Finite Group Databasebeta

← #25159635

Subgroups — #25159635

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583196C211yesmaximal, characteristic
2C2×C4×#10621884C211yesmaximal, characteristic
3C4⋊C4×D172C211yesmaximal, characteristic
4#19136133C211yesmaximal, characteristic, complemented
5#19136071C211yesmaximal, characteristic, complemented
6#19135990C211yesmaximal, characteristic, complemented
7#19135930C211yesmaximal, characteristic, complemented
8#19135325C211yesmaximal, characteristic, complemented
9#19135154C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic
11#19134932C211yesmaximal, characteristic
12#19134863C211yesmaximal, characteristic, complemented
13#19134841C211yesmaximal, characteristic
14#19134841C211yesmaximal, characteristic
15C43×#2453C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C4⋊C4×D43—21no—
21#14583196—24no—
22C4×#10621884—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×C4×C43⋊C8C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582773—21no—
39#14582773—21no—
40#14582769C2211yescharacteristic
41#14582756—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×#125×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C43×#400—21no—
53C43×#398—21no—
54C43×#391C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#389—21no—
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#387—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884Q814yes—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C4×D172—22no—
73C4×D172—22no—
74C4×D172—22no—
75C4×D172—22no—
76C4×D172—41no—
77C4×D172—41no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C4⋊C4×D43—44no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89#13063258—22no—
90#13063258—22no—
91#13063258—41no—
92#13063256—22no—
93#13063256—22no—
94C4⋊(C43⋊C8)—22no—
95#13063249—22no—
96#13063249—22no—
97#13063249—41no—
98#13063245—22no—
99#13063245—22no—
100#13063245D414yes—
101C4×C43⋊C8—22no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C22×Q8×C43C2311yescharacteristic
105#125×C43—22no—
106#125×C43—41no—
107C4×Q8×C43—22no—
108C4×Q8×C43—41no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43D411yescharacteristic
130#95×C43D411yescharacteristic
131C23×D43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43C2×Q812yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C2×D412yes—
156C2×D172C2×Q812yes—
157C2×D172#4112yes—
158C2×C4×D43—24no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—81no—
166C2×C4×D43—81no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—42no—
175C4⋊C4×C43—42no—
176C4⋊C4×C43—42no—
177C4⋊C4×C43—42no—
178C4⋊C4×C43—42no—
179C4⋊C4×C43C2×D412yes—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—42no—
187#10621884—28no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—42no—
197C4⋊Dic43—81no—
198C4⋊Dic43#4112yes—
199Dic43⋊C4—42no—
200Dic43⋊C4—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8C2×D412yes—
212C2×C43⋊C8C2×Q812yes—
213C23×C43C22×D411yescharacteristic
214C22×D43—22no—
215C22×D43—22no—
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221Q8×C43—22no—
222Q8×C43—22no—
223Q8×C43—41no—
224Q8×C43—41no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43#13512yes—
254C2×C4×C43AGL(1,ℤ/8)12yes—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×Q811yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C2×Dic43—22no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270D172—22no—
271D172—22no—
272D172—22no—
273D172C22⋊Q814yes—
274C4×D43—48no—
275C4×D43—84no—
276C4×D43—84no—
277C43⋊C8—22no—
278C43⋊C8—22no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#26374—431nomaximal, Sylow
282C22×C43#52511yescharacteristic
283C22×C43D4211yescharacteristic
284C22×C43D4×Q811yescharacteristic
285C22×C43C2×#13511yescharacteristic
286C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C43#57711yescharacteristic
288C22×C43#57811yescharacteristic
289C2×D43—24no—
290C2×D43—42no—
291C2×D43—42no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C4×C43—22no—
297C4×C43—22no—
298C4×C43—41no—
299C4×C43—42no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—42no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43C2×C22⋊Q811yescharacteristic
307C4×C43#53911yescharacteristic
308C4×C43#54711yescharacteristic
309C4×C43#55411yescharacteristic
310Dic43—42no—
311Dic43—81no—
312Dic43—81no—
313C2×#478—431no—
314C2×C4×SD16—431no—
315#2453D4311yescharacteristic, complemented
316D4×C4⋊C4—431no—
317#2095—431no—
318#2084—431no—
319#2068—431no—
320#2059—431no—
321#1942—431no—
322#1916—431no—
323#1877—431no—
324#1877—431no—
325#1865—431no—
326#1862—431no—
327#1862—431no—
328C2×C43#244911yescharacteristic
329C2×C43#310511yescharacteristic
330C2×C43#312011yescharacteristic
331C2×C43#326511yescharacteristic
332C2×C43#328311yescharacteristic
333C2×C43#338111yescharacteristic
334C2×C43#338611yescharacteristic
335D43—44no—
336C22×SD16—431no—
337C2×#125C2×D4311yescharacteristic
338C2×C4×Q8C2×D4311yescharacteristic
339C2×C4×D4—431no—
340C2×C4×D4—431no—
341C2×C4×D4—431no—
342C22×C4⋊C4—861no—
343#478—864no—
344C4×SD16—864no—
345C2×#107—431no—
346C2×#107—431no—
347C2×#107—431no—
348C2×#106—431no—
349C2×#106—431no—
350C2×C4⋊C8—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×C4×C8—431no—
358#400—21no—
359#398—21no—
360#391C2×D4311yescharacteristic
361#391C2×D4311yescharacteristic
362#389—21no—
363#389—431no—
364#389—431no—
365#389C2×D4311yescharacteristic
366#389C2×D4311yescharacteristic
367#387—21no—
368#385—861no—
369#385—861no—
370#384—431no—
371#380—861no—
372C4×C4⋊C4C2×D4311yescharacteristic
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#336—431no—
378#336—431no—
379#336—431no—
380#336—431no—
381C43#2637411yescharacteristic, complemented, Sylow
382C22×Q8C22×D4311yescharacteristic
383C22×D4—431no—
384C23×C4—861no—
385C23×C4—861no—
386C23×C4—861no—
387C2×SD16—434no—
388C2×SD16—862no—
389C2×SD16—862no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8—431no—
394#125—22no—
395#125—41no—
396C4×Q8—22no—
397C4×Q8—41no—
398C4×D4—862no—
399C4×D4—862no—
400C4×D4—862no—
401C4×D4—862no—
402C4×D4—1721no—
403C4×D4—1721no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—1724no—
417C2×C4⋊C4C22⋊D4311yescharacteristic
418C2×C4⋊C4C22⋊D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C42—21no—
426C2×C42C22×D4311yescharacteristic
427C2×C42C22×D4311yescharacteristic
428C2×C42C22×D4311yescharacteristic
429#107—862no—
430#107—862no—
431#107—1721no—
432#106—862no—
433#106—862no—
434C4⋊C8—862no—
435#103—862no—
436#103—862no—
437#103—1721no—
438#102—434no—
439#102—862no—
440#102—862no—
441C4×C8—862no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—861no—
449#95—861no—
450#95C22⋊D4311yescharacteristic
451#95C22⋊D4311yescharacteristic
452C24—861no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8Q8×D4312yes—
459C2×D4—432no—
460C2×D4—432no—
461C2×D4—432no—
462C2×D4—861no—
463C2×D4—861no—
464C2×D4—861no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—864no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—3441no—
474C22×C4—3441no—
475C22×C4—1722no—
476C22×C4—1722no—
477C22×C4—1722no—
478C22×C4—1722no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4C2×C22⋊D4311yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C2×C22⋊D4311yescharacteristic
485C22×C4C2×C22⋊D4311yescharacteristic
486C22×C4C2×C22⋊D4311yescharacteristic
487C22×C4C23×D4311yescharacteristic
488SD16—868no—
489C2×C8—432no—
490C2×C8—432no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—432no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—3441no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4D4×D4312yes—
524C22⋊C4—864no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—42no—
534C23—862no—
535C23—862no—
536C23—862no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23C22×C22⋊D4311yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546D4—434no—
547D4—862no—
548D4—862no—
549D4—862no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—862no—
579C2×C4—3444no—
580C2×C4—3444no—
581C2×C4—1728no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4#1306334512yes—
591C2×C4#1306335012yes—
592C2×C4C2×D4×D4311yescharacteristic
593C2×C4C2×Q8×D4311yescharacteristic
594C2×C4#41×D4311yescharacteristic
595C2×C4#41×D4311yescharacteristic
596C2×C4#1306337011yescharacteristic
597C2×C4#1306337311yescharacteristic
598C8—862no—
599C8—862no—
600C8—1721no—
601C8—1721no—
602C22—864no—
603C22—1722no—
604C22—1722no—
605C22—1722no—
606C22—1722no—
607C22—1722no—
608C22—1722no—
609C22#1458340611yescharacteristic
610C22D4×C22⋊D4311yescharacteristic
611C22Q8×C22⋊D4311yescharacteristic
612C22C2×#1306334511yescharacteristic
613C22C2×#1306335011yescharacteristic
614C22#1458370711yescharacteristic
615C22#1458371411yescharacteristic
616C4—22no—
617C4—22no—
618C4—41no—
619C4—41no—
620C4—42no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—3441no—
627C4—3441no—
628C4—1722no—
629C4C22⋊Q8×D4311yescharacteristic
630C4#1458349511yescharacteristic
631C4#1458355111yescharacteristic
632C4#1458360311yescharacteristic
633C2—1724no—
634C2#1913840111yescharacteristic
635C2#1914463811yescharacteristic
636C2#1914480311yescharacteristic
637C2#1914609111yescharacteristic
638C2#1914631311yescharacteristic
639C2#1914746611yescharacteristic
640C2#1914751211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2453C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2453D43
hypocenterC43#26374
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2453

Complements

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

NH ≅ G/Ntype
4. #19136133C2semidirect
5. #19136071C2semidirect
6. #19135990C2semidirect
7. #19135930C2semidirect
8. #19135325C2semidirect
9. #19135154C2semidirect
12. #19134863C2semidirect
15. C43×#2453C2semidirect
315. #2453D43semidirect
381. C43#26374semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
C2×C4×#106218842
C4⋊C4×D1722
#191361332
#191360712
#191359902
#191359302
#191353252
#191351542
#191349322
#191348632
#191348412
C43×#24532
#2637443