Finite Group Databasebeta

← #25116053

Subgroups — #25116053

Order 11008.

752 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143363C211yesmaximal, characteristic
2#19143259C211yesmaximal, characteristic, complemented
3#19143161C211yesmaximal, characteristic, complemented
4#19135299C211yesmaximal, characteristic, complemented
5#19135297C211yesmaximal, characteristic, complemented
6#19135194C211yesmaximal, characteristic, complemented
7#19135192C211yesmaximal, characteristic, complemented
8#19134922C211yesmaximal, characteristic
9#19134920C211yesmaximal, characteristic
10#19134731C211yesmaximal, characteristic, complemented
11#19134614C211yesmaximal, characteristic, complemented
12#19134613C211yesmaximal, characteristic, complemented
13C8×Dic43⋊C4C211yesmaximal, characteristic, complemented
14#19134435C211yesmaximal, characteristic, complemented
15C43×#1764C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#41×Dic43C2211yescharacteristic
19#14583367C2211yescharacteristic
20#14582991C411yescharacteristic, complemented
21#14582991C411yescharacteristic, complemented
22#14582990C411yescharacteristic, complemented
23#14582990C411yescharacteristic, complemented
24#14582984C411yescharacteristic, complemented
25#14582984C411yescharacteristic, complemented
26#14582979C411yescharacteristic, complemented
27#14582979C411yescharacteristic, complemented
28#14582961—21no—
29#14582958—21no—
30#14582954—21no—
31#14582950—21no—
32#14582935C2211yescharacteristic
33#14582927—21no—
34#14582927C2211yescharacteristic
35#14582925—21no—
36#14582925C2211yescharacteristic
37#14582922—21no—
38#14582922C2211yescharacteristic
39#14582922C2211yescharacteristic
40C2×Dic43⋊C8—21no—
41C2×Dic43⋊C8C2211yescharacteristic
42C2×#13063253C2211yescharacteristic
43C2×#13063252C2211yescharacteristic
44C2×#13063251C2211yescharacteristic
45#14582896C2211yescharacteristic
46#14582867C2211yescharacteristic
47#14582865C2211yescharacteristic
48#14582855C2211yescharacteristic
49C2×C8×Dic43C2211yescharacteristic
50C2×C8×Dic43C2211yescharacteristic
51C4×Dic43⋊C4C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582660C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582658C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C2×#104×C43C2211yescharacteristic
62C43×#416C2211yescharacteristic
63C43×#405C2211yescharacteristic
64C2×C4×C8×C43C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063345—22no—
69#13063345—22no—
70C2×#10621885C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73C2×#10621882C2×C411yescharacteristic
74#13063332—22no—
75#13063332—41no—
76C2×#10621877—21no—
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C22×C43⋊C8—21no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82Q8×Dic43C2×C411yescharacteristic
83Q8×Dic43C2×C411yescharacteristic
84#13063290C2×C411yescharacteristic
85#13063290C2×C411yescharacteristic
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43C2×C411yescharacteristic
89D4×Dic43C2×C411yescharacteristic
90#13063287C2×C411yescharacteristic
91#13063287C2×C411yescharacteristic
92(C22⋊D43)⋊C4—21no—
93(C22⋊D43)⋊C4—21no—
94#13063284—21no—
95#13063284C2311yescharacteristic
96#13063282—21no—
97C2×Dic43⋊C4—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101C42×D43—21no—
102#13063258C2×C411yescharacteristic
103#13063258C2×C411yescharacteristic
104#13063256C2×C411yescharacteristic
105#13063256C2×C411yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8D411yescharacteristic
115Dic43⋊C8D411yescharacteristic
116Dic43⋊C8D411yescharacteristic
117Dic43⋊C8D411yescharacteristic
118#13063253—41no—
119#13063252—22no—
120#13063251—41no—
121#13063250C2×C411yescharacteristic
122#13063250C2×C411yescharacteristic
123#13063247C2×C411yescharacteristic
124#13063247C2×C411yescharacteristic
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8—21no—
128(C2×D43)⋊C8—21no—
129#13063236—21no—
130C4×C43⋊C8—21no—
131C8×Dic43—41no—
132C8×Dic43C2×C411yescharacteristic
133C8×Dic43C2×C411yescharacteristic
134C8×Dic43C2×C411yescharacteristic
135C8×Dic43C2×C411yescharacteristic
136C43⋊#95—21no—
137C2×#41×C43C2311yescharacteristic
138#131×C43—22no—
139#131×C43—41no—
140C2×M16×C43—21no—
141C2×M16×C43C2311yescharacteristic
142C2×M16×C43C2311yescharacteristic
143C22×C8×C43—21no—
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146#117×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148#104×C43—22no—
149#103×C43C2×C411yescharacteristic
150#103×C43C2×C411yescharacteristic
151#102×C43C2×C411yescharacteristic
152#102×C43C2×C411yescharacteristic
153#97×C43—21no—
154C4×C8×C43—21no—
155C4×C8×C43—41no—
156#41×C43—21no—
157#41×C43—21no—
158#41×C43#4112yes—
159#41×C43#4112yes—
160C2×Q8×C43C22×C411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43C22×C411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43#4111yescharacteristic
171C22×Dic43#4111yescharacteristic
172#10621898—21no—
173#10621898—21no—
174#10621898—21no—
175#10621898—21no—
176C2×D172C22×C411yescharacteristic
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×Dic86C22×C411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43—42no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—42no—
193C2×C8×C43C22×C411yescharacteristic
194C2×C8×C43C22×C411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43C2×D411yescharacteristic
197C4⋊C4×C43C22×C411yescharacteristic
198C4⋊C4×C43C22×C411yescharacteristic
199C22⋊C4×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C22⋊Dic43—21no—
204C22⋊Dic43—21no—
205C22⋊Dic43—21no—
206#10621885—22no—
207#10621884—22no—
208#10621883—22no—
209#10621882—22no—
210(C2×D43)⋊C4—21no—
211(C2×D43)⋊C4—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43C22×C411yescharacteristic
215C4⋊Dic43C22×C411yescharacteristic
216Dic43⋊C4—24no—
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C22×C411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229C4×Dic43C2×D411yescharacteristic
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877—42no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—42no—
242C2×C43⋊C8C22×C411yescharacteristic
243C2×C43⋊C8C22×C411yescharacteristic
244C2×C43⋊C8C2×D411yescharacteristic
245C2×C43⋊C8C2×D411yescharacteristic
246C23×C43—21no—
247C23×C43C2×#4111yescharacteristic
248C22×D43—21no—
249Q8×C43—21no—
250Q8×C43#11712yes—
251D4×C43—22no—
252D4×C43—22no—
253D4×C43—21no—
254D4×C43#11712yes—
255C2×C4×C43—21no—
256C2×C4×C43—22no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43C23×C411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C2×C4×C432−1+411yescharacteristic
269C22⋊D43—41no—
270C22⋊D43—41no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—42no—
280C2×Dic43—81no—
281C2×Dic43C4×D411yescharacteristic
282C2×Dic43C4×D411yescharacteristic
283C2×Dic43C4×D411yescharacteristic
284C2×Dic43C4×D411yescharacteristic
285D172—21no—
286D172—21no—
287C4×D43—41no—
288C4×D43—41no—
289C4×D43—42no—
290C4×D43—81no—
291Dic86—21no—
292Dic86—21no—
293C8×C43—21no—
294C8×C43—21no—
295C8×C43—21no—
296C8×C43—21no—
297C8×C43—41no—
298C8×C43—41no—
299C43⋊C8—21no—
300C43⋊C8—21no—
301C43⋊C8—21no—
302C43⋊C8—21no—
303C43⋊C8—41no—
304C43⋊C8—41no—
305#22783—431nomaximal, Sylow
306C22×C43—21no—
307C22×C43—21no—
308C22×C43—22no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43C2×C4×D411yescharacteristic
312C22×C43#55211yescharacteristic
313C22×C43#55311yescharacteristic
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C4×C43—22no—
318C4×C43—42no—
319C4×C43—41no—
320C4×C43—41no—
321C4×C43C2×#11711yescharacteristic
322C4×C43#52011yescharacteristic
323C4×C43#54611yescharacteristic
324C4×C43#54811yescharacteristic
325Dic43—21no—
326Dic43—21no—
327Dic43—21no—
328Dic43—42no—
329Dic43—41no—
330Dic43—41no—
331Dic43—41no—
332Dic43#44312yes—
333C4×#135—431no—
334#2925—431no—
335#2906—431no—
336#1937—431no—
337#1937—431no—
338#1922—431no—
339#1922—431no—
340#1876—431no—
341#1876—431no—
342#1837—431no—
343#1806—431no—
344#1806—431no—
345C8×C4⋊C4—431no—
346#1764—431no—
347#1764D4311yescharacteristic, complemented
348C2×C43—21no—
349C2×C43—21no—
350C2×C43—42no—
351C2×C43#235211yescharacteristic
352C2×C43C2×#44311yescharacteristic
353C2×C43#295711yescharacteristic
354D43—81no—
355C2×#135—431no—
356C2×#131—431no—
357C2×#131C2×D4311yescharacteristic
358C4×#41—431no—
359C4×#41—431no—
360C4×Q16—431no—
361C4×Q16—431no—
362C4×SD16—431no—
363C4×SD16—431no—
364C4×SD16—431no—
365C4×SD16—431no—
366C4×D8—431no—
367C4×D8—431no—
368#433—861no—
369#433—861no—
370#432—861no—
371#431—861no—
372#427—431no—
373#424—431no—
374#424—431no—
375#424—861no—
376#424—861no—
377#423—431no—
378#423—431no—
379#423—861no—
380C2×C4⋊C8—431no—
381C2×C4⋊C8—861no—
382C2×#104—431no—
383C2×#104—431no—
384C2×#104—431no—
385C2×#104C2×D4311yescharacteristic
386#416—431no—
387#416C2×D4311yescharacteristic
388#408—431no—
389#408—431no—
390#405—431no—
391#405C2×D4311yescharacteristic
392C2×C4×C8—431no—
393C2×C4×C8—431no—
394C2×C4×C8C2×D4311yescharacteristic
395C4×C4⋊C4—431no—
396#341—431no—
397#341—431no—
398#341—431no—
399#341C2×D4311yescharacteristic
400#339—431no—
401#339—431no—
402#339—431no—
403#339C2×D4311yescharacteristic
404#336—431no—
405#336—431no—
406C43#2278311yescharacteristic, complemented, Sylow
407C2×#41—431no—
408C2×#41C22×D4311yescharacteristic
409#135—862no—
410#135—862no—
411C2×Q16—431no—
412C2×SD16—431no—
413C2×SD16—431no—
414C2×D8—431no—
415#131—22no—
416#131—41no—
417#131—862no—
418#131—1721no—
419C2×M16—21no—
420C2×M16—431no—
421C2×M16—431no—
422C2×M16—861no—
423C2×M16C22×D4311yescharacteristic
424C2×M16C22×D4311yescharacteristic
425C22×C8—21no—
426C22×C8—431no—
427C22×C8—431no—
428C22×C8—861no—
429C22×C8C22×D4311yescharacteristic
430C22×C8C22×D4311yescharacteristic
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8—431no—
434C4×Q8—431no—
435C4×D4—431no—
436C4×D4—431no—
437C4×D4—431no—
438C4×D4—431no—
439C4×D4—861no—
440C4×D4—861no—
441C4×D4—861no—
442C4×D4—861no—
443#117—431no—
444#117—861no—
445#117—861no—
446#117C22×D4311yescharacteristic
447C2×C4⋊C4—861no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—861no—
451C2×C42—861no—
452C2×C42C22×D4311yescharacteristic
453#107—431no—
454#107—431no—
455#106—431no—
456#106—431no—
457C4⋊C8—431no—
458C4⋊C8—431no—
459C4⋊C8—431no—
460C4⋊C8—431no—
461C4⋊C8—861no—
462C4⋊C8—861no—
463C4⋊C8—861no—
464C4⋊C8—861no—
465C4⋊C8—861no—
466C4⋊C8—861no—
467C4⋊C8—861no—
468C4⋊C8—861no—
469#104—22no—
470#104—862no—
471#104—1721no—
472#104—1721no—
473#103—431no—
474#103—431no—
475#103C4×D4311yescharacteristic
476#103C4×D4311yescharacteristic
477#102—431no—
478#102—431no—
479#102C4×D4311yescharacteristic
480#102C4×D4311yescharacteristic
481C22⋊C8—861no—
482C22⋊C8—861no—
483C22⋊C8—861no—
484C22⋊C8—861no—
485#97—21no—
486#97—861no—
487C4×C8—21no—
488C4×C8—41no—
489C4×C8—431no—
490C4×C8—431no—
491C4×C8—431no—
492C4×C8—431no—
493C4×C8—861no—
494C4×C8—1721no—
495#95—861no—
496#41—21no—
497#41—21no—
498#41—861no—
499#41—861no—
500#41—861no—
501#41—861no—
502#41#1062189812yes—
503#41#1062189812yes—
504C2×Q8—431no—
505C2×Q8C2×C4×D4311yescharacteristic
506C2×D4—21no—
507C2×D4—431no—
508C2×D4—861no—
509C2×D4C2×C4×D4311yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—431no—
513C22×C4—431no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4C23×D4311yescharacteristic
521Q16—862no—
522SD16—862no—
523SD16—862no—
524D8—862no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—42no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16—861no—
534M16—1722no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—42no—
542C2×C8—431no—
543C2×C8—431no—
544C2×C8—431no—
545C2×C8—431no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—1722no—
553C2×C8C2×C4×D4311yescharacteristic
554C2×C8C2×C4×D4311yescharacteristic
555C2×C8D4×D4311yescharacteristic
556C2×C8D4×D4311yescharacteristic
557C4⋊C4—431no—
558C4⋊C4—431no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—864no—
564C4⋊C4C2×C4×D4311yescharacteristic
565C4⋊C4C2×C4×D4311yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—861no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C22⋊C4—861no—
571C22⋊C4—861no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—431no—
576C42—431no—
577C42—431no—
578C42—431no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—861no—
584C42—861no—
585C42—861no—
586C23—21no—
587C23—861no—
588C23#41×D4311yescharacteristic
589Q8—21no—
590Q8—861no—
591Q8—861no—
592Q8#1306328212yes—
593D4—22no—
594D4—22no—
595D4—21no—
596D4—861no—
597D4—861no—
598D4—1721no—
599D4—1721no—
600D4#1306328212yes—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—431no—
610C2×C4—431no—
611C2×C4—431no—
612C2×C4—431no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—3441no—
619C2×C4—3441no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4C22×C4×D4311yescharacteristic
628C2×C4C2×D4×D4311yescharacteristic
629C2×C4C2×#1062189811yescharacteristic
630C2×C4C2×#1062189811yescharacteristic
631C2×C4#1306337011yescharacteristic
632C2×C4#1306337211yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—41no—
638C8—41no—
639C8—861no—
640C8—861no—
641C8—861no—
642C8—861no—
643C8—1721no—
644C8—1721no—
645C22—21no—
646C22—21no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—1721no—
651C22—1721no—
652C22—1721no—
653C22C4×D4×D4311yescharacteristic
654C22#1458358211yescharacteristic
655C22#1458359811yescharacteristic
656C4—22no—
657C4—42no—
658C4—41no—
659C4—41no—
660C4—432no—
661C4—861no—
662C4—861no—
663C4—861no—
664C4—1722no—
665C4—1721no—
666C4—1721no—
667C4—1721no—
668C4C2×#1306328211yescharacteristic
669C4#1458337811yescharacteristic
670C4#1458353911yescharacteristic
671C4#1458355811yescharacteristic
672C2—21no—
673C2—21no—
674C2—42no—
675C2—3441no—
676C2#1913751811yescharacteristic
677C2#443×D4311yescharacteristic
678C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1764C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenter#1764D43
hypocenterC43#22783
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1764

Complements

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

NH ≅ G/Ntype
2. #19143259C2semidirect
3. #19143161C2semidirect
4. #19135299C2semidirect
5. #19135297C2semidirect
6. #19135194C2semidirect
7. #19135192C2semidirect
10. #19134731C2semidirect
11. #19134614C2semidirect
12. #19134613C2semidirect
13. C8×Dic43⋊C4C2semidirect
14. #19134435C2semidirect
15. C43×#1764C2semidirect
20. #14582991C4semidirect
21. #14582991C4semidirect
22. #14582990C4semidirect
23. #14582990C4semidirect
24. #14582984C4semidirect
25. #14582984C4semidirect
26. #14582979C4semidirect
27. #14582979C4semidirect
347. #1764D43semidirect
406. C43#22783semidirect

Maximal subgroups

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

subgroupindex
#191433632
#191432592
#191431612
#191352992
#191352972
#191351942
#191351922
#191349222
#191349202
#191347312
#191346142
#191346132
C8×Dic43⋊C42
#191344352
C43×#17642
#2278343