Finite Group Databasebeta

← #25146699

Subgroups — #25146699

Order 11008.

824 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583118C211yesmaximal, characteristic
2#19139811C211yesmaximal, characteristic, complemented
3#19137670C211yesmaximal, characteristic
4#19136016C211yesmaximal, characteristic, complemented
5#19136011C211yesmaximal, characteristic
6#19135916C211yesmaximal, characteristic, complemented
7#19135911C211yesmaximal, characteristic
8#19135544C211yesmaximal, characteristic, complemented
9#19135318C211yesmaximal, characteristic, complemented
10#19134934C211yesmaximal, characteristic, complemented
11#19134927C211yesmaximal, characteristic
12#19134608C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic
14#19134426C211yesmaximal, characteristic, complemented
15C2×C43×#489C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21#14583118—24no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29#14582837—21no—
30#14582837—21no—
31#14582806—21no—
32#14582806—21no—
33#14582806C2211yescharacteristic
34#14582804C2211yescharacteristic
35#14582804C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582792—21no—
38#14582792—21no—
39#14582774—21no—
40#14582764C2211yescharacteristic
41#14582764C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C22⋊C4×Dic43—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4⋊Q8×C43C2211yescharacteristic
54C2×#124×C43C2211yescharacteristic
55C43×#489—24no—
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C23×Dic43—21no—
63C2×#10621885—22no—
64C2×#10621885—22no—
65C2×#10621885—41no—
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71Q8×Dic43—22no—
72Q8×Dic43—41no—
73C4×Dic86—22no—
74C4×Dic86—22no—
75D4×Dic43—22no—
76D4×Dic43—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43D411yescharacteristic
79C2×C4⋊Dic43D411yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C4⋊(C43⋊C8)—22no—
93Dic43⋊C8—41no—
94Dic43⋊C8—41no—
95#13063250—22no—
96#13063250—22no—
97#13063249—22no—
98#13063246—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×Q8×C43—21no—
113C22×Q8×C43C2311yescharacteristic
114C22×D4×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C4⋊Q8×C43—22no—
118C4⋊Q8×C43—22no—
119#124×C43—22no—
120#124×C43D414yes—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#103×C43—22no—
128#103×C43—22no—
129#102×C43—22no—
130#102×C43—22no—
131#97×C43—22no—
132C24×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43—42no—
139C2×Q8×C43—42no—
140C2×Q8×C43—42no—
141C2×Q8×C43C2×D412yes—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43C2×D412yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—81no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86#4112yes—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—42no—
182C22⋊C4×C43—24no—
183C22⋊C4×C43—24no—
184C42×C43C2×D412yes—
185C42×C43#4112yes—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—81no—
189#10621885—44no—
190#10621883—44no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198C4⋊Dic43—42no—
199C4⋊Dic43#4112yes—
200Dic43⋊C4—42no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C4×Dic43—81no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C23×C43—22no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C22×D411yescharacteristic
222Q8×C43—22no—
223Q8×C43—22no—
224Q8×C43—41no—
225Q8×C43—41no—
226Q8×C43—84no—
227D4×C43—22no—
228D4×C43—22no—
229D4×C43—41no—
230D4×C43—41no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43#12112yes—
245C2×C4×C43#12112yes—
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—84no—
277Dic86—22no—
278Dic86—22no—
279Dic86—41no—
280Dic86—41no—
281C8×C43—41no—
282C8×C43—41no—
283C43⋊C8—41no—
284C43⋊C8—41no—
285#25337—431nomaximal, Sylow
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43C2×#12111yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43#54811yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57511yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57811yescharacteristic
300C4×C43—22no—
301C4×C43—22no—
302C4×C43—42no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43#52911yescharacteristic
306C4×C43#54211yescharacteristic
307C4×C43#54611yescharacteristic
308C4×C43#54711yescharacteristic
309Dic43—42no—
310Dic43—41no—
311Dic43—41no—
312Dic43—42no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317C2×#489D4311yescharacteristic
318C2×#464—431no—
319#2568—431no—
320#2367—431no—
321#2074—431no—
322#2073—431no—
323#2056—431no—
324#2055—431no—
325#1987—431no—
326#1940—431no—
327#1878—431no—
328#1877—431no—
329#1805—431no—
330#1804—431no—
331#1763—431no—
332C2×C43—82no—
333C2×C43#242711yescharacteristic
334C2×C43#304011yescharacteristic
335C2×C43#304611yescharacteristic
336C2×C43#331111yescharacteristic
337C2×C43#331311yescharacteristic
338C2×C43#337111yescharacteristic
339C2×C43#337711yescharacteristic
340C22×Q16—431no—
341C22×SD16—431no—
342C2×C4⋊Q8C2×D4311yescharacteristic
343C2×#124C2×D4311yescharacteristic
344C2×C4×Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×D4—431no—
347#489—24no—
348#464—864no—
349C2×C4⋊C8—431no—
350C2×C4⋊C8—431no—
351C2×C4⋊C8—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103C2×D4311yescharacteristic
356C2×#103C2×D4311yescharacteristic
357C2×#102—431no—
358C2×#102C2×D4311yescharacteristic
359C2×#102C2×D4311yescharacteristic
360C2×#97C2×D4311yescharacteristic
361#400—861no—
362#400—861no—
363#391—431no—
364#391—431no—
365#391—431no—
366#391—861no—
367#391—861no—
368#390—431no—
369#388—861no—
370#388—861no—
371#385—861no—
372#382—431no—
373#382—431no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C22⋊C4—861no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#336—431no—
384#336—431no—
385C43#2533711yescharacteristic, complemented, Sylow
386C22×Q8—21no—
387C22×Q8—431no—
388C22×Q8C22×D4311yescharacteristic
389C22×D4C22×D4311yescharacteristic
390C23×C4—861no—
391C2×Q16—862no—
392C2×Q16—862no—
393C2×Q16—1721no—
394C2×SD16—862no—
395C2×SD16—862no—
396C2×SD16—1721no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401C4⋊Q8—22no—
402C4⋊Q8—22no—
403#124—22no—
404#124C22⋊D4314yes—
405C4×Q8—862no—
406C4×Q8—862no—
407C4×Q8—862no—
408C4×Q8—1721no—
409C4×D4—862no—
410C4×D4—1721no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42C22×D4311yescharacteristic
432C4⋊C8—862no—
433C4⋊C8—1721no—
434C4⋊C8—1721no—
435#103—22no—
436#103—22no—
437#103—862no—
438#103—862no—
439#103—862no—
440#102—22no—
441#102—22no—
442#102—862no—
443#97—22no—
444#95—431no—
445#95—431no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457C24—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—432no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8C2×C22⋊D4312yes—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4C2×C22⋊D4312yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—3441no—
491C22×C4—1722no—
492C22×C4—1722no—
493C22×C4D4×D4311yescharacteristic
494C22×C4D4×D4311yescharacteristic
495C22×C4C23×D4311yescharacteristic
496Q16—1724no—
497SD16—1724no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8—861no—
509C2×C8—861no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—432no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—1721no—
522C4⋊C4—1721no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C22⋊C4—24no—
526C22⋊C4—24no—
527C22⋊C4—3441no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C42—861no—
531C42—861no—
532C42—861no—
533C42—861no—
534C42—3441no—
535C42—1722no—
536C42—1722no—
537C42#1062190012yes—
538C42C2×C22⋊D4312yes—
539C23—22no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C2×D4×D4311yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—41no—
550Q8—41no—
551Q8—84no—
552Q8—862no—
553Q8—862no—
554Q8—1721no—
555Q8—1721no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—862no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—862no—
587C2×C4—3444no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4#1306329712yes—
599C2×C4#1306329712yes—
600C2×C4C22×C22⋊D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4C2×#1062190011yescharacteristic
604C2×C4#1306337111yescharacteristic
605C2×C4#1306337211yescharacteristic
606C8—41no—
607C8—41no—
608C8—1721no—
609C8—1721no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22C2×#1306329711yescharacteristic
618C22#1458354211yescharacteristic
619C22#1458355711yescharacteristic
620C22#1458369511yescharacteristic
621C22#1458369511yescharacteristic
622C22#1458370811yescharacteristic
623C22#1458371511yescharacteristic
624C4—22no—
625C4—22no—
626C4—42no—
627C4—81no—
628C4—81no—
629C4—3441no—
630C4—3441no—
631C4—1722no—
632C4—1721no—
633C4—1721no—
634C4—1722no—
635C4—1721no—
636C4—1721no—
637C4#1458342811yescharacteristic
638C4#1458351811yescharacteristic
639C4#1458353711yescharacteristic
640C4#1458354811yescharacteristic
641C2—82no—
642C2#1913817511yescharacteristic
643C2#1914408711yescharacteristic
644C2#1914414911yescharacteristic
645C2#1914663011yescharacteristic
646C2#1914666011yescharacteristic
647C2#1914736211yescharacteristic
648C2#1914743611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#489C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC2×#489D43
hypocenterC43#25337
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
2. #19139811C2semidirect
4. #19136016C2semidirect
6. #19135916C2semidirect
8. #19135544C2semidirect
9. #19135318C2semidirect
10. #19134934C2semidirect
12. #19134608C2semidirect
14. #19134426C2semidirect
385. C43#25337semidirect

Maximal subgroups

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

subgroupindex
C2×#145831182
#191398112
#191376702
#191360162
#191360112
#191359162
#191359112
#191355442
#191353182
#191349342
#191349272
#191346082
#191346032
#191344262
C2×C43×#4892
#2533743