Finite Group Databasebeta

← #25086840

Subgroups — #25086840

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#19147600C211yesmaximal, characteristic, complemented
2#19147516C211yesmaximal, characteristic
3#19147470C211yesmaximal, characteristic
4#19134274C211yesmaximal, characteristic, complemented
5#19134103C211yesmaximal, characteristic, complemented
6#19134050C211yesmaximal, characteristic, complemented
7#19133987C211yesmaximal, characteristic, complemented
8#19133960C211yesmaximal, characteristic
9#19133844C211yesmaximal, characteristic
10#19133835C211yesmaximal, characteristic, complemented
11#19133809C211yesmaximal, characteristic
12#19133751C211yesmaximal, characteristic, complemented
13#19133446C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic
15C43×#3299C211yesmaximal, characteristic
16#14583627C2211yescharacteristic
17#14583627C2211yescharacteristic
18#14583305—21no—
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583298—21no—
22#14583295C2211yescharacteristic
23#14583279C2211yescharacteristic
24#14583277—21no—
25#14583249C2211yescharacteristic
26#14583203—21no—
27#14583199—21no—
28#14583199—21no—
29#14583191—21no—
30#14583191C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583179C2211yescharacteristic
33#14583179C2211yescharacteristic
34#14583109C2211yescharacteristic
35#14583109C2211yescharacteristic
36#14583108—21no—
37#14583108—21no—
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14582999—21no—
42#14582993—21no—
43C4×#10621883—21no—
44C4×#10621883C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
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×Dic172—21no—
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883D411yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063323—21no—
75#13063323—21no—
76#13063317—21no—
77#13063317—21no—
78#13063315—41no—
79#13063315—41no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—41no—
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—41no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
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×Dic86C2×D411yescharacteristic
158Q16×C43—41no—
159Q16×C43—81no—
160C2×C8×C43—21no—
161C2×C8×C43—81no—
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
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×C43—41no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43C2411yescharacteristic
182#10621885—81no—
183#10621885—81no—
184#10621883Q1614yescomplemented
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
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—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206Dic172—42no—
207Dic172—81no—
208C23×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—81no—
216Q8×C43—82no—
217D4×C43—21no—
218D4×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—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—82no—
229C2×C4×C43—161no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237Dic86—21no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86C2×Q1612yes—
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×C43—22no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43D4211yescharacteristic
257C4×C43—21no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43C22×Q1611yescharacteristic
266C4×C43#57511yescharacteristic
267C4×C43#57611yescharacteristic
268C4×C43#57811yescharacteristic
269Dic43—22no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273#3395—431no—
274#3386—431no—
275#3381—431no—
276#3299D4311yescharacteristic
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—42no—
289C2×C43#326811yescharacteristic
290C2×C43D4×Q1611yescharacteristic
291C2×C43#328911yescharacteristic
292#557—431no—
293#557—431no—
294#554C2×D4311yescharacteristic
295D4×Q8C2×D4311yescharacteristic
296#501—861no—
297#500—431no—
298#500—431no—
299#499—861no—
300#498—431no—
301#494—431no—
302#494—861no—
303#487—431no—
304#487C2×D4311yescharacteristic
305#484—21no—
306#479—861no—
307#478—861no—
308#478—861no—
309#477—431no—
310#477—861no—
311#477C2×D4311yescharacteristic
312#475—431no—
313#474—431no—
314#474—431no—
315#467—21no—
316#462—431no—
317#462—431no—
318#462—861no—
319#462—861no—
320#462C2×D4311yescharacteristic
321#451—21no—
322#446—431no—
323C8×Q8—431no—
324C8×Q8—431no—
325#440—861no—
326C4×Q16—861no—
327C4×Q16C2×D4311yescharacteristic
328C4×SD16—431no—
329C4×SD16—861no—
330C8×D4C2×D4311yescharacteristic
331C2×#103—21no—
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—21no—
345C2×Q16—21no—
346C2×Q16—861no—
347C2×Q16—861no—
348C2×Q16—861no—
349C2×Q16—861no—
350C2×Q16C22⋊D4311yescharacteristic
351C2×SD16—431no—
352C22×C8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8—861no—
357C4⋊Q8—861no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#125—21no—
361#125—861no—
362#125—861no—
363#125—1721no—
364#125—1721no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—41no—
368C22⋊Q8—41no—
369C4×Q8—431no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8C22×D4311yescharacteristic
375C4×Q8C22×D4311yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4C22×D4311yescharacteristic
379C2×C4⋊C4—21no—
380#107—21no—
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—431no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8C22×D4311yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—431no—
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—21no—
415#97—861no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8C22×D4311yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—41no—
424C2×Q8—42no—
425C2×Q8—81no—
426C2×Q8—431no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8C2×C22⋊D4311yescharacteristic
430C2×Q8C2×C22⋊D4311yescharacteristic
431C2×D4D4×D4311yescharacteristic
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435Q16—41no—
436Q16—81no—
437Q16—3441no—
438Q16—3441no—
439Q16—3441no—
440Q16—1722no—
441SD16—434no—
442C2×C8—21no—
443C2×C8—81no—
444C2×C8—431no—
445C2×C8—431no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
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—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—431no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4D4×D4311yescharacteristic
474C4⋊C4C2×C22⋊D4311yescharacteristic
475C4⋊C4C2×C22⋊D4311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—861no—
482C42—1721no—
483C42—1721no—
484C42C23×D4311yescharacteristic
485C23—21no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—82no—
494Q8—432no—
495Q8—861no—
496Q8—1721no—
497Q8—1721no—
498Q8—1721no—
499Q8—1721no—
500D4—21no—
501D4Q16×D4312yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—82no—
512C2×C4—161no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—1721no—
516C2×C4—1721no—
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—22no—
530C22—41no—
531C22—41no—
532C22D4×C22⋊D4311yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—81no—
540C4—81no—
541C4—862no—
542C4—3441no—
543C4—3441no—
544C4—1721no—
545C4C2×Q16×D4311yescharacteristic
546C4#1458369711yescharacteristic
547C4#1458370211yescharacteristic
548C4#1458371211yescharacteristic
549C2—42no—
550C2#1914613111yescharacteristic
551C2Q16×C22⋊D4311yescharacteristic
552C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3299C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenter#3299D43
hypocenterC43#19815
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3299

Complements

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

NH ≅ G/Ntype
1. #19147600C2semidirect
4. #19134274C2semidirect
5. #19134103C2semidirect
6. #19134050C2semidirect
7. #19133987C2semidirect
10. #19133835C2semidirect
12. #19133751C2semidirect
13. #19133446C2semidirect
184. #10621883Q16semidirect
343. C43#19815semidirect

Maximal subgroups

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

subgroupindex
#191476002
#191475162
#191474702
#191342742
#191341032
#191340502
#191339872
#191339602
#191338442
#191338352
#191338092
#191337512
#191334462
#191334072
C43×#32992
#1981543