Finite Group Databasebeta

← #25119127

Subgroups — #25119127

Order 11008.

864 conjugacy classes of subgroups.

The subgroup lattice has 748 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#19143338C211yesmaximal, characteristic, complemented
5#19135426C211yesmaximal, characteristic, complemented
6#19135368C211yesmaximal, characteristic, complemented
7#19135305C211yesmaximal, characteristic, complemented
8#19135298C211yesmaximal, characteristic, complemented
9#19134922C211yesmaximal, characteristic, complemented
10#19134922C211yesmaximal, characteristic, complemented
11#19134869C211yesmaximal, characteristic, complemented
12#19134869C211yesmaximal, characteristic, complemented
13#19134454C211yesmaximal, characteristic, complemented
14#19134405C211yesmaximal, characteristic, complemented
15C43×#2906C211yesmaximal, 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#14582976—21no—
32#14582969—21no—
33#14582969—21no—
34#14582964—21no—
35C2×#13063260C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37C2×C4⋊(C43⋊C8)C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39C2×#13063252C2211yescharacteristic
40C2×#13063251C2211yescharacteristic
41C2×#13063251C2211yescharacteristic
42C2×#13063251C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44#14582893C2211yescharacteristic
45#14582893C2211yescharacteristic
46#14582865C2211yescharacteristic
47#14582865C2211yescharacteristic
48C4×#10621877C2211yescharacteristic
49C2×#13063235C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51#14582745C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582658C2211yescharacteristic
56#14582653C2211yescharacteristic
57#14582653C2211yescharacteristic
58C2×#131×C43C2211yescharacteristic
59C2×#131×C43C2211yescharacteristic
60C4×#41×C43C2211yescharacteristic
61C43×#424—21no—
62C43×#424—21no—
63C43×#424C2211yescharacteristic
64C43×#424C2211yescharacteristic
65C43×#423—21no—
66C43×#423C2211yescharacteristic
67C2×C4⋊C8×C43—21no—
68C2×C4⋊C8×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—41no—
86#13063331—41no—
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×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105#13063260—22no—
106#13063260—22no—
107C4⋊(C43⋊C8)C2×C411yescharacteristic
108C4⋊(C43⋊C8)C2×C411yescharacteristic
109C4⋊(C43⋊C8)C2×C411yescharacteristic
110C4⋊(C43⋊C8)C2×C411yescharacteristic
111#13063252—22no—
112#13063252D414yescomplemented
113#13063251—22no—
114#13063251—22no—
115#13063251—41no—
116#13063251—41no—
117#13063248C2×C411yescharacteristic
118#13063248C2×C411yescharacteristic
119#13063248C2×C411yescharacteristic
120#13063248C2×C411yescharacteristic
121#13063245C2×C411yescharacteristic
122#13063245C2×C411yescharacteristic
123#13063245C2×C411yescharacteristic
124#13063245C2×C411yescharacteristic
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129#13063236—21no—
130#13063235—22no—
131C4×C43⋊C8—21no—
132C8×Dic43—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C2×#41×C43C2311yescharacteristic
136#131×C43—22no—
137#131×C43—22no—
138#131×C43—41no—
139#131×C43—41no—
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
158C4⋊C8×C43—21no—
159C4⋊C8×C43—21no—
160C4⋊C8×C43—21no—
161C4⋊C8×C43—21no—
162C4⋊C8×C43—21no—
163C4⋊C8×C43—21no—
164C4⋊C8×C43D411yescharacteristic
165C4⋊C8×C43D411yescharacteristic
166C4⋊C8×C43D411yescharacteristic
167C4⋊C8×C43D411yescharacteristic
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—21no—
202M16×C43—21no—
203M16×C43—21no—
204M16×C43—21no—
205M16×C43—42no—
206M16×C43—42no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—42no—
214C2×C8×C43—42no—
215C2×C8×C43C2×D411yescharacteristic
216C2×C8×C43C2×D411yescharacteristic
217C2×C8×C43C2×D411yescharacteristic
218C2×C8×C43C2×D411yescharacteristic
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—21no—
248C4×Dic43—21no—
249C4×Dic43—21no—
250C4×Dic43C2×D412yes—
251#10621877—21no—
252#10621877—21no—
253#10621877—21no—
254#10621877C2×D412yes—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8C22×C411yescharacteristic
262C2×C43⋊C8C22×C411yescharacteristic
263C2×C43⋊C8C22×C411yescharacteristic
264C2×C43⋊C8C22×C411yescharacteristic
265#10621872—42no—
266#10621872—42no—
267C8×D43—42no—
268C8×D43—42no—
269C23×C43—21no—
270C23×C43C2×#4111yescharacteristic
271C22×D43—21no—
272C22×D43—21no—
273Q8×C43—21no—
274Q8×C43C4×D412yes—
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—21no—
278D4×C43C4×D412yes—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—42no—
287C2×C4×C43—81no—
288C2×C4×C43C4×D411yescharacteristic
289C2×C4×C43C4×D411yescharacteristic
290C2×C4×C43C4×D411yescharacteristic
291C2×C4×C43C4×D411yescharacteristic
292C2×C4×C43C23×C411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43H(5,𝔽2)11yescharacteristic
297C2×C4×C432−1+411yescharacteristic
298C22⋊D43—41no—
299C22⋊D43—41no—
300C22⋊D43—41no—
301C22⋊D43—41no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—22no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310D172—21no—
311D172—21no—
312D172—21no—
313D172—21no—
314D172—42no—
315D172—81no—
316C4×D43—41no—
317C4×D43—41no—
318C4×D43—41no—
319C4×D43—41no—
320Dic86—21no—
321Dic86—21no—
322Dic86—21no—
323Dic86—21no—
324C8×C43—21no—
325C8×C43—21no—
326C8×C43—21no—
327C8×C43—21no—
328C8×C43—41no—
329C8×C43—41no—
330C43⋊C8—21no—
331C43⋊C8—21no—
332C43⋊C8—21no—
333C43⋊C8—21no—
334C43⋊C8—22no—
335C43⋊C8—41no—
336#23017—431nomaximal, Sylow
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—22no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43C2×C4×D411yescharacteristic
343C22×C43#54711yescharacteristic
344C22×C43#55311yescharacteristic
345C2×D43—41no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—41no—
351C4×C43—22no—
352C4×C43—21no—
353C4×C43—21no—
354C4×C43—21no—
355C4×C43—21no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43C2×C4×D411yescharacteristic
359C4×C43#52011yescharacteristic
360C4×C43D4211yescharacteristic
361C4×C43#54811yescharacteristic
362Dic43—42no—
363Dic43—41no—
364Dic43—41no—
365Dic43—81no—
366#3035—431no—
367C2×#444—431no—
368C2×#443—431no—
369#2935—431no—
370#2906D4311yescharacteristic, complemented
371#1963—431no—
372#1950—431no—
373#1938—431no—
374#1937—431no—
375#1876—431no—
376#1876—431no—
377#1866—431no—
378#1866—431no—
379#1768—431no—
380#1759—431no—
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—42no—
384C2×C43#236111yescharacteristic
385C2×C43#295511yescharacteristic
386C2×C43#295711yescharacteristic
387D43—81no—
388D43—81no—
389C2×#135—431no—
390C2×#135—431no—
391C2×#131—431no—
392C2×#131—431no—
393C2×#131C2×D4311yescharacteristic
394C2×#131C2×D4311yescharacteristic
395#532—431no—
396C4×#41C2×D4311yescharacteristic
397#464—431no—
398#464—431no—
399#463—431no—
400#463—431no—
401#462—431no—
402#461—431no—
403#460—431no—
404#459—431no—
405#444—864no—
406#443—864no—
407#436—861no—
408#435—861no—
409#435—861no—
410C8×D4—861no—
411C2×#108—431no—
412C2×#108—431no—
413#424—21no—
414#424—21no—
415#424C2×D4311yescharacteristic
416#424C2×D4311yescharacteristic
417#423—21no—
418#423C2×D4311yescharacteristic
419C2×C4⋊C8—21no—
420C2×C4⋊C8—431no—
421C2×C4⋊C8C2×D4311yescharacteristic
422C2×#104—431no—
423C2×#104—431no—
424C2×#104—431no—
425C2×#104—431no—
426C2×#104—431no—
427C2×#104—431no—
428#416—431no—
429#416—431no—
430#408—431no—
431#408—431no—
432C4×M16—431no—
433C2×#97—431no—
434C2×C4×C8—431no—
435#376—431no—
436#341—431no—
437#341—431no—
438#339—431no—
439#339—431no—
440#336—431no—
441#336—431no—
442C43#2301711yescharacteristic, complemented, Sylow
443C2×#41—431no—
444C2×#41—431no—
445C2×#41C22×D4311yescharacteristic
446#135—862no—
447#135—862no—
448#135—862no—
449#135—862no—
450C2×Q16—431no—
451C2×Q16—431no—
452C2×SD16—431no—
453C2×SD16—431no—
454C2×SD16—431no—
455C2×SD16—431no—
456C2×D8—431no—
457C2×D8—431no—
458#131—22no—
459#131—22no—
460#131—41no—
461#131—41no—
462#131—862no—
463#131—862no—
464#131—1721no—
465#131—1721no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—431no—
469C2×M16—431no—
470C2×M16—861no—
471C2×M16—861no—
472C2×M16C22×D4311yescharacteristic
473C2×M16C22×D4311yescharacteristic
474C22×C8—21no—
475C22×C8—21no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—861no—
479C22×C8—861no—
480C22×C8C22×D4311yescharacteristic
481C22×C8C22×D4311yescharacteristic
482C4⋊Q8—431no—
483#127—431no—
484#124—431no—
485#124—431no—
486#121—861no—
487#121—861no—
488C4×Q8C4×D4311yescharacteristic
489C4×Q8C4×D4311yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—861no—
493C4×D4—861no—
494C4×D4C4×D4311yescharacteristic
495C4×D4C4×D4311yescharacteristic
496#117—21no—
497#117C22×D4311yescharacteristic
498C2×C42—21no—
499C2×C42—431no—
500C2×C42—431no—
501C2×C42C22×D4311yescharacteristic
502#108—862no—
503#108—862no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8—21no—
509C4⋊C8—21no—
510C4⋊C8—431no—
511C4⋊C8—431no—
512C4⋊C8—431no—
513C4⋊C8—431no—
514C4⋊C8C22⋊D4311yescharacteristic
515C4⋊C8C22⋊D4311yescharacteristic
516C4⋊C8C22⋊D4311yescharacteristic
517C4⋊C8C22⋊D4311yescharacteristic
518#104—434no—
519#104—862no—
520#104—862no—
521#104—862no—
522#104—1721no—
523#104—1721no—
524#103—431no—
525#103—431no—
526#103—431no—
527#103—431no—
528#102—431no—
529#102—431no—
530#102—431no—
531#102—431no—
532C22⋊C8—861no—
533C22⋊C8—861no—
534C22⋊C8—861no—
535C22⋊C8—861no—
536#97—862no—
537#97—861no—
538C4×C8—862no—
539C4×C8—861no—
540#95—861no—
541#95—861no—
542#41—21no—
543#41—21no—
544#41—861no—
545#41—861no—
546#41—861no—
547#41—861no—
548#41—861no—
549#41—861no—
550#41—861no—
551#41—861no—
552#41D4×D4312yes—
553#41#1062190212yes—
554C2×Q8—431no—
555C2×Q8—431no—
556C2×Q8C2×C4×D4311yescharacteristic
557C2×D4—21no—
558C2×D4—431no—
559C2×D4—431no—
560C2×D4—861no—
561C2×D4—861no—
562C2×D4—861no—
563C2×D4—861no—
564C2×D4C2×C4×D4311yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4#1062189811yescharacteristic
573C22×C4#1062189811yescharacteristic
574C22×C4C23×D4311yescharacteristic
575Q16—862no—
576Q16—862no—
577SD16—862no—
578SD16—862no—
579SD16—862no—
580SD16—862no—
581D8—862no—
582D8—862no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—42no—
588M16—42no—
589M16—432no—
590M16—861no—
591M16—861no—
592M16—861no—
593M16—1722no—
594M16—1722no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—431no—
604C2×C8—431no—
605C2×C8—431no—
606C2×C8—431no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—1722no—
614C2×C8—1722no—
615C2×C8C2×C22⋊D4311yescharacteristic
616C2×C8C2×C22⋊D4311yescharacteristic
617C2×C8C2×C22⋊D4311yescharacteristic
618C2×C8C2×C22⋊D4311yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4C2×C4×D4311yescharacteristic
624C4⋊C4C2×C4×D4311yescharacteristic
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—861no—
629C22⋊C4—861no—
630C22⋊C4—861no—
631C22⋊C4—861no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—432no—
636C42—861no—
637C42—861no—
638C42—861no—
639C42C2×C4×D4311yescharacteristic
640C42C2×C4×D4311yescharacteristic
641C42C2×C22⋊D4311yescharacteristic
642C42C2×C22⋊D4311yescharacteristic
643C23—21no—
644C23—861no—
645C23—861no—
646C23C2×#1062189811yescharacteristic
647Q8—21no—
648Q8—861no—
649Q8—861no—
650Q8—861no—
651Q8—861no—
652Q8#1306328712yes—
653D4—22no—
654D4—22no—
655D4—21no—
656D4—861no—
657D4—861no—
658D4—861no—
659D4—861no—
660D4—3441no—
661D4—1722no—
662D4—1721no—
663D4—1721no—
664D4—1721no—
665D4—1721no—
666D4#1306328712yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—81no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—862no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4C4×C22⋊D4311yescharacteristic
689C2×C4C4×C22⋊D4311yescharacteristic
690C2×C4C4×C22⋊D4311yescharacteristic
691C2×C4C4×C22⋊D4311yescharacteristic
692C2×C4C22×C4×D4311yescharacteristic
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C22×C22⋊D4311yescharacteristic
695C2×C4C2×#1062190211yescharacteristic
696C2×C4#1306337011yescharacteristic
697C2×C4#1306337311yescharacteristic
698C8—21no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—41no—
703C8—41no—
704C8—861no—
705C8—861no—
706C8—861no—
707C8—861no—
708C8—862no—
709C8—1721no—
710C22—21no—
711C22—21no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—1721no—
716C22—1721no—
717C22—1721no—
718C22—1721no—
719C22—1721no—
720C22—1721no—
721C22C2×C4×C22⋊D4311yescharacteristic
722C22#1458355011yescharacteristic
723C22#1458359711yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—41no—
730C4—41no—
731C4—3441no—
732C4—1722no—
733C4—1721no—
734C4—1721no—
735C4C2×#1306328711yescharacteristic
736C4#1458338011yescharacteristic
737C4D4×C22⋊D4311yescharacteristic
738C4#1458356011yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—3441no—
743C2—3441no—
744C2#1913761111yescharacteristic
745C2#1914349611yescharacteristic
746C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2906C2
socleC22×C43C2×C4×D4
prime radical#19144050C2
cosocleC22×C4×C43C24
hypercenter#2906D43
hypocenterC43#23017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. C2×#14583014C2semidirect
4. #19143338C2semidirect
5. #19135426C2semidirect
6. #19135368C2semidirect
7. #19135305C2semidirect
8. #19135298C2semidirect
9. #19134922C2semidirect
10. #19134922C2semidirect
11. #19134869C2semidirect
12. #19134869C2semidirect
13. #19134454C2semidirect
14. #19134405C2semidirect
15. C43×#2906C2semidirect
21. #14583121C4semidirect
22. #14583121C4semidirect
23. #14583114C4semidirect
24. #14583114C4semidirect
25. #14583109C4semidirect
26. #14583104C4semidirect
27. #14583099C4semidirect
28. #14583094C4semidirect
112. #13063252D4semidirect
370. #2906D43semidirect
442. C43#23017semidirect

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
#191433382
#191354262
#191353682
#191353052
#191352982
#191349222
#191348692
#191344542
#191344052
C43×#29062
#2301743