Finite Group Databasebeta

← #25080457

Subgroups — #25080457

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145156C211yesmaximal, characteristic
2#19144724C211yesmaximal, characteristic, complemented
3#19144719C211yesmaximal, characteristic
4C8×Q8×D43C211yesmaximal, characteristic, complemented
5#19134056C211yesmaximal, characteristic, complemented
6#19134055C211yesmaximal, characteristic, complemented
7#19134042C211yesmaximal, characteristic, complemented
8#19134041C211yesmaximal, characteristic, complemented
9#19133974C211yesmaximal, characteristic, complemented
10#19133944C211yesmaximal, characteristic, complemented
11#19133943C211yesmaximal, characteristic, complemented
12#19133355C211yesmaximal, characteristic, complemented
13#19133292C211yesmaximal, characteristic, complemented
14#19133289C211yesmaximal, characteristic
15C43×#1672C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583450C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583272C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583247C2211yescharacteristic
22#14583228—21no—
23#14583214—21no—
24#14583191C2211yescharacteristic
25#14583185C2211yescharacteristic
26#14583184C2211yescharacteristic
27#14583129—21no—
28#14583129—21no—
29#14583106C2211yescharacteristic
30#14583100C2211yescharacteristic
31#14583099C2211yescharacteristic
32#14583053—21no—
33#14583039—21no—
34Q8×C43⋊C8C2211yescharacteristic
35C8×Dic86—21no—
36C8×Dic86C2211yescharacteristic
37#14583023—21no—
38#14583023C2211yescharacteristic
39#14583006—21no—
40#14583003—21no—
41#14583002—21no—
42#14582998—21no—
43#14582986—21no—
44#14582986—21no—
45#14582955C2211yescharacteristic
46#14582955C2211yescharacteristic
47C4⋊C8×D43—21no—
48C4⋊C8×D43C2211yescharacteristic
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621902—21no—
68C2×Q8×D43D411yescharacteristic
69C2×#10621885—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621884—21no—
74C2×C8×D43—21no—
75C2×C8×D43D411yescharacteristic
76C2×C8×D43D411yescharacteristic
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063316—21no—
80#13063314—21no—
81#13063305—21no—
82#13063301—21no—
83#13063300—21no—
84#13063300—21no—
85Q8×Dic43—21no—
86Q8×Dic43D411yescharacteristic
87C4×Dic86—21no—
88C4×Dic86C2311yescharacteristic
89#13063290—21no—
90#13063290—21no—
91#13063290D411yescharacteristic
92#13063287—21no—
93#13063287—21no—
94#13063283—21no—
95C4⋊C4×D43—21no—
96C4⋊C4×D43D411yescharacteristic
97C42×D43—21no—
98C42×D43C2311yescharacteristic
99#13063258—21no—
100#13063257—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250—21no—
110#13063249—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063248—21no—
115#13063247—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×Q16×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147#10621902—82no—
148Q8×D43—22no—
149Q8×D43—22no—
150C2×D172—21no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—41no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—41no—
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—21no—
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#10621884—42no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—41no—
181(C2×D43)⋊C4—41no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—41no—
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—41no—
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203#10621873—42no—
204#10621873—42no—
205#10621873—42no—
206C8×D43—22no—
207C8×D43—41no—
208C8×D43—42no—
209C22×D43—41no—
210C22×D43#12111yescharacteristic
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215Q8×C43#13512yes—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—41no—
226C2×Dic43#12111yescharacteristic
227C2×Dic43#12111yescharacteristic
228C2×Dic43#12111yescharacteristic
229D172—41no—
230D172—41no—
231D172—41no—
232D172—41no—
233D172—81no—
234D172—82no—
235C4×D43—24no—
236C4×D43—22no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—42no—
242C4×D43—82no—
243Dic86—24no—
244Dic86—21no—
245Dic86—41no—
246Dic86—41no—
247Dic86#13512yes—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43#13712yes—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258#19263—431nomaximal, Sylow
259C22×C43C2×#12111yescharacteristic
260C2×D43—21no—
261C2×D43—21no—
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43#47112yes—
266C4×C43—22no—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13511yescharacteristic
273C4×C43C2×#13711yescharacteristic
274C4×C43#57511yescharacteristic
275Dic43—21no—
276Dic43—21no—
277Dic43—22no—
278Dic43—21no—
279Dic43—41no—
280Dic43—81no—
281#3167—431no—
282#3113—431no—
283#3112—431no—
284C2×C8×Q8—431no—
285#1684—431no—
286#1684—431no—
287#1682—431no—
288#1682—431no—
289#1672—431no—
290#1672D4311yescharacteristic, complemented
291#1666—431no—
292#1666—431no—
293#1568—431no—
294#1552—431no—
295#1551—431no—
296C2×C43#303711yescharacteristic
297C2×C43#305011yescharacteristic
298C2×C43C2×#47111yescharacteristic
299D43—22no—
300D43—161no—
301#533—431no—
302#532—431no—
303C2×C4×Q8—431no—
304#498C2×D4311yescharacteristic
305#492—431no—
306#487—431no—
307#486—431no—
308#483—861no—
309#480—861no—
310#477—431no—
311#477C2×D4311yescharacteristic
312#475—431no—
313#475—431no—
314#465—861no—
315#465—861no—
316#462—431no—
317#462C2×D4311yescharacteristic
318#460—431no—
319#460—431no—
320#451—861no—
321#448—861no—
322C8×Q8—431no—
323C8×Q8—431no—
324C8×Q8—431no—
325C8×Q8—861no—
326C8×Q8—861no—
327C8×Q8C2×D4311yescharacteristic
328#441—861no—
329#441—861no—
330#440—861no—
331#440—861no—
332C4×SD16—861no—
333C4×SD16—861no—
334#432—431no—
335#432—431no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8—861no—
338C2×C4×C8—431no—
339C2×C4×C8—861no—
340#335—431no—
341#335—431no—
342#334—431no—
343#334C2×D4311yescharacteristic
344#333—431no—
345#333C2×D4311yescharacteristic
346#332—431no—
347#332—431no—
348#332—431no—
349#332C2×D4311yescharacteristic
350#331—431no—
351#331—431no—
352C43#1926311yescharacteristic, complemented, Sylow
353C2×#41—861no—
354C22×Q8—431no—
355C2×Q16—21no—
356C2×Q16—861no—
357C2×SD16—861no—
358C2×SD16—861no—
359C2×SD16—861no—
360C2×SD16—861no—
361C22×C8—431no—
362C22×C8—431no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8C22×D4311yescharacteristic
366C4⋊Q8C22×D4311yescharacteristic
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—431no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8C22×D4311yescharacteristic
382C4×D4—861no—
383C4×D4—861no—
384#117—861no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—861no—
387C2×C42—431no—
388C2×C42—861no—
389#107—21no—
390#107—861no—
391#106—21no—
392#106—21no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—21no—
407#103—21no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420#97—861no—
421#97—861no—
422C4×C8—21no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8C22×D4311yescharacteristic
430#41—3442no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—431no—
434C2×Q8—861no—
435C2×Q8—862no—
436C2×Q8—862no—
437C2×Q8—861no—
438C2×Q8D4×D4311yescharacteristic
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—1721no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1721no—
449Q16—42no—
450Q16—1722no—
451SD16—1722no—
452SD16—1722no—
453SD16—1722no—
454SD16—1722no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—862no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—1721no—
465C2×C8—1722no—
466C2×C8D4×D4311yescharacteristic
467C2×C8D4×D4311yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—431no—
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⋊C4D4×D4311yescharacteristic
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C42—21no—
487C42—431no—
488C42—431no—
489C42—431no—
490C42—861no—
491C42—861no—
492C42—861no—
493C42—1721no—
494C42C23×D4311yescharacteristic
495C23—431no—
496C23—1721no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—432no—
502Q8—864no—
503Q8—861no—
504Q8—1721no—
505Q8—1721no—
506Q8#1306334612yes—
507D4—3441no—
508D4—3442no—
509D4—1721no—
510D4—1721no—
511D4—1721no—
512D4—1721no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—431no—
518C2×C4—431no—
519C2×C4—431no—
520C2×C4—862no—
521C2×C4—864no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—3442no—
529C2×C4—1722no—
530C2×C4—1721no—
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4#41×D4311yescharacteristic
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—861no—
539C8—861no—
540C8—1721no—
541C8—1721no—
542C8—1721no—
543C8#1306335712yes—
544C22—432no—
545C22—861no—
546C22—861no—
547C22—3441no—
548C22—3441no—
549C22—3441no—
550C22#121×D4311yescharacteristic
551C4—21no—
552C4—22no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—861no—
557C4—861no—
558C4—861no—
559C4—862no—
560C4—3441no—
561C4—1721no—
562C4#135×D4311yescharacteristic
563C4C2×#1306334611yescharacteristic
564C4C2×#1306335711yescharacteristic
565C4#1458369811yescharacteristic
566C2—862no—
567C2—6881no—
568C2#1914406811yescharacteristic
569C2#1914417111yescharacteristic
570C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1672C2
socleC22×C43C2×#121
prime radical#14583450C22
hypercenter#1672D43
hypocenterC43#19263
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
2. #19144724C2semidirect
4. C8×Q8×D43C2semidirect
5. #19134056C2semidirect
6. #19134055C2semidirect
7. #19134042C2semidirect
8. #19134041C2semidirect
9. #19133974C2semidirect
10. #19133944C2semidirect
11. #19133943C2semidirect
12. #19133355C2semidirect
13. #19133292C2semidirect
15. C43×#1672C2semidirect
290. #1672D43semidirect
352. C43#19263semidirect

Maximal subgroups

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

subgroupindex
#191451562
#191447242
#191447192
C8×Q8×D432
#191340562
#191340552
#191340422
#191340412
#191339742
#191339442
#191339432
#191333552
#191332922
#191332892
C43×#16722
#1926343