Finite Group Databasebeta

← #25066823

Subgroups — #25066823

Order 11008.

604 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144607C211yesmaximal, characteristic
2#19143561C211yesmaximal, characteristic, complemented
3#19133490C211yesmaximal, characteristic, complemented
4#19133485C211yesmaximal, characteristic, complemented
5#19133483C211yesmaximal, characteristic, complemented
6#19133478C211yesmaximal, characteristic, complemented
7#19133445C211yesmaximal, characteristic, complemented
8#19133438C211yesmaximal, characteristic, complemented
9#19133431C211yesmaximal, characteristic, complemented
10#19133424C211yesmaximal, characteristic, complemented
11#19133376C211yesmaximal, characteristic, complemented
12#19133027C211yesmaximal, characteristic, complemented
13#19133003C211yesmaximal, characteristic, complemented
14#19132878C211yesmaximal, characteristic, complemented
15C43×#2966C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583237C411yescharacteristic
18#14583220C411yescharacteristic
19#14583203C411yescharacteristic
20#14583196C411yescharacteristic
21#14583118C411yescharacteristic
22#14583111C411yescharacteristic
23#14583059C411yescharacteristic
24#14583042C411yescharacteristic
25#14583029C2211yescharacteristic
26#14583029C2211yescharacteristic
27C4×#10621885C2211yescharacteristic
28C4×#10621884C2211yescharacteristic
29C4×#10621883C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582978C2211yescharacteristic
33#14582970—21no—
34#14582970—21no—
35#14582952C2211yescharacteristic
36#14582952C2211yescharacteristic
37#14582952C2211yescharacteristic
38#14582950—21no—
39C4×#10621872—21no—
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46#14582629C2211yescharacteristic
47#14582629C2211yescharacteristic
48D4⋊(C43⋊C8)C2211yescharacteristic
49D4⋊(C43⋊C8)C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582620C2211yescharacteristic
53#14582620C2211yescharacteristic
54C8×C43⋊C8C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436C2211yescharacteristic
60C43×#435—21no—
61C8×D4×C43—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#432C2211yescharacteristic
65C43×#405—21no—
66C2×C4×C8×C43C2211yescharacteristic
67C2×#10621898C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621872—21no—
73C2×#10621872—21no—
74C4×Dic86C2×C411yescharacteristic
75C4×Dic86C2311yescharacteristic
76C4×D172C2×C411yescharacteristic
77C4×D172C2311yescharacteristic
78C4×C22⋊D43—21no—
79C4×C22⋊D43—21no—
80#13063284C2×C411yescharacteristic
81#13063282—21no—
82C42×D43—21no—
83#13063258C2×C411yescharacteristic
84#13063258C2×C411yescharacteristic
85#13063256C2×C411yescharacteristic
86#13063256C2×C411yescharacteristic
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)C2×C411yescharacteristic
89C4⋊(C43⋊C8)C2×C411yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94#13063249C2×C411yescharacteristic
95#13063249C2×C411yescharacteristic
96#13063248C2×C411yescharacteristic
97#13063248C2×C411yescharacteristic
98#13063246C2×C411yescharacteristic
99#13063246C2×C411yescharacteristic
100#13063245C2×C411yescharacteristic
101#13063245C2×C411yescharacteristic
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)C2×C411yescharacteristic
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106(C2×D43)⋊C8—21no—
107(C2×D43)⋊C8—21no—
108#13063235—21no—
109#13063235—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×M16×C43—21no—
116C22×C8×C43—21no—
117C22×C8×C43D411yescharacteristic
118C22×C8×C43D411yescharacteristic
119#126×C43—21no—
120#125×C43C2×C411yescharacteristic
121#124×C43C2×C411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43C2×C411yescharacteristic
124#121×C43C2×C411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—21no—
152#10621898—41no—
153#10621898—41no—
154C2×D172C22×C411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×Dic86C22×C411yescharacteristic
159M16×C43—42no—
160C2×C8×C43—22no—
161C2×C8×C43—22no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—42no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C42×C43—21no—
181C42×C43C22×C411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43#4111yescharacteristic
184C42×C43C2411yescharacteristic
185C22⋊Dic43—21no—
186#10621885—41no—
187#10621884—41no—
188#10621883—41no—
189#10621882—41no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43C22×C411yescharacteristic
193C4⋊Dic43C22×C411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207#10621872—42no—
208#10621872—42no—
209C23×C43—21no—
210C23×C43C4×D411yescharacteristic
211C22×D43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—42no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43C4×D411yescharacteristic
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—42no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237D172—21no—
238D172—21no—
239C4×D43—42no—
240C4×D43—42no—
241C4×D43—41no—
242C4×D43—41no—
243Dic86—21no—
244Dic86—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43#13512yes—
250C8×C43#13512yes—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#17932—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43C2×C4×D411yescharacteristic
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43#56811yescharacteristic
278C4×C43#56811yescharacteristic
279C4×C43C2×#13511yescharacteristic
280C4×C43C2×#13511yescharacteristic
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284#3102—431no—
285#2966D4311yescharacteristic, complemented
286#2965—431no—
287#1591—431no—
288#1590—431no—
289#1590—431no—
290#1589—431no—
291#1584—431no—
292#1583—431no—
293#1582—431no—
294#1581—431no—
295#1572—431no—
296#1488—431no—
297#1482—431no—
298#1450—431no—
299C2×C43—41no—
300C2×C43—81no—
301C2×C43#293011yescharacteristic
302C2×C43C4×#13511yescharacteristic
303C2×C43#295511yescharacteristic
304D43—81no—
305#529C2×D4311yescharacteristic
306C4×#41—431no—
307#485—431no—
308#482—431no—
309#479—431no—
310#478—431no—
311#464—431no—
312#463—431no—
313#452—431no—
314#449—431no—
315#446—431no—
316#446—431no—
317#446C2×D4311yescharacteristic
318C8×Q8C2×D4311yescharacteristic
319C4×Q16—431no—
320C4×SD16—431no—
321C4×SD16—431no—
322C4×D8—431no—
323#436—431no—
324#436—431no—
325#436C2×D4311yescharacteristic
326#435—21no—
327#435—861no—
328#435—861no—
329C8×D4—21no—
330C8×D4C2×D4311yescharacteristic
331#433—21no—
332#432C2×D4311yescharacteristic
333#431—431no—
334#431—431no—
335#431—431no—
336#431—861no—
337#405—21no—
338C4×M16—861no—
339C2×C4×C8C2×D4311yescharacteristic
340#335—431no—
341#335—431no—
342#334—431no—
343#334—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350D4⋊C8—431no—
351D4⋊C8—431no—
352#322—431no—
353#322—431no—
354C82—431no—
355C82—431no—
356C43#1793211yescharacteristic, complemented, Sylow
357C2×#41—431no—
358C2×Q16—431no—
359C2×SD16—431no—
360C2×SD16—431no—
361C2×D8—431no—
362C2×M16—21no—
363C2×M16—861no—
364C2×M16—861no—
365C22×C8—21no—
366C22×C8C22⋊D4311yescharacteristic
367C22×C8C22⋊D4311yescharacteristic
368#126—21no—
369#125C4×D4311yescharacteristic
370#124C4×D4311yescharacteristic
371#123—21no—
372C22⋊Q8C4×D4311yescharacteristic
373#121C4×D4311yescharacteristic
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8C22×D4311yescharacteristic
377C4×D4—21no—
378C4×D4—431no—
379C4×D4—431no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4C22×D4311yescharacteristic
383#117—21no—
384#117—431no—
385#117—861no—
386C2×C42—861no—
387C2×C42C22×D4311yescharacteristic
388#107—431no—
389#107—431no—
390#106—431no—
391#106—431no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8C22×D4311yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403#103—431no—
404#103—431no—
405#103—431no—
406#103—431no—
407#102—431no—
408#102—431no—
409#102—431no—
410#102—431no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—431no—
415C22⋊C8—431no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420#97—21no—
421#97—21no—
422#97—861no—
423#97—861no—
424C4×C8—21no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8C22⋊D4311yescharacteristic
431C4×C8C22⋊D4311yescharacteristic
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434#41—1721no—
435#41—1721no—
436C2×Q8—431no—
437C2×Q8C2×C4×D4311yescharacteristic
438C2×D4—21no—
439C2×D4—431no—
440C2×D4—861no—
441C2×D4C2×C4×D4311yescharacteristic
442C22×C4—21no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4C2×C4×D4311yescharacteristic
447C22×C4#1062189811yescharacteristic
448C22×C4C2×C22⋊D4311yescharacteristic
449Q16—1721no—
450SD16—1721no—
451SD16—1721no—
452D8—1721no—
453M16—42no—
454M16—1722no—
455M16—1722no—
456C2×C8—22no—
457C2×C8—22no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8C2×C22⋊D4311yescharacteristic
470C2×C8C2×C22⋊D4311yescharacteristic
471C2×C8C2×C22⋊D4311yescharacteristic
472C2×C8C2×C22⋊D4311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—431no—
478C4⋊C4—431no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4C2×C4×D4311yescharacteristic
482C4⋊C4C2×C4×D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C42—21no—
492C42—861no—
493C42—861no—
494C42—861no—
495C42C2×C4×D4311yescharacteristic
496C42#1062189811yescharacteristic
497C42C2×C22⋊D4311yescharacteristic
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—861no—
501C23C4×C22⋊D4311yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—861no—
505Q8—861no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—861no—
510D4—861no—
511D4—1722no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—1722no—
526C2×C4—1722no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4C4×C22⋊D4311yescharacteristic
530C2×C4C4×C22⋊D4311yescharacteristic
531C2×C4C4×C22⋊D4311yescharacteristic
532C2×C4C22×C4×D4311yescharacteristic
533C2×C4C22×C22⋊D4311yescharacteristic
534C2×C4C2×#1062189811yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—861no—
540C8—861no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C8—1721no—
547C8#1306334512yes—
548C8#1306334512yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22C2×C4×C22⋊D4311yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—1721no—
567C4—1721no—
568C4—1721no—
569C4#1458366411yescharacteristic
570C4#1458366411yescharacteristic
571C4C2×#1306334511yescharacteristic
572C4C2×#1306334511yescharacteristic
573C2—41no—
574C2—81no—
575C2—3441no—
576C2#1914329611yescharacteristic
577C2C4×#1306334511yescharacteristic
578C2#1914349611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2966C2
socleC22×C43C2×C4×D4
prime radical#14583042C4
cosocleC42×C43C24
hypercenter#2966D43
hypocenterC43#17932
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #19143561C2semidirect
3. #19133490C2semidirect
4. #19133485C2semidirect
5. #19133483C2semidirect
6. #19133478C2semidirect
7. #19133445C2semidirect
8. #19133438C2semidirect
9. #19133431C2semidirect
10. #19133424C2semidirect
11. #19133376C2semidirect
12. #19133027C2semidirect
13. #19133003C2semidirect
14. #19132878C2semidirect
15. C43×#2966C2semidirect
285. #2966D43semidirect
356. C43#17932semidirect

Maximal subgroups

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

subgroupindex
#191446072
#191435612
#191334902
#191334852
#191334832
#191334782
#191334452
#191334382
#191334312
#191334242
#191333762
#191330272
#191330032
#191328782
C43×#29662
#1793243