Finite Group Databasebeta

← #25099108

Subgroups — #25099108

Order 11008.

1050 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582946C211yesmaximal, characteristic, complemented
2C2×#104×D43C211yesmaximal, characteristic
3#19143110C211yesmaximal, characteristic
4#19143037C211yesmaximal, characteristic
5#19143011C211yesmaximal, characteristic, complemented
6#19135246C211yesmaximal, characteristic, complemented
7#19135245C211yesmaximal, characteristic, complemented
8#19135244C211yesmaximal, characteristic, complemented
9#19135243C211yesmaximal, characteristic, complemented
10#19135242C211yesmaximal, characteristic, complemented
11#19135241C211yesmaximal, characteristic, complemented
12#19135240C211yesmaximal, characteristic, complemented
13#339×D43C211yesmaximal, characteristic, complemented
14#19134287C211yesmaximal, characteristic, complemented
15C43×#1929C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×M16×D43C2211yescharacteristic
21#117×D43C2211yescharacteristic
22C2×C42×D43C2211yescharacteristic
23#14582946—24no—
24C2×#13063261C2211yescharacteristic, complemented
25C2×#13063260C2211yescharacteristic, complemented
26C2×#13063260C2211yescharacteristic, complemented
27C2×#13063253C2211yescharacteristic
28C2×#13063252C2211yescharacteristic
29C2×#13063251C2211yescharacteristic
30#104×D43—24no—
31#14582906C411yescharacteristic, complemented
32#14582906C411yescharacteristic, complemented
33#14582902C411yescharacteristic, complemented
34#14582902C411yescharacteristic, complemented
35#14582899C411yescharacteristic, complemented
36#14582899C411yescharacteristic, complemented
37#14582897C411yescharacteristic, complemented
38#14582897C411yescharacteristic, complemented
39#14582896C2211yescharacteristic
40#14582895C2211yescharacteristic
41#14582893C2211yescharacteristic
42#14582867C2211yescharacteristic
43#14582866C2211yescharacteristic
44#14582865C2211yescharacteristic
45#14582864—21no—
46#14582864—21no—
47#14582861—21no—
48#14582861—21no—
49#14582857C2211yescharacteristic, complemented
50#14582856—21no—
51#14582855C2211yescharacteristic, complemented
52#14582854C2211yescharacteristic, complemented
53#14582853—21no—
54#14582851—21no—
55C4×#10621872—21no—
56#14582660C2211yescharacteristic, complemented
57#14582659C2211yescharacteristic, complemented
58#14582658C2211yescharacteristic, complemented
59#14582654C2211yescharacteristic, complemented
60#14582653C2211yescharacteristic, complemented
61#14582653C2211yescharacteristic, complemented
62C2×#108×C43C2211yescharacteristic, complemented
63C2×#104×C43C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C43×#408C2211yescharacteristic
66C43×#405C2211yescharacteristic, complemented
67C43×#339C2211yescharacteristic, complemented
68C43×#336C2211yescharacteristic, complemented
69C2×#10621902C2×C411yescharacteristic
70C2×#10621898—21no—
71C2×#10621898C2311yescharacteristic
72C2×#10621900—21no—
73C2×#10621900C2×C411yescharacteristic
74#41×D43—22no—
75#41×D43—22no—
76#41×D43—22no—
77#41×D43—22no—
78C2×Q8×D43C2×C411yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43C2×C411yescharacteristic
81C22×C4×D43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621872—21no—
87C2×#10621872—22no—
88C2×#10621872—22no—
89C2×#10621872—22no—
90C2×#10621872—22no—
91C2×#10621872—21no—
92C2×#10621872C2×C411yescharacteristic
93C2×#10621872C2×C411yescharacteristic
94C2×#10621872C2×C411yescharacteristic
95C2×#10621872C2×C411yescharacteristic
96C2×#10621872D411yescharacteristic
97C2×#10621872D411yescharacteristic
98C2×#10621872D411yescharacteristic
99C2×#10621872D411yescharacteristic
100M16×D43—22no—
101M16×D43—22no—
102M16×D43—22no—
103M16×D43D414yes—
104C22×C43⋊C8C2311yescharacteristic
105C22×C43⋊C8C2311yescharacteristic
106C2×C8×D43—21no—
107C2×C8×D43—21no—
108#13063284C2311yescharacteristic
109#13063283C2×C411yescharacteristic
110#13063283C2×C411yescharacteristic
111#13063282—21no—
112#13063281—21no—
113C4⋊C4×D43C2×C411yescharacteristic
114C4⋊C4×D43C2×C411yescharacteristic
115C22⋊C4×D43—21no—
116C2×C4×Dic43—21no—
117C2×C4×Dic43C2311yescharacteristic
118C42×D43—21no—
119C42×D43—22no—
120C42×D43—22no—
121#13063261—22no—
122#13063260—22no—
123#13063260—22no—
124#13063253—22no—
125#13063252—22no—
126#13063251—22no—
127#13063250C2×C411yescharacteristic, complemented
128#13063250C2×C411yescharacteristic, complemented
129#13063249C2×C411yescharacteristic, complemented
130#13063249C2×C411yescharacteristic, complemented
131#13063248C2×C411yescharacteristic, complemented
132#13063248C2×C411yescharacteristic, complemented
133#13063247C2×C411yescharacteristic, complemented
134#13063247C2×C411yescharacteristic, complemented
135#13063246C2×C411yescharacteristic, complemented
136#13063246C2×C411yescharacteristic, complemented
137#13063245C2×C411yescharacteristic, complemented
138#13063245C2×C411yescharacteristic, complemented
139C22⋊(C43⋊C8)—21no—
140C22⋊(C43⋊C8)—21no—
141(C2×D43)⋊C8—21no—
142(C2×D43)⋊C8—21no—
143(C2×D43)⋊C8—21no—
144(C2×D43)⋊C8—21no—
145#13063236—21no—
146#13063235—21no—
147#13063235—21no—
148C4×C43⋊C8—21no—
149C8×Dic43—21no—
150C8×Dic43—21no—
151C2×#41×C43C2311yescharacteristic
152C2×M16×C43C2311yescharacteristic
153C2×M16×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156#117×C43C2311yescharacteristic
157C2×C42×C43C2311yescharacteristic
158#108×C43—22no—
159#104×C43—22no—
160#103×C43C2×C411yescharacteristic, complemented
161#103×C43C2×C411yescharacteristic, complemented
162#102×C43C2×C411yescharacteristic, complemented
163#102×C43C2×C411yescharacteristic, complemented
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166#97×C43—21no—
167C4×C8×C43—21no—
168C23×D43—21no—
169C23×D43#4111yescharacteristic
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174C2×Q8×C43C22×C411yescharacteristic
175C2×D4×C43—21no—
176C2×D4×C43C22×C411yescharacteristic
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—21no—
181C2×C22⋊D43—21no—
182C2×C22⋊D43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43#4111yescharacteristic
186#10621902—22no—
187#10621902—22no—
188Q8×D43—22no—
189Q8×D43—22no—
190#10621900—22no—
191#10621900—22no—
192#10621900—42no—
193#10621900—42no—
194D4×D43—22no—
195D4×D43—22no—
196D4×D43—42no—
197D4×D43—42no—
198#10621898—21no—
199#10621898—21no—
200#10621898—21no—
201#10621898—21no—
202#10621898—42no—
203#10621898—42no—
204C2×D172—21no—
205C2×D172C22×C411yescharacteristic
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—21no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—42no—
212C2×C4×D43—42no—
213C2×C4×D43—42no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×C4×D43C22×C411yescharacteristic
217C2×C4×D43C22×C411yescharacteristic
218C2×C4×D43C2×D411yescharacteristic
219C2×C4×D43C2×D411yescharacteristic
220C2×C4×D43C2×D412yes—
221C2×C4×D43#4112yes—
222C2×C4×D43#4112yes—
223C2×C4×D43#4112yes—
224C2×Dic86—21no—
225C2×Dic86C22×C411yescharacteristic
226M16×C43—21no—
227M16×C43—21no—
228M16×C43—21no—
229M16×C43C2×D412yes—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43C22×C411yescharacteristic
237C2×C8×C43C22×C411yescharacteristic
238C2×C8×C43C2×D411yescharacteristic
239C2×C8×C43C2×D411yescharacteristic
240C4⋊C4×C43C22×C411yescharacteristic
241C4⋊C4×C43C22×C411yescharacteristic
242C22⋊C4×C43—21no—
243C42×C43—21no—
244C42×C43—21no—
245C42×C43—21no—
246C22⋊Dic43—21no—
247(C2×D43)⋊C4—21no—
248(C2×D43)⋊C4—21no—
249C4⋊Dic43C22×C411yescharacteristic
250C4⋊Dic43C22×C411yescharacteristic
251Dic43⋊C4—21no—
252Dic43⋊C4—21no—
253C4×Dic43—21no—
254C4×Dic43—21no—
255C4×Dic43—21no—
256C4×Dic43—21no—
257C4×Dic43—21no—
258C4×Dic43—42no—
259#10621877—21no—
260#10621877—21no—
261#10621877—21no—
262#10621877C2×D412yes—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8C22×C411yescharacteristic
270C2×C43⋊C8C22×C411yescharacteristic
271C2×C43⋊C8C2×D411yescharacteristic
272C2×C43⋊C8C2×D411yescharacteristic
273#10621872—22no—
274#10621872—22no—
275#10621872—22no—
276#10621872—22no—
277#10621872—24no—
278#10621872—22no—
279#10621872—22no—
280#10621872—22no—
281#10621872—22no—
282#10621872—42no—
283C8×D43—24no—
284C8×D43—42no—
285C23×C43—21no—
286C23×C43C2×#4111yescharacteristic
287C22×D43—21no—
288C22×D43—41no—
289C22×D43—41no—
290C22×D43—42no—
291C22×D43—81no—
292C22×D43—81no—
293C22×D43C4×D411yescharacteristic
294C22×D43C4×D411yescharacteristic
295C22×D43#12412yes—
296C22×D43#12612yes—
297Q8×C43—21no—
298Q8×C43—21no—
299D4×C43—21no—
300D4×C43—21no—
301D4×C43—41no—
302D4×C43—41no—
303C2×C4×C43—22no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43C23×C411yescharacteristic
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4111yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C22⋊D43—41no—
318C22⋊D43—41no—
319C22⋊D43—42no—
320C22⋊D43—42no—
321C2×Dic43—22no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—42no—
328C2×Dic43C4×D411yescharacteristic
329C2×Dic43C4×D411yescharacteristic
330C2×Dic43#12412yes—
331C2×Dic43#12612yes—
332D172—21no—
333D172—21no—
334D172—42no—
335C4×D43—48no—
336C4×D43—42no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—42no—
340C4×D43—81no—
341C4×D43—81no—
342C4×D43#11712yes—
343C4×D43#11712yes—
344C4×D43C4×D412yes—
345C4×D43C4×D412yes—
346C4×D43#12112yes—
347C4×D43#12112yes—
348C4×D43#12312yes—
349C4×D43#12312yes—
350Dic86—21no—
351Dic86—21no—
352Dic86—42no—
353C8×C43—21no—
354C8×C43—21no—
355C8×C43—22no—
356C8×C43—21no—
357C8×C43—21no—
358C8×C43—41no—
359C43⋊C8—21no—
360C43⋊C8—21no—
361C43⋊C8—22no—
362C43⋊C8—21no—
363C43⋊C8—21no—
364C43⋊C8—41no—
365#21071—431nomaximal, Sylow
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—41no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43C2×C4×D411yescharacteristic
372C22×C43C2×#12411yescharacteristic
373C22×C43C2×#12611yescharacteristic
374C2×D43—21no—
375C2×D43—21no—
376C2×D43—21no—
377C2×D43—21no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—41no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—84no—
384C2×D43#38812yes—
385C2×D43#38812yes—
386C4×C43—42no—
387C4×C43—41no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43C2×#11711yescharacteristic
391C4×C43C2×C4×D411yescharacteristic
392C4×C43C2×#12111yescharacteristic
393C4×C43C2×#12311yescharacteristic
394Dic43—42no—
395Dic43—41no—
396Dic43—41no—
397Dic43—41no—
398Dic43#38812yes—
399Dic43#38812yes—
400C2×#430—431no—
401C22×#104—431no—
402#2896—431no—
403#2879—431no—
404#2873—431no—
405#1929—431no—
406#1929—431no—
407#1929—431no—
408#1929—431no—
409#1929—431no—
410#1929—431no—
411#1929—431no—
412#1929D4311yescharacteristic, complemented
413C2×#339—431no—
414#1728—431no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—81no—
418C2×C43C2×#38811yescharacteristic
419C2×C43#295611yescharacteristic
420C2×C43#295611yescharacteristic
421D43—22no—
422D43—22no—
423D43—81no—
424C22×#41—431no—
425C22×M16—431no—
426C22×M16—431no—
427C22×M16—431no—
428C22×M16—431no—
429C2×#117—431no—
430C22×C42—431no—
431#430—864no—
432C2×#108—431no—
433C2×#108—431no—
434C2×#108—431no—
435C2×#108C2×D4311yescharacteristic, complemented
436C2×#104—431no—
437C2×#104—431no—
438C2×#104—431no—
439C2×#104—864no—
440C2×#104C2×D4311yescharacteristic
441#419—431no—
442#419—431no—
443#418—431no—
444#418—431no—
445#417—431no—
446#417—431no—
447#417—431no—
448#417—431no—
449#416—431no—
450#416—431no—
451#416—431no—
452#416C2×D4311yescharacteristic
453#408—431no—
454#408—431no—
455#408—431no—
456#408—861no—
457#408—861no—
458#408C2×D4311yescharacteristic
459#407—861no—
460#407—861no—
461#405—431no—
462#405—431no—
463#405—431no—
464#405—861no—
465#405—861no—
466#405C2×D4311yescharacteristic, complemented
467C4×M16—861no—
468C4×M16—861no—
469#339—431no—
470#339—431no—
471#339—431no—
472#339C2×D4311yescharacteristic, complemented
473#336—431no—
474#336—431no—
475#336—431no—
476#336C2×D4311yescharacteristic, complemented
477C43#2107111yescharacteristic, complemented, Sylow
478C2×#41—431no—
479C2×#41—431no—
480C2×#41—431no—
481C2×#41—861no—
482C2×#41—861no—
483C2×#41—862no—
484C2×#41—862no—
485C2×#41—862no—
486C2×#41—862no—
487C2×#41C22×D4311yescharacteristic
488C22×Q8—431no—
489C22×D4—431no—
490C22×D4—861no—
491C23×C4—431no—
492C23×C4—861no—
493C23×C4—861no—
494C2×M16—431no—
495C2×M16—431no—
496C2×M16—431no—
497C2×M16—431no—
498C2×M16—431no—
499C2×M16—431no—
500C2×M16—431no—
501C2×M16—431no—
502C2×M16—431no—
503C2×M16—434no—
504C2×M16—431no—
505C2×M16—861no—
506C2×M16—862no—
507C2×M16—862no—
508C2×M16—862no—
509C2×M16—862no—
510C2×M16—861no—
511C2×M16—862no—
512C2×M16—862no—
513C2×M16—862no—
514C2×M16C22×D4311yescharacteristic
515C2×M16C22×D4311yescharacteristic
516C22×C8—431no—
517C22×C8—431no—
518C22×C8—861no—
519C22×C8—861no—
520C22×C8C22×D4311yescharacteristic
521C22×C8C22×D4311yescharacteristic
522#117—431no—
523#117—431no—
524#117—431no—
525#117—861no—
526#117—861no—
527#117C22×D4311yescharacteristic
528C2×C4⋊C4—431no—
529C2×C4⋊C4—431no—
530C2×C22⋊C4—861no—
531C2×C42—431no—
532C2×C42—861no—
533C2×C42—862no—
534C2×C42—862no—
535C2×C42—861no—
536C2×C42C22×D4311yescharacteristic
537#108—22no—
538#108—862no—
539#108—862no—
540#108—862no—
541#104—22no—
542#104—862no—
543#104—862no—
544#104—862no—
545#103—431no—
546#103—431no—
547#103—431no—
548#103—431no—
549#103—431no—
550#103—431no—
551#103C4×D4311yescharacteristic, complemented
552#103C4×D4311yescharacteristic, complemented
553#102—431no—
554#102—431no—
555#102—431no—
556#102—431no—
557#102—431no—
558#102—431no—
559#102C4×D4311yescharacteristic, complemented
560#102C4×D4311yescharacteristic, complemented
561C22⋊C8—21no—
562C22⋊C8—21no—
563C22⋊C8—861no—
564C22⋊C8—861no—
565C22⋊C8—861no—
566C22⋊C8—861no—
567C22⋊C8—861no—
568C22⋊C8—861no—
569#97—21no—
570#97—861no—
571#97—861no—
572#97—861no—
573C4×C8—21no—
574C4×C8—861no—
575C4×C8—861no—
576C4×C8—861no—
577C24—431no—
578C24—861no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—862no—
584#41—862no—
585#41—862no—
586#41—862no—
587#41—861no—
588#41—861no—
589#41—861no—
590#41—861no—
591#41—1722no—
592#41—1722no—
593#41—1722no—
594#41—1722no—
595C2×Q8—431no—
596C2×Q8—861no—
597C2×Q8—862no—
598C2×Q8—862no—
599C2×Q8C2×C4×D4311yescharacteristic
600C2×D4—21no—
601C2×D4—431no—
602C2×D4—861no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—861no—
608C2×D4—1722no—
609C2×D4—1722no—
610C2×D4C2×C4×D4311yescharacteristic
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—432no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—1722no—
630C22×C4—1722no—
631C22×C4—1722no—
632C22×C4—1722no—
633C22×C4—1722no—
634C22×C4C23×D4311yescharacteristic
635M16—21no—
636M16—21no—
637M16—21no—
638M16—432no—
639M16—862no—
640M16—862no—
641M16—862no—
642M16—862no—
643M16—864no—
644M16—862no—
645M16—862no—
646M16—862no—
647M16—862no—
648M16—861no—
649M16—861no—
650M16—861no—
651M16—1722no—
652M16D4×D4312yes—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—431no—
660C2×C8—431no—
661C2×C8—431no—
662C2×C8—431no—
663C2×C8—864no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—861no—
670C2×C8—1722no—
671C2×C8C2×C4×D4311yescharacteristic
672C2×C8C2×C4×D4311yescharacteristic
673C2×C8D4×D4311yescharacteristic
674C2×C8D4×D4311yescharacteristic
675C4⋊C4—431no—
676C4⋊C4—431no—
677C4⋊C4—861no—
678C4⋊C4—861no—
679C4⋊C4C2×C4×D4311yescharacteristic
680C4⋊C4C2×C4×D4311yescharacteristic
681C22⋊C4—21no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—861no—
689C42—861no—
690C42—861no—
691C42—861no—
692C42—861no—
693C42—1722no—
694C23—21no—
695C23—431no—
696C23—431no—
697C23—432no—
698C23—432no—
699C23—861no—
700C23—3441no—
701C23—3441no—
702C23—1721no—
703C23—1721no—
704C23—1722no—
705C23#41×D4311yescharacteristic
706Q8—21no—
707Q8—21no—
708Q8—861no—
709Q8—861no—
710Q8—1722no—
711D4—21no—
712D4—21no—
713D4—41no—
714D4—41no—
715D4—861no—
716D4—861no—
717D4—1722no—
718D4—1722no—
719D4—1722no—
720D4—1721no—
721D4—1721no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—431no—
731C2×C4—431no—
732C2×C4—432no—
733C2×C4—432no—
734C2×C4—432no—
735C2×C4—432no—
736C2×C4—432no—
737C2×C4—432no—
738C2×C4—432no—
739C2×C4—432no—
740C2×C4—432no—
741C2×C4—432no—
742C2×C4—862no—
743C2×C4—861no—
744C2×C4—861no—
745C2×C4—861no—
746C2×C4—3441no—
747C2×C4—3441no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4—1728no—
751C2×C4—1722no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4C22×C4×D4311yescharacteristic
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4#41×D4311yescharacteristic
760C2×C4#41×D4311yescharacteristic
761C2×C4#41×D4311yescharacteristic
762C8—21no—
763C8—21no—
764C8—22no—
765C8—21no—
766C8—21no—
767C8—41no—
768C8—861no—
769C8—861no—
770C8—862no—
771C8—861no—
772C8—861no—
773C8—1721no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—432no—
780C22—432no—
781C22—861no—
782C22—861no—
783C22—861no—
784C22—861no—
785C22—3444no—
786C22—1722no—
787C22—1722no—
788C22—1721no—
789C22—1721no—
790C22—1721no—
791C22C4×D4×D4311yescharacteristic
792C22#124×D4311yescharacteristic
793C22#126×D4311yescharacteristic
794C4—42no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—432no—
799C4—432no—
800C4—1722no—
801C4—1721no—
802C4—1721no—
803C4—1721no—
804C4#117×D4311yescharacteristic
805C4C4×D4×D4311yescharacteristic
806C4#121×D4311yescharacteristic
807C4#123×D4311yescharacteristic
808C2—21no—
809C2—21no—
810C2—81no—
811C2—862no—
812C2—862no—
813C2—3441no—
814C2#388×D4311yescharacteristic
815C2#1914350011yescharacteristic
816C2#1914350311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1929C2
socleC22×C43C2×C4×D4
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1929D43
hypocenterC43#21071
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
1. C2×#14582946C2semidirect
5. #19143011C2semidirect
6. #19135246C2semidirect
7. #19135245C2semidirect
8. #19135244C2semidirect
9. #19135243C2semidirect
10. #19135242C2semidirect
11. #19135241C2semidirect
12. #19135240C2semidirect
13. #339×D43C2semidirect
14. #19134287C2semidirect
15. C43×#1929C2semidirect
24. C2×#13063261C22semidirect
25. C2×#13063260C22semidirect
26. C2×#13063260C22semidirect
31. #14582906C4semidirect
32. #14582906C4semidirect
33. #14582902C4semidirect
34. #14582902C4semidirect
35. #14582899C4semidirect
36. #14582899C4semidirect
37. #14582897C4semidirect
38. #14582897C4semidirect
49. #14582857C22semidirect
51. #14582855C22semidirect
52. #14582854C22semidirect
56. #14582660C22semidirect
57. #14582659C22semidirect
58. #14582658C22semidirect
59. #14582654C22semidirect
60. #14582653C22semidirect
61. #14582653C22semidirect
62. C2×#108×C43C22semidirect
66. C43×#405C22semidirect
67. C43×#339C22semidirect
68. C43×#336C22semidirect
127. #13063250C2×C4semidirect
128. #13063250C2×C4semidirect
129. #13063249C2×C4semidirect
130. #13063249C2×C4semidirect
131. #13063248C2×C4semidirect
132. #13063248C2×C4semidirect
133. #13063247C2×C4semidirect
134. #13063247C2×C4semidirect
135. #13063246C2×C4semidirect
136. #13063246C2×C4semidirect
137. #13063245C2×C4semidirect
138. #13063245C2×C4semidirect
160. #103×C43C2×C4semidirect
161. #103×C43C2×C4semidirect
162. #102×C43C2×C4semidirect
163. #102×C43C2×C4semidirect
412. #1929D43semidirect
435. C2×#108C2×D43semidirect
466. #405C2×D43semidirect
472. #339C2×D43semidirect
476. #336C2×D43semidirect
477. C43#21071semidirect
551. #103C4×D43semidirect
552. #103C4×D43semidirect
559. #102C4×D43semidirect
560. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829462
C2×#104×D432
#191431102
#191430372
#191430112
#191352462
#191352452
#191352442
#191352432
#191352422
#191352412
#191352402
#339×D432
#191342872
C43×#19292
#2107143