Finite Group Databasebeta

← #25250998

Subgroups — #25250998

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×#14583334C211yesmaximal, characteristic, complemented
3#19145081C211yesmaximal, characteristic, complemented
4#19136671C214yesmaximal, complemented
5#19136664C214yesmaximal, complemented
6#19136361C211yesmaximal, characteristic, complemented
7#19136342C211yesmaximal, characteristic, complemented
8C2×#14582711C211yesmaximal, characteristic, complemented
9C43×#2957C211yesmaximal, characteristic, complemented
10C2×#13063353—21no—
11C2×#13063347C2211yescharacteristic
12C22×D344C2211yescharacteristic
13#14583468—21no—
14#14583340—21no—
15#14583339C2212yescomplemented
16#14583335—21no—
17#14583334—22no—
18#14583334C2214yes—
19#14583334C2212yescomplemented
20#14583329—22no—
21C2×#13063268—21no—
22C2×#13063266—21no—
23C2×#13063265C2211yescharacteristic
24C2×#13063265C2211yescharacteristic
25#14583288—22no—
26#14583283C2212yescomplemented
27#14583276C2212yescomplemented
28#14582720C2214yescomplemented
29#14582714C2212yescomplemented
30#14582711C2214yescomplemented
31#14582711C2212yescomplemented
32C2×#135×C43C2211yescharacteristic
33C43×#568—21no—
34C43×#444—22no—
35C43×#443C2214yescomplemented
36C2×#108×C43C2211yescharacteristic
37C43×#421—21no—
38C43×#405C2211yescharacteristic
39C2×#10621898—21no—
40C22×D172—21no—
41#13063353—42no—
42#13063353—42no—
43#13063347—21no—
44#13063347—21no—
45#13063347—21no—
46#13063347—21no—
47C2×Dic172C2311yescharacteristic
48C2×#10621873—21no—
49C2×#10621873—22no—
50C2×D344—21no—
51C2×D344—21no—
52C2×D344—21no—
53C2×D344—21no—
54C2×D344—21no—
55C2×D344—22no—
56C2×D344C2312yes—
57C2×D344C2311yescharacteristic
58#13063322—22no—
59#13063313—22no—
60#13063300—42no—
61#13063295—42no—
62#13063271—22no—
63#13063269—22no—
64#13063268—24no—
65#13063268—22no—
66#13063266—24no—
67#13063266—22no—
68#13063265—21no—
69#13063265—21no—
70#13063265C2312yes—
71#13063265C2312yes—
72C2×C43⋊C16—21no—
73C2×C43⋊C16—21no—
74C2×#41×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×C43D411yescharacteristic, complemented
82#131×C43—24no—
83#131×C43—42no—
84C2×M16×C43—21no—
85C2×M16×C43—42no—
86C2×M16×C43D411yescharacteristic
87C22×C8×C43C2311yescharacteristic
88#117×C43D411yescharacteristic
89#108×C43—21no—
90#108×C43C2312yes—
91#104×C43—24no—
92#97×C43D412yes—
93C4×C8×C43C2312yes—
94C23×D43—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—41no—
102C22×C4×C43—41no—
103C22×C4×C43C2×D411yescharacteristic
104C2×C22⋊D43—41no—
105#10621898—41no—
106#10621898—41no—
107#10621898—41no—
108#10621898—41no—
109C2×D172—22no—
110C2×D172—21no—
111C2×D172—41no—
112C2×D172—44no—
113C2×D172—41no—
114C2×D172—41no—
115C2×D172—41no—
116C2×D172—41no—
117C2×C4×D43—41no—
118C2×Dic86—21no—
119Q16×C43—21no—
120Q16×C43C2×D412yes—
121SD16×C43—22no—
122SD16×C43—22no—
123D8×C43—21no—
124D8×C43C2×D412yes—
125M16×C43—22no—
126M16×C43—41no—
127M16×C43—44no—
128M16×C43D812yes—
129M16×C43D812yes—
130C2×C8×C43—41no—
131C2×C8×C43—44no—
132C2×C8×C43C2×D411yescharacteristic
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2×D412yes—
136C2×C8×C43#4111yescharacteristic
137C2×C8×C43#4111yescharacteristic
138C2×C8×C43C2411yescharacteristic
139C4⋊C4×C43—21no—
140C22⋊C4×C43—21no—
141C42×C43C2×D412yes—
142(C2×D43)⋊C4—44no—
143Dic172—21no—
144Dic172—21no—
145D344—22no—
146D344—21no—
147D344—22no—
148D344—21no—
149D344—41no—
150D344—41no—
151D344—44no—
152#10621873—41no—
153#10621873—41no—
154#10621873—44no—
155C43⋊C16—22no—
156C43⋊C16—22no—
157C23×C43—41no—
158C23×C43AGL(1,ℤ/8)11yescharacteristic
159C22×D43—42no—
160C22×D43—41no—
161C22×D43—81no—
162C22×D43—81no—
163C22×D43—162no—
164Q8×C43—22no—
165Q8×C43—41no—
166D4×C43—22no—
167D4×C43—42no—
168D4×C43—42no—
169D4×C43—41no—
170C2×C4×C43—22no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—42no—
174C2×C4×C43#12111yescharacteristic
175C2×C4×C43#12111yescharacteristic
176C2×C4×C43C2×D811yescharacteristic
177C2×C4×C43C2×D811yescharacteristic
178C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C43C22×D411yescharacteristic
180C22⋊D43—81no—
181C22⋊D43—81no—
182C2×Dic43—41no—
183D172—41no—
184D172—42no—
185D172—42no—
186D172—41no—
187D172—81no—
188D172—81no—
189D172—164no—
190C4×D43—81no—
191C4×D43—81no—
192Dic86—41no—
193Dic86—41no—
194C8×C43—42no—
195C8×C43#12111yescharacteristic
196C8×C43#12111yescharacteristic
197C8×C43C2×D814yes—
198C8×C43C22×D411yescharacteristic
199C8×C43C2×#4111yescharacteristic
200#33595—431nomaximal, Sylow
201C22×C43—41no—
202C22×C43—42no—
203C22×C43—161no—
204C22×C43#45911yescharacteristic
205C22×C43#45911yescharacteristic
206C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
207C2×D43—84no—
208C2×D43—82no—
209C2×D43—82no—
210C2×D43—81no—
211C2×D43—162no—
212C2×D43—162no—
213C4×C43—42no—
214C4×C43—42no—
215C4×C43#45911yescharacteristic
216C4×C43#45911yescharacteristic
217C4×C43C2×#12111yescharacteristic
218C4×C43C22×D811yescharacteristic
219Dic43—81no—
220#3414—431no—
221C2×#509—431no—
222#3155—431no—
223#2957D4311yescharacteristic, complemented
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×C43C2×#45911yescharacteristic
234D43—161no—
235D43—162no—
236C2×AGL(1,ℤ/8)—861no—
237C2×#135—431no—
238C2×#135C2×D4311yescharacteristic
239C22×D8—431no—
240#568—21no—
241#535—861no—
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—862no—
254#495—432no—
255#493—432no—
256#444—22no—
257#443C2×D4314yescomplemented
258C2×#108C2×D4311yescharacteristic
259#421—21no—
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—861no—
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#135D17212yescomplemented
278#135C22×D4312yes—
279C2×Q16—431no—
280C2×Q16D17211yescharacteristic, complemented
281C2×SD16—21no—
282C2×SD16—861no—
283C2×SD16—862no—
284C2×D8—432no—
285C2×D8—431no—
286C2×D8—861no—
287C2×D8—861no—
288C2×D8—861no—
289C2×D8—861no—
290C2×D8—861no—
291C2×D8—862no—
292C2×D8D17211yescharacteristic, complemented
293#131—24no—
294#131—42no—
295C2×M16—21no—
296C2×M16—42no—
297C2×M16C22⋊D4311yescharacteristic
298C22×C8C22×D4311yescharacteristic
299#127—862no—
300#124—862no—
301#121—1722no—
302#120—1722no—
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—21no—
317#108C22×D4312yes—
318#104—24no—
319#97C22⋊D4312yes—
320C4×C8C22×D4312yes—
321C24—1721no—
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—41no—
334C2×D4—862no—
335C2×D4—861no—
336C2×D4—1724no—
337C2×D4—1721no—
338C2×D4—1721no—
339C2×D4—1721no—
340C2×D4—1721no—
341C2×D4—1721no—
342C2×D4—1721no—
343C22×C4—41no—
344C22×C4—1721no—
345C22×C4C2×C22⋊D4311yescharacteristic
346Q16—21no—
347Q16—861no—
348Q16—861no—
349Q16C2×D17212yes—
350SD16—22no—
351SD16—22no—
352SD16—1721no—
353SD16—1721no—
354SD16—1724no—
355D8—21no—
356D8—862no—
357D8—861no—
358D8—862no—
359D8—861no—
360D8—1721no—
361D8—1721no—
362D8—1724no—
363D8C2×D17212yes—
364M16—22no—
365M16—41no—
366M16—44no—
367M16#1062188212yes—
368M16#1062188212yes—
369C2×C8—41no—
370C2×C8—44no—
371C2×C8C2×D17211yescharacteristic
372C2×C8C2×D17211yescharacteristic
373C2×C8#1062189811yescharacteristic
374C2×C8#1062189811yescharacteristic
375C2×C8C2×C22⋊D4311yescharacteristic
376C2×C8C2×C22⋊D4312yes—
377C2×C8C23×D4311yescharacteristic
378C4⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—1724no—
381C42C2×C22⋊D4312yes—
382C16—862no—
383C16—862no—
384C23—41no—
385C23—3441no—
386C23—3441no—
387C23—1722no—
388C23—1721no—
389C23—6882no—
390C23#1306335011yescharacteristic
391Q8—22no—
392Q8—41no—
393Q8—1721no—
394Q8—1721no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—3441no—
400D4—3441no—
401D4—3441no—
402D4—3441no—
403D4—1722no—
404D4—1721no—
405D4—1721no—
406D4—1722no—
407D4—6884no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—3441no—
413C2×C4—3441no—
414C2×C4—1721no—
415C2×C4#1306329911yescharacteristic
416C2×C4#1306329911yescharacteristic
417C2×C4C2×#1062188211yescharacteristic
418C2×C4C2×#1062188211yescharacteristic
419C2×C4#1306335011yescharacteristic
420C2×C4C22×C22⋊D4311yescharacteristic
421C8—42no—
422C8#1306329911yescharacteristic
423C8#1306329911yescharacteristic
424C8C2×#1062188214yes—
425C8C22×D17211yescharacteristic
426C8C2×#1062189811yescharacteristic
427C22—41no—
428C22—42no—
429C22—161no—
430C22—3442no—
431C22—3444no—
432C22—3441no—
433C22—3442no—
434C22—6882no—
435C22—6882no—
436C22#1458309411yescharacteristic
437C22#1458309411yescharacteristic
438C22C2×#1306335011yescharacteristic
439C4—42no—
440C4—42no—
441C4—3441no—
442C4#1458309411yescharacteristic
443C4#1458309411yescharacteristic
444C4C2×#1306329911yescharacteristic
445C4C22×#1062188211yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—82no—
450C2—6882no—
451C2—6881no—
452C2C2×#1458309411yescharacteristic
subgroupG/H
centerC2C2×#14583094
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2957C2
socleC2×C43C2×#459
hypercenter#2957D43
hypocenterC43#33595
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
1. #19147729C2semidirect
2. C2×#14583334C2semidirect
3. #19145081C2semidirect
4. #19136671C2semidirect
5. #19136664C2semidirect
6. #19136361C2semidirect
7. #19136342C2semidirect
8. C2×#14582711C2semidirect
9. C43×#2957C2semidirect
15. #14583339C22semidirect
19. #14583334C22semidirect
26. #14583283C22semidirect
27. #14583276C22semidirect
28. #14582720C22semidirect
29. #14582714C22semidirect
30. #14582711C22semidirect
31. #14582711C22semidirect
35. C43×#443C22semidirect
77. #135×C43D4semidirect
79. C2×Q16×C43D4semidirect
81. C2×D8×C43D4semidirect
223. #2957D43semidirect
257. #443C2×D43semidirect
265. C43#33595semidirect
277. #135D172semidirect
280. C2×Q16D172semidirect
292. C2×D8D172semidirect

Maximal subgroups

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

subgroupindex
#191477292
C2×#145833342
#191450812
#191366712
#191366642
#191363612
#191363422
C2×#145827112
C43×#29572
#3359543