Finite Group Databasebeta

← #25086810

Subgroups — #25086810

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147505C211yesmaximal, characteristic
2Q16×Dic86C211yesmaximal, characteristic, complemented
3Q8×#10621883C211yesmaximal, characteristic
4#19134275C211yesmaximal, characteristic, complemented
5#19134099C211yesmaximal, characteristic, complemented
6#19134050C211yesmaximal, characteristic, complemented
7#19133997C211yesmaximal, characteristic, complemented
8#19133994C211yesmaximal, characteristic
9#19133814C211yesmaximal, characteristic, complemented
10#19133760C211yesmaximal, characteristic
11#19133734C211yesmaximal, characteristic, complemented
12#19133729C211yesmaximal, characteristic
13#19133446C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic
15C43×#3299C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17Q8×Dic86C2211yescharacteristic
18#14583309—21no—
19#14583304C2211yescharacteristic
20#14583303—21no—
21#14583302C2211yescharacteristic
22#14583295—21no—
23#14583295C2211yescharacteristic
24#14583278C2211yescharacteristic
25#14583251C2211yescharacteristic
26#14583203—21no—
27#14583194C2211yescharacteristic
28#14583194C2211yescharacteristic
29#14583192—21no—
30#14583192—21no—
31#14583191C2211yescharacteristic
32#14583189—21no—
33#14583189C2211yescharacteristic
34#14583189C2211yescharacteristic
35#14583181—21no—
36#14583181C2211yescharacteristic
37#14583179—21no—
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14582999—21no—
42Q16×Dic43—21no—
43C4×#10621883—21no—
44C4×#10621883C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#554C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#484—21no—
60C43×#477C2211yescharacteristic
61C43×#467—21no—
62C43×#462C2211yescharacteristic
63C43×#451—21no—
64C4×Q16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#103×C43—21no—
67C2×#10621885—41no—
68C2×#10621883D411yescharacteristic
69#13063325—21no—
70#13063325—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063324—21no—
74#13063324—21no—
75#13063324—41no—
76#13063324—41no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82#13063259—21no—
83#13063259—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256D411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063249—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—41no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110#13063236—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×Q8×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—42no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154C22×C4×C43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—41no—
158C2×Dic86—41no—
159C2×Dic86C2×D411yescharacteristic
160Q16×C43—22no—
161Q16×C43—81no—
162C2×C8×C43—21no—
163C2×C8×C43—81no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43C2411yescharacteristic
184#10621885—82no—
185#10621883Q1614yescomplemented
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—41no—
191C4⋊Dic43—41no—
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C23×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—82no—
212Q8×C43—81no—
213Q8×C43#13712yes—
214D4×C43—21no—
215D4×C43C2×Q1612yes—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—82no—
226C2×C4×C43—161no—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43H(5,𝔽2)11yescharacteristic
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234Dic86—21no—
235Dic86—81no—
236Dic86—81no—
237Dic86—161no—
238Dic86—161no—
239Dic86C2×Q1612yes—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—41no—
243C43⋊C8—21no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8C2×Q1612yes—
249#19813—431nomaximal, Sylow
250C22×C43—22no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43D4211yescharacteristic
254C4×C43—22no—
255C4×C43—21no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43C22×Q1611yescharacteristic
263C4×C43C2×#13711yescharacteristic
264C4×C43#57711yescharacteristic
265C4×C43#57811yescharacteristic
266Dic43—22no—
267Dic43—41no—
268Dic43—81no—
269Dic43—81no—
270#3385—431no—
271Q8×Q16—431no—
272Q8×SD16—431no—
273#3299D4311yescharacteristic
274#1723—431no—
275#1692—431no—
276#1684—431no—
277#1676—431no—
278#1675—431no—
279#1645—431no—
280#1637—431no—
281#1633—431no—
282#1632—431no—
283#1584—431no—
284SD16⋊C8—431no—
285C2×C43—42no—
286C2×C43#326611yescharacteristic
287C2×C43D4×Q1611yescharacteristic
288C2×C43#328811yescharacteristic
289Q82—431no—
290Q82—431no—
291#554C2×D4311yescharacteristic
292D4×Q8C2×D4311yescharacteristic
293#501—861no—
294#500—431no—
295#500—431no—
296#500—861no—
297#498—431no—
298#498—861no—
299#494—431no—
300#487—431no—
301#487C2×D4311yescharacteristic
302#484—21no—
303#479—861no—
304#477—431no—
305#477—431no—
306#477—431no—
307#477—861no—
308#477—861no—
309#477C2×D4311yescharacteristic
310#476—431no—
311#476—431no—
312#476—861no—
313#475—431no—
314#475—861no—
315#474—861no—
316#467—21no—
317#462C2×D4311yescharacteristic
318#451—21no—
319#446—431no—
320C8×Q8—431no—
321C8×Q8—431no—
322#440—861no—
323C4×Q16—861no—
324C4×Q16C2×D4311yescharacteristic
325C4×SD16—431no—
326C4×SD16—861no—
327C8×D4C2×D4311yescharacteristic
328C2×#103—21no—
329#335—431no—
330#335—431no—
331#333—431no—
332#333—431no—
333#333—431no—
334#332—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338D4⋊C8—431no—
339#322—431no—
340C43#1981311yescharacteristic, complemented, Sylow
341C22×Q8—21no—
342C2×Q16—21no—
343C2×Q16—1721no—
344C2×Q16C22⋊D4311yescharacteristic
345C2×SD16—431no—
346C22×C8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350C4⋊Q8—861no—
351C4⋊Q8—861no—
352C4⋊Q8—861no—
353C4⋊Q8—861no—
354C4⋊Q8—1721no—
355C4⋊Q8—1721no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#125—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—41no—
362C22⋊Q8—41no—
363C4×Q8—431no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8C22×D4311yescharacteristic
369C4×Q8C22×D4311yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4C22×D4311yescharacteristic
373C2×C4⋊C4—21no—
374#107—21no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#107—861no—
382#107C22⋊D4311yescharacteristic
383#106—431no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—431no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—1721no—
406#103C22⋊D4311yescharacteristic
407#103C22⋊D4311yescharacteristic
408#102—431no—
409#102—861no—
410#102—861no—
411C22⋊C8—21no—
412#97—861no—
413C4×C8—431no—
414C4×C8—431no—
415C4×C8—861no—
416C4×C8—861no—
417C4×C8C22×D4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—41no—
421C2×Q8—42no—
422C2×Q8—81no—
423C2×Q8—431no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—1721no—
427C2×Q8—1721no—
428C2×Q8C2×C22⋊D4311yescharacteristic
429C2×Q8C2×C22⋊D4311yescharacteristic
430C2×D4D4×D4311yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—41no—
434Q16—22no—
435Q16—81no—
436Q16—3442no—
437SD16—434no—
438C2×C8—21no—
439C2×C8—81no—
440C2×C8—431no—
441C2×C8—431no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8C2×C22⋊D4311yescharacteristic
447C2×C8C2×C22⋊D4311yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—431no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4D4×D4311yescharacteristic
468C4⋊C4C2×C22⋊D4311yescharacteristic
469C4⋊C4C2×C22⋊D4311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—861no—
476C42—1721no—
477C42—1721no—
478C42C23×D4311yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—41no—
484Q8—41no—
485Q8—82no—
486Q8—81no—
487Q8—432no—
488Q8—861no—
489Q8—3441no—
490Q8—3441no—
491Q8—6881no—
492Q8—6881no—
493Q8#1306335512yes—
494D4—21no—
495D4Q16×D4312yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—82no—
506C2×C4—161no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4C2×D4×D4311yescharacteristic
512C2×C4C22×C22⋊D4311yescharacteristic
513C2×C4#1306337011yescharacteristic
514C8—21no—
515C8—21no—
516C8—41no—
517C8—432no—
518C8—861no—
519C8—1721no—
520C8—1721no—
521C8—1721no—
522C8—1721no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22D4×C22⋊D4311yescharacteristic
527C4—22no—
528C4—21no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—81no—
534C4—81no—
535C4—862no—
536C4—3441no—
537C4—3441no—
538C4—1721no—
539C4C2×Q16×D4311yescharacteristic
540C4C2×#1306335511yescharacteristic
541C4#1458371011yescharacteristic
542C4#1458371211yescharacteristic
543C2—42no—
544C2#1914610111yescharacteristic
545C2Q16×C22⋊D4311yescharacteristic
546C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3299C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenter#3299D43
hypocenterC43#19813
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3299

Complements

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

NH ≅ G/Ntype
2. Q16×Dic86C2semidirect
4. #19134275C2semidirect
5. #19134099C2semidirect
6. #19134050C2semidirect
7. #19133997C2semidirect
9. #19133814C2semidirect
11. #19133734C2semidirect
13. #19133446C2semidirect
185. #10621883Q16semidirect
340. C43#19813semidirect

Maximal subgroups

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

subgroupindex
#191475052
Q16×Dic862
Q8×#106218832
#191342752
#191340992
#191340502
#191339972
#191339942
#191338142
#191337602
#191337342
#191337292
#191334462
#191334072
C43×#32992
#1981343