Finite Group Databasebeta

← #25113502

Subgroups — #25113502

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148192C211yesmaximal, characteristic
2M16×Dic86C211yesmaximal, characteristic, complemented
3#19137069C211yesmaximal, characteristic, complemented
4#19135512C212yesmaximal, complemented
5#19135425C212yesmaximal, complemented
6#19135424C211yesmaximal, characteristic, complemented
7#19134616C211yesmaximal, characteristic, complemented
8#19134613C212yesmaximal, complemented
9#19134407C212yesmaximal, complemented
10C4×#13063251C211yesmaximal, characteristic, complemented
11C43×#1980C211yesmaximal, characteristic, complemented
12#14583635C411yescharacteristic, complemented
13#14583631C412yescomplemented
14#14583624C411yescharacteristic, complemented
15#14583623C411yescharacteristic, complemented
16#14583618C412yescomplemented
17#14583601—21no—
18#14583592—22no—
19#14583569C411yescharacteristic, complemented
20#14583555—21no—
21#14583445C2212yes—
22#14583431—21no—
23#14583429—22no—
24#41×Dic43C2212yes—
25C4×#10621898C2211yescharacteristic
26C4×#10621900—21no—
27C2×C4×Dic86C2211yescharacteristic
28#14583029—21no—
29#14583027—22no—
30C8×Dic86—21no—
31#14582923C2211yescharacteristic
32#14582922C2212yes—
33C2×#13063253C2212yes—
34C2×#13063252C2212yes—
35C2×#13063252C2212yes—
36C2×#13063251C2211yescharacteristic
37C2×#13063251C2211yescharacteristic
38M16×Dic43C2212yes—
39#14582804—21no—
40#14582795—21no—
41#14582781—22no—
42C4×Dic43⋊C4C2212yes—
43#14582745C2212yes—
44C42×Dic43C2211yescharacteristic
45#14582660C2211yescharacteristic
46#14582660C2211yescharacteristic
47#14582659C2212yes—
48C43×#532C2211yescharacteristic
49C2×#104×C43C2212yes—
50C2×#104×C43C2212yes—
51C4×M16×C43C2211yescharacteristic
52C4×C4⋊C4×C43C2211yescharacteristic
53C2×#10621898C2311yescharacteristic
54C2×#10621900—21no—
55C22×Dic86D411yescharacteristic
56C2×#10621877C2312yes—
57#13063323C2×C412yes—
58#13063321C2×C412yes—
59#13063320—22no—
60#13063318—22no—
61#13063318—22no—
62#13063316—21no—
63#13063315—22no—
64#13063314C2×C412yes—
65#13063312—21no—
66#13063312C2×C412yes—
67#13063311—22no—
68#13063309—22no—
69#13063307—22no—
70#13063306—22no—
71#13063305—21no—
72#13063302—22no—
73#13063297—22no—
74#13063297—22no—
75#13063297—22no—
76#13063296—21no—
77Q8×Dic43C2×C412yes—
78Q8×Dic43C2×C412yes—
79C4×Dic86C2×C411yescharacteristic
80C4×Dic86C2×C411yescharacteristic
81C4×Dic86C2×C411yescharacteristic
82C4×Dic86C2×C412yes—
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86D411yescharacteristic
85C4×Dic86D412yes—
86C4×Dic86D411yescharacteristic
87#13063290—21no—
88C4×D172C2×C411yescharacteristic
89C4×D172C2×C411yescharacteristic
90D4×Dic43—22no—
91D4×Dic43—22no—
92D4×Dic43—21no—
93D4×Dic43C2×C412yes—
94D4×Dic43C2×C412yes—
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97C4×C22⋊D43—22no—
98C4×C22⋊D43—22no—
99(C22⋊D43)⋊C4—22no—
100#13063284—22no—
101#13063284C2311yescharacteristic
102#13063283—21no—
103#13063282—21no—
104#13063281—22no—
105C2×C4⋊Dic43D411yescharacteristic
106C2×Dic43⋊C4—22no—
107C2×Dic43⋊C4D412yes—
108C2×C4×Dic43—22no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113C2×C4×Dic43C2312yes—
114C42×D43—21no—
115C4⋊(C43⋊C8)—21no—
116C4⋊(C43⋊C8)—21no—
117Dic43⋊C8—22no—
118Dic43⋊C8—22no—
119#13063253—42no—
120#13063252—24no—
121#13063252—42no—
122#13063251—22no—
123#13063251—22no—
124#13063235—22no—
125C8×Dic43—22no—
126C43⋊#95—22no—
127C43⋊#95—22no—
128C43⋊#95—22no—
129C2×#41×C43C2312yes—
130C2×M16×C43C2311yescharacteristic
131C2×M16×C43C2311yescharacteristic
132C4⋊Q8×C43C2×C411yescharacteristic
133#127×C43C2×C411yescharacteristic
134#124×C43C2×C412yes—
135#121×C43—21no—
136#121×C43—21no—
137C4×D4×C43—21no—
138C4×D4×C43—21no—
139C2×C4⋊C4×C43—21no—
140C2×C42×C43C2312yes—
141C2×C42×C43C2311yescharacteristic
142#104×C43—24no—
143#104×C43—42no—
144#97×C43—21no—
145C4×C8×C43—21no—
146#95×C43—21no—
147#41×C43—22no—
148#41×C43—22no—
149#41×C43—22no—
150#41×C43—22no—
151C2×Q8×C43C22×C412yes—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—22no—
155C2×D4×C43C22×C412yes—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—21no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43C2×D412yes—
169C22×Dic43C2×D412yes—
170#10621900—44no—
171#10621898—21no—
172#10621898—21no—
173#10621898—21no—
174#10621898—21no—
175C2×D172C22×C411yescharacteristic
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×Dic86—42no—
180C2×Dic86C22⋊C411yescharacteristic
181C2×Dic86C22⋊C411yescharacteristic
182C2×Dic86C22⋊C412yes—
183C2×Dic86C22×C411yescharacteristic
184M16×C43—21no—
185M16×C43—21no—
186M16×C43—21no—
187M16×C43#4112yescomplemented
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—42no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C42×C43—22no—
196C42×C43—22no—
197C42×C43C22×C411yescharacteristic
198C42×C43C22×C411yescharacteristic
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C22⋊Dic43—22no—
202C22⋊Dic43—22no—
203C22⋊Dic43—22no—
204C22⋊Dic43—22no—
205C22⋊Dic43—21no—
206(C2×D43)⋊C4—21no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4—22no—
210C4⋊Dic43—22no—
211C4⋊Dic43—22no—
212C4⋊Dic43C22⋊C411yescharacteristic
213C4⋊Dic43C22⋊C411yescharacteristic
214C4⋊Dic43C22⋊C412yes—
215C4⋊Dic43C22×C411yescharacteristic
216C4⋊Dic43C22×C411yescharacteristic
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221Dic43⋊C4—44no—
222Dic43⋊C4C22⋊C412yes—
223Dic43⋊C4C22⋊C412yes—
224Dic43⋊C4C22⋊C412yes—
225Dic43⋊C4C22⋊C412yes—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—22no—
231C4×Dic43—22no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—42no—
235C4×Dic43—42no—
236C4×Dic43C22×C412yes—
237C4×Dic43C22×C412yes—
238C4×Dic43C2×D412yes—
239C4×Dic43C2×D412yes—
240C4×Dic43#4112yescomplemented
241#10621877—22no—
242#10621877—22no—
243C2×C43⋊C8—22no—
244C23×C43—22no—
245C23×C43C22×D411yescharacteristic
246C22×D43—21no—
247Q8×C43—22no—
248Q8×C43—22no—
249D4×C43—22no—
250D4×C43—22no—
251D4×C43—42no—
252D4×C43—42no—
253D4×C43—42no—
254D4×C43—81no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—41no—
258C2×C4×C43—42no—
259C2×C4×C43—42no—
260C2×C4×C43—42no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C2×C22⋊C411yescharacteristic
265C2×C4×C43C2×C22⋊C411yescharacteristic
266C2×C4×C43C2×C22⋊C411yescharacteristic
267C2×C4×C43C23×C411yescharacteristic
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C43C2×#4111yescharacteristic
271C2×C4×C43H(5,𝔽2)11yescharacteristic
272C2×C4×C432−1+411yescharacteristic
273C22⋊D43—44no—
274C22⋊D43—41no—
275C22⋊D43—41no—
276C22⋊D43—82no—
277C2×Dic43—22no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—22no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284C2×Dic43—44no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—82no—
290C2×Dic43C2×C22⋊C412yes—
291C2×Dic43C2×C22⋊C412yes—
292C2×Dic43C2×C22⋊C412yes—
293C2×Dic43C2×C22⋊C412yes—
294D172—21no—
295D172—21no—
296C4×D43—41no—
297C4×D43—41no—
298C4×D43—42no—
299C4×D43—81no—
300Dic86—22no—
301Dic86—22no—
302Dic86—21no—
303Dic86—21no—
304Dic86—42no—
305C8×C43—22no—
306C8×C43—41no—
307C43⋊C8—42no—
308#22551—431nomaximal, Sylow
309C22×C43—21no—
310C22×C43—21no—
311C22×C43—42no—
312C22×C43—42no—
313C22×C43—42no—
314C22×C43C22×C22⋊C411yescharacteristic
315C22×C43#54811yescharacteristic
316C22×C43#55011yescharacteristic
317C2×D43—41no—
318C2×D43—41no—
319C2×D43—41no—
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—21no—
323C4×C43—42no—
324C4×C43—82no—
325C4×C43#42112yes—
326C4×C43C4×#4111yescharacteristic
327C4×C43#52011yescharacteristic
328C4×C43#54811yescharacteristic
329C4×C43#55011yescharacteristic
330Dic43—22no—
331Dic43—22no—
332Dic43—22no—
333Dic43—22no—
334Dic43—42no—
335Dic43—42no—
336Dic43—41no—
337Dic43—41no—
338Dic43—41no—
339#3480—431no—
340Q8×M16—431no—
341#2295—431no—
342#1980—432no—
343#1980D4311yescharacteristic, complemented
344#1963—432no—
345#1962—431no—
346#1806—432no—
347#1806—431no—
348#1759—432no—
349C4×#104—431no—
350C2×C43—21no—
351C2×C43—21no—
352C2×C43—82no—
353C2×C43#234111yescharacteristic
354C2×C43C2×#42111yescharacteristic
355C2×C43#290111yescharacteristic
356D43—81no—
357#559—431no—
358#559—432no—
359#557—431no—
360#556—431no—
361#556—432no—
362#553—862no—
363#553—861no—
364#550—431no—
365#548—861no—
366#532—432no—
367#532C2×D4311yescharacteristic
368#529—862no—
369#529—861no—
370C4×#41—432no—
371C4×#41—431no—
372C4×#41—861no—
373C2×C4×Q8—431no—
374#446—861no—
375#446—862no—
376C8×Q8—861no—
377#423—432no—
378#423—431no—
379C2×#104—432no—
380C2×#104—431no—
381C2×#104—431no—
382C2×#104—432no—
383C2×#104—432no—
384C2×#104C2×D4312yes—
385C2×#104C2×D4312yes—
386C4×M16—432no—
387C4×M16C2×D4311yescharacteristic
388#391—861no—
389#389—861no—
390#387—862no—
391C4×C4⋊C4—432no—
392C4×C4⋊C4C2×D4311yescharacteristic
393#376—432no—
394C43—431no—
395#339—431no—
396#339—431no—
397#339—432no—
398C43#2255111yescharacteristic, complemented, Sylow
399C2×#41—431no—
400C2×#41—861no—
401C2×#41C22×D4312yes—
402C22×Q8—431no—
403C2×M16—432no—
404C2×M16C22×D4311yescharacteristic
405C2×M16C22×D4311yescharacteristic
406C4⋊Q8—432no—
407C4⋊Q8C4×D4311yescharacteristic
408#127—432no—
409#127C4×D4311yescharacteristic
410#126—862no—
411#126—862no—
412#126—862no—
413#125—862no—
414#125—861no—
415#124—432no—
416#124—432no—
417#124—862no—
418#124—861no—
419#124C4×D4312yes—
420#123—862no—
421#123—862no—
422#123—862no—
423C22⋊Q8—862no—
424C22⋊Q8—861no—
425#121—21no—
426#121—21no—
427#121—861no—
428#121—862no—
429#121—862no—
430#121—862no—
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8—432no—
434C4×Q8—431no—
435C4×Q8—431no—
436C4×Q8—432no—
437C4×Q8—432no—
438C4×Q8—432no—
439C4×Q8—431no—
440C4×Q8—431no—
441C4×Q8—861no—
442C4×D4—21no—
443C4×D4—21no—
444C4×D4—432no—
445C4×D4—432no—
446C4×D4—431no—
447C4×D4—431no—
448C4×D4—862no—
449C4×D4—862no—
450C4×D4—862no—
451C4×D4—861no—
452C4×D4—862no—
453C4×D4—862no—
454C4×D4—861no—
455C4×D4—861no—
456#117—431no—
457#117—862no—
458#117—862no—
459#117—861no—
460#117—861no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—432no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—862no—
465C2×C42—432no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—862no—
469C2×C42—861no—
470C2×C42—861no—
471C2×C42—861no—
472C2×C42C22×D4312yes—
473C2×C42C22×D4311yescharacteristic
474C4⋊C8—862no—
475C4⋊C8—862no—
476C4⋊C8—861no—
477C4⋊C8—861no—
478#104—24no—
479#104—42no—
480#104—862no—
481#104—864no—
482#104—862no—
483#104—1722no—
484#104—1722no—
485#97—21no—
486#97—862no—
487C4×C8—21no—
488C4×C8—862no—
489#95—21no—
490#95—862no—
491#95—862no—
492#95—862no—
493#41—22no—
494#41—22no—
495#41—22no—
496#41—22no—
497#41—861no—
498#41—861no—
499#41—861no—
500#41—861no—
501#41—1724no—
502C2×Q8—431no—
503C2×Q8—431no—
504C2×Q8—432no—
505C2×Q8—431no—
506C2×Q8—1722no—
507C2×Q8C2×C4×D4312yes—
508C2×D4—22no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—431no—
512C2×D4—862no—
513C2×D4—862no—
514C2×D4—861no—
515C2×D4C2×C4×D4312yes—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—432no—
519C22×C4—432no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4D4×D4311yescharacteristic
528C22×C4D4×D4311yescharacteristic
529C22×C4C23×D4311yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—862no—
534M16—862no—
535M16#1062190012yescomplemented
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—862no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—42no—
542C4⋊C4—432no—
543C4⋊C4—431no—
544C4⋊C4—432no—
545C4⋊C4—431no—
546C4⋊C4—432no—
547C4⋊C4—432no—
548C4⋊C4—432no—
549C4⋊C4—431no—
550C4⋊C4—431no—
551C4⋊C4—862no—
552C4⋊C4—862no—
553C4⋊C4—862no—
554C4⋊C4—862no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—1724no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—862no—
561C22⋊C4—862no—
562C22⋊C4—862no—
563C22⋊C4—862no—
564C22⋊C4—862no—
565C22⋊C4—862no—
566C22⋊C4—861no—
567C22⋊C4—861no—
568C22⋊C4—861no—
569C42—22no—
570C42—22no—
571C42—432no—
572C42—432no—
573C42—432no—
574C42—432no—
575C42—432no—
576C42—862no—
577C42—862no—
578C42—861no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—861no—
584C42—1722no—
585C42—1722no—
586C42C2×C4×D4311yescharacteristic
587C42C2×C4×D4311yescharacteristic
588C42D4×D4311yescharacteristic
589C42D4×D4311yescharacteristic
590C23—22no—
591C23—861no—
592C23C2×D4×D4311yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—862no—
596Q8—862no—
597Q8—861no—
598Q8—861no—
599Q8—1722no—
600D4—22no—
601D4—22no—
602D4—42no—
603D4—42no—
604D4—42no—
605D4—81no—
606D4—861no—
607D4—861no—
608D4—3442no—
609D4—1724no—
610D4—1721no—
611D4—1721no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—432no—
621C2×C4—432no—
622C2×C4—432no—
623C2×C4—432no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—3441no—
630C2×C4—3442no—
631C2×C4—1722no—
632C2×C4—1722no—
633C2×C4—1724no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1722no—
641C2×C4C22⋊C4×D4311yescharacteristic
642C2×C4C22⋊C4×D4311yescharacteristic
643C2×C4C22⋊C4×D4311yescharacteristic
644C2×C4C22⋊C4×D4311yescharacteristic
645C2×C4C22×C4×D4311yescharacteristic
646C2×C4C2×D4×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4C2×#1062190011yescharacteristic
649C2×C4#1306337011yescharacteristic
650C2×C4#1306337211yescharacteristic
651C8—22no—
652C8—41no—
653C8—1722no—
654C22—21no—
655C22—21no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—1721no—
660C22—1721no—
661C22—1721no—
662C22C2×C22⋊C4×D4311yescharacteristic
663C22#1458355711yescharacteristic
664C22#1458356911yescharacteristic
665C4—21no—
666C4—21no—
667C4—21no—
668C4—42no—
669C4—82no—
670C4—862no—
671C4—862no—
672C4—862no—
673C4—862no—
674C4—1722no—
675C4—1722no—
676C4—1721no—
677C4—1721no—
678C4—1721no—
679C4#1458291412yes—
680C4C4×#1062190011yescharacteristic
681C4#1458337811yescharacteristic
682C4#1458355511yescharacteristic
683C4#1458356711yescharacteristic
684C2—21no—
685C2—21no—
686C2—82no—
687C2—3441no—
688C2#1913743411yescharacteristic
689C2C2×#1458291411yescharacteristic
690C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1980C2
socleC22×C43C22×C22⋊C4
prime radical#19148192C2
cosocleC22×C4×C43C24
hypercenter#1980D43
hypocenterC43#22551
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. M16×Dic86C2semidirect
3. #19137069C2semidirect
4. #19135512C2semidirect
5. #19135425C2semidirect
6. #19135424C2semidirect
7. #19134616C2semidirect
8. #19134613C2semidirect
9. #19134407C2semidirect
10. C4×#13063251C2semidirect
11. C43×#1980C2semidirect
12. #14583635C4semidirect
13. #14583631C4semidirect
14. #14583624C4semidirect
15. #14583623C4semidirect
16. #14583618C4semidirect
19. #14583569C4semidirect
187. M16×C43#41semidirect
240. C4×Dic43#41semidirect
343. #1980D43semidirect
398. C43#22551semidirect
535. M16#10621900semidirect

Maximal subgroups

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

subgroupindex
#191481922
M16×Dic862
#191370692
#191355122
#191354252
#191354242
#191346162
#191346132
#191344072
C4×#130632512
C43×#19802
#2255143