Finite Group Databasebeta

← #25196528

Subgroups — #25196528

Order 11008.

798 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140717C211yesmaximal, characteristic, complemented
2#19137317C211yesmaximal, characteristic
3#19135740C211yesmaximal, characteristic, complemented
4#19135739C211yesmaximal, characteristic, complemented
5#19135730C211yesmaximal, characteristic, complemented
6#19135729C211yesmaximal, characteristic, complemented
7#19135417C211yesmaximal, characteristic
8#19135399C211yesmaximal, characteristic
9#19134727C211yesmaximal, characteristic, complemented
10#19134724C211yesmaximal, characteristic, complemented
11#19134606C211yesmaximal, characteristic, complemented
12#19134605C211yesmaximal, characteristic, complemented
13#19134592C211yesmaximal, characteristic, complemented
14#19134454C211yesmaximal, characteristic, complemented
15C43×#1802C211yesmaximal, characteristic, complemented
16C2×#13063324C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×#13063316C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063247C2211yescharacteristic
22C2×#13063247C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582832—21no—
30#14582832—21no—
31#14582819—21no—
32#14582819—21no—
33#14582802C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582778—21no—
36#14582778—21no—
37#14582775—21no—
38#14582775—21no—
39#14582768C2211yescharacteristic
40#14582765C2211yescharacteristic
41#14582764C2211yescharacteristic
42#14582764C2211yescharacteristic
43#14582745C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#384C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C22×C4×D43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063324—41no—
67#13063324—41no—
68#13063321—22no—
69#13063321Q814yescomplemented
70#13063316—41no—
71#13063316—41no—
72C4×D172—22no—
73C4×D172—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89C4⋊(C43⋊C8)—22no—
90#13063247—41no—
91#13063247—41no—
92#13063246—41no—
93#13063246—41no—
94#13063245—41no—
95#13063245—41no—
96#13063235—22no—
97C8×Dic43—22no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×D4×C43C2311yescharacteristic
109C23×C4×C43—21no—
110C22×C8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C4×D4×C43—22no—
113C4×D4×C43—22no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121C4⋊C8×C43—22no—
122#102×C43—41no—
123#102×C43—41no—
124C24×C43—21no—
125C23×D43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43C2×Q812yes—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—42no—
136C22×C4×C43—81no—
137C22×C4×C43—81no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—24no—
143C2×C22⋊D43—81no—
144C2×C22⋊D43—81no—
145C2×C22⋊D43—81no—
146C2×C22⋊D43—81no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C22×Dic43C2×D411yescharacteristic
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172C2×Q812yes—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×Dic86—42no—
164C2×Dic86—81no—
165C2×Dic86—81no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—81no—
179C4⋊C4×C43—81no—
180C22⋊C4×C43—42no—
181C42×C43#4112yes—
182C42×C43#4112yes—
183C22⋊Dic43—81no—
184C22⋊Dic43—81no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—81no—
198Dic43⋊C4—81no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43C2×Q812yes—
202C4×Dic43#4112yes—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C23×C43—22no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C22×D411yescharacteristic
217C22×D43—22no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—41no—
227D4×C43—41no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—84no—
242C2×C4×C43#12412yes—
243C2×C4×C43#12412yes—
244C2×C4×C43C22×Q811yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C22⋊D43—84no—
251C22⋊D43—84no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43C22⋊Q812yes—
272C2×Dic43C22⋊Q812yes—
273D172—22no—
274D172—22no—
275D172—41no—
276D172—41no—
277C4×D43—84no—
278Dic86—84no—
279C8×C43—41no—
280C8×C43—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283#29152—431nomaximal, Sylow
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43C2×C22⋊Q811yescharacteristic
292C22×C43C2×#12411yescharacteristic
293C22×C43#53511yescharacteristic
294C22×C43#57611yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57711yescharacteristic
297C22×C43#57711yescharacteristic
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—42no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C4×C43—22no—
306C4×C43—22no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43#55411yescharacteristic
311C4×C43#55411yescharacteristic
312C4×C43#55511yescharacteristic
313C4×C43#55511yescharacteristic
314Dic43—22no—
315Dic43—22no—
316Dic43—41no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320Dic43—81no—
321#2660—431no—
322#2328—431no—
323#2025—431no—
324#2025—431no—
325#2023—431no—
326#2023—431no—
327#1961—431no—
328#1957—431no—
329#1836—431no—
330#1835—431no—
331#1804—431no—
332#1804—431no—
333#1802—431no—
334#1802D4311yescharacteristic, complemented
335#1768—431no—
336C2×C43—82no—
337C2×C43#256311yescharacteristic
338C2×C43#308111yescharacteristic
339C2×C43#308111yescharacteristic
340C2×C43#313611yescharacteristic
341C2×C43#313611yescharacteristic
342C2×C43#322011yescharacteristic
343C2×C43#322111yescharacteristic
344D43—82no—
345C2×C4⋊Q8—431no—
346C2×#127—431no—
347C2×#125—431no—
348C2×C4×D4—431no—
349C2×C4×D4C2×D4311yescharacteristic
350C2×C4⋊C8—431no—
351C2×C4⋊C8C2×D4311yescharacteristic
352C2×#102—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102C2×D4311yescharacteristic
359C2×#102C2×D4311yescharacteristic
360C2×#97—431no—
361C2×C4×C8—431no—
362#398—861no—
363#398—861no—
364#395—861no—
365#395—861no—
366#390—431no—
367#390—431no—
368#386—861no—
369#386—861no—
370#386—861no—
371#386—861no—
372#384—431no—
373#384C2×D4311yescharacteristic
374#382—431no—
375#382—431no—
376#382—431no—
377#376—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340C2×D4311yescharacteristic
385#340C2×D4311yescharacteristic
386#336—431no—
387#336—431no—
388C43#2915211yescharacteristic, complemented, Sylow
389C22×Q8—861no—
390C22×D4—431no—
391C22×D4—861no—
392C22×D4—861no—
393C22×D4C22×D4311yescharacteristic
394C23×C4—21no—
395C23×C4—861no—
396C22×C8—431no—
397C22×C8—431no—
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400C4⋊Q8—1721no—
401C4⋊Q8—1721no—
402#127—434no—
403#127—862no—
404#125—1721no—
405#125—1721no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—862no—
409C4×D4—862no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C4⋊C4C22×D4311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42C22×D4311yescharacteristic
432C4⋊C8—22no—
433C4⋊C8—862no—
434#102—41no—
435#102—41no—
436#102—1721no—
437#102—1721no—
438#102—1721no—
439#102—1721no—
440#102—1721no—
441#102—1721no—
442#97—862no—
443C4×C8—862no—
444#95—431no—
445#95—431no—
446#95—431no—
447#95—431no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454C24—21no—
455C24—861no—
456C2×Q8—3441no—
457C2×Q8—3441no—
458C2×Q8—1722no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—432no—
465C2×D4—864no—
466C2×D4—864no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—3441no—
473C2×D4—3441no—
474C2×D4—3441no—
475C2×D4—3441no—
476C2×D4Q8×D4312yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—3441no—
491C22×C4—3441no—
492C22×C4—1722no—
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4311yescharacteristic
495C22×C4C23×D4311yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—3441no—
523C4⋊C4—3441no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C22⋊C4—42no—
528C22⋊C4—3441no—
529C22⋊C4—3441no—
530C22⋊C4—3441no—
531C22⋊C4—3441no—
532C22⋊C4—1722no—
533C42—432no—
534C42—432no—
535C42—861no—
536C42—861no—
537C42#1062189812yes—
538C42#1062190012yes—
539C23—22no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—862no—
547C23—1721no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23C2×D4×D4311yescharacteristic
554Q8—3444no—
555D4—22no—
556D4—22no—
557D4—41no—
558D4—41no—
559D4—862no—
560D4—862no—
561D4—3444no—
562D4—3444no—
563D4—1721no—
564D4—1721no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—84no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—3444no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4#1306331112yes—
602C2×C4#1306331112yes—
603C2×C4C2×Q8×D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4C2×#1062190011yescharacteristic
606C2×C4C2×#1062189811yescharacteristic
607C2×C4#1306337011yescharacteristic
608C2×C4#1306337111yescharacteristic
609C8—41no—
610C8—41no—
611C8—1721no—
612C8—1721no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—3441no—
621C22—3441no—
622C22—3441no—
623C22—3441no—
624C22—1722no—
625C22—1722no—
626C22—1722no—
627C22C22⋊Q8×D4311yescharacteristic
628C22C2×#1306331111yescharacteristic
629C22#1458346511yescharacteristic
630C22#1458370011yescharacteristic
631C22#1458370311yescharacteristic
632C22#1458370511yescharacteristic
633C22#1458370811yescharacteristic
634C4—22no—
635C4—22no—
636C4—81no—
637C4—81no—
638C4—81no—
639C4—862no—
640C4—862no—
641C4—3441no—
642C4—3441no—
643C4—3441no—
644C4—1721no—
645C4—1721no—
646C4#1458360411yescharacteristic
647C4#1458360711yescharacteristic
648C4#1458361211yescharacteristic
649C4#1458361311yescharacteristic
650C2—82no—
651C2—3442no—
652C2#1913976511yescharacteristic
653C2#1914441911yescharacteristic
654C2#1914442111yescharacteristic
655C2#1914494711yescharacteristic
656C2#1914495211yescharacteristic
657C2#1914564411yescharacteristic
658C2#1914565511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1802C2
socleC23×C43C22×D4
prime radicalC2×#13063321C22
hypercenter#1802D43
hypocenterC43#29152
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. #19140717C2semidirect
3. #19135740C2semidirect
4. #19135739C2semidirect
5. #19135730C2semidirect
6. #19135729C2semidirect
9. #19134727C2semidirect
10. #19134724C2semidirect
11. #19134606C2semidirect
12. #19134605C2semidirect
13. #19134592C2semidirect
14. #19134454C2semidirect
15. C43×#1802C2semidirect
69. #13063321Q8semidirect
334. #1802D43semidirect
388. C43#29152semidirect

Maximal subgroups

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

subgroupindex
#191407172
#191373172
#191357402
#191357392
#191357302
#191357292
#191354172
#191353992
#191347272
#191347242
#191346062
#191346052
#191345922
#191344542
C43×#18022
#2915243