Finite Group Databasebeta

← #25253503

Subgroups — #25253503

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146338C211yesmaximal, characteristic, complemented
2#19136829C211yesmaximal, characteristic, complemented
3#19136803C211yesmaximal, characteristic, complemented
4#19136780C211yesmaximal, characteristic, complemented
5#19136756C211yesmaximal, characteristic, complemented
6#19136689C211yesmaximal, characteristic, complemented
7#19136679C211yesmaximal, characteristic, complemented
8#19136650C211yesmaximal, characteristic, complemented
9#19136516C211yesmaximal, characteristic, complemented
10#19136511C211yesmaximal, characteristic, complemented
11C4×#13063269C211yesmaximal, characteristic, complemented
12D4×C43⋊C16C211yesmaximal, characteristic, complemented
13#19136300C211yesmaximal, characteristic, complemented
14C2×#14582702C211yesmaximal, characteristic, complemented
15C43×#3339C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18#14583558—21no—
19C2×#13063269C2211yescharacteristic
20C2×#13063269C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22C22×C43⋊C16C2211yescharacteristic
23C22×C43⋊C16C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583140C2211yescharacteristic
26#14583135C2211yescharacteristic
27#14583122—21no—
28#14583063—21no—
29#14583040—21no—
30C4×Dic172C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582726C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35#14582702C2211yescharacteristic
36#14582702C2211yescharacteristic
37#14582702C2211yescharacteristic
38#14582702C2211yescharacteristic
39#14582702C2211yescharacteristic
40#14582702C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44#14582699C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C43×#553—21no—
49C43×#499C2211yescharacteristic
50C43×#482—21no—
51C43×#481—21no—
52C43×#478—21no—
53C43×#466C2211yescharacteristic
54C43×#466C2211yescharacteristic
55C4×D8×C43C2211yescharacteristic
56C8×D4×C43C2211yescharacteristic
57C43×#427C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic
59C2×#10621898—21no—
60C22×Dic86—21no—
61#13063347—22no—
62#13063347—41no—
63C2×Dic172—22no—
64C2×Dic172—21no—
65C2×Dic172—41no—
66C2×Dic172C2311yescharacteristic
67C2×Dic172C2311yescharacteristic
68C2×#10621873—21no—
69C2×#10621873—21no—
70C2×D344C2311yescharacteristic
71#13063313—21no—
72#13063311—41no—
73#13063304—21no—
74#13063303—41no—
75#13063299—21no—
76#13063297—41no—
77C4×Dic86—21no—
78(C22⋊D43)⋊C4—41no—
79#13063269—22no—
80#13063269—41no—
81#13063266—41no—
82C2×C43⋊C16—41no—
83C2×C43⋊C16—41no—
84C2×C43⋊C16C2311yescharacteristic
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063250—21no—
90#13063250—21no—
91#13063247—21no—
92C2×D8×C43C2311yescharacteristic
93C22×C8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95#126×C43—41no—
96#125×C43—21no—
97#123×C43—41no—
98#121×C43—21no—
99#121×C43—21no—
100#121×C43—41no—
101C4×D4×C43—21no—
102C4×D4×C43—41no—
103C4×D4×C43D411yescharacteristic
104#117×C43—21no—
105C2×C4⋊C4×C43—21no—
106#107×C43—21no—
107#107×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#106×C43—21no—
111#106×C43—21no—
112C4⋊C8×C43D411yescharacteristic
113#102×C43—21no—
114#102×C43—21no—
115#102×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C2×D4×C43—21no—
120C2×D4×C43—41no—
121C2×D4×C43—41no—
122C2×D4×C43D811yescharacteristic
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C2×C22⋊D43—41no—
128C2×C22⋊D43—41no—
129C22×Dic43—41no—
130#10621898—42no—
131#10621898—81no—
132C2×D172—21no—
133C2×C4×D43—41no—
134C2×Dic86—21no—
135C2×Dic86—21no—
136C2×Dic86—42no—
137C2×Dic86—41no—
138C2×Dic86—81no—
139D8×C43—21no—
140D8×C43—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43C2×D411yescharacteristic
146C2×C8×C43C2×D411yescharacteristic
147C2×C8×C43C2×D411yescharacteristic
148C2×C8×C43C2411yescharacteristic
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—41no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43—41no—
155C4⋊C4×C43D811yescharacteristic
156C22⋊C4×C43—41no—
157C22⋊C4×C43—41no—
158C22⋊C4×C43—41no—
159C22⋊C4×C43—41no—
160C22⋊C4×C43D811yescharacteristic
161C22⋊C4×C43D811yescharacteristic
162C42×C43—41no—
163C42×C43C2×D411yescharacteristic
164C22⋊Dic43—41no—
165(C2×D43)⋊C4—41no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168C4⋊Dic43—21no—
169Dic43⋊C4—41no—
170Dic43⋊C4—41no—
171C4×Dic43—41no—
172Dic172—21no—
173Dic172—21no—
174Dic172—21no—
175Dic172—42no—
176Dic172#4112yes—
177D344—21no—
178D344—21no—
179#10621873—42no—
180#10621873—81no—
181C43⋊C16—21no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43—41no—
186C23×C43C2×D811yescharacteristic
187C23×C43C2×D811yescharacteristic
188C22×D43—41no—
189D4×C43—22no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—82no—
193D4×C43—161no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—161no—
202C2×C4×C43—161no—
203C2×C4×C43C2×D811yescharacteristic
204C2×C4×C43C2×D811yescharacteristic
205C2×C4×C43C2×D811yescharacteristic
206C2×C4×C43C2×D811yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C22⋊D43—82no—
209C22⋊D43—82no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—82no—
214D172—41no—
215D172—41no—
216C4×D43—82no—
217Dic86—22no—
218Dic86—41no—
219Dic86—41no—
220Dic86—41no—
221Dic86—82no—
222C8×C43—21no—
223C8×C43—21no—
224C8×C43—21no—
225C8×C43C2×#4111yescharacteristic
226C8×C43H(5,𝔽2)11yescharacteristic
227#33868—431nomaximal, Sylow
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43#50812yes—
237C22×C43C22×D811yescharacteristic
238C2×D43—81no—
239C2×D43—81no—
240C2×D43—81no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—81no—
246C4×C43—81no—
247C4×C43—81no—
248C4×C43#54611yescharacteristic
249C4×C43#57711yescharacteristic
250Dic43—42no—
251Dic43—81no—
252Dic43—81no—
253#3339D4311yescharacteristic, complemented
254#3285—431no—
255#2242—431no—
256#2237—431no—
257#2233—431no—
258#2229—431no—
259#2217—431no—
260#2215—431no—
261#2210—431no—
262#2186—431no—
263#2185—431no—
264C4×SD32—431no—
265D4×C16—431no—
266#2138—431no—
267C2×#358—431no—
268C2×C43—22no—
269C2×C43—41no—
270C2×C43—161no—
271C2×C43#329411yescharacteristic
272C2×C43C2×#50811yescharacteristic
273C2×C43#341611yescharacteristic
274D43—161no—
275C2×#135—431no—
276C22×Q16—431no—
277#553—21no—
278#548—861no—
279C2×SD32—431no—
280C2×SD32—431no—
281C2×D16—431no—
282C22×C16—431no—
283C22×C16—431no—
284#499C2×D4311yescharacteristic
285#495—431no—
286#482—21no—
287#481—21no—
288#478—21no—
289#467—431no—
290#466—431no—
291#466C2×D4311yescharacteristic
292#466C2×D4311yescharacteristic
293#464—861no—
294#452—861no—
295#448—861no—
296C4×Q16—431no—
297C4×D8C2×D4311yescharacteristic
298C8×D4C2×D4311yescharacteristic
299#427C2×D4311yescharacteristic
300C2×#107C2×D4311yescharacteristic
301#367—431no—
302#367—431no—
303#366—431no—
304C4⋊C16—431no—
305#358—431no—
306#358—431no—
307#358—431no—
308#358—431no—
309#358—431no—
310#358—431no—
311#357—431no—
312#357—431no—
313#357—431no—
314#357—431no—
315C22⋊C16—431no—
316C22⋊C16—431no—
317C4×C16—431no—
318C43#3386811yescharacteristic, complemented, Sylow
319C2×#41—861no—
320C22×Q8—861no—
321#135—862no—
322#135—1721no—
323C2×Q16—431no—
324C2×Q16—431no—
325C2×Q16—862no—
326C2×Q16—861no—
327C2×Q16—1721no—
328C2×SD16—861no—
329C2×SD16—861no—
330C2×D8—431no—
331C2×D8C22×D4311yescharacteristic
332C22×C8C22×D4311yescharacteristic
333C22×C8C22×D4311yescharacteristic
334#126—41no—
335#125—21no—
336#124—861no—
337#124—1721no—
338#123—41no—
339C22⋊Q8—861no—
340C22⋊Q8—1721no—
341#121—21no—
342#121—21no—
343#121—41no—
344#121—861no—
345#121—1721no—
346C4×Q8—861no—
347C4×D4—21no—
348C4×D4—41no—
349C4×D4—1721no—
350C4×D4C22⋊D4311yescharacteristic
351#117—21no—
352C2×C4⋊C4—21no—
353SD32—862no—
354SD32—1721no—
355D16—1721no—
356C2×C16—431no—
357C2×C16—431no—
358C2×C16—431no—
359C2×C16—431no—
360C2×C16—1721no—
361C2×C16—1721no—
362#107—21no—
363#107—431no—
364#107C22×D4311yescharacteristic
365#107C22×D4311yescharacteristic
366#107C22×D4311yescharacteristic
367#106—21no—
368#106—21no—
369C4⋊C8C22⋊D4311yescharacteristic
370#103—861no—
371#103—861no—
372#102—21no—
373#102—21no—
374#102—21no—
375#102—861no—
376C22⋊C8C22⋊D4311yescharacteristic
377C22⋊C8C22⋊D4311yescharacteristic
378C4×C8C22×D4311yescharacteristic
379#41—3441no—
380#41—1722no—
381C2×Q8—861no—
382C2×Q8—861no—
383C2×Q8—3441no—
384C2×Q8—1722no—
385C2×Q8—1721no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—861no—
390C2×D4—1721no—
391C2×D4—1721no—
392C2×D4#1062188211yescharacteristic
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—1721no—
396C22×C4—1721no—
397C22×C4C2×C22⋊D4311yescharacteristic
398C22×C4C2×C22⋊D4311yescharacteristic
399Q16—432no—
400Q16—861no—
401Q16—861no—
402Q16—861no—
403Q16—1722no—
404SD16—3441no—
405SD16—1722no—
406D8—21no—
407D8—21no—
408D8—861no—
409D8—861no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8C2×C22⋊D4311yescharacteristic
415C2×C8C2×C22⋊D4311yescharacteristic
416C2×C8C2×C22⋊D4311yescharacteristic
417C2×C8C23×D4311yescharacteristic
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—861no—
425C4⋊C4—1721no—
426C4⋊C4—1721no—
427C4⋊C4#1062188211yescharacteristic
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—1721no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4#1062188211yescharacteristic
437C22⋊C4#1062188211yescharacteristic
438C42—41no—
439C42—1721no—
440C42C2×C22⋊D4311yescharacteristic
441C16—861no—
442C16—861no—
443C16—861no—
444C16—861no—
445C23—41no—
446C23—1721no—
447C23C2×#1062188211yescharacteristic
448C23C2×#1062188211yescharacteristic
449Q8—862no—
450Q8—3442no—
451Q8—1721no—
452Q8—1721no—
453Q8—1721no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—82no—
458D4—161no—
459D4—3442no—
460D4—3442no—
461D4—1721no—
462D4—1721no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—161no—
471C2×C4—161no—
472C2×C4—3442no—
473C2×C4—3442no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4C2×#1062188211yescharacteristic
478C2×C4C2×#1062188211yescharacteristic
479C2×C4C2×#1062188211yescharacteristic
480C2×C4C2×#1062188211yescharacteristic
481C2×C4C22×C22⋊D4311yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8#41×D4311yescharacteristic
486C8#1306337111yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—3441no—
496C22—3441no—
497C22—3441no—
498C22#1458332912yes—
499C22C22×#1062188211yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—81no—
505C4—81no—
506C4—81no—
507C4—3441no—
508C4—3441no—
509C4—1722no—
510C4#1458353711yescharacteristic
511C4#1458370711yescharacteristic
512C2—22no—
513C2—41no—
514C2—161no—
515C2—6881no—
516C2#1914640211yescharacteristic
517C2C2×#1458332911yescharacteristic
518C2#1914774211yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3339C2
socleC22×C43C22×D8
hypercenter#3339D43
hypocenterC43#33868
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #19146338C2semidirect
2. #19136829C2semidirect
3. #19136803C2semidirect
4. #19136780C2semidirect
5. #19136756C2semidirect
6. #19136689C2semidirect
7. #19136679C2semidirect
8. #19136650C2semidirect
9. #19136516C2semidirect
10. #19136511C2semidirect
11. C4×#13063269C2semidirect
12. D4×C43⋊C16C2semidirect
13. #19136300C2semidirect
14. C2×#14582702C2semidirect
15. C43×#3339C2semidirect
253. #3339D43semidirect
318. C43#33868semidirect

Maximal subgroups

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

subgroupindex
#191463382
#191368292
#191368032
#191367802
#191367562
#191366892
#191366792
#191366502
#191365162
#191365112
C4×#130632692
D4×C43⋊C162
#191363002
C2×#145827022
C43×#33392
#3386843