Finite Group Databasebeta

← #25159638

Subgroups — #25159638

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×#14583199C211yesmaximal, characteristic
2C2×C4×#10621883C211yesmaximal, characteristic
3#19138456C211yesmaximal, characteristic, complemented
4#19136134C211yesmaximal, characteristic, complemented
5#19136072C211yesmaximal, characteristic, complemented
6#19135987C211yesmaximal, characteristic, complemented
7#19135933C211yesmaximal, characteristic, complemented
8#19135325C211yesmaximal, characteristic, complemented
9#19135154C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic
11#19134929C211yesmaximal, characteristic
12#19134862C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic
14#19134842C211yesmaximal, characteristic
15D4×C4⋊C4×C43C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19#14583199—24no—
20C4×#10621883—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582840—21no—
35#14582830—21no—
36#14582805C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582797C2211yescharacteristic
40#14582794—21no—
41#14582781—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C22×C4⋊C4×C43—21no—
54C43×#389C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#385—21no—
57C43×#385—21no—
58C43×#384C2211yescharacteristic
59C43×#380—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C2×#10621883—22no—
63C2×#10621883—22no—
64C2×#10621883Q814yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063317—22no—
70#13063317—41no—
71C4×Dic86—22no—
72C4×Dic86—41no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C4×Dic43—21no—
82#13063258—22no—
83#13063258—22no—
84#13063258—41no—
85#13063256—22no—
86#13063256—22no—
87C4⋊(C43⋊C8)—22no—
88#13063248—22no—
89#13063248—22no—
90#13063248—41no—
91#13063246—22no—
92#13063246—22no—
93#13063246D414yes—
94C4×C43⋊C8—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C22×D4×C43C2311yescharacteristic
102C23×C4×C43—21no—
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43—22no—
109C4×D4×C43—41no—
110C4×D4×C43—41no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—44no—
116C2×C4⋊C4×C43D411yescharacteristic
117C2×C4⋊C4×C43D411yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
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×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43C2×D412yes—
136C2×D4×C43C2×Q812yes—
137C2×D4×C43#4112yes—
138C22×C4×C43—24no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—81no—
149C22×C4×C43—81no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86C2×Q812yes—
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—81no—
178C4⋊C4×C43#4112yes—
179C22⋊C4×C43—24no—
180C22⋊C4×C43—42no—
181C22⋊C4×C43—42no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188#10621883—28no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×D412yes—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—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—22no—
215C23×C43—22no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43C22×D411yescharacteristic
221D4×C43—22no—
222D4×C43—22no—
223D4×C43—22no—
224D4×C43C22⋊Q814yes—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
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—48no—
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—84no—
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—22no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273Dic86—22no—
274Dic86—22no—
275Dic86—41no—
276Dic86—41no—
277C43⋊C8—22no—
278C43⋊C8—22no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#26374—431nomaximal, Sylow
282C22×C43—24no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43#52511yescharacteristic
290C22×C43D4211yescharacteristic
291C22×C43D4×Q811yescharacteristic
292C22×C43C2×#13511yescharacteristic
293C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57811yescharacteristic
296C4×C43—22no—
297C4×C43—22no—
298C4×C43—42no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43C2×C22⋊Q811yescharacteristic
306C4×C43#53911yescharacteristic
307C4×C43#54711yescharacteristic
308C4×C43#55411yescharacteristic
309Dic43—42no—
310Dic43—42no—
311Dic43—81no—
312Dic43—81no—
313C2×#478—431no—
314C2×C4×SD16—431no—
315#2453—431no—
316D4×C4⋊C4D4311yescharacteristic
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—44no—
329C2×C43#244911yescharacteristic
330C2×C43#310511yescharacteristic
331C2×C43#312011yescharacteristic
332C2×C43#326511yescharacteristic
333C2×C43#328311yescharacteristic
334C2×C43#338111yescharacteristic
335C2×C43#338611yescharacteristic
336C22×SD16—431no—
337C2×#125—431no—
338C2×C4×Q8—431no—
339C2×C4×D4C2×D4311yescharacteristic
340C2×C4×D4C2×D4311yescharacteristic
341C2×C4×D4C2×D4311yescharacteristic
342C22×C4⋊C4—21no—
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—861no—
359#398—861no—
360#391—431no—
361#391—431no—
362#389—431no—
363#389—431no—
364#389—861no—
365#389C2×D4311yescharacteristic
366#389C2×D4311yescharacteristic
367#387—861no—
368#385—21no—
369#385—21no—
370#384C2×D4311yescharacteristic
371#380—21no—
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×Q8—431no—
383C22×D4C22×D4311yescharacteristic
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—21no—
387C2×SD16—434no—
388C2×SD16—862no—
389C2×SD16—862no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8—431no—
394#125—862no—
395#125—1721no—
396C4×Q8—862no—
397C4×Q8—1721no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—41no—
403C4×D4—41no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—44no—
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—861no—
417C2×C4⋊C4C22⋊D4311yescharacteristic
418C2×C4⋊C4C22⋊D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C42—861no—
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—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95C22⋊D4311yescharacteristic
451#95C22⋊D4311yescharacteristic
452C24—21no—
453C2×Q8—432no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4#1062189812yes—
463C2×D4D4×D4312yes—
464C2×D4Q8×D4312yes—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—81no—
476C22×C4—81no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
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—81no—
512C4⋊C4—432no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4#1062189812yes—
524C22⋊C4—24no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—1722no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C22×C22⋊D4311yescharacteristic
542Q8—862no—
543Q8—862no—
544Q8—1721no—
545Q8—1721no—
546D4—22no—
547D4—22no—
548D4—22no—
549D4#1306330314yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
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—48no—
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—84no—
577C2×C4—84no—
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—1721no—
589C2×C4—1721no—
590C2×C4#1306334512yes—
591C2×C4#1306335112yes—
592C2×C4C2×D4×D4311yescharacteristic
593C2×C4C2×Q8×D4311yescharacteristic
594C2×C4C2×#1062189811yescharacteristic
595C2×C4C2×#1062189811yescharacteristic
596C2×C4#1306337011yescharacteristic
597C2×C4#1306337311yescharacteristic
598C8—862no—
599C8—862no—
600C8—1721no—
601C8—1721no—
602C22—24no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22#1458341011yescharacteristic
610C22D4×C22⋊D4311yescharacteristic
611C22Q8×C22⋊D4311yescharacteristic
612C22C2×#1306334511yescharacteristic
613C22C2×#1306335111yescharacteristic
614C22#1458371011yescharacteristic
615C22#1458371411yescharacteristic
616C4—22no—
617C4—22no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—3441no—
626C4—3441no—
627C4—1722no—
628C4—1722no—
629C4C2×#1306330311yescharacteristic
630C4#1458349611yescharacteristic
631C4#1458355011yescharacteristic
632C4#1458360411yescharacteristic
633C2—44no—
634C2#1913840411yescharacteristic
635C2#1914464211yescharacteristic
636C2#1914480911yescharacteristic
637C2#1914608611yescharacteristic
638C2#1914631311yescharacteristic
639C2#1914747011yescharacteristic
640C2#1914751611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C4⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterD4×C4⋊C4D43
hypocenterC43#26374
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #19138456C2semidirect
4. #19136134C2semidirect
5. #19136072C2semidirect
6. #19135987C2semidirect
7. #19135933C2semidirect
8. #19135325C2semidirect
9. #19135154C2semidirect
12. #19134862C2semidirect
381. C43#26374semidirect

Maximal subgroups

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

subgroupindex
C2×#145831992
C2×C4×#106218832
#191384562
#191361342
#191360722
#191359872
#191359332
#191353252
#191351542
#191349292
#191348622
#191348422
D4×C4⋊C4×C432
#2637443