Finite Group Databasebeta

← #25086845

Subgroups — #25086845

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147512C211yesmaximal, characteristic
2#19147466C211yesmaximal, characteristic
3#19146473C211yesmaximal, characteristic
4#19134270C211yesmaximal, characteristic, complemented
5#19134099C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19133987C211yesmaximal, characteristic, complemented
8#19133957C211yesmaximal, characteristic
9#19133842C211yesmaximal, characteristic
10#19133837C211yesmaximal, characteristic, complemented
11#19133807C211yesmaximal, characteristic
12#19133753C211yesmaximal, characteristic, complemented
13#19133446C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic
15C43×#3395C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17Q8×D172C2211yescharacteristic
18#14583309—21no—
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583298—21no—
22#14583295C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583236—21no—
26#14583206—21no—
27#14583196—21no—
28#14583196—21no—
29#14583194—21no—
30#14583194C2211yescharacteristic
31#14583194C2211yescharacteristic
32#14583184C2211yescharacteristic
33#14583176C2211yescharacteristic
34#14583176C2211yescharacteristic
35#14583139—21no—
36#14583109C2211yescharacteristic
37#14583053—21no—
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14582997—21no—
41C4×#10621884—21no—
42C4×#10621884C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#103×D43—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#557C2211yescharacteristic
57C43×#557C2211yescharacteristic
58C43×#494—21no—
59C43×#494C2211yescharacteristic
60C43×#462—21no—
61C43×#462—21no—
62C43×#462C2211yescharacteristic
63C43×#462C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×Q16×C43—21no—
66C4×Q16×C43C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×#10621885—21no—
69C2×#10621884D411yescharacteristic
70C2×C8×D43—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063317—21no—
75#13063305—21no—
76#13063305—41no—
77#13063303—41no—
78#13063301—21no—
79C4×D172—21no—
80C4×D172—21no—
81C4×D172C2311yescharacteristic
82C4⋊C4×D43—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—41no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256D411yescharacteristic
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249D411yescharacteristic
105#13063248—21no—
106#13063248—41no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111#13063236—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43—21no—
118C2×Q16×C43—21no—
119C2×Q16×C43D411yescharacteristic
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43C2311yescharacteristic
123C4⋊Q8×C43C2311yescharacteristic
124#125×C43—21no—
125#125×C43—21no—
126#125×C43—41no—
127#125×C43—41no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131C4×Q8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4×Q8×C43C2311yescharacteristic
135#107×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
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—
158Q16×C43—41no—
159Q16×C43—42no—
160Q16×C43—81no—
161Q16×C43—81no—
162Q16×C43—81no—
163C2×C8×C43—21no—
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—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C4⋊C4×C43C2×D411yescharacteristic
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43—41no—
187C42×C43C2411yescharacteristic
188#10621885—81no—
189#10621884Q1614yescomplemented
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—41no—
198C4⋊Dic43C2×D411yescharacteristic
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C8×D43—81no—
208C22×D43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43C2×Q1612yes—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43H(5,𝔽2)11yescharacteristic
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233D172—21no—
234D172C2×Q1612yes—
235C4×D43—41no—
236C4×D43—41no—
237C4×D43—82no—
238C4×D43—161no—
239Dic86—41no—
240Dic86—41no—
241Dic86—82no—
242Dic86—81no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—41no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8C2×Q1612yes—
252#19815—431nomaximal, Sylow
253C22×C43D4211yescharacteristic
254C2×D43—22no—
255C2×D43—41no—
256C2×D43—41no—
257C4×C43—22no—
258C4×C43—21no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43C22×Q1611yescharacteristic
267C4×C43#57511yescharacteristic
268C4×C43#57611yescharacteristic
269C4×C43#57811yescharacteristic
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273#3395D4311yescharacteristic, complemented
274#3386—431no—
275#3381—431no—
276#3299—431no—
277#1723—431no—
278#1692—431no—
279#1684—431no—
280#1674—431no—
281#1669—431no—
282#1649—431no—
283#1648—431no—
284#1644—431no—
285#1636—431no—
286#1584—431no—
287SD16⋊C8—431no—
288C2×C43#326811yescharacteristic
289C2×C43D4×Q1611yescharacteristic
290C2×C43#328911yescharacteristic
291D43—42no—
292#557C2×D4311yescharacteristic
293#557C2×D4311yescharacteristic
294#554—431no—
295D4×Q8—431no—
296#501—861no—
297#500—431no—
298#500—431no—
299#499—861no—
300#498—431no—
301#494—21no—
302#494C2×D4311yescharacteristic
303#487—431no—
304#487—431no—
305#484—861no—
306#479—861no—
307#478—861no—
308#478—861no—
309#477—431no—
310#477—431no—
311#477—861no—
312#475—431no—
313#474—431no—
314#474—431no—
315#467—861no—
316#462—21no—
317#462—21no—
318#462—431no—
319#462C2×D4311yescharacteristic
320#462C2×D4311yescharacteristic
321#451—861no—
322#446—431no—
323C8×Q8—431no—
324C8×Q8C2×D4311yescharacteristic
325#440—861no—
326C4×Q16—21no—
327C4×Q16C2×D4311yescharacteristic
328C4×SD16—431no—
329C4×SD16—861no—
330C8×D4—431no—
331C2×#103—861no—
332#335—431no—
333#335—431no—
334#333—431no—
335#332—431no—
336#332—431no—
337#332—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341D4⋊C8—431no—
342#322—431no—
343C43#1981511yescharacteristic, complemented, Sylow
344C22×Q8—861no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—861no—
350C2×Q16C22⋊D4311yescharacteristic
351C2×SD16—431no—
352C22×C8—861no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—861no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#125—21no—
361#125—21no—
362#125—41no—
363#125—41no—
364#125—861no—
365C22⋊Q8—861no—
366C22⋊Q8—861no—
367C22⋊Q8—1721no—
368C22⋊Q8—1721no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C22×D4311yescharacteristic
374C4×Q8C22×D4311yescharacteristic
375C4×Q8C22×D4311yescharacteristic
376C4×D4—431no—
377C4×D4—861no—
378C4×D4—861no—
379C2×C4⋊C4—861no—
380#107—861no—
381#107—861no—
382#107—861no—
383#107—861no—
384#107—861no—
385#107—861no—
386#107—1721no—
387#107C22⋊D4311yescharacteristic
388#106—431no—
389#106—861no—
390#106—861no—
391#106—861no—
392C4⋊C8—21no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8C22×D4311yescharacteristic
399#103—21no—
400#103—21no—
401#103—431no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—1721no—
409#103C22⋊D4311yescharacteristic
410#103C22⋊D4311yescharacteristic
411#102—431no—
412#102—861no—
413#102—861no—
414C22⋊C8—861no—
415#97—861no—
416C4×C8—21no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—861no—
420C4×C8C22×D4311yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—3441no—
426C2×Q8—1721no—
427C2×Q8—1722no—
428C2×Q8D4×D4311yescharacteristic
429C2×Q8C2×C22⋊D4311yescharacteristic
430C2×Q8C2×C22⋊D4311yescharacteristic
431C2×D4—431no—
432C22×C4—861no—
433C22×C4—1721no—
434C22×C4—1721no—
435Q16—41no—
436Q16—42no—
437Q16—81no—
438Q16—81no—
439Q16—81no—
440Q16—3441no—
441SD16—434no—
442C2×C8—21no—
443C2×C8—431no—
444C2×C8—431no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—3441no—
450C2×C8C2×C22⋊D4311yescharacteristic
451C2×C8C2×C22⋊D4311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—431no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4D4×D4311yescharacteristic
474C4⋊C4C2×C22⋊D4311yescharacteristic
475C4⋊C4C2×C22⋊D4311yescharacteristic
476C22⋊C4—861no—
477C22⋊C4—1721no—
478C22⋊C4—1721no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42—41no—
484C42C23×D4311yescharacteristic
485C23—861no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—3441no—
496Q8—3442no—
497Q8—1721no—
498Q8—1721no—
499Q8Q16×D4312yes—
500D4—432no—
501D4—861no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—861no—
511C2×C4—3442no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—6881no—
517C2×C4C2×D4×D4311yescharacteristic
518C2×C4C22×C22⋊D4311yescharacteristic
519C2×C4#1306337011yescharacteristic
520C8—21no—
521C8—21no—
522C8—41no—
523C8—432no—
524C8—861no—
525C8—1721no—
526C8—1721no—
527C8—1721no—
528C8—1721no—
529C22—862no—
530C22—1721no—
531C22—1721no—
532C22D4×C22⋊D4311yescharacteristic
533C4—22no—
534C4—21no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—3441no—
543C4—3441no—
544C4—1721no—
545C4C2×Q16×D4311yescharacteristic
546C4#1458369711yescharacteristic
547C4#1458370211yescharacteristic
548C4#1458371211yescharacteristic
549C2—1722no—
550C2#1914613611yescharacteristic
551C2Q16×C22⋊D4311yescharacteristic
552C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3395C2
socleC22×C43D42
prime radicalC2×D172C2×D4
hypercenter#3395D43
hypocenterC43#19815
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3395

Complements

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

NH ≅ G/Ntype
4. #19134270C2semidirect
5. #19134099C2semidirect
6. #19134053C2semidirect
7. #19133987C2semidirect
10. #19133837C2semidirect
12. #19133753C2semidirect
13. #19133446C2semidirect
15. C43×#3395C2semidirect
189. #10621884Q16semidirect
273. #3395D43semidirect
343. C43#19815semidirect

Maximal subgroups

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

subgroupindex
#191475122
#191474662
#191464732
#191342702
#191340992
#191340532
#191339872
#191339572
#191338422
#191338372
#191338072
#191337532
#191334462
#191334052
C43×#33952
#1981543