Finite Group Databasebeta

← #25082011

Subgroups — #25082011

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145515C211yesmaximal, characteristic, complemented
2#19144075C211yesmaximal, characteristic, complemented
3#19144050C211yesmaximal, characteristic, complemented
4#19134039C212yesmaximal, complemented
5#19134032C212yesmaximal, complemented
6#19133955C212yesmaximal, complemented
7#19133950C212yesmaximal, complemented
8#19133370C211yesmaximal, characteristic, complemented
9#19133270C211yesmaximal, characteristic, complemented
10C2×#14582642C211yesmaximal, characteristic, complemented
11C43×#2988C211yesmaximal, characteristic, complemented
12C2×#13063350—21no—
13C2×#13063345—21no—
14#14583449C2211yescharacteristic
15C2×#13063322C2211yescharacteristic
16#14583276C2212yes—
17#14583246C2212yes—
18#14583121—21no—
19#14583114—21no—
20#14583109C2211yescharacteristic, complemented
21#14583104C2211yescharacteristic, complemented
22#14583099—21no—
23#14583099C2212yes—
24#14583099C2211yescharacteristic, complemented
25#14583095—21no—
26#14583095—21no—
27#14583094—21no—
28#14583094C2212yes—
29#14583094C2211yescharacteristic, complemented
30#14583035—22no—
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582903—21no—
34#14582893—21no—
35#14582652C2212yescomplemented
36#14582652C2212yescomplemented
37#14582644C2212yescomplemented
38#14582642C2212yes—
39#14582642C2212yes—
40#14582642C2212yescomplemented
41C4×#41×C43C2211yescharacteristic
42C8×Q8×C43C2212yescomplemented
43C8×D4×C43—22no—
44C8×D4×C43C2212yescomplemented
45C43×#431—21no—
46C43×#431C2211yescharacteristic
47C2×C4⋊C8×C43—21no—
48C2×C4⋊C8×C43C2211yescharacteristic
49C2×#10621898—21no—
50C22×D172—21no—
51C22×D172—21no—
52C22×D172—21no—
53#13063350—44no—
54#13063345—44no—
55C2×#10621885—21no—
56C2×#10621883—21no—
57C2×#10621884—22no—
58C2×#10621884—21no—
59C2×D344—22no—
60C2×D344—22no—
61C2×#10621882—22no—
62C2×#10621882—21no—
63C2×#10621877—21no—
64C22×C43⋊C8—21no—
65#13063325C2311yescharacteristic
66#13063322—21no—
67#13063322—21no—
68#13063322—21no—
69#13063322C2312yes—
70#13063322C2311yescharacteristic
71#13063313—21no—
72#13063299—21no—
73#13063299—21no—
74C4×D172—21no—
75C4×D172—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)C2312yes—
79C4⋊(C43⋊C8)C2311yescharacteristic
80C4⋊(C43⋊C8)C2311yescharacteristic
81#13063248—21no—
82#13063248—21no—
83#13063247—22no—
84#13063247—22no—
85#13063245—22no—
86#13063245—22no—
87#13063245—21no—
88#13063245—21no—
89C2×#41×C43D411yescharacteristic
90C22×C8×C43—21no—
91C22×C8×C43—22no—
92C4×Q8×C43D411yescharacteristic
93C4×Q8×C43C2311yescharacteristic
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43D411yescharacteristic
97C4×D4×C43C2311yescharacteristic
98#117×C43—21no—
99#117×C43D411yescharacteristic
100C2×C42×C43—21no—
101C2×C42×C43C2311yescharacteristic
102C4⋊C8×C43—22no—
103C4⋊C8×C43—21no—
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D411yescharacteristic
106C4⋊C8×C43C2312yes—
107C22⋊C8×C43—22no—
108C22⋊C8×C43D412yes—
109C4×C8×C43—22no—
110C4×C8×C43C2312yes—
111C23×D43—41no—
112#41×C43—22no—
113#41×C43D814yescomplemented
114C2×Q8×C43C2×D411yescharacteristic
115C2×D4×C43—21no—
116C2×D4×C43C2×D411yescharacteristic
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C2×C22⋊D43—41no—
124#10621898—42no—
125#10621898—42no—
126C2×D172—21no—
127C2×D172—22no—
128C2×D172—22no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—22no—
132C2×D172—41no—
133C2×D172—41no—
134C2×D172—41no—
135C2×D172—42no—
136C2×D172—42no—
137C2×D172—81no—
138C2×D172—81no—
139C2×D172—82no—
140C2×C4×D43—41no—
141C2×Dic86—21no—
142C2×C8×C43—22no—
143C2×C8×C43—82no—
144C2×C8×C43—81no—
145C2×C8×C43C2×D412yes—
146C2×C8×C43C2×D412yes—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43C2×D411yescharacteristic
150C4⋊C4×C43C2×D411yescharacteristic
151C22⋊C4×C43—21no—
152C22⋊C4×C43—21no—
153C22⋊C4×C43—21no—
154C42×C43—21no—
155C42×C43—21no—
156C42×C43—21no—
157C42×C43C2×D411yescharacteristic
158C42×C43C2×D411yescharacteristic
159C42×C43#4111yescharacteristic
160C42×C43C2411yescharacteristic
161#10621885—42no—
162#10621884—42no—
163#10621884—44no—
164#10621883—42no—
165#10621882—42no—
166#10621882—44no—
167(C2×D43)⋊C4—41no—
168(C2×D43)⋊C4—41no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171#10621877—42no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—21no—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—42no—
176D344—82no—
177D344—82no—
178C23×C43—21no—
179C23×C43#12111yescharacteristic
180C22×D43—41no—
181C22×D43—42no—
182C22×D43—82no—
183C22×D43—82no—
184C22×D43—82no—
185Q8×C43—21no—
186Q8×C43C2×D812yes—
187D4×C43—24no—
188D4×C43—21no—
189D4×C43C2×D812yes—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—24no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—81no—
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43C2×D812yes—
204C2×C4×C43#13512yes—
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C2×C4×C43C2×#4111yescharacteristic
208C22⋊D43—82no—
209C2×Dic43—41no—
210D172—42no—
211D172—41no—
212D172—42no—
213D172—41no—
214D172—41no—
215D172—42no—
216D172—41no—
217D172—42no—
218D172—81no—
219D172—82no—
220D172—82no—
221D172—82no—
222D172—82no—
223C4×D43—82no—
224Dic86—41no—
225Dic86—41no—
226C8×C43—22no—
227C8×C43—22no—
228C8×C43—42no—
229C43⋊C8—41no—
230C43⋊C8—41no—
231C43⋊C8—42no—
232#19410—431nomaximal, Sylow
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—22no—
236C22×C43—41no—
237C22×C43—41no—
238C22×C43#46612yes—
239C22×C43C2×#12111yescharacteristic
240C2×D43—82no—
241C2×D43—81no—
242C2×D43—82no—
243C2×D43—81no—
244C2×D43—82no—
245C2×D43—81no—
246C2×D43—164no—
247C4×C43—21no—
248C4×C43—22no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—41no—
252C4×C43—41no—
253C4×C43#46612yes—
254C4×C43C22×D811yescharacteristic
255C4×C43C2×#13511yescharacteristic
256C4×C43#57611yescharacteristic
257C4×C43#57711yescharacteristic
258Dic43—81no—
259#3205—431no—
260#3038—431no—
261#3035—431no—
262#2988D4311yescharacteristic, complemented
263#1682—432no—
264#1681—432no—
265#1668—432no—
266#1667—432no—
267#1571—431no—
268#1547—431no—
269C2×#331—431no—
270C2×C43—22no—
271C2×C43—42no—
272C2×C43#304511yescharacteristic
273C2×C43C2×#46611yescharacteristic
274C2×C43#306811yescharacteristic
275D43—161no—
276D43—162no—
277C2×AGL(1,ℤ/8)—861no—
278C2×#135—861no—
279#532—431no—
280C2×#127—431no—
281C4×#41C2×D4311yescharacteristic
282#493—432no—
283#486—432no—
284#464—861no—
285#463—861no—
286#462—431no—
287#461—431no—
288#460—432no—
289#460—431no—
290#460—861no—
291#459—432no—
292#459—431no—
293#459—861no—
294#459—861no—
295#459—861no—
296#447—862no—
297C8×Q8C2×D4312yescomplemented
298C8×D4—22no—
299C8×D4C2×D4312yescomplemented
300#431—21no—
301#431C2×D4311yescharacteristic
302#423—431no—
303C2×C4⋊C8—21no—
304C2×C4⋊C8—431no—
305C2×C4⋊C8C2×D4311yescharacteristic
306#418—861no—
307#416—861no—
308#335—432no—
309#335—432no—
310#332—432no—
311#331—432no—
312#331—432no—
313#331—432no—
314C43#1941011yescharacteristic, complemented, Sylow
315C2×#41—861no—
316C2×#41D17211yescharacteristic
317C22×D4—861no—
318C22×D4—861no—
319C22×D4—861no—
320AGL(1,ℤ/8)—1724no—
321#135—1724no—
322C2×Q16—861no—
323C2×SD16—861no—
324C2×SD16—862no—
325C2×SD16—861no—
326C2×D8—861no—
327C2×D8—862no—
328C2×D8—862no—
329C2×D8—862no—
330C2×M16—861no—
331C22×C8—21no—
332C22×C8—22no—
333C22×C8—861no—
334C4⋊Q8—431no—
335#127—432no—
336#127—431no—
337#127—861no—
338#127—861no—
339#127—861no—
340#124—861no—
341#121—861no—
342#121—861no—
343C4×Q8D17211yescharacteristic
344C4×Q8C22×D4311yescharacteristic
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—861no—
348C4×D4—861no—
349C4×D4D17211yescharacteristic
350C4×D4C22×D4311yescharacteristic
351#117—21no—
352#117D17211yescharacteristic
353C2×C42—21no—
354C2×C42C22×D4311yescharacteristic
355C4⋊C8—22no—
356C4⋊C8—21no—
357C4⋊C8—431no—
358C4⋊C8—431no—
359C4⋊C8—432no—
360C4⋊C8—861no—
361C4⋊C8—861no—
362C4⋊C8C22⋊D4311yescharacteristic
363C4⋊C8C22⋊D4311yescharacteristic
364C4⋊C8C22×D4312yes—
365#103—861no—
366#103—861no—
367#102—862no—
368#102—862no—
369#102—861no—
370#102—861no—
371#102—862no—
372#102—862no—
373C22⋊C8—22no—
374C22⋊C8C22⋊D4312yes—
375C4×C8—22no—
376C4×C8C22×D4312yes—
377C24—1721no—
378#41—22no—
379#41—1722no—
380#41—1722no—
381#41D34414yescomplemented
382C2×Q8—861no—
383C2×Q8C2×D17211yescharacteristic
384C2×D4—21no—
385C2×D4—862no—
386C2×D4—861no—
387C2×D4—861no—
388C2×D4—862no—
389C2×D4—861no—
390C2×D4—862no—
391C2×D4—3441no—
392C2×D4—3441no—
393C2×D4—3442no—
394C2×D4—1721no—
395C2×D4—1721no—
396C2×D4—1721no—
397C2×D4—1721no—
398C2×D4—1722no—
399C2×D4—1722no—
400C2×D4C2×D17211yescharacteristic
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—1721no—
405C22×C4C2×D17211yescharacteristic
406C22×C4#1062189811yescharacteristic
407C22×C4C2×C22⋊D4311yescharacteristic
408Q16—1722no—
409SD16—1722no—
410SD16—1724no—
411SD16—1722no—
412D8—3442no—
413D8—3442no—
414D8—1722no—
415D8—1724no—
416M16—1722no—
417C2×C8—22no—
418C2×C8—82no—
419C2×C8—81no—
420C2×C8—862no—
421C2×C8—861no—
422C2×C8—861no—
423C2×C8—1722no—
424C2×C8C2×C22⋊D4312yes—
425C2×C8C2×C22⋊D4312yes—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4C2×D17211yescharacteristic
431C4⋊C4C2×D17211yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C42—21no—
438C42—21no—
439C42—21no—
440C42C2×D17211yescharacteristic
441C42#1062189811yescharacteristic
442C42C2×C22⋊D4311yescharacteristic
443C42C23×D4311yescharacteristic
444C23—21no—
445C23—3442no—
446C23—3442no—
447C23—3442no—
448C23—1721no—
449C23—1722no—
450C23#1306329911yescharacteristic
451Q8—21no—
452Q8—1721no—
453Q8—1721no—
454Q8C2×D34412yes—
455D4—24no—
456D4—21no—
457D4—3442no—
458D4—3441no—
459D4—3442no—
460D4—3442no—
461D4—3442no—
462D4—3442no—
463D4—1722no—
464D4—1721no—
465D4—1722no—
466D4—1721no—
467D4—1721no—
468D4—1722no—
469D4—1721no—
470D4—1722no—
471D4C2×D34412yes—
472C2×C4—21no—
473C2×C4—24no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—3442no—
483C2×C4—1721no—
484C2×C4#1306329911yescharacteristic
485C2×C4#1306329911yescharacteristic
486C2×C4#1306329911yescharacteristic
487C2×C4C2×D34412yes—
488C2×C4#1306334712yes—
489C2×C4C22×C22⋊D4311yescharacteristic
490C2×C4C22×D17211yescharacteristic
491C2×C4C2×#1062189811yescharacteristic
492C8—22no—
493C8—22no—
494C8—42no—
495C8—1721no—
496C8—1721no—
497C8—1722no—
498C22—21no—
499C22—21no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—3442no—
504C22—3441no—
505C22—3442no—
506C22—3441no—
507C22—3441no—
508C22—3442no—
509C22—6884no—
510C22#1458313512yes—
511C22C2×#1306329911yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—22no—
516C4—41no—
517C4—41no—
518C4—3441no—
519C4#1458313512yes—
520C4C22×D34411yescharacteristic
521C4C2×#1306334711yescharacteristic
522C4#1458370211yescharacteristic
523C4#1458370711yescharacteristic
524C2—22no—
525C2—42no—
526C2—6882no—
527C2—6881no—
528C2#1914413411yescharacteristic
529C2C2×#1458313511yescharacteristic
530C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×#121
hypercenter#2988D43
hypocenterC43#19410
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #19145515C2semidirect
2. #19144075C2semidirect
3. #19144050C2semidirect
4. #19134039C2semidirect
5. #19134032C2semidirect
6. #19133955C2semidirect
7. #19133950C2semidirect
8. #19133370C2semidirect
9. #19133270C2semidirect
10. C2×#14582642C2semidirect
11. C43×#2988C2semidirect
20. #14583109C22semidirect
21. #14583104C22semidirect
24. #14583099C22semidirect
29. #14583094C22semidirect
35. #14582652C22semidirect
36. #14582652C22semidirect
37. #14582644C22semidirect
40. #14582642C22semidirect
42. C8×Q8×C43C22semidirect
44. C8×D4×C43C22semidirect
113. #41×C43D8semidirect
262. #2988D43semidirect
297. C8×Q8C2×D43semidirect
299. C8×D4C2×D43semidirect
314. C43#19410semidirect
381. #41D344semidirect

Maximal subgroups

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

subgroupindex
#191455152
#191440752
#191440502
#191340392
#191340322
#191339552
#191339502
#191333702
#191332702
C2×#145826422
C43×#29882
#1941043