Finite Group Databasebeta

← #25148181

Subgroups — #25148181

Order 11008.

778 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583303C211yesmaximal, characteristic, complemented
2C2×#14583187C211yesmaximal, characteristic
3#19139766C211yesmaximal, characteristic
4#19137682C211yesmaximal, characteristic, complemented
5#19136079C211yesmaximal, characteristic, complemented
6#19136078C211yesmaximal, characteristic, complemented
7#19135983C211yesmaximal, characteristic
8#19135979C211yesmaximal, characteristic
9#19135541C211yesmaximal, characteristic, complemented
10#19135363C211yesmaximal, characteristic, complemented
11#19135362C211yesmaximal, characteristic, complemented
12#19135312C211yesmaximal, characteristic, complemented
13#19135217C211yesmaximal, characteristic
14#102×Dic43C211yesmaximal, characteristic
15C43×#1925C211yesmaximal, characteristic
16C2×#13063324C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19#14583303—24no—
20#14583187—24no—
21C2×#13063259C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063257C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582811—21no—
33#14582811—21no—
34#14582805—21no—
35#14582803—21no—
36#14582802C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582796—21no—
40#14582765C2211yescharacteristic
41#14582764C2211yescharacteristic
42#14582757—21no—
43#14582757—21no—
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×Dic43⋊C4—21no—
47C4×Dic43⋊C4C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Dic86—21no—
62C22×Dic86—21no—
63C23×Dic43—21no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063324—22no—
67#13063324—22no—
68#13063324—22no—
69#13063324D414yes—
70D4×Dic43—22no—
71D4×Dic43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259—22no—
90#13063258—22no—
91#13063258—22no—
92#13063257—22no—
93#13063256—22no—
94C4⋊(C43⋊C8)—22no—
95Dic43⋊C8—22no—
96Dic43⋊C8—22no—
97#13063246—22no—
98#13063246—22no—
99C8×Dic43—22no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#107×C43—22no—
121#102×C43—22no—
122#102×C43Q814yescomplemented
123#95×C43—21no—
124C24×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43C2×Q812yes—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2411yescharacteristic
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43—42no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×Dic86—24no—
149C2×Dic86—42no—
150C2×Dic86—81no—
151C2×Dic86—81no—
152C2×Dic86—81no—
153C2×Dic86—81no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43C2×Q812yes—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43C2×D412yes—
165C4⋊C4×C43C2×Q812yes—
166C22⋊C4×C43—81no—
167C22⋊C4×C43—81no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—81no—
171C22⋊Dic43—42no—
172C22⋊Dic43—81no—
173C22⋊Dic43—81no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—81no—
182C4⋊Dic43C2×D412yes—
183Dic43⋊C4—24no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—42no—
187Dic43⋊C4—81no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—42no—
191C4×Dic43—81no—
192C4×Dic43C2×D412yes—
193C4×Dic43#4112yes—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8#4112yes—
200C23×C43—22no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43C22×D411yescharacteristic
208D4×C43—22no—
209D4×C43—22no—
210D4×C43—41no—
211D4×C43—41no—
212C2×C4×C43—22no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×Q811yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—22no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—84no—
254C2×Dic43#12112yes—
255C2×Dic43#12112yes—
256C2×Dic43#13512yes—
257C2×Dic43#13712yes—
258Dic86—84no—
259Dic86—84no—
260C8×C43—22no—
261C8×C43—41no—
262C43⋊C8—22no—
263C43⋊C8—41no—
264#25450—431nomaximal, Sylow
265C22×C43—42no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—81no—
271C22×C43—81no—
272C22×C43C2×#12111yescharacteristic
273C22×C43#54711yescharacteristic
274C22×C43D4×Q811yescharacteristic
275C22×C43C2×#13511yescharacteristic
276C22×C43C2×#13711yescharacteristic
277C22×C43#57611yescharacteristic
278C22×C43#57611yescharacteristic
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—42no—
282C4×C43—42no—
283C4×C43—81no—
284C4×C43#53311yescharacteristic
285C4×C43#54111yescharacteristic
286C4×C43#54811yescharacteristic
287C4×C43D4×Q811yescharacteristic
288Dic43—22no—
289Dic43—41no—
290Dic43—41no—
291Dic43—42no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295Dic43#46414yes—
296C2×#500—431no—
297C2×#476—431no—
298#2563—431no—
299#2369—431no—
300#2085—431no—
301#2085—431no—
302#2067—431no—
303#2067—431no—
304#1987—431no—
305#1949—431no—
306#1949—431no—
307#1939—431no—
308#1925—431no—
309#1925D4311yescharacteristic
310C4×#102—431no—
311C2×C43—82no—
312C2×C43#242911yescharacteristic
313C2×C43C2×#46411yescharacteristic
314C2×C43#304111yescharacteristic
315C2×C43#334111yescharacteristic
316C2×C43#335711yescharacteristic
317C2×C43#338011yescharacteristic
318C2×C43#338511yescharacteristic
319C2×C4⋊Q8—431no—
320C2×C4⋊Q8—431no—
321C2×C4×D4—431no—
322#500—864no—
323#476—864no—
324C2×#107—431no—
325C2×#107—431no—
326C2×#107—431no—
327C2×#107C2×D4311yescharacteristic
328C2×#106—431no—
329C2×#106—431no—
330C2×C4⋊C8—431no—
331C2×C4⋊C8—431no—
332C2×C4⋊C8—431no—
333C2×#102—431no—
334C2×#102—431no—
335C2×#102C2×D4311yescharacteristic
336C2×#102C2×D4311yescharacteristic
337C2×C4×C8—431no—
338#393—861no—
339#393—861no—
340#391—861no—
341#391—861no—
342#390—431no—
343#390C2×D4311yescharacteristic
344#389—431no—
345#389—431no—
346#389—861no—
347#382—431no—
348#382—431no—
349#380—861no—
350#380—861no—
351C4×C4⋊C4—431no—
352C4×C4⋊C4—431no—
353C4×C4⋊C4—431no—
354C4×C4⋊C4—861no—
355C4×C4⋊C4C2×D4311yescharacteristic
356#340—431no—
357#340—431no—
358#340—431no—
359#340—431no—
360#340—431no—
361#340C2×D4311yescharacteristic
362#336—431no—
363#336C2×D4311yescharacteristic
364C43#2545011yescharacteristic, complemented, Sylow
365C22×Q8—861no—
366C22×Q8—861no—
367C22×D4C22×D4311yescharacteristic
368C23×C4—861no—
369C22×C8—431no—
370C22×C8—431no—
371C22×C8C22×D4311yescharacteristic
372C22×C8C22×D4311yescharacteristic
373C4⋊Q8—434no—
374C4⋊Q8—862no—
375C4⋊Q8—862no—
376C4⋊Q8—862no—
377C4×D4—862no—
378C4×D4—862no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C42—21no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—861no—
401C2×C42—861no—
402C2×C42C22×D4311yescharacteristic
403#107—22no—
404#107—862no—
405#107—862no—
406#107—862no—
407#106—862no—
408#106—862no—
409C4⋊C8—862no—
410C4⋊C8—862no—
411C4⋊C8—862no—
412#102—22no—
413#102—862no—
414#102—862no—
415#102Dic8614yescomplemented
416C4×C8—862no—
417#95—21no—
418#95—431no—
419#95—431no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427#95—861no—
428C24—21no—
429C2×Q8—864no—
430C2×Q8—3441no—
431C2×Q8—3441no—
432C2×Q8—3441no—
433C2×Q8—3441no—
434C2×Q8—1722no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×Dic8612yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—1722no—
453C22×C4—1722no—
454C22×C4—1722no—
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—432no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8C2×Dic8612yes—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—432no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—864no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—3441no—
486C4⋊C4—3441no—
487C4⋊C4—1722no—
488C4⋊C4C2×Dic8612yes—
489C4⋊C4D4×D4312yes—
490C22⋊C4—81no—
491C22⋊C4—81no—
492C22⋊C4—3441no—
493C22⋊C4—3441no—
494C22⋊C4—1722no—
495C42—21no—
496C42—21no—
497C42—81no—
498C42—432no—
499C42—432no—
500C42—861no—
501C42—861no—
502C42—3441no—
503C42—1722no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C2×D4×D4311yescharacteristic
512Q8—3444no—
513Q8—3444no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—862no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—3444no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4C22×Dic8611yescharacteristic
560C2×C4#41×D4311yescharacteristic
561C2×C4#41×D4311yescharacteristic
562C2×C4#1306337211yescharacteristic
563C2×C4#1306337211yescharacteristic
564C8—22no—
565C8—41no—
566C8—862no—
567C8—1721no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#121×D4311yescharacteristic
576C22#1458354711yescharacteristic
577C22D4×Dic8611yescharacteristic
578C22#135×D4311yescharacteristic
579C22#137×D4311yescharacteristic
580C22#1458370011yescharacteristic
581C22#1458370311yescharacteristic
582C4—41no—
583C4—42no—
584C4—42no—
585C4—41no—
586C4—81no—
587C4—434no—
588C4—862no—
589C4—3441no—
590C4—3441no—
591C4—3441no—
592C4—1721no—
593C4—1722no—
594C4—1721no—
595C4#1458345211yescharacteristic
596C4#1458350611yescharacteristic
597C4#1458355711yescharacteristic
598C4D4×Dic8611yescharacteristic
599C2—82no—
600C2#1913819111yescharacteristic
601C2#464×D4311yescharacteristic
602C2#1914409311yescharacteristic
603C2#1914701211yescharacteristic
604C2#1914721411yescharacteristic
605C2#1914746211yescharacteristic
606C2#1914750611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1925D43
hypocenterC43#25450
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
1. C2×#14583303C2semidirect
4. #19137682C2semidirect
5. #19136079C2semidirect
6. #19136078C2semidirect
9. #19135541C2semidirect
10. #19135363C2semidirect
11. #19135362C2semidirect
12. #19135312C2semidirect
122. #102×C43Q8semidirect
364. C43#25450semidirect
415. #102Dic86semidirect

Maximal subgroups

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

subgroupindex
C2×#145833032
C2×#145831872
#191397662
#191376822
#191360792
#191360782
#191359832
#191359792
#191355412
#191353632
#191353622
#191353122
#191352172
#102×Dic432
C43×#19252
#2545043