Finite Group Databasebeta

← #25250995

Subgroups — #25250995

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147729C211yesmaximal, characteristic, complemented
2#19145076C211yesmaximal, characteristic, complemented
3#19143512C211yesmaximal, characteristic, complemented
4#19136669C214yesmaximal, complemented
5#19136662C214yesmaximal, complemented
6#19136360C211yesmaximal, characteristic, complemented
7#19136345C211yesmaximal, characteristic, complemented
8C2×#14582712C211yesmaximal, characteristic, complemented
9C2×C43×#509C211yesmaximal, characteristic, complemented
10C2×#13063351—21no—
11C2×#13063347C2211yescharacteristic
12#14583666—21no—
13#14583466—21no—
14#14583340—21no—
15#14583339C2212yescomplemented
16#14583335—21no—
17#14583334C2212yescomplemented
18#14583329—22no—
19C2×#13063265C2211yescharacteristic
20#14583287—22no—
21#14583282C2212yescomplemented
22#14583274C2212yescomplemented
23#14583021—22no—
24#14583016C2214yescomplemented
25C2×#13063261C2211yescharacteristic
26#14582916—21no—
27#14582854C2211yescharacteristic
28#14582719C2214yescomplemented
29#14582716C2212yescomplemented
30#14582713C2212yescomplemented
31#14582712C2214yescomplemented
32C2×#135×C43C2211yescharacteristic
33C22×D8×C43C2211yescharacteristic
34C43×#509—22no—
35C43×#509C2214yes—
36C2×SD32×C43—21no—
37C2×D16×C43—21no—
38C2×M32×C43C2211yescharacteristic
39C2×#10621898—21no—
40#13063351—42no—
41#13063351—42no—
42#13063347—21no—
43#13063347—21no—
44#13063347—21no—
45#13063347—21no—
46C2×Dic172C2311yescharacteristic
47C2×#10621873—21no—
48C2×#10621883—22no—
49C2×D344C2311yescharacteristic
50C2×#10621882—22no—
51#13063332—24no—
52#13063332—42no—
53C2×#10621877—21no—
54C2×#10621877—42no—
55C2×#10621877D411yescharacteristic
56#13063321—22no—
57#13063312—22no—
58#13063296—42no—
59#13063294—42no—
60#13063284D411yescharacteristic
61#13063271—22no—
62#13063269—22no—
63#13063268—22no—
64#13063266—22no—
65#13063265—21no—
66#13063265C2312yes—
67C2×C43⋊C16—21no—
68#13063261—21no—
69#13063261C2312yes—
70#13063252—24no—
71#13063235D412yes—
72C8×Dic43C2312yes—
73C2×#41×C43—21no—
74C22×D4×C43—21no—
75#135×C43—21no—
76#135×C43—21no—
77#135×C43D412yescomplemented
78#135×C43C2312yes—
79C2×Q16×C43D411yescharacteristic, complemented
80C2×SD16×C43—21no—
81C2×D8×C43—21no—
82C2×D8×C43—21no—
83C2×D8×C43—21no—
84C2×D8×C43—21no—
85C2×D8×C43—21no—
86C2×D8×C43D411yescharacteristic, complemented
87C2×D8×C43C2312yes—
88C22×C8×C43C2311yescharacteristic
89SD32×C43—24no—
90D16×C43—24no—
91M32×C43—21no—
92M32×C43C2312yes—
93C2×C16×C43—21no—
94C24×C43—41no—
95#41×C43—22no—
96#41×C43—22no—
97#41×C43—41no—
98#41×C43—41no—
99C2×Q8×C43—21no—
100C2×D4×C43—21no—
101C2×D4×C43—22no—
102C2×D4×C43—41no—
103C2×D4×C43—41no—
104C2×D4×C43—41no—
105C2×D4×C43—41no—
106C2×D4×C43—41no—
107C2×D4×C43—41no—
108C22×C4×C43—41no—
109C22×C4×C43C2×D411yescharacteristic
110C2×C22⋊D43—44no—
111C2×C22⋊D43—41no—
112#10621898—41no—
113#10621898—41no—
114#10621898—41no—
115#10621898—41no—
116C2×D172—21no—
117C2×C4×D43—41no—
118C2×Dic86—21no—
119Q16×C43—21no—
120Q16×C43C2×D412yes—
121SD16×C43—22no—
122SD16×C43—22no—
123D8×C43—21no—
124D8×C43—22no—
125D8×C43—22no—
126D8×C43—41no—
127D8×C43—41no—
128D8×C43C2×D412yes—
129C2×C8×C43C2×D411yescharacteristic
130C2×C8×C43C2×D411yescharacteristic
131C2×C8×C43C2×D411yescharacteristic
132C2×C8×C43#4111yescharacteristic
133C2×C8×C43#4111yescharacteristic
134C2×C8×C43C2411yescharacteristic
135C22⋊Dic43—21no—
136C22⋊Dic43—44no—
137#10621883—44no—
138#10621882—44no—
139C4⋊Dic43—21no—
140C4×Dic43C2×D412yes—
141#10621877—22no—
142#10621877—41no—
143#10621877—44no—
144#10621877D812yes—
145#10621877D812yes—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—44no—
148C2×C43⋊C8C2×D412yes—
149Dic172—21no—
150Dic172—21no—
151D344—21no—
152D344—21no—
153#10621873—41no—
154#10621873—41no—
155C16×C43—22no—
156C43⋊C16—22no—
157C23×C43—41no—
158C23×C43—42no—
159C23×C43—81no—
160C23×C43—81no—
161C23×C43—162no—
162C23×C43AGL(1,ℤ/8)11yescharacteristic
163C22×D43—41no—
164Q8×C43—22no—
165Q8×C43—41no—
166D4×C43—22no—
167D4×C43—42no—
168D4×C43—42no—
169D4×C43—42no—
170D4×C43—42no—
171D4×C43—41no—
172D4×C43—81no—
173D4×C43—81no—
174C2×C4×C43—41no—
175C2×C4×C43—42no—
176C2×C4×C43—42no—
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43C2×D811yescharacteristic
180C2×C4×C43C2×D811yescharacteristic
181C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C22⋊D43—81no—
184C22⋊D43—81no—
185C22⋊D43—164no—
186C2×Dic43—22no—
187C2×Dic43—41no—
188D172—41no—
189D172—41no—
190C4×D43—81no—
191C4×D43—81no—
192Dic86—41no—
193Dic86—41no—
194C8×C43#12111yescharacteristic
195C8×C43#12111yescharacteristic
196C8×C43C22×D411yescharacteristic
197C8×C43C2×#4111yescharacteristic
198C43⋊C8—42no—
199C43⋊C8C2×D814yes—
200#33595—431nomaximal, Sylow
201C22×C43—41no—
202C22×C43—42no—
203C22×C43—84no—
204C22×C43—82no—
205C22×C43—161no—
206C22×C43—162no—
207C22×C43—162no—
208C22×C43#45911yescharacteristic
209C22×C43#45911yescharacteristic
210C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
211C2×D43—82no—
212C2×D43—81no—
213C4×C43—42no—
214C4×C43#45911yescharacteristic
215C4×C43#45911yescharacteristic
216C4×C43C2×#12111yescharacteristic
217C4×C43C22×D811yescharacteristic
218Dic43—42no—
219Dic43—81no—
220#3414—431no—
221C2×#509D4311yescharacteristic, complemented
222#3155—431no—
223#2957—431no—
224#2213—434no—
225#2212—434no—
226#2153—431no—
227#2148—431no—
228C2×#361—431no—
229C2×C43—21no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43—82no—
233C2×C43—162no—
234C2×C43C2×#45911yescharacteristic
235D43—161no—
236C2×AGL(1,ℤ/8)—861no—
237C2×#135—431no—
238C2×#135C2×D4311yescharacteristic
239C22×D8C2×D4311yescharacteristic
240#568—861no—
241#535—861no—
242#510—432no—
243#510—861no—
244#509—22no—
245#509—432no—
246#509—861no—
247#509C2×D4314yes—
248#508—862no—
249C2×SD32—21no—
250C2×D16—21no—
251C2×M32—431no—
252C2×M32C2×D4311yescharacteristic
253#496—862no—
254#495—432no—
255#493—432no—
256#444—862no—
257#443—434no—
258C2×#108—431no—
259#421—861no—
260#405—431no—
261#364—434no—
262#362—432no—
263#361—434no—
264#361—432no—
265C43#3359511yescharacteristic, complemented, Sylow
266C2×#41—21no—
267C2×#41—861no—
268C22×D4—21no—
269AGL(1,ℤ/8)—1722no—
270AGL(1,ℤ/8)—1722no—
271#135—21no—
272#135—21no—
273#135—861no—
274#135—861no—
275#135—861no—
276#135—861no—
277#135C22⋊D4312yescomplemented
278#135C22×D4312yes—
279C2×Q16—431no—
280C2×Q16C22⋊D4311yescharacteristic, complemented
281C2×SD16—21no—
282C2×SD16—862no—
283C2×SD16—861no—
284C2×D8—21no—
285C2×D8—21no—
286C2×D8—21no—
287C2×D8—21no—
288C2×D8—21no—
289C2×D8—431no—
290C2×D8—862no—
291C2×D8C22⋊D4311yescharacteristic, complemented
292C2×D8C22×D4312yes—
293#131—864no—
294#131—1722no—
295C2×M16—431no—
296C2×M16—861no—
297C2×M16—1722no—
298C22×C8C22×D4311yescharacteristic
299#127—862no—
300#124—862no—
301#121—1722no—
302#120—1722no—
303#117—431no—
304Q32—862no—
305SD32—24no—
306SD32—862no—
307SD32—862no—
308D16—24no—
309D16—862no—
310M32—21no—
311M32—432no—
312M32—861no—
313M32C22×D4312yes—
314C2×C16—21no—
315C2×C16—861no—
316#108—432no—
317#108—861no—
318#104—864no—
319#97—432no—
320C4×C8—432no—
321C24—41no—
322#41—22no—
323#41—22no—
324#41—41no—
325#41—41no—
326#41—1721no—
327#41—1721no—
328#41—1721no—
329#41—1721no—
330C2×Q8—21no—
331C2×Q8—861no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—861no—
341C2×D4—1724no—
342C2×D4—1721no—
343C22×C4—41no—
344C22×C4—1721no—
345C22×C4D4×D4311yescharacteristic
346Q16—21no—
347Q16—861no—
348Q16—861no—
349Q16C2×C22⋊D4312yes—
350SD16—22no—
351SD16—22no—
352SD16—1724no—
353SD16—1721no—
354SD16—1721no—
355D8—21no—
356D8—22no—
357D8—22no—
358D8—41no—
359D8—41no—
360D8—861no—
361D8—861no—
362D8—1724no—
363D8C2×C22⋊D4312yes—
364M16—432no—
365M16—432no—
366M16—862no—
367M16—1724no—
368M16—1721no—
369C2×C8—432no—
370C2×C8—1724no—
371C2×C8—1721no—
372C2×C8D4×D4311yescharacteristic
373C2×C8#1062190011yescharacteristic
374C2×C8#1062190011yescharacteristic
375C2×C8C2×C22⋊D4311yescharacteristic
376C2×C8C2×C22⋊D4311yescharacteristic
377C2×C8C23×D4311yescharacteristic
378C4⋊C4—861no—
379C22⋊C4—861no—
380C22⋊C4—1724no—
381C42—432no—
382C16—22no—
383C16—862no—
384C23—41no—
385C23—42no—
386C23—81no—
387C23—81no—
388C23—162no—
389C23—1721no—
390C23#1306334911yescharacteristic
391Q8—22no—
392Q8—41no—
393Q8—1721no—
394Q8—1721no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—42no—
400D4—42no—
401D4—81no—
402D4—81no—
403D4—3441no—
404D4—3441no—
405D4—1721no—
406D4—1721no—
407D4—6884no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—862no—
412C2×C4—3441no—
413C2×C4—3441no—
414C2×C4—1721no—
415C2×C4#1306329711yescharacteristic
416C2×C4#1306329711yescharacteristic
417C2×C4D8×D4311yescharacteristic
418C2×C4D8×D4311yescharacteristic
419C2×C4#1306334911yescharacteristic
420C2×C4C2×D4×D4311yescharacteristic
421C8—434no—
422C8—1722no—
423C8#1306329711yescharacteristic
424C8#1306329711yescharacteristic
425C8C22×C22⋊D4311yescharacteristic
426C8C2×#1062190011yescharacteristic
427C22—41no—
428C22—42no—
429C22—84no—
430C22—82no—
431C22—161no—
432C22—162no—
433C22—162no—
434C22—3442no—
435C22—3441no—
436C22#1458309211yescharacteristic
437C22#1458309211yescharacteristic
438C22C2×#1306334911yescharacteristic
439C4—42no—
440C4—3441no—
441C4—1722no—
442C4#1458309211yescharacteristic
443C4#1458309211yescharacteristic
444C4C2×#1306329711yescharacteristic
445C4C2×D8×D4311yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—82no—
450C2—162no—
451C2—6881no—
452C2C2×#1458309211yescharacteristic
subgroupG/H
centerC2C2×#14583092
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#509C2
socleC2×C43C2×#459
hypercenterC2×#509D43
hypocenterC43#33595
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. #19147729C2semidirect
2. #19145076C2semidirect
3. #19143512C2semidirect
4. #19136669C2semidirect
5. #19136662C2semidirect
6. #19136360C2semidirect
7. #19136345C2semidirect
8. C2×#14582712C2semidirect
9. C2×C43×#509C2semidirect
15. #14583339C22semidirect
17. #14583334C22semidirect
21. #14583282C22semidirect
22. #14583274C22semidirect
24. #14583016C22semidirect
28. #14582719C22semidirect
29. #14582716C22semidirect
30. #14582713C22semidirect
31. #14582712C22semidirect
77. #135×C43D4semidirect
79. C2×Q16×C43D4semidirect
86. C2×D8×C43D4semidirect
221. C2×#509D43semidirect
265. C43#33595semidirect
277. #135C22⋊D43semidirect
280. C2×Q16C22⋊D43semidirect
291. C2×D8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191477292
#191450762
#191435122
#191366692
#191366622
#191363602
#191363452
C2×#145827122
C2×C43×#5092
#3359543