Finite Group Databasebeta

← #25099182

Subgroups — #25099182

Order 11008.

1000 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#430×D43C211yesmaximal, characteristic, complemented
2C2×#14582914C211yesmaximal, characteristic
3#421×D43C211yesmaximal, characteristic
4#413×D43C211yesmaximal, characteristic
5#19143012C211yesmaximal, characteristic, complemented
6#19135267C211yesmaximal, characteristic, complemented
7#19135266C211yesmaximal, characteristic, complemented
8#19135265C211yesmaximal, characteristic, complemented
9#19135264C211yesmaximal, characteristic, complemented
10#19135263C211yesmaximal, characteristic, complemented
11#19135262C211yesmaximal, characteristic, complemented
12#19135261C211yesmaximal, characteristic, complemented
13#344×D43C211yesmaximal, characteristic, complemented
14#19134303C211yesmaximal, characteristic, complemented
15C43×#1932C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×M16×D43C2211yescharacteristic
21C2×#13063282C2211yescharacteristic
22#117×D43C2211yescharacteristic
23#14582948C2211yescharacteristic, complemented
24#14582947C2211yescharacteristic, complemented
25#14582947C2211yescharacteristic, complemented
26#14582946—22no—
27#108×D43—22no—
28#14582917C2211yescharacteristic
29#14582916C2211yescharacteristic
30#14582915C2211yescharacteristic
31#14582914—22no—
32#14582914—21no—
33#14582914—21no—
34#14582914—21no—
35#14582914—21no—
36C2×#13063253C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38C2×#13063251C2211yescharacteristic
39#104×D43—22no—
40#14582883C2211yescharacteristic
41#14582882C412yescomplemented
42#14582881C2211yescharacteristic
43#14582881C2211yescharacteristic
44#14582880C412yescomplemented
45#101×D43C412yescomplemented
46#100×D43C412yescomplemented
47#14582856—21no—
48#14582856—21no—
49#14582853—21no—
50#14582853—21no—
51C4×#10621877C2211yescharacteristic, complemented
52M16×Dic43C2211yescharacteristic, complemented
53M16×Dic43C2211yescharacteristic, complemented
54#14582671C2211yescharacteristic, complemented
55#14582670C2211yescharacteristic, complemented
56#14582669C2211yescharacteristic, complemented
57#14582660C2211yescharacteristic, complemented
58#14582659C2211yescharacteristic, complemented
59#14582658C2211yescharacteristic, complemented
60C43×#430C2211yescharacteristic, complemented
61C43×#421C2211yescharacteristic
62C2×#104×C43C2211yescharacteristic
63C43×#413C2211yescharacteristic
64C4×M16×C43C2211yescharacteristic, complemented
65C43×#344C2211yescharacteristic, complemented
66C43×#339C2211yescharacteristic, complemented
67C2×#10621902C2×C411yescharacteristic
68C2×#10621898—21no—
69C2×#10621898C2311yescharacteristic
70C2×#10621900—21no—
71C2×#10621900C2×C411yescharacteristic
72#41×D43—21no—
73#41×D43—21no—
74#41×D43—21no—
75#41×D43—21no—
76#41×D43—21no—
77#41×D43—21no—
78#41×D43—21no—
79#41×D43—21no—
80C2×Q8×D43C2×C411yescharacteristic
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621872—21no—
90C2×#10621872—21no—
91C2×#10621872—21no—
92C2×#10621872—21no—
93M16×D43—21no—
94M16×D43—21no—
95M16×D43—21no—
96M16×D43—21no—
97M16×D43—21no—
98M16×D43—21no—
99M16×D43—21no—
100M16×D43—21no—
101M16×D43—21no—
102M16×D43—21no—
103M16×D43C2×C412yes—
104M16×D43C2×C412yes—
105M16×D43C2×C412yes—
106M16×D43C2×C412yes—
107M16×D43D412yes—
108M16×D43D412yes—
109C2×C8×D43—21no—
110C2×C8×D43—21no—
111C2×C8×D43—21no—
112C2×C8×D43—21no—
113#13063284C2311yescharacteristic
114#13063283—21no—
115#13063282—21no—
116#13063282—21no—
117#13063282—21no—
118#13063282D411yescharacteristic
119#13063282D411yescharacteristic
120#13063282D411yescharacteristic
121#13063282D411yescharacteristic
122#13063281—21no—
123C2×Dic43⋊C4—21no—
124C4⋊C4×D43—21no—
125C2×(C2×D43)⋊C4—21no—
126C22⋊C4×D43—21no—
127C2×C4×Dic43C2311yescharacteristic
128C42×D43—21no—
129#13063261—22no—
130#13063260—22no—
131#13063260—22no—
132#13063253—21no—
133#13063253—21no—
134#13063253—22no—
135#13063252—21no—
136#13063252—21no—
137#13063252—22no—
138#13063251—22no—
139#13063251—21no—
140#13063251—21no—
141#13063244C2×C412yescomplemented
142#13063243C2×C412yescomplemented
143#13063243C2×C412yescomplemented
144#13063242C2×C412yescomplemented
145#13063241C2×C412yescomplemented
146#13063241C2×C412yescomplemented
147#13063236—21no—
148#13063235—21no—
149#13063235—21no—
150C4×C43⋊C8—21no—
151C8×Dic43—21no—
152C8×Dic43—21no—
153C2×#41×C43C2311yescharacteristic
154C2×M16×C43C2311yescharacteristic
155C2×M16×C43C2311yescharacteristic
156C2×M16×C43C2311yescharacteristic
157C2×M16×C43C2311yescharacteristic
158#117×C43C2311yescharacteristic
159C2×C42×C43C2311yescharacteristic
160#108×C43—22no—
161#104×C43—22no—
162#104×C43—21no—
163#104×C43—21no—
164#101×C43C2×C412yescomplemented
165#100×C43C2×C412yescomplemented
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—21no—
187#10621902—21no—
188#10621902—21no—
189#10621902—21no—
190Q8×D43—21no—
191Q8×D43—21no—
192Q8×D43—21no—
193Q8×D43—21no—
194#10621900—21no—
195#10621900—21no—
196#10621900—21no—
197#10621900—21no—
198#10621900—41no—
199#10621900—41no—
200#10621900—41no—
201#10621900—41no—
202D4×D43—21no—
203D4×D43—21no—
204D4×D43—21no—
205D4×D43—21no—
206D4×D43—41no—
207D4×D43—41no—
208D4×D43—41no—
209D4×D43—41no—
210#10621898—21no—
211#10621898—21no—
212#10621898—21no—
213#10621898—21no—
214#10621898—41no—
215#10621898—41no—
216#10621898—41no—
217#10621898—41no—
218C2×D172—21no—
219C2×D172C22×C411yescharacteristic
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—41no—
224C2×C4×D43—41no—
225C2×C4×D43—41no—
226C2×C4×D43—41no—
227C2×C4×D43—41no—
228C2×C4×D43C22×C411yescharacteristic
229C2×C4×D43C22×C411yescharacteristic
230C2×C4×D43C2×D411yescharacteristic
231C2×C4×D43C2×D411yescharacteristic
232C2×C4×D43C2×D411yescharacteristic
233C2×C4×D43C2×D411yescharacteristic
234C2×C4×D43#4111yescharacteristic
235C2×C4×D43#4111yescharacteristic
236C2×C4×D43#4111yescharacteristic
237C2×C4×D43#4111yescharacteristic
238C2×C4×D43#4111yescharacteristic
239C2×C4×D43#4111yescharacteristic
240C2×Dic86—21no—
241C2×Dic86C22×C411yescharacteristic
242M16×C43—21no—
243M16×C43—21no—
244M16×C43—21no—
245M16×C43—21no—
246M16×C43—21no—
247M16×C43C22×C412yes—
248M16×C43C22×C412yes—
249M16×C43C2×D412yes—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C4⋊C4×C43—21no—
255C22⋊C4×C43—21no—
256C42×C43—21no—
257C42×C43—21no—
258C42×C43C2×D411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C22⋊Dic43—21no—
261(C2×D43)⋊C4—21no—
262(C2×D43)⋊C4—21no—
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—41no—
266C4⋊Dic43—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—41no—
272C4×Dic43—21no—
273C4×Dic43—21no—
274C4×Dic43—41no—
275C4×Dic43C2×D411yescharacteristic
276C4×Dic43C2×D411yescharacteristic
277#10621877—21no—
278#10621877—21no—
279#10621877—21no—
280#10621877—21no—
281#10621877—21no—
282#10621877C22×C412yes—
283#10621877C22×C412yes—
284#10621877C2×D412yes—
285C2×C43⋊C8—21no—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289#10621872—22no—
290#10621872—22no—
291#10621872—22no—
292#10621872—22no—
293#10621872—22no—
294#10621872—22no—
295#10621872—41no—
296#10621872—41no—
297C8×D43—22no—
298C8×D43—22no—
299C8×D43—22no—
300C8×D43—22no—
301C8×D43—22no—
302C8×D43—22no—
303C8×D43—41no—
304C8×D43—41no—
305C23×C43—21no—
306C23×C43C2×#4111yescharacteristic
307C22×D43—21no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—81no—
311C22×D43—82no—
312C22×D43#11711yescharacteristic
313C22×D43#11711yescharacteristic
314C22×D43#12311yescharacteristic
315C22×D43#12311yescharacteristic
316C22×D43#12411yescharacteristic
317C22×D43#12411yescharacteristic
318Q8×C43—21no—
319Q8×C43—21no—
320D4×C43—21no—
321D4×C43—21no—
322D4×C43—41no—
323D4×C43—41no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—81no—
331C2×C4×C43C23×C411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C2×#4111yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C22⋊D43—41no—
338C22⋊D43—41no—
339C22⋊D43—41no—
340C22⋊D43—41no—
341C22⋊D43—41no—
342C22⋊D43—41no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—81no—
350C2×Dic43#11711yescharacteristic
351C2×Dic43#11711yescharacteristic
352C2×Dic43#12311yescharacteristic
353C2×Dic43#12311yescharacteristic
354C2×Dic43#12411yescharacteristic
355C2×Dic43#12411yescharacteristic
356D172—21no—
357D172—21no—
358D172—41no—
359D172—41no—
360C4×D43—41no—
361C4×D43—41no—
362C4×D43—41no—
363C4×D43—41no—
364C4×D43—41no—
365C4×D43—41no—
366C4×D43—82no—
367C4×D43C4×D411yescharacteristic
368C4×D43C4×D411yescharacteristic
369C4×D43C4×D411yescharacteristic
370C4×D43C4×D411yescharacteristic
371C4×D43C4×D411yescharacteristic
372C4×D43C4×D411yescharacteristic
373C4×D43C4×D411yescharacteristic
374C4×D43C4×D411yescharacteristic
375C4×D43#12111yescharacteristic
376C4×D43#12111yescharacteristic
377C4×D43#12111yescharacteristic
378C4×D43#12111yescharacteristic
379C4×D43#12611yescharacteristic
380C4×D43#12611yescharacteristic
381C4×D43#12611yescharacteristic
382C4×D43#12611yescharacteristic
383Dic86—21no—
384Dic86—21no—
385Dic86—41no—
386Dic86—41no—
387C8×C43—22no—
388C8×C43—22no—
389C8×C43—22no—
390C8×C43—41no—
391C43⋊C8—22no—
392C43⋊C8—22no—
393C43⋊C8—22no—
394C43⋊C8—41no—
395#21080—431nomaximal, Sylow
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—81no—
399C22×C43C2×#11711yescharacteristic
400C22×C43C2×#12311yescharacteristic
401C22×C43C2×#12411yescharacteristic
402C2×D43—41no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—82no—
410C2×D43—82no—
411C2×D43—81no—
412C2×D43#38811yescharacteristic
413C2×D43#38811yescharacteristic
414C2×D43#38811yescharacteristic
415C2×D43#38811yescharacteristic
416C4×C43—41no—
417C4×C43—41no—
418C4×C43—41no—
419C4×C43—81no—
420C4×C43C2×C4×D411yescharacteristic
421C4×C43C2×C4×D411yescharacteristic
422C4×C43C2×#12111yescharacteristic
423C4×C43C2×#12611yescharacteristic
424Dic43—41no—
425Dic43—41no—
426Dic43—41no—
427Dic43—81no—
428Dic43#38811yescharacteristic
429Dic43#38811yescharacteristic
430Dic43#38811yescharacteristic
431Dic43#38811yescharacteristic
432C2×#430—431no—
433C2×#421—431no—
434C2×#421—431no—
435C2×#413—431no—
436#2873—431no—
437#1932—431no—
438#1932—431no—
439#1932—431no—
440#1932—431no—
441#1932—431no—
442#1932—431no—
443#1932—431no—
444#1932D4311yescharacteristic, complemented
445C2×#344—431no—
446#1733—431no—
447C2×C43—21no—
448C2×C43—21no—
449C2×C43—21no—
450C2×C43—81no—
451C2×C43C2×#38811yescharacteristic
452D43—21no—
453D43—21no—
454D43—21no—
455D43—21no—
456D43—81no—
457C22×#41—431no—
458C22×M16—431no—
459C22×M16—431no—
460C22×M16—431no—
461C22×M16—431no—
462C2×#117—431no—
463C2×#117—431no—
464#430—431no—
465#430—431no—
466#430—431no—
467#430—862no—
468#430C2×D4311yescharacteristic, complemented
469C2×#108—862no—
470#421—431no—
471#421—431no—
472#421—431no—
473#421—861no—
474#421—861no—
475#421—861no—
476#421—861no—
477#421—862no—
478#421C2×D4311yescharacteristic
479C2×#104—431no—
480C2×#104—431no—
481C2×#104—431no—
482C2×#104—862no—
483C2×#104C2×D4311yescharacteristic
484#413—431no—
485#413—431no—
486#413—431no—
487#413—432no—
488#413—432no—
489#413C2×D4311yescharacteristic
490C2×#101—432no—
491C2×#100—432no—
492#405—861no—
493#405—861no—
494#405—861no—
495#405—861no—
496C4×M16—431no—
497C4×M16—431no—
498C4×M16—431no—
499C4×M16C2×D4311yescharacteristic, complemented
500#344—431no—
501#344—431no—
502#344—431no—
503#344C2×D4311yescharacteristic, complemented
504#339—431no—
505#339—431no—
506#339—431no—
507#339C2×D4311yescharacteristic, complemented
508C43#2108011yescharacteristic, complemented, Sylow
509C2×#41—431no—
510C2×#41—431no—
511C2×#41—431no—
512C2×#41—861no—
513C2×#41—861no—
514C2×#41—861no—
515C2×#41—861no—
516C2×#41—861no—
517C2×#41—861no—
518C2×#41—861no—
519C2×#41—861no—
520C2×#41—861no—
521C2×#41—861no—
522C2×#41C22×D4311yescharacteristic
523C22×Q8—431no—
524C22×D4—431no—
525C22×D4—861no—
526C23×C4—431no—
527C23×C4—861no—
528C2×M16—431no—
529C2×M16—431no—
530C2×M16—431no—
531C2×M16—432no—
532C2×M16—432no—
533C2×M16—432no—
534C2×M16—432no—
535C2×M16—432no—
536C2×M16—432no—
537C2×M16—431no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—861no—
541C2×M16—861no—
542C2×M16—861no—
543C2×M16—861no—
544C2×M16—861no—
545C2×M16—861no—
546C2×M16—861no—
547C2×M16—861no—
548C2×M16—861no—
549C2×M16—861no—
550C2×M16—861no—
551C2×M16—861no—
552C2×M16C22×D4311yescharacteristic
553C2×M16C22×D4311yescharacteristic
554C2×M16C22×D4311yescharacteristic
555C2×M16C22×D4311yescharacteristic
556C22×C8—861no—
557C22×C8—861no—
558C22×C8—861no—
559C22×C8—861no—
560#117—431no—
561#117—431no—
562#117—431no—
563#117—431no—
564#117—431no—
565#117—861no—
566#117—861no—
567#117—861no—
568#117—861no—
569#117—861no—
570#117C22×D4311yescharacteristic
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—431no—
576C2×C42—861no—
577C2×C42C22×D4311yescharacteristic
578#108—22no—
579#108—862no—
580#108—862no—
581#108—862no—
582#104—22no—
583#104—21no—
584#104—21no—
585#104—862no—
586#104—861no—
587#104—861no—
588#104—861no—
589#104—861no—
590#104—862no—
591#104—862no—
592#104—861no—
593#104—861no—
594#101—432no—
595#101—432no—
596#101—432no—
597#101C4×D4312yescomplemented
598#100—432no—
599#100—432no—
600#100—432no—
601#100C4×D4312yescomplemented
602#97—21no—
603#97—861no—
604#97—861no—
605#97—861no—
606C4×C8—21no—
607C4×C8—861no—
608C4×C8—861no—
609C4×C8—861no—
610C24—431no—
611C24—861no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616#41—861no—
617#41—861no—
618#41—861no—
619#41—861no—
620#41—861no—
621#41—861no—
622#41—861no—
623#41—861no—
624#41—861no—
625#41—861no—
626#41—861no—
627#41—861no—
628#41—1721no—
629#41—1721no—
630#41—1721no—
631#41—1721no—
632#41—1721no—
633#41—1721no—
634#41—1721no—
635#41—1721no—
636C2×Q8—431no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—861no—
640C2×Q8—861no—
641C2×Q8—861no—
642C2×Q8C2×C4×D4311yescharacteristic
643C2×D4—21no—
644C2×D4—431no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4—861no—
652C2×D4—861no—
653C2×D4—1721no—
654C2×D4—1721no—
655C2×D4—1721no—
656C2×D4—1721no—
657C2×D4C2×C4×D4311yescharacteristic
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—431no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—1721no—
679C22×C4—1721no—
680C22×C4—1721no—
681C22×C4—1721no—
682C22×C4—1721no—
683C22×C4C23×D4311yescharacteristic
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—432no—
690M16—432no—
691M16—432no—
692M16—862no—
693M16—862no—
694M16—862no—
695M16—862no—
696M16—862no—
697M16—862no—
698M16—861no—
699M16—861no—
700M16—861no—
701M16—861no—
702M16—861no—
703M16—1721no—
704M16—1721no—
705M16C2×C4×D4312yes—
706M16C2×C4×D4312yes—
707M16D4×D4312yes—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—862no—
713C2×C8—862no—
714C2×C8—862no—
715C2×C8—862no—
716C2×C8—862no—
717C2×C8—862no—
718C2×C8—861no—
719C2×C8—861no—
720C2×C8—861no—
721C2×C8—861no—
722C2×C8—1721no—
723C2×C8—1721no—
724C4⋊C4—21no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4—861no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4—1721no—
731C22⋊C4—21no—
732C22⋊C4—861no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C22⋊C4—1721no—
738C42—21no—
739C42—21no—
740C42—431no—
741C42—431no—
742C42—861no—
743C42—861no—
744C42—1721no—
745C42D4×D4311yescharacteristic
746C42D4×D4311yescharacteristic
747C23—21no—
748C23—431no—
749C23—431no—
750C23—431no—
751C23—431no—
752C23—431no—
753C23—431no—
754C23—861no—
755C23—3441no—
756C23—3442no—
757C23—1721no—
758C23—1721no—
759C23#41×D4311yescharacteristic
760Q8—21no—
761Q8—21no—
762Q8—861no—
763Q8—861no—
764Q8—1721no—
765Q8—1721no—
766D4—21no—
767D4—21no—
768D4—41no—
769D4—41no—
770D4—861no—
771D4—861no—
772D4—1721no—
773D4—1721no—
774D4—1721no—
775D4—1721no—
776D4—1721no—
777D4—1721no—
778D4—1721no—
779D4—1721no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—81no—
787C2×C4—431no—
788C2×C4—431no—
789C2×C4—431no—
790C2×C4—431no—
791C2×C4—431no—
792C2×C4—431no—
793C2×C4—431no—
794C2×C4—431no—
795C2×C4—431no—
796C2×C4—431no—
797C2×C4—431no—
798C2×C4—431no—
799C2×C4—431no—
800C2×C4—431no—
801C2×C4—431no—
802C2×C4—431no—
803C2×C4—431no—
804C2×C4—431no—
805C2×C4—431no—
806C2×C4—431no—
807C2×C4—431no—
808C2×C4—431no—
809C2×C4—861no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—3442no—
813C2×C4—3441no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4—1721no—
820C2×C4—1721no—
821C2×C4—1721no—
822C2×C4—1721no—
823C2×C4C22×C4×D4311yescharacteristic
824C2×C4C2×D4×D4311yescharacteristic
825C2×C4C2×D4×D4311yescharacteristic
826C2×C4#41×D4311yescharacteristic
827C2×C4#41×D4311yescharacteristic
828C2×C4#41×D4311yescharacteristic
829C8—22no—
830C8—22no—
831C8—22no—
832C8—41no—
833C8—862no—
834C8—862no—
835C8—862no—
836C8—1721no—
837C22—41no—
838C22—41no—
839C22—81no—
840C22—431no—
841C22—431no—
842C22—431no—
843C22—431no—
844C22—3441no—
845C22—3442no—
846C22—3442no—
847C22—1721no—
848C22—1721no—
849C22—1721no—
850C22—1721no—
851C22—1721no—
852C22—1721no—
853C22—1721no—
854C22#117×D4311yescharacteristic
855C22#123×D4311yescharacteristic
856C22#124×D4311yescharacteristic
857C4—41no—
858C4—41no—
859C4—41no—
860C4—81no—
861C4—431no—
862C4—431no—
863C4—431no—
864C4—431no—
865C4—3441no—
866C4—1721no—
867C4—1721no—
868C4—1721no—
869C4C4×D4×D4311yescharacteristic
870C4C4×D4×D4311yescharacteristic
871C4#121×D4311yescharacteristic
872C4#126×D4311yescharacteristic
873C2—21no—
874C2—21no—
875C2—21no—
876C2—81no—
877C2—861no—
878C2—861no—
879C2—861no—
880C2—861no—
881C2—3441no—
882C2#388×D4311yescharacteristic
subgroupG/H
centerC4#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1932C2
socleC2×C43C2×#388
prime radicalC2×#41×D43C22
cosocleC22×C4×C43C24
hypercenter#1932D43
hypocenterC43#21080
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1932

Complements

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

NH ≅ G/Ntype
1. #430×D43C2semidirect
5. #19143012C2semidirect
6. #19135267C2semidirect
7. #19135266C2semidirect
8. #19135265C2semidirect
9. #19135264C2semidirect
10. #19135263C2semidirect
11. #19135262C2semidirect
12. #19135261C2semidirect
13. #344×D43C2semidirect
14. #19134303C2semidirect
15. C43×#1932C2semidirect
23. #14582948C22semidirect
24. #14582947C22semidirect
25. #14582947C22semidirect
41. #14582882C4semidirect
44. #14582880C4semidirect
45. #101×D43C4semidirect
46. #100×D43C4semidirect
51. C4×#10621877C22semidirect
52. M16×Dic43C22semidirect
53. M16×Dic43C22semidirect
54. #14582671C22semidirect
55. #14582670C22semidirect
56. #14582669C22semidirect
57. #14582660C22semidirect
58. #14582659C22semidirect
59. #14582658C22semidirect
60. C43×#430C22semidirect
64. C4×M16×C43C22semidirect
65. C43×#344C22semidirect
66. C43×#339C22semidirect
141. #13063244C2×C4semidirect
142. #13063243C2×C4semidirect
143. #13063243C2×C4semidirect
144. #13063242C2×C4semidirect
145. #13063241C2×C4semidirect
146. #13063241C2×C4semidirect
164. #101×C43C2×C4semidirect
165. #100×C43C2×C4semidirect
444. #1932D43semidirect
468. #430C2×D43semidirect
499. C4×M16C2×D43semidirect
503. #344C2×D43semidirect
507. #339C2×D43semidirect
508. C43#21080semidirect
597. #101C4×D43semidirect
601. #100C4×D43semidirect

Maximal subgroups

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

subgroupindex
#430×D432
C2×#145829142
#421×D432
#413×D432
#191430122
#191352672
#191352662
#191352652
#191352642
#191352632
#191352622
#191352612
#344×D432
#191343032
C43×#19322
#2108043