Finite Group Databasebeta

← #25084230

Subgroups — #25084230

Order 11008.

590 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
1#19145922C211yesmaximal, characteristic
2#19145816C211yesmaximal, characteristic, complemented
3#19145716C211yesmaximal, characteristic, complemented
4#19143751C211yesmaximal, characteristic, complemented
5#19134138C211yesmaximal, characteristic, complemented
6#19134131C211yesmaximal, characteristic, complemented
7#19134122C211yesmaximal, characteristic, complemented
8#19134117C211yesmaximal, characteristic, complemented
9#19134014C211yesmaximal, characteristic, complemented
10#19134007C211yesmaximal, characteristic, complemented
11#19133998C211yesmaximal, characteristic, complemented
12#19133993C211yesmaximal, characteristic, complemented
13#19133378C211yesmaximal, characteristic, complemented
14#19133288C211yesmaximal, characteristic, complemented
15C2×C43×#333C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583305—21no—
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583261—21no—
22#14583247C2211yescharacteristic
23#14583247C2211yescharacteristic
24#14583229—21no—
25#14583212—21no—
26#14583212—21no—
27#14583212—21no—
28#14583200—21no—
29#14583195C2211yescharacteristic
30#14583191C2211yescharacteristic
31#14583191C2211yescharacteristic
32#14583190C2211yescharacteristic
33#14583186C2211yescharacteristic
34#14583186C2211yescharacteristic
35#14583176—21no—
36#14583176—21no—
37#14583135—21no—
38#14583128—21no—
39#14583115—21no—
40#14583100C2211yescharacteristic
41#14583095C2211yescharacteristic
42#14583026C2211yescharacteristic
43#14583023C2211yescharacteristic
44#14582976C2211yescharacteristic
45#14582970—21no—
46#14582964C2211yescharacteristic
47C8×C22⋊D43—21no—
48#14582959—21no—
49#14582956C2211yescharacteristic
50#14582952C2211yescharacteristic
51#14582924—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C2×C4⋊Q8×C43C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#333C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621873—21no—
69C2×D344—21no—
70C2×#10621872—21no—
71C2×C8×D43—21no—
72#13063325C2311yescharacteristic
73#13063322C2311yescharacteristic
74#13063319—21no—
75#13063317D411yescharacteristic
76#13063313—21no—
77#13063313D411yescharacteristic
78#13063308—21no—
79#13063304D411yescharacteristic
80#13063299—21no—
81#13063299—21no—
82#13063299D411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×D172—21no—
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87C4×C22⋊D43—21no—
88#13063282—21no—
89#13063259—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258—21no—
96#13063257—21no—
97#13063256—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)D411yescharacteristic
100C4⋊(C43⋊C8)D411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063248—21no—
107#13063248—21no—
108#13063247—21no—
109#13063247—21no—
110#13063247—21no—
111#13063245—21no—
112#13063245—21no—
113#13063245—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)D411yescharacteristic
119C22⋊(C43⋊C8)D411yescharacteristic
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063236—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C22×Q8×C43—21no—
128C22×C8×C43—21no—
129C22×C8×C43—21no—
130C4⋊Q8×C43—21no—
131C4⋊Q8×C43—21no—
132C4⋊Q8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134C4⋊Q8×C43C2311yescharacteristic
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43—21no—
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143C4⋊C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—82no—
148C22×C4×C43—41no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43#4111yescharacteristic
152C2×C22⋊D43—21no—
153C2×C22⋊D43—41no—
154#10621898—82no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172C2×D411yescharacteristic
159C2×C4×D43—21no—
160C2×C4×D43—41no—
161C2×Dic86—21no—
162C2×Dic86C2×D411yescharacteristic
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C2×C8×C43—81no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43C2×D411yescharacteristic
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201D344—81no—
202#10621873—81no—
203#10621872—81no—
204C8×D43—81no—
205C23×C43#12111yescharacteristic
206C22×D43—21no—
207C22×D43—41no—
208Q8×C43—81no—
209Q8×C43—81no—
210Q8×C43—82no—
211C2×C4×C43—22no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—82no—
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—42no—
226C22⋊D43—82no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—41no—
231D172—21no—
232D172—21no—
233D172—41no—
234D172—41no—
235D172—41no—
236D172—41no—
237D172—81no—
238C4×D43—41no—
239C4×D43—41no—
240C4×D43—82no—
241Dic86—21no—
242Dic86—21no—
243Dic86—81no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#19591—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43#47212yes—
258C22×C43C2×#12111yescharacteristic
259C2×D43—41no—
260C2×D43—41no—
261C2×D43—41no—
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43#57711yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278Dic43—81no—
279#3247—431no—
280#3238—431no—
281#3226—431no—
282#2994—431no—
283#1698—431no—
284#1697—431no—
285#1696—431no—
286#1695—431no—
287#1678—431no—
288#1677—431no—
289#1676—431no—
290#1675—431no—
291#1573—431no—
292#1551—431no—
293C2×#333D4311yescharacteristic, complemented
294C2×C43—22no—
295C2×C43#304611yescharacteristic
296C2×C43#306311yescharacteristic
297C2×C43C2×#47211yescharacteristic
298D43—81no—
299D43—161no—
300#532—431no—
301C2×C4⋊Q8C2×D4311yescharacteristic
302#529—431no—
303#501—861no—
304#500—431no—
305#500—431no—
306#489—861no—
307#486—431no—
308#486—431no—
309#483—861no—
310#480—861no—
311#480—861no—
312#480—861no—
313#478—861no—
314#477—431no—
315#477—431no—
316#477—431no—
317#476—431no—
318#476—431no—
319#476—431no—
320#474—861no—
321#474—861no—
322#466—861no—
323#465—861no—
324#463—861no—
325#460—431no—
326#459—431no—
327#446—431no—
328C8×Q8—431no—
329#436—431no—
330#435—861no—
331C8×D4—431no—
332C8×D4—861no—
333#433—861no—
334#432—431no—
335#431—431no—
336#424—861no—
337C2×C4⋊C8C2×D4311yescharacteristic
338C2×C4⋊C8C2×D4311yescharacteristic
339#335—431no—
340#335—431no—
341#334—431no—
342#334—431no—
343#333—431no—
344#333—431no—
345#333C2×D4311yescharacteristic
346#333C2×D4311yescharacteristic
347#333C2×D4311yescharacteristic
348#333C2×D4311yescharacteristic
349#331—431no—
350#331—431no—
351C43#1959111yescharacteristic, complemented, Sylow
352C2×#41—861no—
353C22×Q8—21no—
354C2×SD16—861no—
355C2×D8—861no—
356C2×M16—861no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—861no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—431no—
364C4⋊Q8C22×D4311yescharacteristic
365C4⋊Q8C22×D4311yescharacteristic
366#127—431no—
367#126—861no—
368#125—431no—
369#124—431no—
370#124—861no—
371#123—861no—
372C22⋊Q8—431no—
373#121—431no—
374#121—861no—
375#121—861no—
376C4×Q8—431no—
377C4×D4—431no—
378C4×D4—861no—
379C4×D4—861no—
380C4×D4—861no—
381#117—861no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C42C22×D4311yescharacteristic
385#107—861no—
386#107—861no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—861no—
408#103—861no—
409#103—861no—
410#102—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—431no—
420C22⋊C8—431no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—861no—
425#97—861no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—861no—
429#41—3442no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—82no—
434C2×Q8—431no—
435C2×Q8—861no—
436C2×D4—431no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—1721no—
442C22×C4—41no—
443C22×C4—861no—
444C22×C4—1721no—
445C22×C4#1062189811yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4D4×D4311yescharacteristic
448SD16—3441no—
449D8—3441no—
450M16—3441no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8—81no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—3441no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—431no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C42—861no—
486C42#1062189811yescharacteristic
487C42D4×D4311yescharacteristic
488C42D4×D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—861no—
491C23—1721no—
492C23#1306329811yescharacteristic
493Q8—81no—
494Q8—81no—
495Q8—82no—
496Q8—861no—
497Q8—861no—
498Q8—3441no—
499D4—861no—
500D4—861no—
501D4—3441no—
502D4—3442no—
503D4—1722no—
504D4—1721no—
505D4—1721no—
506D4—1721no—
507D4—1721no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—3442no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4#1306329811yescharacteristic
524C2×C4#1306329811yescharacteristic
525C2×C4#1306329811yescharacteristic
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C2×#1062189811yescharacteristic
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C22—21no—
540C22—21no—
541C22—3441no—
542C22—3441no—
543C22—3441no—
544C22—1721no—
545C22—1721no—
546C22—1721no—
547C22#1458316812yes—
548C22C2×#1306329811yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—81no—
554C4—81no—
555C4—3441no—
556C4—1721no—
557C4—1721no—
558C4—1721no—
559C4#1458370511yescharacteristic
560C4#1458370511yescharacteristic
561C4#1458371211yescharacteristic
562C4#1458371211yescharacteristic
563C2—22no—
564C2—3441no—
565C2—6881no—
566C2#1914415011yescharacteristic
567C2#1914428411yescharacteristic
568C2C2×#1458316811yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#333C2
socleC22×C43C2×#121
prime radical#19145922C2
hypercenterC2×#333D43
hypocenterC43#19591
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. #19145816C2semidirect
3. #19145716C2semidirect
4. #19143751C2semidirect
5. #19134138C2semidirect
6. #19134131C2semidirect
7. #19134122C2semidirect
8. #19134117C2semidirect
9. #19134014C2semidirect
10. #19134007C2semidirect
11. #19133998C2semidirect
12. #19133993C2semidirect
13. #19133378C2semidirect
14. #19133288C2semidirect
15. C2×C43×#333C2semidirect
293. C2×#333D43semidirect
351. C43#19591semidirect

Maximal subgroups

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

subgroupindex
#191459222
#191458162
#191457162
#191437512
#191341382
#191341312
#191341222
#191341172
#191340142
#191340072
#191339982
#191339932
#191333782
#191332882
C2×C43×#3332
#1959143