Finite Group Databasebeta

← #25067187

Subgroups — #25067187

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145197C211yesmaximal, characteristic
2#19143567C211yesmaximal, characteristic
3#19143524C211yesmaximal, characteristic, complemented
4#19133503C211yesmaximal, characteristic, complemented
5#19133501C211yesmaximal, characteristic, complemented
6#19133498C211yesmaximal, characteristic, complemented
7#19133494C211yesmaximal, characteristic, complemented
8C8×Dic172C211yesmaximal, characteristic, complemented
9C8×#10621885C211yesmaximal, characteristic, complemented
10C8×#10621883C211yesmaximal, characteristic, complemented
11#19133359C211yesmaximal, characteristic, complemented
12#19133066C211yesmaximal, characteristic, complemented
13#19133057C211yesmaximal, characteristic
14C8×#10621872C211yesmaximal, characteristic, complemented
15C8×SD16×C43C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17#14583431C2211yescharacteristic
18#14583306C411yescharacteristic
19#14583290C411yescharacteristic
20#14583266C411yescharacteristic
21#14583257C411yescharacteristic
22#14583158C411yescharacteristic
23#14583156C411yescharacteristic
24#14583144C411yescharacteristic
25#14583142C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583028—21no—
28#14583026C2211yescharacteristic
29#14583026C2211yescharacteristic
30C8×Dic86—21no—
31C8×Dic86C2211yescharacteristic
32C8×Dic86C2211yescharacteristic
33C4×Dic172C2211yescharacteristic
34C4×#10621885C2211yescharacteristic
35C4×#10621883C2211yescharacteristic
36#14582977C2211yescharacteristic
37#14582973—21no—
38C8×C22⋊D43—21no—
39#14582957—21no—
40#14582955C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582924—21no—
43#14582921C2211yescharacteristic
44#14582854—21no—
45#14582853—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
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#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×Dic172C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621877—21no—
71C2×#10621872—21no—
72C2×#10621872C2×C411yescharacteristic
73C2×#10621872C2×C411yescharacteristic
74C2×C8×D43D411yescharacteristic
75C2×C8×D43D411yescharacteristic
76#13063324C2×C411yescharacteristic
77#13063323C2×C411yescharacteristic
78#13063318—21no—
79#13063316C2×C411yescharacteristic
80#13063315—21no—
81#13063312C2×C411yescharacteristic
82#13063307—21no—
83#13063305C2×C411yescharacteristic
84#13063305C2×C411yescharacteristic
85#13063303—21no—
86#13063301C2×C411yescharacteristic
87#13063296C2×C411yescharacteristic
88C4×Dic86—21no—
89C4×Dic86C2311yescharacteristic
90C4×Dic86C2311yescharacteristic
91C4×C22⋊D43—21no—
92#13063284—21no—
93#13063282—21no—
94C42×D43C2311yescharacteristic
95#13063259C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
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#13063236—21no—
117#13063235—21no—
118#13063235—21no—
119#13063235—21no—
120#13063235C2×C411yescharacteristic
121#13063235C2×C411yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×SD16×C43C2×C411yescharacteristic
130C22×C8×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—
140C4×C8×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—
148C2×C4×D43C22×C411yescharacteristic
149C2×C4×D43C2×D411yescharacteristic
150C2×C4×D43#4111yescharacteristic
151C2×Dic86—21no—
152C2×Dic86C22×C411yescharacteristic
153C2×Dic86C22×C411yescharacteristic
154SD16×C43—22no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—42no—
159C2×C8×C43C22×C411yescharacteristic
160C2×C8×C43C22×C411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43C22×C411yescharacteristic
165C4⋊C4×C43C22×C411yescharacteristic
166C22⋊C4×C43—21no—
167C42×C43—21no—
168C42×C43C2411yescharacteristic
169C22⋊Dic43—21no—
170C22⋊Dic43—21no—
171C22⋊Dic43—21no—
172#10621885—22no—
173#10621883—22no—
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⋊Dic43C22×C411yescharacteristic
181C4⋊Dic43C22×C411yescharacteristic
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43C22×C411yescharacteristic
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43#4111yescharacteristic
194#10621877—42no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202Dic172—22no—
203#10621872—22no—
204#10621872—22no—
205#10621872—42no—
206C8×D43—22no—
207C8×D43—41no—
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—42no—
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—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86—21no—
239Dic86—42no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43#13112yes—
246C8×C43#13712yes—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8#13112yes—
254#17965—431nomaximal, Sylow
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43C2×C4×D411yescharacteristic
259C2×D43—21no—
260C2×D43—21no—
261C2×D43—21no—
262C4×C43—21no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43C2×#13111yescharacteristic
267C4×C43C2×#13111yescharacteristic
268C4×C43C2×#13711yescharacteristic
269C4×C43#57511yescharacteristic
270Dic43—21no—
271Dic43—21no—
272Dic43—21no—
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277#3172—431no—
278#2966—431no—
279#2960—431no—
280#1593—431no—
281#1593—431no—
282#1592—431no—
283#1592—431no—
284C8×Q16—431no—
285C8×Q16—431no—
286C8×SD16—431no—
287C8×SD16D4311yescharacteristic, complemented
288#1569—431no—
289#1497—431no—
290#1495—431no—
291C8×M16—431no—
292C2×C43—81no—
293C2×C43#293111yescharacteristic
294C2×C43C4×#13711yescharacteristic
295C2×C43#295511yescharacteristic
296D43—41no—
297#533—431no—
298#529—431no—
299#501—431no—
300#497—431no—
301#491—431no—
302#489—431no—
303#470—431no—
304#470—431no—
305#468—431no—
306#468—431no—
307#446—431no—
308#446—431no—
309#446—431no—
310#446—861no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—861no—
314C8×Q8C2×D4311yescharacteristic
315C4×Q16—431no—
316C4×Q16—431no—
317C4×SD16—431no—
318C4×SD16C2×D4311yescharacteristic
319#436—431no—
320#435—861no—
321C8×D4—861no—
322C8×D4C2×D4311yescharacteristic
323#433—861no—
324#432—431no—
325#431—431no—
326#424—861no—
327#423—431no—
328#405—861no—
329#405—861no—
330C4×M16—431no—
331C2×C4×C8—431no—
332#335—431no—
333#335—431no—
334#334—431no—
335#334C2×D4311yescharacteristic
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8C2×D4311yescharacteristic
342D4⋊C8—431no—
343D4⋊C8C2×D4311yescharacteristic
344#322—431no—
345#322—431no—
346C82—431no—
347C82C2×D4311yescharacteristic
348C43#1796511yescharacteristic, complemented, Sylow
349C2×Q16—431no—
350C2×Q16—431no—
351C2×SD16—431no—
352C2×SD16C4×D4311yescharacteristic
353C2×M16—431no—
354C2×M16—431no—
355C2×M16—861no—
356C2×M16—861no—
357C22×C8—21no—
358C22×C8—431no—
359C22×C8—431no—
360C4⋊Q8—431no—
361C4⋊Q8—431no—
362#126—861no—
363#125—431no—
364#125—861no—
365#124—431no—
366#123—861no—
367C22⋊Q8—431no—
368C22⋊Q8—431no—
369C22⋊Q8—431no—
370C22⋊Q8—861no—
371#121—431no—
372C4×Q8—431no—
373C4×Q8—431no—
374C4×Q8—861no—
375C4×Q8C22×D4311yescharacteristic
376C4×D4—861no—
377C4×D4C22×D4311yescharacteristic
378#117—861no—
379#117—861no—
380C2×C42—431no—
381#107—431no—
382#107—431no—
383#106—431no—
384#106C4×D4311yescharacteristic
385C4⋊C8—21no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103C4×D4311yescharacteristic
403#102—431no—
404#102C4×D4311yescharacteristic
405C22⋊C8—21no—
406C22⋊C8—861no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409#97—431no—
410#97—431no—
411#97—861no—
412#97—861no—
413#97—861no—
414#97—861no—
415C4×C8—21no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426C2×Q8—431no—
427C2×Q8—431no—
428C2×Q8—861no—
429C2×Q8C2×C4×D4311yescharacteristic
430C2×D4—861no—
431C2×D4C2×C4×D4311yescharacteristic
432C22×C4—21no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—431no—
436Q16—862no—
437Q16—862no—
438SD16—22no—
439SD16—862no—
440M16—862no—
441M16—862no—
442M16—1722no—
443M16—1722no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—862no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—1721no—
457C2×C8C2×C4×D4311yescharacteristic
458C2×C8C2×C4×D4311yescharacteristic
459C2×C8D4×D4311yescharacteristic
460C2×C8D4×D4311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—431no—
463C4⋊C4—431no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4C2×C4×D4311yescharacteristic
475C4⋊C4C2×C4×D4311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C42—21no—
484C42—431no—
485C42—431no—
486C42—431no—
487C42—861no—
488C42—861no—
489C42C23×D4311yescharacteristic
490C23—21no—
491C23—431no—
492Q8—21no—
493Q8—21no—
494Q8—861no—
495Q8—861no—
496Q8—861no—
497Q8—861no—
498Q8—1722no—
499D4—21no—
500D4—21no—
501D4—1722no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—431no—
508C2×C4—431no—
509C2×C4—431no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—1721no—
519C2×C4C22×C4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4#41×D4311yescharacteristic
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—432no—
528C8—861no—
529C8—861no—
530C8—861no—
531C8—1721no—
532C8—1721no—
533C8—1721no—
534C8#1306333112yes—
535C8#1306335412yes—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—861no—
540C22—861no—
541C22—861no—
542C22C4×D4×D4311yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—861no—
548C4—861no—
549C4—861no—
550C4—1721no—
551C4—1721no—
552C4—1721no—
553C4—1721no—
554C4#131×D4311yescharacteristic
555C4C2×#1306333111yescharacteristic
556C4C2×#1306335411yescharacteristic
557C4#1458369611yescharacteristic
558C2—81no—
559C2—1721no—
560C2#1914330211yescharacteristic
561C2C4×#1306335411yescharacteristic
562C2#1914349311yescharacteristic
subgroupG/H
centerC2×C8D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×SD16×C43C2
socleC22×C43C2×C4×D4
prime radical#13063296C2×C4
cosocleC42×C43C24
hypercenterC8×SD16D43
hypocenterC43#17965
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
3. #19143524C2semidirect
4. #19133503C2semidirect
5. #19133501C2semidirect
6. #19133498C2semidirect
7. #19133494C2semidirect
8. C8×Dic172C2semidirect
9. C8×#10621885C2semidirect
10. C8×#10621883C2semidirect
11. #19133359C2semidirect
12. #19133066C2semidirect
14. C8×#10621872C2semidirect
15. C8×SD16×C43C2semidirect
287. C8×SD16D43semidirect
348. C43#17965semidirect

Maximal subgroups

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

subgroupindex
#191451972
#191435672
#191435242
#191335032
#191335012
#191334982
#191334942
C8×Dic1722
C8×#106218852
C8×#106218832
#191333592
#191330662
#191330572
C8×#106218722
C8×SD16×C432
#1796543