Finite Group Databasebeta

← #25159680

Subgroups — #25159680

Order 11008.

856 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583191C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic
3#19137515C211yesmaximal, characteristic, complemented
4#19136116C211yesmaximal, characteristic
5#19136076C211yesmaximal, characteristic, complemented
6#19135983C211yesmaximal, characteristic
7#19135925C211yesmaximal, characteristic, complemented
8#19135325C211yesmaximal, characteristic, complemented
9#19135154C211yesmaximal, characteristic, complemented
10#19134953C211yesmaximal, characteristic
11#19134953C211yesmaximal, characteristic
12#19134862C211yesmaximal, characteristic, complemented
13#19134848C211yesmaximal, characteristic, complemented
14#19134842C211yesmaximal, characteristic
15C43×#2452C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583191—24no—
21C4×#10621883—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582794—21no—
38#14582794—21no—
39#14582765C2211yescharacteristic
40#14582763—21no—
41#14582750—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4⋊Q8×C43C2211yescharacteristic
51C2×C22⋊Q8×C43—21no—
52C2×C4×D4×C43C2211yescharacteristic
53C43×#396—21no—
54C43×#393—21no—
55C43×#390C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#385—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883Q814yescomplemented
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C4×Dic86—22no—
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×Dic86—22no—
73C4×Dic86—41no—
74C4×Dic86—41no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86#13063258—22no—
87#13063258—22no—
88#13063258—22no—
89#13063256—22no—
90#13063256—41no—
91C4⋊(C43⋊C8)—22no—
92#13063248—22no—
93#13063248—22no—
94#13063248D414yes—
95#13063246—22no—
96#13063246—22no—
97#13063246—41no—
98C4×C43⋊C8—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C22×Q8×C43—21no—
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C4⋊Q8×C43—22no—
107C4⋊Q8×C43—41no—
108C22⋊Q8×C43—44no—
109C4×D4×C43—22no—
110C4×D4×C43—41no—
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×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127#95×C43—21no—
128#95×C43—21no—
129#95×C43D411yescharacteristic
130#95×C43D411yescharacteristic
131C24×C43—21no—
132C2×Q8×C43—42no—
133C2×Q8×C43—42no—
134C2×Q8×C43—81no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43C2×Q812yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—81no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86C2×D412yes—
162C2×Dic86C2×Q812yes—
163C2×Dic86#4112yes—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43—42no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43C2×D412yes—
175C22⋊C4×C43—42no—
176C22⋊C4×C43—42no—
177C22⋊C4×C43—42no—
178C22⋊C4×C43—42no—
179C22⋊C4×C43—81no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186#10621883—28no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43#4112yes—
193Dic43⋊C4—24no—
194Dic43⋊C4—42no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198C4×Dic43—24no—
199C4×Dic43—42no—
200C4×Dic43—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×C43—22no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43C22×D411yescharacteristic
221Q8×C43—84no—
222D4×C43—22no—
223D4×C43—22no—
224D4×C43—41no—
225D4×C43—41no—
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—21no—
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—84no—
252C2×C4×C43#13512yes—
253C2×C4×C43AGL(1,ℤ/8)12yes—
254C2×C4×C43C22×D411yescharacteristic
255C2×C4×C43C22×Q811yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272Dic86—22no—
273Dic86—22no—
274Dic86—22no—
275Dic86C22⋊Q814yescomplemented
276C43⋊C8—22no—
277C43⋊C8—22no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280#26377—431nomaximal, Sylow
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43#52511yescharacteristic
289C22×C43D4211yescharacteristic
290C22×C43D4×Q811yescharacteristic
291C22×C43C2×#13511yescharacteristic
292C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C43#57711yescharacteristic
294C22×C43#57811yescharacteristic
295C4×C43—22no—
296C4×C43—22no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—41no—
300C4×C43—42no—
301C4×C43—41no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43C2×C22⋊Q811yescharacteristic
305C4×C43#53911yescharacteristic
306C4×C43#54711yescharacteristic
307C4×C43#55411yescharacteristic
308Dic43—24no—
309Dic43—42no—
310Dic43—81no—
311Dic43—81no—
312C2×#477—431no—
313C2×C4×SD16—431no—
314#2452D4311yescharacteristic
315#2351—431no—
316#2092—431no—
317#2085—431no—
318#2067—431no—
319#2058—431no—
320#1942—431no—
321#1916—431no—
322#1880—431no—
323#1880—431no—
324#1865—431no—
325#1863—431no—
326#1862—431no—
327C2×C43—82no—
328C2×C43#244911yescharacteristic
329C2×C43#310611yescharacteristic
330C2×C43#312111yescharacteristic
331C2×C43#326511yescharacteristic
332C2×C43#328511yescharacteristic
333C2×C43#338111yescharacteristic
334C2×C43#338611yescharacteristic
335C22×SD16—431no—
336C2×C4⋊Q8C2×D4311yescharacteristic
337C2×C22⋊Q8—21no—
338C2×C4×Q8—431no—
339C2×C4×Q8—431no—
340C2×C4×Q8—431no—
341C2×C4×D4C2×D4311yescharacteristic
342#477—864no—
343C4×SD16—864no—
344C2×#107—431no—
345C2×#107—431no—
346C2×#107—431no—
347C2×#106—431no—
348C2×#106—431no—
349C2×C4⋊C8—431no—
350C2×#103—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×C4×C8—431no—
357#396—21no—
358#393—21no—
359#390C2×D4311yescharacteristic
360#390C2×D4311yescharacteristic
361#389—431no—
362#389—431no—
363#389—861no—
364#389—861no—
365#389C2×D4311yescharacteristic
366#389C2×D4311yescharacteristic
367#385—21no—
368#382—431no—
369#382—861no—
370C4×C4⋊C4—861no—
371C4×C4⋊C4C2×D4311yescharacteristic
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#336—431no—
377#336—431no—
378#336—431no—
379#336—431no—
380C43#2637711yescharacteristic, complemented, Sylow
381C22×Q8—21no—
382C22×Q8—431no—
383C22×D4C22×D4311yescharacteristic
384C23×C4—21no—
385C2×SD16—434no—
386C2×SD16—862no—
387C2×SD16—862no—
388C22×C8—431no—
389C22×C8—431no—
390C22×C8—431no—
391C22×C8—431no—
392C4⋊Q8—22no—
393C4⋊Q8—41no—
394C22⋊Q8—44no—
395C4×Q8—862no—
396C4×Q8—862no—
397C4×Q8—862no—
398C4×Q8—862no—
399C4×Q8—1721no—
400C4×Q8—1721no—
401C4×D4—22no—
402C4×D4—41no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—861no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4C22⋊D4311yescharacteristic
415C2×C4⋊C4C22⋊D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C42—861no—
425C2×C42—861no—
426C2×C42—861no—
427C2×C42C22×D4311yescharacteristic
428C2×C42C22×D4311yescharacteristic
429C2×C42C22×D4311yescharacteristic
430#107—862no—
431#107—862no—
432#107—862no—
433#106—862no—
434#106—1721no—
435C4⋊C8—862no—
436#103—434no—
437#103—862no—
438#103—862no—
439#102—862no—
440#102—862no—
441#102—1721no—
442C4×C8—862no—
443#95—21no—
444#95—21no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95C22⋊D4311yescharacteristic
450#95C22⋊D4311yescharacteristic
451C24—21no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×Q8—432no—
456C2×Q8—432no—
457C2×Q8—432no—
458C2×Q8—861no—
459C2×Q8—861no—
460C2×Q8—861no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4Q8×D4312yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4C2×C22⋊D4311yescharacteristic
478C22×C4C2×C22⋊D4311yescharacteristic
479C22×C4C2×C22⋊D4311yescharacteristic
480C22×C4C2×C22⋊D4311yescharacteristic
481C22×C4C2×C22⋊D4311yescharacteristic
482C22×C4C2×C22⋊D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484SD16—868no—
485C2×C8—432no—
486C2×C8—432no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—861no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—432no—
508C4⋊C4—864no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4—1722no—
518C4⋊C4D4×D4312yes—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—864no—
531C42—1722no—
532C42—1722no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23C22×C22⋊D4311yescharacteristic
541Q8—84no—
542Q8—434no—
543Q8—862no—
544Q8—862no—
545Q8—862no—
546D4—22no—
547D4—22no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
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—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—84no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4#1306334512yes—
589C2×C4#1306335112yes—
590C2×C4C2×D4×D4311yescharacteristic
591C2×C4C2×Q8×D4311yescharacteristic
592C2×C4#41×D4311yescharacteristic
593C2×C4#41×D4311yescharacteristic
594C2×C4#1306337011yescharacteristic
595C2×C4#1306337311yescharacteristic
596C8—862no—
597C8—862no—
598C8—1721no—
599C8—1721no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#1458340611yescharacteristic
608C22D4×C22⋊D4311yescharacteristic
609C22Q8×C22⋊D4311yescharacteristic
610C22C2×#1306334511yescharacteristic
611C22C2×#1306335111yescharacteristic
612C22#1458371011yescharacteristic
613C22#1458371411yescharacteristic
614C4—22no—
615C4—22no—
616C4—41no—
617C4—41no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—81no—
623C4—864no—
624C4—3441no—
625C4—3441no—
626C4—1722no—
627C4C22⋊Q8×D4311yescharacteristic
628C4#1458349511yescharacteristic
629C4#1458355111yescharacteristic
630C4#1458360311yescharacteristic
631C2—82no—
632C2#1913840111yescharacteristic
633C2#1914464911yescharacteristic
634C2#1914481811yescharacteristic
635C2#1914608611yescharacteristic
636C2#1914633211yescharacteristic
637C2#1914747011yescharacteristic
638C2#1914751611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2452C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2452D43
hypocenterC43#26377
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. C2×#14583191C2semidirect
3. #19137515C2semidirect
5. #19136076C2semidirect
7. #19135925C2semidirect
8. #19135325C2semidirect
9. #19135154C2semidirect
12. #19134862C2semidirect
13. #19134848C2semidirect
64. C2×#10621883Q8semidirect
275. Dic86C22⋊Q8semidirect
380. C43#26377semidirect

Maximal subgroups

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

subgroupindex
C2×#145831912
C2×C4×#106218832
#191375152
#191361162
#191360762
#191359832
#191359252
#191353252
#191351542
#191349532
#191348622
#191348482
#191348422
C43×#24522
#2637743