Finite Group Databasebeta

← #25110483

Subgroups — #25110483

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145019C211yesmaximal, characteristic
2#19143311C211yesmaximal, characteristic, complemented
3#19143310C211yesmaximal, characteristic, complemented
4#19135425C211yesmaximal, characteristic, complemented
5#19135425C211yesmaximal, characteristic, complemented
6#19134925C211yesmaximal, characteristic, complemented
7#19134924C211yesmaximal, characteristic, complemented
8#19134923C211yesmaximal, characteristic, complemented
9#19134922C211yesmaximal, characteristic, complemented
10#19134921C211yesmaximal, characteristic, complemented
11#19134920C211yesmaximal, characteristic, complemented
12#19134919C211yesmaximal, characteristic, complemented
13#19134731C211yesmaximal, characteristic, complemented
14#19134345C211yesmaximal, characteristic, complemented
15C43×#1876C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063332C2211yescharacteristic
21C2×#13063331C2211yescharacteristic
22#14583445C2211yescharacteristic
23#14583445C2211yescharacteristic
24#14583284C411yescharacteristic, complemented
25#14583282C411yescharacteristic, complemented
26#14583280C411yescharacteristic, complemented
27#14583280C411yescharacteristic, complemented
28#14583277C411yescharacteristic, complemented
29#14583274C411yescharacteristic, complemented
30#14583270C411yescharacteristic, complemented
31#14583270C411yescharacteristic, complemented
32#14582973—21no—
33#14582973—21no—
34#14582970—21no—
35#14582970—21no—
36#14582968—21no—
37#14582968—21no—
38#14582967—21no—
39#14582967—21no—
40#14582922C2211yescharacteristic
41#14582922C2211yescharacteristic
42C2×#13063253C2211yescharacteristic
43C2×#13063253C2211yescharacteristic
44C2×#13063252C2211yescharacteristic
45C2×#13063252C2211yescharacteristic
46C2×#13063251C2211yescharacteristic
47C2×#13063251C2211yescharacteristic
48#14582867C2211yescharacteristic
49#14582866C2211yescharacteristic
50#14582865C2211yescharacteristic
51C2×#13063235C2211yescharacteristic
52C2×C8×Dic43C2211yescharacteristic
53#14582745C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582663C2211yescharacteristic
56#14582663C2211yescharacteristic
57#14582654C2211yescharacteristic
58#14582653C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#135×C43C2211yescharacteristic
61C2×#131×C43C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C43×#408C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C2×#10621898C2311yescharacteristic
69#13063347—41no—
70#13063347—41no—
71#13063345—41no—
72#13063345—41no—
73#13063345—41no—
74#13063345—41no—
75C2×Dic172C2×C411yescharacteristic
76C2×#10621885C2×C411yescharacteristic
77C2×#10621885C2×C411yescharacteristic
78C2×#10621873C2×C411yescharacteristic
79C2×#10621873C2×C411yescharacteristic
80C2×#10621883C2×C411yescharacteristic
81C2×#10621883C2×C411yescharacteristic
82C2×#10621884C2×C411yescharacteristic
83C2×#10621884C2×C411yescharacteristic
84C2×D344C2×C411yescharacteristic
85C2×#10621882C2×C411yescharacteristic
86C2×#10621882C2×C411yescharacteristic
87#13063333—41no—
88#13063333—41no—
89#13063332—41no—
90#13063332—41no—
91#13063331—41no—
92#13063331—41no—
93C2×#10621877—21no—
94C2×#10621877C2311yescharacteristic
95C2×#10621877C2311yescharacteristic
96C2×#10621872—21no—
97C2×#10621872—21no—
98C22×C43⋊C8—21no—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C2×C8×D43—21no—
102C2×C8×D43—21no—
103#13063323C2×C411yescharacteristic
104#13063323C2×C411yescharacteristic
105#13063321C2×C411yescharacteristic
106#13063321C2×C411yescharacteristic
107#13063314C2×C411yescharacteristic
108#13063314C2×C411yescharacteristic
109#13063312C2×C411yescharacteristic
110#13063312C2×C411yescharacteristic
111#13063297—21no—
112#13063297—21no—
113#13063297—21no—
114#13063297—21no—
115C4×C22⋊D43—21no—
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119C2×C4×Dic43C2311yescharacteristic
120C2×C4×Dic43C2311yescharacteristic
121Dic43⋊C8—21no—
122Dic43⋊C8—21no—
123Dic43⋊C8—21no—
124Dic43⋊C8—21no—
125#13063253—41no—
126#13063253—41no—
127#13063252—41no—
128#13063252—41no—
129#13063251—41no—
130#13063251—41no—
131C22⋊(C43⋊C8)—21no—
132C22⋊(C43⋊C8)—21no—
133(C2×D43)⋊C8—21no—
134(C2×D43)⋊C8—21no—
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137#13063235D411yescharacteristic
138#13063235D411yescharacteristic
139#13063235D411yescharacteristic
140#13063235D411yescharacteristic
141C8×Dic43C2×C411yescharacteristic
142C8×Dic43C2×C411yescharacteristic
143C8×Dic43C2×C411yescharacteristic
144C8×Dic43C2×C411yescharacteristic
145C43⋊#95—21no—
146C43⋊#95—21no—
147C2×#41×C43C2311yescharacteristic
148C2×#41×C43C2311yescharacteristic
149#135×C43—41no—
150#135×C43—41no—
151C2×Q16×C43C2×C411yescharacteristic
152C2×SD16×C43C2×C411yescharacteristic
153C2×SD16×C43C2×C411yescharacteristic
154C2×D8×C43C2×C411yescharacteristic
155#131×C43—41no—
156#131×C43—41no—
157C2×M16×C43—21no—
158C2×M16×C43C2311yescharacteristic
159C2×M16×C43C2311yescharacteristic
160C22×C8×C43—21no—
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163C2×C42×C43C2311yescharacteristic
164#104×C43—41no—
165#104×C43—41no—
166C22⋊C8×C43—21no—
167C22⋊C8×C43—21no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174#41×C43—21no—
175#41×C43—21no—
176C2×Q8×C43C22×C411yescharacteristic
177C2×Q8×C43C22×C411yescharacteristic
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43C22×C411yescharacteristic
181C2×D4×C43C22×C411yescharacteristic
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43C2411yescharacteristic
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—21no—
192C22×Dic43—21no—
193C22×Dic43#4111yescharacteristic
194C22×Dic43#4111yescharacteristic
195#10621898—21no—
196#10621898—21no—
197#10621898—21no—
198#10621898—21no—
199#10621898—21no—
200#10621898—21no—
201#10621898—21no—
202#10621898—21no—
203C2×D172C22×C411yescharacteristic
204C2×D172C22×C411yescharacteristic
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×Dic86C22×C411yescharacteristic
208C2×Dic86C22×C411yescharacteristic
209Q16×C43—41no—
210SD16×C43—41no—
211SD16×C43—41no—
212D8×C43—41no—
213M16×C43—21no—
214M16×C43—21no—
215M16×C43—21no—
216M16×C43—21no—
217M16×C43—42no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C2×C8×C43—42no—
225C2×C8×C43C22×C411yescharacteristic
226C2×C8×C43C22×C411yescharacteristic
227C2×C8×C43C2×D411yescharacteristic
228C2×C8×C43C2×D411yescharacteristic
229C42×C43—21no—
230C42×C43—21no—
231C22⋊Dic43—21no—
232C22⋊Dic43—21no—
233C22⋊Dic43—21no—
234C22⋊Dic43—21no—
235#10621885—41no—
236#10621885—41no—
237#10621884—41no—
238#10621884—41no—
239#10621883—41no—
240#10621883—41no—
241#10621882—41no—
242#10621882—41no—
243(C2×D43)⋊C4—21no—
244(C2×D43)⋊C4—21no—
245(C2×D43)⋊C4—21no—
246(C2×D43)⋊C4—21no—
247Dic43⋊C4—21no—
248Dic43⋊C4—21no—
249Dic43⋊C4—21no—
250Dic43⋊C4—21no—
251C4×Dic43—21no—
252C4×Dic43—21no—
253C4×Dic43C22×C411yescharacteristic
254C4×Dic43C22×C411yescharacteristic
255C4×Dic43C2×D411yescharacteristic
256C4×Dic43C2×D411yescharacteristic
257#10621877—21no—
258#10621877—21no—
259#10621877—21no—
260#10621877—21no—
261#10621877—42no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—42no—
269C2×C43⋊C8C22×C411yescharacteristic
270C2×C43⋊C8C22×C411yescharacteristic
271C2×C43⋊C8C2×D411yescharacteristic
272C2×C43⋊C8C2×D411yescharacteristic
273Dic172—41no—
274D344—41no—
275#10621873—41no—
276#10621873—41no—
277#10621872—42no—
278#10621872—42no—
279C8×D43—42no—
280C8×D43—42no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43C2×#4111yescharacteristic
284C22×D43—21no—
285C22×D43—21no—
286Q8×C43—21no—
287Q8×C43—21no—
288Q8×C43—21no—
289Q8×C43—21no—
290D4×C43—21no—
291D4×C43—21no—
292D4×C43—21no—
293D4×C43—21no—
294D4×C43—41no—
295D4×C43—41no—
296D4×C43—41no—
297D4×C43—41no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43C23×C411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C22⋊D43—41no—
314C22⋊D43—41no—
315C22⋊D43—41no—
316C22⋊D43—41no—
317C22⋊D43—81no—
318C22⋊D43—81no—
319C22⋊D43—81no—
320C22⋊D43—81no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43C4×D411yescharacteristic
329C2×Dic43C4×D411yescharacteristic
330C2×Dic43C4×D411yescharacteristic
331C2×Dic43C4×D411yescharacteristic
332D172—21no—
333D172—21no—
334D172—21no—
335D172—21no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—41no—
340Dic86—21no—
341Dic86—21no—
342Dic86—21no—
343Dic86—21no—
344C8×C43—21no—
345C8×C43—21no—
346C8×C43—21no—
347C8×C43—21no—
348C8×C43—41no—
349C8×C43—41no—
350C43⋊C8—21no—
351C43⋊C8—21no—
352C43⋊C8—21no—
353C43⋊C8—21no—
354C43⋊C8—41no—
355C43⋊C8—41no—
356#22282—431nomaximal, Sylow
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43C2×C4×D411yescharacteristic
366C22×C43#54011yescharacteristic
367C22×C43#54011yescharacteristic
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C4×C43—41no—
375C4×C43—41no—
376C4×C43—81no—
377C4×C43#51811yescharacteristic
378C4×C43#51811yescharacteristic
379C4×C43#53511yescharacteristic
380C4×C43#53511yescharacteristic
381Dic43—21no—
382Dic43—21no—
383Dic43—21no—
384Dic43—21no—
385Dic43—41no—
386Dic43—41no—
387Dic43—81no—
388#3147—431no—
389#2932—431no—
390#2932—431no—
391#1963—431no—
392#1963—431no—
393#1876—431no—
394#1876—431no—
395#1876—431no—
396#1876—431no—
397#1876—431no—
398#1876—431no—
399#1876—431no—
400#1876D4311yescharacteristic, complemented
401#1837—431no—
402#1746—431no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—81no—
406C2×C43—81no—
407C2×C43#232811yescharacteristic
408C2×C43#295711yescharacteristic
409C2×C43#295711yescharacteristic
410D43—81no—
411D43—81no—
412C2×#135—431no—
413C2×#135—431no—
414C2×#135—431no—
415C2×#135C2×D4311yescharacteristic
416C2×#131—431no—
417C2×#131—431no—
418C2×#131—431no—
419C2×#131C2×D4311yescharacteristic
420#532—431no—
421#532—431no—
422#495—431no—
423#495—431no—
424#495—431no—
425#495—431no—
426#494—431no—
427#493—431no—
428#492—431no—
429#492—431no—
430#435—861no—
431#435—861no—
432#435—861no—
433#435—861no—
434#435—861no—
435#435—861no—
436#435—861no—
437#435—861no—
438#423—431no—
439#423—431no—
440C2×#104—431no—
441C2×#104—431no—
442C2×#104—431no—
443C2×#104—431no—
444C2×#104—431no—
445C2×#104—431no—
446C2×#104C2×D4311yescharacteristic
447C2×#104C2×D4311yescharacteristic
448#408—431no—
449#408—431no—
450#408—431no—
451#408C2×D4311yescharacteristic
452C2×#97—431no—
453C2×C4×C8—431no—
454#376—431no—
455#341—431no—
456#341—431no—
457#341—431no—
458#341C2×D4311yescharacteristic
459#336—431no—
460#336—431no—
461#336—431no—
462#336C2×D4311yescharacteristic
463C43#2228211yescharacteristic, complemented, Sylow
464C2×#41—431no—
465C2×#41—431no—
466C2×#41C22×D4311yescharacteristic
467C2×#41C22×D4311yescharacteristic
468#135—41no—
469#135—41no—
470#135—1721no—
471#135—1721no—
472#135—1721no—
473#135—1721no—
474#135—1721no—
475#135—1721no—
476C2×Q16—431no—
477C2×Q16—431no—
478C2×Q16—431no—
479C2×Q16C4×D4311yescharacteristic
480C2×SD16—431no—
481C2×SD16—431no—
482C2×SD16—431no—
483C2×SD16—431no—
484C2×SD16—431no—
485C2×SD16—431no—
486C2×SD16C4×D4311yescharacteristic
487C2×SD16C4×D4311yescharacteristic
488C2×D8—431no—
489C2×D8—431no—
490C2×D8—431no—
491C2×D8C4×D4311yescharacteristic
492#131—41no—
493#131—41no—
494#131—1721no—
495#131—1721no—
496#131—1721no—
497#131—1721no—
498#131—1721no—
499#131—1721no—
500C2×M16—21no—
501C2×M16—431no—
502C2×M16—431no—
503C2×M16—861no—
504C2×M16—861no—
505C2×M16—861no—
506C2×M16C22×D4311yescharacteristic
507C2×M16C22×D4311yescharacteristic
508C22×C8—21no—
509C22×C8—431no—
510C22×C8—431no—
511C22×C8—861no—
512C22×C8—861no—
513C22×C8—861no—
514C22×C8C22×D4311yescharacteristic
515C22×C8C22×D4311yescharacteristic
516C4⋊Q8—431no—
517C4⋊Q8—431no—
518#127—431no—
519#127—431no—
520#124—431no—
521#124—431no—
522#124—431no—
523#124—431no—
524#121—861no—
525#121—861no—
526#121—861no—
527#121—861no—
528C4×D4—861no—
529C4×D4—861no—
530C4×D4—861no—
531C4×D4—861no—
532C2×C42—431no—
533C2×C42—431no—
534C2×C42C22×D4311yescharacteristic
535C4⋊C8—861no—
536C4⋊C8—861no—
537C4⋊C8—861no—
538C4⋊C8—861no—
539#104—41no—
540#104—41no—
541#104—1721no—
542#104—1721no—
543#104—1721no—
544#104—1721no—
545#104—1721no—
546#104—1721no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—861no—
550C22⋊C8—861no—
551C22⋊C8—861no—
552C22⋊C8—861no—
553C22⋊C8—861no—
554C22⋊C8—861no—
555#97—431no—
556#97—431no—
557#97—431no—
558#97—431no—
559C4×C8—431no—
560C4×C8—431no—
561C4×C8—431no—
562C4×C8—431no—
563#95—861no—
564#95—861no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—861no—
574#41—861no—
575#41—861no—
576#41—861no—
577#41—861no—
578#41—861no—
579#41—861no—
580#41—861no—
581C2×Q8—431no—
582C2×Q8—431no—
583C2×Q8C2×C4×D4311yescharacteristic
584C2×Q8C2×C4×D4311yescharacteristic
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—431no—
588C2×D4—431no—
589C2×D4—861no—
590C2×D4—861no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—861no—
595C2×D4C2×C4×D4311yescharacteristic
596C2×D4C2×C4×D4311yescharacteristic
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—431no—
601C22×C4—431no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4C23×D4311yescharacteristic
606Q16—41no—
607Q16—1721no—
608Q16—1721no—
609Q16—1721no—
610SD16—41no—
611SD16—41no—
612SD16—1721no—
613SD16—1721no—
614SD16—1721no—
615SD16—1721no—
616SD16—1721no—
617SD16—1721no—
618D8—41no—
619D8—1721no—
620D8—1721no—
621D8—1721no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—42no—
627M16—861no—
628M16—861no—
629M16—861no—
630M16—861no—
631M16—1722no—
632M16—1722no—
633M16—1722no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—42no—
641C2×C8—431no—
642C2×C8—431no—
643C2×C8—431no—
644C2×C8—431no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8—861no—
650C2×C8—861no—
651C2×C8—1722no—
652C2×C8—1722no—
653C2×C8—1722no—
654C2×C8C2×C4×D4311yescharacteristic
655C2×C8C2×C4×D4311yescharacteristic
656C2×C8D4×D4311yescharacteristic
657C2×C8D4×D4311yescharacteristic
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C22⋊C4—861no—
663C22⋊C4—861no—
664C22⋊C4—861no—
665C22⋊C4—861no—
666C22⋊C4—861no—
667C22⋊C4—861no—
668C22⋊C4—861no—
669C22⋊C4—861no—
670C42—21no—
671C42—21no—
672C42—431no—
673C42—431no—
674C42—431no—
675C42—431no—
676C42—861no—
677C42—861no—
678C23—21no—
679C23—21no—
680C23—861no—
681C23—861no—
682C23#41×D4311yescharacteristic
683Q8—21no—
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—861no—
688Q8—861no—
689Q8—861no—
690Q8—861no—
691D4—21no—
692D4—21no—
693D4—21no—
694D4—21no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—861no—
700D4—861no—
701D4—861no—
702D4—861no—
703D4—3441no—
704D4—3441no—
705D4—3441no—
706D4—3441no—
707D4—1721no—
708D4—1721no—
709D4—1721no—
710D4—1721no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—431no—
721C2×C4—431no—
722C2×C4—431no—
723C2×C4—431no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4C22×C4×D4311yescharacteristic
736C2×C4C2×D4×D4311yescharacteristic
737C2×C4#1306337011yescharacteristic
738C2×C4#1306337011yescharacteristic
739C2×C4#1306337011yescharacteristic
740C2×C4#1306337111yescharacteristic
741C8—21no—
742C8—21no—
743C8—21no—
744C8—21no—
745C8—41no—
746C8—41no—
747C8—861no—
748C8—861no—
749C8—861no—
750C8—861no—
751C8—1721no—
752C8—1721no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—1721no—
762C22—1721no—
763C22—1721no—
764C22—1721no—
765C22—1721no—
766C22—1721no—
767C22C4×D4×D4311yescharacteristic
768C22#1458349911yescharacteristic
769C22#1458350111yescharacteristic
770C4—41no—
771C4—41no—
772C4—81no—
773C4—861no—
774C4—861no—
775C4—861no—
776C4—861no—
777C4—3441no—
778C4—1721no—
779C4—1721no—
780C4#1458337111yescharacteristic
781C4#1458337211yescharacteristic
782C4#1458346411yescharacteristic
783C4#1458346511yescharacteristic
784C2—21no—
785C2—21no—
786C2—81no—
787C2—81no—
788C2—3441no—
789C2—3441no—
790C2#1913731611yescharacteristic
791C2#1914350711yescharacteristic
792C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1876C2
socleC22×C43C2×C4×D4
prime radical#19145019C2
cosocleC22×C4×C43C24
hypercenter#1876D43
hypocenterC43#22282
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. #19143311C2semidirect
3. #19143310C2semidirect
4. #19135425C2semidirect
5. #19135425C2semidirect
6. #19134925C2semidirect
7. #19134924C2semidirect
8. #19134923C2semidirect
9. #19134922C2semidirect
10. #19134921C2semidirect
11. #19134920C2semidirect
12. #19134919C2semidirect
13. #19134731C2semidirect
14. #19134345C2semidirect
15. C43×#1876C2semidirect
24. #14583284C4semidirect
25. #14583282C4semidirect
26. #14583280C4semidirect
27. #14583280C4semidirect
28. #14583277C4semidirect
29. #14583274C4semidirect
30. #14583270C4semidirect
31. #14583270C4semidirect
400. #1876D43semidirect
463. C43#22282semidirect

Maximal subgroups

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

subgroupindex
#191450192
#191433112
#191433102
#191354252
#191349252
#191349242
#191349232
#191349222
#191349212
#191349202
#191349192
#191347312
#191343452
C43×#18762
#2228243