Finite Group Databasebeta

← #25987042

Subgroups — #25987042

Order 11008.

1648 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149006C211yesmaximal, characteristic
2#19148400C211yesmaximal, characteristic, complemented
3#19147529C212yesmaximal, complemented
4#19147518C214yesmaximal, complemented
5Q8×Dic172C212yesmaximal, complemented
6#19147439C214yesmaximal, complemented
7#19147411C212yesmaximal, complemented
8#19147293C212yesmaximal, complemented
9#19145880C214yesmaximal, complemented
10#19145811C211yesmaximal, characteristic, complemented
11#19145733C211yesmaximal, characteristic
12#19144826C214yesmaximal, complemented
13#19144718C211yesmaximal, characteristic
14#19144635C211yesmaximal, characteristic, complemented
15C43×#2985C211yesmaximal, characteristic, complemented
16#14583653—22no—
17#14583634C2212yes—
18Q8×Dic86C2212yes—
19Q8×Dic86C2212yes—
20#14583629—21no—
21#14583627C2212yes—
22#14583627C2214yes—
23#14583626—22no—
24#14583624—21no—
25#14583623—21no—
26#14583622C2212yes—
27Q8×D172C2212yes—
28#14583564—21no—
29#14583528—22no—
30#14583527C2212yes—
31#14583522—22no—
32#14583520C2214yes—
33#14583472—22no—
34#14583456C2211yescharacteristic
35#14583456C2211yescharacteristic
36#14583451—22no—
37#14583449C2211yescharacteristic
38#14583376C2212yes—
39C2×C4×Dic86C2211yescharacteristic
40#14583308C2214yes—
41#14583308C2212yes—
42#14583304C2211yescharacteristic
43#14583304C2214yes—
44#14583297C2211yescharacteristic
45#14583268C2212yes—
46#14583259C2214yes—
47#14583254C2214yes—
48#14583246C2211yescharacteristic
49#14583246C2211yescharacteristic
50#14583241C2214yes—
51#14583235C2212yes—
52#14583224C2214yes—
53#14583213C2212yes—
54#14583207C2214yes—
55#14583200C2214yes—
56#14583200C2214yes—
57#14583195C2212yes—
58#14583195C2212yes—
59#14583195C2214yes—
60#14583195C2214yes—
61#14583195C2212yes—
62#14583185C2212yes—
63#14583185C2214yes—
64#14583180C2214yes—
65#14583122C2214yes—
66#14583122C2214yes—
67#14583110C2212yes—
68#14583100C2212yes—
69#14583057C2212yes—
70#14583040C2212yes—
71#14583007C2214yes—
72#14583001C2214yes—
73#14583001C2214yes—
74C4×Dic172C2212yes—
75C4×Dic172C2212yes—
76C4×Dic172C2214yes—
77C4×#10621873C2214yes—
78C43×#533C2211yescharacteristic
79C43×#446C2212yes—
80C43×#446C2214yes—
81C8×Q8×C43C2212yes—
82C43×#433C2214yes—
83C43×#432C2211yescharacteristic
84C43×#431C2211yescharacteristic
85C2×#10621898—21no—
86C22×Dic86C2311yescharacteristic
87C2×Q8×D43—22no—
88C2×Dic172C2312yes—
89C2×Dic172C2312yes—
90C2×#10621873C2314yes—
91#13063325C2311yescharacteristic
92#13063325C2311yescharacteristic
93#13063325C2311yescharacteristic
94#13063325C2314yes—
95#13063325C2314yes—
96#13063325C2311yescharacteristic
97#13063325C2311yescharacteristic
98#13063324—22no—
99#13063324—22no—
100#13063324—24no—
101#13063324—22no—
102#13063324—24no—
103#13063323—22no—
104#13063323—24no—
105#13063322C2311yescharacteristic
106#13063320—24no—
107#13063320—24no—
108#13063317—21no—
109#13063317C2312yes—
110#13063317C2314yes—
111#13063316—22no—
112#13063315—24no—
113#13063315—24no—
114#13063315—24no—
115#13063314—22no—
116#13063313—21no—
117#13063313C2314yes—
118#13063311—24no—
119#13063310—24no—
120#13063307—24no—
121#13063305—22no—
122#13063305—24no—
123#13063304—21no—
124#13063304—21no—
125#13063304—21no—
126#13063304C2312yes—
127#13063303—24no—
128#13063302—24no—
129#13063301—22no—
130#13063299—21no—
131#13063299C2312yes—
132Q8×Dic43—22no—
133Q8×Dic43—22no—
134C4×Dic86—21no—
135C4×Dic86—21no—
136C4×Dic86—21no—
137C4×Dic86—21no—
138C4×Dic86—21no—
139C4×Dic86C2312yes—
140C4×Dic86C2312yes—
141C4×Dic86C2314yes—
142C4×Dic86C2314yes—
143C4×Dic86C2314yes—
144C4×Dic86C2312yes—
145#13063290—22no—
146#13063290—24no—
147#13063290—22no—
148#13063290—22no—
149C4×D172—21no—
150C4×D172C2312yes—
151C4×D172C2314yes—
152#13063287—22no—
153#13063284—21no—
154#13063284C2312yes—
155#13063283—22no—
156#13063281—24no—
157C2×C4⋊Dic43C2311yescharacteristic
158C2×Dic43⋊C4—21no—
159C2×C4×Dic43—21no—
160#13063259C2314yes—
161#13063259C2312yes—
162#13063259C2314yes—
163#13063259C2314yes—
164#13063259C2312yes—
165#13063257C2314yes—
166#13063257C2314yes—
167#13063250C2314yes—
168#13063250C2312yes—
169#13063250C2312yes—
170#13063250C2312yes—
171#13063250C2312yes—
172#13063250C2314yes—
173#13063250C2314yes—
174#13063247C2314yes—
175#13063247C2314yes—
176#13063247C2314yes—
177C4⋊Q8×C43D411yescharacteristic
178C4⋊Q8×C43D411yescharacteristic
179#125×C43D412yes—
180C22⋊Q8×C43D412yes—
181C22⋊Q8×C43D412yes—
182C4×Q8×C43C2312yes—
183C4×Q8×C43C2312yes—
184#117×C43C2312yes—
185C2×C42×C43C2311yescharacteristic
186C4⋊C8×C43C2312yes—
187C4⋊C8×C43C2312yes—
188C4⋊C8×C43C2314yes—
189C4⋊C8×C43C2314yes—
190C22⋊C8×C43C2312yes—
191C22⋊C8×C43C2312yes—
192#97×C43C2312yes—
193#97×C43C2314yes—
194C4×C8×C43C2311yescharacteristic
195C4×C8×C43C2311yescharacteristic
196C4×C8×C43C2314yes—
197C2×Q8×C43C2×D412yes—
198C2×Q8×C43C2×D412yes—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—22no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205Q8×D43—84no—
206#10621898—82no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172C2412yes—
210C2×C4×D43—22no—
211C2×C4×D43—24no—
212C2×Dic86—21no—
213C2×Dic86—24no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—24no—
217C2×Dic86—21no—
218C2×Dic86—24no—
219C2×Dic86—21no—
220C2×Dic86C2412yes—
221C2×Dic86C2412yes—
222C2×C8×C43C2412yes—
223C2×C8×C43C2412yes—
224C2×C8×C43C2414yes—
225C4⋊C4×C43C2×D412yes—
226C4⋊C4×C43C2×D412yes—
227C4⋊C4×C43C2×D414yes—
228C4⋊C4×C43C2×D414yes—
229C4⋊C4×C43C2×D412yes—
230C4⋊C4×C43C2×D412yes—
231C22⋊C4×C43C2×D414yes—
232C42×C43C2×D411yescharacteristic
233C42×C43C2×D411yescharacteristic
234C42×C43C2411yescharacteristic
235C42×C43C2414yes—
236C42×C43C2411yescharacteristic
237C22⋊Dic43—22no—
238C22⋊Dic43—22no—
239(C2×D43)⋊C4—24no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—22no—
242(C2×D43)⋊C4—22no—
243(C2×D43)⋊C4—24no—
244C4⋊Dic43—21no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43—24no—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256C4⋊Dic43C2412yes—
257C4⋊Dic43C2412yes—
258Dic43⋊C4—22no—
259Dic43⋊C4—22no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—22no—
263Dic43⋊C4—24no—
264Dic43⋊C4—24no—
265Dic43⋊C4—22no—
266Dic43⋊C4—22no—
267Dic43⋊C4—24no—
268Dic43⋊C4—22no—
269C4×Dic43—22no—
270C4×Dic43—22no—
271C4×Dic43—24no—
272C4×Dic43—24no—
273C4×Dic43—24no—
274C4×Dic43—22no—
275C4×Dic43—22no—
276Dic172—24no—
277Dic172—24no—
278#10621873—28no—
279C23×C43C22×D411yescharacteristic
280C22×D43—22no—
281Q8×C43—24no—
282Q8×C43—42no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—41no—
286C2×C4×C43C22×D411yescharacteristic
287C2×C4×C43C22×D414yes—
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C22×D414yes—
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C22×D411yescharacteristic
293C2×C4×C43C2511yescharacteristic
294C22⋊D43—82no—
295C2×Dic43—24no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—81no—
304D172—24no—
305D172—42no—
306D172—81no—
307C4×D43—44no—
308C4×D43—84no—
309Dic86—24no—
310Dic86—22no—
311Dic86—22no—
312Dic86—22no—
313Dic86—42no—
314Dic86—42no—
315Dic86—81no—
316Dic86—84no—
317Dic86—81no—
318Dic86—84no—
319Dic862−1+414yes—
320C8×C43—24no—
321C8×C43—22no—
322C8×C43—22no—
323#61854—431nomaximal, Sylow
324C22×C43—21no—
325C22×C43—21no—
326C22×C43—21no—
327C22×C43C23×D411yescharacteristic
328C2×D43—42no—
329C2×D43—42no—
330C2×D43—42no—
331C4×C43—21no—
332C4×C43—24no—
333C4×C43—21no—
334C4×C43—21no—
335C4×C43—21no—
336C4×C43—24no—
337C4×C43#57812yes—
338C4×C43C2×2−1+412yes—
339Dic43—24no—
340Dic43—42no—
341Dic43—42no—
342Dic43—42no—
343Dic43—42no—
344Dic43—42no—
345Dic43—42no—
346#3550—431no—
347#3502—431no—
348#3387—432no—
349#3386—434no—
350Q8×Q16—432no—
351#3377—434no—
352#3375—432no—
353#3365—432no—
354#3243—434no—
355#3237—431no—
356#3228—431no—
357#3121—434no—
358#3112—431no—
359#3104—431no—
360#2985D4311yescharacteristic, complemented
361C2×C43—41no—
362C2×C43#348611yescharacteristic
363C2×C43C2×#57811yescharacteristic
364C2×C43#358511yescharacteristic
365D43—82no—
366#563—862no—
367#559—432no—
368Q82—432no—
369Q82—432no—
370Q82—861no—
371#557—432no—
372#557—434no—
373#557—861no—
374#557—862no—
375#556—432no—
376#556—861no—
377D4×Q8—432no—
378D4×Q8—861no—
379#544—432no—
380#544—862no—
381#542—434no—
382#542—862no—
383#536—862no—
384#533—431no—
385#533—431no—
386#533—862no—
387#533C2×D4311yescharacteristic
388#532—431no—
389#519—432no—
390C2×C4×Q8—431no—
391#501—432no—
392#501—434no—
393#500—431no—
394#500—434no—
395#498—431no—
396#491—432no—
397#489—434no—
398#488—434no—
399#486—431no—
400#486—431no—
401#485—434no—
402#484—432no—
403#482—434no—
404#480—432no—
405#479—434no—
406#478—434no—
407#478—434no—
408#477—432no—
409#477—432no—
410#477—432no—
411#477—434no—
412#477—434no—
413#475—432no—
414#475—434no—
415#474—434no—
416#464—434no—
417#464—434no—
418#462—432no—
419#460—432no—
420#451—432no—
421#448—432no—
422#446C2×D4312yes—
423#446C2×D4314yes—
424C8×Q8C2×D4312yes—
425#441—434no—
426#440—434no—
427#440—434no—
428C4×Q16—432no—
429C4×Q16—432no—
430C4×Q16—434no—
431C4×SD16—434no—
432#433C2×D4314yes—
433#432C2×D4311yescharacteristic
434#431C2×D4311yescharacteristic
435C43#6185411yescharacteristic, complemented, Sylow
436C2×#41—861no—
437C22×Q8—431no—
438C22×Q8—862no—
439C2×Q16—432no—
440C2×Q16—432no—
441C2×SD16—434no—
442C4⋊Q8—431no—
443C4⋊Q8—431no—
444C4⋊Q8—431no—
445C4⋊Q8—431no—
446C4⋊Q8—434no—
447C4⋊Q8—434no—
448C4⋊Q8—431no—
449C4⋊Q8—862no—
450C4⋊Q8—864no—
451C4⋊Q8—862no—
452C4⋊Q8—864no—
453C4⋊Q8—862no—
454C4⋊Q8—862no—
455C4⋊Q8—864no—
456C4⋊Q8D17211yescharacteristic
457C4⋊Q8D17211yescharacteristic
458#127—431no—
459#126—864no—
460#126—864no—
461#125—432no—
462#125—434no—
463#125—864no—
464#125—862no—
465#125—864no—
466#125—864no—
467#125—861no—
468#125D17212yes—
469#124—434no—
470#124—862no—
471#124—864no—
472#124—861no—
473#123—864no—
474#123—864no—
475C22⋊Q8—432no—
476C22⋊Q8—862no—
477C22⋊Q8—861no—
478C22⋊Q8—861no—
479C22⋊Q8—861no—
480C22⋊Q8—862no—
481C22⋊Q8—864no—
482C22⋊Q8—864no—
483C22⋊Q8—864no—
484C22⋊Q8D17212yes—
485C22⋊Q8D17212yes—
486#121—432no—
487#121—861no—
488C4×Q8—432no—
489C4×Q8—432no—
490C4×Q8—434no—
491C4×Q8—434no—
492C4×Q8—432no—
493C4×Q8—434no—
494C4×Q8—862no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8—862no—
498C4×Q8—864no—
499C4×Q8—862no—
500C4×Q8—861no—
501C4×Q8—861no—
502C4×Q8—861no—
503C4×Q8—861no—
504C4×Q8—861no—
505C4×Q8C22×D4312yes—
506C4×Q8C22×D4312yes—
507C4×D4—432no—
508C4×D4—434no—
509C4×D4—862no—
510C4×D4—861no—
511#117—432no—
512#117—861no—
513#117—862no—
514#117—864no—
515#117C22×D4312yes—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—861no—
518C2×C42—861no—
519C2×C42C22×D4311yescharacteristic
520#107—432no—
521#107—434no—
522#107—432no—
523#107—434no—
524#107—434no—
525#106—434no—
526#106—434no—
527C4⋊C8C22×D4312yes—
528C4⋊C8C22×D4312yes—
529C4⋊C8C22×D4314yes—
530C4⋊C8C22×D4314yes—
531#103—432no—
532#103—432no—
533#103—434no—
534#103—432no—
535#103—432no—
536#103—434no—
537#103—434no—
538#102—434no—
539#102—434no—
540#102—434no—
541C22⋊C8C22×D4312yes—
542C22⋊C8C22×D4312yes—
543#97C22×D4312yes—
544#97C22×D4314yes—
545C4×C8C22×D4311yescharacteristic
546C4×C8C22×D4311yescharacteristic
547C4×C8C22×D4314yes—
548#41—3442no—
549C2×Q8—432no—
550C2×Q8—432no—
551C2×Q8—864no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—864no—
555C2×Q8—864no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8—3444no—
560C2×Q8C2×D17212yes—
561C2×Q8C2×D17212yes—
562C2×D4—432no—
563C2×D4—862no—
564C2×D4—861no—
565C2×D4—861no—
566C22×C4—861no—
567C22×C4—861no—
568C22×C4—864no—
569C22×C4—862no—
570C22×C4C2×D17211yescharacteristic
571C22×C4C2×D17211yescharacteristic
572C22×C4C23×D4311yescharacteristic
573Q16—864no—
574Q16—864no—
575SD16—868no—
576C2×C8C23×D4312yes—
577C2×C8C23×D4312yes—
578C2×C8C23×D4314yes—
579C4⋊C4—432no—
580C4⋊C4—432no—
581C4⋊C4—432no—
582C4⋊C4—432no—
583C4⋊C4—432no—
584C4⋊C4—861no—
585C4⋊C4—862no—
586C4⋊C4—862no—
587C4⋊C4—861no—
588C4⋊C4—864no—
589C4⋊C4—864no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—864no—
594C4⋊C4—862no—
595C4⋊C4—862no—
596C4⋊C4—861no—
597C4⋊C4—862no—
598C4⋊C4—864no—
599C4⋊C4—864no—
600C4⋊C4—862no—
601C4⋊C4—864no—
602C4⋊C4—861no—
603C4⋊C4—864no—
604C4⋊C4C2×D17212yes—
605C4⋊C4C2×D17212yes—
606C4⋊C4C2×D17212yes—
607C4⋊C4C2×D17212yes—
608C4⋊C4C2×D17214yes—
609C4⋊C4C2×D17214yes—
610C22⋊C4—862no—
611C22⋊C4—862no—
612C22⋊C4—864no—
613C22⋊C4—862no—
614C22⋊C4—864no—
615C22⋊C4—862no—
616C22⋊C4—864no—
617C22⋊C4C2×D17214yes—
618C42—862no—
619C42—862no—
620C42—862no—
621C42—862no—
622C42—864no—
623C42—864no—
624C42—864no—
625C42C2×D17211yescharacteristic
626C42C2×D17211yescharacteristic
627C42C23×D4311yescharacteristic
628C42C23×D4314yes—
629C42C23×D4311yescharacteristic
630C23—862no—
631C23C22×D17211yescharacteristic
632Q8—24no—
633Q8—42no—
634Q8—434no—
635Q8—864no—
636Q8—862no—
637Q8—862no—
638Q8—862no—
639Q8—3444no—
640Q8—3441no—
641Q8—3441no—
642Q8—3444no—
643Q8—1722no—
644Q8—1722no—
645D4—864no—
646D4—3441no—
647D4—3442no—
648D4—1722no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—864no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—862no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—3444no—
661C2×C4—3441no—
662C2×C4—1724no—
663C2×C4C22×D17211yescharacteristic
664C2×C4C22×D17211yescharacteristic
665C2×C4C22×D17214yes—
666C2×C4C22×D17214yes—
667C2×C4C22×D17211yescharacteristic
668C2×C4C22×D17211yescharacteristic
669C2×C4C22×D17211yescharacteristic
670C2×C4C24×D4311yescharacteristic
671C8—24no—
672C8—22no—
673C8—22no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—1722no—
678C22—1722no—
679C22—1722no—
680C22C23×D17211yescharacteristic
681C4—21no—
682C4—24no—
683C4—21no—
684C4—21no—
685C4—24no—
686C4—21no—
687C4—864no—
688C4—1722no—
689C4—1722no—
690C4—1722no—
691C4—1722no—
692C4—1722no—
693C4—1722no—
694C4#1458371612yes—
695C42−1+4×D4312yes—
696C2—41no—
697C2—3442no—
698C2#1914824711yescharacteristic
699C2C2×#1458371611yescharacteristic
700C2#1914937611yescharacteristic
subgroupG/H
centerC22C23×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#2985C2
socleC22×C43C23×D4
prime radical#14583449C22
hypercenter#2985D43
hypocenterC43#61854
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #533 ◁ #2985

Complements

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

NH ≅ G/Ntype
2. #19148400C2semidirect
3. #19147529C2semidirect
4. #19147518C2semidirect
5. Q8×Dic172C2semidirect
6. #19147439C2semidirect
7. #19147411C2semidirect
8. #19147293C2semidirect
9. #19145880C2semidirect
10. #19145811C2semidirect
12. #19144826C2semidirect
14. #19144635C2semidirect
15. C43×#2985C2semidirect
360. #2985D43semidirect
435. C43#61854semidirect

Maximal subgroups

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

subgroupindex
#191490062
#191484002
#191475292
#191475182
Q8×Dic1722
#191474392
#191474112
#191472932
#191458802
#191458112
#191457332
#191448262
#191447182
#191446352
C43×#29852
#6185443