Finite Group Databasebeta

← #25086819

Subgroups — #25086819

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#19147507C211yesmaximal, characteristic
2Q16×Dic86C211yesmaximal, characteristic, complemented
3Q8×#10621873C211yesmaximal, characteristic
4#19146473C211yesmaximal, characteristic
5#19134272C211yesmaximal, characteristic, complemented
6#19134101C211yesmaximal, characteristic, complemented
7#19134054C211yesmaximal, characteristic, complemented
8#19133999C211yesmaximal, characteristic, complemented
9#19133995C211yesmaximal, characteristic
10#19133818C211yesmaximal, characteristic, complemented
11#19133762C211yesmaximal, characteristic
12#19133737C211yesmaximal, characteristic, complemented
13#19133732C211yesmaximal, characteristic
14#19133409C211yesmaximal, characteristic
15C43×#1584C211yesmaximal, characteristic, complemented
16Q8×Dic86C2211yescharacteristic
17Q8×Dic86C2211yescharacteristic
18#14583609C2211yescharacteristic
19Q8×D172C2211yescharacteristic
20#14583308—21no—
21#14583304C2211yescharacteristic
22#14583304C2211yescharacteristic
23#14583303—21no—
24#14583297—21no—
25#14583297C2211yescharacteristic
26#14583279C2211yescharacteristic
27#14583250C2211yescharacteristic
28#14583250C2211yescharacteristic
29#14583236—21no—
30#14583207—21no—
31#14583195C2211yescharacteristic
32#14583194C2211yescharacteristic
33#14583194C2211yescharacteristic
34#14583194C2211yescharacteristic
35#14583192—21no—
36#14583192—21no—
37#14583190—21no—
38#14583190C2211yescharacteristic
39#14583190C2211yescharacteristic
40#14583185—21no—
41#14583185C2211yescharacteristic
42#14583180—21no—
43#14583139—21no—
44#14583109C2211yescharacteristic
45#14583053—21no—
46C8×Dic86C2211yescharacteristic
47#14583001—21no—
48Q16×Dic43—21no—
49C4×#10621873—21no—
50C4×#10621873C2211yescharacteristic
51C8×D172C2211yescharacteristic
52#103×D43—21no—
53#14582652C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582628C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Dic172—41no—
69C2×#10621885—21no—
70C2×#10621873D411yescharacteristic
71C2×C8×D43—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063324—21no—
80#13063324—21no—
81#13063324—41no—
82#13063324—41no—
83#13063317—21no—
84#13063305—21no—
85#13063305—41no—
86#13063303—41no—
87#13063301—21no—
88Q8×Dic43—21no—
89Q8×Dic43—21no—
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86C2311yescharacteristic
93C4×D172—21no—
94C4×D172—21no—
95C4×D172C2311yescharacteristic
96C4⋊C4×D43—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063258—21no—
103#13063258—21no—
104#13063258—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108#13063257—21no—
109#13063257—21no—
110#13063257D411yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113Dic43⋊C8—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—41no—
119#13063250D411yescharacteristic
120#13063249—21no—
121#13063249—21no—
122#13063249—21no—
123#13063248—21no—
124#13063247—21no—
125#13063247—21no—
126#13063247D411yescharacteristic
127(C2×D43)⋊C8—21no—
128C8×Dic43—21no—
129C2×Q16×C43D411yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43D411yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#103×C43D411yescharacteristic
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×Q8×C43C2×D411yescharacteristic
146Q8×D43—42no—
147Q8×D43—81no—
148C2×D172C2×D411yescharacteristic
149C2×C4×D43—21no—
150C2×C4×D43—41no—
151C2×C4×D43—41no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—41no—
157C2×Dic86—41no—
158C2×Dic86—41no—
159C2×Dic86C2×D411yescharacteristic
160Q16×C43—22no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C42×C43—21no—
173C42×C43—21no—
174C42×C43C2411yescharacteristic
175#10621885—81no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—41no—
178(C2×D43)⋊C4—41no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—41no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202Dic172—82no—
203#10621873Q1614yescomplemented
204C8×D43—81no—
205C22×D43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43#13712yes—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43H(5,𝔽2)11yescharacteristic
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224D172—21no—
225D172C2×Q1612yes—
226C4×D43—41no—
227C4×D43—41no—
228C4×D43—82no—
229C4×D43—161no—
230Dic86—21no—
231Dic86—41no—
232Dic86—41no—
233Dic86—82no—
234Dic86—81no—
235Dic86—81no—
236Dic86—81no—
237Dic86—161no—
238Dic86—161no—
239Dic86C2×Q1612yes—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43C2×Q1612yes—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#19813—431nomaximal, Sylow
250C22×C43D4211yescharacteristic
251C2×D43—22no—
252C2×D43—41no—
253C2×D43—41no—
254C4×C43—22no—
255C4×C43—21no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43C22×Q1611yescharacteristic
260C4×C43C2×#13711yescharacteristic
261C4×C43#57711yescharacteristic
262C4×C43#57811yescharacteristic
263Dic43—22no—
264Dic43—41no—
265Dic43—41no—
266Dic43—81no—
267Dic43—81no—
268Dic43—81no—
269Dic43—81no—
270#3385—431no—
271Q8×Q16—431no—
272Q8×SD16—431no—
273#3299—431no—
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#1584D4311yescharacteristic, complemented
284SD16⋊C8—431no—
285C2×C43#326611yescharacteristic
286C2×C43D4×Q1611yescharacteristic
287C2×C43#328811yescharacteristic
288D43—42no—
289Q82—431no—
290Q82—431no—
291#554—431no—
292D4×Q8—431no—
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#487—431no—
302#484—861no—
303#479—861no—
304#477—431no—
305#477—431no—
306#477—431no—
307#477—431no—
308#477—861no—
309#477—861no—
310#476—431no—
311#476—431no—
312#476—861no—
313#475—431no—
314#475—861no—
315#474—861no—
316#467—861no—
317#462—431no—
318#451—861no—
319#446C2×D4311yescharacteristic
320C8×Q8—431no—
321C8×Q8C2×D4311yescharacteristic
322#440—861no—
323C4×Q16—861no—
324C4×Q16C2×D4311yescharacteristic
325C4×SD16—431no—
326C4×SD16—861no—
327C8×D4—431no—
328C2×#103—861no—
329#335—431no—
330#335C2×D4311yescharacteristic
331#333—431no—
332#333—431no—
333#333—431no—
334#332—431no—
335Q8⋊C8—431no—
336Q8⋊C8C2×D4311yescharacteristic
337Q8⋊C8C2×D4311yescharacteristic
338D4⋊C8—431no—
339#322C2×D4311yescharacteristic
340C43#1981311yescharacteristic, complemented, Sylow
341C22×Q8—861no—
342C2×Q16—861no—
343C2×Q16—1721no—
344C2×Q16D17211yescharacteristic
345C2×SD16—431no—
346C22×C8—861no—
347C4⋊Q8—431no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351C4⋊Q8—861no—
352C4⋊Q8—861no—
353C4⋊Q8—861no—
354C4⋊Q8—861no—
355C4⋊Q8—861no—
356C4⋊Q8—1721no—
357C4⋊Q8—1721no—
358#125—861no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8—1721no—
362C22⋊Q8—1721no—
363C4×Q8—431no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8C22×D4311yescharacteristic
369C4×Q8C22×D4311yescharacteristic
370C4×D4—431no—
371C4×D4—861no—
372C4×D4—861no—
373C2×C4⋊C4—861no—
374#107—861no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#107—861no—
382#107D17211yescharacteristic
383#106—431no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—431no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—1721no—
406#103D17211yescharacteristic
407#103D17211yescharacteristic
408#102—431no—
409#102—861no—
410#102—861no—
411C22⋊C8—861no—
412#97—21no—
413C4×C8—21no—
414C4×C8—861no—
415C4×C8C22×D4311yescharacteristic
416C4×C8C22×D4311yescharacteristic
417C4×C8C22×D4311yescharacteristic
418C2×Q8—431no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—3441no—
424C2×Q8—1721no—
425C2×Q8—1721no—
426C2×Q8—1721no—
427C2×Q8—1722no—
428C2×Q8C2×D17211yescharacteristic
429C2×Q8C2×D17211yescharacteristic
430C2×D4—431no—
431C22×C4—861no—
432C22×C4—1721no—
433C22×C4—1721no—
434Q16—22no—
435Q16—3442no—
436Q16—3441no—
437SD16—434no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—3441no—
444C2×C8C2×D17211yescharacteristic
445C2×C8C2×D17211yescharacteristic
446C2×C8D4×D4311yescharacteristic
447C2×C8D4×D4311yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—431no—
451C4⋊C4—431no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—1721no—
462C4⋊C4—1721no—
463C4⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4C2×D17211yescharacteristic
469C4⋊C4C2×D17211yescharacteristic
470C22⋊C4—861no—
471C22⋊C4—1721no—
472C22⋊C4—1721no—
473C42—21no—
474C42—21no—
475C42—861no—
476C42—1721no—
477C42—1721no—
478C42C23×D4311yescharacteristic
479C23—861no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—432no—
484Q8—861no—
485Q8—3441no—
486Q8—3441no—
487Q8—3441no—
488Q8—3442no—
489Q8—1721no—
490Q8—1721no—
491Q8—6881no—
492Q8—6881no—
493Q8#1306335812yes—
494D4—432no—
495D4—861no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—3442no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—6881no—
511C2×C4C2×D4×D4311yescharacteristic
512C2×C4C22×D17211yescharacteristic
513C2×C4#1306337111yescharacteristic
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—1721no—
521C8—1721no—
522C8Q16×D4312yes—
523C22—862no—
524C22—1721no—
525C22—1721no—
526C22D4×D17211yescharacteristic
527C4—21no—
528C4—22no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—862no—
533C4—3441no—
534C4—3441no—
535C4—3441no—
536C4—3441no—
537C4—1721no—
538C4—1721no—
539C4C2×Q16×D4311yescharacteristic
540C4C2×#1306335811yescharacteristic
541C4#1458371111yescharacteristic
542C4#1458371311yescharacteristic
543C2—1722no—
544C2#1914611011yescharacteristic
545C2Q16×D17211yescharacteristic
546C2#1914636211yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1584C2
socleC22×C43D42
prime radicalC2×D172C2×D4
hypercenter#1584D43
hypocenterC43#19813
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1584

Complements

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

NH ≅ G/Ntype
2. Q16×Dic86C2semidirect
5. #19134272C2semidirect
6. #19134101C2semidirect
7. #19134054C2semidirect
8. #19133999C2semidirect
10. #19133818C2semidirect
12. #19133737C2semidirect
15. C43×#1584C2semidirect
203. #10621873Q16semidirect
283. #1584D43semidirect
340. C43#19813semidirect

Maximal subgroups

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

subgroupindex
#191475072
Q16×Dic862
Q8×#106218732
#191464732
#191342722
#191341012
#191340542
#191339992
#191339952
#191338182
#191337622
#191337372
#191337322
#191334092
C43×#15842
#1981343