Finite Group Databasebeta

← #25099842

Subgroups — #25099842

Order 11008.

780 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143391C211yesmaximal, characteristic
2#19143242C211yesmaximal, characteristic, complemented
3#19143022C211yesmaximal, characteristic, complemented
4#19135245C211yesmaximal, characteristic, complemented
5#19135194C211yesmaximal, characteristic, complemented
6#19135192C211yesmaximal, characteristic, complemented
7#19134925C211yesmaximal, characteristic
8#19134919C211yesmaximal, characteristic
9#19134873C211yesmaximal, characteristic, complemented
10#19134867C211yesmaximal, characteristic, complemented
11#19134503C211yesmaximal, characteristic, complemented
12#104×Dic43C211yesmaximal, characteristic, complemented
13#19134399C211yesmaximal, characteristic, complemented
14#19134342C211yesmaximal, characteristic, complemented
15C43×#1929C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C2×#13063331C2211yescharacteristic
19#41×Dic43C2211yescharacteristic
20#14583367C2211yescharacteristic
21#14583008C411yescharacteristic, complemented
22#14583008C411yescharacteristic, complemented
23#14583003C411yescharacteristic, complemented
24#14583003C411yescharacteristic, complemented
25#14583002C411yescharacteristic, complemented
26#14583002C411yescharacteristic, complemented
27#14582996C411yescharacteristic, complemented
28#14582996C411yescharacteristic, complemented
29#14582957—21no—
30#14582957—21no—
31#14582953—21no—
32#14582953—21no—
33C2×#13063261C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582927C2211yescharacteristic
36#14582925C2211yescharacteristic
37C2×#13063253C2211yescharacteristic
38C2×#13063252C2211yescharacteristic
39C2×#13063251C2211yescharacteristic
40#14582896C2211yescharacteristic
41#14582866C2211yescharacteristic
42#14582856—21no—
43#14582855C2211yescharacteristic
44#14582853—21no—
45M16×Dic43C2211yescharacteristic
46M16×Dic43C2211yescharacteristic
47C4×#10621872—21no—
48C2×#13063235C2211yescharacteristic
49C2×#13063235C2211yescharacteristic
50#97×D43—21no—
51C42×Dic43C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582658C2211yescharacteristic
57#14582654C2211yescharacteristic
58#14582653C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C2×#104×C43C2211yescharacteristic
62C43×#416C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063345—22no—
69#13063345—22no—
70C2×#10621885C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73C2×#10621882C2×C411yescharacteristic
74#13063333—22no—
75#13063333—22no—
76#13063331—22no—
77#13063331—22no—
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621872—21no—
81C2×#10621872—21no—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86Q8×Dic43C2×C411yescharacteristic
87Q8×Dic43C2×C411yescharacteristic
88#13063290C2×C411yescharacteristic
89#13063290C2×C411yescharacteristic
90D4×Dic43—21no—
91D4×Dic43—21no—
92D4×Dic43C2×C411yescharacteristic
93D4×Dic43C2×C411yescharacteristic
94#13063287C2×C411yescharacteristic
95#13063287C2×C411yescharacteristic
96(C22⋊D43)⋊C4—21no—
97(C22⋊D43)⋊C4—21no—
98#13063284—21no—
99#13063284C2311yescharacteristic
100#13063282—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106C42×D43—21no—
107#13063261—22no—
108#13063258C2×C411yescharacteristic
109#13063258C2×C411yescharacteristic
110#13063256C2×C411yescharacteristic
111#13063256C2×C411yescharacteristic
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116#13063253—22no—
117#13063252—22no—
118#13063251—22no—
119#13063250C2×C411yescharacteristic
120#13063250C2×C411yescharacteristic
121#13063247C2×C411yescharacteristic
122#13063247C2×C411yescharacteristic
123C22⋊(C43⋊C8)—21no—
124C22⋊(C43⋊C8)—21no—
125#13063236—21no—
126#13063235—21no—
127#13063235—21no—
128#13063235C2×C411yescharacteristic
129#13063235C2×C411yescharacteristic
130#13063235C2×C411yescharacteristic
131#13063235C2×C411yescharacteristic
132#13063235D411yescharacteristic
133#13063235D411yescharacteristic
134#13063235D411yescharacteristic
135#13063235D411yescharacteristic
136C4×C43⋊C8—21no—
137C8×Dic43—21no—
138C8×Dic43—21no—
139C2×#41×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C2×M16×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144#117×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#108×C43—22no—
147#104×C43—22no—
148#103×C43C2×C411yescharacteristic
149#103×C43C2×C411yescharacteristic
150#102×C43C2×C411yescharacteristic
151#102×C43C2×C411yescharacteristic
152C22⋊C8×C43—21no—
153C22⋊C8×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—
160C2×Q8×C43C22×C411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43C22×C411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43#4111yescharacteristic
171C22×Dic43#4111yescharacteristic
172#10621898—21no—
173#10621898—21no—
174#10621898#4112yes—
175#10621898#4112yes—
176C2×D172C22×C411yescharacteristic
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×Dic86C22×C411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43#4112yes—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43C22×C411yescharacteristic
192C2×C8×C43C22×C411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43C22×C411yescharacteristic
196C4⋊C4×C43C22×C411yescharacteristic
197C22⋊C4×C43—21no—
198C42×C43—21no—
199C42×C43—21no—
200C42×C43—21no—
201C22⋊Dic43—21no—
202C22⋊Dic43—21no—
203C22⋊Dic43—21no—
204#10621885—22no—
205#10621884—22no—
206#10621883—22no—
207#10621882—22no—
208(C2×D43)⋊C4—21no—
209(C2×D43)⋊C4—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212C4⋊Dic43C22×C411yescharacteristic
213C4⋊Dic43C22×C411yescharacteristic
214Dic43⋊C4—21no—
215Dic43⋊C4—21no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—42no—
224C4×Dic43—42no—
225C4×Dic43C22×C411yescharacteristic
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877#4112yes—
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⋊C8C22×C411yescharacteristic
240C2×C43⋊C8C22×C411yescharacteristic
241C2×C43⋊C8C2×D411yescharacteristic
242C2×C43⋊C8C2×D411yescharacteristic
243#10621872—24no—
244#10621872—24no—
245C8×D43—24no—
246C8×D43—24no—
247C23×C43—21no—
248C23×C43C2×#4111yescharacteristic
249C22×D43—21no—
250Q8×C43—21no—
251Q8×C43—21no—
252D4×C43—21no—
253D4×C43—21no—
254D4×C43—41no—
255D4×C43—41no—
256C2×C4×C43—22no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43C23×C411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C22⋊D43—22no—
271C22⋊D43—22no—
272C2×Dic43—21no—
273C2×Dic43—22no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—81no—
281C2×Dic43—81no—
282C2×Dic43C4×D411yescharacteristic
283C2×Dic43C4×D411yescharacteristic
284C2×Dic43C4×D411yescharacteristic
285C2×Dic43C4×D411yescharacteristic
286D172—21no—
287D172#11712yes—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—81no—
291C4×D43—81no—
292Dic86—21no—
293Dic86#11712yes—
294C8×C43—21no—
295C8×C43—21no—
296C8×C43—21no—
297C8×C43—22no—
298C8×C43—21no—
299C8×C43—41no—
300C43⋊C8—21no—
301C43⋊C8—21no—
302C43⋊C8—21no—
303C43⋊C8—22no—
304C43⋊C8—21no—
305C43⋊C8—41no—
306#21139—431nomaximal, Sylow
307C22×C43—21no—
308C22×C43—21no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—41no—
312C22×C43C2×C4×D411yescharacteristic
313C22×C43#52911yescharacteristic
314C22×C43#52911yescharacteristic
315C2×D43—22no—
316C2×D43—41no—
317C2×D43—41no—
318C4×C43—42no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43—41no—
322C4×C43C2×#11711yescharacteristic
323C4×C43C4×#4111yescharacteristic
324C4×C43#52511yescharacteristic
325C4×C43#52511yescharacteristic
326Dic43—21no—
327Dic43—21no—
328Dic43—21no—
329Dic43—21no—
330Dic43—22no—
331Dic43—42no—
332Dic43—41no—
333Dic43—41no—
334#2943—431no—
335#2923—431no—
336#2875—431no—
337#1929—431no—
338#1929D4311yescharacteristic, complemented
339#1922—431no—
340#1922—431no—
341#1876—431no—
342#1876—431no—
343#1866—431no—
344#1866—431no—
345#1778—431no—
346C4×#104—431no—
347C4×#104—431no—
348#1745—431no—
349C2×C43—21no—
350C2×C43—21no—
351C2×C43—81no—
352C2×C43#229011yescharacteristic
353C2×C43#295611yescharacteristic
354C2×C43#295611yescharacteristic
355D43—42no—
356C2×#135—431no—
357C2×#131—431no—
358C2×#131—431no—
359C4×#41—431no—
360C4×#41—431no—
361#442—431no—
362#442—431no—
363#441—431no—
364#441—431no—
365#440—431no—
366#440—431no—
367#440—431no—
368#440—431no—
369#433—861no—
370#433—861no—
371#432—861no—
372#432—861no—
373C2×#108—431no—
374C2×#108C2×D4311yescharacteristic
375#427—431no—
376#424—431no—
377#424—431no—
378C2×#104—431no—
379C2×#104—431no—
380C2×#104—431no—
381C2×#104C2×D4311yescharacteristic
382#416—431no—
383#416C2×D4311yescharacteristic
384#408—431no—
385#408C2×D4311yescharacteristic
386#405—431no—
387#405—861no—
388#405—861no—
389#405C2×D4311yescharacteristic
390C4×M16—431no—
391C4×M16—431no—
392C4×M16—861no—
393C2×#97—431no—
394C2×#97—431no—
395C2×#97—861no—
396C43—431no—
397#341—431no—
398#341—431no—
399#339—431no—
400#339—431no—
401#339—431no—
402#339C2×D4311yescharacteristic
403#336—431no—
404#336—431no—
405#336—431no—
406#336C2×D4311yescharacteristic
407C43#2113911yescharacteristic, complemented, Sylow
408C2×#41—431no—
409C2×#41C22×D4311yescharacteristic
410#135—862no—
411#135—862no—
412C2×Q16—431no—
413C2×SD16—431no—
414C2×SD16—431no—
415C2×D8—431no—
416#131—862no—
417#131—862no—
418#131—862no—
419#131—862no—
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—
430C22×C8C22×D4311yescharacteristic
431C22×C8C22×D4311yescharacteristic
432C4×Q8—431no—
433C4×Q8—431no—
434C4×Q8—431no—
435C4×Q8—431no—
436C4×D4—431no—
437C4×D4—431no—
438C4×D4—431no—
439C4×D4—431no—
440C4×D4—861no—
441C4×D4—861no—
442C4×D4—861no—
443C4×D4—861no—
444#117—431no—
445#117—861no—
446#117—861no—
447#117C22×D4311yescharacteristic
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42—861no—
453C2×C42—861no—
454C2×C42C22×D4311yescharacteristic
455#108—22no—
456#108—862no—
457#107—431no—
458#107—431no—
459#106—431no—
460#106—431no—
461C4⋊C8—861no—
462C4⋊C8—861no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465#104—22no—
466#104—862no—
467#104—862no—
468#104—862no—
469#103—431no—
470#103—431no—
471#103C4×D4311yescharacteristic
472#103C4×D4311yescharacteristic
473#102—431no—
474#102—431no—
475#102C4×D4311yescharacteristic
476#102C4×D4311yescharacteristic
477C22⋊C8—21no—
478C22⋊C8—21no—
479C22⋊C8—861no—
480C22⋊C8—861no—
481#97—21no—
482#97—431no—
483#97—431no—
484#97—431no—
485#97—431no—
486#97—431no—
487#97—431no—
488#97—431no—
489#97—431no—
490#97—861no—
491#97—861no—
492#97—861no—
493C4×C8—21no—
494C4×C8—861no—
495C4×C8—861no—
496C4×C8—861no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41—432no—
502#41—432no—
503#41—861no—
504#41—861no—
505C2×Q8—431no—
506C2×Q8C2×C4×D4311yescharacteristic
507C2×D4—21no—
508C2×D4—431no—
509C2×D4—861no—
510C2×D4C2×C4×D4311yescharacteristic
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—431no—
514C22×C4—431no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4C23×D4311yescharacteristic
522Q16—862no—
523SD16—862no—
524SD16—862no—
525D8—862no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—432no—
530M16—864no—
531M16—864no—
532M16—861no—
533M16—861no—
534M16—861no—
535M16#1062190012yes—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—431no—
543C2×C8—431no—
544C2×C8—431no—
545C2×C8—431no—
546C2×C8—864no—
547C2×C8—864no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8C2×C4×D4311yescharacteristic
555C2×C8C2×C4×D4311yescharacteristic
556C2×C8D4×D4311yescharacteristic
557C2×C8D4×D4311yescharacteristic
558C4⋊C4—431no—
559C4⋊C4—431no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4C2×C4×D4311yescharacteristic
565C4⋊C4C2×C4×D4311yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—861no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C22⋊C4—861no—
571C22⋊C4—861no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—431no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—861no—
584C42—861no—
585C42—861no—
586C42—1722no—
587C42—1722no—
588C23—21no—
589C23—861no—
590C23#41×D4311yescharacteristic
591Q8—21no—
592Q8—21no—
593Q8—432no—
594Q8—861no—
595D4—21no—
596D4—21no—
597D4—41no—
598D4—41no—
599D4—432no—
600D4—862no—
601D4—862no—
602D4—861no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—431no—
612C2×C4—431no—
613C2×C4—431no—
614C2×C4—431no—
615C2×C4—861no—
616C2×C4—862no—
617C2×C4—862no—
618C2×C4—862no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—3441no—
622C2×C4—3441no—
623C2×C4—3441no—
624C2×C4—3441no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4C22×C4×D4311yescharacteristic
630C2×C4C2×D4×D4311yescharacteristic
631C2×C4#41×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4#41×D4311yescharacteristic
634C2×C4C2×#1062190011yescharacteristic
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—22no—
640C8—41no—
641C8—861no—
642C8—861no—
643C8—862no—
644C8—861no—
645C8—861no—
646C8—1721no—
647C22—21no—
648C22—21no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—862no—
653C22—1721no—
654C22—1721no—
655C22C4×D4×D4311yescharacteristic
656C22#1458342811yescharacteristic
657C22#1458343211yescharacteristic
658C4—42no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—862no—
663C4—861no—
664C4—861no—
665C4—861no—
666C4—861no—
667C4—1722no—
668C4—1721no—
669C4—1721no—
670C4#117×D4311yescharacteristic
671C4C4×#1062190011yescharacteristic
672C4#1458340711yescharacteristic
673C4#1458340911yescharacteristic
674C2—21no—
675C2—21no—
676C2—81no—
677C2—1722no—
678C2#1913703711yescharacteristic
679C2#1914350011yescharacteristic
680C2#1914350311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1929C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenter#1929D43
hypocenterC43#21139
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
2. #19143242C2semidirect
3. #19143022C2semidirect
4. #19135245C2semidirect
5. #19135194C2semidirect
6. #19135192C2semidirect
9. #19134873C2semidirect
10. #19134867C2semidirect
11. #19134503C2semidirect
12. #104×Dic43C2semidirect
13. #19134399C2semidirect
14. #19134342C2semidirect
15. C43×#1929C2semidirect
21. #14583008C4semidirect
22. #14583008C4semidirect
23. #14583003C4semidirect
24. #14583003C4semidirect
25. #14583002C4semidirect
26. #14583002C4semidirect
27. #14582996C4semidirect
28. #14582996C4semidirect
338. #1929D43semidirect
407. C43#21139semidirect

Maximal subgroups

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

subgroupindex
#191433912
#191432422
#191430222
#191352452
#191351942
#191351922
#191349252
#191349192
#191348732
#191348672
#191345032
#104×Dic432
#191343992
#191343422
C43×#19292
#2113943