Finite Group Databasebeta

← #25079468

Subgroups — #25079468

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145136C211yesmaximal, characteristic
2#19144636C211yesmaximal, characteristic
3#462×D43C211yesmaximal, characteristic
4Q8×#10621872C211yesmaximal, characteristic
5#19134114C211yesmaximal, characteristic, complemented
6#19134112C211yesmaximal, characteristic, complemented
7#19134104C211yesmaximal, characteristic, complemented
8#19134098C211yesmaximal, characteristic, complemented
9#19133989C211yesmaximal, characteristic, complemented
10#19133987C211yesmaximal, characteristic, complemented
11#19133979C211yesmaximal, characteristic, complemented
12#19133344C211yesmaximal, characteristic
13#19133282C211yesmaximal, characteristic
14#19133278C211yesmaximal, characteristic
15C43×#1672C211yesmaximal, characteristic, complemented
16C2×Q16×D43—21no—
17#14583454C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19C4×Q8×D43C2211yescharacteristic
20#14583306—21no—
21#14583306—21no—
22#14583304C2211yescharacteristic
23#14583302C2211yescharacteristic
24#14583295C2211yescharacteristic
25#14583236—21no—
26#14583191C2211yescharacteristic
27#14583110C2211yescharacteristic
28#14583110C2211yescharacteristic
29#14583109C2211yescharacteristic
30#14583109C2211yescharacteristic
31#14583108—21no—
32#14583107—21no—
33#14583106C2211yescharacteristic
34#14583056—21no—
35#14583029—21no—
36#14583029C2211yescharacteristic
37#14583026—21no—
38#14583026C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14582993—21no—
41#14582991—21no—
42#14582951C2211yescharacteristic
43#14582938—21no—
44#14582938—21no—
45#14582921—21no—
46#14582921C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48#103×D43—21no—
49C4×#10621872—21no—
50C4×#10621872C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43D411yescharacteristic
69C2×Dic172—21no—
70C2×Dic172—21no—
71C2×#10621885—21no—
72C2×#10621885—21no—
73C2×#10621885—21no—
74Q16×D43—44no—
75C2×#10621872—21no—
76C2×#10621872D411yescharacteristic
77C2×#10621872D411yescharacteristic
78C2×C8×D43—21no—
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063324—21no—
82#13063324—21no—
83#13063323—21no—
84#13063316—21no—
85#13063305—21no—
86#13063301—21no—
87Q8×Dic43—21no—
88Q8×Dic43D411yescharacteristic
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91#13063290—21no—
92#13063290—21no—
93#13063290D411yescharacteristic
94#13063283—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97C4⋊C4×D43—21no—
98C4⋊C4×D43D411yescharacteristic
99C42×D43—21no—
100C42×D43C2311yescharacteristic
101#13063259—21no—
102#13063259—21no—
103#13063258—21no—
104#13063258—21no—
105#13063258—21no—
106#13063256—21no—
107#13063256—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116#13063250—21no—
117#13063250—21no—
118#13063249—21no—
119#13063248—21no—
120#13063248—21no—
121#13063248—21no—
122(C2×D43)⋊C8—21no—
123#13063235—21no—
124#13063235—21no—
125#13063235D411yescharacteristic
126#13063235D411yescharacteristic
127C4×C43⋊C8—21no—
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43—21no—
130C2×Q16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#103×C43—21no—
143C4×C8×C43—21no—
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148Q8×D43—22no—
149Q8×D43—41no—
150Q8×D43—42no—
151Q8×D43—42no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—41no—
155C2×C4×D43C2×D411yescharacteristic
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43#4111yescharacteristic
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86C2×D411yescharacteristic
163Q16×C43—42no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C42×C43—21no—
176C42×C43C2411yescharacteristic
177#10621885—42no—
178#10621885—42no—
179#10621885—42no—
180(C2×D43)⋊C4—41no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—41no—
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206Dic172—42no—
207Dic172—42no—
208#10621872—22no—
209#10621872—42no—
210#10621872Q1614yescomplemented
211C8×D43—42no—
212C22×D43#12111yescharacteristic
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—81no—
217Q8×C43AGL(1,ℤ/8)12yes—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43#12111yescharacteristic
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—41no—
235C4×D43—42no—
236C4×D43—81no—
237C4×D43—82no—
238C4×D43C2×Q1612yes—
239C4×D43#13712yes—
240Dic86—21no—
241Dic86—21no—
242Dic86—42no—
243Dic86—41no—
244Dic86—41no—
245Dic86—41no—
246Dic86—41no—
247Dic86—82no—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43C2×Q1612yescomplemented
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8C2×Q1612yescomplemented
258#19172—431nomaximal, Sylow
259C22×C43C2×#12111yescharacteristic
260C2×D43—21no—
261C2×D43—21no—
262C2×D43#46212yes—
263C4×C43—22no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43C22×Q1611yescharacteristic
269C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C4×C43C2×#13711yescharacteristic
271C4×C43#57511yescharacteristic
272Dic43—21no—
273Dic43—21no—
274Dic43—41no—
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278Dic43#46212yes—
279#3165—431no—
280#3104—431no—
281C2×#462—431no—
282Q8×M16—431no—
283#1694—431no—
284#1694—431no—
285#1692—431no—
286#1692—431no—
287#1674—431no—
288#1674—431no—
289#1672—431no—
290#1672D4311yescharacteristic, complemented
291#1565—431no—
292#1550—431no—
293#1549—431no—
294C2×C43C2×#46211yescharacteristic
295C2×C43#305511yescharacteristic
296C2×C43#306911yescharacteristic
297D43—22no—
298C22×Q16—861no—
299#533—431no—
300C2×C4⋊Q8—431no—
301C2×C4×Q8—431no—
302#501—861no—
303#501—861no—
304#500—431no—
305#500—431no—
306#498—431no—
307#498C2×D4311yescharacteristic
308#484—861no—
309#477—431no—
310#477C2×D4311yescharacteristic
311#462—431no—
312#462—431no—
313#462—431no—
314#462—431no—
315#462—431no—
316#462—861no—
317#462—861no—
318#462C2×D4311yescharacteristic
319#451—861no—
320#446—431no—
321#446—431no—
322#446—861no—
323#446—861no—
324C8×Q8—431no—
325C8×Q8C2×D4311yescharacteristic
326C4×Q16—861no—
327C4×Q16—861no—
328#431—431no—
329#428—861no—
330#428—861no—
331#423—431no—
332#423—861no—
333C2×C4⋊C8—431no—
334C2×#103—861no—
335C4×M16—431no—
336C4×M16—861no—
337#335—431no—
338#335—431no—
339#334—431no—
340#334C2×D4311yescharacteristic
341#333—431no—
342#333C2×D4311yescharacteristic
343#332—431no—
344#332—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348#332C2×D4311yescharacteristic
349C43#1917211yescharacteristic, complemented, Sylow
350C22×Q8—431no—
351C22×Q8—861no—
352C2×Q16—21no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×Q16—861no—
356C2×Q16—861no—
357C2×Q16—861no—
358C2×Q16—1724no—
359C2×M16—431no—
360C2×M16—431no—
361C2×M16—861no—
362C22×C8—861no—
363C4⋊Q8—431no—
364C4⋊Q8—431no—
365C4⋊Q8—861no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8C22×D4311yescharacteristic
369C4⋊Q8C22×D4311yescharacteristic
370#125—861no—
371C22⋊Q8—861no—
372C22⋊Q8—861no—
373C4×Q8—431no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8C22×D4311yescharacteristic
381#117—861no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C42—431no—
387C2×C42—861no—
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#107—861no—
394#106—21no—
395#106—21no—
396#106—861no—
397#106—861no—
398C4⋊C8—21no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8C22×D4311yescharacteristic
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—21no—
411#103—21no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418C22⋊C8—861no—
419#97—431no—
420#97—431no—
421#97—861no—
422#97—861no—
423C4×C8—21no—
424C4×C8—431no—
425C4×C8—861no—
426C4×C8—861no—
427C4×C8C22×D4311yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—431no—
431C2×Q8—861no—
432C2×Q8—862no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×Q8—1721no—
436C2×Q8—1722no—
437C2×Q8—1722no—
438C2×Q8—1721no—
439C2×Q8D4×D4311yescharacteristic
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—1721no—
446Q16—42no—
447Q16—1722no—
448Q16—1722no—
449Q16—1722no—
450Q16—1722no—
451Q16—1722no—
452M16—434no—
453M16—862no—
454M16—1722no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—1722no—
464C2×C8D4×D4311yescharacteristic
465C2×C8D4×D4311yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C4⋊C4D4×D4311yescharacteristic
485C22⋊C4—1721no—
486C42—21no—
487C42—431no—
488C42—431no—
489C42—431no—
490C42—861no—
491C42—861no—
492C42—861no—
493C42—1721no—
494C42C23×D4311yescharacteristic
495C23—431no—
496Q8—21no—
497Q8—41no—
498Q8—41no—
499Q8—81no—
500Q8—861no—
501Q8—861no—
502Q8—3442no—
503Q8—1722no—
504Q8—1721no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508Q8#1306335212yes—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—431no—
514C2×C4—432no—
515C2×C4—432no—
516C2×C4—431no—
517C2×C4—431no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—3441no—
523C2×C4—3442no—
524C2×C4—1721no—
525C2×C4—1722no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C2×D4×D4311yescharacteristic
530C2×C4#41×D4311yescharacteristic
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—432no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C8Q16×D4312yescomplemented
541C22—432no—
542C22—861no—
543C22—861no—
544C22#121×D4311yescharacteristic
545C4—22no—
546C4—21no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—432no—
551C4—861no—
552C4—861no—
553C4—3441no—
554C4—3441no—
555C4—1721no—
556C4—1721no—
557C4C2×Q16×D4311yescharacteristic
558C4C2×#1306335211yescharacteristic
559C4#137×D4311yescharacteristic
560C4#1458369611yescharacteristic
561C2—862no—
562C2#462×D4311yescharacteristic
563C2#1914420711yescharacteristic
564C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1672D43
hypocenterC43#19172
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
5. #19134114C2semidirect
6. #19134112C2semidirect
7. #19134104C2semidirect
8. #19134098C2semidirect
9. #19133989C2semidirect
10. #19133987C2semidirect
11. #19133979C2semidirect
15. C43×#1672C2semidirect
210. #10621872Q16semidirect
252. C8×C43C2×Q16semidirect
257. C43⋊C8C2×Q16semidirect
290. #1672D43semidirect
349. C43#19172semidirect
540. C8Q16×D43semidirect

Maximal subgroups

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

subgroupindex
#191451362
#191446362
#462×D432
Q8×#106218722
#191341142
#191341122
#191341042
#191340982
#191339892
#191339872
#191339792
#191333442
#191332822
#191332782
C43×#16722
#1917243