Finite Group Databasebeta

← #25102452

Subgroups — #25102452

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×#14583664C211yesmaximal, characteristic, complemented
2#19143809C211yesmaximal, characteristic
3C2×#14583019C211yesmaximal, characteristic, complemented
4#19143296C211yesmaximal, characteristic, complemented
5#19134924C211yesmaximal, characteristic, complemented
6#19134919C211yesmaximal, characteristic, complemented
7#19134894C211yesmaximal, characteristic, complemented
8#19134868C211yesmaximal, characteristic, complemented
9#19134867C211yesmaximal, characteristic, complemented
10#19134798C211yesmaximal, characteristic, complemented
11#19134537C211yesmaximal, characteristic, complemented
12#19134437C211yesmaximal, characteristic, complemented
13#19134432C211yesmaximal, characteristic, complemented
14#19134378C211yesmaximal, characteristic, complemented
15C2×C43×#443C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18#14583664—24no—
19#14583664—24no—
20C2×#13063333—21no—
21C2×#13063333C2211yescharacteristic
22C2×#13063332C2211yescharacteristic
23C2×#13063331—21no—
24C2×#13063331C2211yescharacteristic
25C22×#10621872—21no—
26C22×#10621872C2211yescharacteristic
27C2×M16×D43—21no—
28C2×M16×D43C2211yescharacteristic
29#14583406C2211yescharacteristic
30#14583060C411yescharacteristic, complemented
31#14583058C411yescharacteristic, complemented
32#14583053C411yescharacteristic, complemented
33#14583048C411yescharacteristic, complemented
34#14583043C411yescharacteristic, complemented
35#14583041C411yescharacteristic, complemented
36#14583036C411yescharacteristic, complemented
37#14583031C411yescharacteristic, complemented
38#14583019—24no—
39#14582975—21no—
40#14582975—21no—
41#14582970—21no—
42#14582970—21no—
43C2×#13063260C2211yescharacteristic, complemented
44#14582927C2211yescharacteristic, complemented
45C2×#13063253C2211yescharacteristic
46C2×#13063252C2211yescharacteristic
47C2×#13063252C2211yescharacteristic, complemented
48C2×#13063251C2211yescharacteristic
49#14582896C2211yescharacteristic
50#14582895C2211yescharacteristic
51#14582866C2211yescharacteristic, complemented
52#14582862C2211yescharacteristic
53C2×(C2×D43)⋊C8C2211yescharacteristic
54#14582854C2211yescharacteristic, complemented
55C2×#13063235C2211yescharacteristic, complemented
56C4×(C2×D43)⋊C4C2211yescharacteristic
57#14582664C2211yescharacteristic, complemented
58#14582663C2211yescharacteristic, complemented
59#14582660C2211yescharacteristic, complemented
60#14582659C2211yescharacteristic, complemented
61#14582654C2211yescharacteristic, complemented
62#14582653C2211yescharacteristic, complemented
63C2×#135×C43C2211yescharacteristic
64C2×#131×C43C2211yescharacteristic
65C2×#131×C43C2211yescharacteristic, complemented
66C43×#443—24no—
67C2×#108×C43C2211yescharacteristic, complemented
68C2×#104×C43C2211yescharacteristic
69C2×#104×C43C2211yescharacteristic, complemented
70C2×C4×C8×C43C2211yescharacteristic, complemented
71C2×#10621902C2×C411yescharacteristic
72C2×#10621898—21no—
73C2×#10621898C2311yescharacteristic
74C2×#10621900—21no—
75C2×#10621900C2×C411yescharacteristic
76#41×D43—22no—
77#41×D43—22no—
78#41×D43—22no—
79#41×D43—22no—
80C2×Q8×D43C2×C411yescharacteristic
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85#13063345—22no—
86#13063345—22no—
87C2×#10621885C2×C411yescharacteristic
88C2×#10621883C2×C411yescharacteristic
89C2×#10621884C2×C411yescharacteristic
90C2×#10621882C2×C411yescharacteristic
91#13063333—28no—
92#13063333—22no—
93#13063333—22no—
94#13063332—22no—
95#13063332—22no—
96#13063331—28no—
97#13063331—22no—
98#13063331D414yescomplemented
99C2×#10621877—21no—
100C2×#10621877C2311yescharacteristic
101C2×#10621877C2311yescharacteristic
102C2×#10621872—28no—
103C2×#10621872—21no—
104C2×#10621872—21no—
105C2×#10621872—22no—
106C2×#10621872—22no—
107C2×#10621872—21no—
108C2×#10621872D411yescharacteristic
109C2×#10621872D411yescharacteristic
110C2×#10621872D411yescharacteristic
111C2×#10621872D411yescharacteristic
112M16×D43—28no—
113M16×D43—22no—
114M16×D43—22no—
115C22×C43⋊C8—21no—
116C22×C43⋊C8C2311yescharacteristic
117C22×C43⋊C8C2311yescharacteristic
118C2×C8×D43—21no—
119C2×C8×D43—21no—
120C2×C8×D43—21no—
121#13063306—21no—
122#13063301C2×C411yescharacteristic
123#13063301C2×C411yescharacteristic
124#13063296C2×C411yescharacteristic
125#13063296C2×C411yescharacteristic
126#13063293—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129#13063284C2311yescharacteristic
130C2×(C2×D43)⋊C4—21no—
131C2×C4×Dic43C2311yescharacteristic
132#13063260—22no—
133Dic43⋊C8—21no—
134Dic43⋊C8—21no—
135#13063253—22no—
136#13063252—22no—
137#13063252—22no—
138#13063251—22no—
139#13063250C2×C411yescharacteristic
140#13063250C2×C411yescharacteristic
141#13063249C2×C411yescharacteristic
142#13063249C2×C411yescharacteristic
143#13063247C2×C411yescharacteristic
144#13063247C2×C411yescharacteristic
145#13063246C2×C411yescharacteristic
146#13063246C2×C411yescharacteristic
147C22⋊(C43⋊C8)—21no—
148C22⋊(C43⋊C8)—21no—
149(C2×D43)⋊C8—21no—
150(C2×D43)⋊C8—21no—
151(C2×D43)⋊C8C2×C411yescharacteristic
152(C2×D43)⋊C8C2×C411yescharacteristic
153(C2×D43)⋊C8C2×C411yescharacteristic
154(C2×D43)⋊C8C2×C411yescharacteristic
155#13063235—22no—
156#13063235—21no—
157C8×Dic43—21no—
158C43⋊#95—21no—
159C2×#41×C43C2311yescharacteristic
160C2×#41×C43C2311yescharacteristic
161#135×C43—22no—
162#135×C43—22no—
163C2×Q16×C43C2×C411yescharacteristic
164C2×SD16×C43C2×C411yescharacteristic
165C2×SD16×C43C2×C411yescharacteristic
166C2×D8×C43C2×C411yescharacteristic
167#131×C43—22no—
168#131×C43—22no—
169#131×C43—22no—
170#131×C43D414yescomplemented
171C2×M16×C43—21no—
172C2×M16×C43—21no—
173C2×M16×C43C2311yescharacteristic
174C2×M16×C43C2311yescharacteristic
175C22×C8×C43—21no—
176C22×C8×C43—21no—
177C22×C8×C43C2311yescharacteristic
178C22×C8×C43C2311yescharacteristic
179C2×C42×C43C2311yescharacteristic
180#108×C43—22no—
181#104×C43—22no—
182#104×C43—22no—
183C4×C8×C43—22no—
184C23×D43—21no—
185C23×D43#4111yescharacteristic
186#41×C43—21no—
187#41×C43—21no—
188#41×C43—21no—
189#41×C43—21no—
190#41×C43—21no—
191#41×C43—21no—
192#41×C43C2×D412yes—
193#41×C43#4112yes—
194C2×Q8×C43C22×C411yescharacteristic
195C2×Q8×C43C22×C411yescharacteristic
196C2×D4×C43—21no—
197C2×D4×C43—21no—
198C2×D4×C43C22×C411yescharacteristic
199C2×D4×C43C22×C411yescharacteristic
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—21no—
205C2×C22⋊D43—21no—
206C2×C22⋊D43—21no—
207C2×C22⋊D43—21no—
208C2×C22⋊D43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43#4111yescharacteristic
212#10621902—22no—
213#10621902—22no—
214Q8×D43—22no—
215Q8×D43—22no—
216#10621900—24no—
217#10621900—24no—
218#10621900—22no—
219#10621900—22no—
220D4×D43—24no—
221D4×D43—24no—
222D4×D43—22no—
223D4×D43—22no—
224#10621898—24no—
225#10621898—24no—
226#10621898—21no—
227#10621898—21no—
228#10621898C2×D412yes—
229#10621898#4112yes—
230C2×D172—21no—
231C2×D172C22×C411yescharacteristic
232C2×C4×D43—24no—
233C2×C4×D43—24no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43C22×C411yescharacteristic
242C2×C4×D43C22×C411yescharacteristic
243C2×C4×D43C2×D411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×Dic86—21no—
246C2×Dic86C22×C411yescharacteristic
247Q16×C43—22no—
248SD16×C43—22no—
249SD16×C43—22no—
250D8×C43—22no—
251M16×C43—21no—
252M16×C43—24no—
253M16×C43—21no—
254M16×C43—21no—
255M16×C43—42no—
256M16×C43C2×D412yes—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—24no—
261C2×C8×C43—21no—
262C2×C8×C43—42no—
263C2×C8×C43C22×C411yescharacteristic
264C2×C8×C43C22×C411yescharacteristic
265C2×C8×C43C2×D411yescharacteristic
266C2×C8×C43C2×D411yescharacteristic
267C2×C8×C43C2×D412yes—
268C2×C8×C43C2×D412yes—
269C42×C43—21no—
270C42×C43—21no—
271C22⋊Dic43—21no—
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274#10621885—22no—
275#10621884—22no—
276#10621883—22no—
277#10621882—22no—
278(C2×D43)⋊C4—21no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—42no—
281C4⋊Dic43C22×C411yescharacteristic
282C4⋊Dic43C22×C411yescharacteristic
283Dic43⋊C4—21no—
284Dic43⋊C4—21no—
285C4×Dic43—21no—
286C4×Dic43—21no—
287C4×Dic43—21no—
288#10621877—24no—
289#10621877—21no—
290#10621877—21no—
291#10621877—21no—
292#10621877C2×D412yes—
293C2×C43⋊C8—24no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8C22×C411yescharacteristic
301C2×C43⋊C8C22×C411yescharacteristic
302C2×C43⋊C8C2×D411yescharacteristic
303C2×C43⋊C8C2×D411yescharacteristic
304#10621872—24no—
305#10621872—24no—
306#10621872—22no—
307#10621872—22no—
308#10621872—24no—
309#10621872—22no—
310#10621872—22no—
311C8×D43—24no—
312C8×D43—24no—
313C8×D43—24no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43C2×#4111yescharacteristic
317C22×D43—21no—
318C22×D43—24no—
319C22×D43—21no—
320C22×D43—21no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43—81no—
324C22×D43—81no—
325C22×D43C4×D411yescharacteristic
326C22×D43C4×D411yescharacteristic
327Q8×C43—21no—
328Q8×C43—21no—
329Q8×C43—21no—
330Q8×C43C4×D412yes—
331D4×C43—22no—
332D4×C43—22no—
333D4×C43—21no—
334D4×C43—21no—
335D4×C43—21no—
336D4×C43—41no—
337D4×C43—41no—
338D4×C43C4×D412yes—
339C2×C4×C43—21no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—21no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43C23×C411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43C2×#4111yescharacteristic
354C22⋊D43—24no—
355C22⋊D43—24no—
356C22⋊D43—22no—
357C22⋊D43—22no—
358C22⋊D43—81no—
359C22⋊D43—81no—
360C2×Dic43—24no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43C4×D411yescharacteristic
370C2×Dic43C4×D411yescharacteristic
371D172—24no—
372D172—21no—
373D172C4×D412yes—
374C4×D43—24no—
375C4×D43—24no—
376C4×D43—21no—
377C4×D43—21no—
378C4×D43—21no—
379C4×D43—21no—
380C4×D43—22no—
381C4×D43—21no—
382C4×D43—21no—
383C4×D43—21no—
384C4×D43—22no—
385C4×D43—21no—
386Dic86—24no—
387Dic86—21no—
388Dic86C4×D412yes—
389C8×C43—21no—
390C8×C43—21no—
391C8×C43—22no—
392C8×C43—41no—
393C8×C43#12012yes—
394C8×C43#12012yes—
395C43⋊C8—21no—
396C43⋊C8—21no—
397C43⋊C8—22no—
398C43⋊C8—21no—
399C43⋊C8—21no—
400C43⋊C8—41no—
401#21468—431nomaximal, Sylow
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—22no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43—41no—
410C22×C43C2×C4×D411yescharacteristic
411C22×C43#52511yescharacteristic
412C22×C43#52511yescharacteristic
413C2×D43—21no—
414C2×D43—21no—
415C2×D43—21no—
416C2×D43—21no—
417C2×D43—21no—
418C2×D43—22no—
419C2×D43—21no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—81no—
423C2×D43—81no—
424C2×D43—84no—
425C4×C43—22no—
426C4×C43—42no—
427C4×C43—41no—
428C4×C43C2×C4×D411yescharacteristic
429C4×C43C2×C4×D411yescharacteristic
430C4×C43C2×#12011yescharacteristic
431C4×C43#52511yescharacteristic
432Dic43—21no—
433Dic43—22no—
434Dic43—21no—
435Dic43—41no—
436Dic43—41no—
437Dic43—81no—
438C2×#568—431no—
439#3002—431no—
440C2×#444—431no—
441C2×#443D4311yescharacteristic, complemented
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#1753—431no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—42no—
456C2×C43—81no—
457C2×C43C4×#12011yescharacteristic
458C2×C43#295611yescharacteristic
459C2×C43#295711yescharacteristic
460D43—41no—
461D43—41no—
462D43—42no—
463C22×#41—431no—
464C2×#135—431no—
465C2×#135C2×D4311yescharacteristic
466#568—864no—
467#568—864no—
468C2×#131—431no—
469C2×#131—431no—
470C2×#131—431no—
471C2×#131—861no—
472C2×#131—861no—
473C2×#131C2×D4311yescharacteristic
474C2×#131C2×D4311yescharacteristic, complemented
475C22×M16—431no—
476C22×M16—431no—
477C22×M16—861no—
478C22×M16—861no—
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—24no—
490#436—861no—
491#436—861no—
492#435—861no—
493#435—861no—
494C2×#108—431no—
495C2×#108C2×D4311yescharacteristic, complemented
496#424—431no—
497C2×#104—431no—
498C2×#104—431no—
499C2×#104—431no—
500C2×#104—431no—
501C2×#104C2×D4311yescharacteristic
502C2×#104C2×D4311yescharacteristic, complemented
503#416—431no—
504#416—431no—
505#408—431no—
506#407—431no—
507C2×C22⋊C8—431no—
508#405—431no—
509C2×#97—431no—
510C2×C4×C8C2×D4311yescharacteristic, complemented
511C4×C22⋊C4—431no—
512#341—431no—
513#341—431no—
514#339—431no—
515#339—431no—
516#336—431no—
517#336—431no—
518C43#2146811yescharacteristic, complemented, Sylow
519C2×#41—431no—
520C2×#41—431no—
521C2×#41—431no—
522C2×#41—861no—
523C2×#41—861no—
524C2×#41—862no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—862no—
528C2×#41C22×D4311yescharacteristic
529C2×#41C22×D4311yescharacteristic
530C22×Q8—431no—
531C22×D4—431no—
532C22×D4—861no—
533C23×C4—431no—
534C23×C4—861no—
535#135—22no—
536#135—22no—
537#135—862no—
538#135—862no—
539C2×Q16—431no—
540C2×Q16C4×D4311yescharacteristic
541C2×SD16—431no—
542C2×SD16—431no—
543C2×SD16C4×D4311yescharacteristic
544C2×SD16C4×D4311yescharacteristic
545C2×D8—431no—
546C2×D8C4×D4311yescharacteristic
547#131—22no—
548#131—22no—
549#131—22no—
550#131—434no—
551#131—868no—
552#131—862no—
553#131—868no—
554#131—862no—
555#131—862no—
556#131—862no—
557#131—862no—
558#131C22⋊D4314yescomplemented
559C2×M16—21no—
560C2×M16—21no—
561C2×M16—431no—
562C2×M16—431no—
563C2×M16—431no—
564C2×M16—431no—
565C2×M16—431no—
566C2×M16—431no—
567C2×M16—861no—
568C2×M16—861no—
569C2×M16—868no—
570C2×M16—861no—
571C2×M16—862no—
572C2×M16—868no—
573C2×M16—862no—
574C2×M16—862no—
575C2×M16—861no—
576C2×M16—862no—
577C2×M16C22×D4311yescharacteristic
578C2×M16C22×D4311yescharacteristic
579C22×C8—21no—
580C22×C8—21no—
581C22×C8—431no—
582C22×C8—431no—
583C22×C8—861no—
584C22×C8—861no—
585C22×C8—861no—
586C22×C8—861no—
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—861no—
599C2×C42—431no—
600C2×C42C22×D4311yescharacteristic
601#108—22no—
602#108—862no—
603C4⋊C8—861no—
604C4⋊C8—861no—
605#104—22no—
606#104—22no—
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—431no—
620C22⋊C8—431no—
621C22⋊C8—431no—
622C22⋊C8—431no—
623C22⋊C8—861no—
624C22⋊C8—861no—
625C22⋊C8—861no—
626C22⋊C8—861no—
627#97—862no—
628#97—861no—
629C4×C8—22no—
630C4×C8—861no—
631#95—861no—
632C24—431no—
633C24—861no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—432no—
641#41—432no—
642#41—864no—
643#41—864no—
644#41—862no—
645#41—864no—
646#41—864no—
647#41—862no—
648#41—862no—
649#41—862no—
650#41—861no—
651#41—861no—
652#41#1062189812yes—
653#41C2×C22⋊D4312yes—
654C2×Q8—431no—
655C2×Q8—861no—
656C2×Q8—862no—
657C2×Q8—862no—
658C2×Q8C2×C4×D4311yescharacteristic
659C2×Q8C2×C4×D4311yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—431no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4—862no—
666C2×D4—864no—
667C2×D4—864no—
668C2×D4—861no—
669C2×D4—861no—
670C2×D4—862no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4C2×C4×D4311yescharacteristic
674C2×D4C2×C4×D4311yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—431no—
681C22×C4—431no—
682C22×C4—431no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—864no—
686C22×C4—864no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4C23×D4311yescharacteristic
695Q16—22no—
696Q16—862no—
697SD16—22no—
698SD16—22no—
699SD16—862no—
700SD16—862no—
701D8—22no—
702D8—862no—
703M16—21no—
704M16—24no—
705M16—21no—
706M16—21no—
707M16—42no—
708M16—432no—
709M16—864no—
710M16—864no—
711M16—864no—
712M16—861no—
713M16—862no—
714M16—862no—
715M16—862no—
716M16—862no—
717M16—864no—
718M16—861no—
719M16—861no—
720M16C2×C22⋊D4312yes—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—24no—
725C2×C8—21no—
726C2×C8—42no—
727C2×C8—431no—
728C2×C8—431no—
729C2×C8—431no—
730C2×C8—431no—
731C2×C8—864no—
732C2×C8—864no—
733C2×C8—864no—
734C2×C8—861no—
735C2×C8—861no—
736C2×C8—861no—
737C2×C8—861no—
738C2×C8—861no—
739C2×C8—864no—
740C2×C8—861no—
741C2×C8C2×C4×D4311yescharacteristic
742C2×C8C2×C4×D4311yescharacteristic
743C2×C8D4×D4312yes—
744C2×C8D4×D4311yescharacteristic
745C2×C8D4×D4311yescharacteristic
746C2×C8C2×C22⋊D4312yes—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C22⋊C4—861no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—1722no—
757C42—21no—
758C42—21no—
759C42—861no—
760C42—861no—
761C42—861no—
762C23—21no—
763C23—21no—
764C23—431no—
765C23—431no—
766C23—864no—
767C23—861no—
768C23—861no—
769C23—861no—
770C23—3441no—
771C23—3441no—
772C23—1721no—
773C23—1721no—
774C23#41×D4311yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—432no—
779Q8—864no—
780Q8—861no—
781Q8C4×C22⋊D4312yes—
782D4—22no—
783D4—22no—
784D4—21no—
785D4—21no—
786D4—21no—
787D4—41no—
788D4—41no—
789D4—432no—
790D4—864no—
791D4—864no—
792D4—864no—
793D4—862no—
794D4—862no—
795D4—861no—
796D4—3441no—
797D4—3441no—
798D4C4×C22⋊D4312yes—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—431no—
809C2×C4—431no—
810C2×C4—864no—
811C2×C4—864no—
812C2×C4—864no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—861no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—861no—
821C2×C4—862no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—862no—
826C2×C4—861no—
827C2×C4—861no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4—1721no—
831C2×C4C22×C4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C22×C22⋊D4311yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4C2×#1062189811yescharacteristic
837C8—21no—
838C8—21no—
839C8—22no—
840C8—41no—
841C8—861no—
842C8—861no—
843C8—861no—
844C8—861no—
845C8—862no—
846C8—1721no—
847C8#1306329312yes—
848C8#1306329312yes—
849C22—21no—
850C22—21no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—861no—
858C22—862no—
859C22—861no—
860C22—861no—
861C22—861no—
862C22—861no—
863C22—861no—
864C22—3441no—
865C22—3441no—
866C22—3444no—
867C22—1721no—
868C22—1721no—
869C22C4×D4×D4311yescharacteristic
870C22#1458340611yescharacteristic
871C22#1458340811yescharacteristic
872C4—22no—
873C4—42no—
874C4—41no—
875C4—861no—
876C4—861no—
877C4—862no—
878C4—3441no—
879C4—1721no—
880C4—1721no—
881C4C4×D4×D4311yescharacteristic
882C4C2×C4×C22⋊D4311yescharacteristic
883C4C2×#1306329311yescharacteristic
884C4#1458340811yescharacteristic
885C2—21no—
886C2—21no—
887C2—42no—
888C2—81no—
889C2—1721no—
890C2—1721no—
891C2—1722no—
892C2C4×#1306329311yescharacteristic
893C2#1914350011yescharacteristic
894C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#443C2
socleC22×C43C2×C4×D4
prime radical#19143809C2
cosocleC22×C4×C43C24
hypercenterC2×#443D43
hypocenterC43#21468
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
1. C2×#14583664C2semidirect
3. C2×#14583019C2semidirect
4. #19143296C2semidirect
5. #19134924C2semidirect
6. #19134919C2semidirect
7. #19134894C2semidirect
8. #19134868C2semidirect
9. #19134867C2semidirect
10. #19134798C2semidirect
11. #19134537C2semidirect
12. #19134437C2semidirect
13. #19134432C2semidirect
14. #19134378C2semidirect
15. C2×C43×#443C2semidirect
30. #14583060C4semidirect
31. #14583058C4semidirect
32. #14583053C4semidirect
33. #14583048C4semidirect
34. #14583043C4semidirect
35. #14583041C4semidirect
36. #14583036C4semidirect
37. #14583031C4semidirect
43. C2×#13063260C22semidirect
44. #14582927C22semidirect
47. C2×#13063252C22semidirect
51. #14582866C22semidirect
54. #14582854C22semidirect
55. C2×#13063235C22semidirect
57. #14582664C22semidirect
58. #14582663C22semidirect
59. #14582660C22semidirect
60. #14582659C22semidirect
61. #14582654C22semidirect
62. #14582653C22semidirect
65. C2×#131×C43C22semidirect
67. C2×#108×C43C22semidirect
69. C2×#104×C43C22semidirect
70. C2×C4×C8×C43C22semidirect
98. #13063331D4semidirect
170. #131×C43D4semidirect
441. C2×#443D43semidirect
474. C2×#131C2×D43semidirect
495. C2×#108C2×D43semidirect
502. C2×#104C2×D43semidirect
510. C2×C4×C8C2×D43semidirect
518. C43#21468semidirect
558. #131C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836642
#191438092
C2×#145830192
#191432962
#191349242
#191349192
#191348942
#191348682
#191348672
#191347982
#191345372
#191344372
#191344322
#191343782
C2×C43×#4432
#2146843