Finite Group Databasebeta

← #25084228

Subgroups — #25084228

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#19145921C211yesmaximal, characteristic
2#19145716C211yesmaximal, characteristic, complemented
3#19143755C211yesmaximal, characteristic, complemented
4#19134137C211yesmaximal, characteristic, complemented
5#19134130C211yesmaximal, characteristic, complemented
6#19134121C211yesmaximal, characteristic, complemented
7#19134116C211yesmaximal, characteristic, complemented
8#19134013C211yesmaximal, characteristic, complemented
9#19134006C211yesmaximal, characteristic, complemented
10#19133997C211yesmaximal, characteristic, complemented
11#19133992C211yesmaximal, characteristic, complemented
12#19133381C211yesmaximal, characteristic, complemented
13#19133291C211yesmaximal, characteristic, complemented
14C2×#14582648C211yesmaximal, characteristic, complemented
15C43×#3238C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583247C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583212—21no—
22#14583212—21no—
23#14583196—21no—
24#14583194C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583176—21no—
27#14583176—21no—
28#14583133—21no—
29#14583130—21no—
30#14583111—21no—
31#14583099C2211yescharacteristic
32#14583094C2211yescharacteristic
33#14583030C2211yescharacteristic
34Q8×C43⋊C8C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582952C2211yescharacteristic
41#14582926—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582648C2211yescharacteristic
51#14582648C2211yescharacteristic
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#501—21no—
59C43×#489—21no—
60C43×#483—21no—
61C43×#480—21no—
62C43×#477C2211yescharacteristic
63C43×#477C2211yescharacteristic
64C43×#476C2211yescharacteristic
65C43×#476C2211yescharacteristic
66C43×#432C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621882—21no—
70C2×#10621877—21no—
71C22×C43⋊C8—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063322C2311yescharacteristic
76#13063313—21no—
77#13063299—21no—
78#13063299—21no—
79C4×D172—21no—
80C4×D172—21no—
81#13063258—21no—
82#13063258—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)D411yescharacteristic
92C4⋊(C43⋊C8)D411yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249—21no—
98#13063246—21no—
99#13063245—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107C22⋊(C43⋊C8)D411yescharacteristic
108C22⋊(C43⋊C8)D411yescharacteristic
109#13063236—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C22×Q8×C43—21no—
114C4⋊Q8×C43—21no—
115C4⋊Q8×C43—21no—
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43D411yescharacteristic
124#121×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143#97×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—82no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—41no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—41no—
157#10621898—82no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C42×C43—21no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187#10621884—81no—
188#10621882—81no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193#10621877—81no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C23×C43—21no—
206C23×C43#12111yescharacteristic
207C22×D43—41no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—81no—
211Q8×C43—81no—
212Q8×C43—82no—
213D4×C43—21no—
214D4×C43—21no—
215D4×C43—42no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—82no—
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—82no—
236C2×Dic43—41no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—81no—
242C4×D43—82no—
243Dic86—81no—
244C8×C43—41no—
245C8×C43—41no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#19591—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43#47212yes—
261C22×C43C2×#12111yescharacteristic
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43#57711yescharacteristic
275C4×C43#57711yescharacteristic
276C4×C43#57811yescharacteristic
277C4×C43#57811yescharacteristic
278Dic43—81no—
279#3247—431no—
280#3238D4311yescharacteristic, complemented
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×#333—431no—
294C2×C43—22no—
295C2×C43—81no—
296C2×C43#304611yescharacteristic
297C2×C43#306311yescharacteristic
298C2×C43C2×#47211yescharacteristic
299D43—161no—
300#532—431no—
301C2×C4⋊Q8C2×D4311yescharacteristic
302#529C2×D4311yescharacteristic
303#501—21no—
304#500—431no—
305#500—431no—
306#489—21no—
307#486—431no—
308#486—431no—
309#483—21no—
310#480—21no—
311#480—861no—
312#480—861no—
313#478—861no—
314#477—431no—
315#477C2×D4311yescharacteristic
316#477C2×D4311yescharacteristic
317#476—431no—
318#476C2×D4311yescharacteristic
319#476C2×D4311yescharacteristic
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#432C2×D4311yescharacteristic
335#431—431no—
336#424—861no—
337C2×C4⋊C8—431no—
338C2×C4⋊C8—431no—
339#335—431no—
340#335—431no—
341#334—431no—
342#334—431no—
343#333—431no—
344#333—431no—
345#333—431no—
346#333—431no—
347#333—431no—
348#333—431no—
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—861no—
358C22×C8—861no—
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—21no—
368#125C22⋊D4311yescharacteristic
369#124—861no—
370#124C22⋊D4311yescharacteristic
371#123—21no—
372C22⋊Q8C22⋊D4311yescharacteristic
373#121—861no—
374#121—861no—
375#121C22⋊D4311yescharacteristic
376C4×Q8C22×D4311yescharacteristic
377C4×D4—21no—
378C4×D4—861no—
379C4×D4—861no—
380C4×D4C22×D4311yescharacteristic
381#117—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C42C22×D4311yescharacteristic
385#107—21no—
386#107—21no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—21no—
393#106—21no—
394#106—861no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—21no—
408#103—21no—
409#103—861no—
410#102—21no—
411#102—21no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—21no—
420C22⋊C8—431no—
421C22⋊C8—431no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—21no—
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—861no—
435C2×Q8C2×C22⋊D4311yescharacteristic
436C2×D4—21no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4—1721no—
441C2×D4C2×C22⋊D4311yescharacteristic
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—1721no—
445C22×C4D4×D4311yescharacteristic
446C22×C4#1062190011yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448SD16—3441no—
449D8—3441no—
450M16—3441no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—3441no—
462C2×C8—3441no—
463C2×C8—3441no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4C2×C22⋊D4311yescharacteristic
477C4⋊C4C2×C22⋊D4311yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C42—21no—
486C42D4×D4311yescharacteristic
487C42#1062190011yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—21no—
491C23—1721no—
492C23#1306329711yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—81no—
496Q8—81no—
497Q8—82no—
498Q8—3441no—
499D4—21no—
500D4—21no—
501D4—42no—
502D4—3441no—
503D4—3442no—
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—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—82no—
521C2×C4—3442no—
522C2×C4—1721no—
523C2×C4#1306329711yescharacteristic
524C2×C4#1306329711yescharacteristic
525C2×C4#1306329711yescharacteristic
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C2×C4C2×#1062190011yescharacteristic
529C8—41no—
530C8—41no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—3441no—
545C22—3441no—
546C22—3441no—
547C22#1458316712yes—
548C22C2×#1306329711yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—3441no—
559C4#1458370711yescharacteristic
560C4#1458370811yescharacteristic
561C4#1458371411yescharacteristic
562C4#1458371511yescharacteristic
563C2—22no—
564C2—81no—
565C2—6881no—
566C2#1914414911yescharacteristic
567C2#1914428211yescharacteristic
568C2C2×#1458316711yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3238C2
socleC22×C43C2×#121
prime radical#19145921C2
hypercenter#3238D43
hypocenterC43#19591
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
2. #19145716C2semidirect
3. #19143755C2semidirect
4. #19134137C2semidirect
5. #19134130C2semidirect
6. #19134121C2semidirect
7. #19134116C2semidirect
8. #19134013C2semidirect
9. #19134006C2semidirect
10. #19133997C2semidirect
11. #19133992C2semidirect
12. #19133381C2semidirect
13. #19133291C2semidirect
14. C2×#14582648C2semidirect
15. C43×#3238C2semidirect
280. #3238D43semidirect
351. C43#19591semidirect

Maximal subgroups

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

subgroupindex
#191459212
#191457162
#191437552
#191341372
#191341302
#191341212
#191341162
#191340132
#191340062
#191339972
#191339922
#191333812
#191332912
C2×#145826482
C43×#32382
#1959143