Finite Group Databasebeta

← #25250994

Subgroups — #25250994

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
2C2×#14583335C211yesmaximal, characteristic, complemented
3#19143513C211yesmaximal, characteristic, complemented
4#19136668C214yesmaximal, complemented
5#19136661C214yesmaximal, complemented
6#19136361C211yesmaximal, characteristic, complemented
7#19136344C211yesmaximal, characteristic, complemented
8C2×#14582712C211yesmaximal, characteristic, complemented
9C43×#3155C211yesmaximal, characteristic, complemented
10C2×#13063347C2211yescharacteristic
11#14583665—21no—
12#14583340C2212yescomplemented
13#14583339—21no—
14#14583335—22no—
15#14583335C2214yes—
16#14583335C2212yescomplemented
17#14583334—21no—
18#14583329—22no—
19C2×#13063269—21no—
20C2×#13063266—21no—
21C2×#13063265C2211yescharacteristic
22C2×#13063265C2211yescharacteristic
23#14583022—22no—
24#14583017C2214yescomplemented
25C2×#13063261C2211yescharacteristic
26#14582917—21no—
27#14582720C2214yescomplemented
28#14582715C2212yescomplemented
29#14582712C2214yescomplemented
30#14582712C2212yescomplemented
31C2×AGL(1,ℤ/8)×C43—21no—
32C2×#135×C43C2211yescharacteristic
33C22×D8×C43C2211yescharacteristic
34C43×#535—21no—
35C43×#496—22no—
36C43×#495C2212yescomplemented
37C43×#493C2212yescomplemented
38C43×#405C2211yescharacteristic
39C2×#10621898—21no—
40#13063347—21no—
41#13063347—21no—
42#13063347D412yescomplemented
43#13063347C2312yes—
44C2×Dic172D411yescharacteristic, complemented
45C2×#10621873—21no—
46C2×D344D411yescharacteristic, complemented
47#13063333—42no—
48#13063331—24no—
49C2×#10621877—21no—
50M16×D43—42no—
51#13063271—22no—
52#13063269—24no—
53#13063269—22no—
54#13063268—22no—
55#13063266—24no—
56#13063266—22no—
57#13063265—21no—
58#13063265—21no—
59#13063265C2312yes—
60#13063265C2312yes—
61C2×C43⋊C16—21no—
62C2×C43⋊C16—21no—
63#13063261—21no—
64#13063261C2312yes—
65#13063253—24no—
66C2×#41×C43—21no—
67C22×D4×C43—21no—
68AGL(1,ℤ/8)×C43—42no—
69AGL(1,ℤ/8)×C43—42no—
70#135×C43—21no—
71#135×C43—21no—
72#135×C43—21no—
73#135×C43—21no—
74C2×Q16×C43C2311yescharacteristic
75C2×SD16×C43—21no—
76C2×SD16×C43—22no—
77C2×D8×C43—21no—
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—22no—
81C2×D8×C43—21no—
82C2×D8×C43—21no—
83C2×D8×C43C2312yes—
84C2×D8×C43C2311yescharacteristic
85C2×M16×C43D411yescharacteristic
86C22×C8×C43C2311yescharacteristic
87#127×C43—22no—
88#124×C43—22no—
89#121×C43—42no—
90#120×C43—42no—
91#117×C43D411yescharacteristic
92#97×C43D412yes—
93C4×C8×C43C2312yes—
94C24×C43—41no—
95#41×C43—41no—
96#41×C43—41no—
97#41×C43—41no—
98#41×C43—41no—
99C2×Q8×C43—21no—
100C2×D4×C43—22no—
101C2×D4×C43—21no—
102C2×D4×C43—44no—
103C2×D4×C43—41no—
104C2×D4×C43—41no—
105C2×D4×C43—41no—
106C2×D4×C43—41no—
107C2×D4×C43—41no—
108C2×D4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43C2×D411yescharacteristic
111C2×C22⋊D43—41no—
112#10621898—22no—
113#10621898—22no—
114#10621898—41no—
115#10621898—41no—
116C2×D172—21no—
117C2×C4×D43—41no—
118C2×Dic86—21no—
119Q16×C43—21no—
120Q16×C43—21no—
121SD16×C43—41no—
122SD16×C43—41no—
123SD16×C43—44no—
124D8×C43—22no—
125D8×C43—21no—
126D8×C43—22no—
127D8×C43—21no—
128D8×C43—41no—
129D8×C43—41no—
130D8×C43—44no—
131M16×C43D812yes—
132M16×C43D812yes—
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2×D411yescharacteristic
136C2×C8×C43C2×D412yes—
137C2×C8×C43#4111yescharacteristic
138C2×C8×C43#4111yescharacteristic
139C2×C8×C43C2411yescharacteristic
140C4⋊C4×C43—21no—
141C22⋊C4×C43—21no—
142C22⋊C4×C43—44no—
143C42×C43C2×D412yes—
144#10621877—22no—
145#10621877—41no—
146C2×C43⋊C8—41no—
147Dic172—21no—
148Dic172C2×D412yes—
149D344—21no—
150D344C2×D412yes—
151#10621873—22no—
152#10621873—22no—
153#10621872—44no—
154C8×D43—44no—
155C43⋊C16—22no—
156C43⋊C16—22no—
157C23×C43—42no—
158C23×C43—41no—
159C23×C43—81no—
160C23×C43—81no—
161C23×C43—162no—
162C23×C43AGL(1,ℤ/8)11yescharacteristic
163C22×D43—41no—
164Q8×C43—41no—
165Q8×C43—41no—
166D4×C43—42no—
167D4×C43—41no—
168D4×C43—41no—
169D4×C43—42no—
170D4×C43—81no—
171D4×C43—81no—
172D4×C43—81no—
173D4×C43—81no—
174D4×C43—164no—
175C2×C4×C43—22no—
176C2×C4×C43—41no—
177C2×C4×C43—81no—
178C2×C4×C43—81no—
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43C2×D811yescharacteristic
182C2×C4×C43C2×D811yescharacteristic
183C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C43C22×D411yescharacteristic
185C22⋊D43—42no—
186C22⋊D43—42no—
187C2×Dic43—41no—
188D172—22no—
189D172—41no—
190C4×D43—42no—
191C4×D43—42no—
192Dic86—22no—
193Dic86—41no—
194C8×C43#12111yescharacteristic
195C8×C43#12111yescharacteristic
196C8×C43C2×D814yes—
197C8×C43C22×D411yescharacteristic
198C8×C43C2×#4111yescharacteristic
199C43⋊C8—42no—
200#33595—431nomaximal, Sylow
201C22×C43—41no—
202C22×C43—84no—
203C22×C43—82no—
204C22×C43—82no—
205C22×C43—81no—
206C22×C43—162no—
207C22×C43—162no—
208C22×C43#45911yescharacteristic
209C22×C43#45911yescharacteristic
210C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
211C2×D43—42no—
212C2×D43—161no—
213C4×C43—42no—
214C4×C43—81no—
215C4×C43#45911yescharacteristic
216C4×C43#45911yescharacteristic
217C4×C43C2×#12111yescharacteristic
218C4×C43C22×D811yescharacteristic
219Dic43—42no—
220#3414—431no—
221C2×#509—431no—
222#3155D4311yescharacteristic, complemented
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—161no—
233C2×C43—162no—
234C2×C43C2×#45911yescharacteristic
235D43—82no—
236C2×AGL(1,ℤ/8)—21no—
237C2×#135—431no—
238C2×#135C2×D4311yescharacteristic
239C22×D8C2×D4311yescharacteristic
240#568—861no—
241#535—21no—
242#510—432no—
243#510—861no—
244#509—434no—
245#509—432no—
246#509—862no—
247#509—861no—
248#508—862no—
249C2×SD32—861no—
250C2×D16—861no—
251C2×M32—431no—
252C2×M32—431no—
253#496—22no—
254#495C2×D4312yescomplemented
255#493C2×D4312yescomplemented
256#444—862no—
257#443—434no—
258C2×#108—431no—
259#421—861no—
260#405C2×D4311yescharacteristic
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)—42no—
270AGL(1,ℤ/8)—42no—
271#135—21no—
272#135—21no—
273#135—21no—
274#135—21no—
275#135—432no—
276#135—432no—
277#135—861no—
278#135—861no—
279C2×Q16—431no—
280C2×Q16C22×D4311yescharacteristic
281C2×SD16—21no—
282C2×SD16—22no—
283C2×SD16—861no—
284C2×D8—21no—
285C2×D8—21no—
286C2×D8—21no—
287C2×D8—21no—
288C2×D8—21no—
289C2×D8—22no—
290C2×D8—431no—
291C2×D8C22×D4312yes—
292C2×D8C22×D4311yescharacteristic
293#131—864no—
294#131—1722no—
295C2×M16—861no—
296C2×M16—1722no—
297C2×M16C22⋊D4311yescharacteristic
298C22×C8C22×D4311yescharacteristic
299#127—22no—
300#124—22no—
301#121—42no—
302#120—42no—
303#117C22⋊D4311yescharacteristic
304Q32—862no—
305SD32—864no—
306SD32—862no—
307SD32—862no—
308D16—864no—
309D16—862no—
310M32—432no—
311M32—432no—
312M32—861no—
313M32—861no—
314C2×C16—861no—
315C2×C16—861no—
316#108—432no—
317#108—861no—
318#104—864no—
319#97C22⋊D4312yes—
320C4×C8C22×D4312yes—
321C24—41no—
322#41—41no—
323#41—41no—
324#41—41no—
325#41—41no—
326#41—862no—
327#41—862no—
328#41—1721no—
329#41—1721no—
330C2×Q8—21no—
331C2×Q8—861no—
332C2×D4—22no—
333C2×D4—21no—
334C2×D4—44no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—861no—
342C2×D4—1721no—
343C22×C4—41no—
344C22×C4—1721no—
345C22×C4C2×C22⋊D4311yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—432no—
349Q16—861no—
350SD16—41no—
351SD16—41no—
352SD16—44no—
353SD16—862no—
354SD16—862no—
355D8—22no—
356D8—21no—
357D8—22no—
358D8—21no—
359D8—41no—
360D8—41no—
361D8—44no—
362D8—432no—
363D8—861no—
364M16—862no—
365M16—1721no—
366M16—1724no—
367M16#1062188212yes—
368M16#1062188212yes—
369C2×C8—1721no—
370C2×C8—1724no—
371C2×C8D4×D4311yescharacteristic
372C2×C8D4×D4311yescharacteristic
373C2×C8#1062190011yescharacteristic
374C2×C8#1062190011yescharacteristic
375C2×C8C2×C22⋊D4311yescharacteristic
376C2×C8C2×C22⋊D4312yes—
377C2×C8C23×D4311yescharacteristic
378C4⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—44no—
381C42C2×C22⋊D4312yes—
382C16—862no—
383C16—862no—
384C23—42no—
385C23—41no—
386C23—81no—
387C23—81no—
388C23—162no—
389C23—1721no—
390C23#1306335111yescharacteristic
391Q8—41no—
392Q8—41no—
393Q8—862no—
394Q8—1721no—
395D4—42no—
396D4—41no—
397D4—41no—
398D4—42no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—164no—
404D4—862no—
405D4—1722no—
406D4—1722no—
407D4—1721no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—1721no—
413C2×C4—1722no—
414C2×C4—1722no—
415C2×C4#1306329611yescharacteristic
416C2×C4#1306329611yescharacteristic
417C2×C4C2×#1062188211yescharacteristic
418C2×C4C2×#1062188211yescharacteristic
419C2×C4#1306335111yescharacteristic
420C2×C4C22×C22⋊D4311yescharacteristic
421C8—1722no—
422C8#1306329611yescharacteristic
423C8#1306329611yescharacteristic
424C8C2×#1062188214yes—
425C8C2×D4×D4311yescharacteristic
426C8C2×#1062190011yescharacteristic
427C22—41no—
428C22—82no—
429C22—84no—
430C22—81no—
431C22—82no—
432C22—162no—
433C22—162no—
434C22—1722no—
435C22—6881no—
436C22#1458309111yescharacteristic
437C22#1458309111yescharacteristic
438C22C2×#1306335111yescharacteristic
439C4—42no—
440C4—81no—
441C4—1722no—
442C4#1458309111yescharacteristic
443C4#1458309111yescharacteristic
444C4C2×#1306329611yescharacteristic
445C4C22×#1062188211yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—162no—
450C2—161no—
451C2—3442no—
452C2C2×#1458309111yescharacteristic
subgroupG/H
centerC2C2×#14583091
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3155C2
socleC2×C43C2×#459
hypercenter#3155D43
hypocenterC43#33595
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #3155

Complements

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

NH ≅ G/Ntype
1. #19147729C2semidirect
2. C2×#14583335C2semidirect
3. #19143513C2semidirect
4. #19136668C2semidirect
5. #19136661C2semidirect
6. #19136361C2semidirect
7. #19136344C2semidirect
8. C2×#14582712C2semidirect
9. C43×#3155C2semidirect
12. #14583340C22semidirect
16. #14583335C22semidirect
24. #14583017C22semidirect
27. #14582720C22semidirect
28. #14582715C22semidirect
29. #14582712C22semidirect
30. #14582712C22semidirect
36. C43×#495C22semidirect
37. C43×#493C22semidirect
42. #13063347D4semidirect
44. C2×Dic172D4semidirect
46. C2×D344D4semidirect
222. #3155D43semidirect
254. #495C2×D43semidirect
255. #493C2×D43semidirect
265. C43#33595semidirect

Maximal subgroups

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

subgroupindex
#191477292
C2×#145833352
#191435132
#191366682
#191366612
#191363612
#191363442
C2×#145827122
C43×#31552
#3359543