Finite Group Databasebeta

← #25067727

Subgroups — #25067727

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144677C211yesmaximal, characteristic
2#19143599C211yesmaximal, characteristic
3M16×Dic86C211yesmaximal, characteristic, complemented
4#19133505C211yesmaximal, characteristic, complemented
5#19133487C211yesmaximal, characteristic, complemented
6#19133468C211yesmaximal, characteristic, complemented
7#19133454C211yesmaximal, characteristic, complemented
8#19133447C211yesmaximal, characteristic, complemented
9#19133440C211yesmaximal, characteristic, complemented
10#19133409C211yesmaximal, characteristic, complemented
11C8×Dic172C211yesmaximal, characteristic, complemented
12#19133384C211yesmaximal, characteristic, complemented
13#19133061C211yesmaximal, characteristic
14#19132991C211yesmaximal, characteristic, complemented
15C43×#1453C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583230C411yescharacteristic
19#14583213C411yescharacteristic
20#14583207C411yescharacteristic
21#14583207C411yescharacteristic
22#14583122C411yescharacteristic
23#14583122C411yescharacteristic
24#14583057C411yescharacteristic
25#14583040C411yescharacteristic
26#14583029C2211yescharacteristic
27#14583029C2211yescharacteristic
28#14583029C2211yescharacteristic
29#14583027—21no—
30#14583027—21no—
31C8×Dic86C2211yescharacteristic
32C8×Dic86C2211yescharacteristic
33C8×Dic86C2211yescharacteristic
34C4×Dic172C2211yescharacteristic
35C4×Dic172C2211yescharacteristic
36C4×#10621873C2211yescharacteristic
37C4×#10621873C2211yescharacteristic
38#14582978C2211yescharacteristic
39#14582975—21no—
40#14582968—21no—
41C8×D172C2211yescharacteristic
42#14582961—21no—
43#14582952C2211yescharacteristic
44#14582923C2211yescharacteristic
45#14582922—21no—
46#14582856—21no—
47M16×Dic43—21no—
48#14582652C2211yescharacteristic
49#14582652C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582631C2211yescharacteristic
55#14582631C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58#14582628C2211yescharacteristic
59#14582628C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#322C2211yescharacteristic
64C43×#322C2211yescharacteristic
65C43×#322C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C22×Dic86C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×Dic172C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×#10621873C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×C8×D43—21no—
75#13063319—21no—
76#13063317C2×C411yescharacteristic
77#13063313C2×C411yescharacteristic
78#13063308—21no—
79#13063304C2×C411yescharacteristic
80#13063299C2×C411yescharacteristic
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86C2×C411yescharacteristic
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×Dic86C2311yescharacteristic
88C4×D172C2311yescharacteristic
89C4×C22⋊D43—21no—
90#13063282—21no—
91C2×C4⋊Dic43C2×C411yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×C4×Dic43—21no—
94#13063259C2×C411yescharacteristic
95#13063259C2×C411yescharacteristic
96#13063257C2×C411yescharacteristic
97#13063257C2×C411yescharacteristic
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063250C2×C411yescharacteristic
112#13063250C2×C411yescharacteristic
113#13063250C2×C411yescharacteristic
114#13063250C2×C411yescharacteristic
115#13063247C2×C411yescharacteristic
116#13063247C2×C411yescharacteristic
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120#13063235—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8—21no—
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C2×M16×C43D411yescharacteristic
128C2×M16×C43D411yescharacteristic
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43C2×C411yescharacteristic
132C4⋊C8×C43C2×C411yescharacteristic
133C22⋊C8×C43—21no—
134C22⋊C8×C43C2×C411yescharacteristic
135C22⋊C8×C43C2×C411yescharacteristic
136#97×C43D411yescharacteristic
137#97×C43D411yescharacteristic
138C4×C8×C43C2311yescharacteristic
139C4×C8×C43C2311yescharacteristic
140C4×C8×C43C2311yescharacteristic
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172C22×C411yescharacteristic
151C2×C4×D43—21no—
152C2×Dic86—22no—
153C2×Dic86—21no—
154C2×Dic86—41no—
155C2×Dic86C22×C411yescharacteristic
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158M16×C43—22no—
159M16×C43—41no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C22×C411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C42×C43C22×C411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43#4111yescharacteristic
173C42×C43C2411yescharacteristic
174C22⋊Dic43—21no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43C22×C411yescharacteristic
181C4⋊Dic43C22×C411yescharacteristic
182C4⋊Dic43C22×C411yescharacteristic
183C4⋊Dic43C22×C411yescharacteristic
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197#10621877—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202Dic172—22no—
203Dic172—41no—
204#10621873—22no—
205#10621873—41no—
206#10621872—42no—
207C8×D43—42no—
208C23×C43C4×D411yescharacteristic
209C22×D43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43C23×C411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C22⋊D43—81no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—42no—
230C2×Dic43—81no—
231D172—21no—
232D172—21no—
233C4×D43—41no—
234C4×D43—41no—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86—21no—
239Dic86—21no—
240Dic86—42no—
241Dic86#13112yes—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43#13712yes—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256#18012—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43C2×C4×D411yescharacteristic
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43C2×#13111yescharacteristic
269C4×C43#56811yescharacteristic
270C4×C43C2×#13711yescharacteristic
271C4×C43#57511yescharacteristic
272Dic43—22no—
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278Dic43—41no—
279#3108—431no—
280#2969—431no—
281Q8×M16—431no—
282#1593—431no—
283#1590—431no—
284#1587—431no—
285#1585—431no—
286#1584—431no—
287#1583—431no—
288SD16⋊C8—431no—
289C8×Q16—431no—
290#1574—431no—
291#1495—431no—
292#1479—431no—
293#1453D4311yescharacteristic, complemented
294C2×C43—41no—
295C2×C43#293311yescharacteristic
296C2×C43C4×#13711yescharacteristic
297C2×C43#295711yescharacteristic
298D43—81no—
299#529—431no—
300C2×C4×Q8—431no—
301#483—431no—
302#480—431no—
303#479—431no—
304#479—431no—
305#464—431no—
306#464—431no—
307#451—431no—
308#448—431no—
309#446—431no—
310#446—431no—
311#446—431no—
312#446—861no—
313#446—861no—
314C8×Q8—431no—
315C8×Q8—431no—
316C8×Q8—431no—
317C4×Q16—431no—
318C4×Q16—431no—
319C4×SD16—431no—
320C4×SD16—431no—
321#436—431no—
322#436—861no—
323#435—861no—
324C8×D4—431no—
325#433—861no—
326#431—431no—
327#431C2×D4311yescharacteristic
328#431C2×D4311yescharacteristic
329#423—431no—
330#423—861no—
331#405—861no—
332C4×M16—861no—
333C4×M16C2×D4311yescharacteristic
334#335—431no—
335#335—431no—
336#334—431no—
337#334—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343Q8⋊C8—431no—
344D4⋊C8—431no—
345D4⋊C8—431no—
346#322C2×D4311yescharacteristic
347#322C2×D4311yescharacteristic
348#322C2×D4311yescharacteristic
349C82C2×D4311yescharacteristic
350C43#1801211yescharacteristic, complemented, Sylow
351C22×Q8—431no—
352C2×Q16—431no—
353C2×Q16—431no—
354C2×SD16—431no—
355C2×SD16—431no—
356C2×M16—861no—
357C2×M16—861no—
358C2×M16D17211yescharacteristic
359C2×M16D17211yescharacteristic
360C22×C8—861no—
361#126—861no—
362#125—431no—
363#124—431no—
364#123—861no—
365C22⋊Q8—431no—
366#121—431no—
367C4×Q8—431no—
368C4×Q8—431no—
369C4×Q8—431no—
370C4×Q8—431no—
371C4×Q8—431no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×D4—431no—
375C4×D4—861no—
376#117—861no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C42—861no—
380C2×C42C22×D4311yescharacteristic
381#107—431no—
382#107—431no—
383#106—431no—
384#106—431no—
385C4⋊C8—21no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8C4×D4311yescharacteristic
398C4⋊C8C4×D4311yescharacteristic
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#103—431no—
404#103—431no—
405#102—431no—
406#102—431no—
407C22⋊C8—21no—
408C22⋊C8—861no—
409C22⋊C8—861no—
410C22⋊C8—861no—
411C22⋊C8C4×D4311yescharacteristic
412C22⋊C8C4×D4311yescharacteristic
413#97—861no—
414#97—861no—
415#97—861no—
416#97D17211yescharacteristic
417#97D17211yescharacteristic
418C4×C8—861no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426C4×C8C22×D4311yescharacteristic
427C4×C8C22×D4311yescharacteristic
428C2×Q8—431no—
429C2×Q8—431no—
430C2×Q8—431no—
431C2×Q8—862no—
432C2×Q8—861no—
433C2×Q8—1721no—
434C2×D4—431no—
435C2×D4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4C2×C4×D4311yescharacteristic
440C22×C4C2×D17211yescharacteristic
441C22×C4#1062189811yescharacteristic
442Q16—862no—
443Q16—1721no—
444SD16—862no—
445SD16—1721no—
446M16—22no—
447M16—41no—
448M16—1722no—
449M16—1722no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—1722no—
457C2×C8C2×C4×D4311yescharacteristic
458C2×C8C2×C4×D4311yescharacteristic
459C2×C8C2×C4×D4311yescharacteristic
460C2×C8C2×C4×D4311yescharacteristic
461C2×C8C2×D17211yescharacteristic
462C2×C8C2×D17211yescharacteristic
463C2×C8C2×D17211yescharacteristic
464C2×C8C2×D17211yescharacteristic
465C4⋊C4—431no—
466C4⋊C4—431no—
467C4⋊C4—431no—
468C4⋊C4—431no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C42—861no—
484C42—861no—
485C42—861no—
486C42—861no—
487C42—861no—
488C42C2×C4×D4311yescharacteristic
489C42C2×D17211yescharacteristic
490C42#1062189811yescharacteristic
491C42C23×D4311yescharacteristic
492C23—861no—
493C23C4×D17211yescharacteristic
494Q8—432no—
495Q8—861no—
496Q8—861no—
497Q8—861no—
498Q8—861no—
499Q8—861no—
500Q8—1722no—
501D4—861no—
502D4—861no—
503D4—3441no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—3441no—
517C2×C4—1722no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4C4×D17211yescharacteristic
521C2×C4C4×D17211yescharacteristic
522C2×C4C4×D17211yescharacteristic
523C2×C4C22×C4×D4311yescharacteristic
524C2×C4C22×D17211yescharacteristic
525C2×C4C2×#1062189811yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C8#1306335812yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—1721no—
544C22—1721no—
545C22—1721no—
546C22C2×C4×D17211yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—862no—
552C4—1721no—
553C4—1721no—
554C4—1721no—
555C4—1721no—
556C4—1721no—
557C4—1721no—
558C4#131×D4311yescharacteristic
559C4#1458366411yescharacteristic
560C4C2×#1306335811yescharacteristic
561C4#1458369911yescharacteristic
562C2—41no—
563C2—3441no—
564C2#1914332311yescharacteristic
565C2C4×#1306335811yescharacteristic
566C2#1914351311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1453C2
socleC22×C43C2×C4×D4
prime radical#13063299C2×C4
cosocleC42×C43C24
hypercenter#1453D43
hypocenterC43#18012
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
3. M16×Dic86C2semidirect
4. #19133505C2semidirect
5. #19133487C2semidirect
6. #19133468C2semidirect
7. #19133454C2semidirect
8. #19133447C2semidirect
9. #19133440C2semidirect
10. #19133409C2semidirect
11. C8×Dic172C2semidirect
12. #19133384C2semidirect
14. #19132991C2semidirect
15. C43×#1453C2semidirect
293. #1453D43semidirect
350. C43#18012semidirect

Maximal subgroups

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

subgroupindex
#191446772
#191435992
M16×Dic862
#191335052
#191334872
#191334682
#191334542
#191334472
#191334402
#191334092
C8×Dic1722
#191333842
#191330612
#191329912
C43×#14532
#1801243