Finite Group Databasebeta

← #25063813

Subgroups — #25063813

Order 11008.

974 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148683C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19136958C211yesmaximal, characteristic, complemented
4#19133121C211yesmaximal, characteristic
5#19133119C212yesmaximal
6#19133105C212yesmaximal, complemented
7#19133094C211yesmaximal, characteristic, complemented
8#19133092C212yesmaximal, complemented
9#19133080C212yesmaximal
10#19133079C211yesmaximal, characteristic
11C43×#1506C211yesmaximal, characteristic, complemented
12#14583625C412yescomplemented
13#14583624C411yescharacteristic, complemented
14#14583624C411yescharacteristic, complemented
15#14583623C411yescharacteristic, complemented
16#14583621C412yescomplemented
17#14583591—21no—
18#14583582—22no—
19#14583564C411yescharacteristic, complemented
20#14583562—21no—
21#14583508—22no—
22#14583507—21no—
23#14583451C2212yes—
24#14583435C2212yes—
25#14583433C2211yescharacteristic
26#14583375—21no—
27C2×C4×Dic86—21no—
28C2×C4×Dic86C2211yescharacteristic
29#14583027—22no—
30#14583026—21no—
31#14583023—21no—
32#14582953C2212yes—
33#14582952C2211yescharacteristic
34#14582949C2212yes—
35C4×C4⋊Dic43—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37#14582750—22no—
38#14582750C2212yes—
39#14582744C2212yes—
40#14582637C2212yes—
41#14582636C2212yes—
42#14582636C2212yes—
43#14582635C2211yescharacteristic
44#14582635C2211yescharacteristic
45#14582634C2212yes—
46#14582632C2211yescharacteristic
47#14582632C2211yescharacteristic
48C43×#533C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#376C2211yescharacteristic
51C43×#328C2212yes—
52C43×#328C2212yes—
53C22×Dic86D411yescharacteristic
54C2×Q8×D43—21no—
55#13063324—22no—
56#13063324C2×C412yes—
57#13063323—21no—
58#13063323C2×C412yes—
59#13063320—22no—
60#13063320—22no—
61#13063320—22no—
62#13063319—21no—
63#13063319—22no—
64#13063317—22no—
65#13063317C2×C411yescharacteristic
66#13063316—21no—
67#13063316—22no—
68#13063316C2×C412yes—
69#13063315—22no—
70#13063315—22no—
71#13063315—22no—
72#13063314C2×C412yes—
73#13063313C2×C411yescharacteristic
74#13063309—22no—
75#13063308—21no—
76#13063305—21no—
77#13063304C2311yescharacteristic
78#13063303—22no—
79#13063303—22no—
80#13063302—22no—
81#13063301—21no—
82#13063299C2311yescharacteristic
83Q8×Dic43—21no—
84Q8×Dic43C2×C412yes—
85Q8×Dic43C2×C412yes—
86C4×Dic86—28no—
87C4×Dic86—22no—
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86C2×C411yescharacteristic
90C4×Dic86C2×C412yes—
91C4×Dic86C2×C411yescharacteristic
92C4×Dic86D411yescharacteristic
93C4×Dic86D411yescharacteristic
94C4×Dic86D412yes—
95#13063290—21no—
96#13063290—22no—
97#13063290C2×C412yes—
98C4×D172C2×C411yescharacteristic
99#13063287C2×C412yes—
100C4×C22⋊D43—21no—
101(C22⋊D43)⋊C4—22no—
102#13063283—21no—
103#13063283—22no—
104#13063282—21no—
105#13063282—22no—
106#13063281—22no—
107C2×C4⋊Dic43—21no—
108C2×C4⋊Dic43D411yescharacteristic
109C2×Dic43⋊C4—22no—
110C2×Dic43⋊C4D412yes—
111C2×C4×Dic43—22no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—22no—
114C2×C4×Dic43C2312yes—
115C4⋊(C43⋊C8)—21no—
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)C2311yescharacteristic
119C22⋊(C43⋊C8)C2311yescharacteristic
120#13063235—22no—
121C4×C43⋊C8—21no—
122C8×Dic43—22no—
123C43⋊#95—22no—
124C43⋊#95C2312yes—
125C4⋊Q8×C43C2×C411yescharacteristic
126C4⋊Q8×C43C2×C411yescharacteristic
127#125×C43—21no—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43C2312yes—
130C4×Q8×C43—21no—
131C4×Q8×C43C2×C412yes—
132#117×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2312yes—
137#97×C43—21no—
138#95×C43—21no—
139#95×C43C2311yescharacteristic
140#95×C43C2311yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43C22×C412yes—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—21no—
149C22×Dic43—22no—
150C22×Dic43C2×D412yes—
151C22×Dic43C2×D412yes—
152Q8×D43—44no—
153C2×D172C22×C411yescharacteristic
154C2×C4×D43—21no—
155C2×C4×D43—22no—
156C2×Dic86—24no—
157C2×Dic86—22no—
158C2×Dic86C22⋊C412yes—
159C2×Dic86C22⋊C411yescharacteristic
160C2×Dic86C22⋊C411yescharacteristic
161C2×Dic86C22×C411yescharacteristic
162C2×C8×C43—22no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43C22×C412yes—
169C22⋊C4×C43—22no—
170C42×C43—24no—
171C42×C43—22no—
172C42×C43C22×C411yescharacteristic
173C42×C43C22×C411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C22⋊Dic43—21no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—22no—
183(C2×D43)⋊C4—22no—
184C4⋊Dic43—24no—
185C4⋊Dic43—22no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43C22⋊C411yescharacteristic
189C4⋊Dic43C22⋊C411yescharacteristic
190C4⋊Dic43C22⋊C412yes—
191C4⋊Dic43C22×C411yescharacteristic
192C4⋊Dic43C22×C411yescharacteristic
193Dic43⋊C4—28no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4C22⋊C412yes—
204Dic43⋊C4C22⋊C412yes—
205Dic43⋊C4C22⋊C412yes—
206Dic43⋊C4C22⋊C412yes—
207C4×Dic43—28no—
208C4×Dic43—21no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43—82no—
213C4×Dic43—81no—
214C4×Dic43C22×C412yes—
215C4×Dic43C22×C412yes—
216C4×Dic43C2×D412yes—
217C4×Dic43C2×D412yes—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C23×C43C22×D411yescharacteristic
221C22×D43—21no—
222Q8×C43—42no—
223Q8×C43—42no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43C2×C22⋊C411yescharacteristic
238C2×C4×C43C2×C22⋊C411yescharacteristic
239C2×C4×C43C2×C22⋊C411yescharacteristic
240C2×C4×C43C23×C411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C22⋊D43—41no—
243C22⋊D43—41no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256C2×Dic43C2×C22⋊C412yes—
257D172—41no—
258C4×D43—42no—
259C4×D43—44no—
260Dic86—22no—
261Dic86—24no—
262Dic86—44no—
263Dic86—41no—
264Dic86#10414yes—
265C8×C43—42no—
266C43⋊C8—41no—
267C43⋊C8—41no—
268#17549—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43C22×C22⋊C411yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57811yescharacteristic
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—42no—
285C4×C43—42no—
286C4×C43C2×#10412yes—
287Dic43—22no—
288Dic43—22no—
289Dic43—22no—
290Dic43—44no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294Dic43C2×#10414yes—
295#3523—431no—
296#2984—431no—
297#2276—431no—
298#1509—431no—
299#1509—432no—
300#1506—432no—
301#1506D4311yescharacteristic, complemented
302#1503—432no—
303#1503—431no—
304#1500—431no—
305#1500—432no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43#288411yescharacteristic
309C2×C43#289811yescharacteristic
310C2×C43C22×#10411yescharacteristic
311D43—81no—
312#557—431no—
313#557—431no—
314#557—432no—
315#556—431no—
316#556—432no—
317#552—862no—
318#552—861no—
319D4×Q8—431no—
320D4×Q8—861no—
321#541—861no—
322#541—862no—
323#533—432no—
324#533C2×D4311yescharacteristic
325#529—432no—
326#529—431no—
327#519—861no—
328C2×C4×Q8—431no—
329C2×C4×Q8—861no—
330#446—862no—
331#446—861no—
332C8×Q8—861no—
333#432—432no—
334#432C2×D4311yescharacteristic
335#431—431no—
336#431—432no—
337C4×C4⋊C4—431no—
338C4×C4⋊C4—432no—
339C4×C4⋊C4—862no—
340C4×C4⋊C4—861no—
341#376—432no—
342#376C2×D4311yescharacteristic
343#328—432no—
344#328—432no—
345#328—432no—
346#328—431no—
347#328—431no—
348#328C2×D4312yes—
349#328C2×D4312yes—
350#327—432no—
351#327—431no—
352#327—431no—
353C43#1754911yescharacteristic, complemented, Sylow
354C22×Q8—431no—
355C22×Q8—861no—
356C4⋊Q8—432no—
357C4⋊Q8—432no—
358C4⋊Q8—862no—
359C4⋊Q8—861no—
360C4⋊Q8C4×D4311yescharacteristic
361C4⋊Q8C4×D4311yescharacteristic
362#126—862no—
363#126—862no—
364#126—862no—
365#126—862no—
366#126—861no—
367#125—21no—
368#125—432no—
369#125—431no—
370#125—862no—
371#125—862no—
372#125—862no—
373#125—862no—
374#125—862no—
375#125—861no—
376#124—432no—
377#124—431no—
378#123—862no—
379#123—861no—
380C22⋊Q8—21no—
381C22⋊Q8—431no—
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C22⋊Q8—862no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387C22⋊Q8C22×D4312yes—
388#121—431no—
389C4×Q8—21no—
390C4×Q8—431no—
391C4×Q8—432no—
392C4×Q8—431no—
393C4×Q8—431no—
394C4×Q8—432no—
395C4×Q8—431no—
396C4×Q8—432no—
397C4×Q8—432no—
398C4×Q8—432no—
399C4×Q8—431no—
400C4×Q8—862no—
401C4×Q8—868no—
402C4×Q8—862no—
403C4×Q8—861no—
404C4×Q8—861no—
405C4×Q8C4×D4312yes—
406C4×D4—432no—
407C4×D4—431no—
408C4×D4—862no—
409C4×D4—861no—
410#117—21no—
411#117—862no—
412#117—862no—
413#117—862no—
414#117—861no—
415#117—861no—
416C2×C4⋊C4—432no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4—861no—
420C2×C42—21no—
421C2×C42—432no—
422C2×C42—862no—
423C2×C42—862no—
424C2×C42—861no—
425C2×C42C22×D4311yescharacteristic
426C4⋊C8—21no—
427C4⋊C8—862no—
428C4⋊C8—862no—
429C4⋊C8—861no—
430C22⋊C8—431no—
431C22⋊C8—431no—
432C22⋊C8C22×D4312yes—
433#97—21no—
434#97—862no—
435C4×C8—862no—
436C4×C8—861no—
437#95—21no—
438#95—432no—
439#95—862no—
440#95C22×D4311yescharacteristic
441#95C22×D4311yescharacteristic
442C2×Q8—21no—
443C2×Q8—431no—
444C2×Q8—432no—
445C2×Q8—431no—
446C2×Q8—431no—
447C2×Q8—862no—
448C2×Q8—864no—
449C2×Q8—1724no—
450C2×Q8C2×C4×D4312yes—
451C2×D4—431no—
452C2×D4—861no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—861no—
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4C23×D4311yescharacteristic
463C2×C8—22no—
464C2×C8—861no—
465C2×C8—861no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—432no—
472C4⋊C4—431no—
473C4⋊C4—432no—
474C4⋊C4—431no—
475C4⋊C4—432no—
476C4⋊C4—432no—
477C4⋊C4—432no—
478C4⋊C4—431no—
479C4⋊C4—431no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—862no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C4⋊C4—868no—
489C4⋊C4—864no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4C2×C4×D4312yes—
495C22⋊C4—22no—
496C22⋊C4—862no—
497C22⋊C4—862no—
498C22⋊C4—862no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C22⋊C4—861no—
503C22⋊C4—861no—
504C42—24no—
505C42—22no—
506C42—432no—
507C42—432no—
508C42—432no—
509C42—432no—
510C42—862no—
511C42—862no—
512C42—862no—
513C42—868no—
514C42—861no—
515C42—3441no—
516C42—3442no—
517C42C2×C4×D4311yescharacteristic
518C42C2×C4×D4311yescharacteristic
519C42D4×D4311yescharacteristic
520C42D4×D4311yescharacteristic
521C23—861no—
522C23C2×D4×D4311yescharacteristic
523Q8—42no—
524Q8—42no—
525Q8—434no—
526Q8—864no—
527Q8—862no—
528Q8—1721no—
529Q8—1724no—
530D4—1721no—
531D4—1721no—
532D4—1721no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—432no—
546C2×C4—432no—
547C2×C4—432no—
548C2×C4—432no—
549C2×C4—864no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—864no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—1724no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4C22⋊C4×D4311yescharacteristic
561C2×C4C22⋊C4×D4311yescharacteristic
562C2×C4C22⋊C4×D4311yescharacteristic
563C2×C4C22⋊C4×D4311yescharacteristic
564C2×C4C22×C4×D4311yescharacteristic
565C2×C4C2×D4×D4311yescharacteristic
566C8—42no—
567C8—1721no—
568C8—1721no—
569C22—21no—
570C22—21no—
571C22—1721no—
572C22—1721no—
573C22—1721no—
574C22C2×C22⋊C4×D4311yescharacteristic
575C22#1458370811yescharacteristic
576C22#1458371511yescharacteristic
577C4—21no—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—42no—
586C4—434no—
587C4—862no—
588C4—862no—
589C4—862no—
590C4—1724no—
591C4—1721no—
592C4—1721no—
593C4—1721no—
594C4#104×D4312yes—
595C2—21no—
596C2—21no—
597C2—3441no—
598C2#1914305711yescharacteristic
599C2#1914312711yescharacteristic
600C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1506C2
socleC22×C43C22×C22⋊C4
prime radical#13063299C23
cosocleC22×C4×C43C24
hypercenter#1506D43
hypocenterC43#17549
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19136958C2semidirect
6. #19133105C2semidirect
7. #19133094C2semidirect
8. #19133092C2semidirect
11. C43×#1506C2semidirect
12. #14583625C4semidirect
13. #14583624C4semidirect
14. #14583624C4semidirect
15. #14583623C4semidirect
16. #14583621C4semidirect
19. #14583564C4semidirect
301. #1506D43semidirect
353. C43#17549semidirect

Maximal subgroups

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

subgroupindex
#191486832
#191436852
#191369582
#191331212
#191331192
#191331052
#191330942
#191330922
#191330802
#191330792
C43×#15062
#1754943