Finite Group Databasebeta

← #25102462

Subgroups — #25102462

Order 11008.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2#19143817C211yesmaximal, characteristic
3C2×#14583022C211yesmaximal, characteristic, complemented
4C2×#14583017C211yesmaximal, characteristic, complemented
5#19143298C211yesmaximal, characteristic, complemented
6#19134921C211yesmaximal, characteristic, complemented
7#19134921C211yesmaximal, characteristic, complemented
8#19134895C211yesmaximal, characteristic, complemented
9#19134873C211yesmaximal, characteristic, complemented
10#19134873C211yesmaximal, characteristic, complemented
11#19134802C211yesmaximal, characteristic, complemented
12#19134540C211yesmaximal, characteristic, complemented
13#19134439C211yesmaximal, characteristic, complemented
14#19134432C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063347C2211yescharacteristic
19#14583665—24no—
20#14583665—24no—
21C2×#13063333—21no—
22C2×#13063333—21no—
23C2×#13063331C2211yescharacteristic
24C2×#13063331C2211yescharacteristic
25C2×#13063331C2211yescharacteristic
26C2×#13063331C2211yescharacteristic
27C2×#13063331C2211yescharacteristic, complemented
28C22×#10621877C2211yescharacteristic
29C2×M16×D43—21no—
30C2×M16×D43—21no—
31#14583410C2211yescharacteristic
32#14583063C411yescharacteristic, complemented
33#14583063C411yescharacteristic, complemented
34#14583057C411yescharacteristic, complemented
35#14583052C411yescharacteristic, complemented
36#14583046C411yescharacteristic, complemented
37#14583046C411yescharacteristic, complemented
38#14583040C411yescharacteristic, complemented
39#14583035C411yescharacteristic, complemented
40#14583022—24no—
41#14583017—24no—
42#14582975—21no—
43#14582975—21no—
44#14582968—21no—
45#14582968—21no—
46C2×#13063261C2211yescharacteristic, complemented
47C2×#13063261C2211yescharacteristic, complemented
48#14582925C2211yescharacteristic, complemented
49C2×#13063253C2211yescharacteristic
50C2×#13063253C2211yescharacteristic
51C2×#13063253C2211yescharacteristic
52C2×#13063253C2211yescharacteristic
53C2×#13063253C2211yescharacteristic, complemented
54C2×#13063253C2211yescharacteristic, complemented
55#14582896C2211yescharacteristic
56#14582896C2211yescharacteristic
57#14582865C2211yescharacteristic, complemented
58#14582863C2211yescharacteristic
59#14582854C2211yescharacteristic, complemented
60#14582664C2211yescharacteristic, complemented
61#14582664C2211yescharacteristic, complemented
62#14582659C2211yescharacteristic, complemented
63#14582659C2211yescharacteristic, complemented
64C22×M16×C43C2211yescharacteristic
65C2×C22⋊C8×C43C2211yescharacteristic
66C2×#97×C43C2211yescharacteristic, complemented
67C2×C4×C8×C43C2211yescharacteristic, complemented
68C4×C22⋊C4×C43C2211yescharacteristic
69C43×#336C2211yescharacteristic, complemented
70C43×#336C2211yescharacteristic, complemented
71C2×#10621898—21no—
72C2×#10621898—21no—
73C2×#10621898—22no—
74C2×#10621898—22no—
75C2×#10621898—22no—
76C2×#10621898—22no—
77C2×#10621898C2×C411yescharacteristic
78C2×#10621898C2×C411yescharacteristic
79C2×#10621898C2311yescharacteristic
80C2×#10621898C2311yescharacteristic
81C2×#10621898C2311yescharacteristic
82C22×Dic86C2×C411yescharacteristic
83C22×D172C2×C411yescharacteristic
84C22×C22⋊D43—21no—
85C22×C4×D43—21no—
86#13063347—22no—
87#13063347—22no—
88#13063347—22no—
89#13063347—22no—
90C2×Dic172C2×C411yescharacteristic
91C2×Dic172C2×C411yescharacteristic
92C2×#10621873C2×C411yescharacteristic
93C2×#10621873C2×C411yescharacteristic
94C2×#10621873C2×C411yescharacteristic
95C2×#10621873C2×C411yescharacteristic
96C2×D344C2×C411yescharacteristic
97C2×D344C2×C411yescharacteristic
98#13063333—28no—
99#13063333—28no—
100#13063331—22no—
101#13063331—22no—
102#13063331—22no—
103#13063331—22no—
104#13063331—22no—
105#13063331—22no—
106#13063331—22no—
107#13063331—22no—
108#13063331D414yescomplemented
109#13063331D414yescomplemented
110C2×#10621877—21no—
111C2×#10621877—22no—
112C2×#10621877—22no—
113C2×#10621877C2311yescharacteristic
114C2×#10621877C2311yescharacteristic
115C2×#10621877C2311yescharacteristic
116C2×#10621877C2311yescharacteristic
117C2×#10621872—21no—
118C2×#10621872—21no—
119C2×#10621872—21no—
120C2×#10621872—21no—
121C2×#10621872—21no—
122M16×D43—28no—
123M16×D43—28no—
124C22×C43⋊C8—21no—
125C2×C8×D43—21no—
126C2×C8×D43—21no—
127C2×C8×D43—21no—
128C2×C8×D43—21no—
129C2×C8×D43—21no—
130#13063308—21no—
131#13063304C2×C411yescharacteristic
132#13063304C2×C411yescharacteristic
133#13063299C2×C411yescharacteristic
134#13063299C2×C411yescharacteristic
135#13063294—21no—
136C4×C22⋊D43—21no—
137C4×C22⋊D43—21no—
138#13063284C2311yescharacteristic
139#13063261—22no—
140#13063261—22no—
141Dic43⋊C8—21no—
142Dic43⋊C8—21no—
143#13063253—22no—
144#13063253—22no—
145#13063253—22no—
146#13063253—22no—
147#13063253—22no—
148#13063253—22no—
149#13063250C2×C411yescharacteristic
150#13063250C2×C411yescharacteristic
151#13063250C2×C411yescharacteristic
152#13063250C2×C411yescharacteristic
153#13063247C2×C411yescharacteristic
154#13063247C2×C411yescharacteristic
155#13063247C2×C411yescharacteristic
156#13063247C2×C411yescharacteristic
157C22⋊(C43⋊C8)—21no—
158C22⋊(C43⋊C8)—21no—
159(C2×D43)⋊C8—21no—
160(C2×D43)⋊C8—21no—
161#13063235—21no—
162C8×Dic43—21no—
163C23×C4×C43C2311yescharacteristic
164C2×M16×C43—22no—
165C2×M16×C43—22no—
166C2×M16×C43D411yescharacteristic
167C2×M16×C43D411yescharacteristic
168C2×M16×C43D411yescharacteristic
169C2×M16×C43D411yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C42×C43C2311yescharacteristic
176C2×C42×C43C2311yescharacteristic
177C22⋊C8×C43C2×C411yescharacteristic
178C22⋊C8×C43C2×C411yescharacteristic
179C22⋊C8×C43C2×C411yescharacteristic
180C22⋊C8×C43C2×C411yescharacteristic
181#97×C43—22no—
182C4×C8×C43—22no—
183#95×C43—21no—
184C24×C43#4111yescharacteristic
185C23×D43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C22×C411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43#4111yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C2×C22⋊D43—21no—
203C2×C22⋊D43—21no—
204C2×C22⋊D43—21no—
205C2×C22⋊D43—21no—
206C2×C22⋊D43—21no—
207C22×Dic43—21no—
208#10621898—24no—
209#10621898—24no—
210#10621898—24no—
211#10621898—24no—
212#10621898—21no—
213#10621898—21no—
214#10621898—21no—
215#10621898—21no—
216#10621898—22no—
217#10621898—22no—
218#10621898—21no—
219#10621898—21no—
220#10621898—21no—
221#10621898—21no—
222#10621898—22no—
223#10621898—22no—
224#10621898C2×D412yes—
225#10621898C2×D412yes—
226#10621898#4112yes—
227#10621898#4112yes—
228C2×D172—21no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172C22×C411yescharacteristic
232C2×D172C22×C411yescharacteristic
233C2×D172C22×C411yescharacteristic
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×Dic86—21no—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86C22×C411yescharacteristic
245C2×Dic86C22×C411yescharacteristic
246C2×Dic86C22×C411yescharacteristic
247M16×C43—22no—
248M16×C43—22no—
249M16×C43—22no—
250M16×C43—22no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C2×C8×C43—21no—
257C2×C8×C43C22×C411yescharacteristic
258C2×C8×C43C22×C411yescharacteristic
259C2×C8×C43C22×C411yescharacteristic
260C2×C8×C43C22×C411yescharacteristic
261C2×C8×C43C2×D411yescharacteristic
262C2×C8×C43C2×D411yescharacteristic
263C2×C8×C43C2×D411yescharacteristic
264C2×C8×C43C2×D411yescharacteristic
265C2×C8×C43C2×D412yes—
266C2×C8×C43C2×D412yes—
267C22⋊C4×C43—42no—
268C42×C43—21no—
269C42×C43—21no—
270C42×C43—21no—
271C42×C43—21no—
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—21no—
277C4⋊Dic43C22×C411yescharacteristic
278C4⋊Dic43C22×C411yescharacteristic
279Dic43⋊C4—21no—
280Dic43⋊C4—21no—
281C4×Dic43—21no—
282#10621877—24no—
283#10621877—21no—
284#10621877—21no—
285#10621877—21no—
286#10621877—21no—
287#10621877—21no—
288#10621877—21no—
289#10621877C2×D412yes—
290#10621877C2×D412yes—
291C2×C43⋊C8—24no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296Dic172—22no—
297Dic172—22no—
298D344—22no—
299D344—22no—
300#10621873—22no—
301#10621873—22no—
302#10621873—22no—
303#10621873—22no—
304#10621872—24no—
305#10621872—24no—
306#10621872—24no—
307#10621872—24no—
308#10621872—42no—
309C8×D43—24no—
310C8×D43—24no—
311C8×D43—24no—
312C8×D43—24no—
313C8×D43—42no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—41no—
317C23×C43—41no—
318C23×C43C4×D411yescharacteristic
319C23×C43C4×D411yescharacteristic
320C23×C43C2×#4111yescharacteristic
321C22×D43—21no—
322C22×D43—21no—
323C22×D43—24no—
324C22×D43—21no—
325C22×D43—81no—
326C22×D43—81no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—22no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43C4×D411yescharacteristic
344C2×C4×C43C4×D411yescharacteristic
345C2×C4×C43C23×C411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C2×#4111yescharacteristic
350C2×C4×C43C2×#4111yescharacteristic
351C22⋊D43—24no—
352C22⋊D43—24no—
353C22⋊D43—22no—
354C22⋊D43—22no—
355C22⋊D43—22no—
356C22⋊D43—22no—
357C22⋊D43—41no—
358C22⋊D43—41no—
359C22⋊D43—81no—
360C22⋊D43—81no—
361C2×Dic43—24no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—21no—
367D172—24no—
368D172—21no—
369D172—21no—
370D172—21no—
371D172—21no—
372D172C4×D412yes—
373D172C4×D412yes—
374C4×D43—24no—
375C4×D43—24no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—41no—
381C4×D43—41no—
382Dic86—24no—
383Dic86—21no—
384Dic86—21no—
385Dic86—21no—
386Dic86—21no—
387Dic86C4×D412yes—
388Dic86C4×D412yes—
389C8×C43—21no—
390C8×C43—21no—
391C8×C43—21no—
392C8×C43—21no—
393C8×C43—21no—
394C8×C43—21no—
395C8×C43#12012yes—
396C8×C43#12012yes—
397C43⋊C8—22no—
398C43⋊C8—22no—
399C43⋊C8—41no—
400C43⋊C8—41no—
401#21468—431nomaximal, Sylow
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43C2×C4×D411yescharacteristic
413C22×C43#52511yescharacteristic
414C22×C43#52511yescharacteristic
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—41no—
423C2×D43—41no—
424C2×D43—84no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—42no—
428C4×C43—81no—
429C4×C43C2×C4×D411yescharacteristic
430C4×C43C2×C4×D411yescharacteristic
431C4×C43C2×#12011yescharacteristic
432C4×C43#52511yescharacteristic
433Dic43—22no—
434Dic43—22no—
435Dic43—41no—
436Dic43—41no—
437Dic43—41no—
438C2×#568—431no—
439#3002—431no—
440C2×#444—431no—
441C2×#443—431no—
442#2930—431no—
443#1876—431no—
444#1876—431no—
445#1871—431no—
446#1866—431no—
447#1866—431no—
448#1855—431no—
449#1789—431no—
450#1765—431no—
451#1764—431no—
452#1753D4311yescharacteristic, complemented
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—41no—
456C2×C43—41no—
457C2×C43C4×#12011yescharacteristic
458C2×C43#295611yescharacteristic
459C2×C43#295711yescharacteristic
460D43—42no—
461D43—42no—
462D43—81no—
463C22×#41—431no—
464C2×#135—431no—
465C2×#135—431no—
466#568—864no—
467#568—864no—
468C2×#131—431no—
469C2×#131—431no—
470C2×#131—431no—
471C2×#131—431no—
472C2×#131—431no—
473C2×#131—861no—
474C2×#131—861no—
475C22×M16—431no—
476C22×M16—861no—
477C22×M16—861no—
478C22×M16C2×D4311yescharacteristic
479#525—431no—
480#452—431no—
481#452—431no—
482#451—431no—
483#450—431no—
484#449—431no—
485#449—431no—
486#448—431no—
487#447—431no—
488#444—864no—
489#443—864no—
490#436—861no—
491#436—861no—
492#435—861no—
493#435—861no—
494C2×#108—431no—
495C2×#108—431no—
496#424—431no—
497C2×#104—431no—
498C2×#104—431no—
499C2×#104—431no—
500C2×#104—431no—
501C2×#104—431no—
502C2×#104—431no—
503#416—431no—
504#416—431no—
505#408—431no—
506#407—431no—
507C2×C22⋊C8C2×D4311yescharacteristic
508#405—431no—
509C2×#97C2×D4311yescharacteristic, complemented
510C2×C4×C8C2×D4311yescharacteristic, complemented
511C4×C22⋊C4C2×D4311yescharacteristic
512#341—431no—
513#341—431no—
514#339—431no—
515#339—431no—
516#336C2×D4311yescharacteristic, complemented
517#336C2×D4311yescharacteristic, complemented
518C43#2146811yescharacteristic, complemented, Sylow
519C2×#41—431no—
520C2×#41—431no—
521C2×#41—431no—
522C2×#41—431no—
523C2×#41—431no—
524C2×#41—862no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—862no—
528C2×#41—861no—
529C2×#41—861no—
530C22×Q8—431no—
531C22×D4—431no—
532C22×D4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535#135—862no—
536#135—862no—
537#135—862no—
538#135—862no—
539C2×Q16—431no—
540C2×Q16—431no—
541C2×SD16—431no—
542C2×SD16—431no—
543C2×SD16—431no—
544C2×SD16—431no—
545C2×D8—431no—
546C2×D8—431no—
547#131—434no—
548#131—434no—
549#131—862no—
550#131—862no—
551#131—862no—
552#131—862no—
553#131—868no—
554#131—868no—
555#131—862no—
556#131—862no—
557#131—862no—
558#131—862no—
559C2×M16—22no—
560C2×M16—22no—
561C2×M16—431no—
562C2×M16—431no—
563C2×M16—431no—
564C2×M16—431no—
565C2×M16—868no—
566C2×M16—868no—
567C2×M16—862no—
568C2×M16—862no—
569C2×M16—861no—
570C2×M16—861no—
571C2×M16—861no—
572C2×M16—861no—
573C2×M16—861no—
574C2×M16—861no—
575C2×M16D17211yescharacteristic
576C2×M16D17211yescharacteristic
577C2×M16D17211yescharacteristic
578C2×M16D17211yescharacteristic
579C22×C8—861no—
580C22×C8—861no—
581C22×C8—861no—
582C22×C8—861no—
583C22×C8—861no—
584C22×C8—861no—
585C22×C8C22×D4311yescharacteristic
586C22×C8C22×D4311yescharacteristic
587C22×C8C22×D4311yescharacteristic
588C22×C8C22×D4311yescharacteristic
589#123—861no—
590C22⋊Q8—431no—
591C22⋊Q8—431no—
592#121—431no—
593#121—431no—
594#120—861no—
595C4×D4—861no—
596C4×D4—861no—
597#117—431no—
598C2×C22⋊C4—21no—
599C2×C42C22×D4311yescharacteristic
600C2×C42C22×D4311yescharacteristic
601#108—862no—
602#108—862no—
603C4⋊C8—861no—
604C4⋊C8—861no—
605#104—862no—
606#104—862no—
607#104—862no—
608#104—862no—
609#104—862no—
610#104—862no—
611#103—431no—
612#103—431no—
613#103—431no—
614#103—431no—
615#102—431no—
616#102—431no—
617#102—431no—
618#102—431no—
619C22⋊C8—861no—
620C22⋊C8—861no—
621C22⋊C8—861no—
622C22⋊C8—861no—
623C22⋊C8C4×D4311yescharacteristic
624C22⋊C8C4×D4311yescharacteristic
625C22⋊C8C4×D4311yescharacteristic
626C22⋊C8C4×D4311yescharacteristic
627#97—22no—
628#97—861no—
629C4×C8—22no—
630C4×C8—861no—
631#95—21no—
632C24—861no—
633C24#1062189811yescharacteristic
634#41—432no—
635#41—432no—
636#41—432no—
637#41—432no—
638#41—862no—
639#41—862no—
640#41—862no—
641#41—862no—
642#41—864no—
643#41—864no—
644#41—864no—
645#41—864no—
646#41—861no—
647#41—861no—
648#41—861no—
649#41—861no—
650#41—861no—
651#41—861no—
652#41—861no—
653#41—861no—
654C2×Q8—431no—
655C2×Q8—431no—
656C2×Q8—431no—
657C2×Q8—862no—
658C2×Q8—862no—
659C2×Q8—861no—
660C2×D4—431no—
661C2×D4—431no—
662C2×D4—431no—
663C2×D4—862no—
664C2×D4—862no—
665C2×D4—864no—
666C2×D4—864no—
667C2×D4—861no—
668C2×D4—861no—
669C2×D4—861no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4—861no—
674C2×D4—861no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—864no—
682C22×C4—864no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4C2×C4×D4311yescharacteristic
690C22×C4C2×C4×D4311yescharacteristic
691C22×C4C2×D17211yescharacteristic
692C22×C4C2×D17211yescharacteristic
693C22×C4#1062189811yescharacteristic
694C22×C4C23×D4311yescharacteristic
695Q16—862no—
696Q16—862no—
697SD16—862no—
698SD16—862no—
699SD16—862no—
700SD16—862no—
701D8—862no—
702D8—862no—
703M16—22no—
704M16—22no—
705M16—22no—
706M16—22no—
707M16—432no—
708M16—432no—
709M16—864no—
710M16—864no—
711M16—864no—
712M16—861no—
713M16—861no—
714M16—864no—
715M16—864no—
716M16—861no—
717M16—861no—
718M16—861no—
719M16—861no—
720M16—1722no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—864no—
728C2×C8—864no—
729C2×C8—864no—
730C2×C8—861no—
731C2×C8—861no—
732C2×C8—864no—
733C2×C8—864no—
734C2×C8—861no—
735C2×C8—861no—
736C2×C8—1722no—
737C2×C8C2×C4×D4311yescharacteristic
738C2×C8C2×C4×D4311yescharacteristic
739C2×C8C2×C4×D4311yescharacteristic
740C2×C8C2×C4×D4311yescharacteristic
741C2×C8C2×D17211yescharacteristic
742C2×C8C2×D17211yescharacteristic
743C2×C8C2×D17211yescharacteristic
744C2×C8C2×D17211yescharacteristic
745C2×C8D4×D4312yes—
746C2×C8D4×D4312yes—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C22⋊C4—42no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—861no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—861no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—864no—
767C23—861no—
768C23—861no—
769C23—861no—
770C23—3441no—
771C23—3441no—
772C23C4×D17211yescharacteristic
773C23C4×D17211yescharacteristic
774C23C2×#1062189811yescharacteristic
775Q8—432no—
776Q8—432no—
777Q8—864no—
778Q8—861no—
779Q8—861no—
780Q8—861no—
781Q8—861no—
782D4—432no—
783D4—432no—
784D4—864no—
785D4—864no—
786D4—864no—
787D4—862no—
788D4—862no—
789D4—862no—
790D4—862no—
791D4—861no—
792D4—861no—
793D4—861no—
794D4—861no—
795D4—3441no—
796D4—3441no—
797D4—1721no—
798D4—1721no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—864no—
816C2×C4—864no—
817C2×C4—864no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4C4×D17211yescharacteristic
830C2×C4C4×D17211yescharacteristic
831C2×C4C22×C4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C22×D17211yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4#41×D4311yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—21no—
841C8—21no—
842C8—21no—
843C8—862no—
844C8—862no—
845C8—1721no—
846C8—1721no—
847C8#1306329512yes—
848C8#1306329512yes—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—81no—
858C22—81no—
859C22—862no—
860C22—862no—
861C22—3444no—
862C22—1721no—
863C22—1721no—
864C22—1721no—
865C22—1721no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22C2×C4×D17211yescharacteristic
870C22#1458340811yescharacteristic
871C22#1458340811yescharacteristic
872C4—21no—
873C4—21no—
874C4—42no—
875C4—81no—
876C4—862no—
877C4—862no—
878C4—1721no—
879C4—1721no—
880C4—1721no—
881C4C4×D4×D4311yescharacteristic
882C4C4×D4×D4311yescharacteristic
883C4C2×#1306329511yescharacteristic
884C4#1458341111yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—3441no—
890C2—1722no—
891C2—1722no—
892C2C4×#1306329511yescharacteristic
893C2#1914350611yescharacteristic
894C2#1914351311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1753C2
socleC22×C43C2×C4×D4
prime radical#19143817C2
cosocleC22×C4×C43C24
hypercenter#1753D43
hypocenterC43#21468
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14583022C2semidirect
4. C2×#14583017C2semidirect
5. #19143298C2semidirect
6. #19134921C2semidirect
7. #19134921C2semidirect
8. #19134895C2semidirect
9. #19134873C2semidirect
10. #19134873C2semidirect
11. #19134802C2semidirect
12. #19134540C2semidirect
13. #19134439C2semidirect
14. #19134432C2semidirect
15. C43×#1753C2semidirect
27. C2×#13063331C22semidirect
32. #14583063C4semidirect
33. #14583063C4semidirect
34. #14583057C4semidirect
35. #14583052C4semidirect
36. #14583046C4semidirect
37. #14583046C4semidirect
38. #14583040C4semidirect
39. #14583035C4semidirect
46. C2×#13063261C22semidirect
47. C2×#13063261C22semidirect
48. #14582925C22semidirect
53. C2×#13063253C22semidirect
54. C2×#13063253C22semidirect
57. #14582865C22semidirect
59. #14582854C22semidirect
60. #14582664C22semidirect
61. #14582664C22semidirect
62. #14582659C22semidirect
63. #14582659C22semidirect
66. C2×#97×C43C22semidirect
67. C2×C4×C8×C43C22semidirect
69. C43×#336C22semidirect
70. C43×#336C22semidirect
108. #13063331D4semidirect
109. #13063331D4semidirect
452. #1753D43semidirect
509. C2×#97C2×D43semidirect
510. C2×C4×C8C2×D43semidirect
516. #336C2×D43semidirect
517. #336C2×D43semidirect
518. C43#21468semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191438172
C2×#145830222
C2×#145830172
#191432982
#191349212
#191348952
#191348732
#191348022
#191345402
#191344392
#191344322
C43×#17532
#2146843