Finite Group Databasebeta

← #25082126

Subgroups — #25082126

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#19145733C211yesmaximal, characteristic, complemented
2#19144758C211yesmaximal, characteristic, complemented
3#19144656C211yesmaximal, characteristic
4#19143703C211yesmaximal, characteristic, complemented
5#19134040C211yesmaximal, characteristic, complemented
6#19134033C211yesmaximal, characteristic, complemented
7#19134012C211yesmaximal, characteristic, complemented
8#19134005C211yesmaximal, characteristic, complemented
9#19134000C211yesmaximal, characteristic, complemented
10#19133995C211yesmaximal, characteristic, complemented
11#19133978C211yesmaximal, characteristic, complemented
12#19133971C211yesmaximal, characteristic, complemented
13#19133291C211yesmaximal, characteristic, complemented
14#19133250C211yesmaximal, characteristic, complemented
15C43×#1572C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583241—21no—
24#14583224—21no—
25#14583224—21no—
26#14583224—21no—
27#14583200—21no—
28#14583200—21no—
29#14583195C2211yescharacteristic
30#14583195C2211yescharacteristic
31#14583190C2211yescharacteristic
32#14583190C2211yescharacteristic
33#14583110C2211yescharacteristic
34#14583105C2211yescharacteristic
35#14583100C2211yescharacteristic
36#14583095C2211yescharacteristic
37#14583063—21no—
38#14583046—21no—
39C8×Dic86C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14583007—21no—
42#14583001—21no—
43C4×#10621873—21no—
44C4×D344—21no—
45C8×D172C2211yescharacteristic
46C8×D172C2211yescharacteristic
47(C22⋊D43)⋊C8—21no—
48(C22⋊D43)⋊C8—21no—
49#14582951—21no—
50C2×C4⋊(C43⋊C8)C2211yescharacteristic
51C4⋊C8×D43—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69C2×Dic172—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×D344—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063317—21no—
81#13063313—21no—
82#13063304—21no—
83#13063304—21no—
84#13063299—21no—
85#13063299—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88C4×Dic86D411yescharacteristic
89C4×Dic86C2311yescharacteristic
90C4×D172—21no—
91C4×D172—21no—
92C4×D172D411yescharacteristic
93C4×D172C2311yescharacteristic
94C4×C22⋊D43—21no—
95C4×C22⋊D43—21no—
96#13063284—21no—
97#13063284D411yescharacteristic
98#13063282—21no—
99C42×D43—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107#13063257—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063247—21no—
124#13063247—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×C22⋊D43—41no—
149#10621898—22no—
150#10621898—22no—
151#10621898—82no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—41no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43#4111yescharacteristic
175C42×C43C2411yescharacteristic
176C22⋊Dic43—21no—
177C22⋊Dic43—41no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—41no—
181(C2×D43)⋊C4—41no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43C2×D411yescharacteristic
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—81no—
201Dic172—42no—
202D344—42no—
203#10621873—42no—
204#10621873—42no—
205C8×D43—81no—
206C8×D43—81no—
207C23×C43#12111yescharacteristic
208C22×D43—21no—
209C22×D43—41no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C22⋊D43—24no—
222C22⋊D43—82no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229D172—21no—
230D172—41no—
231D172—41no—
232D172—41no—
233D172—41no—
234D172—81no—
235D172#13512yes—
236C4×D43—24no—
237C4×D43—41no—
238C4×D43—41no—
239C4×D43—81no—
240C4×D43—82no—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244Dic86—81no—
245Dic86—81no—
246Dic86#13512yes—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19419—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43C2×#12111yescharacteristic
262C2×D43—22no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43C2×#13511yescharacteristic
273C4×C43C2×#13511yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—22no—
277Dic43—41no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281Dic43—81no—
282#3228—431no—
283#3116—431no—
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#1572D4311yescharacteristic, complemented
295#1551—431no—
296#1542—431no—
297C2×C43—41no—
298C2×C43#304611yescharacteristic
299C2×C43#305011yescharacteristic
300C2×C43#306811yescharacteristic
301D43—42no—
302D43—161no—
303#533—431no—
304#532—431no—
305C4×#41—431no—
306#500—431no—
307#498—431no—
308#486—431no—
309#486—431no—
310#485—861no—
311#482—861no—
312#482—861no—
313#482—861no—
314#478—861no—
315#478—861no—
316#477—431no—
317#477—431no—
318#476—431no—
319#476—431no—
320#462—431no—
321#461—431no—
322#460—431no—
323#459—431no—
324#452—861no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#441—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335C8×D4—861no—
336#432C2×D4311yescharacteristic
337#431—861no—
338#431C2×D4311yescharacteristic
339#431C2×D4311yescharacteristic
340C2×C4⋊C8—431no—
341C2×C4⋊C8—861no—
342#335C2×D4311yescharacteristic
343#335C2×D4311yescharacteristic
344#334C2×D4311yescharacteristic
345#334C2×D4311yescharacteristic
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—431no—
356C2×#41—861no—
357C2×Q16—861no—
358C2×SD16—861no—
359C2×SD16—861no—
360C2×D8—861no—
361C22×C8—861no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—431no—
367#127—431no—
368#125—861no—
369#124—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—861no—
373#121—861no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×D4—431no—
379C4×D4—431no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4—861no—
383C4×D4—861no—
384#117—431no—
385#117—861no—
386#117—861no—
387C2×C42—861no—
388C2×C42C22×D4311yescharacteristic
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8D17211yescharacteristic
403C4⋊C8D17211yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—861no—
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—21no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8D17211yescharacteristic
425C22⋊C8D17211yescharacteristic
426#97—21no—
427C4×C8—21no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432#41—862no—
433#41—862no—
434#41—3442no—
435C2×Q8—431no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×D4—431no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—1721no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1721no—
449C22×C4C2×D17211yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4#1062190211yescharacteristic
452Q16—1722no—
453SD16—1722no—
454SD16—1722no—
455D8—1722no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—3441no—
463C2×C8—3441no—
464C2×C8—3441no—
465C2×C8C2×D17211yescharacteristic
466C2×C8C2×D17211yescharacteristic
467C2×C8C2×D17211yescharacteristic
468C2×C8C2×D17211yescharacteristic
469C4⋊C4—431no—
470C4⋊C4—431no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—861no—
488C42—861no—
489C42—861no—
490C42—1721no—
491C42C2×D17211yescharacteristic
492C42D4×D4311yescharacteristic
493C42#1062190211yescharacteristic
494C42C23×D4311yescharacteristic
495C23—861no—
496C23—1721no—
497C23#1306330011yescharacteristic
498Q8—432no—
499Q8—861no—
500Q8—3441no—
501Q8—3441no—
502Q8—1721no—
503Q8—1721no—
504D4—432no—
505D4—864no—
506D4—861no—
507D4—3441no—
508D4—3442no—
509D4—1721no—
510D4—1721no—
511D4—1721no—
512D4—1721no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—864no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—3442no—
523C2×C4—3441no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306330011yescharacteristic
530C2×C4#1306330011yescharacteristic
531C2×C4#1306330011yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C22×D17211yescharacteristic
534C2×C4C2×#1062190211yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—862no—
549C22—3441no—
550C22—3441no—
551C22—3441no—
552C22—1721no—
553C22—1721no—
554C22C2×#1306330011yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—862no—
560C4—3441no—
561C4—3441no—
562C4—3441no—
563C4—1721no—
564C4—1721no—
565C4#135×D4311yescharacteristic
566C4#135×D4311yescharacteristic
567C4#1458371111yescharacteristic
568C4#1458371611yescharacteristic
569C2—41no—
570C2—1722no—
571C2—6881no—
572C2#1914414711yescharacteristic
573C2#1914417711yescharacteristic
574C2#1914432411yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1572C2
socleC22×C43C2×#121
prime radical#19144656C2
hypercenter#1572D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
1. #19145733C2semidirect
2. #19144758C2semidirect
4. #19143703C2semidirect
5. #19134040C2semidirect
6. #19134033C2semidirect
7. #19134012C2semidirect
8. #19134005C2semidirect
9. #19134000C2semidirect
10. #19133995C2semidirect
11. #19133978C2semidirect
12. #19133971C2semidirect
13. #19133291C2semidirect
14. #19133250C2semidirect
15. C43×#1572C2semidirect
294. #1572D43semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191457332
#191447582
#191446562
#191437032
#191340402
#191340332
#191340122
#191340052
#191340002
#191339952
#191339782
#191339712
#191332912
#191332502
C43×#15722
#1941943