Finite Group Databasebeta

← #25160005

Subgroups — #25160005

Order 11008.

878 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×#14583198C211yesmaximal, characteristic
2C2×#14583001C211yesmaximal, characteristic
3#19138457C211yesmaximal, characteristic, complemented
4#19137496C211yesmaximal, characteristic
5#19136135C211yesmaximal, characteristic, complemented
6#19136070C211yesmaximal, characteristic, complemented
7#19135985C211yesmaximal, characteristic, complemented
8#19135936C211yesmaximal, characteristic, complemented
9#19135159C211yesmaximal, characteristic, complemented
10#19134930C211yesmaximal, characteristic
11#19134930C211yesmaximal, characteristic
12#19134855C211yesmaximal, characteristic
13#19134848C211yesmaximal, characteristic, complemented
14#19134839C211yesmaximal, characteristic
15C43×#1943C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C2×#13063316C2211yescharacteristic
18C2×C4×Dic86C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×C4⋊C4×D43—21no—
23#14583198—24no—
24#14583001—24no—
25C2×#13063259C2211yescharacteristic
26C2×#13063258C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35#14582840—21no—
36#14582833—21no—
37#14582804C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582794—21no—
42#14582785—21no—
43#14582773—21no—
44#14582770—21no—
45#14582768C2211yescharacteristic
46#14582758—21no—
47C4×Dic43⋊C4C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#389C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×Dic86C2311yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621873—22no—
67C2×#10621873—22no—
68C2×#10621873Q814yes—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063316—22no—
72#13063316—41no—
73C4×Dic86—22no—
74C4×Dic86—41no—
75C4×D172—22no—
76C4×D172—41no—
77#13063287—22no—
78#13063287—22no—
79#13063287—22no—
80#13063287—41no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4D411yescharacteristic
91C2×Dic43⋊C4D411yescharacteristic
92C4⋊C4×D43—44no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43C2311yescharacteristic
98C2×C4×Dic43C2311yescharacteristic
99#13063259—22no—
100#13063258—22no—
101#13063256—41no—
102Dic43⋊C8—22no—
103#13063250—22no—
104#13063248—22no—
105#13063248—41no—
106#13063247D414yes—
107#13063245—22no—
108#13063245—22no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95D411yescharacteristic
116C43⋊#95D411yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126#107×C43—22no—
127#106×C43—22no—
128#97×C43—22no—
129#95×C43—21no—
130#95×C43—21no—
131C23×D43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172C2×D412yes—
150C2×D172C2×Q812yes—
151C2×D172#4112yes—
152C2×C4×D43—24no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—81no—
160C2×C4×D43—81no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86C2×Q812yes—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43C2×D412yes—
172C2×C8×C43C2×Q812yes—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—42no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43#4112yes—
183C42×C43—21no—
184C42×C43—21no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—42no—
187(C2×D43)⋊C4—42no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—42no—
192C4⋊Dic43—42no—
193C4⋊Dic43C2×D412yes—
194Dic43⋊C4—22no—
195Dic43⋊C4—41no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
198Dic43⋊C4—42no—
199Dic43⋊C4—42no—
200Dic43⋊C4—81no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212#10621873—28no—
213C23×C43C22×D411yescharacteristic
214C22×D43—22no—
215C22×D43—22no—
216C22×D43—22no—
217C22×D43—41no—
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C2×C4×C43—22no—
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—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×Q811yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C432−1+411yescharacteristic
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43AGL(1,ℤ/8)12yes—
266D172—22no—
267D172—22no—
268D172—22no—
269D172C22⋊Q814yes—
270C4×D43—48no—
271C4×D43—84no—
272C4×D43—84no—
273Dic86—22no—
274Dic86—22no—
275Dic86—41no—
276Dic86—41no—
277C8×C43—22no—
278C8×C43—22no—
279C43⋊C8—41no—
280C43⋊C8—41no—
281#26398—431nomaximal, Sylow
282C22×C43#52511yescharacteristic
283C22×C43D4211yescharacteristic
284C22×C43D4×Q811yescharacteristic
285C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C43#57511yescharacteristic
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—42no—
297C4×C43—41no—
298C4×C43—41no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43—81no—
302C4×C43C2×C22⋊Q811yescharacteristic
303C4×C43#53911yescharacteristic
304C4×C43#54711yescharacteristic
305C4×C43#55411yescharacteristic
306Dic43—22no—
307Dic43—41no—
308Dic43—42no—
309Dic43—41no—
310Dic43—41no—
311Dic43—42no—
312Dic43—81no—
313C2×#478—431no—
314C2×#440—431no—
315#2453—431no—
316D4×C4⋊C4—431no—
317#2096—431no—
318#2083—431no—
319#2068—431no—
320#2059—431no—
321#1943D4311yescharacteristic, complemented
322#1917—431no—
323#1877—431no—
324#1877—431no—
325#1864—431no—
326#1863—431no—
327#1862—431no—
328C2×C43#244911yescharacteristic
329C2×C43#311411yescharacteristic
330C2×C43#312011yescharacteristic
331C2×C43#326911yescharacteristic
332C2×C43#327211yescharacteristic
333C2×C43#338611yescharacteristic
334C2×C43#338811yescharacteristic
335D43—44no—
336C22×SD16—431no—
337C2×#125—431no—
338C2×C4×Q8—431no—
339C2×C4×D4—431no—
340C2×C4×D4—431no—
341C2×C4×D4—431no—
342C22×C4⋊C4—861no—
343#478—864no—
344#440—864no—
345C2×#107—431no—
346C2×#107—431no—
347C2×#107C2×D4311yescharacteristic
348C2×#106—431no—
349C2×#106C2×D4311yescharacteristic
350C2×C4⋊C8—431no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#97C2×D4311yescharacteristic
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—861no—
369#385—861no—
370#384—431no—
371#380—861no—
372C4×C4⋊C4—431no—
373#340—431no—
374#340—431no—
375#340C2×D4311yescharacteristic
376#340C2×D4311yescharacteristic
377#336—431no—
378#336—431no—
379#336—431no—
380#336—431no—
381C43#2639811yescharacteristic, complemented, Sylow
382C22×Q8—431no—
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×C8C22×D4311yescharacteristic
393C22×C8C22×D4311yescharacteristic
394#125—862no—
395#125—1721no—
396C4×Q8—862no—
397C4×Q8—1721no—
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—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—1724no—
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—431no—
426C2×C42—431no—
427C2×C42—861no—
428C2×C42C22×D4311yescharacteristic
429#107—22no—
430#107—862no—
431#107—862no—
432#106—22no—
433#106—1721no—
434C4⋊C8—862no—
435#103—862no—
436#103—862no—
437#103—1721no—
438#102—434no—
439#102—862no—
440#102—862no—
441#97—22no—
442#95—21no—
443#95—21no—
444#95—431no—
445#95—431no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452C24—861no—
453C2×Q8—432no—
454C2×Q8—861no—
455C2×Q8—861no—
456C2×Q8—861no—
457C2×Q8—861no—
458C2×Q8—861no—
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—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—431no—
473C22×C4—864no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—3441no—
478C22×C4—3441no—
479C22×C4—1722no—
480C22×C4—1722no—
481C22×C4—1722no—
482C22×C4—1722no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4D4×D4311yescharacteristic
486C22×C4D4×D4311yescharacteristic
487C22×C4C23×D4311yescharacteristic
488SD16—868no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8D4×D4312yes—
500C2×C8Q8×D4312yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—432no—
511C4⋊C4—862no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—3441no—
516C4⋊C4—1721no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C4⋊C4—1722no—
521C4⋊C4—1722no—
522C4⋊C4—1722no—
523C4⋊C4#1062189812yes—
524C22⋊C4—864no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C42—21no—
528C42—21no—
529C42—861no—
530C42—861no—
531C42—861no—
532C42—861no—
533C42—1722no—
534C23—862no—
535C23—862no—
536C23—862no—
537C23—1721no—
538C23—1721no—
539C23—1721no—
540C23—1721no—
541C23C2×D4×D4311yescharacteristic
542Q8—862no—
543Q8—862no—
544Q8—1721no—
545Q8—1721no—
546D4—434no—
547D4—862no—
548D4—862no—
549D4—862no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—432no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—862no—
582C2×C4—3444no—
583C2×C4—3444no—
584C2×C4—1728no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4C2×D4×D4311yescharacteristic
593C2×C4C2×Q8×D4311yescharacteristic
594C2×C4#41×D4311yescharacteristic
595C2×C4C2×#1062189811yescharacteristic
596C2×C4#1306337111yescharacteristic
597C2×C4#1306337311yescharacteristic
598C8—22no—
599C8—22no—
600C8—1721no—
601C8—1721no—
602C22—864no—
603C22—1722no—
604C22—1722no—
605C22—1722no—
606C22—1722no—
607C22—1722no—
608C22—1722no—
609C22#1458340811yescharacteristic
610C22#1458353311yescharacteristic
611C22#1458356411yescharacteristic
612C22AGL(1,ℤ/8)×D4311yescharacteristic
613C22#1458369511yescharacteristic
614C22#1458370811yescharacteristic
615C22#1458371511yescharacteristic
616C4—42no—
617C4—41no—
618C4—41no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4—862no—
623C4—3441no—
624C4—1721no—
625C4—1722no—
626C4—1721no—
627C4—1721no—
628C4—1722no—
629C4C22⋊Q8×D4311yescharacteristic
630C4#1458349711yescharacteristic
631C4#1458355011yescharacteristic
632C4#1458360911yescharacteristic
633C2—1724no—
634C2#1913841111yescharacteristic
635C2#1914473111yescharacteristic
636C2#1914480711yescharacteristic
637C2#1914615711yescharacteristic
638C2#1914619211yescharacteristic
639C2#1914751311yescharacteristic
640C2#1914753511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1943C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1943D43
hypocenterC43#26398
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
3. #19138457C2semidirect
5. #19136135C2semidirect
6. #19136070C2semidirect
7. #19135985C2semidirect
8. #19135936C2semidirect
9. #19135159C2semidirect
13. #19134848C2semidirect
15. C43×#1943C2semidirect
321. #1943D43semidirect
381. C43#26398semidirect

Maximal subgroups

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

subgroupindex
C2×#145831982
C2×#145830012
#191384572
#191374962
#191361352
#191360702
#191359852
#191359362
#191351592
#191349302
#191348552
#191348482
#191348392
C43×#19432
#2639843