Finite Group Databasebeta

← #25119123

Subgroups — #25119123

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×#14583018C211yesmaximal, characteristic, complemented
3C2×#14583013C211yesmaximal, characteristic, complemented
4#19143341C211yesmaximal, characteristic, complemented
5#19143163C211yesmaximal, characteristic, complemented
6#19135427C211yesmaximal, characteristic, complemented
7#19135370C211yesmaximal, characteristic, complemented
8#19135307C211yesmaximal, characteristic, complemented
9#19135300C211yesmaximal, characteristic, complemented
10#19134920C211yesmaximal, characteristic, complemented
11#19134920C211yesmaximal, characteristic, complemented
12#19134871C211yesmaximal, characteristic, complemented
13#19134871C211yesmaximal, characteristic, complemented
14#19134452C211yesmaximal, characteristic, complemented
15C43×#1759C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063333C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063332C2211yescharacteristic
21C2×#13063332C2211yescharacteristic
22#14583449C2211yescharacteristic
23#14583121C411yescharacteristic, complemented
24#14583121C411yescharacteristic, complemented
25#14583114C411yescharacteristic, complemented
26#14583114C411yescharacteristic, complemented
27#14583109C411yescharacteristic, complemented
28#14583104C411yescharacteristic, complemented
29#14583099C411yescharacteristic, complemented
30#14583094C411yescharacteristic, complemented
31#14583018—24no—
32#14583013—24no—
33#14582978—21no—
34#14582972—21no—
35#14582972—21no—
36C8×D172—21no—
37C2×#13063260C2211yescharacteristic
38C2×#13063260C2211yescharacteristic
39#14582926—21no—
40#14582926—21no—
41#14582926C2211yescharacteristic
42#14582926C2211yescharacteristic
43#14582923—21no—
44#14582923C2211yescharacteristic
45C2×C4⋊(C43⋊C8)—21no—
46C2×C4⋊(C43⋊C8)C2211yescharacteristic
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48C2×#13063253C2211yescharacteristic
49C2×#13063253C2211yescharacteristic
50C2×#13063253C2211yescharacteristic
51C2×#13063253C2211yescharacteristic
52#14582893C2211yescharacteristic
53#14582893C2211yescharacteristic
54#14582867C2211yescharacteristic
55#14582867C2211yescharacteristic
56C2×#13063236C2211yescharacteristic
57C2×C4×C43⋊C8C2211yescharacteristic
58#14582663C2211yescharacteristic
59#14582663C2211yescharacteristic
60#14582654C2211yescharacteristic
61#14582654C2211yescharacteristic
62C4×#41×C43C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C2×#104×C43C2211yescharacteristic
65C4×M16×C43C2211yescharacteristic
66C43×#376C2211yescharacteristic
67C43×#339C2211yescharacteristic
68C43×#339C2211yescharacteristic
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#13063333—22no—
84#13063333—22no—
85#13063333—41no—
86#13063333—41no—
87#13063332—22no—
88#13063332—22no—
89#13063332—41no—
90#13063332—41no—
91C2×#10621877—21no—
92C2×#10621877—21no—
93C2×#10621877C2311yescharacteristic
94C2×#10621877C2311yescharacteristic
95C2×#10621872—21no—
96C2×#10621872—21no—
97C22×C43⋊C8—21no—
98C22×C43⋊C8—21no—
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103C2×C8×D43—21no—
104C2×C8×D43—21no—
105#13063325C2×C411yescharacteristic
106#13063322C2×C411yescharacteristic
107#13063313C2×C411yescharacteristic
108#13063313C2×C411yescharacteristic
109#13063299—21no—
110#13063299—21no—
111C4×D172—21no—
112C4×D172—21no—
113#13063260—22no—
114#13063260—22no—
115C4⋊(C43⋊C8)—21no—
116C4⋊(C43⋊C8)—21no—
117C4⋊(C43⋊C8)—21no—
118C4⋊(C43⋊C8)—21no—
119C4⋊(C43⋊C8)—21no—
120C4⋊(C43⋊C8)—21no—
121C4⋊(C43⋊C8)C2×C411yescharacteristic
122C4⋊(C43⋊C8)C2×C411yescharacteristic
123C4⋊(C43⋊C8)C2×C411yescharacteristic
124C4⋊(C43⋊C8)C2×C411yescharacteristic
125C4⋊(C43⋊C8)D411yescharacteristic
126C4⋊(C43⋊C8)D411yescharacteristic
127C4⋊(C43⋊C8)D411yescharacteristic
128C4⋊(C43⋊C8)D411yescharacteristic
129#13063253—22no—
130#13063253—22no—
131#13063253—41no—
132#13063253—41no—
133#13063248C2×C411yescharacteristic
134#13063248C2×C411yescharacteristic
135#13063248C2×C411yescharacteristic
136#13063248C2×C411yescharacteristic
137#13063245C2×C411yescharacteristic
138#13063245C2×C411yescharacteristic
139#13063245C2×C411yescharacteristic
140#13063245C2×C411yescharacteristic
141(C2×D43)⋊C8—21no—
142(C2×D43)⋊C8—21no—
143(C2×D43)⋊C8—21no—
144(C2×D43)⋊C8—21no—
145#13063236—22no—
146C4×C43⋊C8—22no—
147C2×#41×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C2×M16×C43C2311yescharacteristic
150C4×Q8×C43C2×C411yescharacteristic
151C4×Q8×C43C2×C411yescharacteristic
152C4×D4×C43—21no—
153C4×D4×C43—21no—
154C4×D4×C43C2×C411yescharacteristic
155C4×D4×C43C2×C411yescharacteristic
156#117×C43—21no—
157#117×C43C2311yescharacteristic
158C2×C42×C43—21no—
159C2×C42×C43C2311yescharacteristic
160C2×C42×C43C2311yescharacteristic
161C2×C42×C43C2311yescharacteristic
162#104×C43—22no—
163#104×C43D414yescomplemented
164#97×C43—21no—
165C4×C8×C43—21no—
166#95×C43—21no—
167#95×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—21no—
179C22×C4×C43—21no—
180C22×C4×C43#4111yescharacteristic
181C22×C4×C43#4111yescharacteristic
182C22×C4×C43C2411yescharacteristic
183C2×C22⋊D43—21no—
184C2×C22⋊D43—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×C43C2×D412yes—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43C22×C411yescharacteristic
210C4⋊C4×C43C22×C411yescharacteristic
211C22⋊C4×C43—21no—
212C22⋊C4×C43—21no—
213C22⋊C4×C43—21no—
214C42×C43—21no—
215C42×C43—21no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43C22×C411yescharacteristic
221C42×C43C22×C411yescharacteristic
222C42×C43C2×D412yes—
223C42×C43C2×D411yescharacteristic
224C42×C43C2×D411yescharacteristic
225#10621885—22no—
226#10621885—22no—
227#10621884—22no—
228#10621884—22no—
229#10621883—22no—
230#10621883—22no—
231#10621882—22no—
232#10621882—22no—
233(C2×D43)⋊C4—21no—
234(C2×D43)⋊C4—21no—
235(C2×D43)⋊C4—21no—
236(C2×D43)⋊C4—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239#10621877—21no—
240#10621877—21no—
241#10621877—21no—
242#10621877—21no—
243#10621877—42no—
244#10621877—42no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—42no—
256C2×C43⋊C8—42no—
257C2×C43⋊C8C22×C411yescharacteristic
258C2×C43⋊C8C22×C411yescharacteristic
259C2×C43⋊C8C22×C411yescharacteristic
260C2×C43⋊C8C22×C411yescharacteristic
261C2×C43⋊C8C2×D411yescharacteristic
262C2×C43⋊C8C2×D411yescharacteristic
263C2×C43⋊C8C2×D411yescharacteristic
264C2×C43⋊C8C2×D411yescharacteristic
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—22no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—42no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—81no—
294C2×C4×C43C4×D411yescharacteristic
295C2×C4×C43C4×D411yescharacteristic
296C2×C4×C43C4×D411yescharacteristic
297C2×C4×C43C4×D411yescharacteristic
298C2×C4×C43C23×C411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C432−1+411yescharacteristic
304C22⋊D43—41no—
305C22⋊D43—41no—
306C22⋊D43—41no—
307C22⋊D43—41no—
308C2×Dic43—21no—
309C2×Dic43—21no—
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—22no—
325C8×C43—41no—
326C43⋊C8—21no—
327C43⋊C8—21no—
328C43⋊C8—21no—
329C43⋊C8—21no—
330C43⋊C8—21no—
331C43⋊C8—21no—
332C43⋊C8—21no—
333C43⋊C8—21no—
334C43⋊C8—41no—
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—42no—
357C4×C43—41no—
358C4×C43—41no—
359C4×C43—81no—
360C4×C43C2×C4×D411yescharacteristic
361C4×C43#52011yescharacteristic
362C4×C43D4211yescharacteristic
363C4×C43#54811yescharacteristic
364Dic43—41no—
365Dic43—41no—
366#3035—431no—
367C2×#444—431no—
368C2×#443—431no—
369#2935—431no—
370#2906—431no—
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#1759D4311yescharacteristic, complemented
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×#131—431no—
394C2×#131—431no—
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—431no—
414#424—431no—
415#424—861no—
416#424—861no—
417#423—431no—
418#423—861no—
419C2×C4⋊C8—431no—
420C2×C4⋊C8—431no—
421C2×C4⋊C8—861no—
422C2×#104—431no—
423C2×#104—431no—
424C2×#104—431no—
425C2×#104—431no—
426C2×#104C2×D4311yescharacteristic
427C2×#104C2×D4311yescharacteristic
428#416—431no—
429#416—431no—
430#408—431no—
431#408—431no—
432C4×M16C2×D4311yescharacteristic
433C2×#97—431no—
434C2×C4×C8—431no—
435#376C2×D4311yescharacteristic
436#341—431no—
437#341—431no—
438#339C2×D4311yescharacteristic
439#339C2×D4311yescharacteristic
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—862no—
459#131—862no—
460#131—862no—
461#131—862no—
462#131—1721no—
463#131—1721no—
464#131—1721no—
465#131—1721no—
466C2×M16—431no—
467C2×M16—431no—
468C2×M16—861no—
469C2×M16—861no—
470C2×M16—861no—
471C2×M16—861no—
472C2×M16C22×D4311yescharacteristic
473C2×M16C22×D4311yescharacteristic
474C22×C8—431no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8—431no—
478C22×C8—861no—
479C22×C8—861no—
480C22×C8—861no—
481C22×C8—861no—
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×C42C22×D4311yescharacteristic
500C2×C42C22×D4311yescharacteristic
501C2×C42C22×D4311yescharacteristic
502#108—862no—
503#108—862no—
504C4⋊C8—431no—
505C4⋊C8—431no—
506C4⋊C8—431no—
507C4⋊C8—431no—
508C4⋊C8—431no—
509C4⋊C8—431no—
510C4⋊C8—431no—
511C4⋊C8—431no—
512C4⋊C8—861no—
513C4⋊C8—861no—
514C4⋊C8—861no—
515C4⋊C8—861no—
516C4⋊C8—861no—
517C4⋊C8—861no—
518#104—22no—
519#104—862no—
520#104—862no—
521#104—1721no—
522#104—1721no—
523#104D17214yescomplemented
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—21no—
537#97—862no—
538C4×C8—21no—
539C4×C8—862no—
540#95—21no—
541#95—21no—
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#41C2×D17212yes—
553#41#1062189812yes—
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—21no—
569C22×C4—21no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4#1062190011yescharacteristic
573C22×C4#1062190011yescharacteristic
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—861no—
587M16—861no—
588M16—861no—
589M16—861no—
590M16—1722no—
591M16—1722no—
592M16—1722no—
593M16—1722no—
594M16C2×D17212yes—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—431no—
598C2×C8—431no—
599C2×C8—431no—
600C2×C8—431no—
601C2×C8—431no—
602C2×C8—431no—
603C2×C8—431no—
604C2×C8—431no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—1722no—
616C2×C8—1722no—
617C2×C8—1722no—
618C2×C8—1722no—
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—21no—
636C42—21no—
637C42—21no—
638C42C2×C4×D4311yescharacteristic
639C42C2×C4×D4311yescharacteristic
640C42C2×D17212yes—
641C42D4×D4311yescharacteristic
642C42D4×D4311yescharacteristic
643C23—21no—
644C23—861no—
645C23—861no—
646C23C2×#1062190011yescharacteristic
647Q8—21no—
648Q8—861no—
649Q8—861no—
650Q8—861no—
651Q8—861no—
652Q8C4×D17212yes—
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—
666D4C4×D17212yes—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—861no—
683C2×C4—861no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4(C22⋊D43)⋊C411yescharacteristic
689C2×C4(C22⋊D43)⋊C411yescharacteristic
690C2×C4(C22⋊D43)⋊C411yescharacteristic
691C2×C4(C22⋊D43)⋊C411yescharacteristic
692C2×C4C22×C4×D4311yescharacteristic
693C2×C4C2×D4×D4311yescharacteristic
694C2×C4C22×D17211yescharacteristic
695C2×C4C2×#1062189811yescharacteristic
696C2×C4#1306337111yescharacteristic
697C2×C4#1306337211yescharacteristic
698C8—22no—
699C8—41no—
700C8—861no—
701C8—861no—
702C8—861no—
703C8—861no—
704C8—861no—
705C8—861no—
706C8—861no—
707C8—861no—
708C8—1721no—
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×(C22⋊D43)⋊C411yescharacteristic
722C22#1458355311yescharacteristic
723C22#1458359511yescharacteristic
724C4—21no—
725C4—21no—
726C4—22no—
727C4—21no—
728C4—21no—
729C4—42no—
730C4—41no—
731C4—41no—
732C4—81no—
733C4—1721no—
734C4—1721no—
735C4C2×C4×D17211yescharacteristic
736C4#1458337911yescharacteristic
737C4D4×D17211yescharacteristic
738C4#1458355811yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—3441no—
743C2—3441no—
744C2#1913760911yescharacteristic
745C2#1914349411yescharacteristic
746C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1759C2
socleC22×C43C2×C4×D4
prime radical#19144050C2
cosocleC22×C4×C43C24
hypercenter#1759D43
hypocenterC43#23017
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. C2×#14583018C2semidirect
3. C2×#14583013C2semidirect
4. #19143341C2semidirect
5. #19143163C2semidirect
6. #19135427C2semidirect
7. #19135370C2semidirect
8. #19135307C2semidirect
9. #19135300C2semidirect
10. #19134920C2semidirect
11. #19134920C2semidirect
12. #19134871C2semidirect
13. #19134871C2semidirect
14. #19134452C2semidirect
15. C43×#1759C2semidirect
23. #14583121C4semidirect
24. #14583121C4semidirect
25. #14583114C4semidirect
26. #14583114C4semidirect
27. #14583109C4semidirect
28. #14583104C4semidirect
29. #14583099C4semidirect
30. #14583094C4semidirect
163. #104×C43D4semidirect
380. #1759D43semidirect
442. C43#23017semidirect
523. #104D172semidirect

Maximal subgroups

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

subgroupindex
#191440502
C2×#145830182
C2×#145830132
#191433412
#191431632
#191354272
#191353702
#191353072
#191353002
#191349202
#191348712
#191344522
C43×#17592
#2301743