Finite Group Databasebeta

← #25080334

Subgroups — #25080334

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#19145933C211yesmaximal, characteristic
2#19145776C211yesmaximal, characteristic
3#19145340C211yesmaximal, characteristic, complemented
4#19143599C211yesmaximal, characteristic
5#19134178C211yesmaximal, characteristic, complemented
6#19134150C211yesmaximal, characteristic, complemented
7#19134095C211yesmaximal, characteristic, complemented
8#19134085C211yesmaximal, characteristic, complemented
9#19134047C211yesmaximal, characteristic, complemented
10#19134019C211yesmaximal, characteristic, complemented
11#19133978C211yesmaximal, characteristic, complemented
12#19133966C211yesmaximal, characteristic, complemented
13#19133259C211yesmaximal, characteristic, complemented
14#19133253C211yesmaximal, characteristic, complemented
15C43×#1565C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583301—21no—
20#14583297C2211yescharacteristic
21#14583279C2211yescharacteristic
22#14583254—21no—
23#14583250C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583241—21no—
26#14583224—21no—
27#14583207—21no—
28#14583195C2211yescharacteristic
29#14583190C2211yescharacteristic
30#14583185C2211yescharacteristic
31#14583185C2211yescharacteristic
32#14583180C2211yescharacteristic
33#14583180C2211yescharacteristic
34#14583157—21no—
35#14583157—21no—
36#14583140—21no—
37#14583128—21no—
38#14583122—21no—
39#14583110C2211yescharacteristic
40#14583105C2211yescharacteristic
41#14583029C2211yescharacteristic
42C8×Dic86C2211yescharacteristic
43#14583007—21no—
44#14583007—21no—
45#14582978C2211yescharacteristic
46#14582975—21no—
47#14582968—21no—
48C8×D172C2211yescharacteristic
49#14582961—21no—
50#14582952C2211yescharacteristic
51#14582856—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×Dic172—21no—
68C2×Dic172—21no—
69C2×Dic172—21no—
70C2×#10621873—21no—
71C2×#10621872—21no—
72C2×C8×D43—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063319—21no—
78#13063317—21no—
79#13063317—21no—
80#13063317D411yescharacteristic
81#13063313D411yescharacteristic
82#13063308—21no—
83#13063304—21no—
84#13063304—21no—
85#13063304—21no—
86#13063304—21no—
87#13063304D411yescharacteristic
88#13063299D411yescharacteristic
89C4×Dic86—21no—
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86—21no—
93C4×Dic86C2311yescharacteristic
94C4×D172C2311yescharacteristic
95C4×C22⋊D43—21no—
96#13063284—21no—
97#13063284—21no—
98#13063282—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063257—21no—
103#13063257—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126#13063235—21no—
127C4×C43⋊C8—21no—
128C8×Dic43—21no—
129C2×M16×C43D411yescharacteristic
130C2×M16×C43D411yescharacteristic
131C22×C8×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139#97×C43D411yescharacteristic
140#97×C43D411yescharacteristic
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×D172C2×D411yescharacteristic
149C2×C4×D43—21no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C2×D411yescharacteristic
155M16×C43—22no—
156M16×C43—41no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—81no—
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C42×C43C2×D411yescharacteristic
167C42×C43C2×D411yescharacteristic
168C42×C43#4111yescharacteristic
169C42×C43C2411yescharacteristic
170C22⋊Dic43—21no—
171C22⋊Dic43—41no—
172C22⋊Dic43—41no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C2×D411yescharacteristic
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200Dic172—42no—
201Dic172—42no—
202Dic172—81no—
203#10621873—81no—
204#10621872—42no—
205C8×D43—42no—
206C23×C43#12111yescharacteristic
207C22×D43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43#12111yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C22⋊D43—81no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227D172—21no—
228D172—21no—
229C4×D43—41no—
230C4×D43—41no—
231Dic86—21no—
232Dic86—21no—
233Dic86—41no—
234Dic86—41no—
235Dic86—41no—
236Dic86—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—81no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43#13512yes—
248C43⋊C8—41no—
249C43⋊C8—41no—
250#19251—431nomaximal, Sylow
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43C2×#12111yescharacteristic
255C2×D43—41no—
256C2×D43—41no—
257C2×D43—41no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43C2×#13511yescharacteristic
263C4×C43#57511yescharacteristic
264C4×C43#57711yescharacteristic
265C4×C43#57811yescharacteristic
266Dic43—41no—
267Dic43—41no—
268Dic43—41no—
269Dic43—81no—
270Dic43—81no—
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#1670—431no—
285#1565D4311yescharacteristic, complemented
286#1544—431no—
287#1542—431no—
288C2×C43—41no—
289C2×C43#303511yescharacteristic
290C2×C43#306311yescharacteristic
291C2×C43#306911yescharacteristic
292D43—81no—
293#533—431no—
294#533—431no—
295#529—431no—
296#499—861no—
297#498—431no—
298#494—431no—
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#475—431no—
308#475—431no—
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×Q8—431no—
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#431C2×D4311yescharacteristic
329C2×C4⋊C8C2×D4311yescharacteristic
330#405—861no—
331C4×M16C2×D4311yescharacteristic
332#335C2×D4311yescharacteristic
333#335C2×D4311yescharacteristic
334#334C2×D4311yescharacteristic
335#334C2×D4311yescharacteristic
336#333—431no—
337#333—431no—
338#332—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344C43#1925111yescharacteristic, complemented, Sylow
345C2×Q16—861no—
346C2×Q16—861no—
347C2×Q16—861no—
348C2×SD16—861no—
349C2×M16—861no—
350C2×M16D17211yescharacteristic
351C2×M16D17211yescharacteristic
352C22×C8—21no—
353C22×C8—861no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
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—431no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8—861no—
375C4×D4—431no—
376C4×D4—861no—
377#117—861no—
378#117—861no—
379#117—861no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—21no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—861no—
399#103—861no—
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—21no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414#97—861no—
415#97D17211yescharacteristic
416#97D17211yescharacteristic
417C4×C8—21no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8C22×D4311yescharacteristic
421C4×C8C22×D4311yescharacteristic
422C2×Q8—431no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×D4—431no—
428C2×D4—861no—
429C22×C4—861no—
430C22×C4C2×D17211yescharacteristic
431C22×C4D4×D4311yescharacteristic
432C22×C4#1062190211yescharacteristic
433Q16—3441no—
434Q16—1722no—
435Q16—1722no—
436SD16—3441no—
437M16—22no—
438M16—41no—
439M16—1722no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—81no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—1722no—
448C2×C8C2×D17211yescharacteristic
449C2×C8C2×D17211yescharacteristic
450C2×C8C2×D17211yescharacteristic
451C2×C8C2×D17211yescharacteristic
452C4⋊C4—431no—
453C4⋊C4—431no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C22⋊C4—861no—
471C22⋊C4—861no—
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—861no—
478C42—1721no—
479C42—1721no—
480C42C2×D17211yescharacteristic
481C42D4×D4311yescharacteristic
482C42#1062190211yescharacteristic
483C42C23×D4311yescharacteristic
484C23—861no—
485C23#1306330011yescharacteristic
486Q8—861no—
487Q8—861no—
488Q8—3441no—
489Q8—1721no—
490Q8—1721no—
491Q8—1721no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495D4—861no—
496D4—861no—
497D4—3441no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4#1306330011yescharacteristic
513C2×C4#1306330011yescharacteristic
514C2×C4#1306330011yescharacteristic
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C22×D17211yescharacteristic
517C2×C4C2×#1062190211yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—1721no—
526C8—1721no—
527C8#1306334712yes—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—1721no—
532C22—1721no—
533C22—1721no—
534C22C2×#1306330011yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—3441no—
540C4—3441no—
541C4—3441no—
542C4—3441no—
543C4—1721no—
544C4—1721no—
545C4—1721no—
546C4C2×#1306334711yescharacteristic
547C4#1458369911yescharacteristic
548C4#1458370911yescharacteristic
549C4#1458371511yescharacteristic
550C2—41no—
551C2—3441no—
552C2#1914405211yescharacteristic
553C2#1914428711yescharacteristic
554C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1565C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#1565D43
hypocenterC43#19251
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
3. #19145340C2semidirect
5. #19134178C2semidirect
6. #19134150C2semidirect
7. #19134095C2semidirect
8. #19134085C2semidirect
9. #19134047C2semidirect
10. #19134019C2semidirect
11. #19133978C2semidirect
12. #19133966C2semidirect
13. #19133259C2semidirect
14. #19133253C2semidirect
15. C43×#1565C2semidirect
285. #1565D43semidirect
344. C43#19251semidirect

Maximal subgroups

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

subgroupindex
#191459332
#191457762
#191453402
#191435992
#191341782
#191341502
#191340952
#191340852
#191340472
#191340192
#191339782
#191339662
#191332592
#191332532
C43×#15652
#1925143