Finite Group Databasebeta

← #25068012

Subgroups — #25068012

Order 11008.

598 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#19143755C211yesmaximal, characteristic, complemented
3#19143725C211yesmaximal, characteristic, complemented
4#19133500C211yesmaximal, characteristic, complemented
5#19133477C211yesmaximal, characteristic, complemented
6#19133476C211yesmaximal, characteristic, complemented
7#19133470C211yesmaximal, characteristic, complemented
8#19133448C211yesmaximal, characteristic, complemented
9#19133421C211yesmaximal, characteristic, complemented
10#19133404C211yesmaximal, characteristic, complemented
11#19133399C211yesmaximal, characteristic, complemented
12#19133371C211yesmaximal, characteristic, complemented
13#19132983C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#1495C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583237C411yescharacteristic
18#14583220C411yescharacteristic
19#14583203C411yescharacteristic
20#14583196C411yescharacteristic
21#14583118C411yescharacteristic
22#14583111C411yescharacteristic
23#14583059C411yescharacteristic
24#14583042C411yescharacteristic
25#14583030C2211yescharacteristic
26Q8×C43⋊C8C2211yescharacteristic
27#14583023C2211yescharacteristic
28#14583023C2211yescharacteristic
29C4×#10621885C2211yescharacteristic
30C4×#10621884C2211yescharacteristic
31C4×#10621883C2211yescharacteristic
32C4×#10621882C2211yescharacteristic
33#14582977C2211yescharacteristic
34#14582976C2211yescharacteristic
35#14582976C2211yescharacteristic
36#14582975—21no—
37#14582975—21no—
38#14582971—21no—
39D4×C43⋊C8—21no—
40D4×C43⋊C8C2211yescharacteristic
41#14582960—21no—
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582951—21no—
45#14582926—21no—
46#14582921—21no—
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582651C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#529C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#423C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621898C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77C4×Dic86C2×C411yescharacteristic
78C4×Dic86C2311yescharacteristic
79C4×D172C2×C411yescharacteristic
80C4×D172C2311yescharacteristic
81C4×C22⋊D43—21no—
82C4×C22⋊D43—21no—
83#13063284C2×C411yescharacteristic
84#13063282—21no—
85C42×D43—21no—
86#13063258C2×C411yescharacteristic
87#13063258C2×C411yescharacteristic
88#13063256C2×C411yescharacteristic
89#13063256C2×C411yescharacteristic
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2×C411yescharacteristic
94C4⋊(C43⋊C8)C2×C411yescharacteristic
95C4⋊(C43⋊C8)D411yescharacteristic
96C4⋊(C43⋊C8)D411yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101#13063249C2×C411yescharacteristic
102#13063249C2×C411yescharacteristic
103#13063248C2×C411yescharacteristic
104#13063248C2×C411yescharacteristic
105#13063246C2×C411yescharacteristic
106#13063246C2×C411yescharacteristic
107#13063245C2×C411yescharacteristic
108#13063245C2×C411yescharacteristic
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)C2×C411yescharacteristic
112C22⋊(C43⋊C8)C2×C411yescharacteristic
113C22⋊(C43⋊C8)D411yescharacteristic
114C22⋊(C43⋊C8)D411yescharacteristic
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117#13063236—21no—
118C4×C43⋊C8—21no—
119C4×C43⋊C8C2311yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—21no—
124C8×Dic43—21no—
125C2×M16×C43—21no—
126#126×C43—21no—
127#125×C43C2×C411yescharacteristic
128#124×C43C2×C411yescharacteristic
129#123×C43—21no—
130C22⋊Q8×C43C2×C411yescharacteristic
131#121×C43C2×C411yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43—21no—
134C4×D4×C43C2311yescharacteristic
135#117×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C22⋊C8×C43—21no—
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—22no—
153#10621898—41no—
154C2×D172C22×C411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×Dic86C22×C411yescharacteristic
159M16×C43—81no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C22×C411yescharacteristic
169C4⋊C4×C43C22×C411yescharacteristic
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C42×C43—21no—
176C42×C43C22×C411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C42×C43#4111yescharacteristic
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181#10621885—22no—
182#10621884—41no—
183#10621883—22no—
184#10621882—41no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187C4⋊Dic43C22×C411yescharacteristic
188C4⋊Dic43C22×C411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194#10621877—81no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—81no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207#10621872—81no—
208#10621872—81no—
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#13112yes—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#18033—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×C43C2×#13111yescharacteristic
278C4×C43#56811yescharacteristic
279C4×C43#57611yescharacteristic
280C4×C43#57811yescharacteristic
281Dic43—22no—
282Dic43—41no—
283Dic43—41no—
284#3102—431no—
285#2994—431no—
286#2991—431no—
287#1592—431no—
288#1589—431no—
289#1588—431no—
290#1588—431no—
291#1584—431no—
292#1581—431no—
293SD16⋊C8—431no—
294C8×Q16—431no—
295#1571—431no—
296#1495D4311yescharacteristic, complemented
297#1477—431no—
298#1454—431no—
299C2×C43—41no—
300C2×C43—81no—
301C2×C43#293311yescharacteristic
302C2×C43#295111yescharacteristic
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—
316C8×Q8—431no—
317C8×Q8—431no—
318C8×Q8—431no—
319C4×Q16—431no—
320C4×SD16—431no—
321C4×SD16—431no—
322C4×D8—431no—
323#436—431no—
324#436—431no—
325#436—431no—
326#436—861no—
327#436—861no—
328#435—861no—
329C8×D4—431no—
330C8×D4—861no—
331#433—861no—
332#431—431no—
333#431—431no—
334#431—861no—
335#431C2×D4311yescharacteristic
336#424—861no—
337#423—861no—
338#423C2×D4311yescharacteristic
339C2×C4⋊C8—431no—
340#335—431no—
341#335—431no—
342#335—431no—
343#335—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346Q8⋊C8C2×D4311yescharacteristic
347Q8⋊C8C2×D4311yescharacteristic
348D4⋊C8—431no—
349D4⋊C8—431no—
350D4⋊C8C2×D4311yescharacteristic
351D4⋊C8C2×D4311yescharacteristic
352#322—431no—
353#322—431no—
354#322—431no—
355C82—431no—
356C43#1803311yescharacteristic, 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—
365C2×M16—861no—
366C22×C8—861no—
367C22×C8—861no—
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—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—431no—
408#103—431no—
409#103—431no—
410#103—431no—
411#102—431no—
412#102—431no—
413#102—431no—
414#102—431no—
415C22⋊C8—21no—
416C22⋊C8—431no—
417C22⋊C8—431no—
418C22⋊C8—431no—
419C22⋊C8—431no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—861no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434#41—862no—
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×C4D4×D4311yescharacteristic
448C22×C4#1062190011yescharacteristic
449Q16—862no—
450SD16—862no—
451SD16—1721no—
452D8—1721no—
453M16—81no—
454M16—3441no—
455M16—3441no—
456M16—3441no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—3441no—
472C2×C8—3441no—
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
496C42D4×D4311yescharacteristic
497C42#1062190011yescharacteristic
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—861no—
501C23(C22⋊D43)⋊C411yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—432no—
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×C4(C22⋊D43)⋊C411yescharacteristic
530C2×C4(C22⋊D43)⋊C411yescharacteristic
531C2×C4(C22⋊D43)⋊C411yescharacteristic
532C2×C4C22×C4×D4311yescharacteristic
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×#1062190011yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—861no—
540C8—861no—
541C8—861no—
542C8—861no—
543C8—861no—
544C8—861no—
545C8—861no—
546C8—861no—
547C8—1721no—
548C8—1721no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22C2×(C22⋊D43)⋊C411yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—862no—
567C4—1721no—
568C4—1721no—
569C4#131×D4311yescharacteristic
570C4#1458366411yescharacteristic
571C4#1458370311yescharacteristic
572C4#1458371511yescharacteristic
573C2—41no—
574C2—81no—
575C2—3441no—
576C2#1914332511yescharacteristic
577C2#1914346611yescharacteristic
578C2#1914349411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1495C2
socleC22×C43C2×C4×D4
prime radical#14583042C4
cosocleC42×C43C24
hypercenter#1495D43
hypocenterC43#18033
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #19143755C2semidirect
3. #19143725C2semidirect
4. #19133500C2semidirect
5. #19133477C2semidirect
6. #19133476C2semidirect
7. #19133470C2semidirect
8. #19133448C2semidirect
9. #19133421C2semidirect
10. #19133404C2semidirect
11. #19133399C2semidirect
12. #19133371C2semidirect
13. #19132983C2semidirect
14. #19132895C2semidirect
15. C43×#1495C2semidirect
296. #1495D43semidirect
356. C43#18033semidirect

Maximal subgroups

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

subgroupindex
#191446072
#191437552
#191437252
#191335002
#191334772
#191334762
#191334702
#191334482
#191334212
#191334042
#191333992
#191333712
#191329832
#191328952
C43×#14952
#1803343