Finite Group Databasebeta

← #25082128

Subgroups — #25082128

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145731C211yesmaximal, characteristic, complemented
2#19144655C211yesmaximal, characteristic
3#19143706C211yesmaximal, characteristic, complemented
4#19134041C211yesmaximal, characteristic, complemented
5#19134034C211yesmaximal, characteristic, complemented
6#19134013C211yesmaximal, characteristic, complemented
7#19134006C211yesmaximal, characteristic, complemented
8#19133997C211yesmaximal, characteristic, complemented
9#19133992C211yesmaximal, characteristic, complemented
10#19133975C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133376C211yesmaximal, characteristic, complemented
13#19133291C211yesmaximal, characteristic, complemented
14#19133252C211yesmaximal, characteristic, complemented
15C43×#3116C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583247C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583223—21no—
22#14583223—21no—
23#14583223—21no—
24#14583196—21no—
25#14583196—21no—
26#14583194C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583099C2211yescharacteristic
29#14583094C2211yescharacteristic
30#14583044—21no—
31Q8×C43⋊C8C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33C4×#10621884—21no—
34C4×#10621882—21no—
35D4×C43⋊C8—21no—
36D4×C43⋊C8—21no—
37D4×C43⋊C8C2211yescharacteristic
38D4×C43⋊C8C2211yescharacteristic
39#14582952—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42C2×C4⋊(C43⋊C8)—21no—
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#485—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#452—21no—
64C43×#441—21no—
65C43×#440—21no—
66C43×#432C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621882—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063322C2311yescharacteristic
75#13063313—21no—
76#13063299—21no—
77#13063299—21no—
78C4×D172—21no—
79C4×D172—21no—
80#13063258—21no—
81#13063258—21no—
82#13063258—21no—
83#13063256—21no—
84#13063256—21no—
85#13063256—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)D411yescharacteristic
90C4⋊(C43⋊C8)D411yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063246—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)D411yescharacteristic
107C22⋊(C43⋊C8)D411yescharacteristic
108C4×C43⋊C8—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43D411yescharacteristic
114C2×Q16×C43—21no—
115C2×SD16×C43—21no—
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#125×C43—21no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43—21no—
123C4×Q8×C43D411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43D411yescharacteristic
128C4×D4×C43C2311yescharacteristic
129#117×C43—21no—
130#117×C43—21no—
131#117×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×C22⋊D43—41no—
158#10621898—82no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164Q16×C43—42no—
165SD16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43#4111yescharacteristic
189C42×C43C2411yescharacteristic
190#10621884—42no—
191#10621882—42no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43#12111yescharacteristic
209C22×D43—41no—
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—81no—
214Q8×C43#13512yes—
215D4×C43—24no—
216D4×C43—21no—
217D4×C43#13512yes—
218C2×C4×C43—24no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—81no—
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C22⋊D43—82no—
239C2×Dic43—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—81no—
245C4×D43—82no—
246Dic86—81no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19419—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—22no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43C2×#12111yescharacteristic
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—22no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43C2×#13511yescharacteristic
278C4×C43C2×#13511yescharacteristic
279C4×C43#57711yescharacteristic
280C4×C43#57811yescharacteristic
281Dic43—81no—
282#3228—431no—
283#3116D4311yescharacteristic, complemented
284#3106—431no—
285#2988—431no—
286#1682—431no—
287#1681—431no—
288#1678—431no—
289#1677—431no—
290#1676—431no—
291#1675—431no—
292#1672—431no—
293#1671—431no—
294#1572—431no—
295#1551—431no—
296#1542—431no—
297C2×C43—41no—
298C2×C43—42no—
299C2×C43#304611yescharacteristic
300C2×C43#305011yescharacteristic
301C2×C43#306811yescharacteristic
302D43—161no—
303#533C2×D4311yescharacteristic
304#532—431no—
305C4×#41C2×D4311yescharacteristic
306#500—431no—
307#498—431no—
308#486—431no—
309#486—431no—
310#485—21no—
311#482—861no—
312#482—861no—
313#482—861no—
314#478—861no—
315#478—861no—
316#477—431no—
317#477C2×D4311yescharacteristic
318#476—431no—
319#476C2×D4311yescharacteristic
320#462C2×D4311yescharacteristic
321#461C2×D4311yescharacteristic
322#460—431no—
323#459—431no—
324#452—21no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#441—21no—
329#440—21no—
330C4×SD16—861no—
331C4×D8—861no—
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335C8×D4—861no—
336#432C2×D4311yescharacteristic
337#431—431no—
338#431—431no—
339#431—861no—
340C2×C4⋊C8—431no—
341C2×C4⋊C8—861no—
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#331—431no—
353#331—431no—
354C43#1941911yescharacteristic, complemented, Sylow
355C2×#41—861no—
356C2×#41C22⋊D4311yescharacteristic
357C2×Q16—21no—
358C2×SD16—21no—
359C2×SD16—861no—
360C2×D8—861no—
361C22×C8—861no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8C22×D4311yescharacteristic
366C4⋊Q8C22×D4311yescharacteristic
367#127—431no—
368#125—21no—
369#124—861no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372#121—861no—
373#121—861no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C22⋊D4311yescharacteristic
377C4×Q8C22×D4311yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4C22⋊D4311yescharacteristic
383C4×D4C22×D4311yescharacteristic
384#117—21no—
385#117—21no—
386#117C22⋊D4311yescharacteristic
387C2×C42—21no—
388C2×C42C22×D4311yescharacteristic
389#107—21no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—21no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—861no—
412#102—21no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—431no—
422C22⋊C8—431no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—21no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432#41—22no—
433#41—22no—
434#41—3442no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—861no—
438C2×Q8C2×C22⋊D4311yescharacteristic
439C2×D4—21no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—1721no—
444C2×D4C2×C22⋊D4311yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—1721no—
449C22×C4D4×D4311yescharacteristic
450C22×C4#1062190011yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452Q16—42no—
453SD16—42no—
454SD16—1722no—
455D8—1722no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—3441no—
467C2×C8—3441no—
468C2×C8—3441no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4C2×C22⋊D4311yescharacteristic
480C4⋊C4C2×C22⋊D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—41no—
491C42D4×D4311yescharacteristic
492C42#1062190011yescharacteristic
493C42C2×C22⋊D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—21no—
496C23—1721no—
497C23#1306329711yescharacteristic
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—81no—
502Q8—3441no—
503Q8#1306334512yes—
504D4—24no—
505D4—21no—
506D4—3441no—
507D4—3442no—
508D4—1721no—
509D4—1721no—
510D4—1721no—
511D4—1721no—
512D4#1306334512yes—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—81no—
527C2×C4—3442no—
528C2×C4—1721no—
529C2×C4#1306329711yescharacteristic
530C2×C4#1306329711yescharacteristic
531C2×C4#1306329711yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C22×C22⋊D4311yescharacteristic
534C2×C4C2×#1062190011yescharacteristic
535C8—41no—
536C8—41no—
537C8—861no—
538C8—861no—
539C8—861no—
540C8—861no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22C2×#1306329711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—3441no—
565C4C2×#1306334511yescharacteristic
566C4C2×#1306334511yescharacteristic
567C4#1458370811yescharacteristic
568C4#1458371511yescharacteristic
569C2—41no—
570C2—42no—
571C2—6881no—
572C2#1914414911yescharacteristic
573C2#1914417311yescharacteristic
574C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3116C2
socleC22×C43C2×#121
prime radical#19144655C2
hypercenter#3116D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3116

Complements

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

NH ≅ G/Ntype
1. #19145731C2semidirect
3. #19143706C2semidirect
4. #19134041C2semidirect
5. #19134034C2semidirect
6. #19134013C2semidirect
7. #19134006C2semidirect
8. #19133997C2semidirect
9. #19133992C2semidirect
10. #19133975C2semidirect
11. #19133968C2semidirect
12. #19133376C2semidirect
13. #19133291C2semidirect
14. #19133252C2semidirect
15. C43×#3116C2semidirect
283. #3116D43semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191457312
#191446552
#191437062
#191340412
#191340342
#191340132
#191340062
#191339972
#191339922
#191339752
#191339682
#191333762
#191332912
#191332522
C43×#31162
#1941943