Finite Group Databasebeta

← #25097373

Subgroups — #25097373

Order 11008.

1462 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583379C211yesmaximal, characteristic
2C2×#14582941C211yesmaximal, characteristic, complemented
3C2×#14582935C211yesmaximal, characteristic, complemented
4C2×#14582867C211yesmaximal, characteristic
5#19137188C211yesmaximal, characteristic
6#19134797C212yesmaximal, complemented
7#19134795C212yesmaximal, complemented
8#19134789C212yesmaximal, complemented
9#19134784C212yesmaximal, complemented
10C2×#14582661C211yesmaximal, characteristic, complemented
11C43×#1736C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C23×C43⋊C8C2211yescharacteristic
14#14583379—24no—
15#14583379—24no—
16C2×C4×Dic86—21no—
17C2×C4×D172—21no—
18C2×(C22⋊D43)⋊C4—22no—
19C2×#13063284C2211yescharacteristic
20C2×#13063283C2212yes—
21C22×C4⋊Dic43C2211yescharacteristic
22C2×C4⋊C4×D43C2212yes—
23#14582941—24no—
24#14582935—24no—
25C2×#13063259C2212yes—
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063257C2212yes—
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31#14582867C418yescomplemented
32C2×(C2×D43)⋊C8C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34#14582804—21no—
35#14582800—21no—
36#14582778—22no—
37#14582756C2212yes—
38#14582756C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C22×M16×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C22×C4⋊C4×C43C2211yescharacteristic
44C43×#340C2212yes—
45C43×#340C2212yes—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898C2×C414yes—
51C2×#10621898Q814yes—
52C22×Dic86D411yescharacteristic
53C22×D172D411yescharacteristic
54C22×C22⋊D43D412yes—
55C23×Dic43—21no—
56C22×C4×D43—22no—
57C22×C4×D43C2312yes—
58C22×C43⋊C8—22no—
59C22×C43⋊C8—22no—
60C22×C43⋊C8C2×C414yescomplemented
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C4×Dic86—28no—
64C4×D172—28no—
65(C22⋊D43)⋊C4—216no—
66#13063284—22no—
67#13063284—22no—
68#13063283—24no—
69#13063283—24no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43D414yes—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2312yes—
76C2×Dic43⋊C4—22no—
77C4⋊C4×D43—24no—
78C4⋊C4×D43—24no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×C4×Dic43—22no—
84C2×C4×Dic43—21no—
85#13063259—24no—
86#13063258—22no—
87#13063258—22no—
88#13063257—24no—
89#13063256—22no—
90#13063256—22no—
91(C2×D43)⋊C8C2×C418yescomplemented
92(C2×D43)⋊C8C2×C418yescomplemented
93C43⋊#95—22no—
94C43⋊#95—22no—
95C23×C4×C43—21no—
96C23×C4×C43C2311yescharacteristic
97C2×M16×C43—22no—
98C2×M16×C43—22no—
99C2×M16×C43C2×C414yescomplemented
100C22×C8×C43C2312yes—
101#117×C43—22no—
102#117×C43D414yes—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2312yes—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C42×C43—21no—
111C24×C43C2×D411yescharacteristic
112C23×D43C2×D412yes—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—42no—
117C22×C4×C43—81no—
118C22×C4×C43—81no—
119C22×C4×C43C22×C412yes—
120C22×C4×C43C2×D412yes—
121C22×C4×C43C2×D412yes—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×Q812yes—
124C22×C4×C43#4112yes—
125C22×C4×C43#4112yes—
126C22×C4×C43C2411yescharacteristic
127C2×C22⋊D43—24no—
128C2×C22⋊D43—24no—
129C2×C22⋊D43C4⋊C418yes—
130C22×Dic43—24no—
131C22×Dic43—22no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—81no—
135C22×Dic43—81no—
136C22×Dic43C2×D412yes—
137#10621898—28no—
138#10621898—28no—
139#10621898—28no—
140#10621898—28no—
141C2×D172—22no—
142C2×D172—22no—
143C2×D172C4⋊C414yes—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—28no—
149C2×C4×D43—82no—
150C2×C4×D43—82no—
151C2×C4×D43C22×C414yes—
152C2×C4×D43C2×Q814yes—
153C2×Dic86—22no—
154C2×Dic86—22no—
155C2×Dic86C4⋊C414yes—
156M16×C43—28no—
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C2×C8×C43C22×C414yes—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—42no—
165C4⋊C4×C43C2×D412yes—
166C4⋊C4×C43C2×D412yes—
167C22⋊C4×C43—24no—
168C42×C43—24no—
169C22⋊Dic43—42no—
170(C2×D43)⋊C4—28no—
171(C2×D43)⋊C4—82no—
172(C2×D43)⋊C4—82no—
173C4⋊Dic43—24no—
174C4⋊Dic43—22no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43C2×D414yes—
180Dic43⋊C4—28no—
181C4×Dic43—28no—
182C4×Dic43—42no—
183C2×C43⋊C8—28no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8C22×C412yes—
189C2×C43⋊C8C22×C412yes—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43C2×C4⋊C412yes—
195C23×C43#12012yes—
196C23×C43#12312yes—
197C23×C43C22×D411yescharacteristic
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—22no—
204C22×D43C2×C4⋊C414yes—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—84no—
215C2×C4×C43C2×C4⋊C412yes—
216C2×C4×C43C4×D414yes—
217C2×C4×C43C4×D414yes—
218C2×C4×C43#12012yes—
219C2×C4×C43C22⋊Q814yes—
220C2×C4×C43C22⋊Q814yes—
221C2×C4×C43#12312yes—
222C2×C4×C43C23×C411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×Q811yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—216no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—24no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—84no—
241C2×Dic43C2×C4⋊C414yes—
242D172—28no—
243C4×D43—24no—
244C4×D43—24no—
245C4×D43—24no—
246C4×D43—24no—
247C4×D43—88no—
248Dic86—28no—
249C8×C43—24no—
250C43⋊C8—22no—
251C43⋊C8—22no—
252#20849—431nomaximal, Sylow
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43#38514yes—
260C22×C43C22×C4⋊C411yescharacteristic
261C22×C43C2×#12011yescharacteristic
262C22×C43C2×#12311yescharacteristic
263C22×C43#57611yescharacteristic
264C22×C43#57711yescharacteristic
265C22×C43#57711yescharacteristic
266C22×C43#57811yescharacteristic
267C2×D43—24no—
268C2×D43—24no—
269C2×D43—24no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—42no—
273C2×D43—42no—
274C4×C43—42no—
275C4×C43—42no—
276C4×C43—82no—
277C4×C43#38514yes—
278C4×C43C2×C4×D411yescharacteristic
279C4×C43C2×C4×D411yescharacteristic
280C4×C43C2×C22⋊Q811yescharacteristic
281C4×C43C2×C22⋊Q811yescharacteristic
282Dic43—24no—
283Dic43—44no—
284Dic43—81no—
285Dic43—81no—
286C2×#520—431no—
287C2×#428—431no—
288C2×#427—431no—
289C2×#408—431no—
290#2311—431no—
291#1854—432no—
292#1854—432no—
293#1853—432no—
294#1852—432no—
295#1736D4311yescharacteristic, complemented
296C2×#340—431no—
297C2×C43—24no—
298C2×C43C2×#38511yescharacteristic
299C2×C43#291211yescharacteristic
300C2×C43#291311yescharacteristic
301C2×C43#301211yescharacteristic
302C2×C43#301311yescharacteristic
303C2×C43#309611yescharacteristic
304C2×C43#309711yescharacteristic
305D43—44no—
306C22×#41—431no—
307C22×M16C2×D4311yescharacteristic
308C23×C8—431no—
309#520—864no—
310#520—864no—
311C2×C4×Q8—861no—
312C2×C4×D4—861no—
313C2×C4×D4—862no—
314C2×#117—431no—
315C2×#117—432no—
316C2×#117C2×D4311yescharacteristic
317C22×C4⋊C4—431no—
318C22×C4⋊C4—432no—
319C22×C4⋊C4C2×D4311yescharacteristic
320#428—864no—
321#427—864no—
322C2×#107—432no—
323C2×#107—431no—
324C2×#107—431no—
325C2×#106—432no—
326C2×#106—431no—
327C2×#106—431no—
328#408—438no—
329C2×C22⋊C8—432no—
330C2×C22⋊C8—432no—
331#391—861no—
332#390—861no—
333#386—862no—
334#380—432no—
335#380—432no—
336#340—432no—
337#340—432no—
338#340C2×D4312yes—
339#340C2×D4312yes—
340C43#2084911yescharacteristic, complemented, Sylow
341C2×#41—434no—
342C2×#41—434no—
343C2×#41—862no—
344C2×#41—862no—
345C2×#41—862no—
346C2×#41—862no—
347C22×Q8—431no—
348C22×D4—432no—
349C22×D4—431no—
350C23×C4—21no—
351C23×C4—432no—
352C23×C4—862no—
353C23×C4—861no—
354C23×C4C22×D4311yescharacteristic
355C2×M16—22no—
356C2×M16—22no—
357C2×M16C4×D4314yescomplemented
358C22×C8—434no—
359C22×C8—431no—
360C22×C8—431no—
361C22×C8—862no—
362C22×C8—862no—
363C22×C8C22×D4312yes—
364C4×Q8—868no—
365C4×D4—868no—
366C4×D4—8616no—
367#117—22no—
368#117—864no—
369#117—864no—
370#117—862no—
371#117—862no—
372#117D17214yes—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—434no—
377C2×C4⋊C4—432no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—864no—
381C2×C4⋊C4—862no—
382C2×C4⋊C4—862no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—864no—
385C2×C4⋊C4C22×D4312yes—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—862no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—862no—
392C2×C22⋊C4—861no—
393C2×C42—21no—
394C2×C42—862no—
395C2×C42—861no—
396#107—864no—
397#107—862no—
398#107—862no—
399#106—864no—
400#106—862no—
401#106—862no—
402C22⋊C8—438no—
403C22⋊C8—438no—
404#95—862no—
405#95—862no—
406C24—432no—
407C24D4×D4311yescharacteristic
408#41—868no—
409#41—868no—
410#41—868no—
411#41—868no—
412C2×Q8—434no—
413C2×Q8—862no—
414C2×Q8—862no—
415C2×D4—438no—
416C2×D4—434no—
417C2×D4—864no—
418C2×D4—864no—
419C2×D4—862no—
420C2×D4—862no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—42no—
425C22×C4—81no—
426C22×C4—81no—
427C22×C4—432no—
428C22×C4—434no—
429C22×C4—434no—
430C22×C4—868no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—864no—
436C22×C4—862no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—3442no—
440C22×C4—3442no—
441C22×C4—3441no—
442C22×C4—3441no—
443C22×C4C2×C4×D4312yes—
444C22×C4C2×D17212yes—
445C22×C4#1062189812yes—
446C22×C4D4×D4311yescharacteristic
447C22×C4D4×D4312yes—
448C22×C4#1062190012yes—
449C22×C4Q8×D4312yes—
450C22×C4C23×D4311yescharacteristic
451M16—28no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—432no—
455C2×C8—432no—
456C2×C8—868no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8C2×C4×D4314yes—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—42no—
467C4⋊C4—434no—
468C4⋊C4—868no—
469C4⋊C4—864no—
470C4⋊C4—862no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4C2×D17212yes—
476C4⋊C4C2×D17212yes—
477C22⋊C4—24no—
478C22⋊C4—868no—
479C22⋊C4—3442no—
480C22⋊C4—3442no—
481C22⋊C4—1722no—
482C42—24no—
483C42—868no—
484C42—1722no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—434no—
490C23—862no—
491C23—862no—
492C23—862no—
493C23—862no—
494C23—862no—
495C23—862no—
496C23C4⋊C4×D4312yes—
497C23#1306329512yes—
498C23#1306330712yes—
499C23C2×D4×D4311yescharacteristic
500Q8—868no—
501D4—8616no—
502D4—868no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—84no—
513C2×C4—434no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—864no—
517C2×C4—864no—
518C2×C4—864no—
519C2×C4—864no—
520C2×C4—864no—
521C2×C4—3448no—
522C2×C4—3444no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1722no—
530C2×C4—1722no—
531C2×C4C4⋊C4×D4312yes—
532C2×C4(C22⋊D43)⋊C414yes—
533C2×C4C4×D17214yes—
534C2×C4#1306329512yes—
535C2×C4#1306330314yes—
536C2×C4#1306330514yes—
537C2×C4#1306330712yes—
538C2×C4C22×C4×D4311yescharacteristic
539C2×C4C2×D4×D4311yescharacteristic
540C2×C4C22×D17211yescharacteristic
541C2×C4C2×Q8×D4311yescharacteristic
542C2×C4C2×#1062190011yescharacteristic
543C2×C4C2×#1062189811yescharacteristic
544C8—24no—
545C8—862no—
546C8—862no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—864no—
554C22—864no—
555C22—864no—
556C22—1722no—
557C22—1722no—
558C22—1722no—
559C22—1722no—
560C22#1458277314yes—
561C22C2×C4⋊C4×D4311yescharacteristic
562C22C2×#1306329511yescharacteristic
563C22C2×#1306330711yescharacteristic
564C22#1458370311yescharacteristic
565C22#1458370811yescharacteristic
566C22#1458370911yescharacteristic
567C22#1458371511yescharacteristic
568C4—42no—
569C4—42no—
570C4—82no—
571C4—864no—
572C4—3441no—
573C4—3441no—
574C4—1724no—
575C4#1458277314yes—
576C4C2×(C22⋊D43)⋊C411yescharacteristic
577C4C2×C4×D17211yescharacteristic
578C4C2×#1306330311yescharacteristic
579C4C2×#1306330511yescharacteristic
580C2—24no—
581C2—1724no—
582C2C2×#1458277311yescharacteristic
583C2#1914318911yescharacteristic
584C2#1914319411yescharacteristic
585C2#1914390111yescharacteristic
586C2#1914391211yescharacteristic
587C2#1914455111yescharacteristic
588C2#1914456211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1736C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1736D43
hypocenterC43#20849
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#14582941C2semidirect
3. C2×#14582935C2semidirect
6. #19134797C2semidirect
7. #19134795C2semidirect
8. #19134789C2semidirect
9. #19134784C2semidirect
10. C2×#14582661C2semidirect
11. C43×#1736C2semidirect
31. #14582867C4semidirect
60. C22×C43⋊C8C2×C4semidirect
91. (C2×D43)⋊C8C2×C4semidirect
92. (C2×D43)⋊C8C2×C4semidirect
99. C2×M16×C43C2×C4semidirect
295. #1736D43semidirect
340. C43#20849semidirect
357. C2×M16C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833792
C2×#145829412
C2×#145829352
C2×#145828672
#191371882
#191347972
#191347952
#191347892
#191347842
C2×#145826612
C43×#17362
#2084943