Finite Group Databasebeta

← #25080331

Subgroups — #25080331

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145935C211yesmaximal, characteristic
2#19145778C211yesmaximal, characteristic
3#19145338C211yesmaximal, characteristic, complemented
4#19143598C211yesmaximal, characteristic
5#19134175C211yesmaximal, characteristic, complemented
6#19134147C211yesmaximal, characteristic, complemented
7#19134095C211yesmaximal, characteristic, complemented
8#19134081C211yesmaximal, characteristic, complemented
9#19134045C211yesmaximal, characteristic, complemented
10#19134017C211yesmaximal, characteristic, complemented
11#19133977C211yesmaximal, characteristic, complemented
12#19133346C211yesmaximal, characteristic, complemented
13#19133258C211yesmaximal, characteristic, complemented
14#19133251C211yesmaximal, characteristic, complemented
15C43×#1670C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18#14583436C2211yescharacteristic
19#14583299—21no—
20#14583297C2211yescharacteristic
21#14583255—21no—
22#14583249C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583238—21no—
25#14583225—21no—
26#14583209—21no—
27#14583194C2211yescharacteristic
28#14583190C2211yescharacteristic
29#14583176C2211yescharacteristic
30#14583176C2211yescharacteristic
31#14583154—21no—
32#14583154—21no—
33#14583139—21no—
34#14583129—21no—
35#14583124—21no—
36#14583109C2211yescharacteristic
37#14583105C2211yescharacteristic
38#14583030C2211yescharacteristic
39#14583006—21no—
40#14583006—21no—
41#14582978—21no—
42#14582978C2211yescharacteristic
43#14582969—21no—
44#14582964C2211yescharacteristic
45#14582959—21no—
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582853—21no—
50C4×#10621872C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582650C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#494C2211yescharacteristic
61C43×#475C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621873—21no—
69C2×#10621872—21no—
70C2×#10621872D411yescharacteristic
71C2×#10621872D411yescharacteristic
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063320—21no—
77#13063316—21no—
78#13063316—21no—
79#13063316D411yescharacteristic
80#13063314D411yescharacteristic
81#13063310—21no—
82#13063305—21no—
83#13063305—21no—
84#13063301—21no—
85#13063301—21no—
86#13063301D411yescharacteristic
87#13063300D411yescharacteristic
88Q8×Dic43—21no—
89Q8×Dic43—21no—
90#13063290—21no—
91#13063290—21no—
92C4×D172—21no—
93C4×D172C2311yescharacteristic
94#13063283—21no—
95#13063283—21no—
96#13063282—21no—
97C42×D43C2311yescharacteristic
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063257—21no—
102#13063257—21no—
103#13063257—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109#13063250—21no—
110#13063249—21no—
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063249—21no—
115#13063248—21no—
116#13063247—21no—
117#13063245—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123#13063236—21no—
124#13063235D411yescharacteristic
125#13063235D411yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×Q16×C43—21no—
130C2×Q16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D172—21no—
148C2×D172C2×D411yescharacteristic
149C2×C4×D43—21no—
150C2×C4×D43C2×D411yescharacteristic
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43#4111yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155Q16×C43—42no—
156Q16×C43—42no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C2×D411yescharacteristic
168C42×C43—21no—
169C42×C43C2411yescharacteristic
170#10621885—81no—
171(C2×D43)⋊C4—21no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—41no—
177(C2×D43)⋊C4—41no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—41no—
184C4⋊Dic43—41no—
185C4⋊Dic43C2×D411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190C4×Dic43—41no—
191C4×Dic43—41no—
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200#10621873—81no—
201#10621872—22no—
202#10621872—41no—
203#10621872—42no—
204C8×D43—42no—
205C8×D43—81no—
206C22×D43—21no—
207C22×D43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×Dic43—21no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43#12111yescharacteristic
225C2×Dic43#12111yescharacteristic
226C2×Dic43#12111yescharacteristic
227D172—21no—
228D172—21no—
229D172—81no—
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—41no—
235C4×D43—41no—
236C4×D43—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—81no—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43#13512yes—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250#19251—431nomaximal, Sylow
251C22×C43C2×#12111yescharacteristic
252C2×D43—21no—
253C2×D43—21no—
254C2×D43—21no—
255C2×D43—41no—
256C2×D43—41no—
257C2×D43—41no—
258C4×C43—21no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43C2×#13511yescharacteristic
264C4×C43#57511yescharacteristic
265C4×C43#57711yescharacteristic
266C4×C43#57811yescharacteristic
267Dic43—21no—
268Dic43—21no—
269Dic43—21no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273#3248—431no—
274#3233—431no—
275#3185—431no—
276#2969—431no—
277#1704—431no—
278#1700—431no—
279#1691—431no—
280#1689—431no—
281#1683—431no—
282#1679—431no—
283#1672—431no—
284#1670D4311yescharacteristic, complemented
285#1565—431no—
286#1544—431no—
287#1542—431no—
288C2×C43#303511yescharacteristic
289C2×C43#306311yescharacteristic
290C2×C43#306911yescharacteristic
291D43—41no—
292D43—81no—
293#533—431no—
294#533—431no—
295#529—431no—
296#499—861no—
297#498—431no—
298#494C2×D4311yescharacteristic
299#488—861no—
300#487—431no—
301#487—431no—
302#485—861no—
303#482—861no—
304#479—861no—
305#477—431no—
306#476—431no—
307#475C2×D4311yescharacteristic
308#475C2×D4311yescharacteristic
309#474—431no—
310#474—431no—
311#470—861no—
312#470—861no—
313#467—861no—
314#465—861no—
315#464—861no—
316#462—431no—
317#461—431no—
318#446—431no—
319C8×Q8C2×D4311yescharacteristic
320#441—861no—
321#441—861no—
322#436—431no—
323#436—861no—
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#431—431no—
328#431—431no—
329C2×C4⋊C8—431no—
330#405—861no—
331C4×M16—431no—
332#335—431no—
333#335C2×D4311yescharacteristic
334#334—431no—
335#334—431no—
336#333—431no—
337#333—431no—
338#332—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332C2×D4311yescharacteristic
343#332C2×D4311yescharacteristic
344C43#1925111yescharacteristic, complemented, Sylow
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—861no—
348C2×SD16—861no—
349C2×M16—431no—
350C2×M16—431no—
351C2×M16—861no—
352C22×C8—861no—
353C22×C8—861no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—861no—
359#125—431no—
360#125—861no—
361#125—861no—
362#124—431no—
363#123—861no—
364C22⋊Q8—431no—
365C22⋊Q8—861no—
366C22⋊Q8—861no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369#121—431no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8C22×D4311yescharacteristic
375C4×D4—431no—
376C4×D4—861no—
377#117—861no—
378#117—861no—
379#117—861no—
380C2×C42—431no—
381#107—861no—
382#107—861no—
383#107—861no—
384#106—21no—
385#106—21no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—21no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—21no—
399#103—21no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#102—861no—
408#102—861no—
409#102—861no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414#97—431no—
415#97—431no—
416#97—861no—
417C4×C8—21no—
418C4×C8—431no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8C22×D4311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8D4×D4311yescharacteristic
427C2×D4—431no—
428C2×D4—861no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—861no—
433Q16—42no—
434Q16—42no—
435Q16—3441no—
436SD16—3441no—
437M16—862no—
438M16—1721no—
439M16—1722no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—431no—
444C2×C8—431no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—3441no—
449C2×C8—1722no—
450C2×C8D4×D4311yescharacteristic
451C2×C8D4×D4311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—431no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4D4×D4311yescharacteristic
470C22⋊C4—861no—
471C22⋊C4—861no—
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—21no—
478C42—431no—
479C42—431no—
480C42—431no—
481C42—1721no—
482C42—1721no—
483C42C23×D4311yescharacteristic
484C23—431no—
485C23—861no—
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—3441no—
493Q8—1721no—
494Q8—1721no—
495D4—861no—
496D4—861no—
497D4—3441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—431no—
503C2×C4—431no—
504C2×C4—431no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C2×D4×D4311yescharacteristic
517C2×C4#41×D4311yescharacteristic
518C8—21no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—861no—
523C8—861no—
524C8—1721no—
525C8—1721no—
526C8—1721no—
527C8#1306334612yes—
528C22—861no—
529C22—861no—
530C22—861no—
531C22—1721no—
532C22—1721no—
533C22—1721no—
534C22#121×D4311yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—81no—
539C4—81no—
540C4—861no—
541C4—861no—
542C4—861no—
543C4—3441no—
544C4—3441no—
545C4—1721no—
546C4C2×#1306334611yescharacteristic
547C4#1458369511yescharacteristic
548C4#1458370611yescharacteristic
549C4#1458371211yescharacteristic
550C2—3441no—
551C2—1721no—
552C2#1914404511yescharacteristic
553C2#1914428511yescharacteristic
554C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1670C2
socleC22×C43C2×#121
prime radical#13063300D4
hypercenter#1670D43
hypocenterC43#19251
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1670

Complements

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

NH ≅ G/Ntype
3. #19145338C2semidirect
5. #19134175C2semidirect
6. #19134147C2semidirect
7. #19134095C2semidirect
8. #19134081C2semidirect
9. #19134045C2semidirect
10. #19134017C2semidirect
11. #19133977C2semidirect
12. #19133346C2semidirect
13. #19133258C2semidirect
14. #19133251C2semidirect
15. C43×#1670C2semidirect
284. #1670D43semidirect
344. C43#19251semidirect

Maximal subgroups

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

subgroupindex
#191459352
#191457782
#191453382
#191435982
#191341752
#191341472
#191340952
#191340812
#191340452
#191340172
#191339772
#191333462
#191332582
#191332512
C43×#16702
#1925143