Finite Group Databasebeta

← #25079618

Subgroups — #25079618

Order 11008.

614 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145313C211yesmaximal, characteristic, complemented
2#19144656C211yesmaximal, characteristic
3#19144385C211yesmaximal, characteristic, complemented
4#19143613C211yesmaximal, characteristic, complemented
5#19134171C211yesmaximal, characteristic, complemented
6#19134129C211yesmaximal, characteristic, complemented
7#19134119C211yesmaximal, characteristic, complemented
8#19134061C211yesmaximal, characteristic, complemented
9#19134054C211yesmaximal, characteristic, complemented
10#19134012C211yesmaximal, characteristic, complemented
11#19134000C211yesmaximal, characteristic, complemented
12#19133944C211yesmaximal, characteristic, complemented
13#19133303C211yesmaximal, characteristic, complemented
14#19133288C211yesmaximal, characteristic, complemented
15C43×#1565C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583224—21no—
24#14583207—21no—
25#14583200—21no—
26#14583195C2211yescharacteristic
27#14583195C2211yescharacteristic
28#14583190C2211yescharacteristic
29#14583190C2211yescharacteristic
30#14583185C2211yescharacteristic
31#14583180C2211yescharacteristic
32#14583145—21no—
33#14583145—21no—
34#14583100C2211yescharacteristic
35#14583095C2211yescharacteristic
36#14583046—21no—
37C8×Dic86C2211yescharacteristic
38C8×Dic86C2211yescharacteristic
39#14583001—21no—
40#14583001—21no—
41C4×#10621873—21no—
42C4×D344—21no—
43#14582978C2211yescharacteristic
44#14582978C2211yescharacteristic
45#14582975—21no—
46#14582975—21no—
47#14582956C2211yescharacteristic
48#14582954—21no—
49#14582937—21no—
50#14582896—21no—
51#14582851—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69C2×#10621873—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×D344—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063317—21no—
80#13063313—21no—
81#13063304—21no—
82#13063304—21no—
83#13063299—21no—
84#13063299—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86D411yescharacteristic
88C4×Dic86C2311yescharacteristic
89C4×D172—21no—
90C4×D172—21no—
91C4×D172D411yescharacteristic
92C4×D172C2311yescharacteristic
93C4×C22⋊D43—21no—
94C4×C22⋊D43—21no—
95#13063284—21no—
96#13063284D411yescharacteristic
97#13063282—21no—
98C42×D43—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126#13063236—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×M16×C43D411yescharacteristic
130C2×M16×C43D411yescharacteristic
131C22×C8×C43—21no—
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139#97×C43D411yescharacteristic
140#97×C43D411yescharacteristic
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×C22⋊D43—41no—
149#10621898—22no—
150#10621898—41no—
151#10621898—82no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—41no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164M16×C43—22no—
165M16×C43—41no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—42no—
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180C22⋊Dic43—41no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—41no—
184(C2×D43)⋊C4—41no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C2×D411yescharacteristic
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203D344—42no—
204#10621873—42no—
205#10621873—42no—
206#10621873—42no—
207#10621872—42no—
208#10621872—42no—
209C23×C43#12111yescharacteristic
210C22×D43—21no—
211C22×D43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—41no—
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C22⋊D43—42no—
224C22⋊D43—82no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231D172—21no—
232D172—21no—
233D172—41no—
234D172—41no—
235D172—41no—
236D172—41no—
237D172—81no—
238C4×D43—42no—
239C4×D43—41no—
240C4×D43—41no—
241C4×D43—81no—
242C4×D43—82no—
243Dic86—21no—
244Dic86—41no—
245Dic86—41no—
246Dic86—81no—
247Dic86—81no—
248Dic86#13712yes—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43#13512yes—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#19183—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43C2×#12111yescharacteristic
264C2×D43—41no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43C2×#13511yescharacteristic
275C4×C43C2×#13711yescharacteristic
276C4×C43#57511yescharacteristic
277C4×C43#57511yescharacteristic
278Dic43—22no—
279Dic43—41no—
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284#3182—431no—
285#3106—431no—
286#3076—431no—
287#2971—431no—
288#1703—431no—
289#1697—431no—
290#1695—431no—
291#1685—431no—
292#1684—431no—
293#1678—431no—
294#1676—431no—
295#1666—431no—
296#1565D4311yescharacteristic, complemented
297#1554—431no—
298#1551—431no—
299C2×C43—41no—
300C2×C43#303511yescharacteristic
301C2×C43#305611yescharacteristic
302C2×C43#306811yescharacteristic
303D43—81no—
304D43—161no—
305#533—431no—
306#532—431no—
307C4×#41—431no—
308#500—431no—
309#492—431no—
310#487—431no—
311#486—431no—
312#482—861no—
313#479—861no—
314#478—861no—
315#477—431no—
316#477—431no—
317#476—431no—
318#476—431no—
319#475—431no—
320#474—431no—
321#468—861no—
322#468—861no—
323#460—431no—
324#459—431no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#440—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332#436—431no—
333#436—431no—
334#436—861no—
335#436—861no—
336#432—431no—
337#432—861no—
338#431C2×D4311yescharacteristic
339#427—861no—
340C2×C4⋊C8C2×D4311yescharacteristic
341#416—861no—
342C4×M16—861no—
343C4×M16C2×D4311yescharacteristic
344#335C2×D4311yescharacteristic
345#335C2×D4311yescharacteristic
346#334C2×D4311yescharacteristic
347#334C2×D4311yescharacteristic
348#333—431no—
349#333—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#331—431no—
355#331—431no—
356C43#1918311yescharacteristic, complemented, Sylow
357C2×#41—431no—
358C2×#41—861no—
359C2×SD16—861no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×D8—861no—
363C2×M16—861no—
364C2×M16—861no—
365C2×M16D17211yescharacteristic
366C2×M16D17211yescharacteristic
367C22×C8—21no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8—431no—
371#127—431no—
372#125—861no—
373#124—861no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—861no—
377#121—861no—
378C4×Q8—431no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—431no—
383C4×D4—431no—
384C4×D4—861no—
385C4×D4—861no—
386C4×D4—861no—
387C4×D4—861no—
388#117—431no—
389#117—861no—
390#117—861no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393#107—861no—
394#107—861no—
395#107—861no—
396#107—861no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401C4⋊C8—21no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—21no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427#97D17211yescharacteristic
428#97D17211yescharacteristic
429C4×C8—21no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434#41—862no—
435#41—3442no—
436#41—1721no—
437C2×Q8—431no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×D4—431no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—1721no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—1721no—
451C22×C4C2×D17211yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4#1062190211yescharacteristic
454SD16—1722no—
455SD16—1722no—
456SD16—1722no—
457D8—1722no—
458M16—22no—
459M16—41no—
460M16—1722no—
461M16—1722no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—42no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8C2×D17211yescharacteristic
470C2×C8C2×D17211yescharacteristic
471C2×C8C2×D17211yescharacteristic
472C2×C8C2×D17211yescharacteristic
473C4⋊C4—431no—
474C4⋊C4—431no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—1721no—
484C4⋊C4—1721no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C42—861no—
492C42—861no—
493C42—861no—
494C42—1721no—
495C42C2×D17211yescharacteristic
496C42D4×D4311yescharacteristic
497C42#1062190211yescharacteristic
498C42C23×D4311yescharacteristic
499C23—861no—
500C23—1721no—
501C23#1306330011yescharacteristic
502Q8—432no—
503Q8—861no—
504Q8—3441no—
505Q8—3441no—
506Q8—1721no—
507Q8—1721no—
508D4—861no—
509D4—861no—
510D4—3441no—
511D4—3442no—
512D4—1722no—
513D4—1721no—
514D4—1721no—
515D4—1721no—
516D4—1721no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—3442no—
526C2×C4—3441no—
527C2×C4—1722no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4#1306330011yescharacteristic
534C2×C4#1306330011yescharacteristic
535C2×C4#1306330011yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C22×D17211yescharacteristic
538C2×C4C2×#1062190211yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—1721no—
547C8—1721no—
548C8#1306334712yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—3441no—
553C22—3441no—
554C22—3441no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22C2×#1306330011yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—862no—
564C4—3441no—
565C4—3441no—
566C4—3441no—
567C4—1721no—
568C4—1721no—
569C4C2×#1306334711yescharacteristic
570C4#137×D4311yescharacteristic
571C4#1458369511yescharacteristic
572C4#1458369911yescharacteristic
573C2—41no—
574C2—3441no—
575C2—6881no—
576C2#1914405211yescharacteristic
577C2#1914422611yescharacteristic
578C2#1914432411yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1565C2
socleC22×C43C2×#121
prime radical#19144656C2
hypercenter#1565D43
hypocenterC43#19183
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
1. #19145313C2semidirect
3. #19144385C2semidirect
4. #19143613C2semidirect
5. #19134171C2semidirect
6. #19134129C2semidirect
7. #19134119C2semidirect
8. #19134061C2semidirect
9. #19134054C2semidirect
10. #19134012C2semidirect
11. #19134000C2semidirect
12. #19133944C2semidirect
13. #19133303C2semidirect
14. #19133288C2semidirect
15. C43×#1565C2semidirect
296. #1565D43semidirect
356. C43#19183semidirect

Maximal subgroups

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

subgroupindex
#191453132
#191446562
#191443852
#191436132
#191341712
#191341292
#191341192
#191340612
#191340542
#191340122
#191340002
#191339442
#191333032
#191332882
C43×#15652
#1918343