Finite Group Databasebeta

← #25252156

Subgroups — #25252156

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#19145178C211yesmaximal, characteristic, complemented
2#19145171C211yesmaximal, characteristic
3#19136876C211yesmaximal, characteristic, complemented
4#19136849C211yesmaximal, characteristic, complemented
5#19136821C211yesmaximal, characteristic, complemented
6#19136817C211yesmaximal, characteristic, complemented
7#19136694C211yesmaximal, characteristic, complemented
8#19136692C211yesmaximal, characteristic, complemented
9#19136690C211yesmaximal, characteristic, complemented
10#19136688C211yesmaximal, characteristic, complemented
11C4×#13063270C211yesmaximal, characteristic, complemented
12C4×#13063268C211yesmaximal, characteristic, complemented
13C4×#13063269C211yesmaximal, characteristic, complemented
14C4×C16×D43C211yesmaximal, characteristic, complemented
15C4×SD32×C43C211yesmaximal, characteristic, complemented
16#14583453—21no—
17#14583446—21no—
18C2×#13063270C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20C2×#13063268C2211yescharacteristic
21C2×C16×D43C2211yescharacteristic
22C2×C16×D43C2211yescharacteristic
23#14583303C2211yescharacteristic
24#14583303C2211yescharacteristic
25#14583277C2211yescharacteristic
26#14583274C2211yescharacteristic
27#14583248—21no—
28#14583244—21no—
29#14583141C2211yescharacteristic
30#14583139—21no—
31#14583137C2211yescharacteristic
32#14583136C2211yescharacteristic
33#14583134—21no—
34#14583132C2211yescharacteristic
35C4×Dic172C2211yescharacteristic
36C4×#10621885—21no—
37C4×D344C2211yescharacteristic
38C4×#10621882—21no—
39C4×C8×D43C2211yescharacteristic
40#14582727C2211yescharacteristic
41#14582726C2211yescharacteristic
42#14582726C2211yescharacteristic
43#14582704C2211yescharacteristic
44#14582703C2211yescharacteristic
45#14582702C2211yescharacteristic
46#14582701C2211yescharacteristic
47#14582700C2211yescharacteristic
48#14582699C2211yescharacteristic
49C4×C43⋊C16C2211yescharacteristic
50C16×Dic43C2211yescharacteristic
51C16×Dic43C2211yescharacteristic
52C2×SD32×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic
54C4×D8×C43C2211yescharacteristic
55C43×#367C2211yescharacteristic
56C43×#358C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C4×C16×C43C2211yescharacteristic
59C2×#10621898—41no—
60C2×Dic172C2311yescharacteristic
61C2×#10621885—21no—
62C2×D344C2311yescharacteristic
63C2×#10621882—21no—
64C2×C8×D43D411yescharacteristic
65C2×C8×D43C2311yescharacteristic
66#13063324—21no—
67#13063324—21no—
68#13063323—21no—
69#13063321—21no—
70#13063315—41no—
71#13063311—41no—
72#13063305—21no—
73#13063303—41no—
74#13063301—21no—
75#13063300—21no—
76#13063298—41no—
77#13063296—21no—
78C4×Dic86—21no—
79C4×Dic86—41no—
80C4×D172—21no—
81C4×C22⋊D43—41no—
82#13063282—41no—
83C42×D43D411yescharacteristic
84#13063270—22no—
85#13063269—22no—
86#13063268—22no—
87C2×C43⋊C16C2311yescharacteristic
88C2×C43⋊C16C2311yescharacteristic
89C16×D43—22no—
90C16×D43—22no—
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95#13063250—21no—
96#13063249—21no—
97#13063248—21no—
98#13063247—21no—
99#13063246—21no—
100#13063245—21no—
101C4×C43⋊C8D411yescharacteristic
102C8×Dic43D411yescharacteristic
103C8×Dic43C2311yescharacteristic
104C2×Q16×C43C2311yescharacteristic
105C2×D8×C43C2311yescharacteristic
106C4×Q8×C43—21no—
107C4×D4×C43—21no—
108SD32×C43—22no—
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#103×C43—21no—
114#102×C43—21no—
115C4×C8×C43C2311yescharacteristic
116C2×Q8×C43—21no—
117C2×D4×C43—21no—
118C22×C4×C43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122#10621898—84no—
123C2×D172—21no—
124C2×D172—41no—
125C2×C4×D43—41no—
126C2×C4×D43D811yescharacteristic
127C2×C4×D43D811yescharacteristic
128C2×C4×D43C2×D411yescharacteristic
129C2×Dic86—21no—
130C2×Dic86—41no—
131C2×Dic86—41no—
132Q16×C43—21no—
133Q16×C43—21no—
134D8×C43—21no—
135D8×C43—21no—
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2411yescharacteristic
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—41no—
141C22⋊C4×C43—41no—
142C42×C43—41no—
143C42×C43C2×D411yescharacteristic
144C22⋊Dic43—41no—
145#10621885—42no—
146#10621882—42no—
147(C2×D43)⋊C4—41no—
148(C2×D43)⋊C4—41no—
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×Dic43D811yescharacteristic
162C4×Dic43D811yescharacteristic
163C4×Dic43C2×D411yescharacteristic
164C2×C43⋊C8C2×D411yescharacteristic
165C2×C43⋊C8C2×D411yescharacteristic
166Dic172—21no—
167Dic172—21no—
168D344—21no—
169D344—21no—
170C8×D43—21no—
171C8×D43—21no—
172C8×D43—22no—
173C16×C43—21no—
174C16×C43#4112yescomplemented
175C43⋊C16—21no—
176C43⋊C16#4112yescomplemented
177C23×C43—41no—
178C22×D43—41no—
179C22×D43C2×D811yescharacteristic
180Q8×C43—41no—
181Q8×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—82no—
188C2×C4×C43C2×D811yescharacteristic
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43C22×D411yescharacteristic
191C22⋊D43—82no—
192C22⋊D43—82no—
193C22⋊D43—82no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43C2×D811yescharacteristic
198C2×Dic43C2×D811yescharacteristic
199C2×Dic43C2×D811yescharacteristic
200D172—41no—
201D172—41no—
202D172—82no—
203C4×D43—21no—
204C4×D43—21no—
205C4×D43—22no—
206C4×D43—82no—
207C4×D43SD3214yescomplemented
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—81no—
219C22×C43—81no—
220C22×C43—81no—
221C22×C43C22×D811yescharacteristic
222C2×D43—21no—
223C2×D43—21no—
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43C2×SD3212yes—
228C4×C43—21no—
229C4×C43—81no—
230C4×C43—81no—
231C4×C43—81no—
232C4×C43C2×SD3212yes—
233C4×C43#53211yescharacteristic
234C4×C43C2×#13511yescharacteristic
235Dic43—21no—
236Dic43—81no—
237Dic43—81no—
238Dic43—81no—
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#2217—431no—
251C4×SD32—431no—
252C4×SD32—431no—
253C4×SD32—431no—
254C4×SD32D4311yescharacteristic, complemented
255C2×C4×C16—431no—
256C2×C43—161no—
257C2×C43#316911yescharacteristic
258C2×C43C22×SD3211yescharacteristic
259C2×C43C2×#50811yescharacteristic
260D43—22no—
261D43—161no—
262#533—861no—
263#532—861no—
264C2×SD32—431no—
265C2×SD32—431no—
266C2×SD32—431no—
267C2×SD32C2×D4311yescharacteristic
268C22×C16—431no—
269C22×C16—431no—
270#500—431no—
271#500—431no—
272#494—431no—
273#493—431no—
274#487—861no—
275#486—861no—
276#467—431no—
277#467—431no—
278#467—861no—
279#466—431no—
280#466—431no—
281#466—861no—
282C4×Q16—431no—
283C4×Q16—861no—
284C4×Q16C2×D4311yescharacteristic
285C4×D8—431no—
286C4×D8—861no—
287C4×D8C2×D4311yescharacteristic
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×C16C2×D4311yescharacteristic
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×C8—431no—
315C4⋊Q8—861no—
316C4⋊Q8—861no—
317C4⋊Q8—861no—
318#127—861no—
319#125—1721no—
320#124—1721no—
321C22⋊Q8—861no—
322C22⋊Q8—861no—
323C22⋊Q8—1721no—
324#121—861no—
325#121—861no—
326#121—1721no—
327C4×Q8—21no—
328C4×Q8—861no—
329C4×Q8—1721no—
330C4×D4—21no—
331C4×D4—861no—
332C4×D4—1721no—
333#117—1721no—
334C2×C42—431no—
335SD32—22no—
336SD32—862no—
337SD32—862no—
338SD32—862no—
339C2×C16—431no—
340C2×C16—431no—
341C2×C16—862no—
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×C8C22×D4311yescharacteristic
363#41—3444no—
364C2×Q8—21no—
365C2×Q8—861no—
366C2×Q8—1721no—
367C2×Q8—1721no—
368C2×D4—21no—
369C2×D4—861no—
370C2×D4—1721no—
371C2×D4—1721no—
372C2×D4—1721no—
373C2×D4—1721no—
374C22×C4—41no—
375C22×C4—431no—
376C22×C4—431no—
377C22×C4—431no—
378C22×C4—1721no—
379Q16—21no—
380Q16—21no—
381Q16—861no—
382Q16—861no—
383Q16—1722no—
384D8—21no—
385D8—21no—
386D8—861no—
387D8—861no—
388D8—1722no—
389C2×C8—431no—
390C2×C8—431no—
391C2×C8—862no—
392C2×C8—861no—
393C2×C8—861no—
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—1721no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
414C42—41no—
415C42—431no—
416C42—431no—
417C42—431no—
418C42—1721no—
419C42D4×D4311yescharacteristic
420C16—21no—
421C16—432no—
422C16—861no—
423C16#1062189812yescomplemented
424C23—41no—
425C23—431no—
426C23—1721no—
427Q8—41no—
428Q8—41no—
429Q8—3442no—
430Q8—3442no—
431Q8—1721no—
432Q8—1721no—
433D4—41no—
434D4—41no—
435D4—3442no—
436D4—3442no—
437D4—3442no—
438D4—3442no—
439D4—1721no—
440D4—1721no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—82no—
445C2×C4—431no—
446C2×C4—431no—
447C2×C4—434no—
448C2×C4—431no—
449C2×C4—862no—
450C2×C4—861no—
451C2×C4—861no—
452C2×C4—3442no—
453C2×C4—1721no—
454C2×C4—1721no—
455C2×C4—1721no—
456C2×C4D8×D4311yescharacteristic
457C2×C4D8×D4311yescharacteristic
458C2×C4C2×D4×D4311yescharacteristic
459C8—21no—
460C8—432no—
461C8—861no—
462C8#41×D4311yescharacteristic
463C8C2×#1062189811yescharacteristic
464C22—81no—
465C22—81no—
466C22—81no—
467C22—432no—
468C22—861no—
469C22—861no—
470C22—3441no—
471C22—3441no—
472C22—3441no—
473C22C2×D8×D4311yescharacteristic
474C4—21no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4—432no—
479C4—432no—
480C4—861no—
481C4—3441no—
482C4—3441no—
483C4—3441no—
484C4SD32×D4312yes—
485C4#1458344611yescharacteristic
486C4#135×D4311yescharacteristic
487C2—161no—
488C2—862no—
489C2—6881no—
490C2#1914517111yescharacteristic
491C2C2×SD32×D4311yescharacteristic
492C2#508×D4311yescharacteristic
subgroupG/H
centerC2×C4D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC4×SD32×C43C2
socleC22×C43C22×D8
prime radical#19145171C2
hypercenterC4×SD32D43
hypocenterC43#33736
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×SD32

Complements

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

NH ≅ G/Ntype
1. #19145178C2semidirect
3. #19136876C2semidirect
4. #19136849C2semidirect
5. #19136821C2semidirect
6. #19136817C2semidirect
7. #19136694C2semidirect
8. #19136692C2semidirect
9. #19136690C2semidirect
10. #19136688C2semidirect
11. C4×#13063270C2semidirect
12. C4×#13063268C2semidirect
13. C4×#13063269C2semidirect
14. C4×C16×D43C2semidirect
15. C4×SD32×C43C2semidirect
174. C16×C43#41semidirect
176. C43⋊C16#41semidirect
207. C4×D43SD32semidirect
254. C4×SD32D43semidirect
305. C43#33736semidirect
423. C16#10621898semidirect

Maximal subgroups

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

subgroupindex
#191451782
#191451712
#191368762
#191368492
#191368212
#191368172
#191366942
#191366922
#191366902
#191366882
C4×#130632702
C4×#130632682
C4×#130632692
C4×C16×D432
C4×SD32×C432
#3373643