Finite Group Databasebeta

← #25252154

Subgroups — #25252154

Order 11008.

558 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145176C211yesmaximal, characteristic, complemented
2#19145169C211yesmaximal, characteristic
3#19136876C211yesmaximal, characteristic, complemented
4#19136849C211yesmaximal, characteristic, complemented
5#19136821C211yesmaximal, characteristic, complemented
6#19136817C211yesmaximal, characteristic, complemented
7#19136693C211yesmaximal, characteristic, complemented
8#19136691C211yesmaximal, characteristic, complemented
9#19136689C211yesmaximal, characteristic, complemented
10#19136450C211yesmaximal, characteristic, complemented
11SD32×Dic43C211yesmaximal, characteristic, complemented
12#19136446C211yesmaximal, characteristic, complemented
13#19136444C211yesmaximal, characteristic, complemented
14C2×C16×Dic43C211yesmaximal, characteristic, complemented
15C43×#2217C211yesmaximal, characteristic, complemented
16#14583451—21no—
17#14583444—21no—
18C2×#13063270C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20C2×#13063268C2211yescharacteristic
21C22×C43⋊C16C2211yescharacteristic
22#14583303C2211yescharacteristic
23#14583303C2211yescharacteristic
24#14583277C2211yescharacteristic
25#14583274C2211yescharacteristic
26#14583248—21no—
27#14583244—21no—
28#14583140C2211yescharacteristic
29#14583138—21no—
30#14583135C2211yescharacteristic
31#14583133—21no—
32Q16×Dic43C2211yescharacteristic
33#14582993C2211yescharacteristic
34#14582991—21no—
35D8×Dic43C2211yescharacteristic
36#14582981C2211yescharacteristic
37#14582979—21no—
38C2×C8×Dic43C2211yescharacteristic
39#14582727C2211yescharacteristic
40#14582726C2211yescharacteristic
41#14582726C2211yescharacteristic
42#14582704C2211yescharacteristic
43#14582703C2211yescharacteristic
44#14582702C2211yescharacteristic
45#14582701C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582699C2211yescharacteristic
48C16×Dic43C2211yescharacteristic
49C16×Dic43C2211yescharacteristic
50C16×Dic43C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C22×C16×C43C2211yescharacteristic
54C43×#467C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#367C2211yescharacteristic
57C43×#358C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×#10621900—41no—
60C2×Dic172C2311yescharacteristic
61C2×#10621885—21no—
62C2×D344C2311yescharacteristic
63C2×#10621882—21no—
64C22×C43⋊C8D411yescharacteristic
65#13063324—21no—
66#13063324—21no—
67#13063323—21no—
68#13063321—21no—
69#13063315—41no—
70#13063311—41no—
71#13063304—21no—
72#13063302—41no—
73#13063299—21no—
74#13063297—41no—
75Q8×Dic43—21no—
76#13063290—21no—
77#13063290—41no—
78D4×Dic43—21no—
79#13063287—21no—
80(C22⋊D43)⋊C4—41no—
81#13063281—41no—
82C2×C4×Dic43D411yescharacteristic
83#13063270—22no—
84#13063269—22no—
85#13063268—22no—
86C2×C43⋊C16—22no—
87C2×C43⋊C16C2311yescharacteristic
88C2×C43⋊C16C2311yescharacteristic
89#13063259C2311yescharacteristic
90#13063259C2311yescharacteristic
91#13063258—21no—
92#13063258—21no—
93#13063250—21no—
94#13063249—21no—
95#13063248—21no—
96#13063247—21no—
97#13063246—21no—
98#13063245—21no—
99C8×Dic43D411yescharacteristic
100C8×Dic43D411yescharacteristic
101C8×Dic43C2311yescharacteristic
102C8×Dic43C2311yescharacteristic
103C2×Q16×C43C2311yescharacteristic
104C2×D8×C43C2311yescharacteristic
105C22×C8×C43C2311yescharacteristic
106C22⋊Q8×C43—21no—
107#121×C43—21no—
108SD32×C43—22no—
109C2×C16×C43—22no—
110C2×C16×C43C2311yescharacteristic
111C2×C16×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#107×C43C2311yescharacteristic
114#103×C43—21no—
115#102×C43—21no—
116C2×Q8×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—41no—
119C22×C4×C43C2×D411yescharacteristic
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C22×Dic43—41no—
124C22×Dic43D811yescharacteristic
125C22×Dic43D811yescharacteristic
126#10621900—84no—
127C2×D172—21no—
128C2×C4×D43—41no—
129C2×Dic86—21no—
130C2×Dic86—41no—
131C2×Dic86—41no—
132Q16×C43—21no—
133Q16×C43—21no—
134D8×C43—21no—
135D8×C43—21no—
136C2×C8×C43—21no—
137C2×C8×C43—21no—
138C2×C8×C43C2×D411yescharacteristic
139C2×C8×C43C2411yescharacteristic
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—41no—
143C22⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C22⋊Dic43—41no—
146C22⋊Dic43—41no—
147#10621885—42no—
148#10621882—42no—
149(C2×D43)⋊C4—41no—
150(C2×D43)⋊C4—41no—
151C4⋊Dic43—21no—
152C4⋊Dic43—21no—
153C4⋊Dic43—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156Dic43⋊C4—41no—
157Dic43⋊C4—41no—
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160C4×Dic43—41no—
161C4×Dic43—41no—
162C4×Dic43D811yescharacteristic
163C4×Dic43D811yescharacteristic
164C4×Dic43C2×D411yescharacteristic
165C4×Dic43C2×D411yescharacteristic
166C2×C43⋊C8—22no—
167C2×C43⋊C8C2×D411yescharacteristic
168C2×C43⋊C8C2×D411yescharacteristic
169Dic172—21no—
170Dic172—21no—
171D344—21no—
172D344—21no—
173C16×C43—21no—
174C16×C43#4112yescomplemented
175C43⋊C16—21no—
176C43⋊C16#4112yescomplemented
177C23×C43—41no—
178C23×C43C2×D811yescharacteristic
179C22×D43—41no—
180Q8×C43—41no—
181Q8×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—82no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43C2×D811yescharacteristic
191C2×C4×C43C22×D411yescharacteristic
192C22⋊D43—82no—
193C22⋊D43—82no—
194C22⋊D43—82no—
195C2×Dic43—22no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—82no—
200C2×Dic43SD3214yescomplemented
201C2×Dic43C2×D811yescharacteristic
202C2×Dic43C2×D811yescharacteristic
203C2×Dic43C2×D811yescharacteristic
204C2×Dic43C2×D811yescharacteristic
205D172—41no—
206D172—41no—
207C4×D43—82no—
208Dic86—41no—
209Dic86—41no—
210Dic86—82no—
211Dic86—82no—
212C8×C43—21no—
213C8×C43C2×#4111yescharacteristic
214C8×C43C2×#4111yescharacteristic
215C43⋊C8—21no—
216C43⋊C8#13512yes—
217#33736—431nomaximal, Sylow
218C22×C43—21no—
219C22×C43—21no—
220C22×C43—81no—
221C22×C43—81no—
222C22×C43—81no—
223C22×C43C2×SD3212yes—
224C22×C43C22×D811yescharacteristic
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—81no—
228C4×C43—21no—
229C4×C43—81no—
230C4×C43—81no—
231C4×C43—81no—
232C4×C43#53211yescharacteristic
233C4×C43C2×#13511yescharacteristic
234Dic43—21no—
235Dic43—81no—
236Dic43—81no—
237Dic43—81no—
238Dic43C2×SD3212yes—
239Dic43C2×SD3212yes—
240Dic43#50812yes—
241#3170—431no—
242#3169—431no—
243#2254—431no—
244#2248—431no—
245#2241—431no—
246#2240—431no—
247#2217—431no—
248#2217—431no—
249#2217—431no—
250#2217D4311yescharacteristic, complemented
251C4×SD32—431no—
252C4×SD32—431no—
253C4×SD32—431no—
254C4×SD32—431no—
255C2×C4×C16—431no—
256C2×C43—22no—
257C2×C43—161no—
258C2×C43#316911yescharacteristic
259C2×C43C22×SD3211yescharacteristic
260C2×C43C2×#50811yescharacteristic
261D43—161no—
262#533—861no—
263#532—861no—
264C2×SD32—431no—
265C2×SD32—431no—
266C2×SD32—431no—
267C2×SD32C2×D4311yescharacteristic
268C22×C16—431no—
269C22×C16C2×D4311yescharacteristic
270#500—431no—
271#500—431no—
272#494—431no—
273#493—431no—
274#487—861no—
275#486—861no—
276#467—431no—
277#467—861no—
278#467C2×D4311yescharacteristic
279#466—431no—
280#466—861no—
281#466C2×D4311yescharacteristic
282C4×Q16—431no—
283C4×Q16—431no—
284C4×Q16—861no—
285C4×D8—431no—
286C4×D8—431no—
287C4×D8—861no—
288C2×C4×C8—431no—
289#367—431no—
290#367—431no—
291#367—431no—
292#367C2×D4311yescharacteristic
293#358—431no—
294#358—431no—
295#358—431no—
296#358C2×D4311yescharacteristic
297#357—431no—
298#357—431no—
299#357—431no—
300#357C2×D4311yescharacteristic
301C4×C16—431no—
302C4×C16—431no—
303C4×C16—431no—
304C4×C16—431no—
305C43#3373611yescharacteristic, complemented, Sylow
306C2×#41—1721no—
307C2×Q16—431no—
308C2×Q16—861no—
309C2×Q16C22×D4311yescharacteristic
310C2×D8—431no—
311C2×D8—861no—
312C2×D8C22×D4311yescharacteristic
313C22×C8—431no—
314C22×C8C22×D4311yescharacteristic
315C4⋊Q8—861no—
316C4⋊Q8—861no—
317C4⋊Q8—861no—
318#127—861no—
319#125—1721no—
320#124—1721no—
321C22⋊Q8—21no—
322C22⋊Q8—861no—
323C22⋊Q8—1721no—
324#121—21no—
325#121—861no—
326#121—1721no—
327C4×Q8—861no—
328C4×Q8—861no—
329C4×Q8—1721no—
330C4×D4—861no—
331C4×D4—861no—
332C4×D4—1721no—
333#117—1721no—
334C2×C42—431no—
335SD32—22no—
336SD32—862no—
337SD32—862no—
338SD32—862no—
339C2×C16—22no—
340C2×C16—431no—
341C2×C16—431no—
342C2×C16—862no—
343C2×C16C22×D4311yescharacteristic
344C2×C16C22×D4311yescharacteristic
345#107—431no—
346#107—431no—
347#107—861no—
348#107—861no—
349#107C22×D4311yescharacteristic
350#107C22×D4311yescharacteristic
351#103—21no—
352#103—861no—
353#103—861no—
354#103—861no—
355#102—21no—
356#102—861no—
357#102—861no—
358#102—861no—
359C4×C8—431no—
360C4×C8—431no—
361C4×C8—431no—
362C4×C8—431no—
363#41—3444no—
364C2×Q8—21no—
365C2×Q8—861no—
366C2×Q8—1721no—
367C2×Q8—1721no—
368C2×D4—21no—
369C2×D4—41no—
370C2×D4—861no—
371C2×D4—1721no—
372C2×D4—1721no—
373C2×D4—1721no—
374C22×C4—431no—
375C22×C4—431no—
376C22×C4—1721no—
377C22×C4—1721no—
378C22×C4D4×D4311yescharacteristic
379Q16—21no—
380Q16—21no—
381Q16—861no—
382Q16—861no—
383Q16—1722no—
384D8—21no—
385D8—21no—
386D8—861no—
387D8—861no—
388D8—1722no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—431no—
392C2×C8—431no—
393C2×C8—862no—
394C2×C8D4×D4311yescharacteristic
395C2×C8C23×D4311yescharacteristic
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—861no—
400C4⋊C4—861no—
401C4⋊C4—1721no—
402C4⋊C4—1721no—
403C4⋊C4—1721no—
404C4⋊C4—1721no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C4⋊C4—1721no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C42—431no—
415C42—431no—
416C42—431no—
417C42—431no—
418C42—1721no—
419C42—1721no—
420C16—21no—
421C16—432no—
422C16—861no—
423C16#1062190012yescomplemented
424C23—41no—
425C23—1721no—
426C23D8×D4311yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—3442no—
430Q8—3442no—
431Q8—1721no—
432Q8—1721no—
433D4—41no—
434D4—41no—
435D4—82no—
436D4—3442no—
437D4—3442no—
438D4—3442no—
439D4—1721no—
440D4—1721no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—434no—
447C2×C4—431no—
448C2×C4—431no—
449C2×C4—431no—
450C2×C4—431no—
451C2×C4—862no—
452C2×C4—3442no—
453C2×C4—3442no—
454C2×C4—1721no—
455C2×C4—1721no—
456C2×C4—1721no—
457C2×C4D8×D4311yescharacteristic
458C2×C4C2×D4×D4311yescharacteristic
459C8—21no—
460C8—432no—
461C8—861no—
462C8#41×D4311yescharacteristic
463C8C2×#1062190011yescharacteristic
464C22—21no—
465C22—21no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—3441no—
470C22—3441no—
471C22—3441no—
472C22SD32×D4312yes—
473C22C2×D8×D4311yescharacteristic
474C4—21no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4—432no—
479C4—432no—
480C4—432no—
481C4—861no—
482C4—3441no—
483C4—3441no—
484C4—3441no—
485C4#1458344411yescharacteristic
486C4#135×D4311yescharacteristic
487C2—22no—
488C2—161no—
489C2—6881no—
490C2#1914516911yescharacteristic
491C2C2×SD32×D4311yescharacteristic
492C2#508×D4311yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2217C2
socleC22×C43C22×D8
prime radical#19145169C2
hypercenter#2217D43
hypocenterC43#33736
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #19145176C2semidirect
3. #19136876C2semidirect
4. #19136849C2semidirect
5. #19136821C2semidirect
6. #19136817C2semidirect
7. #19136693C2semidirect
8. #19136691C2semidirect
9. #19136689C2semidirect
10. #19136450C2semidirect
11. SD32×Dic43C2semidirect
12. #19136446C2semidirect
13. #19136444C2semidirect
14. C2×C16×Dic43C2semidirect
15. C43×#2217C2semidirect
174. C16×C43#41semidirect
176. C43⋊C16#41semidirect
200. C2×Dic43SD32semidirect
250. #2217D43semidirect
305. C43#33736semidirect
423. C16#10621900semidirect

Maximal subgroups

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

subgroupindex
#191451762
#191451692
#191368762
#191368492
#191368212
#191368172
#191366932
#191366912
#191366892
#191364502
SD32×Dic432
#191364462
#191364442
C2×C16×Dic432
C43×#22172
#3373643