4—861no—
565C4×D4—861no—
566C4×D4—861no—
567C4×D4—861no—
568C4×D4—861no—
569C4×D4—861no—
570C4×D4—861no—
571C4×D4—861no—
572C4×D4—861no—
573C4×D4C4×D4311yescharacteristic
574C4×D4C4×D4311yescharacteristic
575#117—21no—
576#117—431no—
577#117—861no—
578#117—861no—
579#117—861no—
580#117—861no—
581#117—861no—
582#117—861no—
583#117—861no—
584#117C22×D4311yescharacteristic
585C2×C4⋊C4—862no—
586C2×C22⋊C4—862no—
587C2×C42—21no—
588C2×C42—431no—
589C2×C42—431no—
590C2×C42—431no—
591C2×C42—431no—
592C2×C42—431no—
593C2×C42—431no—
594C2×C42—431no—
595C2×C42—431no—
596C2×C42—431no—
597C2×C42—431no—
598C2×C42—431no—
599C2×C42—432no—
600C2×C42—861no—
601C2×C42C22×D4312yes—
602C2×C42C22×D4311yescharacteristic
603#104—24no—
604#104—864no—
605#104—864no—
606#104—864no—
607#97—21no—
608#97—862no—
609#97—861no—
610C4×C8—21no—
611C4×C8—862no—
612C4×C8—861no—
613#95—21no—
614#95—21no—
615#95—862no—
616#95—862no—
617#95—861no—
618#95—861no—
619C24—431no—
620#41—22no—
621#41—22no—
622#41—862no—
623#41—862no—
624#41—1724no—
625#41—1724no—
626C2×Q8—431no—
627C2×Q8—861no—
628C2×Q8—861no—
629C2×Q8C2×C4×D4311yescharacteristic
630C2×D4—21no—
631C2×D4—431no—
632C2×D4—861no—
633C2×D4—861no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4C2×C4×D4311yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—431no—
645C22×C4—431no—
646C22×C4—431no—
647C22×C4—431no—
648C22×C4—431no—
649C22×C4—431no—
650C22×C4—431no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—862no—
660C22×C4—862no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—862no—
665C22×C4—1722no—
666C22×C4—1722no—
667C22×C4D4×D4311yescharacteristic
668C22×C4D4×D4311yescharacteristic
669C22×C4C23×D4311yescharacteristic
670M16—22no—
671M16—434no—
672M16—868no—
673M16—862no—
674M16#1062189814yescomplemented
675C2×C8—22no—
676C2×C8—868no—
677C2×C8—862no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—431no—
681C4⋊C4—431no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—1724no—
697C4⋊C4C2×C4×D4311yescharacteristic
698C4⋊C4C2×C4×D4311yescharacteristic
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—861no—
703C22⋊C4—861no—
704C22⋊C4—861no—
705C22⋊C4—861no—
706C22⋊C4—861no—
707C22⋊C4—861no—
708C22⋊C4—861no—
709C22⋊C4—861no—
710C22⋊C4—861no—
711C22⋊C4—861no—
712C22⋊C4—861no—
713C22⋊C4—861no—
714C22⋊C4—861no—
715C22⋊C4—861no—
716C22⋊C4—861no—
717C22⋊C4—1724no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—22no—
722C42—22no—
723C42—431no—
724C42—431no—
725C42—431no—
726C42—431no—
727C42—431no—
728C42—431no—
729C42—431no—
730C42—431no—
731C42—431no—
732C42—431no—
733C42—431no—
734C42—431no—
735C42—861no—
736C42—861no—
737C42—861no—
738C42—862no—
739C42—862no—
740C42C2×C4×D4311yescharacteristic
741C42C2×C4×D4311yescharacteristic
742C42D4×D4311yescharacteristic
743C42D4×D4311yescharacteristic
744C23—21no—
745C23—431no—
746C23—431no—
747C23—862no—
748C23—862no—
749C23—861no—
750C23—1721no—
751C23C2×D4×D4311yescharacteristic
752Q8—21no—
753Q8—21no—
754Q8—861no—
755Q8—861no—
756Q8—1722no—
757Q8—1722no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—861no—
762D4—861no—
763D4—1722no—
764D4—1722no—
765D4—1722no—
766D4—1722no—
767D4—1722no—
768D4—1722no—
769D4—1722no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—431no—
782C2×C4—431no—
783C2×C4—431no—
784C2×C4—431no—
785C2×C4—431no—
786C2×C4—431no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—862no—
790C2×C4—862no—
791C2×C4—862no—
792C2×C4—862no—
793C2×C4—861no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1722no—
807C2×C4—1722no—
808C2×C4—1721no—
809C2×C4—1722no—
810C2×C4—1722no—
811C2×C4—1722no—
812C2×C4—1722no—
813C2×C4C22⋊C4×D4311yescharacteristic
814C2×C4C22⋊C4×D4311yescharacteristic
815C2×C4C22⋊C4×D4311yescharacteristic
816C2×C4C22⋊C4×D4311yescharacteristic
817C2×C4C22×C4×D4311yescharacteristic
818C2×C4C2×D4×D4311yescharacteristic
819C2×C4#41×D4312yes—
820C2×C4C2×#1062189812yes—
821C8—24no—
822C8—864no—
823C22—21no—
824C22—21no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—432no—
829C22—861no—
830C22—861no—
831C22—861no—
832C22—861no—
833C22—861no—
834C22—1724no—
835C22—1721no—
836C22—1721no—
837C22—1721no—
838C22C2×C22⋊C4×D4311yescharacteristic
839C22#1458344612yes—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—82no—
848C4—432no—
849C4—861no—
850C4—861no—
851C4—861no—
852C4—861no—
853C4—861no—
854C4—3442no—
855C4—1721no—
856C4—1721no—
857C4—1721no—
858C4#1458336711yescharacteristic
859C4C4×#1062189811yescharacteristic
860C4#1458340812yes—
861C2—22no—
862C2—81no—
863C2—862no—
864C2—3441no—
865C2—1721no—
866C2#1913708111yescharacteristic
867C2#421×D4311yescharacteristic
868C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1759C2
socleC22×C43C22×C22⋊C4
prime radical#19147888C2
cosocleC22×C4×C43C24
hypercenter#1759D43
hypocenterC43#21383
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. C4×M16×D43C2semidirect
3. #19136987C2semidirect
4. #19135537C2semidirect
5. #19135512C2semidirect
6. #19134896C2semidirect
7. #19134894C2semidirect
8. #19134408C2semidirect
9. #19134406C2semidirect
10. #19134405C2semidirect
11. C43×#1759C2semidirect
13. #14583453C4semidirect
14. #14583453C4semidirect
16. #14583446C4semidirect
17. #14583446C4semidirect
19. #14583436C4semidirect
20. #14583436C4semidirect
21. #14583431C4semidirect
22. #14583431C4semidirect
236. M16×C43#41semidirect
305. #10621877#41semidirect
437. #1759D43semidirect
493. C43#21383semidirect
674. M16#10621898semidirect

Maximal subgroups

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

subgroupindex
#191478882
C4×M16×D432
#191369872
#191355372
#191355122
#191348962
#191348942
#191344082
#191344062
#191344052
C43×#17592
#2138343