Finite Group Databasebeta

← #25084211

Subgroups — #25084211

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145933C211yesmaximal, characteristic
2#19145748C211yesmaximal, characteristic, complemented
3#19145624C211yesmaximal, characteristic
4#19143757C211yesmaximal, characteristic
5#19134150C211yesmaximal, characteristic, complemented
6#19134143C211yesmaximal, characteristic, complemented
7#19134114C211yesmaximal, characteristic, complemented
8#19134109C211yesmaximal, characteristic, complemented
9#19134026C211yesmaximal, characteristic, complemented
10#19134019C211yesmaximal, characteristic, complemented
11#19133990C211yesmaximal, characteristic, complemented
12#19133985C211yesmaximal, characteristic, complemented
13#19133296C211yesmaximal, characteristic, complemented
14C2×#14582646C211yesmaximal, characteristic, complemented
15C43×#1573C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583293—21no—
22#14583268—21no—
23#14583250C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583235—21no—
26#14583235—21no—
27#14583207—21no—
28#14583195—21no—
29#14583195—21no—
30#14583185C2211yescharacteristic
31#14583180C2211yescharacteristic
32#14583140—21no—
33#14583128—21no—
34#14583122—21no—
35#14583110C2211yescharacteristic
36#14583110C2211yescharacteristic
37#14583110C2211yescharacteristic
38#14583105C2211yescharacteristic
39#14583105C2211yescharacteristic
40#14583105C2211yescharacteristic
41#14583057—21no—
42#14583040—21no—
43#14583029C2211yescharacteristic
44C8×Dic86C2211yescharacteristic
45#14582978C2211yescharacteristic
46#14582967—21no—
47C8×D172C2211yescharacteristic
48(C22⋊D43)⋊C8—21no—
49#14582959—21no—
50#14582924—21no—
51C2×C4⋊(C43⋊C8)C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C22×Dic86—21no—
68C2×Dic172—21no—
69C2×Dic172—21no—
70C2×Dic172—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063325—21no—
78#13063325—21no—
79#13063325—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063325C2311yescharacteristic
83#13063325C2311yescharacteristic
84#13063319—21no—
85#13063317—21no—
86#13063317D411yescharacteristic
87#13063313D411yescharacteristic
88#13063308—21no—
89#13063304—21no—
90#13063304—21no—
91#13063304D411yescharacteristic
92#13063299D411yescharacteristic
93C4×Dic86—21no—
94C4×Dic86—21no—
95C4×Dic86C2311yescharacteristic
96C4×D172C2311yescharacteristic
97C4×C22⋊D43—21no—
98#13063284—21no—
99#13063282—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—21no—
102#13063259—21no—
103#13063259—21no—
104#13063259—21no—
105#13063259—21no—
106#13063259—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#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063250—21no—
121#13063250—21no—
122#13063250—21no—
123#13063250—21no—
124#13063247—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127#13063235—21no—
128C8×Dic43—21no—
129C22×C8×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43D411yescharacteristic
140C22⋊C8×C43D411yescharacteristic
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C22×Dic43—41no—
149C2×D172C2×D411yescharacteristic
150C2×C4×D43—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—41no—
156C2×Dic86—81no—
157C2×Dic86—81no—
158C2×Dic86C2×D411yescharacteristic
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—81no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43C2×D411yescharacteristic
170C42×C43#4111yescharacteristic
171C42×C43C2411yescharacteristic
172C22⋊Dic43—21no—
173C22⋊Dic43—41no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—41no—
187C4⋊Dic43—41no—
188C4⋊Dic43C2×D411yescharacteristic
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—81no—
201Dic172—81no—
202Dic172—81no—
203Dic172—81no—
204#10621873—81no—
205#10621873—81no—
206#10621873—81no—
207#10621872—81no—
208C8×D43—81no—
209C23×C43#12111yescharacteristic
210C22×D43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C22⋊D43—42no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—82no—
231D172—21no—
232D172—21no—
233C4×D43—41no—
234C4×D43—41no—
235Dic86—21no—
236Dic86—21no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—82no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256#19590—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43#47312yes—
260C22×C43C2×#12111yescharacteristic
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43#57611yescharacteristic
269C4×C43#57711yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272Dic43—41no—
273Dic43—41no—
274Dic43—41no—
275Dic43—81no—
276Dic43—81no—
277Dic43—81no—
278Dic43—81no—
279#3248—431no—
280#3230—431no—
281#3218—431no—
282#2994—431no—
283#1700—431no—
284#1699—431no—
285#1694—431no—
286#1693—431no—
287#1680—431no—
288#1679—431no—
289#1674—431no—
290#1673—431no—
291#1573D4311yescharacteristic, complemented
292#1552—431no—
293C2×#332—431no—
294C2×C43—22no—
295C2×C43#304611yescharacteristic
296C2×C43#306211yescharacteristic
297C2×C43C2×#47311yescharacteristic
298D43—81no—
299#533—431no—
300C2×C4⋊Q8—431no—
301#529—431no—
302#500—431no—
303#500—431no—
304#497—861no—
305#491—861no—
306#487—431no—
307#487—431no—
308#484—861no—
309#484—861no—
310#479—861no—
311#477—861no—
312#477—861no—
313#475—431no—
314#474—431no—
315#467—861no—
316#465—861no—
317#464—861no—
318#462—431no—
319#462—431no—
320#462—431no—
321#461—431no—
322#461—431no—
323#461—431no—
324#451—861no—
325#448—861no—
326#446—431no—
327C8×Q8—431no—
328#436—431no—
329#435—861no—
330C8×D4—431no—
331C8×D4—861no—
332#433—861no—
333#432C2×D4311yescharacteristic
334#431C2×D4311yescharacteristic
335#424—861no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8C2×D4311yescharacteristic
338#335C2×D4311yescharacteristic
339#335C2×D4311yescharacteristic
340#334C2×D4311yescharacteristic
341#334C2×D4311yescharacteristic
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348#332—431no—
349#332—431no—
350C43#1959011yescharacteristic, complemented, Sylow
351C22×Q8—861no—
352C2×Q16—861no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×SD16—861no—
356C2×SD16—861no—
357C2×SD16—861no—
358C2×M16—861no—
359C22×C8—21no—
360C22×C8—861no—
361C22×C8—861no—
362C4⋊Q8—431no—
363C4⋊Q8—431no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369#126—861no—
370#125—431no—
371#125—861no—
372#124—431no—
373#123—861no—
374C22⋊Q8—431no—
375C22⋊Q8—861no—
376C22⋊Q8—861no—
377#121—431no—
378C4×Q8—431no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×D4—431no—
382C4×D4—861no—
383#117—861no—
384#117—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C42C22×D4311yescharacteristic
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394C4⋊C8—21no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8D17211yescharacteristic
401C4⋊C8D17211yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#102—861no—
418C22⋊C8—21no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8D17211yescharacteristic
422C22⋊C8D17211yescharacteristic
423#97—21no—
424#97—861no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427C4×C8C22×D4311yescharacteristic
428C2×Q8—431no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—3441no—
434C2×Q8—3441no—
435C2×Q8—1721no—
436C2×D4—431no—
437C2×D4—861no—
438C22×C4—861no—
439C22×C4—1721no—
440C22×C4C2×D17211yescharacteristic
441C22×C4D4×D4311yescharacteristic
442C22×C4#1062190211yescharacteristic
443Q16—3441no—
444Q16—3441no—
445Q16—3441no—
446SD16—3441no—
447SD16—3441no—
448SD16—3441no—
449M16—3441no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—3441no—
458C2×C8—3441no—
459C2×C8C2×D17211yescharacteristic
460C2×C8C2×D17211yescharacteristic
461C2×C8C2×D17211yescharacteristic
462C2×C8C2×D17211yescharacteristic
463C4⋊C4—431no—
464C4⋊C4—431no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
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—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—1721no—
487C42—861no—
488C42—1721no—
489C42C2×D17211yescharacteristic
490C42D4×D4311yescharacteristic
491C42#1062190211yescharacteristic
492C42C23×D4311yescharacteristic
493C23—861no—
494C23#1306330011yescharacteristic
495Q8—861no—
496Q8—861no—
497Q8—3442no—
498Q8—1721no—
499Q8—1721no—
500Q8—1721no—
501Q8—1721no—
502Q8—1721no—
503Q8—1721no—
504Q8—1721no—
505Q8—1721no—
506D4—861no—
507D4—861no—
508D4—1722no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—3442no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4#1306330011yescharacteristic
525C2×C4#1306330011yescharacteristic
526C2×C4#1306330011yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C22×D17211yescharacteristic
529C2×C4C2×#1062190211yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—1721no—
539C8—1721no—
540C22—21no—
541C22—21no—
542C22—1721no—
543C22—1721no—
544C22—1721no—
545C22#1458317512yes—
546C22C2×#1306330011yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—3441no—
552C4—3441no—
553C4—3441no—
554C4—3441no—
555C4—1721no—
556C4—1721no—
557C4—1721no—
558C4#1458370311yescharacteristic
559C4#1458370811yescharacteristic
560C4#1458371111yescharacteristic
561C4#1458371611yescharacteristic
562C2—22no—
563C2—3441no—
564C2#1914414711yescharacteristic
565C2#1914427611yescharacteristic
566C2C2×#1458317511yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1573C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#1573D43
hypocenterC43#19590
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
2. #19145748C2semidirect
5. #19134150C2semidirect
6. #19134143C2semidirect
7. #19134114C2semidirect
8. #19134109C2semidirect
9. #19134026C2semidirect
10. #19134019C2semidirect
11. #19133990C2semidirect
12. #19133985C2semidirect
13. #19133296C2semidirect
14. C2×#14582646C2semidirect
15. C43×#1573C2semidirect
291. #1573D43semidirect
350. C43#19590semidirect

Maximal subgroups

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

subgroupindex
#191459332
#191457482
#191456242
#191437572
#191341502
#191341432
#191341142
#191341092
#191340262
#191340192
#191339902
#191339852
#191332962
C2×#145826462
C43×#15732
#1959043