Finite Group Databasebeta

← #25114365

Subgroups — #25114365

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582938C211yesmaximal, characteristic
2#19137487C211yesmaximal, characteristic
3#19137471C211yesmaximal, characteristic
4#19135324C211yesmaximal, characteristic, complemented
5#19135190C211yesmaximal, characteristic, complemented
6#19135177C211yesmaximal, characteristic, complemented
7#19135176C211yesmaximal, characteristic, complemented
8#19135163C211yesmaximal, characteristic, complemented
9#19134689C211yesmaximal, characteristic
10#19134680C211yesmaximal, characteristic
11#19134629C211yesmaximal, characteristic
12#19134492C211yesmaximal, characteristic, complemented
13#107×Dic43C211yesmaximal, characteristic, complemented
14#19134380C211yesmaximal, characteristic
15C43×#1944C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C2×#13063283C2211yescharacteristic
18C2×C4⋊C4×D43C2211yescharacteristic
19#14582938C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×(C2×D43)⋊C8C2211yescharacteristic
25C2×C8×Dic43C2211yescharacteristic
26#14582798C2211yescharacteristic
27#14582798C2211yescharacteristic
28#14582791—21no—
29#14582789—21no—
30#14582786—21no—
31#14582780—21no—
32#14582766—21no—
33#14582756—21no—
34#14582756C2211yescharacteristic
35#14582756C2211yescharacteristic
36C4⋊C4×Dic43—21no—
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×C4⋊Dic43C2211yescharacteristic
40C4×C4⋊Dic43C2211yescharacteristic
41C4×(C2×D43)⋊C4C2211yescharacteristic
42#14582746—21no—
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43C2311yescharacteristic
62C2×#10621872—22no—
63C2×#10621872—22no—
64C2×#10621872C2×C414yes—
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67#13063283—22no—
68#13063283C2×C414yes—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C4⋊C4×D43—22no—
77C4⋊C4×D43C2×C414yes—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4D411yescharacteristic
82C2×(C2×D43)⋊C4D411yescharacteristic
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43C2311yescharacteristic
89#13063259C2×C414yes—
90#13063258C2×C414yes—
91#13063257—22no—
92#13063256C2×C414yes—
93(C2×D43)⋊C8—22no—
94C8×Dic43—22no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114#107×C43—22no—
115#106×C43C2×C414yes—
116#97×C43—22no—
117#95×C43—21no—
118#95×C43—21no—
119C23×D43C2×D411yescharacteristic
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—24no—
139C2×C4×D43—81no—
140C2×C4×D43—81no—
141C2×C4×D43C22×C412yes—
142C2×C4×D43#4112yes—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43C22×C412yes—
147C2×C8×C43#4112yes—
148C2×C8×C43#4112yes—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43—81no—
157C4⋊C4×C43C22×C412yes—
158C4⋊C4×C43C22×C412yes—
159C42×C43—21no—
160C42×C43—21no—
161(C2×D43)⋊C4—22no—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—41no—
164(C2×D43)⋊C4—42no—
165(C2×D43)⋊C4—81no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—42no—
173C4⋊Dic43—81no—
174C4⋊Dic43C22×C412yes—
175C4⋊Dic43C22×C412yes—
176Dic43⋊C4—24no—
177C4×Dic43—21no—
178C4×Dic43—21no—
179C4×Dic43—24no—
180C4×Dic43—81no—
181C4×Dic43—81no—
182C4×Dic43—81no—
183C4×Dic43—81no—
184C2×C43⋊C8—21no—
185C2×C43⋊C8—21no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8C22×C412yes—
190#10621872—28no—
191C23×C43C22×D411yescharacteristic
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43C4×D412yes—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43C23×C411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C432−1+411yescharacteristic
222C2×C4×C432−1+411yescharacteristic
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43C4×D412yes—
243C2×Dic43#13712yes—
244C4×D43—22no—
245C4×D43—22no—
246C4×D43—22no—
247C4×D43—22no—
248C4×D43—84no—
249C8×C43—41no—
250C8×C43#11714yes—
251C43⋊C8—22no—
252C43⋊C8—41no—
253#22623—431nomaximal, Sylow
254C22×C43C2×C4×D411yescharacteristic
255C22×C43#54711yescharacteristic
256C22×C43#54711yescharacteristic
257C22×C43C2×#13711yescharacteristic
258C22×C43#57511yescharacteristic
259C22×C43#57611yescharacteristic
260C22×C43#57711yescharacteristic
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—22no—
264C2×D43—41no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—42no—
271C4×C43—42no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43C2×#11711yescharacteristic
275C4×C43#51911yescharacteristic
276C4×C43#55211yescharacteristic
277C4×C43#55211yescharacteristic
278Dic43—22no—
279Dic43—22no—
280Dic43—41no—
281Dic43—42no—
282Dic43—42no—
283Dic43—81no—
284Dic43—81no—
285C2×#428—431no—
286#2347—431no—
287#2345—431no—
288#1944D4311yescharacteristic, complemented
289#1941—431no—
290#1921—431no—
291#1920—431no—
292#1919—431no—
293#1918—431no—
294#1825—431no—
295#1823—431no—
296#1809—431no—
297#1776—431no—
298C4×#107—431no—
299#1753—431no—
300C2×C43#234411yescharacteristic
301C2×C43C4×#13711yescharacteristic
302C2×C43#294611yescharacteristic
303C2×C43#334611yescharacteristic
304C2×C43#335011yescharacteristic
305C2×C43#335511yescharacteristic
306C2×C43#335611yescharacteristic
307D43—42no—
308C22×M16—431no—
309C2×#117—431no—
310C22×C4⋊C4—431no—
311#428—438no—
312C2×#107—431no—
313C2×#107—431no—
314C2×#107C2×D4311yescharacteristic
315C2×#106—431no—
316C2×#106—431no—
317C2×#106C2×D4311yescharacteristic
318C2×C22⋊C8—431no—
319C2×#97C2×D4311yescharacteristic
320C2×C4×C8—431no—
321#389—431no—
322#389—431no—
323#389C2×D4311yescharacteristic
324#389C2×D4311yescharacteristic
325#388—861no—
326#388—861no—
327#387—861no—
328#387—861no—
329#383—861no—
330#380—431no—
331#380—431no—
332#380—861no—
333C4×C4⋊C4—431no—
334C4×C4⋊C4—431no—
335C4×C4⋊C4—431no—
336C4×C4⋊C4—431no—
337C4×C4⋊C4—861no—
338C4×C22⋊C4—431no—
339C4×C22⋊C4—861no—
340#340—431no—
341#340—431no—
342#340—431no—
343#340—431no—
344#340—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340C2×D4311yescharacteristic
349#340C2×D4311yescharacteristic
350#336—431no—
351#336—431no—
352C43#2262311yescharacteristic, complemented, Sylow
353C23×C4—431no—
354C23×C4—861no—
355C2×M16—434no—
356C2×M16—862no—
357C2×M16—862no—
358C22×C8—431no—
359C22×C8—431no—
360C22×C8C22×D4311yescharacteristic
361C22×C8C22×D4311yescharacteristic
362#117—434no—
363#117—862no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—434no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C22⋊C4—431no—
380C2×C22⋊C4—431no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C42—431no—
385C2×C42—861no—
386C2×C42—861no—
387C2×C42—861no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42C22×D4311yescharacteristic
391#107—22no—
392#107—434no—
393#107—434no—
394#106—434no—
395#106—862no—
396#106C4×D4314yes—
397C22⋊C8—862no—
398#97—22no—
399C4×C8—862no—
400#95—21no—
401#95—21no—
402#95—431no—
403#95—431no—
404#95—861no—
405#95—861no—
406#95—861no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412C24—431no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—431no—
418C22×C4—431no—
419C22×C4—432no—
420C22×C4—432no—
421C22×C4—431no—
422C22×C4—864no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—3441no—
432C22×C4—3441no—
433C22×C4D4×D4311yescharacteristic
434C22×C4D4×D4311yescharacteristic
435C22×C4C23×D4311yescharacteristic
436M16—868no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—432no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8C2×C4×D4312yes—
447C2×C8#1062190012yes—
448C2×C8#1062190212yes—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—432no—
458C4⋊C4—432no—
459C4⋊C4—864no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—3441no—
467C4⋊C4—1722no—
468C4⋊C4C2×C4×D4312yes—
469C4⋊C4C2×C4×D4312yes—
470C22⋊C4—862no—
471C22⋊C4—864no—
472C22⋊C4—3441no—
473C22⋊C4—1721no—
474C22⋊C4—1722no—
475C42—21no—
476C42—21no—
477C42—864no—
478C42—861no—
479C42—861no—
480C42—3441no—
481C42—3441no—
482C42—3441no—
483C42—3441no—
484C23—432no—
485C23—861no—
486C23—861no—
487C23—861no—
488C23—861no—
489C23—861no—
490C23—861no—
491C23C2×D4×D4311yescharacteristic
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—432no—
511C2×C4—432no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—861no—
521C2×C4—862no—
522C2×C4—862no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—3444no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4C22×C4×D4311yescharacteristic
537C2×C4#41×D4311yescharacteristic
538C2×C4C2×#1062190011yescharacteristic
539C2×C4C2×#1062190211yescharacteristic
540C2×C4#1306337211yescharacteristic
541C2×C4#1306337311yescharacteristic
542C8—41no—
543C8—862no—
544C8—1721no—
545C8#1306328314yes—
546C22—862no—
547C22—862no—
548C22—862no—
549C22—1721no—
550C22—1721no—
551C22—1721no—
552C22—1721no—
553C22C4×D4×D4311yescharacteristic
554C22#1458354911yescharacteristic
555C22#1458355211yescharacteristic
556C22#137×D4311yescharacteristic
557C22#1458369511yescharacteristic
558C22#1458370311yescharacteristic
559C22#1458370811yescharacteristic
560C4—42no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—81no—
565C4—81no—
566C4—862no—
567C4—862no—
568C4—3441no—
569C4—3441no—
570C4—1722no—
571C4—1722no—
572C4—1721no—
573C4C2×#1306328311yescharacteristic
574C4#1458337511yescharacteristic
575C4#1458358311yescharacteristic
576C4#1458358711yescharacteristic
577C2—1722no—
578C2#1913746311yescharacteristic
579C2#1914341711yescharacteristic
580C2#1914342611yescharacteristic
581C2#1914707911yescharacteristic
582C2#1914713911yescharacteristic
583C2#1914719611yescharacteristic
584C2#1914720511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1944C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1944D43
hypocenterC43#22623
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
4. #19135324C2semidirect
5. #19135190C2semidirect
6. #19135177C2semidirect
7. #19135176C2semidirect
8. #19135163C2semidirect
12. #19134492C2semidirect
13. #107×Dic43C2semidirect
15. C43×#1944C2semidirect
19. #14582938C4semidirect
288. #1944D43semidirect
352. C43#22623semidirect

Maximal subgroups

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

subgroupindex
C2×#145829382
#191374872
#191374712
#191353242
#191351902
#191351772
#191351762
#191351632
#191346892
#191346802
#191346292
#191344922
#107×Dic432
#191343802
C43×#19442
#2262343