Finite Group Databasebeta

← #25106256

Subgroups — #25106256

Order 11008.

1108 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#423×D43C211yesmaximal, characteristic, complemented
3#19136987C211yesmaximal, characteristic, complemented
4#19135576C211yesmaximal, characteristic, complemented
5#19135575C211yesmaximal, characteristic, complemented
6#19135428C211yesmaximal, characteristic, complemented
7#19134894C214yesmaximal, complemented
8#19134613C214yesmaximal, complemented
9C43×#1963C211yesmaximal, characteristic, complemented
10C2×M16×D43C2212yes—
11#14583456C2211yescharacteristic
12#14583454C411yescharacteristic, complemented
13#14583454C411yescharacteristic, complemented
14#14583447C411yescharacteristic, complemented
15#14583447C411yescharacteristic, complemented
16#14583431—21no—
17#14583431—21no—
18#14583430—21no—
19#14583430—21no—
20#14583428C412yescomplemented
21#14583428C412yescomplemented
22#14583409—21no—
23#14583409—21no—
24#14583406C2212yes—
25#41×Dic43C2212yes—
26C4×#10621900—21no—
27C4×#10621900—21no—
28C2×C42×D43C2211yescharacteristic
29#14582923C2211yescharacteristic
30#14582922C2212yes—
31#14582921—21no—
32#14582921—21no—
33C4⋊C8×D43—21no—
34C4⋊C8×D43—21no—
35C2×#13063252C2214yes—
36#14582766—21no—
37#14582763—21no—
38#14582761—21no—
39#14582758—21no—
40C4×Dic43⋊C4C2212yes—
41C4×(C2×D43)⋊C4C2212yes—
42#14582745C2211yescharacteristic
43#14582660C2214yes—
44#14582659C2214yes—
45C43×#532C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C2×#104×C43C2214yes—
48C43×#376C2211yescharacteristic
49C2×#10621900—21no—
50C2×#10621900—21no—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621877C2312yes—
55C2×#10621872—22no—
56M16×D43—44no—
57C2×C8×D43—22no—
58#13063325C2×C411yescharacteristic
59#13063325C2×C411yescharacteristic
60#13063318—22no—
61#13063318—22no—
62#13063317C2×C412yes—
63#13063316—21no—
64#13063316—21no—
65#13063312—21no—
66#13063312—21no—
67#13063307—22no—
68#13063307—22no—
69#13063306—22no—
70#13063305—21no—
71#13063305—21no—
72#13063304—21no—
73#13063304—21no—
74#13063301C2×C412yes—
75#13063301C2×C412yes—
76#13063296—21no—
77#13063296—21no—
78#13063296C2×C412yes—
79#13063296C2×C412yes—
80#13063293—22no—
81Q8×Dic43C2×C412yes—
82Q8×Dic43C2×C412yes—
83C4×Dic86—21no—
84C4×Dic86—21no—
85#13063290—21no—
86#13063290—21no—
87D4×Dic43—22no—
88D4×Dic43—22no—
89D4×Dic43—21no—
90D4×Dic43—21no—
91D4×Dic43C2×C412yes—
92D4×Dic43C2×C412yes—
93C4×C22⋊D43—22no—
94C4×C22⋊D43—22no—
95(C22⋊D43)⋊C4—22no—
96(C22⋊D43)⋊C4—22no—
97#13063284—22no—
98#13063284C2312yes—
99#13063283—21no—
100#13063283—21no—
101#13063281—22no—
102#13063281—22no—
103C2×Dic43⋊C4—22no—
104C2×(C2×D43)⋊C4—22no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43C2312yes—
109C2×C4×Dic43C2311yescharacteristic
110C42×D43C2×C411yescharacteristic
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43C2×C411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43D411yescharacteristic
118C4⋊(C43⋊C8)—21no—
119C4⋊(C43⋊C8)—21no—
120Dic43⋊C8—22no—
121Dic43⋊C8—22no—
122#13063252—44no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C2×#41×C43C2312yes—
128C2×M16×C43C2312yes—
129C4⋊Q8×C43C2×C411yescharacteristic
130#127×C43C2×C411yescharacteristic
131#124×C43C2×C412yes—
132#121×C43—21no—
133#121×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C2×C42×C43C2312yes—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43—21no—
140#104×C43—44no—
141#95×C43—21no—
142#95×C43—21no—
143C23×D43C2×D411yescharacteristic
144#41×C43—24no—
145#41×C43—24no—
146C2×Q8×C43C22×C412yes—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—22no—
150C2×D4×C43C22×C412yes—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164#10621900—44no—
165#10621900—44no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22⋊C411yescharacteristic
174C2×C4×D43C22⋊C411yescharacteristic
175C2×C4×D43C22⋊C411yescharacteristic
176C2×C4×D43C22⋊C411yescharacteristic
177C2×C4×D43C22⋊C411yescharacteristic
178C2×C4×D43C22×C411yescharacteristic
179C2×C4×D43C22×C411yescharacteristic
180C2×C4×D43C2×D411yescharacteristic
181C2×C4×D43C2×D411yescharacteristic
182C2×Dic86—21no—
183C2×Dic86—21no—
184M16×C43—24no—
185C2×C8×C43—22no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C22⋊C4×C43—22no—
189C22⋊C4×C43—22no—
190C42×C43—22no—
191C42×C43—22no—
192C42×C43C22×C411yescharacteristic
193C42×C43C22×C411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198C22⋊Dic43—22no—
199C22⋊Dic43—22no—
200C22⋊Dic43—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—44no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—22no—
207C4⋊Dic43—22no—
208C4⋊Dic43C22×C412yes—
209C4⋊Dic43C22×C412yes—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—44no—
215C4×Dic43—22no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43C22⋊C411yescharacteristic
221C4×Dic43C22⋊C411yescharacteristic
222C4×Dic43C22⋊C411yescharacteristic
223C4×Dic43C22⋊C411yescharacteristic
224C4×Dic43C22⋊C411yescharacteristic
225C4×Dic43C22⋊C411yescharacteristic
226C4×Dic43C22⋊C411yescharacteristic
227C4×Dic43C22⋊C411yescharacteristic
228C4×Dic43C22×C411yescharacteristic
229C4×Dic43C22×C411yescharacteristic
230C4×Dic43C2×D411yescharacteristic
231C4×Dic43C2×D411yescharacteristic
232#10621877—24no—
233C2×C43⋊C8—22no—
234#10621872—44no—
235C8×D43—44no—
236C23×C43—22no—
237C23×C43C22×D411yescharacteristic
238C22×D43—22no—
239C22×D43—22no—
240C22×D43—41no—
241C22×D43C2×C22⋊C411yescharacteristic
242C22×D43C2×C22⋊C411yescharacteristic
243Q8×C43—24no—
244D4×C43—24no—
245D4×C43—42no—
246D4×C43—42no—
247D4×C43—44no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—42no—
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C23×C411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43H(5,𝔽2)12yes—
263C2×C4×C432−1+412yes—
264C22⋊D43—44no—
265C22⋊D43—44no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—41no—
271C2×Dic43—44no—
272C2×Dic43—44no—
273C2×Dic43—42no—
274C2×Dic43—42no—
275C2×Dic43—42no—
276C2×Dic43C2×C22⋊C411yescharacteristic
277C2×Dic43C2×C22⋊C411yescharacteristic
278C2×Dic43C2×C22⋊C411yescharacteristic
279C2×Dic43C2×C22⋊C411yescharacteristic
280C2×Dic43C2×C22⋊C411yescharacteristic
281C2×Dic43C2×C22⋊C411yescharacteristic
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—22no—
285C4×D43—22no—
286C4×D43—21no—
287C4×D43—21no—
288C4×D43—21no—
289C4×D43—21no—
290C4×D43—22no—
291C4×D43—22no—
292C4×D43—41no—
293C4×D43—41no—
294C4×D43—41no—
295C4×D43—41no—
296Dic86—42no—
297Dic86—42no—
298C8×C43—42no—
299C43⋊C8—42no—
300#21857—431nomaximal, Sylow
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43C22×C22⋊C411yescharacteristic
307C22×C43#53712yes—
308C2×D43—21no—
309C2×D43—21no—
310C2×D43—21no—
311C2×D43—21no—
312C2×D43—21no—
313C2×D43—44no—
314C2×D43#42112yes—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—42no—
320C4×C43—82no—
321C4×C43#52012yes—
322C4×C43#53511yescharacteristic
323C4×C43#53611yescharacteristic
324Dic43—21no—
325Dic43—21no—
326Dic43—21no—
327Dic43—21no—
328Dic43—21no—
329Dic43—42no—
330Dic43—42no—
331Dic43—82no—
332Dic43#42112yes—
333#3444—431no—
334C2×#423—431no—
335#2283—431no—
336#1995—431no—
337#1995—431no—
338#1963—431no—
339#1963D4311yescharacteristic, complemented
340#1871—434no—
341#1806—434no—
342C2×C43—22no—
343C2×C43—82no—
344C2×C43#231111yescharacteristic
345C2×C43C2×#42111yescharacteristic
346C2×C43C2×#42111yescharacteristic
347D43—22no—
348D43—41no—
349C22×M16—432no—
350#533—431no—
351#533—431no—
352#533—431no—
353#532—431no—
354#532—431no—
355#532C2×D4311yescharacteristic
356#529—432no—
357#529—432no—
358#529—861no—
359#529—861no—
360#529—861no—
361#529—861no—
362#525—432no—
363#525—861no—
364#525—861no—
365C4×#41—432no—
366C4×#41—861no—
367C4×#41—861no—
368C22×C42—431no—
369#423—432no—
370#423—431no—
371#423—861no—
372#423—861no—
373#423C2×D4311yescharacteristic
374C2×C4⋊C8—861no—
375C2×C4⋊C8—861no—
376C2×#104—434no—
377C2×#104C2×D4314yes—
378#383—861no—
379#382—861no—
380#381—861no—
381#380—861no—
382C4×C4⋊C4—432no—
383C4×C22⋊C4—432no—
384#376—431no—
385#376C2×D4311yescharacteristic
386#339—434no—
387#339—434no—
388C43#2185711yescharacteristic, complemented, Sylow
389C2×#41—861no—
390C2×#41—861no—
391C2×#41C22×D4312yes—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4—431no—
395C2×M16—432no—
396C2×M16—862no—
397C2×M16—1724no—
398C2×M16C22×D4312yes—
399C22×C8—862no—
400C4⋊Q8—431no—
401C4⋊Q8—431no—
402C4⋊Q8C4×D4311yescharacteristic
403#127C4×D4311yescharacteristic
404#126—862no—
405#126—862no—
406#125—432no—
407#125—861no—
408#125—861no—
409#124—861no—
410#124—861no—
411#124C4×D4312yes—
412#123—862no—
413#123—862no—
414#123—862no—
415C22⋊Q8—432no—
416C22⋊Q8—432no—
417C22⋊Q8—861no—
418C22⋊Q8—861no—
419C22⋊Q8—861no—
420C22⋊Q8—861no—
421#121—21no—
422#121—21no—
423#121—432no—
424#121—432no—
425#121—861no—
426#121—861no—
427#120—862no—
428C4×Q8—432no—
429C4×Q8—432no—
430C4×Q8—861no—
431C4×Q8—861no—
432C4×Q8—861no—
433C4×Q8—861no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—432no—
437C4×D4—432no—
438C4×D4—861no—
439C4×D4—861no—
440C4×D4—862no—
441C4×D4—862no—
442C4×D4—862no—
443C4×D4—862no—
444C4×D4—862no—
445C4×D4—862no—
446#117—432no—
447#117—862no—
448#117—862no—
449#117—862no—
450#117—861no—
451#117—861no—
452C2×C4⋊C4—862no—
453C2×C22⋊C4—862no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C2×C42—431no—
463C2×C42—431no—
464C2×C42—431no—
465C2×C42—432no—
466C2×C42—862no—
467C2×C42C22×D4312yes—
468C2×C42C22×D4311yescharacteristic
469C4⋊C8—21no—
470C4⋊C8—21no—
471C4⋊C8—862no—
472C4⋊C8—862no—
473C4⋊C8—861no—
474C4⋊C8—861no—
475#104—44no—
476#104—1724no—
477#95—21no—
478#95—21no—
479#95—862no—
480#95—862no—
481#95—861no—
482#95—861no—
483C24—431no—
484#41—24no—
485#41—24no—
486#41—1724no—
487#41—1724no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8C2×C4×D4312yes—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—862no—
495C2×D4—862no—
496C2×D4C2×C4×D4312yes—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—431no—
510C22×C4—431no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—862no—
515C22×C4—862no—
516C22×C4—862no—
517C22×C4—862no—
518C22×C4—862no—
519C22×C4—1722no—
520C22×C4—1722no—
521C22×C4D4×D4311yescharacteristic
522C22×C4D4×D4311yescharacteristic
523C22×C4C23×D4311yescharacteristic
524M16—24no—
525M16—864no—
526M16—1724no—
527C2×C8—22no—
528C2×C8—862no—
529C2×C8—1724no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—432no—
533C4⋊C4—432no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—862no—
541C4⋊C4—862no—
542C4⋊C4—1724no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—862no—
546C22⋊C4—862no—
547C22⋊C4—862no—
548C22⋊C4—862no—
549C22⋊C4—862no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—1724no—
553C42—22no—
554C42—22no—
555C42—431no—
556C42—431no—
557C42—431no—
558C42—431no—
559C42—431no—
560C42—431no—
561C42—431no—
562C42—431no—
563C42—431no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42—862no—
568C42—862no—
569C42—862no—
570C42—862no—
571C42—862no—
572C42C2×C4×D4311yescharacteristic
573C42C2×C4×D4311yescharacteristic
574C42D4×D4311yescharacteristic
575C42D4×D4311yescharacteristic
576C23—22no—
577C23—431no—
578C23—431no—
579C23—862no—
580C23—862no—
581C23—1721no—
582C23C2×D4×D4311yescharacteristic
583Q8—24no—
584Q8—1722no—
585Q8—1722no—
586D4—24no—
587D4—42no—
588D4—42no—
589D4—44no—
590D4—1724no—
591D4—1724no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—431no—
601C2×C4—431no—
602C2×C4—431no—
603C2×C4—431no—
604C2×C4—431no—
605C2×C4—431no—
606C2×C4—862no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—862no—
619C2×C4—862no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1724no—
625C2×C4—1721no—
626C2×C4—1724no—
627C2×C4—1722no—
628C2×C4—1722no—
629C2×C4—1722no—
630C2×C4C22⋊C4×D4311yescharacteristic
631C2×C4C22⋊C4×D4311yescharacteristic
632C2×C4C22⋊C4×D4311yescharacteristic
633C2×C4C22⋊C4×D4311yescharacteristic
634C2×C4C22×C4×D4311yescharacteristic
635C2×C4C2×D4×D4311yescharacteristic
636C2×C4#1306337012yes—
637C2×C4#1306337212yes—
638C8—42no—
639C8—1722no—
640C22—21no—
641C22—21no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—432no—
646C22—861no—
647C22—861no—
648C22—861no—
649C22—861no—
650C22—861no—
651C22—1724no—
652C22C2×C22⋊C4×D4311yescharacteristic
653C22#1458347812yes—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—42no—
659C4—82no—
660C4—432no—
661C4—861no—
662C4—861no—
663C4—861no—
664C4—861no—
665C4—861no—
666C4—3442no—
667C4—1722no—
668C4—1722no—
669C4#1458337812yes—
670C4#1458346211yescharacteristic
671C4#1458346911yescharacteristic
672C2—22no—
673C2—82no—
674C2—862no—
675C2—1721no—
676C2#1913718511yescharacteristic
677C2#421×D4311yescharacteristic
678C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1963C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC22×C4×C43C24
hypercenter#1963D43
hypocenterC43#21857
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #423×D43C2semidirect
3. #19136987C2semidirect
4. #19135576C2semidirect
5. #19135575C2semidirect
6. #19135428C2semidirect
7. #19134894C2semidirect
8. #19134613C2semidirect
9. C43×#1963C2semidirect
12. #14583454C4semidirect
13. #14583454C4semidirect
14. #14583447C4semidirect
15. #14583447C4semidirect
20. #14583428C4semidirect
21. #14583428C4semidirect
339. #1963D43semidirect
388. C43#21857semidirect

Maximal subgroups

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

subgroupindex
#191478902
#423×D432
#191369872
#191355762
#191355752
#191354282
#191348942
#191346132
C43×#19632
#2185743