Finite Group Databasebeta

← #25123952

Subgroups — #25123952

Order 11008.

1250 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583530C211yesmaximal, characteristic, complemented
2C2×#14582898C211yesmaximal, characteristic
3C2×#14582896C211yesmaximal, characteristic
4#19137188C211yesmaximal, characteristic
5#19135745C212yesmaximal, complemented
6#19135740C212yesmaximal, complemented
7#19135735C212yesmaximal, complemented
8#19135730C212yesmaximal, complemented
9#19134314C211yesmaximal, characteristic, complemented
10#19134291C211yesmaximal, characteristic, complemented
11C2×C43×#340C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14#14583530—24no—
15#14583530—24no—
16C2×#13063324—21no—
17C2×#13063324C2212yes—
18C2×#13063316—21no—
19C2×#13063316C2212yes—
20C2×#13063304—22no—
21C2×#13063284C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23#14582898—24no—
24#14582896—24no—
25C2×#13063250C2211yescharacteristic
26C2×#13063250C2211yescharacteristic
27C2×#13063248C2212yes—
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063245C2212yes—
31#14582804C2212yes—
32#14582800C2212yes—
33#14582778—22no—
34#14582756—21no—
35#14582756—21no—
36#14582661C2212yes—
37#14582661C2212yes—
38#14582653C2212yes—
39#14582653C2212yes—
40C23×C8×C43C2211yescharacteristic
41C22×C4⋊C4×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C43×#340C2212yes—
44C43×#340C2212yes—
45C2×#10621898—22no—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898Q814yescomplemented
51C22×Dic86—22no—
52C22×Dic86C2311yescharacteristic
53C22×D172C2311yescharacteristic
54C22×C22⋊D43—21no—
55C22×C4×D43—21no—
56C2×#10621877—22no—
57C2×#10621877—22no—
58C2×#10621877—22no—
59C22×C43⋊C8C2312yes—
60#13063324—28no—
61#13063324—24no—
62#13063324—24no—
63#13063316—28no—
64#13063316—24no—
65#13063316—24no—
66#13063304—216no—
67#13063284—22no—
68#13063284—22no—
69#13063284—22no—
70#13063284D414yes—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—22no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43D412yes—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—22no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43C2312yes—
84#13063250—22no—
85#13063250—22no—
86#13063248—24no—
87#13063247—22no—
88#13063247—22no—
89#13063245—24no—
90C43⋊#95—22no—
91C43⋊#95—22no—
92C23×C4×C43—21no—
93C23×C4×C43—21no—
94C23×C4×C43C2311yescharacteristic
95C22×C8×C43—22no—
96C22×C8×C43—22no—
97C22×C8×C43—22no—
98C22×C8×C43C2311yescharacteristic
99C22×C8×C43C2311yescharacteristic
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43D414yes—
106C2×C4⋊C4×C43C2312yes—
107C2×C4⋊C4×C43C2312yes—
108C24×C43C2×D411yescharacteristic
109C23×D43—21no—
110C22×C4×C43—24no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—42no—
114C22×C4×C43—81no—
115C22×C4×C43—81no—
116C22×C4×C43—81no—
117C22×C4×C43—81no—
118C22×C4×C43C2×D412yes—
119C22×C4×C43C2×D412yes—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×Q812yes—
122C22×C4×C43#4112yes—
123C22×C4×C43#4112yes—
124C22×C4×C43#4112yes—
125C22×C4×C43C2411yescharacteristic
126C2×C22⋊D43—24no—
127C2×C22⋊D43—42no—
128C2×C22⋊D43—42no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D412yes—
133C22×Dic43C2×D412yes—
134#10621898—28no—
135#10621898—28no—
136#10621898—44no—
137#10621898—44no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172C2×Q812yes—
144C2×C4×D43—24no—
145C2×C4×D43—42no—
146C2×C4×D43—42no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—28no—
153C2×Dic86—82no—
154C2×Dic86—82no—
155C2×Dic86C2×Q812yes—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—44no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—42no—
168C4⋊C4×C43C2×D414yes—
169C22⋊Dic43—24no—
170C22⋊Dic43—24no—
171(C2×D43)⋊C4—82no—
172(C2×D43)⋊C4—82no—
173C4⋊Dic43—28no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43C2×D412yes—
179C4⋊Dic43C2×D412yes—
180Dic43⋊C4—28no—
181Dic43⋊C4—28no—
182C4×Dic43—24no—
183C4×Dic43—22no—
184C4×Dic43—22no—
185#10621877—44no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43#12012yes—
194C23×C43C22⋊Q812yes—
195C23×C43#12412yes—
196C23×C43C22×D411yescharacteristic
197C22×D43—22no—
198C22×D43—41no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C2×C4×C43—24no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—84no—
211C2×C4×C43—84no—
212C2×C4×C43#12012yes—
213C2×C4×C43C22⋊Q814yes—
214C2×C4×C43C22⋊Q812yes—
215C2×C4×C43C22⋊Q814yes—
216C2×C4×C43#12414yes—
217C2×C4×C43#12412yes—
218C2×C4×C43#12414yes—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×Q811yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—48no—
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241D172—22no—
242D172—22no—
243D172—41no—
244D172—41no—
245C4×D43—48no—
246Dic86—22no—
247Dic86—22no—
248Dic86—41no—
249Dic86—41no—
250Dic86—88no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—42no—
254#23458—431nomaximal, Sylow
255C22×C43—22no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—22no—
260C22×C43—22no—
261C22×C43#39314yes—
262C22×C43C2×#12011yescharacteristic
263C22×C43C2×C22⋊Q811yescharacteristic
264C22×C43C2×#12411yescharacteristic
265C22×C43#57611yescharacteristic
266C22×C43#57711yescharacteristic
267C22×C43#57711yescharacteristic
268C22×C43#57811yescharacteristic
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C4×C43—44no—
277C4×C43—82no—
278C4×C43#39314yes—
279C4×C43C2×C22⋊Q811yescharacteristic
280C4×C43C2×C22⋊Q811yescharacteristic
281C4×C43C2×#12411yescharacteristic
282C4×C43C2×#12411yescharacteristic
283Dic43—42no—
284Dic43—42no—
285Dic43—42no—
286Dic43—42no—
287Dic43—42no—
288C2×#544—431no—
289C2×#417—431no—
290C2×#416—431no—
291#2311—431no—
292#2026—432no—
293#2025—432no—
294#2024—432no—
295#2023—432no—
296#1736—431no—
297C2×#340D4311yescharacteristic, complemented
298#1729—431no—
299C2×C43—24no—
300C2×C43C2×#39311yescharacteristic
301C2×C43#301211yescharacteristic
302C2×C43#301311yescharacteristic
303C2×C43#308311yescharacteristic
304C2×C43#308411yescharacteristic
305C2×C43#313611yescharacteristic
306C2×C43#313711yescharacteristic
307D43—82no—
308C22×#41—431no—
309C22×M16—431no—
310C23×C8C2×D4311yescharacteristic
311#544—864no—
312#544—864no—
313C2×C4⋊Q8—432no—
314C2×C4⋊Q8—861no—
315C2×#125—432no—
316C2×#125—861no—
317C2×C22⋊Q8—862no—
318C2×#117—431no—
319C2×#117—431no—
320C22×C4⋊C4C2×D4311yescharacteristic
321C22×C4⋊C4C2×D4311yescharacteristic
322#417—864no—
323#416—864no—
324C2×#103—431no—
325C2×#103—431no—
326C2×#103—432no—
327C2×#102—431no—
328C2×#102—431no—
329C2×#102—432no—
330#391—432no—
331#390—432no—
332#386—862no—
333#380—861no—
334#380—861no—
335#340—432no—
336#340—432no—
337#340C2×D4312yes—
338#340C2×D4312yes—
339#336—432no—
340#336—432no—
341C43#2345811yescharacteristic, complemented, Sylow
342C2×#41—434no—
343C2×#41—862no—
344C2×#41—862no—
345C2×#41—862no—
346C2×#41—862no—
347C2×#41—862no—
348C22×Q8—431no—
349C22×Q8—862no—
350C22×D4—431no—
351C22×D4—861no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—861no—
355C23×C4C22×D4311yescharacteristic
356C2×M16—862no—
357C2×M16—862no—
358C2×M16—862no—
359C22×C8—22no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—432no—
363C22×C8C22×D4311yescharacteristic
364C22×C8C22×D4311yescharacteristic
365C4⋊Q8—864no—
366C4⋊Q8—868no—
367C4⋊Q8—864no—
368#125—864no—
369#125—868no—
370#125—864no—
371C22⋊Q8—8616no—
372#117—434no—
373#117—862no—
374#117—862no—
375#117—862no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4D17214yes—
389C2×C4⋊C4C22×D4312yes—
390C2×C4⋊C4C22×D4312yes—
391C2×C22⋊C4—432no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—862no—
394C2×C22⋊C4—862no—
395C2×C42—432no—
396C2×C42—861no—
397#103—862no—
398#103—862no—
399#103—864no—
400#102—862no—
401#102—862no—
402#102—864no—
403#95—862no—
404#95—862no—
405C24—861no—
406C24D4×D4311yescharacteristic
407#41—868no—
408#41—868no—
409#41—1724no—
410#41—1724no—
411C2×Q8—432no—
412C2×Q8—868no—
413C2×Q8—861no—
414C2×Q8—861no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×Q8—861no—
418C2×Q8—3442no—
419C2×Q8—3442no—
420C2×D4—432no—
421C2×D4—864no—
422C2×D4—861no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—861no—
426C2×D4—861no—
427C2×D4—1722no—
428C2×D4—1722no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4—81no—
437C22×C4—432no—
438C22×C4—432no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—864no—
443C22×C4—1722no—
444C22×C4—1722no—
445C22×C4C2×D17212yes—
446C22×C4#1062189812yes—
447C22×C4#1062189812yes—
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4312yes—
450C22×C4#1062190012yes—
451C22×C4Q8×D4312yes—
452C22×C4C23×D4311yescharacteristic
453M16—1724no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—44no—
461C2×C8—862no—
462C2×C8—862no—
463C2×C8—862no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—42no—
469C4⋊C4—432no—
470C4⋊C4—432no—
471C4⋊C4—868no—
472C4⋊C4—868no—
473C4⋊C4—868no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4C2×D17214yes—
479C22⋊C4—864no—
480C22⋊C4—864no—
481C22⋊C4—3442no—
482C22⋊C4—3442no—
483C42—864no—
484C42—862no—
485C42—862no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—862no—
491C23—1721no—
492C23—1721no—
493C23—1721no—
494C23—1721no—
495C23—1721no—
496C23—1721no—
497C23#1306329512yes—
498C23#1306330312yes—
499C23#1306331112yes—
500C23C2×D4×D4311yescharacteristic
501Q8—862no—
502Q8—862no—
503Q8—3448no—
504Q8—1721no—
505Q8—1721no—
506D4—862no—
507D4—862no—
508D4—1728no—
509D4—1721no—
510D4—1721no—
511C2×C4—24no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—84no—
518C2×C4—84no—
519C2×C4—862no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—862no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1728no—
535C2×C4#1306329512yes—
536C2×C4#1306330312yes—
537C2×C4#1306330314yes—
538C2×C4#1306330514yes—
539C2×C4#1306331112yes—
540C2×C4#1306331114yes—
541C2×C4#1306331314yes—
542C2×C4C2×D4×D4311yescharacteristic
543C2×C4C22×D17211yescharacteristic
544C2×C4C2×Q8×D4311yescharacteristic
545C2×C4C2×#1062190011yescharacteristic
546C2×C4C2×#1062189811yescharacteristic
547C2×C4C2×#1062189811yescharacteristic
548C8—41no—
549C8—41no—
550C8—1722no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22—3441no—
561C22—1722no—
562C22—1722no—
563C22—1722no—
564C22#1458281214yes—
565C22C2×#1306329511yescharacteristic
566C22C2×#1306330311yescharacteristic
567C22C2×#1306331111yescharacteristic
568C22#1458370011yescharacteristic
569C22#1458370511yescharacteristic
570C22#1458370511yescharacteristic
571C22#1458371211yescharacteristic
572C4—44no—
573C4—82no—
574C4—1722no—
575C4—1722no—
576C4—1722no—
577C4—1722no—
578C4—1722no—
579C4#1458281214yes—
580C4C2×#1306330311yescharacteristic
581C4C2×#1306330511yescharacteristic
582C4C2×#1306331111yescharacteristic
583C4C2×#1306331311yescharacteristic
584C2—24no—
585C2—3442no—
586C2C2×#1458281211yescharacteristic
587C2#1914390411yescharacteristic
588C2#1914391511yescharacteristic
589C2#1914445111yescharacteristic
590C2#1914446211yescharacteristic
591C2#1914494711yescharacteristic
592C2#1914495811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#340C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenterC2×#340D43
hypocenterC43#23458
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
1. C2×#14583530C2semidirect
5. #19135745C2semidirect
6. #19135740C2semidirect
7. #19135735C2semidirect
8. #19135730C2semidirect
9. #19134314C2semidirect
10. #19134291C2semidirect
11. C2×C43×#340C2semidirect
50. C2×#10621898Q8semidirect
297. C2×#340D43semidirect
341. C43#23458semidirect

Maximal subgroups

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

subgroupindex
C2×#145835302
C2×#145828982
C2×#145828962
#191371882
#191357452
#191357402
#191357352
#191357302
#191343142
#191342912
C2×C43×#3402
#2345843