Finite Group Databasebeta

← #25166519

Subgroups — #25166519

Order 11008.

800 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583257C211yesmaximal, characteristic
2C2×#14583005C211yesmaximal, characteristic, complemented
3#19138432C211yesmaximal, characteristic, complemented
4#19138396C211yesmaximal, characteristic
5#19135926C211yesmaximal, characteristic, complemented
6#19135918C211yesmaximal, characteristic, complemented
7#19135691C211yesmaximal, characteristic
8#19135448C211yesmaximal, characteristic
9#19135294C211yesmaximal, characteristic
10#19135283C211yesmaximal, characteristic, complemented
11#19135270C211yesmaximal, characteristic, complemented
12#19134947C211yesmaximal, characteristic
13#19134864C211yesmaximal, characteristic, complemented
14#19134465C211yesmaximal, characteristic, complemented
15C43×#2065C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063324C2211yescharacteristic
19C2×#13063312C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22#14583257—24no—
23#14583005—24no—
24C2×#13063256C2211yescharacteristic
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582835—21no—
35#14582829—21no—
36#14582827—21no—
37#14582820—21no—
38#14582805C2211yescharacteristic
39#14582805C2211yescharacteristic
40#14582804—21no—
41#14582804C2211yescharacteristic
42#14582802C2211yescharacteristic
43#14582798C2211yescharacteristic
44#14582795C2211yescharacteristic
45#14582793—21no—
46#14582792—21no—
47#14582784—21no—
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×Dic172—22no—
65C2×Dic172—22no—
66C2×Dic172—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063324—22no—
73#13063324—41no—
74#13063312—22no—
75#13063312—41no—
76#13063290—22no—
77#13063290—22no—
78#13063290—41no—
79#13063290—41no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43D411yescharacteristic
82C2×C4⋊Dic43D411yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97#13063256—41no—
98#13063250—22no—
99#13063250—22no—
100#13063248—22no—
101#13063248—22no—
102#13063248D414yes—
103#13063246—22no—
104#13063235—22no—
105#13063235—22no—
106C4×C43⋊C8—22no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×D4×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#106×C43—22no—
128C4⋊C8×C43—22no—
129#102×C43—22no—
130#102×C43—22no—
131#95×C43—21no—
132C24×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—42no—
164C2×Dic86—42no—
165C2×Dic86—81no—
166C2×Dic86C2×D412yes—
167C2×Dic86#4112yes—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43#4112yes—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—81no—
180C4⋊C4×C43C2×D412yes—
181C22⋊C4×C43—42no—
182C22⋊C4×C43—81no—
183C42×C43—21no—
184C42×C43—21no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—81no—
189#10621883—44no—
190C4⋊Dic43—22no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43—81no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—81no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8C2×D412yes—
212C2×C43⋊C8#4112yes—
213Dic172—28no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43C22×D411yescharacteristic
222D4×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
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#13712yes—
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×C4×C432−1+411yescharacteristic
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—22no—
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—41no—
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—
271Dic86—22no—
272Dic86—22no—
273Dic86—22no—
274Dic86—22no—
275Dic86—41no—
276Dic86—41no—
277Dic86—41no—
278Dic86—41no—
279Dic86—84no—
280C8×C43—22no—
281C8×C43—41no—
282C43⋊C8—22no—
283C43⋊C8—22no—
284#26846—431nomaximal, Sylow
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43#53211yescharacteristic
293C22×C43D4211yescharacteristic
294C22×C43#54811yescharacteristic
295C22×C43C2×#13711yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57711yescharacteristic
299C4×C43—22no—
300C4×C43—41no—
301C4×C43—42no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43#52511yescharacteristic
305C4×C43#54211yescharacteristic
306C4×C43#54711yescharacteristic
307C4×C43#55111yescharacteristic
308Dic43—42no—
309Dic43—42no—
310Dic43—41no—
311Dic43—41no—
312Dic43—41no—
313Dic43—41no—
314Dic43—81no—
315Dic43—81no—
316C2×#489—431no—
317C2×#441—431no—
318#2451—431no—
319#2448—431no—
320#2065D4311yescharacteristic
321#2058—431no—
322#2056—431no—
323#2015—431no—
324#1968—431no—
325#1936—431no—
326#1935—431no—
327#1933—431no—
328#1880—431no—
329#1865—431no—
330#1770—431no—
331C2×C43—161no—
332C2×C43#246111yescharacteristic
333C2×C43#317311yescharacteristic
334C2×C43#318111yescharacteristic
335C2×C43#327511yescharacteristic
336C2×C43#327811yescharacteristic
337C2×C43#336911yescharacteristic
338C2×C43#337111yescharacteristic
339C22×Q16—431no—
340C22×SD16—431no—
341C2×C4⋊Q8—431no—
342C2×#124—431no—
343C2×C4×Q8—431no—
344C2×C4×Q8—431no—
345#489—864no—
346#441—864no—
347C2×#106—431no—
348C2×#106C2×D4311yescharacteristic
349C2×C4⋊C8C2×D4311yescharacteristic
350C2×#103—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#102—431no—
356C2×#102C2×D4311yescharacteristic
357C2×#102C2×D4311yescharacteristic
358C2×#97—431no—
359C2×#97—431no—
360C2×C4×C8—431no—
361#399—861no—
362#398—861no—
363#397—861no—
364#395—861no—
365#391—431no—
366#391—431no—
367#391—431no—
368#391—861no—
369#390—431no—
370#390C2×D4311yescharacteristic
371#389—431no—
372#389—431no—
373#389C2×D4311yescharacteristic
374#388—861no—
375#388—861no—
376#387—861no—
377C4×C4⋊C4—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340C2×D4311yescharacteristic
382#336—431no—
383#336—431no—
384C43#2684611yescharacteristic, complemented, Sylow
385C22×Q8—431no—
386C22×Q8—431no—
387C22×Q8—861no—
388C22×D4C22×D4311yescharacteristic
389C2×Q16—862no—
390C2×Q16—862no—
391C2×Q16—862no—
392C2×SD16—862no—
393C2×SD16—862no—
394C2×SD16—1721no—
395C22×C8—431no—
396C22×C8—431no—
397C22×C8C22×D4311yescharacteristic
398C22×C8C22×D4311yescharacteristic
399C4⋊Q8—862no—
400C4⋊Q8—1721no—
401#124—862no—
402#124—1721no—
403C4×Q8—862no—
404C4×Q8—862no—
405C4×Q8—1721no—
406C4×Q8—1721no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—861no—
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×C42C22×D4311yescharacteristic
431#106—22no—
432#106—1721no—
433C4⋊C8—22no—
434#103—434no—
435#103—862no—
436#103—862no—
437#103—862no—
438#103—862no—
439#102—22no—
440#102—22no—
441#102—862no—
442#97—862no—
443#97—862no—
444C4×C8—862no—
445#95—21no—
446#95—431no—
447#95—431no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—21no—
457C2×Q8—432no—
458C2×Q8—432no—
459C2×Q8—861no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×Q8—861no—
464C2×Q8—861no—
465C2×Q8—861no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—3441no—
470C2×Q8—1722no—
471C2×Q8—1722no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492Q16—868no—
493SD16—1724no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—432no—
500C2×C8—432no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8#1062190012yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—81no—
512C4⋊C4—862no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—3441no—
518C4⋊C4—3441no—
519C4⋊C4—1721no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4D4×D4312yes—
524C22⋊C4—42no—
525C22⋊C4—81no—
526C22⋊C4—3441no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C42—21no—
531C42—21no—
532C42—861no—
533C42—861no—
534C42—861no—
535C42—861no—
536C42—1722no—
537C42—1722no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23C2×D4×D4311yescharacteristic
546Q8—862no—
547Q8—862no—
548Q8—862no—
549Q8—862no—
550Q8—3444no—
551Q8—1721no—
552Q8—1721no—
553Q8—1721no—
554Q8—1721no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559C2×C4—21no—
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—1721no—
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#1306335412yes—
598C2×C4C2×D4×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4C2×#1062190011yescharacteristic
602C2×C4#1306337111yescharacteristic
603C2×C4#1306337311yescharacteristic
604C8—22no—
605C8—41no—
606C8—862no—
607C8—862no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22#1458344411yescharacteristic
616C22#1458353311yescharacteristic
617C22#1458355911yescharacteristic
618C22C2×#1306335411yescharacteristic
619C22#1458369611yescharacteristic
620C22#1458370911yescharacteristic
621C22#1458370911yescharacteristic
622C4—22no—
623C4—41no—
624C4—42no—
625C4—81no—
626C4—81no—
627C4—3441no—
628C4—3441no—
629C4—1722no—
630C4—1722no—
631C4—1721no—
632C4—1721no—
633C4—1721no—
634C4—1721no—
635C4#1458340911yescharacteristic
636C4#1458352211yescharacteristic
637C4#1458355111yescharacteristic
638C4#1458357411yescharacteristic
639C2—161no—
640C2#1913856311yescharacteristic
641C2#1914520711yescharacteristic
642C2#1914529711yescharacteristic
643C2#1914623211yescharacteristic
644C2#1914626411yescharacteristic
645C2#1914733411yescharacteristic
646C2#1914736111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2065C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2065D43
hypocenterC43#26846
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
2. C2×#14583005C2semidirect
3. #19138432C2semidirect
5. #19135926C2semidirect
6. #19135918C2semidirect
10. #19135283C2semidirect
11. #19135270C2semidirect
13. #19134864C2semidirect
14. #19134465C2semidirect
384. C43#26846semidirect

Maximal subgroups

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

subgroupindex
C2×#145832572
C2×#145830052
#191384322
#191383962
#191359262
#191359182
#191356912
#191354482
#191352942
#191352832
#191352702
#191349472
#191348642
#191344652
C43×#20652
#2684643