Finite Group Databasebeta

← #25123976

Subgroups — #25123976

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583527C211yesmaximal, characteristic, complemented
2#19143115C211yesmaximal, characteristic
3#19143112C211yesmaximal, characteristic
4#19137183C211yesmaximal, characteristic
5#19135755C214yesmaximal, complemented
6#19135750C214yesmaximal, complemented
7C2×#14582667C211yesmaximal, characteristic, complemented
8#19134305C211yesmaximal, characteristic, complemented
9C43×#1733C211yesmaximal, characteristic, complemented
10C22×#10621898C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12#14583527—22no—
13#14583527—22no—
14#14583527—22no—
15#14583527C2214yes—
16C2×#13063325—21no—
17C2×#13063324—21no—
18C2×#13063317—21no—
19C2×#13063316—21no—
20C2×#13063302—22no—
21C2×#13063284C2211yescharacteristic
22C22×C4⋊Dic43C2211yescharacteristic
23#14582909C2212yes—
24#14582907C2212yes—
25#14582905C2212yes—
26#14582903C2212yes—
27#14582901—21no—
28#14582901—21no—
29#14582898—21no—
30#14582898—21no—
31#14582896—22no—
32#14582893—22no—
33#14582805C2212yes—
34#14582801C2212yes—
35#14582776—22no—
36#14582756—22no—
37#14582667C2214yes—
38#14582659C2214yes—
39C22×M16×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C2×#117×C43C2211yescharacteristic
42C43×#339C2214yes—
43C2×#10621898—22no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898Q814yescomplemented
51C22×Dic86—22no—
52C22×Dic86C2311yescharacteristic
53C22×D172C2311yescharacteristic
54C22×C22⋊D43—21no—
55C23×Dic43D412yes—
56C22×C4×D43—21no—
57C2×#10621877—21no—
58C2×#10621877—22no—
59C2×#10621877—22no—
60C2×#10621877C2312yes—
61C22×C43⋊C8—21no—
62#13063325—24no—
63#13063325—24no—
64#13063324—24no—
65#13063324—24no—
66#13063317—24no—
67#13063317—24no—
68#13063316—24no—
69#13063316—24no—
70#13063302—28no—
71#13063302—28no—
72#13063284—21no—
73#13063284—21no—
74#13063284D412yes—
75#13063284C2312yes—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43D412yes—
82C2×C4⋊Dic43D411yescharacteristic
83C2×C4⋊Dic43D411yescharacteristic
84C2×C4⋊Dic43C2312yes—
85C2×Dic43⋊C4—22no—
86C2×Dic43⋊C4—22no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—24no—
89C2×C4×Dic43—21no—
90#13063250—22no—
91#13063250—22no—
92#13063248—22no—
93#13063248—22no—
94#13063247—22no—
95#13063247—22no—
96#13063245—22no—
97#13063245—22no—
98C43⋊#95—24no—
99C23×C4×C43C2311yescharacteristic
100C2×M16×C43—21no—
101C2×M16×C43—22no—
102C2×M16×C43—22no—
103C2×M16×C43C2312yes—
104C22×C8×C43—21no—
105#117×C43—21no—
106#117×C43—21no—
107#117×C43—22no—
108#117×C43—22no—
109#117×C43D412yes—
110#117×C43C2312yes—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C42×C43—21no—
117C2×C42×C43C2312yes—
118C24×C43C2×D411yescharacteristic
119C23×D43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×Q812yes—
129C22×C4×C43#4112yes—
130C22×C4×C43#4112yes—
131C22×C4×C43#4112yes—
132C22×C4×C43C2411yescharacteristic
133C2×C22⋊D43—24no—
134C2×C22⋊D43—41no—
135C2×C22⋊D43—41no—
136C2×C22⋊D43—42no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—82no—
143C22×Dic43C2×D414yes—
144#10621898—24no—
145#10621898—24no—
146#10621898—24no—
147#10621898—24no—
148#10621898—42no—
149#10621898—42no—
150#10621898—42no—
151#10621898—42no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172C2×Q812yescomplemented
158C2×C4×D43—24no—
159C2×C4×D43—41no—
160C2×C4×D43—41no—
161C2×C4×D43—42no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—28no—
168C2×Dic86—84no—
169C2×Dic86C2×Q812yescomplemented
170M16×C43—22no—
171M16×C43—22no—
172M16×C43—42no—
173C2×C8×C43—22no—
174C2×C8×C43—42no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43C2×D412yes—
179C4⋊C4×C43C2×D412yes—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—42no—
183C42×C43—22no—
184C42×C43—22no—
185C42×C43—22no—
186C42×C43—22no—
187C22⋊Dic43—22no—
188C22⋊Dic43—22no—
189(C2×D43)⋊C4—84no—
190C4⋊Dic43—28no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—22no—
196C4⋊Dic43—22no—
197C4⋊Dic43C2×D412yes—
198C4⋊Dic43C2×D412yes—
199Dic43⋊C4—28no—
200Dic43⋊C4—28no—
201C4×Dic43—22no—
202C4×Dic43—22no—
203#10621877—22no—
204#10621877—22no—
205#10621877—42no—
206C2×C43⋊C8—22no—
207C2×C43⋊C8—42no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43#12011yescharacteristic
211C23×C43#12011yescharacteristic
212C23×C43C22⋊Q812yes—
213C23×C43#12412yes—
214C23×C43C22×D411yescharacteristic
215C22×D43—22no—
216C22×D43—42no—
217C22×D43—42no—
218C22×D43—41no—
219C22×D43—41no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C2×C4×C43C22⋊Q812yes—
230C2×C4×C43C22⋊Q812yes—
231C2×C4×C43C22⋊Q812yes—
232C2×C4×C43C22⋊Q812yes—
233C2×C4×C43C22⋊Q812yes—
234C2×C4×C43#12412yes—
235C2×C4×C43#12412yes—
236C2×C4×C43#12412yes—
237C2×C4×C43#12412yes—
238C2×C4×C43#12412yes—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C22⋊D43—44no—
246C22⋊D43—44no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—24no—
250C2×Dic43—22no—
251C2×Dic43—42no—
252C2×Dic43—44no—
253C2×Dic43—42no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—44no—
257C2×Dic43—82no—
258D172—22no—
259D172—22no—
260D172—41no—
261D172—41no—
262C4×D43—44no—
263C4×D43—44no—
264Dic86—22no—
265Dic86—22no—
266Dic86—41no—
267Dic86—41no—
268Dic86—88no—
269C8×C43—42no—
270C43⋊C8—42no—
271#23462—431nomaximal, Sylow
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—21no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43#39312yes—
281C22×C43#39312yes—
282C22×C43C2×#12011yescharacteristic
283C22×C43C2×C22⋊Q811yescharacteristic
284C22×C43C2×#12411yescharacteristic
285C2×D43—44no—
286C2×D43—42no—
287C2×D43—82no—
288C2×D43—81no—
289C2×D43—81no—
290C4×C43—42no—
291C4×C43—42no—
292C4×C43—82no—
293C4×C43#39312yes—
294C4×C43#39312yes—
295C4×C43C2×C22⋊Q811yescharacteristic
296C4×C43C2×C22⋊Q811yescharacteristic
297C4×C43C2×#12411yescharacteristic
298C4×C43C2×#12411yescharacteristic
299Dic43—42no—
300Dic43—42no—
301Dic43—44no—
302Dic43—42no—
303C2×#544—431no—
304#2896—431no—
305#2896—431no—
306#2311—431no—
307#2028—434no—
308#2027—434no—
309C2×#343—431no—
310#1733—431no—
311#1733D4311yescharacteristic, complemented
312C2×C43—21no—
313C2×C43—21no—
314C2×C43—22no—
315C2×C43—22no—
316C2×C43C2×#39311yescharacteristic
317C2×C43#301911yescharacteristic
318C2×C43#302011yescharacteristic
319D43—82no—
320C22×#41—431no—
321C22×M16—431no—
322C22×M16C2×D4311yescharacteristic
323#544—434no—
324#544—862no—
325#544—862no—
326#544—862no—
327C2×C4⋊Q8—861no—
328C2×C4⋊Q8—861no—
329C2×#125—861no—
330C2×#125—861no—
331C2×C22⋊Q8—862no—
332C2×#117—431no—
333C2×#117C2×D4311yescharacteristic
334C2×#117C2×D4311yescharacteristic
335C22×C4⋊C4—431no—
336#419—432no—
337#419—432no—
338#418—432no—
339#418—432no—
340#417—861no—
341#417—861no—
342#417—861no—
343#417—861no—
344#416—862no—
345#416—862no—
346#391—432no—
347#390—432no—
348#386—862no—
349#380—862no—
350#343—434no—
351#339—434no—
352#339C2×D4314yes—
353C43#2346211yescharacteristic, complemented, Sylow
354C2×#41—434no—
355C2×#41—862no—
356C2×#41—861no—
357C2×#41—861no—
358C2×#41—862no—
359C2×#41—861no—
360C2×#41—861no—
361C2×#41—862no—
362C22×Q8—431no—
363C22×Q8—862no—
364C22×D4—431no—
365C22×D4—861no—
366C23×C4—432no—
367C23×C4—861no—
368C23×C4C22×D4311yescharacteristic
369C2×M16—21no—
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—432no—
373C2×M16—861no—
374C2×M16—862no—
375C2×M16—862no—
376C2×M16C22×D4312yes—
377C22×C8—21no—
378C22×C8—861no—
379C4⋊Q8—864no—
380C4⋊Q8—864no—
381C4⋊Q8—864no—
382C4⋊Q8—864no—
383#125—864no—
384#125—864no—
385#125—864no—
386#125—864no—
387C22⋊Q8—868no—
388C22⋊Q8—868no—
389#117—21no—
390#117—21no—
391#117—22no—
392#117—22no—
393#117—432no—
394#117—432no—
395#117—861no—
396#117—861no—
397#117D17212yes—
398#117C22×D4312yes—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—432no—
403C2×C4⋊C4—432no—
404C2×C4⋊C4—862no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—862no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—861no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4D17211yescharacteristic
412C2×C4⋊C4D17211yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—861no—
416C2×C22⋊C4—864no—
417C2×C42—21no—
418C2×C42—861no—
419C2×C42C22×D4312yes—
420#103—862no—
421#103—862no—
422#103—862no—
423#103—862no—
424#102—862no—
425#102—862no—
426#102—862no—
427#102—862no—
428#95—864no—
429C24—861no—
430C24D4×D4311yescharacteristic
431#41—864no—
432#41—864no—
433#41—864no—
434#41—864no—
435#41—1722no—
436#41—1722no—
437#41—1722no—
438#41—1722no—
439C2×Q8—432no—
440C2×Q8—868no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—3444no—
447C2×D4—432no—
448C2×D4—864no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—1721no—
455C2×D4—1721no—
456C2×D4—1722no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—434no—
461C22×C4—862no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—862no—
465C22×C4—861no—
466C22×C4—864no—
467C22×C4—3442no—
468C22×C4—1721no—
469C22×C4—1721no—
470C22×C4—1722no—
471C22×C4C2×D17211yescharacteristic
472C22×C4C2×D17211yescharacteristic
473C22×C4#1062189812yes—
474C22×C4#1062189812yes—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4D4×D4311yescharacteristic
478C22×C4#1062190012yes—
479C22×C4Q8×D4312yes—
480C22×C4C23×D4311yescharacteristic
481M16—22no—
482M16—22no—
483M16—42no—
484M16—862no—
485M16—862no—
486M16—1722no—
487C2×C8—22no—
488C2×C8—42no—
489C2×C8—862no—
490C2×C8—1722no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—432no—
495C4⋊C4—432no—
496C4⋊C4—868no—
497C4⋊C4—868no—
498C4⋊C4—868no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—862no—
504C4⋊C4—862no—
505C4⋊C4C2×D17212yes—
506C4⋊C4C2×D17212yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—42no—
510C22⋊C4—862no—
511C22⋊C4—862no—
512C22⋊C4—3444no—
513C42—22no—
514C42—22no—
515C42—22no—
516C42—22no—
517C42—862no—
518C42—862no—
519C23—41no—
520C23—41no—
521C23—862no—
522C23—1722no—
523C23—1722no—
524C23—1721no—
525C23—1721no—
526C23#1306329511yescharacteristic
527C23#1306329511yescharacteristic
528C23#1306330312yes—
529C23#1306331112yes—
530C23C2×D4×D4311yescharacteristic
531Q8—862no—
532Q8—862no—
533Q8—3448no—
534Q8—1721no—
535Q8—1721no—
536D4—862no—
537D4—862no—
538D4—1724no—
539D4—1724no—
540D4—1721no—
541D4—1721no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—864no—
552C2×C4—862no—
553C2×C4—3442no—
554C2×C4—1724no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1724no—
560C2×C4—1724no—
561C2×C4—1724no—
562C2×C4#1306329511yescharacteristic
563C2×C4#1306329511yescharacteristic
564C2×C4#1306330312yes—
565C2×C4#1306330312yes—
566C2×C4#1306330312yes—
567C2×C4#1306330512yes—
568C2×C4#1306330512yes—
569C2×C4#1306331112yes—
570C2×C4#1306331112yes—
571C2×C4#1306331112yes—
572C2×C4#1306331312yes—
573C2×C4#1306331312yes—
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C22×D17211yescharacteristic
576C2×C4C2×Q8×D4311yescharacteristic
577C2×C4C2×#1062190011yescharacteristic
578C2×C4C2×#1062189811yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C8—42no—
581C8—1722no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—42no—
589C22—42no—
590C22—3442no—
591C22—3441no—
592C22—3441no—
593C22—1724no—
594C22—1722no—
595C22#1458281212yes—
596C22#1458281212yes—
597C22C2×#1306329511yescharacteristic
598C22C2×#1306330311yescharacteristic
599C22C2×#1306331111yescharacteristic
600C4—42no—
601C4—42no—
602C4—82no—
603C4—1722no—
604C4—1724no—
605C4—1722no—
606C4—1722no—
607C4#1458281212yes—
608C4#1458281212yes—
609C4C2×#1306330311yescharacteristic
610C4C2×#1306330511yescharacteristic
611C4C2×#1306331111yescharacteristic
612C4C2×#1306331311yescharacteristic
613C2—21no—
614C2—21no—
615C2—22no—
616C2—22no—
617C2—3442no—
618C2C2×#1458281211yescharacteristic
619C2#1914395411yescharacteristic
620C2#1914396111yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1733C2
socleC22×C43C2×#120
prime radicalC22×#10621898C22
hypercenter#1733D43
hypocenterC43#23462
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
1. C2×#14583527C2semidirect
5. #19135755C2semidirect
6. #19135750C2semidirect
7. C2×#14582667C2semidirect
8. #19134305C2semidirect
9. C43×#1733C2semidirect
50. C2×#10621898Q8semidirect
157. C2×D172C2×Q8semidirect
169. C2×Dic86C2×Q8semidirect
311. #1733D43semidirect
353. C43#23462semidirect

Maximal subgroups

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

subgroupindex
C2×#145835272
#191431152
#191431122
#191371832
#191357552
#191357502
C2×#145826672
#191343052
C43×#17332
#2346243