Finite Group Databasebeta

← #25079058

Subgroups — #25079058

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145154C211yesmaximal, characteristic, complemented
2#19144667C211yesmaximal, characteristic, complemented
3#19144656C211yesmaximal, characteristic
4C8×#10621898C211yesmaximal, characteristic, complemented
5#19134054C211yesmaximal, characteristic, complemented
6#19134047C211yesmaximal, characteristic, complemented
7#19134040C211yesmaximal, characteristic, complemented
8#19134033C211yesmaximal, characteristic, complemented
9#19133978C211yesmaximal, characteristic, complemented
10#19133971C211yesmaximal, characteristic, complemented
11#19133944C211yesmaximal, characteristic, complemented
12#19133937C211yesmaximal, characteristic, complemented
13#19133259C211yesmaximal, characteristic, complemented
14#19133255C211yesmaximal, characteristic, complemented
15C43×#1564C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583241—21no—
24#14583224—21no—
25#14583195C2211yescharacteristic
26#14583190C2211yescharacteristic
27#14583185C2211yescharacteristic
28#14583180C2211yescharacteristic
29#14583128—21no—
30#14583128—21no—
31#14583110C2211yescharacteristic
32#14583105C2211yescharacteristic
33#14583100C2211yescharacteristic
34#14583095C2211yescharacteristic
35#14583063—21no—
36#14583046—21no—
37C8×Dic86C2211yescharacteristic
38C8×Dic86C2211yescharacteristic
39C4×Dic172—21no—
40C4×#10621873—21no—
41C4×#10621873—21no—
42C4×#10621873—21no—
43C4×#10621873—21no—
44C4×D344—21no—
45C8×D172C2211yescharacteristic
46C8×D172C2211yescharacteristic
47C8×C22⋊D43—21no—
48C8×C22⋊D43—21no—
49#14582952C2211yescharacteristic
50#14582950—21no—
51C4×C8×D43—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69C2×Dic172—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×D344—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063322C2311yescharacteristic
81#13063317—21no—
82#13063313—21no—
83#13063304—21no—
84#13063304—21no—
85#13063299—21no—
86#13063299—21no—
87C4×Dic86—21no—
88C4×Dic86—21no—
89C4×Dic86D411yescharacteristic
90C4×Dic86C2311yescharacteristic
91C4×D172—21no—
92C4×D172—21no—
93C4×D172D411yescharacteristic
94C4×D172C2311yescharacteristic
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97#13063284—21no—
98#13063284D411yescharacteristic
99#13063282—21no—
100C42×D43—21no—
101#13063259—21no—
102#13063259—21no—
103#13063257—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#13063250—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—
126C4×C43⋊C8—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C22×C8×C43D411yescharacteristic
130C22×C8×C43D411yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
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—22no—
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
164C2×C8×C43—22no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—41no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43#4111yescharacteristic
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179C22⋊Dic43—41no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202Dic172—42no—
203D344—42no—
204#10621873—42no—
205#10621873—42no—
206#10621873—42no—
207#10621873—42no—
208C8×D43—42no—
209C8×D43—42no—
210C23×C43#12111yescharacteristic
211C22×D43—21no—
212C22×D43—41no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C22⋊D43—24no—
225C22⋊D43—82no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232D172—21no—
233D172—41no—
234D172—41no—
235D172—41no—
236D172—41no—
237D172—81no—
238D172#13512yes—
239C4×D43—24no—
240C4×D43—41no—
241C4×D43—41no—
242C4×D43—42no—
243C4×D43—82no—
244Dic86—21no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—81no—
250Dic86#13512yes—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43#13512yes—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19127—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43C2×#12111yescharacteristic
266C2×D43—22no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43#47112yes—
276C4×C43C2×#13511yescharacteristic
277C4×C43C2×#13511yescharacteristic
278C4×C43C2×#13511yescharacteristic
279C4×C43#57511yescharacteristic
280Dic43—22no—
281Dic43—41no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286#3167—431no—
287#3107—431no—
288#3106—431no—
289C8×#41—431no—
290#1684—431no—
291#1683—431no—
292#1682—431no—
293#1681—431no—
294#1672—431no—
295#1671—431no—
296#1666—431no—
297#1665—431no—
298#1564D4311yescharacteristic, complemented
299#1544—431no—
300#1543—431no—
301C2×C43—41no—
302C2×C43#303511yescharacteristic
303C2×C43#305011yescharacteristic
304C2×C43C2×#47111yescharacteristic
305D43—42no—
306D43—161no—
307#533—431no—
308#532—431no—
309C4×#41—431no—
310#498—431no—
311#492—431no—
312#487—431no—
313#486—431no—
314#485—861no—
315#482—861no—
316#477—431no—
317#476—431no—
318#475—431no—
319#474—431no—
320#465—861no—
321#465—861no—
322#462—431no—
323#461—431no—
324#460—431no—
325#459—431no—
326#452—861no—
327#449—861no—
328C8×Q8—431no—
329C8×Q8—431no—
330C4×Q16—861no—
331C4×SD16—861no—
332C4×SD16—861no—
333C4×SD16—861no—
334C4×SD16—861no—
335C4×D8—861no—
336C8×D4—431no—
337C8×D4—431no—
338C8×D4—861no—
339C8×D4—861no—
340#431—431no—
341#431—861no—
342#431C2×D4311yescharacteristic
343#431C2×D4311yescharacteristic
344C2×C4×C8—861no—
345C2×C4×C8C2×D4311yescharacteristic
346#335C2×D4311yescharacteristic
347#335C2×D4311yescharacteristic
348#334C2×D4311yescharacteristic
349#334C2×D4311yescharacteristic
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331—431no—
357#331—431no—
358C43#1912711yescharacteristic, complemented, Sylow
359C2×#41—431no—
360C2×#41—861no—
361C2×Q16—861no—
362C2×SD16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—861no—
367C22×C8—861no—
368C22×C8—861no—
369C22×C8D17211yescharacteristic
370C22×C8D17211yescharacteristic
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—431no—
374#127—431no—
375#125—861no—
376#124—861no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379#121—861no—
380#121—861no—
381C4×Q8—431no—
382C4×Q8—431no—
383C4×Q8—861no—
384C4×Q8—861no—
385C4×D4—431no—
386C4×D4—431no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4—861no—
390C4×D4—861no—
391#117—431no—
392#117—861no—
393#117—861no—
394C2×C42—861no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
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#103—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8D17211yescharacteristic
433C4×C8D17211yescharacteristic
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436#41—862no—
437#41—862no—
438#41—3442no—
439C2×Q8—431no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—431no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—1721no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—1721no—
453C22×C4C2×D17211yescharacteristic
454C22×C4D4×D4311yescharacteristic
455C22×C4#1062190211yescharacteristic
456Q16—1722no—
457SD16—1722no—
458SD16—1722no—
459SD16—1722no—
460SD16—1722no—
461D8—1722no—
462C2×C8—22no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—41no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—1722no—
471C2×C8—1722no—
472C2×C8C2×D17211yescharacteristic
473C2×C8C2×D17211yescharacteristic
474C2×C8C2×D17211yescharacteristic
475C2×C8C2×D17211yescharacteristic
476C4⋊C4—431no—
477C4⋊C4—431no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—1721no—
487C4⋊C4—1721no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—861no—
495C42—861no—
496C42—861no—
497C42—1721no—
498C42C2×D17211yescharacteristic
499C42D4×D4311yescharacteristic
500C42#1062190211yescharacteristic
501C42C23×D4311yescharacteristic
502C23—861no—
503C23—1721no—
504C23#1306330011yescharacteristic
505Q8—432no—
506Q8—861no—
507Q8—3441no—
508Q8—1721no—
509Q8—1721no—
510Q8—1721no—
511Q8—1721no—
512D4—432no—
513D4—864no—
514D4—861no—
515D4—3441no—
516D4—3442no—
517D4—1721no—
518D4—1721no—
519D4—1721no—
520D4—1721no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—864no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—3442no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1722no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306330011yescharacteristic
538C2×C4#1306330011yescharacteristic
539C2×C4#1306330011yescharacteristic
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×D17211yescharacteristic
542C2×C4C2×#1062190211yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—1721no—
551C8—1721no—
552C8#1306334712yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—862no—
557C22—3441no—
558C22—3441no—
559C22—3441no—
560C22—1721no—
561C22—1721no—
562C22C2×#1306330011yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—862no—
567C4—3441no—
568C4—3441no—
569C4—3441no—
570C4—1721no—
571C4—1721no—
572C4#1458316312yes—
573C4#135×D4311yescharacteristic
574C4#135×D4311yescharacteristic
575C4C2×#1306334711yescharacteristic
576C4#1458369911yescharacteristic
577C2—41no—
578C2—1722no—
579C2—6881no—
580C2#1914405211yescharacteristic
581C2#1914417711yescharacteristic
582C2C2×#1458316311yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1564C2
socleC22×C43C2×#121
prime radical#19144656C2
hypercenter#1564D43
hypocenterC43#19127
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
1. #19145154C2semidirect
2. #19144667C2semidirect
4. C8×#10621898C2semidirect
5. #19134054C2semidirect
6. #19134047C2semidirect
7. #19134040C2semidirect
8. #19134033C2semidirect
9. #19133978C2semidirect
10. #19133971C2semidirect
11. #19133944C2semidirect
12. #19133937C2semidirect
13. #19133259C2semidirect
14. #19133255C2semidirect
15. C43×#1564C2semidirect
298. #1564D43semidirect
358. C43#19127semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191446672
#191446562
C8×#106218982
#191340542
#191340472
#191340402
#191340332
#191339782
#191339712
#191339442
#191339372
#191332592
#191332552
C43×#15642
#1912743