Finite Group Databasebeta

← #25103544

Subgroups — #25103544

Order 11008.

868 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#19143498C211yesmaximal, characteristic, complemented
3#19143494C211yesmaximal, characteristic, complemented
4C2×#14583018C211yesmaximal, characteristic, complemented
5#19143023C211yesmaximal, characteristic, complemented
6#19135490C211yesmaximal, characteristic, complemented
7#19135384C211yesmaximal, characteristic, complemented
8#19135265C211yesmaximal, characteristic, complemented
9#19135261C211yesmaximal, characteristic, complemented
10#19135096C211yesmaximal, characteristic, complemented
11#19134647C211yesmaximal, characteristic, complemented
12#19134478C211yesmaximal, characteristic, complemented
13#19134397C211yesmaximal, characteristic, complemented
14#19134394C211yesmaximal, characteristic, complemented
15C43×#1906C211yesmaximal, characteristic, complemented
16#14583697C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063333C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20C2×#13063332C2211yescharacteristic
21C2×#13063332C2211yescharacteristic
22#14583172C412yescomplemented
23#14583167C412yescomplemented
24#14583164C412yescomplemented
25#14583160C412yescomplemented
26#14583021—22no—
27#14583018—22no—
28#14583018—21no—
29#14583018—21no—
30#14583018—21no—
31#14583018—21no—
32#14583016—22no—
33#14583013—22no—
34#14582948C2211yescharacteristic
35#14582947C2211yescharacteristic
36C2×#13063260C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38#14582935C2211yescharacteristic
39#14582917C2211yescharacteristic
40#14582916C2211yescharacteristic
41#14582916C2211yescharacteristic
42C2×#13063253C2211yescharacteristic
43#14582883C2211yescharacteristic
44#14582881C2211yescharacteristic
45#14582872C2211yescharacteristic
46#14582857C2211yescharacteristic
47#14582855—21no—
48#14582855—21no—
49#14582855C2211yescharacteristic
50#14582855C2211yescharacteristic
51#14582855C2211yescharacteristic
52C4×#10621877—21no—
53C4×#10621877C2211yescharacteristic
54C2×#13063236—21no—
55C2×#13063236C2211yescharacteristic
56#14582670C2211yescharacteristic
57#14582669C2211yescharacteristic
58#14582669C2211yescharacteristic
59#14582659C2211yescharacteristic
60C43×#575C2211yescharacteristic
61C4×#41×C43C2211yescharacteristic
62C43×#421C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C43×#410C2211yescharacteristic
65C43×#344C2211yescharacteristic
66C43×#339C2211yescharacteristic
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#13063333—21no—
82#13063333—21no—
83#13063333—21no—
84#13063333—21no—
85#13063332—21no—
86#13063332—21no—
87#13063332—21no—
88#13063332—21no—
89#13063332—21no—
90#13063332—21no—
91#13063332—21no—
92#13063332—21no—
93#13063332C2×C412yes—
94#13063332C2×C412yes—
95#13063332D412yes—
96#13063332D412yes—
97C2×#10621877—21no—
98C2×#10621877—21no—
99C2×#10621877—21no—
100C2×#10621877C2311yescharacteristic
101C2×#10621877C2311yescharacteristic
102C2×#10621877C2311yescharacteristic
103C2×#10621877C2311yescharacteristic
104C2×#10621872—21no—
105C22×C43⋊C8—21no—
106C22×C43⋊C8—21no—
107C22×C43⋊C8—21no—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110C2×C8×D43—21no—
111#13063284C2311yescharacteristic
112#13063261—22no—
113#13063260—22no—
114#13063260—21no—
115#13063260—21no—
116#13063260C2×C412yescomplemented
117#13063260C2×C412yescomplemented
118#13063258—21no—
119#13063256—21no—
120#13063253—21no—
121#13063253—21no—
122#13063253—22no—
123#13063252—22no—
124#13063252—22no—
125#13063244C2×C412yescomplemented
126#13063243C2×C412yescomplemented
127#13063242C2×C412yescomplemented
128#13063241C2×C412yescomplemented
129#13063239—22no—
130#13063236—21no—
131#13063236—21no—
132#13063236—21no—
133#13063236—21no—
134#13063236D411yescharacteristic
135#13063236D411yescharacteristic
136#13063236D411yescharacteristic
137#13063236D411yescharacteristic
138#13063235—21no—
139C4×C43⋊C8—21no—
140C4×C43⋊C8—21no—
141C4×C43⋊C8—21no—
142C4×C43⋊C8—21no—
143C8×Dic43—21no—
144C2×#41×C43C2311yescharacteristic
145C2×#41×C43C2311yescharacteristic
146#137×C43—21no—
147#137×C43C2×C412yes—
148AGL(1,ℤ/8)×C43—21no—
149AGL(1,ℤ/8)×C43C2×C412yes—
150#135×C43—22no—
151C2×M16×C43C2311yescharacteristic
152C2×M16×C43C2311yescharacteristic
153C4×Q8×C43—21no—
154C4×D4×C43—21no—
155C4×D4×C43—22no—
156#117×C43—21no—
157#117×C43C2311yescharacteristic
158#117×C43C2311yescharacteristic
159C2×C42×C43—21no—
160C2×C42×C43C2311yescharacteristic
161#104×C43—22no—
162#104×C43—21no—
163#104×C43—21no—
164#99×C43—22no—
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—22no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43C2411yescharacteristic
184C2×C22⋊D43—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—21no—
199M16×C43C22×C412yes—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C4⋊C4×C43—22no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C22⋊C4×C43—22no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43#4112yes—
208C42×C43—22no—
209C42×C43—21no—
210C42×C43—21no—
211C42×C43—21no—
212C42×C43C2×D411yescharacteristic
213C42×C43C2×D411yescharacteristic
214C22⋊Dic43—21no—
215#10621885—22no—
216#10621885—21no—
217#10621885—21no—
218#10621884—22no—
219#10621884—21no—
220#10621884—21no—
221#10621883—22no—
222#10621883—21no—
223#10621883—21no—
224#10621882—22no—
225#10621882—21no—
226#10621882—21no—
227C4⋊Dic43—21no—
228C4×Dic43—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877—22no—
233#10621877—22no—
234#10621877—22no—
235#10621877—22no—
236#10621877—21no—
237#10621877—21no—
238#10621877—41no—
239#10621877—41no—
240#10621877C22×C412yes—
241#10621877C22×C412yes—
242#10621877C2×D412yes—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—22no—
247C2×C43⋊C8—22no—
248C2×C43⋊C8—22no—
249C2×C43⋊C8—22no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—41no—
252C2×C43⋊C8—41no—
253C2×C43⋊C8C22×C411yescharacteristic
254C2×C43⋊C8C22×C411yescharacteristic
255C2×C43⋊C8C2×D411yescharacteristic
256C2×C43⋊C8C2×D411yescharacteristic
257C2×C43⋊C8C2×D411yescharacteristic
258C2×C43⋊C8C2×D411yescharacteristic
259C2×C43⋊C8C2×D411yescharacteristic
260C2×C43⋊C8C2×D411yescharacteristic
261C2×C43⋊C8#4111yescharacteristic
262C2×C43⋊C8#4111yescharacteristic
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—21no—
290C2×C4×C43—22no—
291C2×C4×C43—21no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—81no—
296C2×C4×C43—82no—
297C2×C4×C43C23×C411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C22⋊D43—41no—
304C22⋊D43—41no—
305C2×Dic43—21no—
306C2×Dic43—41no—
307D172—21no—
308D172—21no—
309C4×D43—41no—
310C4×D43—41no—
311Dic86—21no—
312Dic86—21no—
313C8×C43—22no—
314C8×C43—41no—
315C43⋊C8—22no—
316C43⋊C8—22no—
317C43⋊C8—22no—
318C43⋊C8—41no—
319C43⋊C8C4×D411yescharacteristic
320C43⋊C8C4×D411yescharacteristic
321C43⋊C8C4×D411yescharacteristic
322C43⋊C8C4×D411yescharacteristic
323C43⋊C8#12111yescharacteristic
324C43⋊C8#12111yescharacteristic
325C43⋊C8#12111yescharacteristic
326C43⋊C8#12111yescharacteristic
327#21559—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—42no—
340C4×C43—41no—
341C4×C43—41no—
342C4×C43—41no—
343C4×C43—81no—
344C4×C43C2×C4×D411yescharacteristic
345C4×C43C2×C4×D411yescharacteristic
346C4×C43C2×#12111yescharacteristic
347C4×C43#52911yescharacteristic
348Dic43—41no—
349Dic43—81no—
350#3067—431no—
351#2955—431no—
352#2955—431no—
353C2×#444—431no—
354#2875—431no—
355#1976—431no—
356#1953—431no—
357#1932—431no—
358#1932—431no—
359#1906—431no—
360#1906D4311yescharacteristic, complemented
361#1814—431no—
362#1773—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×#131—431no—
378C2×#131—431no—
379C4×#41C2×D4311yescharacteristic
380#473—432no—
381#472—432no—
382#471—432no—
383#471—432no—
384#444—861no—
385#444—861no—
386#444—861no—
387#444—861no—
388#444—862no—
389#444—862no—
390#443—862no—
391#443—862no—
392#430—431no—
393#430—431no—
394C2×#108—431no—
395C2×#108—431no—
396#427—431no—
397#421—431no—
398#421—431no—
399#421—431no—
400#421C2×D4311yescharacteristic
401C2×#104—431no—
402C2×#104C2×D4311yescharacteristic
403#413—431no—
404#413—431no—
405#410—431no—
406#410C2×D4311yescharacteristic
407#405—431no—
408#405—431no—
409#405—431no—
410#405—431no—
411#405—861no—
412#405—861no—
413C4×M16—431no—
414C4×M16—861no—
415C2×#97—431no—
416C2×#97—861no—
417#344—431no—
418#344—431no—
419#344—431no—
420#344C2×D4311yescharacteristic
421#339—431no—
422#339C2×D4311yescharacteristic
423C43#2155911yescharacteristic, 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—432no—
446#131—432no—
447#131—432no—
448#131—432no—
449#131—861no—
450#131—861no—
451#131—861no—
452#131—861no—
453#131—861no—
454#131—861no—
455#131—861no—
456#131—861no—
457#131—861no—
458#131—861no—
459#131—861no—
460#131—861no—
461C2×M16—431no—
462C2×M16—431no—
463C2×M16—431no—
464C2×M16—431no—
465C2×M16—861no—
466C2×M16—861no—
467C2×M16—861no—
468C2×M16—861no—
469C2×M16C22×D4311yescharacteristic
470C2×M16C22×D4311yescharacteristic
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—861no—
474C22×C8—861no—
475C22×C8—861no—
476C22×C8—861no—
477C4×Q8—21no—
478C4×D4—21no—
479C4×D4—22no—
480#117—21no—
481#117—431no—
482#117C22×D4311yescharacteristic
483#117C22×D4311yescharacteristic
484C2×C42—21no—
485C2×C42C22×D4311yescharacteristic
486#108—432no—
487#108—432no—
488#108—862no—
489#108—861no—
490#108—861no—
491#108—862no—
492#107—861no—
493#106—861no—
494#104—22no—
495#104—21no—
496#104—21no—
497#104—862no—
498#104—862no—
499#104—862no—
500#104—861no—
501#104—861no—
502#101—432no—
503#101—432no—
504#100—432no—
505#100—432no—
506#99—22no—
507#99—862no—
508#97—431no—
509#97—431no—
510#97—431no—
511#97—431no—
512#97—861no—
513#97—861no—
514#97—861no—
515#97—861no—
516#97—861no—
517C4×C8—861no—
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#41D4×D4312yes—
534C2×Q8—431no—
535C2×Q8C2×C4×D4311yescharacteristic
536C2×Q8#1062190011yescharacteristic
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—431no—
540C2×D4—861no—
541C2×D4C2×C4×D4311yescharacteristic
542C2×D4#1062190011yescharacteristic
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
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—21no—
568M16—432no—
569M16—432no—
570M16—432no—
571M16—862no—
572M16—862no—
573M16—862no—
574M16—862no—
575M16—861no—
576M16—861no—
577M16—861no—
578M16—861no—
579M16—861no—
580M16—1721no—
581M16—1721no—
582M16—1721no—
583M16—1721no—
584M16C2×C4×D4312yes—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—431no—
588C2×C8—431no—
589C2×C8—431no—
590C2×C8—431no—
591C2×C8—431no—
592C2×C8—431no—
593C2×C8—431no—
594C2×C8—431no—
595C2×C8—431no—
596C2×C8—431no—
597C2×C8—431no—
598C2×C8—431no—
599C2×C8—862no—
600C2×C8—862no—
601C2×C8—862no—
602C2×C8—862no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—1721no—
608C2×C8—1721no—
609C2×C8—1721no—
610C2×C8—1721no—
611C4⋊C4—22no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—861no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—861no—
618C22⋊C4#1062190012yes—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—861no—
624C42D4×D4311yescharacteristic
625C42D4×D4311yescharacteristic
626C23—21no—
627C23—21no—
628C23—861no—
629C23C2×#1062190011yescharacteristic
630Q8—21no—
631Q8—21no—
632Q8—21no—
633Q8—861no—
634Q8—861no—
635Q8(C22⋊D43)⋊C412yes—
636D4—22no—
637D4—22no—
638D4—21no—
639D4—21no—
640D4—21no—
641D4—41no—
642D4—41no—
643D4—861no—
644D4—861no—
645D4—1721no—
646D4—1721no—
647D4(C22⋊D43)⋊C412yes—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—81no—
659C2×C4—82no—
660C2×C4—861no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4C22×C4×D4311yescharacteristic
665C2×C4C2×D4×D4311yescharacteristic
666C2×C4C2×D4×D4311yescharacteristic
667C2×C4#41×D4311yescharacteristic
668C2×C4#41×D4311yescharacteristic
669C2×C4C2×#1062190011yescharacteristic
670C8—22no—
671C8—41no—
672C8—431no—
673C8—431no—
674C8—431no—
675C8—431no—
676C8—431no—
677C8—431no—
678C8—431no—
679C8—431no—
680C8—862no—
681C8—862no—
682C8—862no—
683C8—1721no—
684C22—22no—
685C22—41no—
686C22—42no—
687C22—41no—
688C22—81no—
689C22—3441no—
690C22—1721no—
691C22C4×#1062190011yescharacteristic
692C22#1458340511yescharacteristic
693C22#1458344411yescharacteristic
694C4—22no—
695C4—41no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—3441no—
701C4—1721no—
702C4C4×D4×D4311yescharacteristic
703C4C2×(C22⋊D43)⋊C411yescharacteristic
704C4#121×D4311yescharacteristic
705C4#1458342611yescharacteristic
706C2—21no—
707C2—21no—
708C2—21no—
709C2—42no—
710C2—81no—
711C2—3441no—
712C2#1913710511yescharacteristic
subgroupG/H
centerC4#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1906C2
socleC2×C43C4×#121
prime radical#19144312C2
cosocleC22×C4×C43C24
hypercenter#1906D43
hypocenterC43#21559
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1906

Complements

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

NH ≅ G/Ntype
2. #19143498C2semidirect
3. #19143494C2semidirect
4. C2×#14583018C2semidirect
5. #19143023C2semidirect
6. #19135490C2semidirect
7. #19135384C2semidirect
8. #19135265C2semidirect
9. #19135261C2semidirect
10. #19135096C2semidirect
11. #19134647C2semidirect
12. #19134478C2semidirect
13. #19134397C2semidirect
14. #19134394C2semidirect
15. C43×#1906C2semidirect
22. #14583172C4semidirect
23. #14583167C4semidirect
24. #14583164C4semidirect
25. #14583160C4semidirect
77. C2×#10621885C2×C4semidirect
78. C2×#10621883C2×C4semidirect
79. C2×#10621884C2×C4semidirect
80. C2×#10621882C2×C4semidirect
116. #13063260C2×C4semidirect
117. #13063260C2×C4semidirect
125. #13063244C2×C4semidirect
126. #13063243C2×C4semidirect
127. #13063242C2×C4semidirect
128. #13063241C2×C4semidirect
360. #1906D43semidirect
423. C43#21559semidirect

Maximal subgroups

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

subgroupindex
#191443122
#191434982
#191434942
C2×#145830182
#191430232
#191354902
#191353842
#191352652
#191352612
#191350962
#191346472
#191344782
#191343972
#191343942
C43×#19062
#2155943