Finite Group Databasebeta

← #25103063

Subgroups — #25103063

Order 11008.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144050C211yesmaximal, characteristic
2C2×#14583019C211yesmaximal, characteristic, complemented
3C2×#14583014C211yesmaximal, characteristic, complemented
4#19143314C211yesmaximal, characteristic, complemented
5#19135514C211yesmaximal, characteristic, complemented
6#19135370C211yesmaximal, characteristic, complemented
7#19135243C211yesmaximal, characteristic, complemented
8#19135243C211yesmaximal, characteristic, complemented
9#19134922C211yesmaximal, characteristic, complemented
10#19134922C211yesmaximal, characteristic, complemented
11#19134615C211yesmaximal, characteristic, complemented
12#19134467C211yesmaximal, characteristic, complemented
13#19134441C211yesmaximal, characteristic, complemented
14#19134434C211yesmaximal, characteristic, complemented
15C43×#2875C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20#14583449C2211yescharacteristic
21#14583121C411yescharacteristic, complemented
22#14583121C411yescharacteristic, complemented
23#14583114C411yescharacteristic, complemented
24#14583114C411yescharacteristic, complemented
25#14583109C411yescharacteristic, complemented
26#14583104C411yescharacteristic, complemented
27#14583099C411yescharacteristic, complemented
28#14583094C411yescharacteristic, complemented
29#14583019—24no—
30#14583014—24no—
31#14582972—21no—
32#14582972—21no—
33#14582972—21no—
34#14582972—21no—
35C2×#13063260C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37#14582923C2211yescharacteristic
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39C2×#13063252C2211yescharacteristic
40C2×#13063252C2211yescharacteristic
41C2×#13063251C2211yescharacteristic
42C2×#13063251C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44C2×#13063251C2211yescharacteristic
45#14582893C2211yescharacteristic
46#14582893C2211yescharacteristic
47#14582865C2211yescharacteristic
48#14582865C2211yescharacteristic
49C2×#13063235C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51C4×C4⋊Dic43C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582658C2211yescharacteristic
56#14582653C2211yescharacteristic
57#14582653C2211yescharacteristic
58C2×#131×C43C2211yescharacteristic
59C2×#131×C43C2211yescharacteristic
60C4×#41×C43C2211yescharacteristic
61C43×#405—21no—
62C43×#405—21no—
63C43×#405C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C4×M16×C43—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#97×C43—21no—
68C2×#97×C43C2211yescharacteristic
69C2×#10621898C2311yescharacteristic
70C2×#10621898C2311yescharacteristic
71#13063345—22no—
72#13063345—22no—
73#13063345—22no—
74#13063345—22no—
75C2×#10621885C2×C411yescharacteristic
76C2×#10621885C2×C411yescharacteristic
77C2×#10621883C2×C411yescharacteristic
78C2×#10621883C2×C411yescharacteristic
79C2×#10621884C2×C411yescharacteristic
80C2×#10621884C2×C411yescharacteristic
81C2×#10621882C2×C411yescharacteristic
82C2×#10621882C2×C411yescharacteristic
83#13063331—22no—
84#13063331—22no—
85#13063331—22no—
86#13063331—22no—
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621872—21no—
90C2×#10621872—21no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—21no—
94C2×C8×D43—21no—
95#13063325C2×C411yescharacteristic
96#13063322C2×C411yescharacteristic
97#13063313C2×C411yescharacteristic
98#13063313C2×C411yescharacteristic
99#13063299—21no—
100#13063299—21no—
101C4×D172—21no—
102C4×D172—21no—
103C2×C4⋊Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106#13063260—22no—
107#13063260—22no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)C2×C411yescharacteristic
111C4⋊(C43⋊C8)C2×C411yescharacteristic
112C4⋊(C43⋊C8)C2×C411yescharacteristic
113C4⋊(C43⋊C8)C2×C411yescharacteristic
114#13063252—22no—
115#13063252—22no—
116#13063251—22no—
117#13063251—22no—
118#13063251—22no—
119#13063251—22no—
120#13063248C2×C411yescharacteristic
121#13063248C2×C411yescharacteristic
122#13063248C2×C411yescharacteristic
123#13063248C2×C411yescharacteristic
124#13063245C2×C411yescharacteristic
125#13063245C2×C411yescharacteristic
126#13063245C2×C411yescharacteristic
127#13063245C2×C411yescharacteristic
128(C2×D43)⋊C8—21no—
129(C2×D43)⋊C8—21no—
130(C2×D43)⋊C8—21no—
131(C2×D43)⋊C8—21no—
132#13063235—22no—
133C8×Dic43—22no—
134C43⋊#95—21no—
135C2×#41×C43C2311yescharacteristic
136#131×C43—22no—
137#131×C43—22no—
138#131×C43—22no—
139#131×C43D414yescomplemented
140C2×M16×C43—21no—
141C2×M16×C43—21no—
142C2×M16×C43C2311yescharacteristic
143C2×M16×C43C2311yescharacteristic
144C22×C8×C43—21no—
145C22×C8×C43—21no—
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C4×Q8×C43C2×C411yescharacteristic
149C4×Q8×C43C2×C411yescharacteristic
150C4×D4×C43—21no—
151C4×D4×C43—21no—
152C4×D4×C43C2×C411yescharacteristic
153C4×D4×C43C2×C411yescharacteristic
154#117×C43—21no—
155#117×C43C2311yescharacteristic
156C2×C42×C43—21no—
157C2×C42×C43C2311yescharacteristic
158#97×C43—21no—
159#97×C43—21no—
160#97×C43—21no—
161#97×C43D411yescharacteristic
162#97×C43D411yescharacteristic
163#97×C43D411yescharacteristic
164#97×C43D411yescharacteristic
165C4×C8×C43—21no—
166C4×C8×C43—21no—
167C4×C8×C43—21no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43C2×D412yes—
171#41×C43#4112yes—
172C2×Q8×C43C22×C411yescharacteristic
173C2×D4×C43—21no—
174C2×D4×C43C22×C411yescharacteristic
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43#4111yescharacteristic
179C22×C4×C43#4111yescharacteristic
180C22×C4×C43C2411yescharacteristic
181C2×C22⋊D43—21no—
182C2×C22⋊D43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185#10621898—21no—
186#10621898—21no—
187#10621898—21no—
188#10621898—21no—
189#10621898—21no—
190#10621898—21no—
191#10621898—21no—
192#10621898—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172C22×C411yescharacteristic
196C2×D172C22×C411yescharacteristic
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×Dic86C22×C411yescharacteristic
200C2×Dic86C22×C411yescharacteristic
201M16×C43—24no—
202M16×C43—21no—
203M16×C43—21no—
204M16×C43—24no—
205M16×C43C2×D412yes—
206M16×C43#4112yes—
207C2×C8×C43—24no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—24no—
213C2×C8×C43C2×D412yes—
214C2×C8×C43C2×D411yescharacteristic
215C2×C8×C43C2×D411yescharacteristic
216C2×C8×C43C2×D411yescharacteristic
217C2×C8×C43C2×D411yescharacteristic
218C2×C8×C43#4112yes—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43C22×C411yescharacteristic
222C4⋊C4×C43C22×C411yescharacteristic
223C22⋊C4×C43—21no—
224C22⋊C4×C43—21no—
225C22⋊C4×C43—21no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43C22×C411yescharacteristic
230C42×C43C22×C411yescharacteristic
231C42×C43C2×D411yescharacteristic
232C42×C43C2×D411yescharacteristic
233#10621885—22no—
234#10621885—22no—
235#10621884—22no—
236#10621884—22no—
237#10621883—22no—
238#10621883—22no—
239#10621882—22no—
240#10621882—22no—
241(C2×D43)⋊C4—21no—
242(C2×D43)⋊C4—21no—
243(C2×D43)⋊C4—21no—
244(C2×D43)⋊C4—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—42no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43—21no—
251C4×Dic43—21no—
252#10621877—21no—
253#10621877—21no—
254#10621877—21no—
255#10621877—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8C22×C411yescharacteristic
263C2×C43⋊C8C22×C411yescharacteristic
264C2×C43⋊C8C22×C411yescharacteristic
265C2×C43⋊C8C22×C411yescharacteristic
266#10621872—42no—
267#10621872—42no—
268C8×D43—42no—
269C8×D43—42no—
270C23×C43—21no—
271C23×C43C2×#4111yescharacteristic
272C22×D43—21no—
273C22×D43—21no—
274Q8×C43—21no—
275Q8×C43C4×D412yes—
276D4×C43—22no—
277D4×C43—22no—
278D4×C43—21no—
279D4×C43C4×D412yes—
280C2×C4×C43—21no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—81no—
288C2×C4×C43—81no—
289C2×C4×C43C4×D411yescharacteristic
290C2×C4×C43C4×D411yescharacteristic
291C2×C4×C43C4×D411yescharacteristic
292C2×C4×C43C4×D411yescharacteristic
293C2×C4×C43C23×C411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43C2×#4111yescharacteristic
299C22⋊D43—41no—
300C22⋊D43—41no—
301C22⋊D43—41no—
302C22⋊D43—41no—
303C2×Dic43—22no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311D172—21no—
312D172—21no—
313D172—21no—
314D172—21no—
315D172—81no—
316D172—81no—
317C4×D43—41no—
318C4×D43—41no—
319C4×D43—41no—
320C4×D43—41no—
321Dic86—21no—
322Dic86—21no—
323Dic86—21no—
324Dic86—21no—
325C8×C43—22no—
326C8×C43—21no—
327C8×C43—22no—
328C8×C43—21no—
329C8×C43#12112yes—
330C8×C43#12112yes—
331C43⋊C8—21no—
332C43⋊C8—21no—
333C43⋊C8—21no—
334C43⋊C8—21no—
335C43⋊C8—41no—
336C43⋊C8—41no—
337#21519—431nomaximal, Sylow
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—22no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43C2×C4×D411yescharacteristic
344C22×C43#52911yescharacteristic
345C22×C43#53211yescharacteristic
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C4×C43—21no—
353C4×C43—21no—
354C4×C43—21no—
355C4×C43—21no—
356C4×C43—22no—
357C4×C43—41no—
358C4×C43—41no—
359C4×C43C2×C4×D411yescharacteristic
360C4×C43C4×#4111yescharacteristic
361C4×C43C2×#12111yescharacteristic
362C4×C43#52511yescharacteristic
363Dic43—42no—
364Dic43—41no—
365Dic43—41no—
366Dic43—81no—
367#3035—431no—
368C2×#444—431no—
369C2×#443—431no—
370#2932—431no—
371#2875D4311yescharacteristic, complemented
372#1980—431no—
373#1950—431no—
374#1929—431no—
375#1929—431no—
376#1876—431no—
377#1876—431no—
378#1806—431no—
379#1771—431no—
380#1765—431no—
381#1764—431no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—42no—
385C2×C43C4×#12111yescharacteristic
386C2×C43#295611yescharacteristic
387C2×C43#295711yescharacteristic
388D43—81no—
389D43—81no—
390C2×#135—431no—
391C2×#135—431no—
392C2×#131—431no—
393C2×#131—431no—
394C2×#131C2×D4311yescharacteristic
395C2×#131C2×D4311yescharacteristic
396#532—431no—
397C4×#41C2×D4311yescharacteristic
398#464—431no—
399#464—431no—
400#463—431no—
401#463—431no—
402#462—431no—
403#461—431no—
404#460—431no—
405#459—431no—
406#444—864no—
407#443—864no—
408#435—861no—
409#435—861no—
410#435—861no—
411#435—861no—
412C2×#108—431no—
413C2×#108—431no—
414#423—431no—
415C2×C4⋊C8—431no—
416C2×#104—431no—
417C2×#104—431no—
418C2×#104—431no—
419C2×#104—431no—
420C2×#104—431no—
421C2×#104—431no—
422#416—431no—
423#416—431no—
424#408—431no—
425#408—431no—
426#405—21no—
427#405—21no—
428#405C2×D4311yescharacteristic
429#405C2×D4311yescharacteristic
430C4×M16—21no—
431C4×M16C2×D4311yescharacteristic
432C2×#97—21no—
433C2×#97—431no—
434C2×#97C2×D4311yescharacteristic
435C2×C4×C8—431no—
436C4×C4⋊C4—431no—
437#341—431no—
438#341—431no—
439#339—431no—
440#339—431no—
441#336—431no—
442#336—431no—
443C43#2151911yescharacteristic, complemented, Sylow
444C2×#41—431no—
445C2×#41—431no—
446C2×#41C22×D4311yescharacteristic
447#135—862no—
448#135—862no—
449#135—862no—
450#135—862no—
451C2×Q16—431no—
452C2×Q16—431no—
453C2×SD16—431no—
454C2×SD16—431no—
455C2×SD16—431no—
456C2×SD16—431no—
457C2×D8—431no—
458C2×D8—431no—
459#131—22no—
460#131—22no—
461#131—22no—
462#131—862no—
463#131—862no—
464#131—862no—
465#131—862no—
466#131D17214yescomplemented
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—431no—
470C2×M16—431no—
471C2×M16—861no—
472C2×M16—861no—
473C2×M16C22×D4311yescharacteristic
474C2×M16C22×D4311yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—431no—
478C22×C8—431no—
479C22×C8—861no—
480C22×C8—861no—
481C22×C8C22×D4311yescharacteristic
482C22×C8C22×D4311yescharacteristic
483C4⋊Q8—431no—
484#127—431no—
485#124—431no—
486#124—431no—
487#121—861no—
488#121—861no—
489C4×Q8C4×D4311yescharacteristic
490C4×Q8C4×D4311yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—861no—
494C4×D4—861no—
495C4×D4C4×D4311yescharacteristic
496C4×D4C4×D4311yescharacteristic
497#117—21no—
498#117C22×D4311yescharacteristic
499C2×C4⋊C4—861no—
500C2×C42—21no—
501C2×C42—431no—
502C2×C42—431no—
503C2×C42C22×D4311yescharacteristic
504#108—862no—
505#108—862no—
506C4⋊C8—431no—
507C4⋊C8—431no—
508C4⋊C8—431no—
509C4⋊C8—431no—
510C4⋊C8—861no—
511C4⋊C8—861no—
512#104—862no—
513#104—862no—
514#104—862no—
515#104—862no—
516#104—862no—
517#104—862no—
518#103—431no—
519#103—431no—
520#103—431no—
521#103—431no—
522#102—431no—
523#102—431no—
524#102—431no—
525#102—431no—
526C22⋊C8—861no—
527C22⋊C8—861no—
528C22⋊C8—861no—
529C22⋊C8—861no—
530#97—21no—
531#97—21no—
532#97—21no—
533#97—862no—
534#97C22⋊D4311yescharacteristic
535#97C22⋊D4311yescharacteristic
536#97C22⋊D4311yescharacteristic
537#97C22⋊D4311yescharacteristic
538C4×C8—21no—
539C4×C8—21no—
540C4×C8—21no—
541C4×C8—862no—
542#95—861no—
543#41—21no—
544#41—21no—
545#41—861no—
546#41—861no—
547#41—861no—
548#41—861no—
549#41—861no—
550#41—861no—
551#41—861no—
552#41—861no—
553#41C2×D17212yes—
554#41#1062189812yes—
555C2×Q8—431no—
556C2×Q8—431no—
557C2×Q8C2×C4×D4311yescharacteristic
558C2×D4—21no—
559C2×D4—431no—
560C2×D4—431no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4—861no—
565C2×D4C2×C4×D4311yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4#1062189811yescharacteristic
574C22×C4#1062189811yescharacteristic
575C22×C4C23×D4311yescharacteristic
576Q16—862no—
577Q16—862no—
578SD16—862no—
579SD16—862no—
580SD16—862no—
581SD16—862no—
582D8—862no—
583D8—862no—
584M16—24no—
585M16—21no—
586M16—21no—
587M16—24no—
588M16—861no—
589M16—861no—
590M16—861no—
591M16—861no—
592M16—1722no—
593M16—1722no—
594M16C2×D17212yes—
595M16#1062189812yes—
596C2×C8—24no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—24no—
602C2×C8—431no—
603C2×C8—431no—
604C2×C8—431no—
605C2×C8—431no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—1722no—
613C2×C8—1722no—
614C2×C8C2×D17212yes—
615C2×C8#1062189812yes—
616C2×C8C2×C22⋊D4311yescharacteristic
617C2×C8C2×C22⋊D4311yescharacteristic
618C2×C8C2×C22⋊D4311yescharacteristic
619C2×C8C2×C22⋊D4311yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—1722no—
625C4⋊C4C2×C4×D4311yescharacteristic
626C4⋊C4C2×C4×D4311yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—861no—
631C22⋊C4—861no—
632C22⋊C4—861no—
633C22⋊C4—861no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—861no—
638C42—861no—
639C42—861no—
640C42—861no—
641C42C2×C4×D4311yescharacteristic
642C42C2×C4×D4311yescharacteristic
643C42C2×C22⋊D4311yescharacteristic
644C42C2×C22⋊D4311yescharacteristic
645C23—21no—
646C23—861no—
647C23—861no—
648C23C2×#1062189811yescharacteristic
649Q8—21no—
650Q8—861no—
651Q8—861no—
652Q8—861no—
653Q8—861no—
654Q8C4×D17212yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—861no—
659D4—861no—
660D4—861no—
661D4—861no—
662D4—3441no—
663D4—3441no—
664D4—1721no—
665D4—1721no—
666D4—1721no—
667D4—1721no—
668D4C4×D17212yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—862no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4C4×C22⋊D4311yescharacteristic
691C2×C4C4×C22⋊D4311yescharacteristic
692C2×C4C4×C22⋊D4311yescharacteristic
693C2×C4C4×C22⋊D4311yescharacteristic
694C2×C4C22×C4×D4311yescharacteristic
695C2×C4C22×C22⋊D4311yescharacteristic
696C2×C4C22×D17211yescharacteristic
697C2×C4C2×#1062189811yescharacteristic
698C2×C4C2×#1062189811yescharacteristic
699C2×C4C2×#1062189811yescharacteristic
700C8—22no—
701C8—21no—
702C8—22no—
703C8—21no—
704C8—861no—
705C8—861no—
706C8—861no—
707C8—861no—
708C8—1721no—
709C8—1721no—
710C8#1306329912yes—
711C8#1306329912yes—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—1721no—
718C22—1721no—
719C22—1721no—
720C22—1721no—
721C22—1721no—
722C22—1721no—
723C22C2×C4×C22⋊D4311yescharacteristic
724C22#1458343311yescharacteristic
725C22#1458344911yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—3441no—
734C4—1722no—
735C4—1721no—
736C4—1721no—
737C4C2×C4×D17211yescharacteristic
738C4C4×#1062189811yescharacteristic
739C4C2×#1306329911yescharacteristic
740C4#1458341011yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—3441no—
745C2—3441no—
746C2C4×#1306329911yescharacteristic
747C2#1914350211yescharacteristic
748C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2875C2
socleC22×C43C2×C4×D4
prime radical#19144050C2
cosocleC22×C4×C43C24
hypercenter#2875D43
hypocenterC43#21519
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. C2×#14583014C2semidirect
4. #19143314C2semidirect
5. #19135514C2semidirect
6. #19135370C2semidirect
7. #19135243C2semidirect
8. #19135243C2semidirect
9. #19134922C2semidirect
10. #19134922C2semidirect
11. #19134615C2semidirect
12. #19134467C2semidirect
13. #19134441C2semidirect
14. #19134434C2semidirect
15. C43×#2875C2semidirect
21. #14583121C4semidirect
22. #14583121C4semidirect
23. #14583114C4semidirect
24. #14583114C4semidirect
25. #14583109C4semidirect
26. #14583104C4semidirect
27. #14583099C4semidirect
28. #14583094C4semidirect
139. #131×C43D4semidirect
371. #2875D43semidirect
443. C43#21519semidirect
466. #131D172semidirect

Maximal subgroups

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

subgroupindex
#191440502
C2×#145830192
C2×#145830142
#191433142
#191355142
#191353702
#191352432
#191349222
#191346152
#191344672
#191344412
#191344342
C43×#28752
#2151943