Finite Group Databasebeta

← #25196369

Subgroups — #25196369

Order 11008.

690 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#19140571C211yesmaximal, characteristic, complemented
2#19137308C211yesmaximal, characteristic
3#19136159C211yesmaximal, characteristic, complemented
4#19136153C211yesmaximal, characteristic, complemented
5#19135831C211yesmaximal, characteristic
6#19135294C211yesmaximal, characteristic
7#19135282C211yesmaximal, characteristic, complemented
8#19135275C211yesmaximal, characteristic
9#19135273C211yesmaximal, characteristic, complemented
10#19134608C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic
12#19134598C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic
14#19134451C211yesmaximal, characteristic, complemented
15C43×#2042C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×Dic43⋊C8C2211yescharacteristic
19C2×Dic43⋊C8C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063235C2211yescharacteristic
25C2×C8×Dic43C2211yescharacteristic
26#14582840—21no—
27#14582839—21no—
28#14582832—21no—
29#14582830—21no—
30#14582806C2211yescharacteristic
31#14582802C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582792—21no—
36#14582792—21no—
37#14582774—21no—
38#14582774—21no—
39#14582769C2211yescharacteristic
40#14582768C2211yescharacteristic
41#14582764C2211yescharacteristic
42#14582745C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×#124×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62Q8×Dic43—22no—
63Q8×Dic43—22no—
64D4×Dic43—22no—
65D4×Dic43—22no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43C2311yescharacteristic
83C2×C4×Dic43C2311yescharacteristic
84Dic43⋊C8—22no—
85Dic43⋊C8—22no—
86#13063249—22no—
87#13063249—41no—
88#13063246—22no—
89#13063246—41no—
90#13063235—41no—
91C8×Dic43—41no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95D411yescharacteristic
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C22×Q8×C43C2311yescharacteristic
104C22×D4×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107#124×C43—22no—
108#124×C43—22no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#103×C43—22no—
116#103×C43—41no—
117#102×C43—22no—
118#102×C43—41no—
119#95×C43—21no—
120C24×C43—21no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43#4112yes—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43#4112yes—
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×Dic43—21no—
143C22×Dic43—42no—
144C22×Dic43—81no—
145C22×Dic43—81no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—81no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C42×C43—21no—
164C42×C43—21no—
165C22⋊Dic43—42no—
166C22⋊Dic43—81no—
167C22⋊Dic43—81no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—42no—
177C4⋊Dic43—81no—
178C4⋊Dic43—81no—
179C4⋊Dic43—81no—
180Dic43⋊C4—81no—
181Dic43⋊C4—81no—
182Dic43⋊C4—81no—
183Dic43⋊C4—81no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—42no—
187C4×Dic43#4112yes—
188C4×Dic43#4112yes—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C23×C43—22no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203Q8×C43—22no—
204Q8×C43—22no—
205Q8×C43—41no—
206Q8×C43—41no—
207D4×C43—22no—
208D4×C43—22no—
209D4×C43—41no—
210D4×C43—41no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×C4×C432−1+411yescharacteristic
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—84no—
255C2×Dic43#12412yes—
256C2×Dic43#12412yes—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#29134—431nomaximal, Sylow
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43#52511yescharacteristic
270C22×C43C2×#12411yescharacteristic
271C22×C43#53711yescharacteristic
272C22×C43#57611yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57811yescharacteristic
276C4×C43—42no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#55211yescharacteristic
282C4×C43#55211yescharacteristic
283C4×C43#55311yescharacteristic
284C4×C43#55311yescharacteristic
285Dic43—22no—
286Dic43—22no—
287Dic43—41no—
288Dic43—41no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292Dic43—81no—
293#2647—431no—
294#2326—431no—
295#2100—431no—
296#2099—431no—
297#2042—431no—
298#2042D4311yescharacteristic
299#1936—431no—
300#1935—431no—
301#1934—431no—
302#1933—431no—
303#1805—431no—
304#1804—431no—
305#1803—431no—
306#1802—431no—
307#1768—431no—
308C2×C43—82no—
309C2×C43#256211yescharacteristic
310C2×C43#311911yescharacteristic
311C2×C43#312011yescharacteristic
312C2×C43#313611yescharacteristic
313C2×C43#313711yescharacteristic
314C2×C43#326211yescharacteristic
315C2×C43#326311yescharacteristic
316C2×#124C2×D4311yescharacteristic
317C2×C4×Q8—431no—
318C2×C4×D4—431no—
319C2×C4⋊C8—431no—
320C2×C4⋊C8—431no—
321C2×#103—431no—
322C2×#103—431no—
323C2×#103C2×D4311yescharacteristic
324C2×#103C2×D4311yescharacteristic
325C2×#102—431no—
326C2×#102—431no—
327C2×#102C2×D4311yescharacteristic
328C2×#102C2×D4311yescharacteristic
329C2×#97—431no—
330C2×C4×C8—431no—
331#400—861no—
332#400—861no—
333#398—861no—
334#398—861no—
335#391—431no—
336#390—431no—
337#389—431no—
338#389—431no—
339#389—431no—
340#389C2×D4311yescharacteristic
341#388—861no—
342#388—861no—
343#385—861no—
344#385—861no—
345#384—431no—
346#384—431no—
347#382—431no—
348#376—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#336—431no—
358#336C2×D4311yescharacteristic
359C43#2913411yescharacteristic, complemented, Sylow
360C22×Q8C22×D4311yescharacteristic
361C22×D4C22×D4311yescharacteristic
362C23×C4—861no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8C22×D4311yescharacteristic
366C22×C8C22×D4311yescharacteristic
367#124—22no—
368#124—22no—
369C4×Q8—862no—
370C4×Q8—862no—
371C4×D4—862no—
372C4×D4—862no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—861no—
396C2×C42C22×D4311yescharacteristic
397C4⋊C8—862no—
398C4⋊C8—862no—
399#103—22no—
400#103—41no—
401#103—862no—
402#103—1721no—
403#102—22no—
404#102—41no—
405#102—862no—
406#102—1721no—
407#97—1721no—
408C4×C8—1721no—
409#95—21no—
410#95—431no—
411#95—431no—
412#95—431no—
413#95—431no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421C24—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8#1062190012yes—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4#1062190012yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—3441no—
446C22×C4—3441no—
447C22×C4—1722no—
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4C23×D4311yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—81no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—3441no—
477C4⋊C4—3441no—
478C4⋊C4—3441no—
479C4⋊C4—3441no—
480C4⋊C4—3441no—
481C4⋊C4—3441no—
482C4⋊C4—3441no—
483C4⋊C4—1722no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—3441no—
487C22⋊C4—3441no—
488C22⋊C4—1722no—
489C42—21no—
490C42—21no—
491C42—432no—
492C42—432no—
493C42—861no—
494C42—861no—
495C42—1722no—
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C2×D4×D4311yescharacteristic
504Q8—22no—
505Q8—22no—
506Q8—41no—
507Q8—41no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—432no—
528C2×C4—432no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—3444no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4#41×D4311yescharacteristic
553C2×C4#41×D4311yescharacteristic
554C2×C4C2×#1062190011yescharacteristic
555C2×C4C2×#1062190011yescharacteristic
556C2×C4#1306337011yescharacteristic
557C2×C4#1306337211yescharacteristic
558C8—41no—
559C8—41no—
560C8—1721no—
561C8—1721no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1458340511yescharacteristic
570C22#124×D4311yescharacteristic
571C22#1458347811yescharacteristic
572C22#1458370311yescharacteristic
573C22#1458370611yescharacteristic
574C22#1458370811yescharacteristic
575C22#1458371311yescharacteristic
576C4—41no—
577C4—41no—
578C4—42no—
579C4—81no—
580C4—81no—
581C4—862no—
582C4—862no—
583C4—3441no—
584C4—3441no—
585C4—3441no—
586C4—3441no—
587C4—1721no—
588C4—1721no—
589C4#1458358611yescharacteristic
590C4#1458358611yescharacteristic
591C4#1458359211yescharacteristic
592C4#1458359211yescharacteristic
593C2—82no—
594C2#1913975511yescharacteristic
595C2#1914479511yescharacteristic
596C2#1914481011yescharacteristic
597C2#1914494611yescharacteristic
598C2#1914495911yescharacteristic
599C2#1914605311yescharacteristic
600C2#1914606311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2042C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2042D43
hypocenterC43#29134
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2042

Complements

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

NH ≅ G/Ntype
1. #19140571C2semidirect
3. #19136159C2semidirect
4. #19136153C2semidirect
7. #19135282C2semidirect
9. #19135273C2semidirect
10. #19134608C2semidirect
12. #19134598C2semidirect
14. #19134451C2semidirect
359. C43#29134semidirect

Maximal subgroups

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

subgroupindex
#191405712
#191373082
#191361592
#191361532
#191358312
#191352942
#191352822
#191352752
#191352732
#191346082
#191346032
#191345982
#191345932
#191344512
C43×#20422
#2913443