Finite Group Databasebeta

← #25102465

Subgroups — #25102465

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×#14583021C211yesmaximal, characteristic, complemented
4C2×#14583013C211yesmaximal, characteristic, complemented
5#19143301C211yesmaximal, characteristic, complemented
6#19134925C211yesmaximal, characteristic, complemented
7#19134894C211yesmaximal, characteristic, complemented
8#19134873C211yesmaximal, characteristic, complemented
9#19134870C211yesmaximal, characteristic, complemented
10#19134801C211yesmaximal, characteristic, complemented
11#19134537C211yesmaximal, characteristic, complemented
12#19134438C211yesmaximal, characteristic, complemented
13#19134433C211yesmaximal, characteristic, complemented
14#19134375C211yesmaximal, characteristic, complemented
15C43×#1876C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18#14583664—24no—
19#14583664—24no—
20C2×#13063333—21no—
21C2×#13063333C2211yescharacteristic
22C2×#13063332C2211yescharacteristic
23C2×#13063332C2211yescharacteristic, complemented
24C2×#13063331—21no—
25C2×#13063331C2211yescharacteristic
26C22×#10621872—21no—
27C22×#10621872C2211yescharacteristic
28C2×M16×D43—21no—
29C2×M16×D43C2211yescharacteristic
30#14583406C2211yescharacteristic
31#14583060C411yescharacteristic, complemented
32#14583058C411yescharacteristic, complemented
33#14583053C411yescharacteristic, complemented
34#14583048C411yescharacteristic, complemented
35#14583043C411yescharacteristic, complemented
36#14583041C411yescharacteristic, complemented
37#14583036C411yescharacteristic, complemented
38#14583031C411yescharacteristic, complemented
39#14583021—24no—
40#14583013—24no—
41#14582974—21no—
42#14582974—21no—
43#14582967—21no—
44#14582967—21no—
45C2×#13063261C2211yescharacteristic, complemented
46C2×#13063260C2211yescharacteristic, complemented
47#14582925C2211yescharacteristic, complemented
48C2×#13063253C2211yescharacteristic
49C2×#13063252C2211yescharacteristic
50C2×#13063252C2211yescharacteristic, complemented
51C2×#13063251C2211yescharacteristic
52#14582896C2211yescharacteristic
53#14582895C2211yescharacteristic
54#14582862C2211yescharacteristic
55C2×(C2×D43)⋊C8C2211yescharacteristic
56#14582857C2211yescharacteristic, complemented
57C2×#13063235C2211yescharacteristic, complemented
58C2×C4×C43⋊C8C2211yescharacteristic, complemented
59C4×(C2×D43)⋊C4C2211yescharacteristic
60#14582663C2211yescharacteristic, complemented
61#14582660C2211yescharacteristic, complemented
62#14582659C2211yescharacteristic, complemented
63#14582653C2211yescharacteristic, complemented
64C2×#135×C43C2211yescharacteristic
65C2×#131×C43C2211yescharacteristic
66C2×#104×C43C2211yescharacteristic
67C2×#104×C43C2211yescharacteristic, complemented
68C43×#408C2211yescharacteristic, complemented
69C43×#341C2211yescharacteristic, complemented
70C43×#336C2211yescharacteristic, 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#13063333D414yescomplemented
94#13063332—22no—
95#13063332—22no—
96#13063332—22no—
97#13063332D414yescomplemented
98#13063331—28no—
99#13063331—22no—
100#13063331—22no—
101C2×#10621877—21no—
102C2×#10621877—21no—
103C2×#10621877C2311yescharacteristic
104C2×#10621877C2311yescharacteristic
105C2×#10621872—28no—
106C2×#10621872—21no—
107C2×#10621872—21no—
108C2×#10621872—21no—
109C2×#10621872—22no—
110C2×#10621872—22no—
111C2×#10621872D411yescharacteristic
112C2×#10621872D411yescharacteristic
113C2×#10621872D411yescharacteristic
114C2×#10621872D411yescharacteristic
115M16×D43—28no—
116M16×D43—22no—
117M16×D43—22no—
118C22×C43⋊C8—21no—
119C22×C43⋊C8—21no—
120C22×C43⋊C8C2311yescharacteristic
121C22×C43⋊C8C2311yescharacteristic
122C2×C8×D43—21no—
123C2×C8×D43—21no—
124C2×C8×D43—21no—
125#13063306—21no—
126#13063301C2×C411yescharacteristic
127#13063301C2×C411yescharacteristic
128#13063296C2×C411yescharacteristic
129#13063296C2×C411yescharacteristic
130#13063293—21no—
131C4×C22⋊D43—21no—
132C4×C22⋊D43—21no—
133#13063284C2311yescharacteristic
134C2×(C2×D43)⋊C4—21no—
135C2×C4×Dic43C2311yescharacteristic
136#13063261—22no—
137#13063260—22no—
138Dic43⋊C8—21no—
139Dic43⋊C8—21no—
140#13063253—22no—
141#13063252—22no—
142#13063252—22no—
143#13063251—22no—
144#13063250C2×C411yescharacteristic
145#13063250C2×C411yescharacteristic
146#13063249C2×C411yescharacteristic
147#13063249C2×C411yescharacteristic
148#13063247C2×C411yescharacteristic
149#13063247C2×C411yescharacteristic
150#13063246C2×C411yescharacteristic
151#13063246C2×C411yescharacteristic
152(C2×D43)⋊C8—21no—
153(C2×D43)⋊C8—21no—
154(C2×D43)⋊C8C2×C411yescharacteristic
155(C2×D43)⋊C8C2×C411yescharacteristic
156(C2×D43)⋊C8C2×C411yescharacteristic
157(C2×D43)⋊C8C2×C411yescharacteristic
158#13063235—22no—
159#13063235—21no—
160C4×C43⋊C8—22no—
161C8×Dic43—21no—
162C43⋊#95—21no—
163C2×#41×C43C2311yescharacteristic
164C2×#41×C43C2311yescharacteristic
165#135×C43—22no—
166#135×C43—22no—
167C2×Q16×C43C2×C411yescharacteristic
168C2×SD16×C43C2×C411yescharacteristic
169C2×SD16×C43C2×C411yescharacteristic
170C2×D8×C43C2×C411yescharacteristic
171#131×C43—22no—
172#131×C43—22no—
173C2×M16×C43—21no—
174C2×M16×C43C2311yescharacteristic
175C2×M16×C43C2311yescharacteristic
176C22×C8×C43—21no—
177C22×C8×C43C2311yescharacteristic
178C22×C8×C43C2311yescharacteristic
179C2×C42×C43C2311yescharacteristic
180#104×C43—22no—
181#104×C43—22no—
182C22⋊C8×C43—21no—
183C22⋊C8×C43—21no—
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—24no—
252M16×C43—21no—
253M16×C43—21no—
254M16×C43—21no—
255M16×C43C2×D412yes—
256C2×C8×C43—24no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43C22×C411yescharacteristic
264C2×C8×C43C22×C411yescharacteristic
265C2×C8×C43C2×D411yescharacteristic
266C2×C8×C43C2×D411yescharacteristic
267C42×C43—21no—
268C42×C43—21no—
269C22⋊Dic43—21no—
270C22⋊Dic43—21no—
271C22⋊Dic43—21no—
272#10621885—22no—
273#10621884—22no—
274#10621883—22no—
275#10621882—22no—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4—21no—
278(C2×D43)⋊C4—42no—
279C4⋊Dic43C22×C411yescharacteristic
280C4⋊Dic43C22×C411yescharacteristic
281Dic43⋊C4—21no—
282Dic43⋊C4—21no—
283C4×Dic43—21no—
284C4×Dic43—21no—
285C4×Dic43—21no—
286#10621877—21no—
287#10621877—24no—
288#10621877—21no—
289#10621877—21no—
290#10621877—42no—
291#10621877C2×D412yes—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—24no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—42no—
298C2×C43⋊C8C22×C411yescharacteristic
299C2×C43⋊C8C22×C411yescharacteristic
300C2×C43⋊C8C2×D411yescharacteristic
301C2×C43⋊C8C2×D412yes—
302C2×C43⋊C8C2×D411yescharacteristic
303C2×C43⋊C8C2×D412yes—
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—21no—
393C8×C43—21no—
394C8×C43—41no—
395C43⋊C8—21no—
396C43⋊C8—21no—
397C43⋊C8—22no—
398C43⋊C8—41no—
399C43⋊C8#12012yes—
400C43⋊C8#12012yes—
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×#443—431no—
442#2930—431no—
443#1876—431no—
444#1876D4311yescharacteristic, complemented
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—431no—
472C2×#131—861no—
473C2×#131—861no—
474C2×#131C2×D4311yescharacteristic
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—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×#104C2×D4311yescharacteristic
502C2×#104C2×D4311yescharacteristic, complemented
503#416—431no—
504#416—431no—
505#408C2×D4311yescharacteristic, complemented
506#407—431no—
507C2×C22⋊C8—431no—
508#405—431no—
509C2×#97—431no—
510C2×C4×C8—431no—
511C4×C22⋊C4—431no—
512#341—431no—
513#341C2×D4311yescharacteristic, complemented
514#339—431no—
515#339—431no—
516#336—431no—
517#336C2×D4311yescharacteristic, complemented
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—434no—
550#131—434no—
551#131—862no—
552#131—862no—
553#131—868no—
554#131—862no—
555#131—862no—
556#131—862no—
557#131—862no—
558#131—868no—
559C2×M16—21no—
560C2×M16—431no—
561C2×M16—431no—
562C2×M16—431no—
563C2×M16—431no—
564C2×M16—431no—
565C2×M16—431no—
566C2×M16—862no—
567C2×M16—862no—
568C2×M16—861no—
569C2×M16—861no—
570C2×M16—868no—
571C2×M16—861no—
572C2×M16—861no—
573C2×M16—862no—
574C2×M16—868no—
575C2×M16—862no—
576C2×M16—861no—
577C2×M16C22×D4311yescharacteristic
578C2×M16C22×D4311yescharacteristic
579C22×C8—21no—
580C22×C8—431no—
581C22×C8—431no—
582C22×C8—861no—
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—862no—
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—21no—
620C22⋊C8—21no—
621C22⋊C8—431no—
622C22⋊C8—431no—
623C22⋊C8—431no—
624C22⋊C8—431no—
625C22⋊C8—861no—
626C22⋊C8—861no—
627#97—862no—
628#97—861no—
629C4×C8—862no—
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#41D4×D4312yes—
653#41#1062190012yes—
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—24no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—432no—
708M16—862no—
709M16—862no—
710M16—862no—
711M16—862no—
712M16—864no—
713M16—864no—
714M16—864no—
715M16—864no—
716M16—861no—
717M16—861no—
718M16—861no—
719M16—1722no—
720M16D4×D4312yes—
721C2×C8—24no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—432no—
729C2×C8—432no—
730C2×C8—431no—
731C2×C8—431no—
732C2×C8—431no—
733C2×C8—431no—
734C2×C8—864no—
735C2×C8—864no—
736C2×C8—864no—
737C2×C8—864no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—861no—
742C2×C8—1722no—
743C2×C8C2×C4×D4311yescharacteristic
744C2×C8C2×C4×D4311yescharacteristic
745C2×C8D4×D4311yescharacteristic
746C2×C8D4×D4311yescharacteristic
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—
781Q8(C22⋊D43)⋊C412yes—
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—
798D4(C22⋊D43)⋊C412yes—
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×C4C2×D4×D4311yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4C2×#1062190011yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—22no—
841C8—21no—
842C8—41no—
843C8—432no—
844C8—432no—
845C8—861no—
846C8—861no—
847C8—862no—
848C8—1721no—
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#1458340711yescharacteristic
871C22#1458340911yescharacteristic
872C4—22no—
873C4—42no—
874C4—41no—
875C4—861no—
876C4—861no—
877C4—862no—
878C4—3441no—
879C4—1721no—
880C4—1721no—
881C4C4×D4×D4311yescharacteristic
882C4C2×(C22⋊D43)⋊C411yescharacteristic
883C4#120×D4311yescharacteristic
884C4#1458340911yescharacteristic
885C2—21no—
886C2—21no—
887C2—42no—
888C2—81no—
889C2—1721no—
890C2—1721no—
891C2—1722no—
892C2#1913710011yescharacteristic
893C2#1914350011yescharacteristic
894C2#1914350911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1876C2
socleC22×C43C2×C4×D4
prime radical#19143809C2
cosocleC22×C4×C43C24
hypercenter#1876D43
hypocenterC43#21468
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
1. C2×#14583664C2semidirect
3. C2×#14583021C2semidirect
4. C2×#14583013C2semidirect
5. #19143301C2semidirect
6. #19134925C2semidirect
7. #19134894C2semidirect
8. #19134873C2semidirect
9. #19134870C2semidirect
10. #19134801C2semidirect
11. #19134537C2semidirect
12. #19134438C2semidirect
13. #19134433C2semidirect
14. #19134375C2semidirect
15. C43×#1876C2semidirect
23. C2×#13063332C22semidirect
31. #14583060C4semidirect
32. #14583058C4semidirect
33. #14583053C4semidirect
34. #14583048C4semidirect
35. #14583043C4semidirect
36. #14583041C4semidirect
37. #14583036C4semidirect
38. #14583031C4semidirect
45. C2×#13063261C22semidirect
46. C2×#13063260C22semidirect
47. #14582925C22semidirect
50. C2×#13063252C22semidirect
56. #14582857C22semidirect
57. C2×#13063235C22semidirect
58. C2×C4×C43⋊C8C22semidirect
60. #14582663C22semidirect
61. #14582660C22semidirect
62. #14582659C22semidirect
63. #14582653C22semidirect
67. C2×#104×C43C22semidirect
68. C43×#408C22semidirect
69. C43×#341C22semidirect
70. C43×#336C22semidirect
93. #13063333D4semidirect
97. #13063332D4semidirect
444. #1876D43semidirect
502. C2×#104C2×D43semidirect
505. #408C2×D43semidirect
513. #341C2×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×#145836642
#191438092
C2×#145830212
C2×#145830132
#191433012
#191349252
#191348942
#191348732
#191348702
#191348012
#191345372
#191344382
#191344332
#191343752
C43×#18762
#2146843