Finite Group Databasebeta

← #25130517

Subgroups — #25130517

Order 11008.

1174 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583176C211yesmaximal, characteristic, complemented
2C2×C4×#10621884C211yesmaximal, characteristic, complemented
3#19139508C211yesmaximal, characteristic
4#19135795C212yesmaximal, complemented
5#19135596C212yesmaximal, complemented
6#19135557C211yesmaximal, characteristic, complemented
7#19135390C211yesmaximal, characteristic, complemented
8#19134917C212yesmaximal, complemented
9#19134794C212yesmaximal, complemented
10#19134600C211yesmaximal, characteristic, complemented
11C2×C43×#556C211yesmaximal, characteristic, complemented
12C22×#10621884C2211yescharacteristic
13C2×#13063299C2212yes—
14C2×#13063296—21no—
15C2×C4×D172C2211yescharacteristic
16#14583176—24no—
17C4×#10621884—24no—
18C2×#13063258C2212yes—
19C2×#13063256C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2212yes—
23C2×#13063245C2212yes—
24C2×#13063245C2211yescharacteristic
25C2×C22⋊(C43⋊C8)C2212yes—
26C2×C22⋊(C43⋊C8)C2212yes—
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582815—22no—
29#14582769C2211yescharacteristic
30#14582759C2212yes—
31#14582756—21no—
32#14582661C2212yes—
33#14582661C2212yes—
34#14582661C2212yes—
35C43×#556—24no—
36C43×#556—24no—
37C2×C4⋊Q8×C43C2211yescharacteristic
38C2×#126×C43—22no—
39C2×#124×C43—21no—
40C2×C22⋊Q8×C43C2212yes—
41C2×C4×Q8×C43—21no—
42C2×C4×Q8×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C2×#117×C43C2212yes—
45C22×D172C2311yescharacteristic
46C22×C22⋊D43—22no—
47C22×C4×D43—21no—
48C2×#10621884—22no—
49C2×#10621884—22no—
50C2×#10621884—22no—
51C22×C43⋊C8C2311yescharacteristic
52C22×C43⋊C8C2312yes—
53C22×C43⋊C8C2311yescharacteristic
54#13063299—24no—
55#13063299—42no—
56#13063296—44no—
57C4×D172—22no—
58C4×D172—22no—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43C2311yescharacteristic
62C2×C4⋊Dic43C2312yes—
63C2×C22⋊Dic43—22no—
64C2×(C2×D43)⋊C4—21no—
65C2×(C2×D43)⋊C4—22no—
66#13063258—24no—
67#13063256—22no—
68C4⋊(C43⋊C8)—22no—
69#13063249—22no—
70#13063249—42no—
71#13063245—24no—
72#13063245—22no—
73C22⋊(C43⋊C8)—24no—
74C22⋊(C43⋊C8)—42no—
75C4×C43⋊C8—22no—
76C43⋊#95—22no—
77C22×Q8×C43—21no—
78C22×Q8×C43C2311yescharacteristic
79C22×D4×C43D411yescharacteristic
80C23×C4×C43C2312yes—
81C4⋊Q8×C43—22no—
82C4⋊Q8×C43D414yescomplemented
83#126×C43—216no—
84#124×C43—28no—
85C22⋊Q8×C43—24no—
86C22⋊Q8×C43—24no—
87C4×Q8×C43—28no—
88C4×Q8×C43—22no—
89C4×Q8×C43D414yescomplemented
90C4×D4×C43—22no—
91C4×D4×C43—22no—
92#117×C43—24no—
93#117×C43—24no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43D411yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2312yes—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43D412yes—
103C2×C42×C43—22no—
104C2×C42×C43—21no—
105C2×C42×C43C2311yescharacteristic
106C24×C43C2×D412yes—
107C23×D43—21no—
108C2×Q8×C43—24no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—42no—
115C2×Q8×C43—42no—
116C2×Q8×C43C2×D412yes—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C2×C22⋊D43—44no—
134C2×C22⋊D43—44no—
135C2×C22⋊D43—82no—
136C22×Dic43—21no—
137C22×Dic43—22no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172#4112yes—
144C2×C4×D43—42no—
145C2×C4×D43—42no—
146C2×C4×D43—42no—
147C4⋊C4×C43—28no—
148C4⋊C4×C43—24no—
149C4⋊C4×C43—24no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43C2×D412yes—
154C4⋊C4×C43C2×D414yes—
155C22⋊C4×C43—28no—
156C22⋊C4×C43—28no—
157C22⋊C4×C43—24no—
158C42×C43—28no—
159C42×C43—24no—
160C42×C43C2×D412yes—
161C42×C43C2×D412yes—
162C22⋊Dic43—44no—
163#10621884—28no—
164(C2×D43)⋊C4—44no—
165(C2×D43)⋊C4—42no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170C4⋊Dic43—42no—
171C4⋊Dic43—81no—
172C2×C43⋊C8—21no—
173C2×C43⋊C8—21no—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—21no—
180C2×C43⋊C8#4112yes—
181C23×C43—22no—
182C23×C43—22no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—22no—
188C23×C43C22×D411yescharacteristic
189C22×D43—22no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196Q8×C43—22no—
197Q8×C43—22no—
198Q8×C43—41no—
199Q8×C43—41no—
200Q8×C43—48no—
201D4×C43—44no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—24no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43#12012yes—
221C2×C4×C43#12012yes—
222C2×C4×C43#13512yes—
223C2×C4×C43AGL(1,ℤ/8)12yes—
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43H(5,𝔽2)11yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C22⋊D43—88no—
231C2×Dic43—41no—
232C2×Dic43—42no—
233C2×Dic43—41no—
234C2×Dic43—42no—
235C2×Dic43—41no—
236C2×Dic43—42no—
237D172—22no—
238D172—22no—
239D172—41no—
240D172—41no—
241C4×D43—84no—
242C43⋊C8—22no—
243C43⋊C8—41no—
244C43⋊C8—42no—
245#24119—431nomaximal, Sylow
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43—42no—
252C22×C43—42no—
253C22×C43C2×#12011yescharacteristic
254C22×C43#54611yescharacteristic
255C22×C43#54711yescharacteristic
256C22×C43C2×#13511yescharacteristic
257C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C43#57711yescharacteristic
259C22×C43#57811yescharacteristic
260C2×D43—42no—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—81no—
267C4×C43—22no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—44no—
271C4×C43—42no—
272C4×C43#44914yes—
273C4×C43#52511yescharacteristic
274C4×C43#53711yescharacteristic
275C4×C43#54811yescharacteristic
276C4×C43#55011yescharacteristic
277Dic43—81no—
278Dic43—82no—
279C2×#556D4311yescharacteristic, complemented
280C2×#474—431no—
281C2×C4×SD16—431no—
282#2537—431no—
283#2036—432no—
284#2000—432no—
285#1990—431no—
286#1954—431no—
287#1875—432no—
288#1854—432no—
289#1803—431no—
290C2×C43—82no—
291C2×C43#240711yescharacteristic
292C2×C43C2×#44911yescharacteristic
293C2×C43#301311yescharacteristic
294C2×C43#330211yescharacteristic
295C2×C43#332411yescharacteristic
296C2×C43#334011yescharacteristic
297C2×C43#335311yescharacteristic
298D43—82no—
299C22×SD16—431no—
300#556—24no—
301#556—24no—
302C2×C4⋊Q8C2×D4311yescharacteristic
303C2×#126—22no—
304C2×#124—21no—
305C2×C22⋊Q8C2×D4312yes—
306C2×#121—432no—
307C2×#121—861no—
308C2×C4×Q8—21no—
309C2×C4×Q8C2×D4311yescharacteristic
310C2×C4×D4—431no—
311C2×C4×D4C2×D4311yescharacteristic
312C2×#117C2×D4312yes—
313#474—864no—
314C4×SD16—864no—
315C2×#107—432no—
316C2×#106—431no—
317C2×C4⋊C8—431no—
318C2×#103—431no—
319C2×#103—432no—
320C2×#102—431no—
321C2×#102—432no—
322C2×C22⋊C8—432no—
323C2×C22⋊C8—432no—
324C2×C4×C8—431no—
325#394—862no—
326#384—431no—
327#380—432no—
328#380—861no—
329#340—432no—
330#340—432no—
331#340—432no—
332C43#2411911yescharacteristic, complemented, Sylow
333C22×Q8—21no—
334C22×Q8C22×D4311yescharacteristic
335C22×D4—431no—
336C22×D4—862no—
337C22×D4C22⋊D4311yescharacteristic
338C23×C4—861no—
339C23×C4C22×D4312yes—
340C2×SD16—862no—
341C2×SD16—862no—
342C2×SD16—862no—
343C22×C8—431no—
344C22×C8—431no—
345C22×C8—432no—
346C4⋊Q8—22no—
347C4⋊Q8C22⋊D4314yescomplemented
348#126—216no—
349#124—28no—
350C22⋊Q8—24no—
351C22⋊Q8—24no—
352#121—864no—
353#121—1722no—
354#121—1724no—
355C4×Q8—28no—
356C4×Q8—22no—
357C4×Q8C22⋊D4314yescomplemented
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—862no—
361C4×D4—862no—
362#117—24no—
363#117—24no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—432no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4C22⋊D4311yescharacteristic
372C2×C4⋊C4C22×D4311yescharacteristic
373C2×C4⋊C4C22×D4312yes—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—861no—
378C2×C22⋊C4—862no—
379C2×C22⋊C4C22⋊D4312yes—
380C2×C42—22no—
381C2×C42—21no—
382C2×C42C22×D4311yescharacteristic
383#107—864no—
384#106—862no—
385C4⋊C8—862no—
386#103—862no—
387#103—1722no—
388#102—862no—
389#102—864no—
390C22⋊C8—864no—
391C22⋊C8—1722no—
392C4×C8—862no—
393#95—862no—
394C24—861no—
395C24C2×C22⋊D4312yes—
396C2×Q8—24no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—42no—
403C2×Q8—42no—
404C2×Q8C2×C22⋊D4312yes—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—432no—
409C2×D4—861no—
410C2×D4—861no—
411C2×D4—861no—
412C2×D4—861no—
413C2×D4—861no—
414C2×D4—3442no—
415C2×D4—1724no—
416C2×D4—1724no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—861no—
427C22×C4—862no—
428C22×C4—1722no—
429C22×C4—1722no—
430C22×C4—1722no—
431C22×C4C2×C22⋊D4312yes—
432C22×C4C2×C22⋊D4311yescharacteristic
433C22×C4C2×C22⋊D4311yescharacteristic
434C22×C4C23×D4311yescharacteristic
435SD16—868no—
436C2×C8—432no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—862no—
441C2×C8—862no—
442C2×C8—861no—
443C2×C8—862no—
444C2×C8—861no—
445C4⋊C4—28no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—862no—
454C4⋊C4—862no—
455C4⋊C4—3441no—
456C4⋊C4—1722no—
457C4⋊C4C2×C22⋊D4312yes—
458C4⋊C4C2×C22⋊D4314yes—
459C22⋊C4—28no—
460C22⋊C4—28no—
461C22⋊C4—24no—
462C22⋊C4—1724no—
463C22⋊C4—1724no—
464C22⋊C4—1722no—
465C42—28no—
466C42—24no—
467C42C2×C22⋊D4312yes—
468C42C2×C22⋊D4312yes—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—862no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23—1721no—
482C23—1721no—
483C23C22×C22⋊D4311yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—48no—
487Q8—41no—
488Q8—41no—
489D4—44no—
490D4—862no—
491D4—862no—
492D4—3448no—
493D4—1721no—
494D4—1721no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—3444no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4#1306329412yes—
521C2×C4#1306329412yes—
522C2×C4#1306334512yes—
523C2×C4#1306335012yes—
524C2×C4C22×C22⋊D4311yescharacteristic
525C2×C4C22×C22⋊D4311yescharacteristic
526C2×C4#41×D4311yescharacteristic
527C2×C4#41×D4311yescharacteristic
528C2×C4#1306337111yescharacteristic
529C2×C4#1306337211yescharacteristic
530C8—862no—
531C8—1722no—
532C8—1721no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—3441no—
541C22—3441no—
542C22—3441no—
543C22—3441no—
544C22—1722no—
545C22—1722no—
546C22—1722no—
547C22C2×#1306329411yescharacteristic
548C22#1458353711yescharacteristic
549C22#1458354811yescharacteristic
550C22C2×#1306334511yescharacteristic
551C22C2×#1306335011yescharacteristic
552C22#1458370711yescharacteristic
553C22#1458371411yescharacteristic
554C4—22no—
555C4—44no—
556C4—42no—
557C4—42no—
558C4—42no—
559C4—3442no—
560C4—3441no—
561C4#1458304414yes—
562C4#1458340611yescharacteristic
563C4#1458347711yescharacteristic
564C4#1458355611yescharacteristic
565C4#1458356811yescharacteristic
566C2—82no—
567C2—3442no—
568C2#1913793411yescharacteristic
569C2C2×#1458304411yescharacteristic
570C2#1914391011yescharacteristic
571C2#1914650611yescharacteristic
572C2#1914682011yescharacteristic
573C2#1914700211yescharacteristic
574C2#1914717311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#556C2
socleC23×C43C22×D4
prime radical#19139508C2
hypercenterC2×#556D43
hypocenterC43#24119
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#14583176C2semidirect
2. C2×C4×#10621884C2semidirect
4. #19135795C2semidirect
5. #19135596C2semidirect
6. #19135557C2semidirect
7. #19135390C2semidirect
8. #19134917C2semidirect
9. #19134794C2semidirect
10. #19134600C2semidirect
11. C2×C43×#556C2semidirect
82. C4⋊Q8×C43D4semidirect
89. C4×Q8×C43D4semidirect
279. C2×#556D43semidirect
332. C43#24119semidirect
347. C4⋊Q8C22⋊D43semidirect
357. C4×Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
C2×C4×#106218842
#191395082
#191357952
#191355962
#191355572
#191353902
#191349172
#191347942
#191346002
C2×C43×#5562
#2411943