Finite Group Databasebeta

← #25086349

Subgroups — #25086349

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621882C211yesmaximal, characteristic
2#19147244C211yesmaximal, characteristic
3#19146880C211yesmaximal, characteristic, complemented
4#19134238C211yesmaximal, characteristic, complemented
5#19134167C211yesmaximal, characteristic, complemented
6#19134055C211yesmaximal, characteristic, complemented
7#19134018C211yesmaximal, characteristic, complemented
8#19133987C211yesmaximal, characteristic, complemented
9#19133863C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133809C211yesmaximal, characteristic, complemented
12#19133758C211yesmaximal, characteristic, complemented
13#19133424C211yesmaximal, characteristic
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3299C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17Q8×D172C2211yescharacteristic
18#14583302—21no—
19#14583302C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583256—21no—
22#14583251C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583242—21no—
26#14583203—21no—
27#14583186C2211yescharacteristic
28#14583184C2211yescharacteristic
29#14583179—21no—
30#14583179C2211yescharacteristic
31#14583176—21no—
32#14583176C2211yescharacteristic
33#14583156—21no—
34#14583114—21no—
35#14583109C2211yescharacteristic
36#14583104C2211yescharacteristic
37#14583053—21no—
38Q8×C43⋊C8C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C4×#10621883—21no—
41C4×#10621882—21no—
42C4×#10621882C2211yescharacteristic
43#14582978C2211yescharacteristic
44#14582906—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#554C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#484—21no—
60C43×#477C2211yescharacteristic
61C43×#467—21no—
62C43×#462C2211yescharacteristic
63C43×#451—21no—
64C4×Q16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#103×C43—21no—
67C2×Q8×D43—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621882D411yescharacteristic
71C2×#10621872—21no—
72#13063325—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063320—41no—
76#13063313—21no—
77#13063305—21no—
78#13063305—41no—
79#13063301—21no—
80C4×Dic86—21no—
81C4×D172—21no—
82C4×D172C2311yescharacteristic
83#13063283—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258D411yescharacteristic
89#13063256—21no—
90#13063256—21no—
91#13063256—41no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063249—21no—
100#13063249—41no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063246—21no—
106#13063246D411yescharacteristic
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—42no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154C22×C4×C43—41no—
155Q8×D43—42no—
156Q8×D43—81no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—41no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163Q16×C43—22no—
164Q16×C43—81no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
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×C43—21no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43C2×D411yescharacteristic
179C4⋊C4×C43C2×D411yescharacteristic
180C4⋊C4×C43C2×D411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43C2411yescharacteristic
187#10621885—81no—
188#10621883—42no—
189#10621882—22no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—41no—
199C4⋊Dic43C2×D411yescharacteristic
200Dic43⋊C4—41no—
201C4×Dic43—41no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208#10621872—81no—
209C23×C43—21no—
210C22×D43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—82no—
217Q8×C43—81no—
218Q8×C43#13512yes—
219D4×C43—21no—
220D4×C43#13712yes—
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—82no—
231C2×C4×C43—161no—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238D172—21no—
239D172—21no—
240C4×D43—41no—
241C4×D43—41no—
242C4×D43—82no—
243Dic86—41no—
244Dic86—41no—
245Dic86—41no—
246Dic86—41no—
247Dic86—82no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19782—431nomaximal, Sylow
258C22×C43—22no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43D4211yescharacteristic
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C4×C43—22no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43C2×#13511yescharacteristic
274C4×C43C2×#13711yescharacteristic
275C4×C43#57611yescharacteristic
276C4×C43#57811yescharacteristic
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280Q8×D8—431no—
281#3360—431no—
282#3328—431no—
283#3299D4311yescharacteristic, complemented
284#1718—431no—
285#1703—431no—
286#1684—431no—
287#1679—431no—
288#1674—431no—
289#1652—431no—
290#1651—431no—
291#1644—431no—
292#1637—431no—
293#1581—431no—
294#1579—431no—
295C2×C43—42no—
296C2×C43#327011yescharacteristic
297C2×C43#328011yescharacteristic
298C2×C43#328911yescharacteristic
299D43—81no—
300#556—431no—
301#554C2×D4311yescharacteristic
302D4×Q8—431no—
303D4×Q8C2×D4311yescharacteristic
304#500—431no—
305#500—861no—
306#498—431no—
307#488—861no—
308#487—431no—
309#487—431no—
310#487—431no—
311#487C2×D4311yescharacteristic
312#485—861no—
313#484—21no—
314#479—861no—
315#477C2×D4311yescharacteristic
316#476—431no—
317#475—431no—
318#474—431no—
319#474—431no—
320#474—861no—
321#474—861no—
322#470—861no—
323#467—21no—
324#463—861no—
325#462—431no—
326#462C2×D4311yescharacteristic
327#461—431no—
328#451—21no—
329#451—861no—
330C8×Q8—431no—
331C8×Q8—431no—
332C4×Q16C2×D4311yescharacteristic
333C4×SD16—861no—
334C4×D8—431no—
335C4×D8—861no—
336#436—431no—
337C8×D4C2×D4311yescharacteristic
338#419—861no—
339C2×#103—21no—
340#335—431no—
341#334—431no—
342#333—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350#322—431no—
351C43#1978211yescharacteristic, complemented, Sylow
352C22×Q8—21no—
353C22×Q8—861no—
354C2×Q16—21no—
355C2×Q16—861no—
356C2×Q16C22⋊D4311yescharacteristic
357C2×SD16—861no—
358C2×D8—431no—
359C2×M16—861no—
360C22×C8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—431no—
363C4⋊Q8—431no—
364C4⋊Q8—861no—
365C4⋊Q8C22×D4311yescharacteristic
366C4⋊Q8C22×D4311yescharacteristic
367#126—1721no—
368#125—21no—
369#124—861no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373C22⋊Q8—41no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376C22⋊Q8—1721no—
377C4×Q8—861no—
378C4×Q8C22×D4311yescharacteristic
379C4×Q8C22×D4311yescharacteristic
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—431no—
383C4×D4—861no—
384C4×D4C22×D4311yescharacteristic
385#117—861no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—431no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#107C22⋊D4311yescharacteristic
394#106—861no—
395#106—861no—
396#106—1721no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—1721no—
415#103C22⋊D4311yescharacteristic
416#103C22⋊D4311yescharacteristic
417#102—431no—
418#102—431no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—21no—
423C22⋊C8—861no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8C22×D4311yescharacteristic
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8—42no—
433C2×Q8—81no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—3441no—
437C2×Q8—1721no—
438C2×Q8—1722no—
439C2×Q8C2×C22⋊D4311yescharacteristic
440C2×Q8C2×C22⋊D4311yescharacteristic
441C2×D4—431no—
442C2×D4D4×D4311yescharacteristic
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—861no—
447C22×C4—1721no—
448Q16—22no—
449Q16—81no—
450Q16—3441no—
451SD16—1722no—
452D8—862no—
453M16—3441no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—431no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4D4×D4311yescharacteristic
481C4⋊C4C2×C22⋊D4311yescharacteristic
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—861no—
487C22⋊C4—1721no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C42—21no—
491C42—21no—
492C42—1721no—
493C42C23×D4311yescharacteristic
494C23—21no—
495C23—861no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—82no—
502Q8—81no—
503Q8—3442no—
504Q8—1721no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508Q8#1306334512yes—
509D4—21no—
510D4—861no—
511D4—861no—
512D4#1306335712yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—161no—
524C2×C4—861no—
525C2×C4—3442no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4C2×D4×D4311yescharacteristic
531C2×C4C22×C22⋊D4311yescharacteristic
532C2×C4#1306337011yescharacteristic
533C8—21no—
534C8—21no—
535C8—41no—
536C8—861no—
537C8—861no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C8—1721no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—1721no—
546C22—1721no—
547C22—1721no—
548C22D4×C22⋊D4311yescharacteristic
549C4—22no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—3441no—
558C4—3441no—
559C4—1721no—
560C4C2×#1306334511yescharacteristic
561C4C2×#1306335711yescharacteristic
562C4#1458370211yescharacteristic
563C4#1458371211yescharacteristic
564C2—42no—
565C2—3441no—
566C2#1914616511yescharacteristic
567C2#1914627611yescharacteristic
568C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3299C2
socleC22×C43D42
prime radicalC2×#10621882D4
hypercenter#3299D43
hypocenterC43#19782
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3299

Complements

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

NH ≅ G/Ntype
3. #19146880C2semidirect
4. #19134238C2semidirect
5. #19134167C2semidirect
6. #19134055C2semidirect
7. #19134018C2semidirect
8. #19133987C2semidirect
9. #19133863C2semidirect
10. #19133858C2semidirect
11. #19133809C2semidirect
12. #19133758C2semidirect
14. #19133414C2semidirect
15. C43×#3299C2semidirect
283. #3299D43semidirect
351. C43#19782semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218822
#191472442
#191468802
#191342382
#191341672
#191340552
#191340182
#191339872
#191338632
#191338582
#191338092
#191337582
#191334242
#191334142
C43×#32992
#1978243