Finite Group Databasebeta

← #25251784

Subgroups — #25251784

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#19145235C211yesmaximal, characteristic, complemented
2#19143471C211yesmaximal, characteristic, complemented
3#19136795C211yesmaximal, characteristic, complemented
4#19136776C211yesmaximal, characteristic, complemented
5#19136745C211yesmaximal, characteristic, complemented
6#19136730C211yesmaximal, characteristic, complemented
7#19136659C211yesmaximal, characteristic, complemented
8#19136652C211yesmaximal, characteristic, complemented
9#19136518C211yesmaximal, characteristic
10#19136462C211yesmaximal, characteristic, complemented
11#19136460C211yesmaximal, characteristic, complemented
12Q32×Dic43C211yesmaximal, characteristic, complemented
13#19136439C211yesmaximal, characteristic, complemented
14#19136399C211yesmaximal, characteristic, complemented
15C43×#2189C211yesmaximal, characteristic, complemented
16#14583522—21no—
17#14583382—21no—
18C2×#13063268C2211yescharacteristic
19C2×#13063266C2211yescharacteristic
20#14583303C2211yescharacteristic
21#14583284C2211yescharacteristic
22#14583260—21no—
23#14583147—21no—
24#14583135C2211yescharacteristic
25#14583002—21no—
26#14583000—21no—
27#14583000—21no—
28Q16×Dic43C2211yescharacteristic
29Q16×Dic43C2211yescharacteristic
30Q16×Dic43C2211yescharacteristic
31D8×Dic43C2211yescharacteristic
32D8×Dic43C2211yescharacteristic
33#14582981C2211yescharacteristic
34C2×#13063259C2211yescharacteristic
35#14582900—21no—
36#14582854C2211yescharacteristic
37#14582725C2211yescharacteristic
38#14582725C2211yescharacteristic
39#14582724C2211yescharacteristic
40#14582724C2211yescharacteristic
41Dic43⋊C16C2211yescharacteristic
42Dic43⋊C16C2211yescharacteristic
43#14582703C2211yescharacteristic
44#14582703C2211yescharacteristic
45#14582703C2211yescharacteristic
46#14582701C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582700C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50#14582674C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×#135×C43C2211yescharacteristic
53C2×Q32×C43C2211yescharacteristic
54C2×SD32×C43C2211yescharacteristic
55C43×#467C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×#10621884—21no—
60C2×D344C2311yescharacteristic
61C2×#10621877D411yescharacteristic
62#13063324—21no—
63#13063320—41no—
64#13063314—21no—
65#13063311—41no—
66#13063307—41no—
67#13063305—41no—
68#13063299—21no—
69Q8×Dic43—21no—
70Q8×Dic43—21no—
71Q8×Dic43—21no—
72D4×Dic43—21no—
73D4×Dic43—21no—
74D4×Dic43—41no—
75D4×Dic43—41no—
76#13063287—21no—
77#13063284—41no—
78#13063284D411yescharacteristic
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—41no—
81#13063268—22no—
82#13063266—22no—
83C2×C43⋊C16C2311yescharacteristic
84C2×C43⋊C16C2311yescharacteristic
85#13063259—21no—
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063258—21no—
90#13063249—21no—
91#13063249—21no—
92#13063249—21no—
93#13063247—21no—
94#13063246—21no—
95#13063246—21no—
96#13063245—21no—
97#13063235D411yescharacteristic
98#13063235D411yescharacteristic
99C8×Dic43C2311yescharacteristic
100C8×Dic43C2311yescharacteristic
101C2×#41×C43—21no—
102#135×C43—22no—
103#135×C43—22no—
104C2×Q16×C43C2311yescharacteristic
105C2×Q16×C43C2311yescharacteristic
106C2×SD16×C43—21no—
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22⋊Q8×C43—21no—
110Q32×C43—22no—
111SD32×C43—22no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#103×C43—21no—
116#41×C43—24no—
117#41×C43—42no—
118C2×Q8×C43—21no—
119C2×Q8×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C2×C22⋊D43—41no—
125C22×Dic43—41no—
126C22×Dic43—41no—
127C22×Dic43—41no—
128C2×D172—21no—
129C2×C4×D43—41no—
130C2×Dic86—41no—
131Q16×C43—21no—
132Q16×C43—21no—
133Q16×C43—21no—
134Q16×C43#4112yes—
135SD16×C43—24no—
136D8×C43—21no—
137D8×C43#4112yes—
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43C2×D411yescharacteristic
141C2×C8×C43C2411yescharacteristic
142C4⋊C4×C43—21no—
143C4⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C22⋊Dic43—41no—
146C22⋊Dic43—41no—
147C22⋊Dic43D811yescharacteristic
148C22⋊Dic43D811yescharacteristic
149#10621884—42no—
150(C2×D43)⋊C4—41no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154C4⋊Dic43—21no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—41no—
158C4⋊Dic43—41no—
159C4⋊Dic43—41no—
160C4⋊Dic43—41no—
161C4⋊Dic43D811yescharacteristic
162C4⋊Dic43D811yescharacteristic
163Dic43⋊C4—41no—
164C4×Dic43—41no—
165C4×Dic43—41no—
166C4×Dic43—41no—
167C4×Dic43C2×D411yescharacteristic
168C4×Dic43C2×D411yescharacteristic
169#10621877—41no—
170C2×C43⋊C8C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172D344—21no—
173D344—21no—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C23×C43C2×D811yescharacteristic
180C22×D43—41no—
181Q8×C43—22no—
182Q8×C43—41no—
183Q8×C43—41no—
184Q8×C43—41no—
185D4×C43—22no—
186D4×C43—44no—
187D4×C43—41no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—44no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C22⋊D43—161no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—161no—
201C2×Dic43—161no—
202C2×Dic43—161no—
203C2×Dic43C2×D811yescharacteristic
204C2×Dic43C2×D811yescharacteristic
205C2×Dic43C2×D811yescharacteristic
206C2×Dic43C2×D811yescharacteristic
207D172—41no—
208D172—41no—
209C4×D43—161no—
210Dic86—161no—
211C8×C43—21no—
212C8×C43C2×#4111yescharacteristic
213C8×C43C2×#4111yescharacteristic
214C43⋊C8—21no—
215C43⋊C8—21no—
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—42no—
229C4×C43—81no—
230C4×C43—81no—
231C4×C43#52511yescharacteristic
232C4×C43#57511yescharacteristic
233Dic43—21no—
234Dic43—21no—
235Dic43—21no—
236Dic43—21no—
237Dic43—81no—
238Dic43—81no—
239Dic43—81no—
240#3175—431no—
241#2951—431no—
242#2236—431no—
243#2232—431no—
244#2227—431no—
245#2224—431no—
246#2211—431no—
247#2210—431no—
248#2189D4311yescharacteristic, complemented
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—861no—
264C2×Q32C2×D4311yescharacteristic
265C2×SD32—431no—
266C2×SD32C2×D4311yescharacteristic
267C2×D16—431no—
268#500—431no—
269#495—431no—
270#489—861no—
271#468—861no—
272#467C2×D4311yescharacteristic
273#466—431no—
274#440—861no—
275#440—861no—
276#440—861no—
277C4×Q16—431no—
278C4×Q16—431no—
279C4×Q16—431no—
280C4×D8—431no—
281C4×D8—431no—
282C4×D8—431no—
283C2×#107—431no—
284#417—861no—
285#405—431no—
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#358C2×D4311yescharacteristic
296#357—431no—
297#357—431no—
298#357—431no—
299#357C2×D4311yescharacteristic
300C22⋊C16—431no—
301C22⋊C16C2×D4311yescharacteristic
302#346—431no—
303C4×C16—431no—
304C43#3368411yescharacteristic, complemented, Sylow
305C2×#41—21no—
306#135—22no—
307#135—22no—
308C2×Q16C22×D4311yescharacteristic
309C2×Q16C22×D4311yescharacteristic
310C2×SD16—21no—
311C2×SD16—861no—
312C2×D8—431no—
313C2×D8C22×D4311yescharacteristic
314C2×M16—431no—
315C22×C8C22×D4311yescharacteristic
316C4⋊Q8—861no—
317#126—1721no—
318#124—861no—
319#124—1721no—
320#123—1721no—
321C22⋊Q8—21no—
322C22⋊Q8—1721no—
323#121—861no—
324C4×Q8—861no—
325C4×Q8—861no—
326C4×Q8—861no—
327C4×D4—861no—
328C4×D4—861no—
329C4×D4—861no—
330C4×D4—1721no—
331C4×D4—1721no—
332#117—431no—
333#117—1721no—
334C2×C4⋊C4—861no—
335C2×C4⋊C4—1721no—
336Q32—22no—
337SD32—22no—
338SD32—862no—
339D16—862no—
340C2×C16—431no—
341C2×C16—431no—
342C2×C16C22×D4311yescharacteristic
343C2×C16C22×D4311yescharacteristic
344#107—431no—
345#107—431no—
346#107—431no—
347#107—861no—
348#107—861no—
349#107C22×D4311yescharacteristic
350#103—21no—
351#103—861no—
352#103—861no—
353#103—861no—
354#102—861no—
355#102—861no—
356#102—861no—
357#102—861no—
358#97—431no—
359#97—431no—
360C4×C8—431no—
361C4×C8—431no—
362#41—24no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—1721no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—861no—
370C2×D4—1721no—
371C22×C4—41no—
372C22×C4—1721no—
373C22×C4—1721no—
374C22×C4—1721no—
375C22×C4—1721no—
376C22×C4D4×D4311yescharacteristic
377Q16—21no—
378Q16—21no—
379Q16—21no—
380Q16#1062190012yes—
381SD16—24no—
382SD16—1722no—
383D8—21no—
384D8—861no—
385D8—861no—
386D8#1062190012yes—
387M16—1721no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—431no—
391C2×C8—431no—
392C2×C8D4×D4311yescharacteristic
393C2×C8C23×D4311yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—431no—
397C4⋊C4—431no—
398C4⋊C4—861no—
399C4⋊C4—861no—
400C4⋊C4—861no—
401C4⋊C4—1721no—
402C4⋊C4—1721no—
403C4⋊C4—1721no—
404C4⋊C4—1721no—
405C4⋊C4—1721no—
406C22⋊C4—41no—
407C22⋊C4—431no—
408C22⋊C4—431no—
409C22⋊C4—1721no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C22⋊C4—1721no—
415C42—431no—
416C42—431no—
417C42—1721no—
418C42—1721no—
419C42—1721no—
420C16—21no—
421C16—21no—
422C16—861no—
423C16—861no—
424C23—41no—
425C23—1721no—
426C23D8×D4311yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
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—431no—
445C2×C4—431no—
446C2×C4—431no—
447C2×C4—431no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4—6881no—
452C2×C4—6881no—
453C2×C4—6881no—
454C2×C4—6881no—
455C2×C4D8×D4311yescharacteristic
456C2×C4C2×D4×D4311yescharacteristic
457C8—21no—
458C8—861no—
459C8—861no—
460C8C2×#1062190011yescharacteristic
461C8C2×#1062190011yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—3441no—
469C22—3441no—
470C22—3441no—
471C22C2×D8×D4311yescharacteristic
472C4—21no—
473C4—42no—
474C4—81no—
475C4—81no—
476C4—861no—
477C4—861no—
478C4—861no—
479C4—861no—
480C4—3441no—
481C4—3441no—
482C4—3441no—
483C4#1458340511yescharacteristic
484C4#1458369511yescharacteristic
485C2—41no—
486C2—82no—
487C2—6881no—
488C2#1914459011yescharacteristic
489C2#1914773311yescharacteristic
490C2#1914774711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2189C2
socleC22×C43C22×D8
prime radical#19136518C2
hypercenter#2189D43
hypocenterC43#33684
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2189

Complements

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

NH ≅ G/Ntype
1. #19145235C2semidirect
2. #19143471C2semidirect
3. #19136795C2semidirect
4. #19136776C2semidirect
5. #19136745C2semidirect
6. #19136730C2semidirect
7. #19136659C2semidirect
8. #19136652C2semidirect
10. #19136462C2semidirect
11. #19136460C2semidirect
12. Q32×Dic43C2semidirect
13. #19136439C2semidirect
14. #19136399C2semidirect
15. C43×#2189C2semidirect
248. #2189D43semidirect
304. C43#33684semidirect

Maximal subgroups

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

subgroupindex
#191452352
#191434712
#191367952
#191367762
#191367452
#191367302
#191366592
#191366522
#191365182
#191364622
#191364602
Q32×Dic432
#191364392
#191363992
C43×#21892
#3368443