Finite Group Databasebeta

← #25987018

Subgroups — #25987018

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#19148400C211yesmaximal, characteristic, complemented
2#19147523C214yesmaximal, complemented
3#19147516C212yesmaximal, complemented
4Q8×#10621883C212yesmaximal, complemented
5#19147357C214yesmaximal, complemented
6#19147331C212yesmaximal, complemented
7#19147276C212yesmaximal, complemented
8#19145887C214yesmaximal, complemented
9#19145789C211yesmaximal, characteristic
10#19145750C211yesmaximal, characteristic, complemented
11#19144818C214yesmaximal, complemented
12#19144721C211yesmaximal, characteristic, complemented
13#19144622C211yesmaximal, characteristic
14#19143690C211yesmaximal, characteristic, complemented
15C43×#3550C211yesmaximal, characteristic
16Q8×Dic86C2212yes—
17#14583629—21no—
18#14583627C2214yes—
19#14583627C2212yes—
20#14583626—22no—
21#14583624—21no—
22#14583528—22no—
23#14583527C2212yes—
24#14583456C2211yescharacteristic
25#14583451—22no—
26#14583376C2212yes—
27C2×C4×Dic86C2211yescharacteristic
28#14583305C2212yes—
29#14583305C2214yes—
30#14583302C2211yescharacteristic
31#14583295C2214yes—
32#14583295C2211yescharacteristic
33#14583263C2212yes—
34#14583258C2214yes—
35#14583253C2214yes—
36#14583249C2211yescharacteristic
37#14583249C2211yescharacteristic
38#14583237C2214yes—
39#14583227C2212yes—
40#14583220C2214yes—
41#14583215C2212yes—
42#14583206C2214yes—
43#14583206C2214yes—
44#14583199C2214yes—
45#14583191C2214yes—
46#14583189C2212yes—
47#14583189C2214yes—
48#14583184C2214yes—
49#14583181C2212yes—
50#14583181C2214yes—
51#14583181C2212yes—
52#14583179C2212yes—
53#14583118C2214yes—
54#14583118C2214yes—
55#14583106C2212yes—
56#14583096C2212yes—
57#14583054C2212yes—
58#14583037C2212yes—
59#14583030C2214yes—
60#14583030C2212yes—
61Q8×C43⋊C8C2212yes—
62#14583004C2214yes—
63#14583004C2214yes—
64#14582999C2214yes—
65C4×#10621885C2214yes—
66C4×#10621883C2212yes—
67C4×#10621883C2212yes—
68C4×#10621883C2214yes—
69#14582960C2214yes—
70#14582956C2211yescharacteristic
71#14582952C2211yescharacteristic
72C43×#563—22no—
73C43×#559C2212yes—
74Q82×C43C2212yes—
75C43×#556—21no—
76C43×#556C2212yes—
77D4×Q8×C43—21no—
78D4×Q8×C43C2212yes—
79C43×#542—22no—
80C43×#542C2214yes—
81C43×#536—22no—
82C43×#533C2211yescharacteristic
83C43×#533C2211yescharacteristic
84C43×#532C2211yescharacteristic
85C22×Dic86C2311yescharacteristic
86C2×#10621885C2314yes—
87C2×#10621883C2312yes—
88C2×#10621883C2312yes—
89#13063325C2311yescharacteristic
90#13063325C2314yes—
91#13063325C2311yescharacteristic
92#13063324—22no—
93#13063324—24no—
94#13063324—22no—
95#13063323—22no—
96#13063323—24no—
97#13063317C2314yes—
98#13063317C2312yes—
99#13063316—22no—
100#13063315—24no—
101#13063315—24no—
102#13063315—24no—
103#13063304—21no—
104#13063304—21no—
105#13063302—24no—
106Q8×Dic43—22no—
107C4×Dic86—21no—
108C4×Dic86—21no—
109C4×Dic86—21no—
110C4×Dic86—21no—
111C4×Dic86C2312yes—
112C4×Dic86C2312yes—
113C4×Dic86C2314yes—
114C4×Dic86C2314yes—
115#13063290—22no—
116#13063290—24no—
117#13063290—22no—
118#13063290—22no—
119#13063284C2312yes—
120#13063281—24no—
121C2×C4⋊Dic43C2311yescharacteristic
122C2×Dic43⋊C4—21no—
123C2×C4×Dic43—21no—
124#13063258C2314yes—
125#13063258C2314yes—
126#13063256C2312yes—
127#13063256C2314yes—
128#13063256C2314yes—
129#13063256C2314yes—
130#13063256C2312yes—
131C4⋊(C43⋊C8)C2312yes—
132C4⋊(C43⋊C8)C2312yes—
133C4⋊(C43⋊C8)C2314yes—
134C4⋊(C43⋊C8)C2314yes—
135#13063249C2314yes—
136#13063249C2314yes—
137#13063249C2314yes—
138#13063248C2314yes—
139#13063248C2312yes—
140#13063248C2312yes—
141#13063246C2312yes—
142#13063246C2312yes—
143#13063246C2314yes—
144#13063246C2314yes—
145C22⋊(C43⋊C8)C2312yes—
146C22⋊(C43⋊C8)C2312yes—
147#13063236C2312yes—
148#13063236C2314yes—
149C4×C43⋊C8C2311yescharacteristic
150C4×C43⋊C8C2311yescharacteristic
151C4×C43⋊C8C2314yes—
152C2×#41×C43—21no—
153C22×Q8×C43—22no—
154C4⋊Q8×C43—24no—
155C4⋊Q8×C43—22no—
156C4⋊Q8×C43D411yescharacteristic
157C4⋊Q8×C43D411yescharacteristic
158C4⋊Q8×C43C2311yescharacteristic
159C4⋊Q8×C43C2311yescharacteristic
160C4⋊Q8×C43C2311yescharacteristic
161C4⋊Q8×C43C2314yes—
162#127×C43C2311yescharacteristic
163#126×C43—24no—
164#126×C43—24no—
165#125×C43—21no—
166#125×C43D412yes—
167#124×C43—22no—
168#124×C43—24no—
169#124×C43—21no—
170#124×C43C2314yes—
171#123×C43—24no—
172#123×C43—24no—
173C22⋊Q8×C43—22no—
174C22⋊Q8×C43—21no—
175C22⋊Q8×C43—22no—
176C22⋊Q8×C43—24no—
177C22⋊Q8×C43—24no—
178C22⋊Q8×C43D412yes—
179C22⋊Q8×C43D412yes—
180C22⋊Q8×C43C2312yes—
181#121×C43—21no—
182#121×C43C2312yes—
183C4×Q8×C43—22no—
184C4×Q8×C43—21no—
185C4×Q8×C43C2312yes—
186C4×Q8×C43C2314yes—
187C4×Q8×C43C2312yes—
188C4×Q8×C43C2312yes—
189C4×D4×C43—22no—
190C4×D4×C43—21no—
191C4×D4×C43C2312yes—
192C4×D4×C43C2314yes—
193#117×C43—21no—
194#117×C43—22no—
195#117×C43C2312yes—
196C2×C42×C43C2311yescharacteristic
197#41×C43—82no—
198C2×Q8×C43—21no—
199C2×Q8×C43—24no—
200C2×Q8×C43—21no—
201C2×Q8×C43—84no—
202C2×Q8×C43C2×D412yes—
203C2×Q8×C43C2×D412yes—
204C2×Q8×C43C2412yes—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—22no—
208C2×D4×C43C2412yes—
209C22×C4×C43—22no—
210C22×C4×C43—24no—
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2411yescharacteristic
214C22×Dic43—21no—
215C22×Dic43—21no—
216C2×Dic86—21no—
217C2×Dic86—24no—
218C2×Dic86—21no—
219C2×Dic86—24no—
220C2×Dic86—21no—
221C2×Dic86C2412yes—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—22no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—22no—
230C4⋊C4×C43C2×D412yes—
231C4⋊C4×C43C2×D412yes—
232C4⋊C4×C43C2×D412yes—
233C4⋊C4×C43C2×D412yes—
234C4⋊C4×C43C2×D414yes—
235C4⋊C4×C43C2×D414yes—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—22no—
240C22⋊C4×C43—24no—
241C22⋊C4×C43—22no—
242C22⋊C4×C43—24no—
243C22⋊C4×C43—22no—
244C22⋊C4×C43C2×D414yes—
245C42×C43—22no—
246C42×C43—24no—
247C42×C43C2×D411yescharacteristic
248C42×C43C2×D411yescharacteristic
249C42×C43C2411yescharacteristic
250C42×C43C2411yescharacteristic
251C42×C43C2414yes—
252C22⋊Dic43—22no—
253#10621885—28no—
254#10621883—24no—
255#10621883—24no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—24no—
260C4⋊Dic43C2412yes—
261C4⋊Dic43C2412yes—
262C4⋊Dic43C2412yes—
263Dic43⋊C4—22no—
264Dic43⋊C4—22no—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—22no—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—22no—
271C4×Dic43—22no—
272C4×Dic43—22no—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43—22no—
276C2×C43⋊C8C2412yes—
277C2×C43⋊C8C2414yes—
278C2×C43⋊C8C2412yes—
279C23×C43—22no—
280C23×C43C22×D411yescharacteristic
281Q8×C43—24no—
282Q8×C43—24no—
283Q8×C43—42no—
284Q8×C43—42no—
285Q8×C43—84no—
286Q8×C43—81no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—42no—
290D4×C43—81no—
291D4×C43—82no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—41no—
298C2×C4×C43—44no—
299C2×C4×C43—84no—
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C22×D411yescharacteristic
302C2×C4×C43C22×D414yes—
303C2×C4×C43C22×D414yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C22×D411yescharacteristic
307C2×C4×C43C2511yescharacteristic
308C2×Dic43—24no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—81no—
314Dic86—24no—
315Dic86—22no—
316Dic86—42no—
317Dic86—81no—
318Dic86—84no—
319Dic862−1+414yes—
320C43⋊C8—22no—
321C43⋊C8—22no—
322C43⋊C8—24no—
323#61853—431nomaximal, Sylow
324C22×C43—21no—
325C22×C43—21no—
326C22×C43—21no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—42no—
330C22×C43C23×D411yescharacteristic
331C4×C43—21no—
332C4×C43—24no—
333C4×C43—21no—
334C4×C43—21no—
335C4×C43—21no—
336C4×C43—24no—
337C4×C43—42no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43#57712yes—
341C4×C43C2×2−1+412yes—
342Dic43—24no—
343Dic43—42no—
344Dic43—42no—
345Dic43—42no—
346#3550D4311yescharacteristic
347#3502—431no—
348#3387—434no—
349#3386—432no—
350Q8×SD16—432no—
351#3371—434no—
352#3369—432no—
353#3364—432no—
354#3244—434no—
355#3235—431no—
356#3231—431no—
357#3121—434no—
358#3113—431no—
359#3103—431no—
360#2985—431no—
361C2×C43—41no—
362C2×C43—82no—
363C2×C43#348611yescharacteristic
364C2×C43C2×#57711yescharacteristic
365C2×C43#358611yescharacteristic
366#563—22no—
367#559C2×D4312yes—
368Q82—432no—
369Q82—861no—
370Q82C2×D4312yes—
371#557—432no—
372#557—434no—
373#557—861no—
374#557—862no—
375#556—21no—
376#556C2×D4312yes—
377D4×Q8—21no—
378D4×Q8C2×D4312yes—
379#544—432no—
380#544—862no—
381#542—22no—
382#542C2×D4314yes—
383#536—22no—
384#533—431no—
385#533—862no—
386#533C2×D4311yescharacteristic
387#533C2×D4311yescharacteristic
388#532C2×D4311yescharacteristic
389#519—432no—
390C2×C4×Q8—431no—
391#501—434no—
392#501—432no—
393#500—431no—
394#498—431no—
395#498—434no—
396#490—432no—
397#489—434no—
398#488—434no—
399#487—431no—
400#487—431no—
401#485—434no—
402#483—432no—
403#482—434no—
404#481—432no—
405#479—434no—
406#479—434no—
407#478—434no—
408#477—434no—
409#476—432no—
410#476—434no—
411#475—432no—
412#475—432no—
413#475—434no—
414#475—434no—
415#474—432no—
416#464—434no—
417#464—434no—
418#462—432no—
419#460—432no—
420#451—432no—
421#448—432no—
422#446—432no—
423#446—434no—
424C8×Q8—432no—
425#441—434no—
426#441—434no—
427#440—434no—
428C4×Q16—434no—
429C4×SD16—432no—
430C4×SD16—432no—
431C4×SD16—434no—
432#433—434no—
433#432—431no—
434#431—431no—
435C43#6185311yescharacteristic, complemented, Sylow
436C2×#41—21no—
437C22×Q8—22no—
438C22×Q8—431no—
439C2×Q16—434no—
440C2×SD16—432no—
441C2×SD16—432no—
442C4⋊Q8—24no—
443C4⋊Q8—22no—
444C4⋊Q8—431no—
445C4⋊Q8—431no—
446C4⋊Q8—434no—
447C4⋊Q8—862no—
448C4⋊Q8—864no—
449C4⋊Q8—862no—
450C4⋊Q8—862no—
451C4⋊Q8—864no—
452C4⋊Q8C22⋊D4311yescharacteristic
453C4⋊Q8C22⋊D4311yescharacteristic
454C4⋊Q8C22×D4311yescharacteristic
455C4⋊Q8C22×D4311yescharacteristic
456C4⋊Q8C22×D4311yescharacteristic
457C4⋊Q8C22×D4314yes—
458#127C22×D4311yescharacteristic
459#126—24no—
460#126—24no—
461#125—21no—
462#125—432no—
463#125—434no—
464#125—864no—
465#125—862no—
466#125—864no—
467#125—864no—
468#125C22⋊D4312yes—
469#124—22no—
470#124—24no—
471#124—21no—
472#124C22×D4314yes—
473#123—24no—
474#123—24no—
475C22⋊Q8—22no—
476C22⋊Q8—21no—
477C22⋊Q8—22no—
478C22⋊Q8—24no—
479C22⋊Q8—24no—
480C22⋊Q8—861no—
481C22⋊Q8—861no—
482C22⋊Q8—864no—
483C22⋊Q8C22⋊D4312yes—
484C22⋊Q8C22⋊D4312yes—
485C22⋊Q8C22×D4312yes—
486#121—21no—
487#121C22×D4312yes—
488C4×Q8—22no—
489C4×Q8—21no—
490C4×Q8—432no—
491C4×Q8—432no—
492C4×Q8—434no—
493C4×Q8—434no—
494C4×Q8—862no—
495C4×Q8—862no—
496C4×Q8—862no—
497C4×Q8—864no—
498C4×Q8—862no—
499C4×Q8—861no—
500C4×Q8—861no—
501C4×Q8—861no—
502C4×Q8—861no—
503C4×Q8C22×D4312yes—
504C4×Q8C22×D4314yes—
505C4×Q8C22×D4312yes—
506C4×Q8C22×D4312yes—
507C4×D4—22no—
508C4×D4—21no—
509C4×D4C22×D4312yes—
510C4×D4C22×D4314yes—
511#117—21no—
512#117—22no—
513#117—432no—
514#117—864no—
515#117C22×D4312yes—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—861no—
518C2×C42—861no—
519C2×C42C22×D4311yescharacteristic
520#107—434no—
521#107—434no—
522#106—432no—
523#106—434no—
524#106—432no—
525#106—434no—
526#106—434no—
527C4⋊C8—432no—
528C4⋊C8—432no—
529C4⋊C8—434no—
530C4⋊C8—434no—
531#103—434no—
532#103—434no—
533#103—434no—
534#103—432no—
535#103—434no—
536#103—432no—
537#102—432no—
538#102—432no—
539#102—434no—
540#102—434no—
541C22⋊C8—432no—
542C22⋊C8—432no—
543#97—432no—
544#97—434no—
545C4×C8—431no—
546C4×C8—431no—
547C4×C8—434no—
548#41—82no—
549C2×Q8—21no—
550C2×Q8—24no—
551C2×Q8—21no—
552C2×Q8—84no—
553C2×Q8—432no—
554C2×Q8—864no—
555C2×Q8—861no—
556C2×Q8—861no—
557C2×Q8—864no—
558C2×Q8—861no—
559C2×Q8C2×C22⋊D4312yes—
560C2×Q8C2×C22⋊D4312yes—
561C2×Q8C23×D4312yes—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4C23×D4312yes—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4C2×C22⋊D4311yescharacteristic
571C22×C4C2×C22⋊D4311yescharacteristic
572C22×C4C23×D4311yescharacteristic
573Q16—868no—
574SD16—864no—
575SD16—864no—
576C2×C8—432no—
577C2×C8—434no—
578C2×C8—432no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—22no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—432no—
588C4⋊C4—432no—
589C4⋊C4—432no—
590C4⋊C4—861no—
591C4⋊C4—862no—
592C4⋊C4—862no—
593C4⋊C4—864no—
594C4⋊C4—864no—
595C4⋊C4—862no—
596C4⋊C4—861no—
597C4⋊C4—864no—
598C4⋊C4—862no—
599C4⋊C4—864no—
600C4⋊C4—861no—
601C4⋊C4—864no—
602C4⋊C4C2×C22⋊D4312yes—
603C4⋊C4C2×C22⋊D4312yes—
604C4⋊C4C2×C22⋊D4312yes—
605C4⋊C4C2×C22⋊D4312yes—
606C4⋊C4C2×C22⋊D4314yes—
607C4⋊C4C2×C22⋊D4314yes—
608C4⋊C4C23×D4312yes—
609C4⋊C4C23×D4312yes—
610C22⋊C4—22no—
611C22⋊C4—24no—
612C22⋊C4—22no—
613C22⋊C4—24no—
614C22⋊C4—22no—
615C22⋊C4—24no—
616C22⋊C4—862no—
617C22⋊C4C2×C22⋊D4314yes—
618C42—22no—
619C42—24no—
620C42—862no—
621C42—862no—
622C42—862no—
623C42—864no—
624C42—864no—
625C42C2×C22⋊D4311yescharacteristic
626C42C2×C22⋊D4311yescharacteristic
627C42C23×D4311yescharacteristic
628C42C23×D4314yes—
629C42C23×D4311yescharacteristic
630C23—22no—
631C23C22×C22⋊D4311yescharacteristic
632Q8—24no—
633Q8—24no—
634Q8—42no—
635Q8—42no—
636Q8—84no—
637Q8—81no—
638Q8—434no—
639Q8—864no—
640Q8—862no—
641Q8—3441no—
642Q8—3444no—
643Q8—1722no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—81no—
648D4—82no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—41no—
655C2×C4—44no—
656C2×C4—84no—
657C2×C4—864no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—3441no—
663C2×C4C22×C22⋊D4311yescharacteristic
664C2×C4C22×C22⋊D4314yes—
665C2×C4C22×C22⋊D4311yescharacteristic
666C2×C4C22×C22⋊D4311yescharacteristic
667C2×C4C22×C22⋊D4314yes—
668C2×C4C22×C22⋊D4311yescharacteristic
669C2×C4C22×C22⋊D4311yescharacteristic
670C2×C4C24×D4311yescharacteristic
671C8—862no—
672C8—862no—
673C8—864no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22C23×C22⋊D4311yescharacteristic
681C4—21no—
682C4—24no—
683C4—21no—
684C4—21no—
685C4—24no—
686C4—21no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—864no—
691C4—1722no—
692C4—1722no—
693C4—1722no—
694C4#1458371012yes—
695C42−1+4×D4312yes—
696C2—41no—
697C2—82no—
698C2#1914824311yescharacteristic
699C2C2×#1458371011yescharacteristic
700C2#1914938211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3550C2
socleC22×C43C23×D4
prime radicalC43×#532C22
hypercenter#3550D43
hypocenterC43#61853
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #533 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #19148400C2semidirect
2. #19147523C2semidirect
3. #19147516C2semidirect
4. Q8×#10621883C2semidirect
5. #19147357C2semidirect
6. #19147331C2semidirect
7. #19147276C2semidirect
8. #19145887C2semidirect
10. #19145750C2semidirect
11. #19144818C2semidirect
12. #19144721C2semidirect
14. #19143690C2semidirect
435. C43#61853semidirect

Maximal subgroups

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

subgroupindex
#191484002
#191475232
#191475162
Q8×#106218832
#191473572
#191473312
#191472762
#191458872
#191457892
#191457502
#191448182
#191447212
#191446222
#191436902
C43×#35502
#6185343