Finite Group Databasebeta

← #25106615

Subgroups — #25106615

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147984C211yesmaximal, characteristic
2#19143231C211yesmaximal, characteristic, complemented
3#19137075C211yesmaximal, characteristic, complemented
4#19135539C211yesmaximal, characteristic, complemented
5#19135538C211yesmaximal, characteristic, complemented
6#19135515C211yesmaximal, characteristic, complemented
7#19135040C212yesmaximal, complemented
8#19135035C212yesmaximal, complemented
9#19134613C212yesmaximal, complemented
10#19134613C212yesmaximal, complemented
11C43×#1980C211yesmaximal, characteristic, complemented
12#14583518C412yescomplemented
13#14583518C412yescomplemented
14#14583510C412yescomplemented
15#14583503C412yescomplemented
16#14583494—21no—
17#14583494—21no—
18#14583486—21no—
19#14583486—21no—
20#14583456C2211yescharacteristic
21#14583429—22no—
22#14583429—22no—
23#14583406C2212yes—
24#41×Dic43C2212yes—
25C2×#13063282C2211yescharacteristic
26C2×#13063282C2211yescharacteristic
27C2×C42×D43C2211yescharacteristic
28#14582961—22no—
29#14582958—22no—
30#14582922C2212yes—
31C2×#13063252C2212yes—
32C2×#13063252C2212yes—
33#14582862C2212yes—
34C4×#10621877C2211yescharacteristic
35#14582796—21no—
36#14582794—21no—
37#14582773—21no—
38#14582770—21no—
39C4×Dic43⋊C4C2211yescharacteristic
40C4×Dic43⋊C4C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42#14582660C2212yes—
43#14582660C2212yes—
44#14582659C2212yes—
45#14582659C2212yes—
46C43×#532C2211yescharacteristic
47C2×#104×C43C2212yes—
48C2×#104×C43C2212yes—
49C4×M16×C43C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C22×C4×D43—21no—
52C22×C4×D43C2311yescharacteristic
53C2×#10621877C2312yes—
54#13063325C2×C411yescharacteristic, complemented
55#13063325C2×C411yescharacteristic, complemented
56#13063320—22no—
57#13063320—22no—
58#13063318—22no—
59#13063318—22no—
60#13063317C2×C412yescomplemented
61#13063315—22no—
62#13063315—22no—
63#13063311—22no—
64#13063311—22no—
65#13063309—22no—
66#13063309—22no—
67#13063306—22no—
68#13063306—22no—
69#13063306—22no—
70#13063304—21no—
71#13063304—21no—
72#13063302—22no—
73#13063302—22no—
74#13063301C2×C412yes—
75#13063301C2×C412yes—
76#13063297—22no—
77#13063297—22no—
78#13063296C2×C412yes—
79#13063296C2×C412yes—
80#13063293—22no—
81Q8×Dic43C2×C412yescomplemented
82Q8×Dic43C2×C412yescomplemented
83C4×Dic86—21no—
84C4×Dic86—21no—
85D4×Dic43—22no—
86D4×Dic43—22no—
87D4×Dic43C2×C412yescomplemented
88D4×Dic43C2×C412yescomplemented
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91#13063284—22no—
92#13063284C2312yes—
93#13063282—42no—
94#13063282C2×C412yes—
95#13063282C2×C412yes—
96#13063282D412yes—
97#13063282D412yes—
98C2×C4⋊Dic43—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4D411yescharacteristic
103C2×Dic43⋊C4D411yescharacteristic
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4D411yescharacteristic
106C2×(C2×D43)⋊C4D411yescharacteristic
107C2×C4×Dic43—22no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43C2311yescharacteristic
110C2×C4×Dic43C2311yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112C42×D43—42no—
113Dic43⋊C8—24no—
114#13063252—42no—
115#13063252—42no—
116(C2×D43)⋊C8—24no—
117#13063236—21no—
118C4×C43⋊C8—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C2×#41×C43C2312yes—
123C2×M16×C43C2312yes—
124C4⋊Q8×C43C2×C411yescharacteristic, complemented
125#127×C43C2×C411yescharacteristic, complemented
126#124×C43C2×C412yescomplemented
127#121×C43—21no—
128#121×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#104×C43—42no—
136#104×C43—42no—
137#97×C43—21no—
138C4×C8×C43—21no—
139#95×C43—21no—
140C23×D43C2×D411yescharacteristic
141#41×C43—22no—
142#41×C43—22no—
143#41×C43—22no—
144#41×C43—22no—
145C2×Q8×C43C22×C412yes—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—22no—
149C2×D4×C43C22×C412yes—
150C22×C4×C43—22no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
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—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43—42no—
170C2×C4×D43C22×C412yes—
171C2×C4×D43C2×D412yes—
172C2×Dic86—21no—
173C2×Dic86—21no—
174M16×C43—22no—
175M16×C43—22no—
176C2×C8×C43—22no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—42no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C42×C43—22no—
183C42×C43—22no—
184C42×C43C22×C411yescharacteristic
185C42×C43C22×C411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4C22⋊C412yes—
197(C2×D43)⋊C4C22⋊C412yes—
198(C2×D43)⋊C4C22⋊C412yes—
199(C2×D43)⋊C4C22⋊C412yes—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43—42no—
205C4⋊Dic43C22×C412yes—
206C4⋊Dic43C22×C412yes—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4—42no—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214Dic43⋊C4C22⋊C412yes—
215Dic43⋊C4C22⋊C412yes—
216Dic43⋊C4C22⋊C412yes—
217Dic43⋊C4C22⋊C412yes—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43—22no—
221C4×Dic43—22no—
222C4×Dic43—22no—
223C4×Dic43—42no—
224C4×Dic43C22×C412yes—
225C4×Dic43C2×D412yes—
226#10621877—22no—
227#10621877—22no—
228C2×C43⋊C8—22no—
229C23×C43—22no—
230C23×C43C22×D411yescharacteristic
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43C2×C22⋊C412yes—
236Q8×C43—22no—
237Q8×C43—22no—
238D4×C43—22no—
239D4×C43—22no—
240D4×C43—42no—
241D4×C43—42no—
242D4×C43—81no—
243D4×C43—81no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43C2×C22⋊C411yescharacteristic
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C23×C411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43H(5,𝔽2)12yes—
262C2×C4×C432−1+412yes—
263C22⋊D43—82no—
264C22⋊D43—82no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—82no—
278C2×Dic43—82no—
279C2×Dic43C2×C22⋊C412yes—
280C2×Dic43C2×C22⋊C412yes—
281C2×Dic43C2×C22⋊C412yes—
282C4×D43—24no—
283C4×D43—24no—
284C4×D43—48no—
285Dic86—81no—
286Dic86—81no—
287C8×C43—42no—
288C43⋊C8—42no—
289#21901—431nomaximal, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43C22×C22⋊C411yescharacteristic
296C22×C43#53511yescharacteristic
297C22×C43#53611yescharacteristic
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—42no—
302C2×D43—42no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—21no—
307C4×C43—42no—
308C4×C43—42no—
309C4×C43—81no—
310C4×C43#52012yes—
311C4×C43#53712yes—
312Dic43—22no—
313Dic43—22no—
314Dic43—22no—
315Dic43—42no—
316Dic43—42no—
317Dic43—42no—
318Dic43—81no—
319#3455—431no—
320#2921—431no—
321#2296—431no—
322#1986—431no—
323#1986—431no—
324#1980—431no—
325#1980D4311yescharacteristic, complemented
326#1897—432no—
327#1896—432no—
328#1806—432no—
329#1806—432no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—82no—
333C2×C43#231111yescharacteristic
334C2×C43#290111yescharacteristic
335C2×C43#290111yescharacteristic
336D43—42no—
337#542—432no—
338#542—432no—
339#541—432no—
340#540—432no—
341#539—861no—
342#539—861no—
343#538—861no—
344#538—861no—
345#533—431no—
346#532C2×D4311yescharacteristic
347#529—862no—
348#529—862no—
349#525—432no—
350C4×#41—432no—
351C2×#117—431no—
352C2×#117—431no—
353C22×C42—431no—
354#433—862no—
355#433—862no—
356#423—432no—
357C2×#104—432no—
358C2×#104—432no—
359C2×#104C2×D4312yes—
360C2×#104C2×D4312yes—
361#407—432no—
362C4×M16—431no—
363C4×M16C2×D4311yescharacteristic
364#389—861no—
365#389—861no—
366#385—861no—
367#385—861no—
368C4×C4⋊C4—431no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4C2×D4311yescharacteristic
372#339—432no—
373#339—432no—
374#339—432no—
375#339—432no—
376C43#2190111yescharacteristic, complemented, Sylow
377C2×#41C22×D4312yes—
378C23×C4—431no—
379C23×C4—861no—
380C2×M16—432no—
381C2×M16C22×D4312yes—
382C4⋊Q8—431no—
383C4⋊Q8—431no—
384C4⋊Q8C4×D4311yescharacteristic, complemented
385#127C4×D4311yescharacteristic, complemented
386#126—862no—
387#126—862no—
388#126—862no—
389#126—862no—
390#125—432no—
391#125—862no—
392#125—862no—
393#124—862no—
394#124—862no—
395#124C4×D4312yescomplemented
396#123—862no—
397#123—862no—
398#123—862no—
399#123—862no—
400#123—862no—
401C22⋊Q8—432no—
402C22⋊Q8—432no—
403C22⋊Q8—862no—
404C22⋊Q8—862no—
405C22⋊Q8—861no—
406C22⋊Q8—861no—
407#121—21no—
408#121—21no—
409#121—432no—
410#121—432no—
411#121—862no—
412#121—862no—
413#120—862no—
414C4×Q8—432no—
415C4×Q8—432no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—432no—
421C4×D4—432no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426#117—432no—
427#117—432no—
428#117—432no—
429#117—432no—
430#117—432no—
431#117—862no—
432#117—1722no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4—861no—
439C2×C4⋊C4—861no—
440C2×C22⋊C4—431no—
441C2×C22⋊C4—431no—
442C2×C22⋊C4—861no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—862no—
447C2×C42—861no—
448C2×C42—1722no—
449C2×C42C22×D4311yescharacteristic
450C2×C42C22×D4311yescharacteristic
451C2×C42C22×D4311yescharacteristic
452C4⋊C8—864no—
453#104—42no—
454#104—42no—
455#104—1722no—
456#104—1722no—
457C22⋊C8—864no—
458#97—21no—
459#97—861no—
460C4×C8—21no—
461C4×C8—861no—
462#95—21no—
463#95—861no—
464#95—861no—
465#95—861no—
466C24—431no—
467#41—22no—
468#41—22no—
469#41—22no—
470#41—22no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8C2×C4×D4312yes—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—862no—
478C2×D4—862no—
479C2×D4C2×C4×D4312yes—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1722no—
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500M16—22no—
501M16—22no—
502M16—862no—
503M16—862no—
504C2×C8—22no—
505C2×C8—862no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—432no—
510C4⋊C4—432no—
511C4⋊C4—432no—
512C4⋊C4—432no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C4⋊C4—1722no—
526C4⋊C4—1722no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—432no—
530C22⋊C4—432no—
531C22⋊C4—432no—
532C22⋊C4—432no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—1722no—
541C42—22no—
542C42—22no—
543C42—432no—
544C42—432no—
545C42—862no—
546C42—862no—
547C42—862no—
548C42—862no—
549C42—862no—
550C42—1722no—
551C42C2×C4×D4311yescharacteristic
552C42C2×C4×D4311yescharacteristic
553C42D4×D4311yescharacteristic
554C42D4×D4311yescharacteristic
555C23—22no—
556C23—432no—
557C23—861no—
558C23—861no—
559C23—1721no—
560C23—1721no—
561C23C2×D4×D4311yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—3441no—
565Q8—3441no—
566D4—22no—
567D4—22no—
568D4—42no—
569D4—42no—
570D4—81no—
571D4—81no—
572D4—3442no—
573D4—3442no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—864no—
591C2×C4—864no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—3442no—
596C2×C4—3442no—
597C2×C4—1728no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4C22⋊C4×D4311yescharacteristic
606C2×C4C22⋊C4×D4311yescharacteristic
607C2×C4C22⋊C4×D4311yescharacteristic
608C2×C4C22⋊C4×D4311yescharacteristic
609C2×C4C22×C4×D4311yescharacteristic
610C2×C4C2×D4×D4311yescharacteristic
611C2×C4#1306337012yes—
612C2×C4#1306337212yes—
613C8—42no—
614C8—1722no—
615C22—21no—
616C22—21no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—862no—
621C22—862no—
622C22—862no—
623C22—1722no—
624C22—1722no—
625C22C2×C22⋊C4×D4311yescharacteristic
626C22#1458346211yescharacteristic
627C22#1458346911yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—42no—
633C4—42no—
634C4—81no—
635C4—862no—
636C4—862no—
637C4—862no—
638C4—3441no—
639C4—1722no—
640C4—1722no—
641C4—1722no—
642C4#1458337812yes—
643C4#1458347812yes—
644C2—21no—
645C2—21no—
646C2—82no—
647C2—1722no—
648C2#1913718511yescharacteristic
649C2#1914313911yescharacteristic
650C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1980C2
socleC22×C43C22×C22⋊C4
prime radical#19147984C2
cosocleC22×C4×C43C24
hypercenter#1980D43
hypocenterC43#21901
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. #19143231C2semidirect
3. #19137075C2semidirect
4. #19135539C2semidirect
5. #19135538C2semidirect
6. #19135515C2semidirect
7. #19135040C2semidirect
8. #19135035C2semidirect
9. #19134613C2semidirect
10. #19134613C2semidirect
11. C43×#1980C2semidirect
12. #14583518C4semidirect
13. #14583518C4semidirect
14. #14583510C4semidirect
15. #14583503C4semidirect
54. #13063325C2×C4semidirect
55. #13063325C2×C4semidirect
60. #13063317C2×C4semidirect
81. Q8×Dic43C2×C4semidirect
82. Q8×Dic43C2×C4semidirect
87. D4×Dic43C2×C4semidirect
88. D4×Dic43C2×C4semidirect
124. C4⋊Q8×C43C2×C4semidirect
125. #127×C43C2×C4semidirect
126. #124×C43C2×C4semidirect
325. #1980D43semidirect
376. C43#21901semidirect
384. C4⋊Q8C4×D43semidirect
385. #127C4×D43semidirect
395. #124C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191479842
#191432312
#191370752
#191355392
#191355382
#191355152
#191350402
#191350352
#191346132
C43×#19802
#2190143