Finite Group Databasebeta

← #25251783

Subgroups — #25251783

Order 11008.

546 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145234C211yesmaximal, characteristic, complemented
2#19136797C211yesmaximal, characteristic, complemented
3#19136775C211yesmaximal, characteristic, complemented
4#19136747C211yesmaximal, characteristic, complemented
5#19136732C211yesmaximal, characteristic, complemented
6#19136657C211yesmaximal, characteristic, complemented
7#19136650C211yesmaximal, characteristic, complemented
8#19136535C211yesmaximal, characteristic, complemented
9#19136518C211yesmaximal, characteristic
10#19136459C211yesmaximal, characteristic, complemented
11#19136457C211yesmaximal, characteristic, complemented
12C4×#13063271C211yesmaximal, characteristic, complemented
13C4×#13063266C211yesmaximal, characteristic, complemented
14#19136402C211yesmaximal, characteristic, complemented
15C43×#2951C211yesmaximal, characteristic, complemented
16#14583520—21no—
17C2×#13063271C2211yescharacteristic
18C2×#13063269C2211yescharacteristic
19C2×#13063268C2211yescharacteristic
20C2×#13063266C2211yescharacteristic
21#14583304C2211yescharacteristic
22#14583283C2211yescharacteristic
23#14583259—21no—
24#14583145—21no—
25#14583140C2211yescharacteristic
26#14583135C2211yescharacteristic
27#14583001—21no—
28C4×Dic172C2211yescharacteristic
29C4×D344C2211yescharacteristic
30#14582724C2211yescharacteristic
31#14582724C2211yescharacteristic
32#14582724C2211yescharacteristic
33#14582724C2211yescharacteristic
34C4⋊(C43⋊C16)C2211yescharacteristic
35C4⋊(C43⋊C16)C2211yescharacteristic
36#14582703C2211yescharacteristic
37#14582703C2211yescharacteristic
38#14582702C2211yescharacteristic
39#14582702C2211yescharacteristic
40#14582700C2211yescharacteristic
41#14582700C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44C22⋊(C43⋊C16)C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46#14582675C2211yescharacteristic
47C4×C43⋊C16C2211yescharacteristic
48C2×#135×C43C2211yescharacteristic
49C43×#520—21no—
50C43×#440—21no—
51C43×#440—21no—
52C4×Q16×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C4×D8×C43C2211yescharacteristic
55C4×D8×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C43×#417—21no—
58C43×#405C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621873—21no—
61C2×D344C2311yescharacteristic
62#13063325—21no—
63#13063320—41no—
64#13063313—21no—
65#13063311—41no—
66#13063307—41no—
67#13063304—21no—
68#13063303—41no—
69#13063299—21no—
70C4×Dic86—21no—
71C4×D172—21no—
72#13063271—22no—
73#13063269—22no—
74#13063268—22no—
75#13063266—22no—
76C2×C43⋊C16C2311yescharacteristic
77C2×C43⋊C16C2311yescharacteristic
78C2×C43⋊C16C2311yescharacteristic
79C2×C43⋊C16C2311yescharacteristic
80#13063259—21no—
81#13063259C2311yescharacteristic
82#13063259C2311yescharacteristic
83#13063250—21no—
84#13063250—21no—
85#13063247—21no—
86#13063247—21no—
87C2×#41×C43—21no—
88#135×C43—22no—
89#135×C43—22no—
90C2×Q16×C43C2311yescharacteristic
91C2×SD16×C43—21no—
92C2×D8×C43C2311yescharacteristic
93C2×M16×C43D411yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—41no—
100C4×D4×C43—41no—
101#117×C43—41no—
102#117×C43D411yescharacteristic
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—41no—
105#107×C43—21no—
106#107×C43C2311yescharacteristic
107#107×C43C2311yescharacteristic
108#103×C43—21no—
109#103×C43—21no—
110#102×C43—21no—
111#102×C43—21no—
112#97×C43D411yescharacteristic
113#97×C43D411yescharacteristic
114C4×C8×C43C2311yescharacteristic
115C4×C8×C43C2311yescharacteristic
116#41×C43—24no—
117#41×C43—42no—
118C2×Q8×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43C2×D411yescharacteristic
126C2×C22⋊D43—41no—
127C2×D172—21no—
128C2×C4×D43—41no—
129C2×Dic86—21no—
130C2×Dic86—41no—
131Q16×C43—21no—
132Q16×C43#4112yes—
133SD16×C43—24no—
134D8×C43—21no—
135D8×C43#4112yes—
136M16×C43—41no—
137C2×C8×C43—21no—
138C2×C8×C43—21no—
139C2×C8×C43C2×D411yescharacteristic
140C2×C8×C43C2×D411yescharacteristic
141C2×C8×C43C2×D411yescharacteristic
142C2×C8×C43C2411yescharacteristic
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43—41no—
147C4⋊C4×C43—41no—
148C4⋊C4×C43D811yescharacteristic
149C4⋊C4×C43D811yescharacteristic
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43D811yescharacteristic
153C22⋊C4×C43D811yescharacteristic
154C42×C43—41no—
155C42×C43—41no—
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C22⋊Dic43—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4—41no—
168C4×Dic43—41no—
169Dic172—21no—
170Dic172—21no—
171D344—21no—
172D344—21no—
173#10621873—42no—
174C43⋊C16—21no—
175C43⋊C16—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C23×C43C2×D811yescharacteristic
180C22×D43—41no—
181Q8×C43—22no—
182Q8×C43—41no—
183D4×C43—22no—
184D4×C43—44no—
185D4×C43—41no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—44no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—161no—
193C2×C4×C43—161no—
194C2×C4×C43—161no—
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C2×D811yescharacteristic
198C2×C4×C43C2×D811yescharacteristic
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C22×D411yescharacteristic
201C22⋊D43—161no—
202C2×Dic43—41no—
203C2×Dic43—41no—
204C2×Dic43—41no—
205D172—41no—
206D172—41no—
207C4×D43—161no—
208Dic86—41no—
209Dic86—41no—
210Dic86—161no—
211C8×C43—21no—
212C8×C43—21no—
213C8×C43—21no—
214C8×C43C2×#4111yescharacteristic
215C8×C43C2×#4111yescharacteristic
216#33684—431nomaximal, Sylow
217C22×C43—21no—
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—42no—
221C22×C43—81no—
222C22×C43—81no—
223C22×C43C22×D811yescharacteristic
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—42no—
233C4×C43—81no—
234C4×C43—81no—
235C4×C43#52511yescharacteristic
236C4×C43#57511yescharacteristic
237Dic43—81no—
238Dic43—81no—
239Dic43—81no—
240#3175—431no—
241#2951D4311yescharacteristic, complemented
242#2236—431no—
243#2232—431no—
244#2227—431no—
245#2224—431no—
246#2211—431no—
247#2210—431no—
248#2189—431no—
249#2186—431no—
250#2175—431no—
251#2175—431no—
252C4×Q32—431no—
253C4×D16—431no—
254#2164—431no—
255C2×C43—41no—
256C2×C43—82no—
257C2×C43#310011yescharacteristic
258C2×C43#341511yescharacteristic
259C2×C43#341711yescharacteristic
260D43—161no—
261C2×#135C2×D4311yescharacteristic
262#542—861no—
263#520—21no—
264C2×Q32—431no—
265C2×SD32—431no—
266C2×SD32—431no—
267C2×D16—431no—
268#500—431no—
269#495—431no—
270#489—861no—
271#468—861no—
272#467—431no—
273#466—431no—
274#440—21no—
275#440—21no—
276#440—861no—
277C4×Q16—431no—
278C4×Q16C2×D4311yescharacteristic
279C4×Q16C2×D4311yescharacteristic
280C4×D8—431no—
281C4×D8C2×D4311yescharacteristic
282C4×D8C2×D4311yescharacteristic
283C2×#107C2×D4311yescharacteristic
284#417—21no—
285#405C2×D4311yescharacteristic
286#366—431no—
287#366—431no—
288#366—431no—
289#366—431no—
290C4⋊C16—431no—
291C4⋊C16—431no—
292#358—431no—
293#358—431no—
294#358—431no—
295#358—431no—
296#357—431no—
297#357—431no—
298#357—431no—
299#357—431no—
300C22⋊C16—431no—
301C22⋊C16—431no—
302#346—431no—
303C4×C16—431no—
304C43#3368411yescharacteristic, complemented, Sylow
305C2×#41—21no—
306#135—22no—
307#135—22no—
308C2×Q16—431no—
309C2×Q16C22×D4311yescharacteristic
310C2×SD16—21no—
311C2×SD16—861no—
312C2×D8—431no—
313C2×D8C22×D4311yescharacteristic
314C2×M16C22⋊D4311yescharacteristic
315C22×C8C22×D4311yescharacteristic
316C4⋊Q8—861no—
317#126—1721no—
318#124—861no—
319#124—1721no—
320#123—1721no—
321C22⋊Q8—861no—
322C22⋊Q8—1721no—
323#121—861no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—861no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—41no—
330C4×D4—41no—
331C4×D4—861no—
332#117—41no—
333#117C22⋊D4311yescharacteristic
334C2×C4⋊C4—21no—
335C2×C4⋊C4—41no—
336Q32—862no—
337SD32—862no—
338SD32—862no—
339D16—862no—
340C2×C16—431no—
341C2×C16—431no—
342C2×C16—431no—
343C2×C16—431no—
344#107—21no—
345#107—431no—
346#107—431no—
347#107—861no—
348#107C22×D4311yescharacteristic
349#107C22×D4311yescharacteristic
350#103—21no—
351#103—21no—
352#103—861no—
353#103—861no—
354#102—21no—
355#102—21no—
356#102—861no—
357#102—861no—
358#97C22⋊D4311yescharacteristic
359#97C22⋊D4311yescharacteristic
360C4×C8C22×D4311yescharacteristic
361C4×C8C22×D4311yescharacteristic
362#41—24no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—861no—
366C2×Q8—1721no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—861no—
370C2×D4—1721no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—1721no—
376C22×C4C2×C22⋊D4311yescharacteristic
377Q16—21no—
378Q16—861no—
379Q16—861no—
380Q16#1062189812yes—
381SD16—24no—
382SD16—1722no—
383D8—21no—
384D8—861no—
385D8—861no—
386D8#1062189812yes—
387M16—41no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8C2×C22⋊D4311yescharacteristic
391C2×C8C2×C22⋊D4311yescharacteristic
392C2×C8C2×C22⋊D4311yescharacteristic
393C2×C8C23×D4311yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4—861no—
400C4⋊C4—861no—
401C4⋊C4—1721no—
402C4⋊C4—1721no—
403C4⋊C4—1721no—
404C4⋊C4#1062188211yescharacteristic
405C4⋊C4#1062188211yescharacteristic
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—1721no—
409C22⋊C4—1721no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C22⋊C4—1721no—
413C22⋊C4#1062188211yescharacteristic
414C22⋊C4#1062188211yescharacteristic
415C42—41no—
416C42—41no—
417C42—1721no—
418C42C2×C22⋊D4311yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C16—861no—
421C16—861no—
422C16—861no—
423C16—861no—
424C23—41no—
425C23—1721no—
426C23C2×#1062188211yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—1721no—
430Q8—1721no—
431Q8—6881no—
432D4—22no—
433D4—44no—
434D4—41no—
435D4—1721no—
436D4—1721no—
437D4—6881no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—44no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—161no—
445C2×C4—161no—
446C2×C4—161no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—6881no—
451C2×C4C2×#1062188211yescharacteristic
452C2×C4C2×#1062188211yescharacteristic
453C2×C4C2×#1062188211yescharacteristic
454C2×C4C2×#1062188211yescharacteristic
455C2×C4C2×#1062188211yescharacteristic
456C2×C4C22×C22⋊D4311yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×#1062189811yescharacteristic
461C8C2×#1062189811yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—3441no—
469C22—3441no—
470C22—3441no—
471C22C22×#1062188211yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—3441no—
481C4—3441no—
482C4—3441no—
483C4#1458341011yescharacteristic
484C4#1458369711yescharacteristic
485C2—41no—
486C2—82no—
487C2—6881no—
488C2#1914459511yescharacteristic
489C2#1914773411yescharacteristic
490C2#1914774611yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2951C2
socleC22×C43C22×D8
prime radical#19136518C2
hypercenter#2951D43
hypocenterC43#33684
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #19145234C2semidirect
2. #19136797C2semidirect
3. #19136775C2semidirect
4. #19136747C2semidirect
5. #19136732C2semidirect
6. #19136657C2semidirect
7. #19136650C2semidirect
8. #19136535C2semidirect
10. #19136459C2semidirect
11. #19136457C2semidirect
12. C4×#13063271C2semidirect
13. C4×#13063266C2semidirect
14. #19136402C2semidirect
15. C43×#2951C2semidirect
241. #2951D43semidirect
304. C43#33684semidirect

Maximal subgroups

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

subgroupindex
#191452342
#191367972
#191367752
#191367472
#191367322
#191366572
#191366502
#191365352
#191365182
#191364592
#191364572
C4×#130632712
C4×#130632662
#191364022
C43×#29512
#3368443