Finite Group Databasebeta

← #25976717

Subgroups — #25976717

Order 11008.

1730 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148460C211yesmaximal, characteristic
2#19148405C211yesmaximal, characteristic, complemented
3#19147442C214yesmaximal, complemented
4#19147399C214yesmaximal, complemented
5#19147364C214yesmaximal, complemented
6#19147336C214yesmaximal, complemented
7#19144958C212yesmaximal, complemented
8#19144941C211yesmaximal, characteristic
9#19144462C212yesmaximal, complemented
10#19144400C211yesmaximal, characteristic, complemented
11#19144122C212yesmaximal, complemented
12#19144067C211yesmaximal, characteristic
13#19143535C211yesmaximal, characteristic, complemented
14#19143432C212yesmaximal, complemented
15C2×C43×#441C211yesmaximal, characteristic, complemented
16C2×#13063356C2212yes—
17#14583634C2212yes—
18Q8×Dic86—21no—
19Q8×Dic86C2212yes—
20#14583628—21no—
21#14583628C2212yes—
22#14583627C2212yes—
23#14583625—22no—
24#14583625C2214yes—
25#14583622—21no—
26#14583621C2214yes—
27#14583609—21no—
28#14583590—22no—
29#14583530—22no—
30#14583530C2212yes—
31#14583496—22no—
32#14583473C2212yes—
33#14583456—22no—
34#14583456C2211yescharacteristic
35#14583456C2211yescharacteristic
36#14583449C2211yescharacteristic
37#14583433—22no—
38#14583380C2212yes—
39#14583377C2212yes—
40#14583268C2212yes—
41#14583266C2214yes—
42#14583264C2212yes—
43#14583260C2214yes—
44#14583259C2212yes—
45#14583259C2212yes—
46#14583255C2214yes—
47#14583248C2214yes—
48#14583209C2214yes—
49#14583206C2214yes—
50#14583198C2214yes—
51#14583194C2212yes—
52#14583188C2214yes—
53#14583184C2212yes—
54#14583183C2214yes—
55#14583123C2214yes—
56#14583123C2214yes—
57#14583121C2214yes—
58#14583109C2212yes—
59#14583107C2214yes—
60#14583107C2214yes—
61#14583099C2212yes—
62#14583027C2214yes—
63#14583027C2214yes—
64#14583003C2214yes—
65#14583002C2214yes—
66#14582991C2214yes—
67#14582984C2214yes—
68#14582939C2212yes—
69#14582925C2212yes—
70#14582923C2211yescharacteristic
71#14582908C2212yes—
72#14582898C2212yes—
73#14582896C2212yes—
74#14582896C2212yes—
75#14582854C2212yes—
76C22×Q16×C43C2211yescharacteristic
77C2×C4×Q8×C43C2211yescharacteristic
78C2×C4×Q8×C43C2211yescharacteristic
79C43×#441C2214yes—
80C43×#441C2214yes—
81C2×#106×C43C2211yescharacteristic
82C2×#103×C43C2211yescharacteristic
83C2×#103×C43C2211yescharacteristic
84C2×#97×C43C2211yescharacteristic
85C2×#10621898C2312yes—
86#13063356—28no—
87C2×#10621885C2314yes—
88C2×#10621884C2314yes—
89C2×#10621877C2312yes—
90#13063325—22no—
91#13063325—22no—
92#13063325D411yescharacteristic
93#13063325D411yescharacteristic
94#13063325C2311yescharacteristic
95#13063325C2311yescharacteristic
96#13063325C2311yescharacteristic
97#13063324—24no—
98#13063324—22no—
99#13063324—24no—
100#13063324C2314yes—
101#13063323C2314yes—
102#13063322C2311yescharacteristic
103#13063320—24no—
104#13063319—24no—
105#13063317—22no—
106#13063317—24no—
107#13063317D412yes—
108#13063317C2312yes—
109#13063316—22no—
110#13063316—24no—
111#13063316—24no—
112#13063316C2314yes—
113#13063315—24no—
114#13063314C2314yes—
115#13063313—22no—
116#13063313C2312yes—
117#13063310—24no—
118#13063308—24no—
119#13063304—21no—
120#13063304—21no—
121#13063304—24no—
122#13063304D412yes—
123#13063304D412yes—
124#13063303—24no—
125#13063301—22no—
126#13063301—22no—
127#13063299—21no—
128#13063299—21no—
129Q8×Dic43—22no—
130Q8×Dic43—22no—
131Q8×Dic43C2314yes—
132Q8×Dic43C2314yes—
133C4×Dic86—22no—
134C4×Dic86—22no—
135C4×Dic86—21no—
136C4×Dic86—21no—
137C4×Dic86—22no—
138C4×Dic86—24no—
139C4×Dic86C2312yes—
140C4×Dic86C2312yes—
141#13063290C2314yes—
142C4×D172—21no—
143C4×D172—21no—
144C4×D172—22no—
145#13063287C2314yes—
146C4×C22⋊D43—24no—
147#13063284—24no—
148#13063284C2312yes—
149#13063284C2312yes—
150#13063283—22no—
151#13063282—24no—
152C4⋊C4×D43—22no—
153#13063258C2314yes—
154#13063256C2314yes—
155C4⋊(C43⋊C8)C2312yes—
156C4⋊(C43⋊C8)C2312yes—
157Dic43⋊C8C2314yes—
158Dic43⋊C8C2314yes—
159#13063250C2312yes—
160#13063250C2312yes—
161#13063250C2312yes—
162#13063250C2312yes—
163#13063249C2314yes—
164#13063249C2314yes—
165#13063248C2314yes—
166#13063247C2312yes—
167#13063247C2312yes—
168#13063247C2312yes—
169#13063247C2312yes—
170#13063245C2314yes—
171#13063235C2314yes—
172C8×Dic43C2314yes—
173C22×Q8×C43C2311yescharacteristic
174C22×Q8×C43C2311yescharacteristic
175C2×Q16×C43—24no—
176C2×Q16×C43C2314yes—
177C22×C8×C43C2311yescharacteristic
178C22×C8×C43C2311yescharacteristic
179C4×Q8×C43—21no—
180C4×Q8×C43—21no—
181C4×Q8×C43—21no—
182C4×Q8×C43—21no—
183C4×Q8×C43C2312yes—
184C4×Q8×C43C2312yes—
185C4×Q8×C43C2312yes—
186C4×Q8×C43C2312yes—
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43—21no—
189C2×C4⋊C4×C43C2311yescharacteristic
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C42×C43—21no—
192C2×C42×C43—21no—
193C2×C42×C43C2311yescharacteristic
194#106×C43C2314yes—
195#103×C43C2314yes—
196#103×C43C2314yes—
197#97×C43C2312yes—
198#97×C43C2312yes—
199C2×Q8×C43—21no—
200C2×Q8×C43—21no—
201C2×Q8×C43—22no—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43#4114yes—
205C2×Q8×C43C2412yes—
206C2×Q8×C43C2412yes—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—22no—
215#10621898—24no—
216#10621898—24no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172C2412yes—
220C2×C4×D43—22no—
221C2×C4×D43—24no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—24no—
225C2×Dic86C2×D412yes—
226C2×Dic86C2×D412yes—
227C2×Dic86C2412yes—
228Q16×C43—28no—
229C2×C8×C43—22no—
230C2×C8×C43—22no—
231C2×C8×C43C2412yes—
232C2×C8×C43C2412yes—
233C4⋊C4×C43—22no—
234C4⋊C4×C43—22no—
235C4⋊C4×C43—22no—
236C4⋊C4×C43—22no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C42×C43—22no—
242C42×C43—22no—
243C42×C43—22no—
244C42×C43—22no—
245C42×C43C2×D411yescharacteristic
246C42×C43C2×D411yescharacteristic
247C42×C43C2411yescharacteristic
248C42×C43C2411yescharacteristic
249C22⋊Dic43—22no—
250C22⋊Dic43C2×D414yes—
251#10621885—28no—
252#10621884—28no—
253(C2×D43)⋊C4—22no—
254(C2×D43)⋊C4—22no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—24no—
263C4⋊Dic43—24no—
264C4⋊Dic43—24no—
265C4⋊Dic43C2×D412yes—
266C4⋊Dic43C2×D412yes—
267C4⋊Dic43C2×D412yes—
268C4⋊Dic43C2×D412yes—
269C4⋊Dic43C2412yes—
270C4⋊Dic43C2412yes—
271Dic43⋊C4—22no—
272Dic43⋊C4—22no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4C2×D414yes—
279Dic43⋊C4C2×D414yes—
280C4×Dic43—22no—
281C4×Dic43—24no—
282C4×Dic43—24no—
283C4×Dic43—24no—
284C4×Dic43C2414yes—
285#10621877—24no—
286C2×C43⋊C8C2414yes—
287C23×C43C22×D411yescharacteristic
288C22×D43—22no—
289Q8×C43—24no—
290Q8×C43—22no—
291Q8×C43—22no—
292Q8×C43—22no—
293Q8×C43—42no—
294Q8×C43C2×#4114yes—
295C2×C4×C43—24no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—42no—
303C2×C4×C43—81no—
304C2×C4×C43—81no—
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C22×D411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C22×D411yescharacteristic
310C2×C4×C43C2×#4112yes—
311C2×C4×C432−1+412yes—
312C2×C4×C43C2511yescharacteristic
313C22⋊D43—44no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43C22×D414yes—
318C2×Dic43C22×D414yes—
319D172—22no—
320D172—22no—
321D172—42no—
322D172—81no—
323C4×D43—44no—
324C4×D43—84no—
325Dic86—22no—
326Dic86—22no—
327Dic86—42no—
328Dic86—42no—
329Dic86—42no—
330Dic86—84no—
331Dic86—81no—
332C8×C43—22no—
333C8×C43—22no—
334C43⋊C8—24no—
335#61335—431nomaximal, Sylow
336C22×C43—21no—
337C22×C43—21no—
338C22×C43#54812yes—
339C22×C43C23×D411yescharacteristic
340C2×D43—42no—
341C2×D43—42no—
342C2×D43—42no—
343C4×C43—21no—
344C4×C43—21no—
345C4×C43—21no—
346C4×C43—21no—
347C4×C43—24no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43#54812yes—
352C4×C43C22×#4111yescharacteristic
353C4×C43C2×2−1+411yescharacteristic
354Dic43—24no—
355Dic43—24no—
356Dic43—42no—
357Dic43—42no—
358Dic43—42no—
359#3507—431no—
360#3502—431no—
361#3377—434no—
362#3374—434no—
363#3371—434no—
364#3369—434no—
365#3137—432no—
366#3135—431no—
367#3084—432no—
368#3078—431no—
369#3044—432no—
370#3037—431no—
371#2961—431no—
372#2947—432no—
373C2×#441D4311yescharacteristic, complemented
374C2×C43—22no—
375C2×C43C2×#54811yescharacteristic
376C2×C43#358611yescharacteristic
377C2×C43#358611yescharacteristic
378D43—82no—
379C2×#137—432no—
380C22×Q16C2×D4311yescharacteristic
381#559—432no—
382Q82—432no—
383Q82—861no—
384#557—434no—
385#557—432no—
386#557—432no—
387#557—862no—
388#557—861no—
389#556—434no—
390#556—861no—
391#554—861no—
392#552—862no—
393#544—432no—
394#544—862no—
395#539—862no—
396#536—432no—
397#533—431no—
398#533—431no—
399#533—862no—
400#532—431no—
401#529—862no—
402#520—432no—
403#519—432no—
404C2×C4×Q8C2×D4311yescharacteristic
405C2×C4×Q8C2×D4311yescharacteristic
406#491—434no—
407#491—432no—
408#490—432no—
409#489—434no—
410#489—432no—
411#489—432no—
412#488—434no—
413#487—434no—
414#479—434no—
415#479—434no—
416#478—434no—
417#477—432no—
418#476—434no—
419#475—432no—
420#475—434no—
421#464—434no—
422#464—434no—
423#464—434no—
424#462—434no—
425#462—434no—
426#462—432no—
427#460—432no—
428#446—434no—
429#446—434no—
430#441—434no—
431#441C2×D4314yes—
432#441C2×D4314yes—
433#440—434no—
434C4×Q16—434no—
435C4×SD16—434no—
436#428—432no—
437C2×#106C2×D4311yescharacteristic
438#424—432no—
439#423—431no—
440#419—432no—
441#417—432no—
442#416—432no—
443#416—432no—
444C2×#103C2×D4311yescharacteristic
445C2×#103C2×D4311yescharacteristic
446#405—432no—
447C2×#97C2×D4311yescharacteristic
448C43#6133511yescharacteristic, complemented, Sylow
449C2×#41—432no—
450C22×Q8C22×D4311yescharacteristic
451C22×Q8C22×D4311yescharacteristic
452#137—868no—
453C2×Q16—24no—
454C2×Q16—434no—
455C2×Q16C22×D4314yes—
456C2×SD16—434no—
457C2×M16—432no—
458C22×C8C22×D4311yescharacteristic
459C22×C8C22×D4311yescharacteristic
460C4⋊Q8—434no—
461C4⋊Q8—434no—
462C4⋊Q8—431no—
463C4⋊Q8—431no—
464C4⋊Q8—431no—
465C4⋊Q8—431no—
466C4⋊Q8—431no—
467C4⋊Q8—862no—
468C4⋊Q8—862no—
469C4⋊Q8—862no—
470C4⋊Q8—864no—
471C4⋊Q8—864no—
472#127—431no—
473#126—864no—
474#126—864no—
475#125—434no—
476#125—432no—
477#125—432no—
478#125—862no—
479#125—864no—
480#125—864no—
481#125—862no—
482#125—864no—
483#125—864no—
484#124—434no—
485#124—432no—
486#124—862no—
487#123—864no—
488#123—864no—
489C22⋊Q8—432no—
490C22⋊Q8—432no—
491C22⋊Q8—864no—
492C22⋊Q8—864no—
493C22⋊Q8—862no—
494C22⋊Q8—862no—
495C22⋊Q8—861no—
496C22⋊Q8—861no—
497#121—861no—
498#121—861no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8—21no—
503C4×Q8—432no—
504C4×Q8—432no—
505C4×Q8—434no—
506C4×Q8—434no—
507C4×Q8—434no—
508C4×Q8—864no—
509C4×Q8—862no—
510C4×Q8—862no—
511C4×Q8—862no—
512C4×Q8—862no—
513C4×Q8—862no—
514C4×Q8—861no—
515C4×Q8—861no—
516C4×Q8C22×D4312yes—
517C4×Q8C22×D4312yes—
518C4×Q8C22×D4312yes—
519C4×Q8C22×D4312yes—
520C4×D4—434no—
521C4×D4—862no—
522C4×D4—864no—
523C4×D4—861no—
524C4×D4—861no—
525#117—432no—
526#117—432no—
527#117—864no—
528#117—864no—
529#117—862no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—862no—
533C2×C4⋊C4C22×D4311yescharacteristic
534C2×C4⋊C4C22×D4311yescharacteristic
535C2×C42—21no—
536C2×C42—21no—
537C2×C42C22×D4311yescharacteristic
538#107—434no—
539#106—434no—
540#106C22×D4314yes—
541C4⋊C8—434no—
542C4⋊C8—434no—
543C4⋊C8—432no—
544C4⋊C8—432no—
545#103—434no—
546#103—434no—
547#103—432no—
548#103—432no—
549#103—432no—
550#103—432no—
551#103—434no—
552#103C22×D4314yes—
553#103C22×D4314yes—
554#102—432no—
555#102—432no—
556#102—432no—
557#102—432no—
558#102—434no—
559#97—434no—
560#97C22×D4312yes—
561#97C22×D4312yes—
562C4×C8—434no—
563#41—864no—
564#41—864no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—432no—
571C2×Q8—432no—
572C2×Q8—432no—
573C2×Q8—864no—
574C2×Q8—861no—
575C2×Q8—861no—
576C2×Q8#1062189814yes—
577C2×Q8C23×D4312yes—
578C2×Q8C23×D4312yes—
579C2×D4—432no—
580C2×D4—862no—
581C2×D4—861no—
582C2×D4—861no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—864no—
588C22×C4—862no—
589C22×C4D4×D4311yescharacteristic
590C22×C4D4×D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592Q16—28no—
593Q16—868no—
594SD16—868no—
595M16—864no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—434no—
599C2×C8C23×D4312yes—
600C2×C8C23×D4312yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—432no—
608C4⋊C4—432no—
609C4⋊C4—434no—
610C4⋊C4—432no—
611C4⋊C4—434no—
612C4⋊C4—432no—
613C4⋊C4—432no—
614C4⋊C4—432no—
615C4⋊C4—864no—
616C4⋊C4—864no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—862no—
626C4⋊C4—861no—
627C4⋊C4—862no—
628C4⋊C4—861no—
629C4⋊C4C23×D4312yes—
630C4⋊C4C23×D4312yes—
631C22⋊C4—434no—
632C22⋊C4—864no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—862no—
636C22⋊C4—862no—
637C22⋊C4—862no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—434no—
643C42—864no—
644C42—864no—
645C42—864no—
646C42—862no—
647C42D4×D4311yescharacteristic
648C42D4×D4311yescharacteristic
649C42C23×D4311yescharacteristic
650C42C23×D4311yescharacteristic
651C23—862no—
652C23C2×D4×D4311yescharacteristic
653Q8—24no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—862no—
659Q8—862no—
660Q8—3441no—
661Q8—3444no—
662Q8—1722no—
663Q8—1722no—
664Q8—1722no—
665Q8C2×#1062189814yes—
666D4—862no—
667D4—862no—
668D4—3441no—
669D4—1722no—
670D4—1724no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—434no—
682C2×C4—434no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—3444no—
687C2×C4—1724no—
688C2×C4C2×D4×D4311yescharacteristic
689C2×C4C2×D4×D4311yescharacteristic
690C2×C4C2×D4×D4311yescharacteristic
691C2×C4C2×D4×D4311yescharacteristic
692C2×C4C2×D4×D4311yescharacteristic
693C2×C4C2×#1062189812yes—
694C2×C4#1306337212yes—
695C2×C4C24×D4311yescharacteristic
696C8—22no—
697C8—22no—
698C8—864no—
699C22—21no—
700C22—21no—
701C22—1722no—
702C22—1722no—
703C22—1722no—
704C22#1458355812yes—
705C22C22×D4×D4311yescharacteristic
706C4—24no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—864no—
715C4—864no—
716C4—1722no—
717C4—1722no—
718C4—1722no—
719C4#1458355812yes—
720C4C22×#1062189811yescharacteristic
721C4C2×#1306337211yescharacteristic
722C2—22no—
723C2—3442no—
724C2C2×#1458355811yescharacteristic
725C2#1914937811yescharacteristic
726C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#441C2
socleC22×C43C23×D4
prime radical#14583449C22
hypercenterC2×#441D43
hypocenterC43#61335
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
2. #19148405C2semidirect
3. #19147442C2semidirect
4. #19147399C2semidirect
5. #19147364C2semidirect
6. #19147336C2semidirect
7. #19144958C2semidirect
9. #19144462C2semidirect
10. #19144400C2semidirect
11. #19144122C2semidirect
13. #19143535C2semidirect
14. #19143432C2semidirect
15. C2×C43×#441C2semidirect
373. C2×#441D43semidirect
448. C43#61335semidirect

Maximal subgroups

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

subgroupindex
#191484602
#191484052
#191474422
#191473992
#191473642
#191473362
#191449582
#191449412
#191444622
#191444002
#191441222
#191440672
#191435352
#191434322
C2×C43×#4412
#6133543