Finite Group Databasebeta

← #25066681

Subgroups — #25066681

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144655C211yesmaximal, characteristic
2#19143706C211yesmaximal, characteristic, complemented
3#19143673C211yesmaximal, characteristic, complemented
4#19133470C211yesmaximal, characteristic, complemented
5#19133456C211yesmaximal, characteristic, complemented
6#19133435C211yesmaximal, characteristic, complemented
7#19133421C211yesmaximal, characteristic, complemented
8#19133416C211yesmaximal, characteristic, complemented
9#19133410C211yesmaximal, characteristic, complemented
10#19133392C211yesmaximal, characteristic, complemented
11#19133387C211yesmaximal, characteristic, complemented
12#19133381C211yesmaximal, characteristic, complemented
13#19132995C211yesmaximal, characteristic, complemented
14#19132895C211yesmaximal, characteristic, complemented
15C43×#1488C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583223C411yescharacteristic
18#14583223C411yescharacteristic
19#14583194C411yescharacteristic
20#14583189C411yescharacteristic
21#14583099C411yescharacteristic
22#14583094C411yescharacteristic
23#14583044C411yescharacteristic
24#14583044C411yescharacteristic
25Q8×C43⋊C8C2211yescharacteristic
26Q8×C43⋊C8C2211yescharacteristic
27C4×#10621884C2211yescharacteristic
28C4×#10621884C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582976C2211yescharacteristic
32#14582976C2211yescharacteristic
33#14582972—21no—
34#14582972—21no—
35D4×C43⋊C8—21no—
36D4×C43⋊C8—21no—
37D4×C43⋊C8C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582964C2211yescharacteristic
40#14582964C2211yescharacteristic
41#14582952—21no—
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44C2×C4⋊(C43⋊C8)—21no—
45C2×C4⋊(C43⋊C8)C2211yescharacteristic
46#14582864—21no—
47#14582864—21no—
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582628C2211yescharacteristic
53#14582628C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C4×#41×C43C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621872—21no—
73C2×#10621872—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79#13063325C2×C411yescharacteristic
80#13063322C2×C411yescharacteristic
81#13063313—21no—
82#13063299—21no—
83#13063299C2×C411yescharacteristic
84#13063299C2×C411yescharacteristic
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87C4×D172C2311yescharacteristic
88#13063258C2×C411yescharacteristic
89#13063258C2×C411yescharacteristic
90#13063256C2×C411yescharacteristic
91#13063256C2×C411yescharacteristic
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2×C411yescharacteristic
96C4⋊(C43⋊C8)C2×C411yescharacteristic
97C4⋊(C43⋊C8)D411yescharacteristic
98C4⋊(C43⋊C8)D411yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249C2×C411yescharacteristic
102#13063249C2×C411yescharacteristic
103#13063246C2×C411yescharacteristic
104#13063246C2×C411yescharacteristic
105#13063245C2×C411yescharacteristic
106#13063245C2×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(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119C4×C43⋊C8—21no—
120C4×C43⋊C8—21no—
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C2×#41×C43C2×C411yescharacteristic
126C4×Q8×C43C2×C411yescharacteristic
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2×C411yescharacteristic
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43C2×C411yescharacteristic
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—21no—
156C2×C22⋊D43—21no—
157#10621898—81no—
158#10621898—81no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172C22×C411yescharacteristic
162C2×D172C22×C411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×Dic86—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C22×C411yescharacteristic
173C4⋊C4×C43C22×C411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43C22×C411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43#4111yescharacteristic
183C42×C43C2411yescharacteristic
184#10621884—22no—
185#10621884—22no—
186#10621882—22no—
187#10621882—22no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C22×C411yescharacteristic
194C4⋊Dic43C22×C411yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—81no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208#10621872—81no—
209#10621872—81no—
210C8×D43—81no—
211C8×D43—81no—
212C23×C43—21no—
213C23×C43C4×D411yescharacteristic
214C22×D43—21no—
215C22×D43—21no—
216Q8×C43—21no—
217Q8×C43#13112yes—
218D4×C43—24no—
219D4×C43—21no—
220D4×C43#13112yes—
221C2×C4×C43—24no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—81no—
233C2×C4×C43C4×D411yescharacteristic
234C2×C4×C43C4×D411yescharacteristic
235C2×C4×C43C4×D411yescharacteristic
236C2×C4×C43C23×C411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C22⋊D43—81no—
240C22⋊D43—81no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243D172—21no—
244D172—21no—
245D172—21no—
246D172—21no—
247D172—81no—
248D172—81no—
249C4×D43—41no—
250C4×D43—41no—
251C4×D43—41no—
252C4×D43—41no—
253Dic86—81no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#17920—431nomaximal, Sylow
269C22×C43—22no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43C2×C4×D411yescharacteristic
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C4×C43—21no—
283C4×C43—22no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43C2×#13111yescharacteristic
290C4×C43C2×#13111yescharacteristic
291C4×C43#57611yescharacteristic
292C4×C43#57711yescharacteristic
293Dic43—41no—
294Dic43—41no—
295#3106—431no—
296#2988—431no—
297#2981—431no—
298#1588—431no—
299#1586—431no—
300#1583—431no—
301#1581—431no—
302#1580—431no—
303SD16⋊C8—431no—
304C8×SD16—431no—
305C8×D8—431no—
306#1573—431no—
307#1488D4311yescharacteristic, complemented
308#1480—431no—
309#1454—431no—
310C2×C43—41no—
311C2×C43—42no—
312C2×C43#292911yescharacteristic
313C2×C43#294611yescharacteristic
314C2×C43#295711yescharacteristic
315D43—81no—
316D43—81no—
317#532—431no—
318C4×#41C2×D4311yescharacteristic
319#482—431no—
320#482—431no—
321#477—431no—
322#476—431no—
323#460—431no—
324#459—431no—
325#449—431no—
326#449—431no—
327C8×Q8—431no—
328C8×Q8—431no—
329C4×SD16—431no—
330C4×SD16—431no—
331C4×D8—431no—
332C4×D8—431no—
333#436—431no—
334#436—431no—
335#435—861no—
336#435—861no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—861no—
342C8×D4—861no—
343#432C2×D4311yescharacteristic
344#431—431no—
345#431—431no—
346#431—861no—
347#431C2×D4311yescharacteristic
348C2×C4⋊C8—431no—
349C2×C4⋊C8—861no—
350#408—861no—
351#408—861no—
352#335—431no—
353#335—431no—
354#334—431no—
355#334—431no—
356Q8⋊C8C2×D4311yescharacteristic
357Q8⋊C8C2×D4311yescharacteristic
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8C2×D4311yescharacteristic
363D4⋊C8C2×D4311yescharacteristic
364#322—431no—
365#322—431no—
366#322—431no—
367C82—431no—
368C43#1792011yescharacteristic, complemented, Sylow
369C2×#41—861no—
370C2×#41C4×D4311yescharacteristic
371C2×SD16—431no—
372C2×SD16—431no—
373C2×D8—431no—
374C2×D8—431no—
375C2×M16—861no—
376C2×M16—861no—
377C22×C8—861no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8—431no—
383#127—431no—
384#124—861no—
385#121—431no—
386#121—431no—
387#121—861no—
388C4×Q8C4×D4311yescharacteristic
389C4×Q8C22×D4311yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4C4×D4311yescharacteristic
396C4×D4C22×D4311yescharacteristic
397#117—21no—
398#117C4×D4311yescharacteristic
399C2×C42—21no—
400C2×C42C22×D4311yescharacteristic
401#107—431no—
402#107—431no—
403#106—431no—
404#106—431no—
405C4⋊C8—21no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—431no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417#103—431no—
418#103—431no—
419#102—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424#102—431no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—431no—
428C22⋊C8—431no—
429C22⋊C8—431no—
430C22⋊C8—431no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437#97—21no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—431no—
441C4×C8—431no—
442C4×C8—861no—
443C4×C8—861no—
444C4×C8C22×D4311yescharacteristic
445C4×C8C22×D4311yescharacteristic
446#41—22no—
447#41—22no—
448#41—3441no—
449#41—3441no—
450C2×Q8—861no—
451C2×Q8C2×C4×D4311yescharacteristic
452C2×D4—21no—
453C2×D4—431no—
454C2×D4—431no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4C2×C4×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4C2×C4×D4311yescharacteristic
466C22×C4D4×D4311yescharacteristic
467C22×C4#1062190011yescharacteristic
468SD16—862no—
469SD16—862no—
470D8—862no—
471D8—862no—
472M16—3441no—
473M16—3441no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—431no—
485C2×C8—431no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—3441no—
489C2×C8—3441no—
490C2×C8—3441no—
491C2×C8—3441no—
492C2×C8—3441no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—861no—
498C4⋊C4C2×C4×D4311yescharacteristic
499C4⋊C4C2×C4×D4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42C2×C4×D4311yescharacteristic
511C42D4×D4311yescharacteristic
512C42#1062190011yescharacteristic
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—861no—
516C23—861no—
517C23(C22⋊D43)⋊C411yescharacteristic
518Q8—21no—
519Q8—3441no—
520Q8#1306333312yes—
521D4—24no—
522D4—21no—
523D4—861no—
524D4—861no—
525D4—861no—
526D4—861no—
527D4—3441no—
528D4—3441no—
529D4—3441no—
530D4—3441no—
531D4#1306333312yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4(C22⋊D43)⋊C411yescharacteristic
551C2×C4(C22⋊D43)⋊C411yescharacteristic
552C2×C4(C22⋊D43)⋊C411yescharacteristic
553C2×C4C22×C4×D4311yescharacteristic
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4C2×#1062190011yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—861no—
561C8—861no—
562C8—861no—
563C8—861no—
564C8—861no—
565C8—861no—
566C8—861no—
567C8—861no—
568C8—1721no—
569C8—1721no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—1721no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22—1721no—
581C22—1721no—
582C22C2×(C22⋊D43)⋊C411yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—1721no—
591C4—1721no—
592C4C2×#1306333311yescharacteristic
593C4C2×#1306333311yescharacteristic
594C4#1458370111yescharacteristic
595C4#1458370611yescharacteristic
596C2—41no—
597C2—42no—
598C2—3441no—
599C2—3441no—
600C2#1914328511yescharacteristic
601C2#1914343011yescharacteristic
602C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1488C2
socleC22×C43C2×C4×D4
prime radical#19144655C2
cosocleC42×C43C24
hypercenter#1488D43
hypocenterC43#17920
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #19143706C2semidirect
3. #19143673C2semidirect
4. #19133470C2semidirect
5. #19133456C2semidirect
6. #19133435C2semidirect
7. #19133421C2semidirect
8. #19133416C2semidirect
9. #19133410C2semidirect
10. #19133392C2semidirect
11. #19133387C2semidirect
12. #19133381C2semidirect
13. #19132995C2semidirect
14. #19132895C2semidirect
15. C43×#1488C2semidirect
307. #1488D43semidirect
368. C43#17920semidirect

Maximal subgroups

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

subgroupindex
#191446552
#191437062
#191436732
#191334702
#191334562
#191334352
#191334212
#191334162
#191334102
#191333922
#191333872
#191333812
#191329952
#191328952
C43×#14882
#1792043