Finite Group Databasebeta

← #25102463

Subgroups — #25102463

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#19143811C211yesmaximal, characteristic
3C2×#14583018C211yesmaximal, characteristic, complemented
4C2×#14583013C211yesmaximal, characteristic, complemented
5#19143299C211yesmaximal, characteristic, complemented
6#19134919C211yesmaximal, characteristic, complemented
7#19134919C211yesmaximal, characteristic, complemented
8#19134871C211yesmaximal, characteristic, complemented
9#19134871C211yesmaximal, characteristic, complemented
10#19134800C211yesmaximal, characteristic, complemented
11#19134540C211yesmaximal, characteristic, complemented
12#19134436C211yesmaximal, characteristic, complemented
13#19134429C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15C43×#1871C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19#14583665—24no—
20#14583665—24no—
21C2×#13063333C2211yescharacteristic
22C2×#13063333C2211yescharacteristic
23C2×#13063333C2211yescharacteristic
24C2×#13063333C2211yescharacteristic
25C2×#13063332C2211yescharacteristic, complemented
26C2×#13063331—21no—
27C2×#13063331—21no—
28C22×#10621877C2211yescharacteristic
29C2×M16×D43—21no—
30C2×M16×D43—21no—
31#14583059C411yescharacteristic, complemented
32#14583059C411yescharacteristic, complemented
33#14583054C411yescharacteristic, complemented
34#14583049C411yescharacteristic, complemented
35#14583042C411yescharacteristic, complemented
36#14583042C411yescharacteristic, complemented
37#14583037C411yescharacteristic, complemented
38#14583032C411yescharacteristic, complemented
39#14583018—24no—
40#14583013—24no—
41#14582977—21no—
42#14582977—21no—
43#14582971—21no—
44#14582971—21no—
45C2×#13063260C2211yescharacteristic, complemented
46C2×#13063260C2211yescharacteristic, complemented
47#14582926C2211yescharacteristic, complemented
48C2×#13063253C2211yescharacteristic
49C2×#13063253C2211yescharacteristic
50C2×#13063253C2211yescharacteristic
51C2×#13063253C2211yescharacteristic
52#14582893C2211yescharacteristic
53#14582893C2211yescharacteristic
54#14582866C2211yescharacteristic, complemented
55#14582863C2211yescharacteristic
56C2×C22⋊(C43⋊C8)C2211yescharacteristic
57#14582855C2211yescharacteristic, complemented
58C2×#13063236C2211yescharacteristic, complemented
59C2×C4×C43⋊C8C2211yescharacteristic, complemented
60#14582663C2211yescharacteristic, complemented
61#14582663C2211yescharacteristic, complemented
62#14582654C2211yescharacteristic, complemented
63#14582654C2211yescharacteristic, complemented
64C22×M16×C43C2211yescharacteristic
65C43×#525C2211yescharacteristic
66C2×#104×C43C2211yescharacteristic, complemented
67C2×#104×C43C2211yescharacteristic, complemented
68C4×C22⋊C4×C43C2211yescharacteristic
69C43×#339C2211yescharacteristic, complemented
70C43×#339C2211yescharacteristic, 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
81C22×Dic86C2×C411yescharacteristic
82C22×D172C2×C411yescharacteristic
83C22×C22⋊D43—21no—
84C22×C4×D43—21no—
85#13063345—22no—
86#13063345—22no—
87#13063345—22no—
88#13063345—22no—
89C2×#10621885C2×C411yescharacteristic
90C2×#10621885C2×C411yescharacteristic
91C2×#10621883C2×C411yescharacteristic
92C2×#10621883C2×C411yescharacteristic
93C2×#10621884C2×C411yescharacteristic
94C2×#10621884C2×C411yescharacteristic
95C2×#10621882C2×C411yescharacteristic
96C2×#10621882C2×C411yescharacteristic
97#13063333—22no—
98#13063333—22no—
99#13063333—22no—
100#13063333—22no—
101#13063333—22no—
102#13063333—22no—
103#13063333D414yescomplemented
104#13063333D414yescomplemented
105#13063332—22no—
106#13063332—22no—
107#13063331—28no—
108#13063331—28no—
109C2×#10621877—22no—
110C2×#10621877—22no—
111C2×#10621877—21no—
112C2×#10621877D411yescharacteristic
113C2×#10621877D411yescharacteristic
114C2×#10621877D411yescharacteristic
115C2×#10621877D411yescharacteristic
116C2×#10621877C2311yescharacteristic
117C2×#10621877C2311yescharacteristic
118C2×#10621872—21no—
119C2×#10621872—21no—
120C2×#10621872—21no—
121C2×#10621872—21no—
122M16×D43—28no—
123M16×D43—28no—
124C22×C43⋊C8—21no—
125C22×C43⋊C8C2311yescharacteristic
126C22×C43⋊C8C2311yescharacteristic
127C22×C43⋊C8C2311yescharacteristic
128C22×C43⋊C8C2311yescharacteristic
129C2×C8×D43—21no—
130C2×C8×D43—21no—
131C2×C8×D43—21no—
132C2×C8×D43—21no—
133#13063260—22no—
134#13063260—22no—
135C4⋊(C43⋊C8)—21no—
136C4⋊(C43⋊C8)—21no—
137#13063253—22no—
138#13063253—22no—
139#13063253—22no—
140#13063253—22no—
141#13063248C2×C411yescharacteristic
142#13063248C2×C411yescharacteristic
143#13063248C2×C411yescharacteristic
144#13063248C2×C411yescharacteristic
145#13063245C2×C411yescharacteristic
146#13063245C2×C411yescharacteristic
147#13063245C2×C411yescharacteristic
148#13063245C2×C411yescharacteristic
149C22⋊(C43⋊C8)—21no—
150C22⋊(C43⋊C8)—21no—
151C22⋊(C43⋊C8)—21no—
152C22⋊(C43⋊C8)—21no—
153C22⋊(C43⋊C8)C2×C411yescharacteristic
154C22⋊(C43⋊C8)C2×C411yescharacteristic
155C22⋊(C43⋊C8)C2×C411yescharacteristic
156C22⋊(C43⋊C8)C2×C411yescharacteristic
157#13063236—22no—
158#13063236—21no—
159C4×C43⋊C8—22no—
160C4×C43⋊C8—21no—
161C2×#41×C43C2311yescharacteristic
162C23×C4×C43C2311yescharacteristic
163C2×M16×C43—21no—
164C2×M16×C43—22no—
165C2×M16×C43—22no—
166C2×M16×C43C2311yescharacteristic
167C2×M16×C43C2311yescharacteristic
168C22×C8×C43—21no—
169#123×C43—21no—
170C22⋊Q8×C43C2×C411yescharacteristic
171C22⋊Q8×C43C2×C411yescharacteristic
172#121×C43C2×C411yescharacteristic
173#121×C43C2×C411yescharacteristic
174#120×C43—21no—
175C4×D4×C43—21no—
176C4×D4×C43—21no—
177#117×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C42×C43C2311yescharacteristic
180C2×C42×C43C2311yescharacteristic
181#104×C43—22no—
182#104×C43—22no—
183#95×C43—21no—
184C24×C43#4111yescharacteristic
185C23×D43—21no—
186#41×C43—21no—
187#41×C43—21no—
188#41×C43—21no—
189#41×C43—21no—
190C2×Q8×C43C22×C411yescharacteristic
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43C22×C411yescharacteristic
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43C22×C411yescharacteristic
203C22×C4×C43C22×C411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43#4111yescharacteristic
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—21no—
211C2×C22⋊D43—21no—
212C2×C22⋊D43—21no—
213C2×C22⋊D43—21no—
214C22×Dic43—21no—
215#10621898—24no—
216#10621898—24no—
217#10621898—24no—
218#10621898—24no—
219#10621898—21no—
220#10621898—21no—
221#10621898—21no—
222#10621898—21no—
223#10621898—22no—
224#10621898—22no—
225#10621898—22no—
226#10621898—22no—
227#10621898C2×D412yes—
228#10621898C2×D412yes—
229#10621898#4112yes—
230#10621898#4112yes—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172C22×C411yescharacteristic
235C2×D172C22×C411yescharacteristic
236C2×C4×D43—24no—
237C2×C4×D43—24no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×Dic86—21no—
243C2×Dic86—22no—
244C2×Dic86—22no—
245C2×Dic86C22×C411yescharacteristic
246C2×Dic86C22×C411yescharacteristic
247M16×C43—24no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43C2×D412yes—
251M16×C43C2×D412yes—
252C2×C8×C43—24no—
253C2×C8×C43—21no—
254C2×C8×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C22×C411yescharacteristic
258C4⋊C4×C43C22×C411yescharacteristic
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C22⋊C4×C43—21no—
262C22⋊C4×C43—21no—
263C22⋊C4×C43—21no—
264C22⋊C4×C43—42no—
265C42×C43—21no—
266C42×C43—21no—
267C42×C43—21no—
268C42×C43—21no—
269C42×C43—21no—
270#10621885—22no—
271#10621885—22no—
272#10621884—22no—
273#10621884—22no—
274#10621883—22no—
275#10621883—22no—
276#10621882—22no—
277#10621882—22no—
278#10621877—22no—
279#10621877—22no—
280#10621877—22no—
281#10621877—22no—
282#10621877—21no—
283#10621877—21no—
284#10621877—21no—
285#10621877—21no—
286#10621877—42no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—42no—
296C2×C43⋊C8C22×C411yescharacteristic
297C2×C43⋊C8C22×C411yescharacteristic
298C2×C43⋊C8C22×C411yescharacteristic
299C2×C43⋊C8C22×C411yescharacteristic
300C2×C43⋊C8C2×D411yescharacteristic
301C2×C43⋊C8C2×D411yescharacteristic
302C2×C43⋊C8C2×D411yescharacteristic
303C2×C43⋊C8C2×D412yes—
304C2×C43⋊C8C2×D411yescharacteristic
305C2×C43⋊C8C2×D412yes—
306#10621872—24no—
307#10621872—24no—
308#10621872—24no—
309#10621872—24no—
310C8×D43—24no—
311C8×D43—24no—
312C8×D43—24no—
313C8×D43—24no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—41no—
318C23×C43—41no—
319C23×C43C4×D411yescharacteristic
320C23×C43C4×D411yescharacteristic
321C23×C43C2×#4111yescharacteristic
322C22×D43—21no—
323C22×D43—21no—
324C22×D43—24no—
325C22×D43—81no—
326C22×D43—81no—
327Q8×C43—21no—
328Q8×C43—21no—
329D4×C43—21no—
330D4×C43—21no—
331D4×C43—41no—
332D4×C43—41no—
333D4×C43—81no—
334D4×C43—81no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—22no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43C4×D411yescharacteristic
357C2×C4×C43C4×D411yescharacteristic
358C2×C4×C43C23×C411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C22×D411yescharacteristic
362C2×C4×C43C2×#4111yescharacteristic
363C2×C4×C43C2×#4111yescharacteristic
364C22⋊D43—24no—
365C22⋊D43—24no—
366C22⋊D43—22no—
367C22⋊D43—22no—
368C22⋊D43—22no—
369C22⋊D43—22no—
370C2×Dic43—24no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373D172—24no—
374D172—21no—
375D172—21no—
376D172C4×D412yes—
377D172C4×D412yes—
378C4×D43—24no—
379C4×D43—24no—
380C4×D43—22no—
381C4×D43—22no—
382C4×D43—22no—
383C4×D43—22no—
384Dic86—24no—
385Dic86—21no—
386Dic86—21no—
387Dic86C4×D412yes—
388Dic86C4×D412yes—
389C8×C43—22no—
390C8×C43—22no—
391C43⋊C8—21no—
392C43⋊C8—21no—
393C43⋊C8—21no—
394C43⋊C8—21no—
395C43⋊C8—21no—
396C43⋊C8—21no—
397C43⋊C8—41no—
398C43⋊C8—41no—
399C43⋊C8#12012yes—
400C43⋊C8#12012yes—
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—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43—81no—
414C22×C43—81no—
415C22×C43C2×C4×D411yescharacteristic
416C22×C43#52511yescharacteristic
417C22×C43#52511yescharacteristic
418C2×D43—22no—
419C2×D43—22no—
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—41no—
429C4×C43—41no—
430C4×C43—41no—
431C4×C43—81no—
432C4×C43C2×C4×D411yescharacteristic
433C4×C43C2×C4×D411yescharacteristic
434C4×C43C2×#12011yescharacteristic
435C4×C43#52511yescharacteristic
436Dic43—22no—
437Dic43—22no—
438C2×#568—431no—
439#3002—431no—
440C2×#444—431no—
441C2×#443—431no—
442#2930—431no—
443#1876—431no—
444#1876—431no—
445#1871D4311yescharacteristic, complemented
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—41no—
456C2×C43—41no—
457C2×C43—81no—
458C2×C43C4×#12011yescharacteristic
459C2×C43#295611yescharacteristic
460C2×C43#295711yescharacteristic
461D43—42no—
462D43—42no—
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#525C2×D4311yescharacteristic
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, complemented
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×C8—431no—
511C4×C22⋊C4C2×D4311yescharacteristic
512#341—431no—
513#341—431no—
514#339C2×D4311yescharacteristic, complemented
515#339C2×D4311yescharacteristic, complemented
516#336—431no—
517#336—431no—
518C43#2146811yescharacteristic, complemented, Sylow
519C2×#41—431no—
520C2×#41—431no—
521C2×#41—431no—
522C2×#41—431no—
523C2×#41—862no—
524C2×#41—862no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—861no—
528C2×#41—861no—
529C2×#41C22×D4311yescharacteristic
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—868no—
550#131—868no—
551#131—862no—
552#131—862no—
553#131—862no—
554#131—862no—
555#131—862no—
556#131—862no—
557#131—862no—
558#131—862no—
559C2×M16—21no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—431no—
563C2×M16—431no—
564C2×M16—431no—
565C2×M16—431no—
566C2×M16—431no—
567C2×M16—431no—
568C2×M16—861no—
569C2×M16—861no—
570C2×M16—861no—
571C2×M16—861no—
572C2×M16—862no—
573C2×M16—862no—
574C2×M16—861no—
575C2×M16—868no—
576C2×M16—868no—
577C2×M16C22×D4311yescharacteristic
578C2×M16C22×D4311yescharacteristic
579C22×C8—21no—
580C22×C8—431no—
581C22×C8—431no—
582C22×C8—431no—
583C22×C8—431no—
584C22×C8—861no—
585C22×C8—861no—
586C22×C8—861no—
587C22×C8—861no—
588C22×C8—861no—
589#123—21no—
590C22⋊Q8C4×D4311yescharacteristic
591C22⋊Q8C4×D4311yescharacteristic
592#121C4×D4311yescharacteristic
593#121C4×D4311yescharacteristic
594#120—21no—
595C4×D4—21no—
596C4×D4—21no—
597#117C22×D4311yescharacteristic
598C2×C22⋊C4—21no—
599C2×C42C22×D4311yescharacteristic
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—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—862no—
630C4×C8—861no—
631#95—21no—
632C24—861no—
633C24#1062190011yescharacteristic
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—432no—
639#41—432no—
640#41—432no—
641#41—432no—
642#41—862no—
643#41—862no—
644#41—862no—
645#41—862no—
646#41—864no—
647#41—864no—
648#41—864no—
649#41—864no—
650#41—861no—
651#41—861no—
652#41—861no—
653#41—861no—
654C2×Q8—431no—
655C2×Q8—431no—
656C2×Q8—862no—
657C2×Q8—862no—
658C2×Q8—861no—
659C2×Q8C2×C4×D4311yescharacteristic
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—431no—
664C2×D4—431no—
665C2×D4—862no—
666C2×D4—862no—
667C2×D4—864no—
668C2×D4—864no—
669C2×D4—861no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4—861no—
674C2×D4C2×C4×D4311yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—864no—
683C22×C4—864no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4C2×C4×D4311yescharacteristic
690C22×C4C2×C4×D4311yescharacteristic
691C22×C4D4×D4311yescharacteristic
692C22×C4D4×D4311yescharacteristic
693C22×C4#1062190011yescharacteristic
694C22×C4C23×D4311yescharacteristic
695Q16—862no—
696Q16—862no—
697SD16—862no—
698SD16—862no—
699SD16—862no—
700SD16—862no—
701D8—862no—
702D8—862no—
703M16—24no—
704M16—21no—
705M16—21no—
706M16—864no—
707M16—864no—
708M16—864no—
709M16—864no—
710M16—862no—
711M16—862no—
712M16—862no—
713M16—862no—
714M16—861no—
715M16—861no—
716M16—861no—
717M16—861no—
718M16—1722no—
719M16D4×D4312yes—
720M16D4×D4312yes—
721C2×C8—24no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—432no—
725C2×C8—432no—
726C2×C8—431no—
727C2×C8—431no—
728C2×C8—431no—
729C2×C8—431no—
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—861no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—1722no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4C2×C4×D4311yescharacteristic
750C4⋊C4C2×C4×D4311yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—41no—
766C23—41no—
767C23—864no—
768C23—861no—
769C23—861no—
770C23—3441no—
771C23—3441no—
772C23(C22⋊D43)⋊C411yescharacteristic
773C23(C22⋊D43)⋊C411yescharacteristic
774C23C2×#1062190011yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—432no—
778Q8—432no—
779Q8—864no—
780Q8—861no—
781Q8—861no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—41no—
786D4—81no—
787D4—81no—
788D4—432no—
789D4—432no—
790D4—864no—
791D4—864no—
792D4—864no—
793D4—862no—
794D4—862no—
795D4—862no—
796D4—862no—
797D4—861no—
798D4—861no—
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—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—864no—
821C2×C4—864no—
822C2×C4—864no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4(C22⋊D43)⋊C411yescharacteristic
830C2×C4(C22⋊D43)⋊C411yescharacteristic
831C2×C4C22×C4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4#41×D4311yescharacteristic
837C8—22no—
838C8—22no—
839C8—432no—
840C8—432no—
841C8—861no—
842C8—861no—
843C8—861no—
844C8—861no—
845C8—861no—
846C8—861no—
847C8—1721no—
848C8—1721no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—81no—
861C22—81no—
862C22—862no—
863C22—862no—
864C22—3444no—
865C22—1721no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22C2×(C22⋊D43)⋊C411yescharacteristic
870C22#1458340911yescharacteristic
871C22#1458340911yescharacteristic
872C4—21no—
873C4—21no—
874C4—42no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—81no—
879C4—862no—
880C4—862no—
881C4C4×D4×D4311yescharacteristic
882C4C4×D4×D4311yescharacteristic
883C4#120×D4311yescharacteristic
884C4#1458340711yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—1722no—
891C2—1722no—
892C2#1913710011yescharacteristic
893C2#1914350111yescharacteristic
894C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1871C2
socleC22×C43C2×C4×D4
prime radical#19143811C2
cosocleC22×C4×C43C24
hypercenter#1871D43
hypocenterC43#21468
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14583018C2semidirect
4. C2×#14583013C2semidirect
5. #19143299C2semidirect
6. #19134919C2semidirect
7. #19134919C2semidirect
8. #19134871C2semidirect
9. #19134871C2semidirect
10. #19134800C2semidirect
11. #19134540C2semidirect
12. #19134436C2semidirect
13. #19134429C2semidirect
14. #19134379C2semidirect
15. C43×#1871C2semidirect
25. C2×#13063332C22semidirect
31. #14583059C4semidirect
32. #14583059C4semidirect
33. #14583054C4semidirect
34. #14583049C4semidirect
35. #14583042C4semidirect
36. #14583042C4semidirect
37. #14583037C4semidirect
38. #14583032C4semidirect
45. C2×#13063260C22semidirect
46. C2×#13063260C22semidirect
47. #14582926C22semidirect
54. #14582866C22semidirect
57. #14582855C22semidirect
58. C2×#13063236C22semidirect
59. C2×C4×C43⋊C8C22semidirect
60. #14582663C22semidirect
61. #14582663C22semidirect
62. #14582654C22semidirect
63. #14582654C22semidirect
66. C2×#104×C43C22semidirect
67. C2×#104×C43C22semidirect
69. C43×#339C22semidirect
70. C43×#339C22semidirect
103. #13063333D4semidirect
104. #13063333D4semidirect
445. #1871D43semidirect
501. C2×#104C2×D43semidirect
502. C2×#104C2×D43semidirect
514. #339C2×D43semidirect
515. #339C2×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
#191438112
C2×#145830182
C2×#145830132
#191432992
#191349192
#191348712
#191348002
#191345402
#191344362
#191344292
#191343792
C43×#18712
#2146843