Finite Group Databasebeta

← #25253509

Subgroups — #25253509

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#19146998C211yesmaximal, characteristic, complemented
2#19136826C211yesmaximal, characteristic, complemented
3#19136800C211yesmaximal, characteristic, complemented
4#19136778C211yesmaximal, characteristic, complemented
5#19136759C211yesmaximal, characteristic, complemented
6#19136693C211yesmaximal, characteristic, complemented
7#19136679C211yesmaximal, characteristic, complemented
8#19136647C211yesmaximal, characteristic, complemented
9#19136518C211yesmaximal, characteristic, complemented
10#19136512C211yesmaximal, characteristic, complemented
11C4×#13063268C211yesmaximal, characteristic, complemented
12D4×C43⋊C16C211yesmaximal, characteristic, complemented
13#19136302C211yesmaximal, characteristic, complemented
14C2×#14582703C211yesmaximal, characteristic, complemented
15C43×#3285C211yesmaximal, characteristic, complemented
16#14583595—21no—
17C2×#13063268C2211yescharacteristic
18C2×#13063268C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20C22×C43⋊C16C2211yescharacteristic
21C22×C43⋊C16C2211yescharacteristic
22#14583301C2211yescharacteristic
23#14583224—21no—
24#14583218—21no—
25#14583200—21no—
26#14583135C2211yescharacteristic
27#14583135C2211yescharacteristic
28C4×D344C2211yescharacteristic
29#14582937C2211yescharacteristic
30C2×#13063259C2211yescharacteristic
31#14582726C2211yescharacteristic
32#14582726C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35#14582703C2211yescharacteristic
36#14582703C2211yescharacteristic
37#14582703C2211yescharacteristic
38#14582703C2211yescharacteristic
39#14582703C2211yescharacteristic
40#14582703C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582700C2211yescharacteristic
43#14582700C2211yescharacteristic
44#14582699C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C2×#135×C43C2211yescharacteristic
49C22×Q16×C43C2211yescharacteristic
50C43×#548—21no—
51C43×#495C2211yescharacteristic
52C43×#467C2211yescharacteristic
53C43×#466C2211yescharacteristic
54C43×#464—21no—
55C43×#452—21no—
56C43×#448—21no—
57C4×Q16×C43C2211yescharacteristic
58C8×D4×C43C2211yescharacteristic
59C2×D344C2311yescharacteristic
60#13063320—41no—
61#13063317—21no—
62#13063307—41no—
63#13063299—21no—
64#13063299—21no—
65#13063297—41no—
66C4×D172—21no—
67(C22⋊D43)⋊C4—41no—
68#13063284—21no—
69C2×C4⋊Dic43—21no—
70#13063268—22no—
71#13063268—41no—
72#13063266—41no—
73C2×C43⋊C16—41no—
74C2×C43⋊C16—41no—
75C2×C43⋊C16C2311yescharacteristic
76C2×C43⋊C16C2311yescharacteristic
77C2×C43⋊C16C2311yescharacteristic
78C2×C43⋊C16C2311yescharacteristic
79#13063259—21no—
80#13063259C2311yescharacteristic
81#13063259C2311yescharacteristic
82#13063259C2311yescharacteristic
83#13063257—21no—
84#13063257—21no—
85#13063247—21no—
86#13063247—21no—
87#13063247—21no—
88C2×#41×C43—21no—
89C22×Q8×C43—21no—
90#135×C43—22no—
91#135×C43—41no—
92C2×Q16×C43—22no—
93C2×Q16×C43—21no—
94C2×Q16×C43—41no—
95C2×Q16×C43C2311yescharacteristic
96C2×Q16×C43C2311yescharacteristic
97C2×SD16×C43—21no—
98C2×SD16×C43—21no—
99C2×D8×C43C2311yescharacteristic
100C22×C8×C43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102#124×C43—21no—
103#124×C43—41no—
104C22⋊Q8×C43—21no—
105C22⋊Q8×C43—41no—
106#121×C43—21no—
107#121×C43—41no—
108C4×Q8×C43—21no—
109C4×D4×C43—41no—
110C4×D4×C43D411yescharacteristic
111#107×C43C2311yescharacteristic
112C4⋊C8×C43D411yescharacteristic
113#103×C43—21no—
114#103×C43—21no—
115#102×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119#41×C43—42no—
120#41×C43—81no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—42no—
124C2×Q8×C43—41no—
125C2×Q8×C43—81no—
126C2×D4×C43—21no—
127C2×D4×C43—41no—
128C2×D4×C43—41no—
129C2×D4×C43D811yescharacteristic
130C22×C4×C43—41no—
131C22×C4×C43—41no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C2×C22⋊D43—41no—
135C2×C22⋊D43—41no—
136C22×Dic43—41no—
137C2×D172—21no—
138C2×C4×D43—41no—
139Q16×C43—21no—
140Q16×C43—21no—
141Q16×C43—21no—
142Q16×C43—42no—
143Q16×C43#4112yes—
144SD16×C43—42no—
145SD16×C43—81no—
146D8×C43—21no—
147D8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43C2×D411yescharacteristic
153C2×C8×C43C2×D411yescharacteristic
154C2×C8×C43C2×D411yescharacteristic
155C2×C8×C43C2411yescharacteristic
156C4⋊C4×C43—21no—
157C4⋊C4×C43—41no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43D811yescharacteristic
160C22⋊C4×C43—41no—
161C22⋊C4×C43—41no—
162C22⋊C4×C43—41no—
163C22⋊C4×C43—41no—
164C22⋊C4×C43D811yescharacteristic
165C22⋊C4×C43D811yescharacteristic
166C42×C43—41no—
167C42×C43C2×D411yescharacteristic
168C22⋊Dic43—41no—
169(C2×D43)⋊C4—41no—
170(C2×D43)⋊C4—41no—
171(C2×D43)⋊C4—41no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—41no—
176Dic43⋊C4—41no—
177Dic43⋊C4—41no—
178C4×Dic43—41no—
179D344—21no—
180D344—21no—
181C43⋊C16—21no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C23×C43—41no—
186C23×C43C2×D811yescharacteristic
187C23×C43C2×D811yescharacteristic
188C22×D43—41no—
189Q8×C43—22no—
190Q8×C43—41no—
191Q8×C43—41no—
192Q8×C43—41no—
193Q8×C43—82no—
194D4×C43—22no—
195D4×C43—41no—
196D4×C43—41no—
197D4×C43—82no—
198D4×C43—82no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—82no—
207C2×C4×C43—82no—
208C2×C4×C43C2×D811yescharacteristic
209C2×C4×C43C2×D811yescharacteristic
210C2×C4×C43C2×D811yescharacteristic
211C2×C4×C43C2×D811yescharacteristic
212C2×C4×C43C22×D411yescharacteristic
213C22⋊D43—82no—
214C22⋊D43—161no—
215C2×Dic43—41no—
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43—161no—
219D172—41no—
220D172—41no—
221C4×D43—161no—
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—42no—
246C4×C43—81no—
247C4×C43—81no—
248C4×C43#54611yescharacteristic
249C4×C43#57711yescharacteristic
250Dic43—81no—
251Dic43—81no—
252Dic43—81no—
253#3339—431no—
254#3285D4311yescharacteristic, complemented
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×#135C2×D4311yescharacteristic
276C22×Q16C2×D4311yescharacteristic
277#553—861no—
278#548—21no—
279C2×SD32—431no—
280C2×SD32—431no—
281C2×D16—431no—
282C22×C16—431no—
283C22×C16—431no—
284#499—431no—
285#495C2×D4311yescharacteristic
286#482—861no—
287#481—861no—
288#478—861no—
289#467C2×D4311yescharacteristic
290#466—431no—
291#466—431no—
292#466C2×D4311yescharacteristic
293#464—21no—
294#452—21no—
295#448—21no—
296C4×Q16C2×D4311yescharacteristic
297C4×D8—431no—
298C8×D4C2×D4311yescharacteristic
299#427—431no—
300C2×#107—431no—
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—21no—
320C22×Q8—21no—
321#135—22no—
322#135—41no—
323C2×Q16—22no—
324C2×Q16—21no—
325C2×Q16—41no—
326C2×Q16C22×D4311yescharacteristic
327C2×Q16C22×D4311yescharacteristic
328C2×SD16—21no—
329C2×SD16—21no—
330C2×D8—431no—
331C2×D8C22×D4311yescharacteristic
332C22×C8C22×D4311yescharacteristic
333C22×C8C22×D4311yescharacteristic
334#126—1721no—
335#125—861no—
336#124—21no—
337#124—41no—
338#123—1721no—
339C22⋊Q8—21no—
340C22⋊Q8—41no—
341#121—21no—
342#121—41no—
343#121—861no—
344#121—861no—
345#121—1721no—
346C4×Q8—21no—
347C4×D4—41no—
348C4×D4—861no—
349C4×D4—1721no—
350C4×D4C22⋊D4311yescharacteristic
351#117—861no—
352C2×C4⋊C4—861no—
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—431no—
363#107—431no—
364#107—431no—
365#107—861no—
366#107C22×D4311yescharacteristic
367#106—861no—
368#106—861no—
369C4⋊C8C22⋊D4311yescharacteristic
370#103—21no—
371#103—21no—
372#102—21no—
373#102—861no—
374#102—861no—
375#102—861no—
376C22⋊C8C22⋊D4311yescharacteristic
377C22⋊C8C22⋊D4311yescharacteristic
378C4×C8C22×D4311yescharacteristic
379#41—42no—
380#41—81no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×Q8—42no—
384C2×Q8—41no—
385C2×Q8—81no—
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—21no—
400Q16—21no—
401Q16—21no—
402Q16—42no—
403Q16#1062190012yes—
404SD16—42no—
405SD16—81no—
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—41no—
420C4⋊C4—41no—
421C4⋊C4—861no—
422C4⋊C4—861no—
423C4⋊C4—861no—
424C4⋊C4—1721no—
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—22no—
450Q8—41no—
451Q8—41no—
452Q8—41no—
453Q8—82no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—82no—
458D4—82no—
459D4—3442no—
460D4—1721no—
461D4—1721no—
462D4—6881no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1721no—
475C2×C4—6881no—
476C2×C4—6881no—
477C2×C4C2×#1062188211yescharacteristic
478C2×C4C2×#1062188211yescharacteristic
479C2×C4C2×#1062188211yescharacteristic
480C2×C4C2×#1062188211yescharacteristic
481C2×C4C22×C22⋊D4311yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8C2×#1062190011yescharacteristic
486C8#1306337011yescharacteristic
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—42no—
505C4—81no—
506C4—81no—
507C4—3441no—
508C4—3441no—
509C4—3441no—
510C4#1458354311yescharacteristic
511C4#1458371011yescharacteristic
512C2—22no—
513C2—41no—
514C2—161no—
515C2—6881no—
516C2#1914640811yescharacteristic
517C2C2×#1458332911yescharacteristic
518C2#1914773911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3285C2
socleC22×C43C22×D8
hypercenter#3285D43
hypocenterC43#33868
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. #19146998C2semidirect
2. #19136826C2semidirect
3. #19136800C2semidirect
4. #19136778C2semidirect
5. #19136759C2semidirect
6. #19136693C2semidirect
7. #19136679C2semidirect
8. #19136647C2semidirect
9. #19136518C2semidirect
10. #19136512C2semidirect
11. C4×#13063268C2semidirect
12. D4×C43⋊C16C2semidirect
13. #19136302C2semidirect
14. C2×#14582703C2semidirect
15. C43×#3285C2semidirect
254. #3285D43semidirect
318. C43#33868semidirect

Maximal subgroups

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

subgroupindex
#191469982
#191368262
#191368002
#191367782
#191367592
#191366932
#191366792
#191366472
#191365182
#191365122
C4×#130632682
D4×C43⋊C162
#191363022
C2×#145827032
C43×#32852
#3386843