Finite Group Databasebeta

← #25086807

Subgroups — #25086807

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#19147504C211yesmaximal, characteristic
2Q8×#10621885C211yesmaximal, characteristic, complemented
3Q8×#10621884C211yesmaximal, characteristic
4#19146468C211yesmaximal, characteristic
5#19134270C211yesmaximal, characteristic, complemented
6#19134104C211yesmaximal, characteristic, complemented
7#19134055C211yesmaximal, characteristic, complemented
8#19133997C211yesmaximal, characteristic, complemented
9#19133993C211yesmaximal, characteristic
10#19133819C211yesmaximal, characteristic, complemented
11#19133762C211yesmaximal, characteristic
12#19133726C211yesmaximal, characteristic
13#19133442C211yesmaximal, characteristic, complemented
14#19133410C211yesmaximal, characteristic
15C43×#1633C211yesmaximal, characteristic, complemented
16Q8×Dic86C2211yescharacteristic
17#14583610C2211yescharacteristic
18Q8×D172C2211yescharacteristic
19#14583307—21no—
20#14583302—21no—
21#14583302C2211yescharacteristic
22#14583302C2211yescharacteristic
23#14583295—21no—
24#14583295C2211yescharacteristic
25#14583251C2211yescharacteristic
26#14583250C2211yescharacteristic
27#14583236—21no—
28#14583204—21no—
29#14583194—21no—
30#14583194C2211yescharacteristic
31#14583191—21no—
32#14583191C2211yescharacteristic
33#14583190C2211yescharacteristic
34#14583186—21no—
35#14583186C2211yescharacteristic
36#14583184—21no—
37#14583184C2211yescharacteristic
38#14583178—21no—
39#14583141—21no—
40#14583110C2211yescharacteristic
41#14583056—21no—
42#14583026C2211yescharacteristic
43Q8×C43⋊C8C2211yescharacteristic
44Q8×C43⋊C8C2211yescharacteristic
45#14583002—21no—
46C4×#10621885—21no—
47C4×#10621885C2211yescharacteristic
48C4×#10621884—21no—
49C4×#10621884C2211yescharacteristic
50#14582964C2211yescharacteristic
51#103×D43—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582631C2211yescharacteristic
58#14582628C2211yescharacteristic
59#14582621C2211yescharacteristic
60Q82×C43C2211yescharacteristic
61C43×#494C2211yescharacteristic
62C43×#477C2211yescharacteristic
63C43×#477C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×Q8⋊C8C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Dic172—21no—
69C2×#10621885D411yescharacteristic
70C2×#10621884D411yescharacteristic
71C2×C8×D43—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—41no—
78#13063316—21no—
79#13063305—21no—
80#13063305—21no—
81#13063305—41no—
82#13063301—41no—
83Q8×Dic43—21no—
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86C4×D172—21no—
87C4×D172C2311yescharacteristic
88#13063287—21no—
89C4⋊C4×D43—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258D411yescharacteristic
97#13063257—21no—
98#13063256—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256D411yescharacteristic
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108#13063250—21no—
109#13063250—41no—
110#13063249—21no—
111#13063249—21no—
112#13063249D411yescharacteristic
113#13063249D411yescharacteristic
114#13063248—21no—
115#13063248—21no—
116#13063248—21no—
117#13063248D411yescharacteristic
118#13063247—21no—
119#13063245—21no—
120#13063245D411yescharacteristic
121(C2×D43)⋊C8—21no—
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C2×Q16×C43—41no—
128C4⋊Q8×C43—21no—
129C4⋊Q8×C43—21no—
130C4⋊Q8×C43—41no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135C4×Q8×C43C2311yescharacteristic
136C4×Q8×C43C2311yescharacteristic
137#107×C43—21no—
138#107×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#103×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149Q8×D43—42no—
150Q8×D43—81no—
151C2×D172C2×D411yescharacteristic
152C2×C4×D43—21no—
153C2×C4×D43—41no—
154C2×C4×D43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—41no—
158C2×Dic86—41no—
159C2×Dic86C2×D411yescharacteristic
160Q16×C43—82no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—41no—
177C42×C43C2411yescharacteristic
178#10621885—22no—
179#10621884Q1614yescomplemented
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
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—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203Dic172—81no—
204C8×D43—81no—
205C22×D43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—81no—
209Q8×C43—81no—
210Q8×C43—161no—
211Q8×C43C2×Q1612yes—
212Q8×C43#13712yes—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43H(5,𝔽2)11yescharacteristic
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227D172—21no—
228D172C2×Q1612yes—
229C4×D43—41no—
230C4×D43—41no—
231C4×D43—82no—
232C4×D43—161no—
233Dic86—21no—
234Dic86—21no—
235Dic86—41no—
236Dic86—41no—
237Dic86—82no—
238Dic86—81no—
239Dic86—161no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43—41no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8C2×Q1612yes—
249#19813—431nomaximal, Sylow
250C22×C43D4211yescharacteristic
251C2×D43—22no—
252C2×D43—41no—
253C2×D43—41no—
254C4×C43—22no—
255C4×C43—22no—
256C4×C43—21no—
257C4×C43—41no—
258C4×C43—41no—
259C4×C43—81no—
260C4×C43—81no—
261C4×C43C22×Q1611yescharacteristic
262C4×C43C2×#13711yescharacteristic
263C4×C43#57711yescharacteristic
264C4×C43#57811yescharacteristic
265Dic43—41no—
266Dic43—41no—
267Dic43—41no—
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#1633D4311yescharacteristic, complemented
282#1632—431no—
283#1584—431no—
284SD16⋊C8—431no—
285C2×C43#326611yescharacteristic
286C2×C43D4×Q1611yescharacteristic
287C2×C43#328811yescharacteristic
288D43—42no—
289Q82—431no—
290Q82C2×D4311yescharacteristic
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#494C2×D4311yescharacteristic
300#487—431no—
301#487—431no—
302#484—861no—
303#479—861no—
304#477—431no—
305#477—431no—
306#477—861no—
307#477—861no—
308#477C2×D4311yescharacteristic
309#477C2×D4311yescharacteristic
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#446—431no—
320C8×Q8—431no—
321C8×Q8—431no—
322#440—861no—
323C4×Q16—431no—
324C4×Q16—861no—
325C4×SD16—431no—
326C4×SD16—861no—
327C8×D4—431no—
328C2×#103—861no—
329#335—431no—
330#335—431no—
331#333—431no—
332#333—431no—
333#333C2×D4311yescharacteristic
334#332—431no—
335Q8⋊C8—431no—
336Q8⋊C8C2×D4311yescharacteristic
337Q8⋊C8C2×D4311yescharacteristic
338D4⋊C8—431no—
339#322—431no—
340C43#1981311yescharacteristic, complemented, Sylow
341C22×Q8—861no—
342C2×Q16—41no—
343C2×Q16—431no—
344C2×Q16—861no—
345C2×SD16—431no—
346C22×C8—861no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—41no—
350C4⋊Q8—431no—
351C4⋊Q8—431no—
352C4⋊Q8—861no—
353C4⋊Q8—861no—
354C4⋊Q8—861no—
355C4⋊Q8—1721no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#125—861no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8—1721no—
362C22⋊Q8—1721no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—431no—
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—21no—
375#107—21no—
376#107—431no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#107—861no—
382#107—861no—
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—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—21no—
397#103—21no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—1721no—
408#102—431no—
409#102—861no—
410#102—861no—
411C22⋊C8—861no—
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—431no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—3441no—
425C2×Q8—1721no—
426C2×Q8—1721no—
427C2×Q8—1722no—
428C2×Q8D4×D4311yescharacteristic
429C2×Q8D4×D4311yescharacteristic
430C2×D4—431no—
431C22×C4—861no—
432C22×C4—1721no—
433C22×C4—1721no—
434Q16—82no—
435Q16—862no—
436Q16—3441no—
437SD16—434no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—431no—
442C2×C8—431no—
443C2×C8—431no—
444C2×C8—431no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—3441no—
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—431no—
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⋊C4—1721no—
468C4⋊C4D4×D4311yescharacteristic
469C4⋊C4D4×D4311yescharacteristic
470C22⋊C4—861no—
471C22⋊C4—1721no—
472C22⋊C4—1721no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—861no—
477C42—1721no—
478C42C23×D4311yescharacteristic
479C23—861no—
480Q8—21no—
481Q8—21no—
482Q8—81no—
483Q8—81no—
484Q8—161no—
485Q8—861no—
486Q8—861no—
487Q8—3441no—
488Q8—3442no—
489Q8—1721no—
490Q8—1721no—
491Q8—6881no—
492Q8Q16×D4312yes—
493Q8#1306335712yes—
494D4—432no—
495D4—861no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—3442no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—6881no—
511C2×C4C2×D4×D4311yescharacteristic
512C2×C4C2×D4×D4311yescharacteristic
513C2×C4#1306337011yescharacteristic
514C8—41no—
515C8—41no—
516C8—41no—
517C8—432no—
518C8—861no—
519C8—861no—
520C8—861no—
521C8—1721no—
522C8—1721no—
523C22—862no—
524C22—1721no—
525C22—1721no—
526C22#1458353111yescharacteristic
527C4—22no—
528C4—22no—
529C4—21no—
530C4—41no—
531C4—41no—
532C4—81no—
533C4—81no—
534C4—3441no—
535C4—3441no—
536C4—1721no—
537C4—1721no—
538C4—1721no—
539C4C2×Q16×D4311yescharacteristic
540C4C2×#1306335711yescharacteristic
541C4#1458370811yescharacteristic
542C4#1458371511yescharacteristic
543C2—1722no—
544C2#1914609811yescharacteristic
545C2#1914634011yescharacteristic
546C2#1914635611yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1633C2
socleC22×C43D42
prime radicalC2×D172C2×D4
hypercenter#1633D43
hypocenterC43#19813
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1633

Complements

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

NH ≅ G/Ntype
2. Q8×#10621885C2semidirect
5. #19134270C2semidirect
6. #19134104C2semidirect
7. #19134055C2semidirect
8. #19133997C2semidirect
10. #19133819C2semidirect
13. #19133442C2semidirect
15. C43×#1633C2semidirect
179. #10621884Q16semidirect
281. #1633D43semidirect
340. C43#19813semidirect

Maximal subgroups

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

subgroupindex
#191475042
Q8×#106218852
Q8×#106218842
#191464682
#191342702
#191341042
#191340552
#191339972
#191339932
#191338192
#191337622
#191337262
#191334422
#191334102
C43×#16332
#1981343