Finite Group Databasebeta

← #25103532

Subgroups — #25103532

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144312C211yesmaximal, characteristic
2#19143496C211yesmaximal, characteristic, complemented
3C2×#14583014C211yesmaximal, characteristic, complemented
4#131×Dic43C211yesmaximal, characteristic, complemented
5#19135492C211yesmaximal, characteristic, complemented
6#19135382C211yesmaximal, characteristic, complemented
7#19135267C211yesmaximal, characteristic, complemented
8#19135263C211yesmaximal, characteristic, complemented
9#19135098C211yesmaximal, characteristic, complemented
10#19135094C211yesmaximal, characteristic, complemented
11#19134647C211yesmaximal, characteristic, complemented
12#19134475C211yesmaximal, characteristic, complemented
13#19134396C211yesmaximal, characteristic, complemented
14#19134395C211yesmaximal, characteristic, complemented
15C43×#2955C211yesmaximal, characteristic, complemented
16#14583697C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×#13063331C2211yescharacteristic
20#41×Dic43C2211yescharacteristic
21#14583172C412yescomplemented
22#14583167C412yescomplemented
23#14583164C412yescomplemented
24#14583160C412yescomplemented
25#14583019—22no—
26#14583014—21no—
27#14583014—21no—
28#14583014—21no—
29#14583014—21no—
30#14583014—22no—
31#14582947C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33C2×#13063260C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582916C2211yescharacteristic
36#14582915C2211yescharacteristic
37C2×#13063252C2211yescharacteristic
38C2×#13063251C2211yescharacteristic
39#14582883C2211yescharacteristic
40#14582881C2211yescharacteristic
41#14582873C2211yescharacteristic
42#14582872C2211yescharacteristic
43#14582857—21no—
44#14582857C2211yescharacteristic
45#14582854—21no—
46#14582854C2211yescharacteristic
47#14582854C2211yescharacteristic
48M16×Dic43—21no—
49M16×Dic43C2211yescharacteristic
50C2×C8×Dic43—21no—
51C2×C8×Dic43C2211yescharacteristic
52#14582671C2211yescharacteristic
53#14582670C2211yescharacteristic
54#14582670C2211yescharacteristic
55#14582669C2211yescharacteristic
56#14582660C2211yescharacteristic
57#14582658C2211yescharacteristic
58C43×#575C2211yescharacteristic
59C2×#131×C43C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C43×#444—22no—
62C43×#443—22no—
63C43×#430C2211yescharacteristic
64C43×#421C2211yescharacteristic
65C43×#421C2211yescharacteristic
66C43×#405C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063356—21no—
69#13063355C2×C412yes—
70#13063351—21no—
71#13063350C2×C412yes—
72#13063345—22no—
73#13063345—21no—
74#13063345—21no—
75#13063345—21no—
76#13063345—21no—
77C2×#10621885C2×C411yescharacteristic, complemented
78C2×#10621883C2×C411yescharacteristic, complemented
79C2×#10621884C2×C411yescharacteristic, complemented
80C2×#10621882C2×C411yescharacteristic, complemented
81#13063332—21no—
82#13063332—21no—
83#13063332C2×C412yes—
84#13063332C2×C412yes—
85#13063331—21no—
86#13063331—21no—
87#13063331—21no—
88#13063331—21no—
89C2×#10621877—21no—
90C2×#10621877C2311yescharacteristic
91C2×#10621877C2311yescharacteristic
92C2×#10621877C2311yescharacteristic
93C2×#10621872—21no—
94C22×C43⋊C8—21no—
95C22×C43⋊C8C2311yescharacteristic
96C2×C8×D43—21no—
97Q8×Dic43—21no—
98D4×Dic43—21no—
99D4×Dic43—22no—
100#13063284—21no—
101#13063284C2311yescharacteristic
102#13063284C2311yescharacteristic
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105#13063260—22no—
106#13063260—21no—
107#13063260—21no—
108#13063260C2×C412yescomplemented
109#13063260C2×C412yescomplemented
110#13063258—21no—
111#13063256—21no—
112#13063252—22no—
113#13063252—21no—
114#13063252—21no—
115#13063251—22no—
116#13063251—21no—
117#13063251—21no—
118#13063244C2×C412yescomplemented
119#13063243C2×C412yescomplemented
120#13063242C2×C412yescomplemented
121#13063241C2×C412yescomplemented
122#13063240—22no—
123#13063239—22no—
124#13063235—21no—
125#13063235—21no—
126#13063235—21no—
127#13063235—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C8×Dic43—21no—
132C8×Dic43D411yescharacteristic
133C8×Dic43D411yescharacteristic
134C8×Dic43D411yescharacteristic
135C8×Dic43D411yescharacteristic
136C2×#41×C43C2311yescharacteristic
137C2×#41×C43C2311yescharacteristic
138#137×C43—21no—
139#137×C43C2×C412yes—
140AGL(1,ℤ/8)×C43—21no—
141AGL(1,ℤ/8)×C43C2×C412yes—
142#135×C43—22no—
143#131×C43—21no—
144#131×C43—21no—
145#131×C43—21no—
146#131×C43—21no—
147#131×C43—21no—
148#131×C43—21no—
149#131×C43D412yes—
150#131×C43D412yes—
151C2×M16×C43—21no—
152C2×M16×C43—21no—
153C2×M16×C43C2311yescharacteristic
154C2×M16×C43C2311yescharacteristic
155C2×M16×C43C2311yescharacteristic
156C22×C8×C43—21no—
157C22×C8×C43—21no—
158C22×C8×C43C2311yescharacteristic
159#117×C43C2311yescharacteristic
160#108×C43—22no—
161#104×C43—22no—
162#104×C43—22no—
163#97×C43—21no—
164C4×C8×C43—21no—
165#41×C43—21no—
166#41×C43—21no—
167#41×C43—21no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43C22×C412yes—
172#41×C43C2×D412yes—
173C2×Q8×C43C22×C411yescharacteristic
174C2×Q8×C43#4111yescharacteristic
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43C22×C411yescharacteristic
178C2×D4×C43#4111yescharacteristic
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43C2411yescharacteristic
182C2×C22⋊D43—21no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185#10621898—21no—
186#10621898—21no—
187#10621898—21no—
188#10621898—21no—
189C2×D172C22×C411yescharacteristic
190C2×C4×D43—21no—
191C2×Dic86C22×C411yescharacteristic
192Q16×C43—22no—
193SD16×C43—22no—
194SD16×C43—22no—
195D8×C43—22no—
196M16×C43—21no—
197M16×C43—21no—
198M16×C43—22no—
199M16×C43—22no—
200M16×C43—21no—
201M16×C43—21no—
202M16×C43—41no—
203M16×C43—41no—
204M16×C43C22×C412yes—
205M16×C43C2×D412yes—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—22no—
209C2×C8×C43—22no—
210C2×C8×C43—21no—
211C2×C8×C43—41no—
212C2×C8×C43—41no—
213C2×C8×C43C2×D411yescharacteristic
214C2×C8×C43C2×D411yescharacteristic
215C2×C8×C43C2×D411yescharacteristic
216C2×C8×C43C2×D411yescharacteristic
217C2×C8×C43#4111yescharacteristic
218C2×C8×C43#4111yescharacteristic
219C4⋊C4×C43—21no—
220C22⋊C4×C43—21no—
221C42×C43—21no—
222C22⋊Dic43—22no—
223C22⋊Dic43—21no—
224C22⋊Dic43#4112yes—
225#10621885—22no—
226#10621885—21no—
227#10621885—21no—
228#10621884—22no—
229#10621884—21no—
230#10621884—21no—
231#10621883—22no—
232#10621883—21no—
233#10621883—21no—
234#10621882—22no—
235#10621882—21no—
236#10621882—21no—
237C4⋊Dic43—22no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4×Dic43—22no—
241C4×Dic43—21no—
242C4×Dic43—21no—
243C4×Dic43—21no—
244C4×Dic43C2×D411yescharacteristic
245C4×Dic43C2×D411yescharacteristic
246#10621877—21no—
247#10621877—21no—
248#10621877—22no—
249#10621877—22no—
250#10621877—21no—
251#10621877—21no—
252#10621877C22×C412yes—
253#10621877C22×C412yes—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—22no—
257C2×C43⋊C8—22no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8C22×C411yescharacteristic
260C2×C43⋊C8C22×C411yescharacteristic
261C2×C43⋊C8C2×D411yescharacteristic
262C2×C43⋊C8C2×D411yescharacteristic
263C2×C43⋊C8#4111yescharacteristic
264C2×C43⋊C8#4111yescharacteristic
265#10621872—41no—
266#10621872—41no—
267C8×D43—41no—
268C8×D43—41no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43C2×#4111yescharacteristic
272C22×D43—21no—
273Q8×C43—21no—
274Q8×C43—21no—
275Q8×C43—21no—
276Q8×C43C4×D412yes—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—21no—
280D4×C43—21no—
281D4×C43—21no—
282D4×C43—41no—
283D4×C43—41no—
284D4×C43C4×D412yes—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—21no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43C23×C411yescharacteristic
293C2×C4×C43C22×D411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C22⋊D43—41no—
299C22⋊D43—41no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—22no—
303C2×Dic43—21no—
304C2×Dic43—42no—
305C2×Dic43—44no—
306C2×Dic43—41no—
307D172—21no—
308D172—21no—
309C4×D43—41no—
310C4×D43—41no—
311Dic86—21no—
312Dic86—21no—
313C8×C43—22no—
314C8×C43—22no—
315C8×C43—41no—
316C8×C43#12111yescharacteristic
317C8×C43#12111yescharacteristic
318C8×C43#12111yescharacteristic
319C8×C43#12111yescharacteristic
320C43⋊C8—22no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323C43⋊C8C4×D411yescharacteristic
324C43⋊C8C4×D411yescharacteristic
325C43⋊C8C4×D411yescharacteristic
326C43⋊C8C4×D411yescharacteristic
327#21558—431nomaximal, Sylow
328C22×C43—22no—
329C22×C43—41no—
330C22×C43—42no—
331C22×C43—41no—
332C22×C43—81no—
333C22×C43C4×#4111yescharacteristic
334C22×C43#52511yescharacteristic
335C22×C43#53211yescharacteristic
336C2×D43—41no—
337C2×D43—81no—
338C4×C43—22no—
339C4×C43—41no—
340C4×C43—81no—
341C4×C43C2×C4×D411yescharacteristic
342C4×C43C2×C4×D411yescharacteristic
343C4×C43C2×#12111yescharacteristic
344C4×C43#52911yescharacteristic
345Dic43—22no—
346Dic43—42no—
347Dic43—41no—
348Dic43—41no—
349Dic43—81no—
350#3067—431no—
351#2955—431no—
352#2955D4311yescharacteristic, complemented
353C2×#443—431no—
354C4×#131—431no—
355#1976—431no—
356#1953—431no—
357#1932—431no—
358#1932—431no—
359#1906—431no—
360#1906—431no—
361#1814—431no—
362#1772—431no—
363#1757—431no—
364#1757—431no—
365C2×C43—21no—
366C2×C43—21no—
367C2×C43—21no—
368C2×C43—42no—
369C2×C43—81no—
370C2×C43C4×#12111yescharacteristic
371D43—81no—
372#575—431no—
373#575C2×D4311yescharacteristic
374C2×#135—431no—
375C2×#131—431no—
376C2×#131—431no—
377C2×#131C2×D4311yescharacteristic
378C2×#131C2×D4311yescharacteristic
379C4×#41—431no—
380#473—432no—
381#472—432no—
382#471—432no—
383#471—432no—
384#444—22no—
385#444—862no—
386#443—22no—
387#443—861no—
388#443—861no—
389#443—861no—
390#443—861no—
391#443—862no—
392#430—431no—
393#430C2×D4311yescharacteristic
394C2×#108—431no—
395C2×#108—431no—
396#427—431no—
397#421—431no—
398#421—431no—
399#421C2×D4311yescharacteristic
400#421C2×D4311yescharacteristic
401C2×#104—431no—
402C2×#104—431no—
403#413—431no—
404#413—431no—
405#410—431no—
406#410—431no—
407#405—431no—
408#405—431no—
409#405—431no—
410#405—861no—
411#405—861no—
412#405C2×D4311yescharacteristic
413C4×M16—431no—
414C4×M16—861no—
415C2×C4×C8—431no—
416C2×C4×C8—861no—
417#344—431no—
418#344—431no—
419#344—431no—
420#344—431no—
421#339—431no—
422#339—431no—
423C43#2155811yescharacteristic, complemented, Sylow
424C2×#41—431no—
425C2×#41C22×D4311yescharacteristic
426C2×#41C22×D4311yescharacteristic
427#137—21no—
428#137—432no—
429#137—861no—
430#137C4×D4312yes—
431AGL(1,ℤ/8)—21no—
432AGL(1,ℤ/8)—432no—
433AGL(1,ℤ/8)—861no—
434AGL(1,ℤ/8)C4×D4312yes—
435#135—22no—
436#135—861no—
437#135—861no—
438#135—861no—
439#135—861no—
440#135—862no—
441C2×Q16—431no—
442C2×SD16—431no—
443C2×SD16—431no—
444C2×D8—431no—
445#131—21no—
446#131—21no—
447#131—21no—
448#131—21no—
449#131—21no—
450#131—21no—
451#131—432no—
452#131—432no—
453#131—861no—
454#131—861no—
455#131—861no—
456#131—861no—
457#131—861no—
458#131—861no—
459#131C22⋊D4312yes—
460#131C22⋊D4312yes—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—431no—
464C2×M16—431no—
465C2×M16—431no—
466C2×M16—861no—
467C2×M16—861no—
468C2×M16C22×D4311yescharacteristic
469C2×M16C22×D4311yescharacteristic
470C2×M16C22×D4311yescharacteristic
471C22×C8—21no—
472C22×C8—21no—
473C22×C8—431no—
474C22×C8—861no—
475C22×C8—861no—
476C22×C8C22×D4311yescharacteristic
477C4×Q8—861no—
478C4×D4—862no—
479C4×D4—861no—
480#117—431no—
481#117—431no—
482#117—861no—
483#117C22×D4311yescharacteristic
484C2×C42—431no—
485C2×C42—861no—
486#108—22no—
487#108—432no—
488#108—432no—
489#108—861no—
490#108—861no—
491#108—862no—
492#107—861no—
493#106—861no—
494#104—22no—
495#104—22no—
496#104—861no—
497#104—861no—
498#104—861no—
499#104—861no—
500#104—862no—
501#104—862no—
502#101—432no—
503#101—432no—
504#100—432no—
505#100—432no—
506#99—862no—
507#99—862no—
508#97—21no—
509#97—861no—
510#97—861no—
511#97—861no—
512#97—861no—
513C4×C8—21no—
514C4×C8—431no—
515C4×C8—431no—
516C4×C8—431no—
517C4×C8—431no—
518C4×C8—861no—
519C4×C8—861no—
520C4×C8—861no—
521C4×C8—861no—
522#41—21no—
523#41—21no—
524#41—21no—
525#41—21no—
526#41—21no—
527#41—21no—
528#41—861no—
529#41—861no—
530#41—861no—
531#41—861no—
532#41C2×C4×D4312yes—
533#41C2×C22⋊D4312yes—
534C2×Q8—431no—
535C2×Q8C2×C4×D4311yescharacteristic
536C2×Q8#1062189811yescharacteristic
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—431no—
540C2×D4—861no—
541C2×D4C2×C4×D4311yescharacteristic
542C2×D4#1062189811yescharacteristic
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—862no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4C23×D4311yescharacteristic
549Q16—22no—
550Q16—861no—
551Q16—861no—
552Q16—862no—
553SD16—22no—
554SD16—22no—
555SD16—861no—
556SD16—861no—
557SD16—861no—
558SD16—861no—
559SD16—862no—
560SD16—862no—
561D8—22no—
562D8—861no—
563D8—861no—
564D8—862no—
565M16—21no—
566M16—21no—
567M16—22no—
568M16—22no—
569M16—21no—
570M16—21no—
571M16—41no—
572M16—41no—
573M16—432no—
574M16—432no—
575M16—862no—
576M16—862no—
577M16—861no—
578M16—861no—
579M16—861no—
580M16—861no—
581M16—1721no—
582M16—1721no—
583M16C2×C4×D4312yes—
584M16C2×C22⋊D4312yes—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—21no—
590C2×C8—41no—
591C2×C8—41no—
592C2×C8—431no—
593C2×C8—431no—
594C2×C8—431no—
595C2×C8—431no—
596C2×C8—431no—
597C2×C8—431no—
598C2×C8—862no—
599C2×C8—862no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—1721no—
604C2×C8—1721no—
605C2×C8D4×D4311yescharacteristic
606C2×C8D4×D4311yescharacteristic
607C2×C8#1062190011yescharacteristic
608C2×C8#1062190011yescharacteristic
609C2×C8C2×C22⋊D4311yescharacteristic
610C2×C8C2×C22⋊D4311yescharacteristic
611C4⋊C4—21no—
612C4⋊C4—862no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C22⋊C4—21no—
616C22⋊C4—432no—
617C22⋊C4—862no—
618C22⋊C4—861no—
619C42—21no—
620C42—431no—
621C42—431no—
622C42—862no—
623C42—861no—
624C42—861no—
625C42—861no—
626C23—21no—
627C23—21no—
628C23—861no—
629C23#41×D4311yescharacteristic
630Q8—21no—
631Q8—21no—
632Q8—21no—
633Q8—861no—
634Q8—861no—
635Q8C4×C22⋊D4312yes—
636D4—22no—
637D4—22no—
638D4—21no—
639D4—21no—
640D4—21no—
641D4—41no—
642D4—41no—
643D4—861no—
644D4—861no—
645D4—1721no—
646D4—1721no—
647D4C4×C22⋊D4312yes—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—861no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—862no—
659C2×C4—1722no—
660C2×C4—1724no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4C22×C4×D4311yescharacteristic
665C2×C4C2×D4×D4311yescharacteristic
666C2×C4C22×C22⋊D4311yescharacteristic
667C2×C4#41×D4311yescharacteristic
668C2×C4C2×#1062190011yescharacteristic
669C2×C4C2×#1062189811yescharacteristic
670C8—22no—
671C8—22no—
672C8—41no—
673C8—431no—
674C8—431no—
675C8—431no—
676C8—431no—
677C8—862no—
678C8—862no—
679C8—1721no—
680C8#1306329711yescharacteristic
681C8#1306329711yescharacteristic
682C8#1306329711yescharacteristic
683C8#1306329711yescharacteristic
684C22—22no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—81no—
689C22—3441no—
690C22—1721no—
691C22C4×#1062190011yescharacteristic
692C22#1458340811yescharacteristic
693C22#1458344511yescharacteristic
694C4—22no—
695C4—41no—
696C4—81no—
697C4—862no—
698C4—3441no—
699C4—1721no—
700C4—1722no—
701C4—1721no—
702C4C4×D4×D4311yescharacteristic
703C4C2×C4×C22⋊D4311yescharacteristic
704C4C2×#1306329711yescharacteristic
705C4#1458342911yescharacteristic
706C2—21no—
707C2—21no—
708C2—21no—
709C2—42no—
710C2—81no—
711C2—3441no—
712C2C4×#1306329711yescharacteristic
subgroupG/H
centerC8#13063297
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2955C2
socleC2×C43C4×#121
prime radical#19144312C2
cosocleC22×C4×C43C24
hypercenter#2955D43
hypocenterC43#21558
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2955

Complements

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

NH ≅ G/Ntype
2. #19143496C2semidirect
3. C2×#14583014C2semidirect
4. #131×Dic43C2semidirect
5. #19135492C2semidirect
6. #19135382C2semidirect
7. #19135267C2semidirect
8. #19135263C2semidirect
9. #19135098C2semidirect
10. #19135094C2semidirect
11. #19134647C2semidirect
12. #19134475C2semidirect
13. #19134396C2semidirect
14. #19134395C2semidirect
15. C43×#2955C2semidirect
21. #14583172C4semidirect
22. #14583167C4semidirect
23. #14583164C4semidirect
24. #14583160C4semidirect
77. C2×#10621885C2×C4semidirect
78. C2×#10621883C2×C4semidirect
79. C2×#10621884C2×C4semidirect
80. C2×#10621882C2×C4semidirect
108. #13063260C2×C4semidirect
109. #13063260C2×C4semidirect
118. #13063244C2×C4semidirect
119. #13063243C2×C4semidirect
120. #13063242C2×C4semidirect
121. #13063241C2×C4semidirect
352. #2955D43semidirect
423. C43#21558semidirect

Maximal subgroups

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

subgroupindex
#191443122
#191434962
C2×#145830142
#131×Dic432
#191354922
#191353822
#191352672
#191352632
#191350982
#191350942
#191346472
#191344752
#191343962
#191343952
C43×#29552
#2155843