Finite Group Databasebeta

← #25126633

Subgroups — #25126633

Order 11008.

836 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063299C211yesmaximal, characteristic
2#19136993C211yesmaximal, characteristic, complemented
3#19136164C211yesmaximal, characteristic, complemented
4#19136115C211yesmaximal, characteristic, complemented
5#19136078C211yesmaximal, characteristic, complemented
6#19136028C211yesmaximal, characteristic, complemented
7#19136023C211yesmaximal, characteristic, complemented
8#19136010C211yesmaximal, characteristic, complemented
9#19135785C211yesmaximal, characteristic
10#19135778C211yesmaximal, characteristic
11C4×#13063259C211yesmaximal, characteristic, complemented
12C4×#13063257C211yesmaximal, characteristic, complemented
13C4×#13063247C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C43C211yesmaximal, characteristic, complemented
16C2×#13063299C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×C4×C22⋊D43—21no—
19C2×#13063259C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27#14582801C2211yescharacteristic
28#14582797C2211yescharacteristic
29#14582790—21no—
30#14582778—21no—
31#14582767—21no—
32#14582765C2211yescharacteristic
33#14582765C2211yescharacteristic
34#14582762—21no—
35#14582759C2211yescharacteristic
36#14582759C2211yescharacteristic
37#14582759C2211yescharacteristic
38C4×C4⋊Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C4×(C2×D43)⋊C4—21no—
42C4×C22⋊Dic43—21no—
43#14582745—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52C22×C42×C43C2211yescharacteristic
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62#13063299—22no—
63#13063299—22no—
64C4×D172—22no—
65C4×D172—22no—
66C4×C22⋊D43—44no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85#13063259—22no—
86#13063259—22no—
87#13063257—22no—
88#13063257—22no—
89#13063247—22no—
90#13063247—22no—
91#13063247—22no—
92#13063247—22no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C23×C4×C43D411yescharacteristic
105C23×C4×C43D411yescharacteristic
106C23×C4×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C42×C43—22no—
112C2×C42×C43—22no—
113C2×C42×C43D411yescharacteristic
114C2×C42×C43D411yescharacteristic
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C22⋊C8×C43—22no—
118C22⋊C8×C43—22no—
119C4×C8×C43—22no—
120C4×C8×C43—22no—
121C24×C43C2×D411yescharacteristic
122C23×D43—21no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—41no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—42no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172#4112yes—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43#4112yes—
171C2×C8×C43#4112yes—
172C42×C43—22no—
173C42×C43—22no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43#4112yes—
177C42×C43#4112yes—
178C22⋊Dic43—42no—
179C22⋊Dic43—42no—
180C22⋊Dic43—42no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43#4112yes—
199Dic43⋊C4—42no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C23×C43—21no—
204C23×C43—21no—
205C23×C43—21no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43#13512yes—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—41no—
217C22×D43—41no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—44no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—44no—
235C2×C4×C43#12312yes—
236C2×C4×C43#12312yes—
237C2×C4×C43#13512yes—
238C2×C4×C43AGL(1,ℤ/8)12yes—
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C22⋊D43—48no—
246C2×Dic43—22no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267D172—22no—
268D172—22no—
269D172—41no—
270D172—41no—
271C4×D43—84no—
272C8×C43—22no—
273C8×C43—22no—
274C8×C43—41no—
275C8×C43—41no—
276#23758—431nomaximal, Sylow
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43—41no—
284C22×C43C2×#12311yescharacteristic
285C22×C43#52511yescharacteristic
286C22×C43#53211yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43C2×#13511yescharacteristic
289C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C43#57511yescharacteristic
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—81no—
295C2×D43—81no—
296C2×D43—81no—
297C2×D43—81no—
298C4×C43—22no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43#48214yes—
303C4×C43#52911yescharacteristic
304C4×C43#52911yescharacteristic
305C4×C43#52911yescharacteristic
306C4×C43#52911yescharacteristic
307Dic43—42no—
308Dic43—81no—
309Dic43—81no—
310Dic43—81no—
311Dic43—81no—
312Dic43—81no—
313Dic43—81no—
314C4×#121—431no—
315#2283—431no—
316#2101—431no—
317#2092—431no—
318#2085—431no—
319#2077—431no—
320#2076—431no—
321#2073—431no—
322#2034—431no—
323#2033—431no—
324C4×#107—431no—
325C4×#106—431no—
326C4×#102—431no—
327C4×#102—431no—
328C4×C22⋊C8D4311yescharacteristic, complemented
329C2×C43—42no—
330C2×C43#239511yescharacteristic
331C2×C43C2×#48211yescharacteristic
332C2×C43#309111yescharacteristic
333C2×C43#310211yescharacteristic
334C2×C43#310511yescharacteristic
335C2×C43#316811yescharacteristic
336C2×C43#317111yescharacteristic
337D43—82no—
338C2×#121—431no—
339C2×C4×D4—431no—
340C2×C4×D4—861no—
341C22×C42C2×D4311yescharacteristic
342C2×#107—431no—
343C2×#107—431no—
344C2×#106—431no—
345C2×#106—431no—
346C2×#102—431no—
347C2×#102—431no—
348C2×#102—431no—
349C2×#102—431no—
350C2×C22⋊C8C2×D4311yescharacteristic
351C2×C22⋊C8C2×D4311yescharacteristic
352C2×C4×C8C2×D4311yescharacteristic
353C2×C4×C8C2×D4311yescharacteristic
354#390—431no—
355#389—431no—
356#388—861no—
357#386—861no—
358#383—861no—
359#382—431no—
360#382—431no—
361#381—861no—
362#380—431no—
363#380—431no—
364#380—431no—
365C4×C4⋊C4—431no—
366C4×C4⋊C4—431no—
367C4×C4⋊C4—431no—
368C4×C22⋊C4—861no—
369C4×C22⋊C4—861no—
370#376—861no—
371#340—431no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#336C2×D4311yescharacteristic
380#336C2×D4311yescharacteristic
381C43#2375811yescharacteristic, complemented, Sylow
382C22×D4—431no—
383C22×D4—861no—
384C23×C4—861no—
385C23×C4D17211yescharacteristic
386C23×C4D17211yescharacteristic
387C23×C4C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389C22×C8C22×D4311yescharacteristic
390C22×C8C22×D4311yescharacteristic
391C22×C8C22×D4311yescharacteristic
392#121—862no—
393#121—862no—
394C4×D4—862no—
395C4×D4—862no—
396C4×D4—1724no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42—861no—
417C2×C42D17211yescharacteristic
418C2×C42D17211yescharacteristic
419C2×C42C22×D4311yescharacteristic
420C2×C42C22×D4311yescharacteristic
421#107—862no—
422#107—862no—
423#106—862no—
424#106—862no—
425#102—862no—
426#102—862no—
427#102—862no—
428#102—862no—
429C22⋊C8—22no—
430C22⋊C8—22no—
431C4×C8—22no—
432C4×C8—22no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442#95—861no—
443#95—861no—
444C24—861no—
445C24C2×D17211yescharacteristic
446C2×D4—432no—
447C2×D4—864no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—1722no—
454C2×D4—1722no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—1722no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4C2×D17211yescharacteristic
478C22×C4C2×D17211yescharacteristic
479C22×C4C2×D17211yescharacteristic
480C22×C4C2×D17211yescharacteristic
481C22×C4C2×D17211yescharacteristic
482C22×C4C23×D4311yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8#1062189812yes—
494C2×C8#1062189812yes—
495C4⋊C4—432no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4—861no—
506C4⋊C4—861no—
507C4⋊C4—861no—
508C4⋊C4—861no—
509C4⋊C4—1722no—
510C22⋊C4—864no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C22⋊C4—1722no—
514C22⋊C4—1722no—
515C22⋊C4—1722no—
516C22⋊C4—1722no—
517C42—22no—
518C42—22no—
519C42—21no—
520C42—21no—
521C42—1722no—
522C42—1722no—
523C42—1722no—
524C42#1062190012yes—
525C42#1062190012yes—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—862no—
533C23—1721no—
534C23—1721no—
535C23—1721no—
536C23—1721no—
537C23—1721no—
538C23—1721no—
539C23#1306334712yes—
540C23C22×D17211yescharacteristic
541D4—862no—
542D4—862no—
543D4—1728no—
544D4—1721no—
545D4—1721no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—44no—
563C2×C4—862no—
564C2×C4—3444no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4#1306330912yes—
586C2×C4#1306330912yes—
587C2×C4#1306334712yes—
588C2×C4#1306335312yes—
589C2×C4#41×D4311yescharacteristic
590C2×C4#41×D4311yescharacteristic
591C2×C4C2×#1062190011yescharacteristic
592C2×C4C2×#1062190011yescharacteristic
593C2×C4C2×#1062189811yescharacteristic
594C2×C4C2×#1062189811yescharacteristic
595C8—22no—
596C8—22no—
597C8—41no—
598C8—41no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—3441no—
607C22—3441no—
608C22—3441no—
609C22—3441no—
610C22—1722no—
611C22—1722no—
612C22—1722no—
613C22C2×#1306330911yescharacteristic
614C22#1458341111yescharacteristic
615C22#1458344911yescharacteristic
616C22C2×#1306334711yescharacteristic
617C22C2×#1306334711yescharacteristic
618C22C2×#1306335311yescharacteristic
619C22#1458369911yescharacteristic
620C4—22no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—3441no—
625C4—3441no—
626C4—3441no—
627C4—3441no—
628C4—3441no—
629C4—3441no—
630C4—1722no—
631C4#1458322414yes—
632C4#1458342911yescharacteristic
633C4#1458342911yescharacteristic
634C4#1458343111yescharacteristic
635C4#1458343111yescharacteristic
636C2—42no—
637C2—3442no—
638C2#1913785511yescharacteristic
639C2C2×#1458322411yescharacteristic
640C2#1914451011yescharacteristic
641C2#1914461511yescharacteristic
642C2#1914464411yescharacteristic
643C2#1914516511yescharacteristic
644C2#1914519011yescharacteristic
subgroupG/H
centerC22×C4C2×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×C22⋊C8×C43C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenterC4×C22⋊C8D43
hypocenterC43#23758
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #19136993C2semidirect
3. #19136164C2semidirect
4. #19136115C2semidirect
5. #19136078C2semidirect
6. #19136028C2semidirect
7. #19136023C2semidirect
8. #19136010C2semidirect
11. C4×#13063259C2semidirect
12. C4×#13063257C2semidirect
13. C4×#13063247C2semidirect
14. C4×#13063247C2semidirect
15. C4×C22⋊C8×C43C2semidirect
328. C4×C22⋊C8D43semidirect
381. C43#23758semidirect

Maximal subgroups

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

subgroupindex
C4×#130632992
#191369932
#191361642
#191361152
#191360782
#191360282
#191360232
#191360102
#191357852
#191357782
C4×#130632592
C4×#130632572
C4×#130632472
C4×C22⋊C8×C432
#2375843