Finite Group Databasebeta

← #25147041

Subgroups — #25147041

Order 11008.

716 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583203C211yesmaximal, characteristic, complemented
2#19144063C211yesmaximal, characteristic
3#19143339C211yesmaximal, characteristic
4#19136043C211yesmaximal, characteristic, complemented
5#19136038C211yesmaximal, characteristic, complemented
6#19135892C211yesmaximal, characteristic, complemented
7#19135892C211yesmaximal, characteristic, complemented
8#19135589C211yesmaximal, characteristic, complemented
9#19135370C211yesmaximal, characteristic, complemented
10#19135108C211yesmaximal, characteristic, complemented
11#19135108C211yesmaximal, characteristic, complemented
12#19134657C211yesmaximal, characteristic, complemented
13#19134652C211yesmaximal, characteristic, complemented
14C4×#13063243C211yesmaximal, characteristic, complemented
15C43×#3142C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C2×#13063355C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21#14583203—21no—
22#14583203—21no—
23#14583203—21no—
24#14583203—21no—
25#14583118—21no—
26#14583118—21no—
27#14583106—21no—
28#14583096—21no—
29#14582977—21no—
30#14582971—21no—
31#14582971—21no—
32D4×C43⋊C8—21no—
33C2×#13063260C2211yescharacteristic
34C2×#13063260C2211yescharacteristic
35C2×#13063258C2211yescharacteristic
36C2×#13063256C2211yescharacteristic
37#14582923C2211yescharacteristic
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39#14582900C2211yescharacteristic
40#14582900C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063243C2211yescharacteristic
44C2×#13063243C2211yescharacteristic
45#14582866C2211yescharacteristic
46#14582866C2211yescharacteristic
47C4×#10621877C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582668C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C2×#125×C43C2211yescharacteristic
58C43×#491—21no—
59C43×#490—21no—
60C43×#488—21no—
61C43×#488—21no—
62C43×#417C2211yescharacteristic
63C43×#417C2211yescharacteristic
64C43×#417C2211yescharacteristic
65C43×#417C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68#13063355—22no—
69#13063355—22no—
70#13063355—41no—
71#13063355—41no—
72C2×#10621885—21no—
73C2×#10621885—21no—
74C2×#10621883—21no—
75C2×#10621883—21no—
76#13063332—22no—
77#13063332—22no—
78#13063332—41no—
79#13063332—41no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877C2311yescharacteristic
83C2×#10621877C2311yescharacteristic
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C22×C43⋊C8—21no—
87C22×C43⋊C8—21no—
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86—21no—
93C4×Dic86—21no—
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×C4×Dic43—21no—
97#13063260—41no—
98#13063260—41no—
99#13063258—21no—
100#13063258—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)D411yescharacteristic
106C4⋊(C43⋊C8)D411yescharacteristic
107C4⋊(C43⋊C8)D411yescharacteristic
108C4⋊(C43⋊C8)D411yescharacteristic
109#13063249—21no—
110#13063249—21no—
111#13063248—21no—
112#13063248—21no—
113#13063248—21no—
114#13063248—21no—
115#13063246—21no—
116#13063246—21no—
117#13063243—22no—
118#13063243—22no—
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121C22⋊(C43⋊C8)—21no—
122C22⋊(C43⋊C8)—21no—
123#13063236—21no—
124C4×C43⋊C8—21no—
125C2×#41×C43C2311yescharacteristic
126C2×#41×C43C2311yescharacteristic
127C2×M16×C43C2311yescharacteristic
128C2×M16×C43C2311yescharacteristic
129C4⋊Q8×C43D411yescharacteristic
130#127×C43D411yescharacteristic
131#125×C43—21no—
132#125×C43—21no—
133#125×C43—21no—
134#125×C43—21no—
135#124×C43D411yescharacteristic
136#124×C43D411yescharacteristic
137#121×C43—21no—
138#121×C43—21no—
139C4×D4×C43—21no—
140C4×D4×C43—21no—
141C2×C4⋊C4×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#103×C43—21no—
147#103×C43—21no—
148#103×C43—21no—
149#103×C43—21no—
150#102×C43—21no—
151#102×C43—21no—
152#102×C43—21no—
153#102×C43—21no—
154#97×C43—21no—
155C4×C8×C43—21no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43—21no—
159#41×C43—21no—
160#41×C43—21no—
161#41×C43—21no—
162#41×C43—21no—
163#41×C43—21no—
164C2×Q8×C43C2×D411yescharacteristic
165C2×Q8×C43C2×D411yescharacteristic
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43C2×D411yescharacteristic
171C2×D4×C43C2×D411yescharacteristic
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43#4111yescharacteristic
177C22×C4×C43#4111yescharacteristic
178C22×C4×C43C2411yescharacteristic
179C22×Dic43—21no—
180C22×Dic43—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186C2×Dic86#4112yes—
187M16×C43—21no—
188M16×C43—21no—
189M16×C43—21no—
190M16×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—41no—
200C4⋊C4×C43—41no—
201C4⋊C4×C43—41no—
202C4⋊C4×C43—41no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C42×C43C2×D411yescharacteristic
208C42×C43C2×D411yescharacteristic
209C42×C43C2×D411yescharacteristic
210C42×C43C2×D411yescharacteristic
211#10621885—42no—
212#10621885—42no—
213#10621883—42no—
214#10621883—42no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217Dic43⋊C4—41no—
218Dic43⋊C4—41no—
219C4×Dic43—41no—
220C4×Dic43—41no—
221#10621877—21no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—42no—
229#10621877—42no—
230#10621877#4112yes—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—42no—
240C2×C43⋊C8—42no—
241C2×C43⋊C8C2×D411yescharacteristic
242C2×C43⋊C8C2×D411yescharacteristic
243C2×C43⋊C8C2×D411yescharacteristic
244C2×C43⋊C8C2×D411yescharacteristic
245C23×C43—21no—
246C23×C43—21no—
247C23×C43C2×#4111yescharacteristic
248Q8×C43—21no—
249Q8×C43—21no—
250Q8×C43—21no—
251Q8×C43—21no—
252D4×C43—21no—
253D4×C43—21no—
254D4×C43—21no—
255D4×C43—21no—
256D4×C43—42no—
257D4×C43—41no—
258D4×C43—41no—
259D4×C43—41no—
260D4×C43—41no—
261D4×C43—81no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—81no—
273C2×C4×C43—81no—
274C2×C4×C43#12111yescharacteristic
275C2×C4×C43#12111yescharacteristic
276C2×C4×C43#12111yescharacteristic
277C2×C4×C43#12111yescharacteristic
278C2×C4×C43C22×D411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43H(5,𝔽2)11yescharacteristic
283C2×C4×C432−1+411yescharacteristic
284C2×Dic43—22no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—81no—
289Dic86—22no—
290Dic86—22no—
291Dic86—41no—
292Dic86—41no—
293C8×C43—41no—
294C8×C43—41no—
295C43⋊C8—21no—
296C43⋊C8—21no—
297C43⋊C8—21no—
298C43⋊C8—21no—
299C43⋊C8—22no—
300C43⋊C8—41no—
301C43⋊C8—41no—
302C43⋊C8—41no—
303#25363—431nomaximal, Sylow
304C22×C43—21no—
305C22×C43—21no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43C2×#12111yescharacteristic
313C22×C43#52911yescharacteristic
314C22×C43#54211yescharacteristic
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—81no—
322C4×C43—81no—
323C4×C43#54611yescharacteristic
324C4×C43#54611yescharacteristic
325C4×C43#54711yescharacteristic
326C4×C43#54811yescharacteristic
327Dic43—42no—
328Dic43—81no—
329#3142D4311yescharacteristic
330C2×#479—431no—
331#3037—431no—
332#2935—431no—
333#2079—431no—
334#2078—431no—
335#2052—431no—
336#2052—431no—
337#1998—431no—
338#1950—431no—
339#1908—431no—
340#1908—431no—
341#1816—431no—
342#1815—431no—
343C4×#101—431no—
344C2×C43—21no—
345C2×C43—21no—
346C2×C43—81no—
347C2×C43—81no—
348C2×C43#242711yescharacteristic
349C2×C43#306711yescharacteristic
350C2×C43#306911yescharacteristic
351C2×#137—431no—
352C2×#137—431no—
353C2×#131—431no—
354C2×#131—431no—
355#532C2×D4311yescharacteristic
356C2×#125C2×D4311yescharacteristic
357C2×C4×Q8—431no—
358#491—21no—
359#490—21no—
360#488—21no—
361#488—21no—
362#479—861no—
363#479—861no—
364#479—861no—
365#479—861no—
366#464—861no—
367#464—861no—
368#462—861no—
369#460—861no—
370#436—861no—
371#435—861no—
372#435—861no—
373C8×D4—861no—
374C2×#108—431no—
375C2×#108—431no—
376C2×#107—431no—
377C2×#106—431no—
378#423—431no—
379C2×C4⋊C8—431no—
380#417—431no—
381#417—431no—
382#417C2×D4311yescharacteristic
383#417C2×D4311yescharacteristic
384#417C2×D4311yescharacteristic
385#417C2×D4311yescharacteristic
386C2×#103—431no—
387C2×#103—431no—
388C2×#101—431no—
389C2×#101—431no—
390#408—431no—
391#408—431no—
392C4×M16—431no—
393C4×M16C2×D4311yescharacteristic
394#343—431no—
395#343—431no—
396#343—431no—
397#343—431no—
398#343—431no—
399#343—431no—
400#341—431no—
401#341—431no—
402C43#2536311yescharacteristic, complemented, Sylow
403C2×#41C22×D4311yescharacteristic
404C2×#41C22×D4311yescharacteristic
405C22×Q8—431no—
406#137—862no—
407#137—862no—
408#137—1721no—
409#137—1721no—
410C2×Q16—861no—
411C2×Q16—861no—
412C2×SD16—861no—
413C2×SD16—861no—
414#131—862no—
415#131—862no—
416#131—1721no—
417#131—1721no—
418C2×M16—431no—
419C2×M16—431no—
420C2×M16—431no—
421C2×M16—431no—
422C2×M16—861no—
423C2×M16—861no—
424C2×M16C22×D4311yescharacteristic
425C2×M16C22×D4311yescharacteristic
426C22×C8—431no—
427C22×C8—431no—
428C22×C8—861no—
429C22×C8—861no—
430C4⋊Q8C22⋊D4311yescharacteristic
431#127C22⋊D4311yescharacteristic
432#125—21no—
433#125—21no—
434#125—21no—
435#125—21no—
436#124C22⋊D4311yescharacteristic
437#124C22⋊D4311yescharacteristic
438#121—21no—
439#121—21no—
440C4×Q8—861no—
441C4×Q8—861no—
442C4×Q8—861no—
443C4×Q8—861no—
444C4×D4—21no—
445C4×D4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4C22×D4311yescharacteristic
451C2×C4⋊C4C22×D4311yescharacteristic
452C2×C42—861no—
453C2×C42C22×D4311yescharacteristic
454#108—1721no—
455#108—1721no—
456#107—861no—
457#107—861no—
458#106—861no—
459#106—861no—
460C4⋊C8—431no—
461C4⋊C8—431no—
462C4⋊C8—431no—
463C4⋊C8—431no—
464C4⋊C8—861no—
465C4⋊C8—861no—
466#103—21no—
467#103—21no—
468#103—21no—
469#103—21no—
470#103—861no—
471#103—861no—
472#103—861no—
473#103—861no—
474#103—861no—
475#103—861no—
476#102—21no—
477#102—21no—
478#102—21no—
479#102—21no—
480#102—861no—
481#102—861no—
482#101—862no—
483#101—862no—
484C22⋊C8—861no—
485C22⋊C8—861no—
486C22⋊C8—861no—
487C22⋊C8—861no—
488#97—21no—
489#97—861no—
490C4×C8—21no—
491C4×C8—861no—
492#41—21no—
493#41—21no—
494#41—21no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500C2×Q8—432no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8C2×C22⋊D4311yescharacteristic
507C2×Q8C2×C22⋊D4311yescharacteristic
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4C2×C22⋊D4311yescharacteristic
513C2×D4C2×C22⋊D4311yescharacteristic
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4#1062190011yescharacteristic
521C22×C4#1062190011yescharacteristic
522C22×C4C23×D4311yescharacteristic
523Q16—1722no—
524Q16—1722no—
525SD16—1722no—
526SD16—1722no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—432no—
532M16—861no—
533M16—861no—
534M16—861no—
535M16—861no—
536M16—861no—
537M16—861no—
538M16—861no—
539M16—1722no—
540M16—1722no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—431no—
544C2×C8—431no—
545C2×C8—431no—
546C2×C8—431no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—1722no—
556C2×C8—1722no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—861no—
568C4⋊C4—861no—
569C4⋊C4—1721no—
570C4⋊C4—1721no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C42—1721no—
576C42—1721no—
577C42D4×D4311yescharacteristic
578C42D4×D4311yescharacteristic
579C42C2×C22⋊D4311yescharacteristic
580C42C2×C22⋊D4311yescharacteristic
581C23—21no—
582C23—21no—
583C23C2×#1062190011yescharacteristic
584Q8—21no—
585Q8—21no—
586Q8—21no—
587Q8—21no—
588Q8—862no—
589Q8—862no—
590Q8—1721no—
591Q8—1721no—
592D4—21no—
593D4—21no—
594D4—21no—
595D4—21no—
596D4—42no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—81no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—862no—
615C2×C4—3441no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1721no—
619C2×C4#1306329711yescharacteristic
620C2×C4#1306329711yescharacteristic
621C2×C4#1306329711yescharacteristic
622C2×C4#1306329711yescharacteristic
623C2×C4C2×D4×D4311yescharacteristic
624C2×C4C22×C22⋊D4311yescharacteristic
625C2×C4#41×D4311yescharacteristic
626C2×C4#41×D4311yescharacteristic
627C2×C4#1306337111yescharacteristic
628C2×C4#1306337211yescharacteristic
629C8—41no—
630C8—41no—
631C8—861no—
632C8—861no—
633C8—861no—
634C8—861no—
635C8—862no—
636C8—1721no—
637C8—1721no—
638C8—1721no—
639C22—21no—
640C22—21no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#1306329711yescharacteristic
648C22#1458342811yescharacteristic
649C22#1458351811yescharacteristic
650C4—21no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—41no—
655C4—41no—
656C4—81no—
657C4—81no—
658C4—3441no—
659C4—1722no—
660C4#1458353711yescharacteristic
661C4#1458354211yescharacteristic
662C4#1458354811yescharacteristic
663C4#1458355711yescharacteristic
664C2—21no—
665C2—21no—
666C2—81no—
667C2—81no—
668C2#1913817511yescharacteristic
669C2#1914431211yescharacteristic
670C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3142C2
socleC22×C43C2×#121
prime radicalC43×#532C22
hypercenter#3142D43
hypocenterC43#25363
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. C2×#14583203C2semidirect
4. #19136043C2semidirect
5. #19136038C2semidirect
6. #19135892C2semidirect
7. #19135892C2semidirect
8. #19135589C2semidirect
9. #19135370C2semidirect
10. #19135108C2semidirect
11. #19135108C2semidirect
12. #19134657C2semidirect
13. #19134652C2semidirect
14. C4×#13063243C2semidirect
402. C43#25363semidirect

Maximal subgroups

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

subgroupindex
C2×#145832032
#191440632
#191433392
#191360432
#191360382
#191358922
#191355892
#191353702
#191351082
#191346572
#191346522
C4×#130632432
C43×#31422
#2536343