Finite Group Databasebeta

← #25067728

Subgroups — #25067728

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#19144673C211yesmaximal, characteristic
2#19143602C211yesmaximal, characteristic
3#19143547C211yesmaximal, characteristic, complemented
4#19133501C211yesmaximal, characteristic, complemented
5#19133465C211yesmaximal, characteristic, complemented
6#19133453C211yesmaximal, characteristic, complemented
7#19133443C211yesmaximal, characteristic, complemented
8#19133436C211yesmaximal, characteristic, complemented
9#19133404C211yesmaximal, characteristic, complemented
10C8×Dic172C211yesmaximal, characteristic, complemented
11#19133382C211yesmaximal, characteristic, complemented
12#19133057C211yesmaximal, characteristic
13#19132988C211yesmaximal, characteristic, complemented
14#19132889C211yesmaximal, characteristic, complemented
15C43×#1590C211yesmaximal, characteristic, complemented
16#14583431C2211yescharacteristic
17C4×Q8×D43C2211yescharacteristic
18#14583231C411yescharacteristic
19#14583211C411yescharacteristic
20#14583209C411yescharacteristic
21#14583208C411yescharacteristic
22#14583120C411yescharacteristic
23#14583119C411yescharacteristic
24#14583056C411yescharacteristic
25#14583036C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583028—21no—
28#14583027—21no—
29#14583026C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31C8×Dic86C2211yescharacteristic
32#14583023C2211yescharacteristic
33C4×Dic172C2211yescharacteristic
34C4×#10621885C2211yescharacteristic
35C4×#10621883C2211yescharacteristic
36#14582975—21no—
37#14582967—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582957—21no—
40#14582951C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582921—21no—
44#14582921C2211yescharacteristic
45#14582857—21no—
46#14582851—21no—
47C4×#10621872C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582629C2211yescharacteristic
55#14582629C2211yescharacteristic
56D4⋊(C43⋊C8)C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582620C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×Q8×D43C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621872—21no—
72C2×#10621872D411yescharacteristic
73C2×#10621872D411yescharacteristic
74C22×C43⋊C8—21no—
75#13063318—21no—
76#13063316C2×C411yescharacteristic
77#13063312C2×C411yescharacteristic
78#13063307—21no—
79#13063305C2×C411yescharacteristic
80#13063296C2×C411yescharacteristic
81Q8×Dic43C2×C411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84C4×Dic86C2311yescharacteristic
85#13063290—21no—
86#13063290C2×C411yescharacteristic
87C4×C22⋊D43—21no—
88#13063284—21no—
89C4⋊C4×D43—21no—
90C4⋊C4×D43C2×C411yescharacteristic
91C42×D43—21no—
92C42×D43C2311yescharacteristic
93#13063259C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063256C2×C411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8C2×C411yescharacteristic
106Dic43⋊C8C2×C411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063249C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111#13063248C2×C411yescharacteristic
112#13063246C2×C411yescharacteristic
113C22⋊(C43⋊C8)—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8C2×C411yescharacteristic
117(C2×D43)⋊C8C2×C411yescharacteristic
118#13063236—21no—
119#13063235—21no—
120#13063235D411yescharacteristic
121#13063235D411yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C2×C22⋊D43—21no—
148Q8×D43—22no—
149Q8×D43—41no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43C22×C411yescharacteristic
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43#4111yescharacteristic
155C2×Dic86—21no—
156C2×Dic86C22×C411yescharacteristic
157C2×Dic86C22×C411yescharacteristic
158SD16×C43—41no—
159M16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43C22×C411yescharacteristic
169C4⋊C4×C43C22×C411yescharacteristic
170C22⋊C4×C43—21no—
171C42×C43—21no—
172C42×C43C2411yescharacteristic
173C22⋊Dic43—21no—
174C22⋊Dic43—21no—
175C22⋊Dic43—21no—
176#10621885—41no—
177#10621883—22no—
178(C2×D43)⋊C4—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43C22×C411yescharacteristic
183C4⋊Dic43C22×C411yescharacteristic
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43C22×C411yescharacteristic
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43#4111yescharacteristic
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—42no—
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—22no—
205#10621872—22no—
206#10621872—41no—
207#10621872—42no—
208C23×C43—21no—
209C22×D43C4×D411yescharacteristic
210Q8×C43—21no—
211Q8×C43—21no—
212D4×C43—21no—
213D4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C23×C411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C22⋊D43—81no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43C4×D411yescharacteristic
228C2×Dic43C4×D411yescharacteristic
229C2×Dic43C4×D411yescharacteristic
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—41no—
235C4×D43—42no—
236C4×D43—81no—
237Dic86—21no—
238Dic86—21no—
239Dic86—21no—
240Dic86—42no—
241Dic86#13112yes—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43#13712yes—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256#18012—431nomaximal, Sylow
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43C2×C4×D411yescharacteristic
261C2×D43—21no—
262C2×D43—21no—
263C2×D43—21no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43C2×#13111yescharacteristic
269C4×C43#56811yescharacteristic
270C4×C43C2×#13711yescharacteristic
271C4×C43#57511yescharacteristic
272Dic43—22no—
273Dic43—21no—
274Dic43—21no—
275Dic43—21no—
276Dic43—41no—
277Dic43—41no—
278Dic43—41no—
279#3108—431no—
280#2969—431no—
281Q8×M16—431no—
282#1593—431no—
283#1590D4311yescharacteristic, complemented
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#1453—431no—
294C2×C43—81no—
295C2×C43#293311yescharacteristic
296C2×C43C4×#13711yescharacteristic
297C2×C43#295711yescharacteristic
298D43—41no—
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—861no—
312#446—861no—
313#446C2×D4311yescharacteristic
314C8×Q8—431no—
315C8×Q8—431no—
316C8×Q8—431no—
317C4×Q16—431no—
318C4×Q16—431no—
319C4×SD16—431no—
320C4×SD16C2×D4311yescharacteristic
321#436—861no—
322#436C2×D4311yescharacteristic
323#435—861no—
324C8×D4—431no—
325#433—861no—
326#431—431no—
327#431—431no—
328#431—431no—
329#423—431no—
330#423—861no—
331#405—861no—
332C4×M16—431no—
333C4×M16—861no—
334#335—431no—
335#335—431no—
336#334—431no—
337#334C2×D4311yescharacteristic
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343Q8⋊C8C2×D4311yescharacteristic
344D4⋊C8—431no—
345D4⋊C8C2×D4311yescharacteristic
346#322—431no—
347#322—431no—
348#322—431no—
349C82C2×D4311yescharacteristic
350C43#1801211yescharacteristic, complemented, Sylow
351C22×Q8—431no—
352C2×Q16—431no—
353C2×Q16—431no—
354C2×SD16—431no—
355C2×SD16C4×D4311yescharacteristic
356C2×M16—21no—
357C2×M16—431no—
358C2×M16—431no—
359C2×M16—861no—
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—861no—
372C4×Q8—861no—
373C4×Q8C22×D4311yescharacteristic
374C4×D4—861no—
375C4×D4C22×D4311yescharacteristic
376#117—861no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C42—431no—
380C2×C42—861no—
381#107—431no—
382#107—431no—
383#106—431no—
384#106C4×D4311yescharacteristic
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⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#103—431no—
404#103C4×D4311yescharacteristic
405#102—431no—
406#102C4×D4311yescharacteristic
407C22⋊C8—21no—
408C22⋊C8—431no—
409C22⋊C8—431no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413#97—21no—
414#97—431no—
415#97—431no—
416#97—861no—
417#97—861no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8C22×D4311yescharacteristic
426C4×C8C22×D4311yescharacteristic
427C4×C8C22×D4311yescharacteristic
428C2×Q8—431no—
429C2×Q8—431no—
430C2×Q8—861no—
431C2×Q8—862no—
432C2×Q8—1721no—
433C2×Q8C2×C4×D4311yescharacteristic
434C2×D4—861no—
435C2×D4C2×C4×D4311yescharacteristic
436C22×C4—21no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—861no—
441C22×C4—861no—
442Q16—862no—
443Q16—1721no—
444SD16—41no—
445SD16—862no—
446M16—42no—
447M16—862no—
448M16—1721no—
449M16—1722no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—1722no—
461C2×C8C2×C4×D4311yescharacteristic
462C2×C8C2×C4×D4311yescharacteristic
463C2×C8D4×D4311yescharacteristic
464C2×C8D4×D4311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—431no—
467C4⋊C4—431no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4C2×C4×D4311yescharacteristic
477C4⋊C4C2×C4×D4311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C42—21no—
484C42—431no—
485C42—431no—
486C42—431no—
487C42—861no—
488C42—861no—
489C42—861no—
490C42—861no—
491C42C23×D4311yescharacteristic
492C23—21no—
493C23—431no—
494Q8—21no—
495Q8—21no—
496Q8—432no—
497Q8—861no—
498Q8—861no—
499Q8—861no—
500Q8—1722no—
501D4—21no—
502D4—21no—
503D4—3441no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—431no—
510C2×C4—431no—
511C2×C4—431no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—3441no—
521C2×C4—1721no—
522C2×C4—1722no—
523C2×C4C22×C4×D4311yescharacteristic
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4#41×D4311yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C8#1306335412yes—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—861no—
544C22—861no—
545C22—861no—
546C22C4×D4×D4311yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—861no—
552C4—861no—
553C4—862no—
554C4—861no—
555C4—1721no—
556C4—1721no—
557C4—1721no—
558C4#131×D4311yescharacteristic
559C4#1458366511yescharacteristic
560C4C2×#1306335411yescharacteristic
561C4#1458369611yescharacteristic
562C2—81no—
563C2—1721no—
564C2#1914332411yescharacteristic
565C2C4×#1306335411yescharacteristic
566C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1590C2
socleC22×C43C2×C4×D4
prime radical#13063296C2×C4
cosocleC42×C43C24
hypercenter#1590D43
hypocenterC43#18012
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
3. #19143547C2semidirect
4. #19133501C2semidirect
5. #19133465C2semidirect
6. #19133453C2semidirect
7. #19133443C2semidirect
8. #19133436C2semidirect
9. #19133404C2semidirect
10. C8×Dic172C2semidirect
11. #19133382C2semidirect
13. #19132988C2semidirect
14. #19132889C2semidirect
15. C43×#1590C2semidirect
283. #1590D43semidirect
350. C43#18012semidirect

Maximal subgroups

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

subgroupindex
#191446732
#191436022
#191435472
#191335012
#191334652
#191334532
#191334432
#191334362
#191334042
C8×Dic1722
#191333822
#191330572
#191329882
#191328892
C43×#15902
#1801243