Finite Group Databasebeta

← #46822430

Subgroups — #46822430

Order 34432.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575481C211yesmaximal, characteristic, complemented
2C2×#22575475C211yesmaximal, characteristic, complemented
3#31771276C211yesmaximal, characteristic, complemented
4#31771251C211yesmaximal, characteristic, complemented
5#31770994C211yesmaximal, characteristic, complemented
6#31770851C211yesmaximal, characteristic, complemented
7#31770841C211yesmaximal, characteristic, complemented
8#31770828C211yesmaximal, characteristic, complemented
9#31770801C211yesmaximal, characteristic, complemented
10#31770769C211yesmaximal, characteristic, complemented
11#31770752C211yesmaximal, characteristic, complemented
12#31770752C211yesmaximal, characteristic, complemented
13#31770741C211yesmaximal, characteristic, complemented
14#31770707C211yesmaximal, characteristic, complemented
15#435×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×#16864402C2211yescharacteristic
18C2×#16864402C2211yescharacteristic, complemented
19C22×D1076C2211yescharacteristic
20#22575481—24no—
21#22575475—24no—
22C2×Dic1076C2211yescharacteristic, complemented
23C2×#16864391C2211yescharacteristic
24C2×#16864391C2211yescharacteristic
25C2×#16864391C2211yescharacteristic, complemented
26C2×#16864391C2211yescharacteristic, complemented
27C2×D2152C2211yescharacteristic
28C2×D2152C2211yescharacteristic
29C2×D2152C2211yescharacteristic
30C2×D2152C2211yescharacteristic
31#22575450C2211yescharacteristic, complemented
32#22575449—21no—
33#22575441C2211yescharacteristic
34#22575438—21no—
35#22575432C2211yescharacteristic
36#22575427C2211yescharacteristic
37#22575427C2211yescharacteristic
38#22575427C2211yescharacteristic, complemented
39#22575426—21no—
40#22575426—21no—
41#22575426—21no—
42#22575421—21no—
43C4×Dic538C2211yescharacteristic, complemented
44C4×D1076C2211yescharacteristic
45#22575415—21no—
46C22⋊C4×D269—21no—
47#22575387C2211yescharacteristic, complemented
48#22575378C2211yescharacteristic, complemented
49#22575378C2211yescharacteristic, complemented
50#22575375C2211yescharacteristic
51#22575375C2211yescharacteristic
52#22575375C2211yescharacteristic, complemented
53#22575375C2211yescharacteristic, complemented
54C2×M16×C269C2211yescharacteristic
55C22×C8×C269C2211yescharacteristic, complemented
56C4×D4×C269C2211yescharacteristic
57C4⋊C8×C269C2211yescharacteristic, complemented
58C22⋊C8×C269C2211yescharacteristic
59C22⋊C8×C269C2211yescharacteristic, complemented
60#97×C269C2211yescharacteristic, complemented
61C23×D269—21no—
62#16864402—22no—
63#16864402—22no—
64#16864402—22no—
65#16864402—41no—
66#16864402—41no—
67#16864402—41no—
68C2×Dic538C2311yescharacteristic
69C2×Dic538C2311yescharacteristic
70C2×D1076—22no—
71C2×D1076—21no—
72C2×D1076—21no—
73C2×D1076—21no—
74C2×D1076—41no—
75C2×D1076C2311yescharacteristic
76C2×D1076C2311yescharacteristic
77C2×D1076C2311yescharacteristic
78C2×D1076C2311yescharacteristic
79C2×C22⋊D269—21no—
80C2×C22⋊D269—21no—
81C2×C22⋊D269—21no—
82C2×C22⋊D269—21no—
83C2×C22⋊D269—21no—
84C2×C22⋊D269—21no—
85C2×C4×D269—21no—
86C2×C4×D269—21no—
87C2×C4×D269—21no—
88C2×C4×D269—21no—
89Dic1076—22no—
90#16864391—22no—
91#16864391—22no—
92#16864391—41no—
93#16864391D414yescomplemented
94D2152—22no—
95D2152—22no—
96D2152—22no—
97D2152—41no—
98C4⋊Dic269C2311yescharacteristic
99C4⋊Dic269C2311yescharacteristic
100#16864381—21no—
101#16864381—21no—
102C22⋊Dic269—21no—
103#16864379—21no—
104#16864379—21no—
105#16864379—21no—
106#16864379—21no—
107#16864379—21no—
108#16864379—21no—
109C4×Dic269—21no—
110C2×D4×C269D411yescharacteristic
111C22×C4×C269C2311yescharacteristic
112C22×C4×C269C2311yescharacteristic
113M16×C269—22no—
114C2×C8×C269—22no—
115C2×C8×C269C2311yescharacteristic
116C2×C8×C269C2311yescharacteristic
117C2×C8×C269C2311yescharacteristic
118C2×C8×C269C2311yescharacteristic
119C4⋊C4×C269D411yescharacteristic
120C22⋊C4×C269D411yescharacteristic
121C22⋊C4×C269D411yescharacteristic
122C42×C269C2311yescharacteristic
123C22×D269—21no—
124C22×D269—21no—
125C22×D269—21no—
126C22×D269—21no—
127C22×D269—42no—
128C22×D269—42no—
129C22×D269—81no—
130Dic538—21no—
131Dic538—21no—
132Dic538—21no—
133Dic538C2×D412yes—
134D1076—21no—
135D1076—21no—
136D1076—21no—
137D1076—21no—
138D1076—21no—
139D1076—21no—
140D1076—21no—
141D1076—42no—
142D1076—42no—
143D1076—81no—
144D1076C2×D412yes—
145C22⋊D269—42no—
146C22⋊D269—42no—
147C22⋊D269—42no—
148C22⋊D269—81no—
149C22⋊D269—81no—
150C22⋊D269—81no—
151C2×Dic269—21no—
152C2×Dic269—21no—
153C2×Dic269—21no—
154C2×Dic269—21no—
155C4×D269—42no—
156C4×D269—42no—
157C4×D269—42no—
158C4×D269—81no—
159C23×C269C2×D411yescharacteristic
160C23×C269C2×D411yescharacteristic
161D4×C269—41no—
162C2×C4×C269—21no—
163C2×C4×C269—21no—
164C2×C4×C269—21no—
165C2×C4×C269—21no—
166C2×C4×C269C2×D411yescharacteristic
167C2×C4×C269C2×D411yescharacteristic
168C2×C4×C269C2×D411yescharacteristic
169C2×C4×C269C2×D411yescharacteristic
170C2×C4×C269C2411yescharacteristic
171C8×C269—21no—
172C8×C269—21no—
173C8×C269—21no—
174C8×C269C2×D412yes—
175C22×C269—21no—
176C22×C269—21no—
177C22×C269—21no—
178C22×C269—21no—
179C22×C269—21no—
180C22×C269—21no—
181C22×C269C22×D411yescharacteristic
182C2×D269—22no—
183C2×D269—41no—
184C2×D269—41no—
185C2×D269—41no—
186C2×D269—41no—
187C2×D269—41no—
188C2×D269—41no—
189C2×D269—41no—
190C2×D269—41no—
191C2×D269—41no—
192C2×D269—41no—
193C2×D269—41no—
194C2×D269—84no—
195C4×C269—21no—
196C4×C269—21no—
197C4×C269—21no—
198C4×C269—21no—
199C4×C269C22×D411yescharacteristic
200C4×C269H(5,𝔽2)11yescharacteristic
201Dic269—22no—
202Dic269—41no—
203Dic269—41no—
204Dic269—41no—
205C2×C269—41no—
206C2×C269—41no—
207C2×C269D4211yescharacteristic
208C2×C269#57511yescharacteristic
209C2×C269#57611yescharacteristic
210D269—42no—
211D269—81no—
212D269—81no—
213D269—81no—
214C269#326811yescharacteristic, complemented, Sylow
215#3268—2691nomaximal, Sylow
216C2×AGL(1,ℤ/8)—2691no—
217C2×#135—2691no—
218#550—2691no—
219#546—2691no—
220#496—2691no—
221#468—2691no—
222#466—2691no—
223#464—2691no—
224#459—2691no—
225#452—2691no—
226#449—2691no—
227#449—2691no—
228#447—2691no—
229#440—2691no—
230#435D26911yescharacteristic, complemented
231C2×#41—2691no—
232C2×#41—2691no—
233C2×#41—2691no—
234C22×D4—2691no—
235AGL(1,ℤ/8)—5384no—
236#135—5384no—
237C2×Q16—2691no—
238C2×SD16—2691no—
239C2×SD16—2691no—
240C2×SD16—2691no—
241C2×SD16—2691no—
242C2×D8—2691no—
243C2×D8—2691no—
244C2×D8—2691no—
245C2×D8—2691no—
246C2×M16C2×D26911yescharacteristic
247C22×C8C2×D26911yescharacteristic, complemented
248#127—2691no—
249#127—5381no—
250#124—2691no—
251#123—5381no—
252C22⋊Q8—2691no—
253#121—2691no—
254#121—2691no—
255#121—2691no—
256#121—5381no—
257#121—5381no—
258#121—5381no—
259#120—5381no—
260C4×Q8—2691no—
261C4×D4—2691no—
262C4×D4—5381no—
263C4×D4C2×D26911yescharacteristic
264C2×C22⋊C4—5381no—
265#107—2691no—
266C4⋊C8C2×D26911yescharacteristic, complemented
267#103—2691no—
268#103—2691no—
269#102—2691no—
270#102—2691no—
271#102—2691no—
272#102—2691no—
273C22⋊C8C2×D26911yescharacteristic
274C22⋊C8C2×D26911yescharacteristic, complemented
275#97C2×D26911yescharacteristic, complemented
276C24—5381no—
277#41—5382no—
278#41—5382no—
279#41—5382no—
280#41—10761no—
281#41—10761no—
282#41—10761no—
283C2×Q8—2691no—
284C2×Q8—2691no—
285C2×D4—2691no—
286C2×D4—2691no—
287C2×D4—2691no—
288C2×D4—2691no—
289C2×D4—5382no—
290C2×D4—5381no—
291C2×D4—5381no—
292C2×D4—5381no—
293C2×D4—5381no—
294C2×D4—5381no—
295C2×D4—5381no—
296C2×D4—5381no—
297C2×D4—5381no—
298C2×D4—5381no—
299C2×D4—10761no—
300C2×D4D107611yescharacteristic
301C22×C4—5381no—
302C22×C4—5381no—
303C22×C4—5381no—
304C22×C4—5381no—
305C22×C4C22×D26911yescharacteristic
306C22×C4C22×D26911yescharacteristic
307Q16—5382no—
308SD16—2694no—
309SD16—5382no—
310SD16—5382no—
311SD16—10761no—
312D8—5382no—
313D8—5382no—
314D8—5382no—
315D8—10761no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D26911yescharacteristic
319C2×C8C22×D26911yescharacteristic
320C2×C8C22×D26911yescharacteristic
321C2×C8C22×D26911yescharacteristic
322C4⋊C4—2691no—
323C4⋊C4—2691no—
324C4⋊C4—5381no—
325C4⋊C4—5381no—
326C4⋊C4D107611yescharacteristic
327C22⋊C4—5381no—
328C22⋊C4—5381no—
329C22⋊C4—5381no—
330C22⋊C4—5381no—
331C22⋊C4—5381no—
332C22⋊C4—5381no—
333C22⋊C4—5381no—
334C22⋊C4D107611yescharacteristic
335C22⋊C4D107611yescharacteristic
336C42—5381no—
337C42C22×D26911yescharacteristic
338C23—5381no—
339C23—5381no—
340C23—5381no—
341C23—5381no—
342C23—10762no—
343C23—10762no—
344C23—21521no—
345C23C2×D107611yescharacteristic
346C23C2×D107611yescharacteristic
347Q8—2692no—
348Q8—5381no—
349Q8—5381no—
350Q8—5381no—
351D4—41no—
352D4—2692no—
353D4—5381no—
354D4—5381no—
355D4—5381no—
356D4—5381no—
357D4—5381no—
358D4—5381no—
359D4—5381no—
360D4—10762no—
361D4—10762no—
362D4—10762no—
363D4—10762no—
364D4—10762no—
365D4—21521no—
366D4—21521no—
367D4—21521no—
368D4—21521no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—5381no—
374C2×C4—5381no—
375C2×C4—5381no—
376C2×C4—5381no—
377C2×C4—10762no—
378C2×C4—10762no—
379C2×C4—10762no—
380C2×C4—21521no—
381C2×C4C2×D107611yescharacteristic
382C2×C4C2×D107611yescharacteristic
383C2×C4C2×D107611yescharacteristic
384C2×C4C2×D107611yescharacteristic
385C2×C4C23×D26911yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D26912yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—5382no—
397C22—10761no—
398C22—10761no—
399C22—10761no—
400C22—10761no—
401C22—10761no—
402C22—10761no—
403C22—10761no—
404C22—10761no—
405C22—10761no—
406C22—10761no—
407C22—10761no—
408C22—21524no—
409C22C22×D107611yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—5382no—
415C4—10761no—
416C4—10761no—
417C4—10761no—
418C4C2×D4×D26911yescharacteristic
419C4#2257549911yescharacteristic
420C2—41no—
421C2—41no—
422C2—10762no—
423C2—21521no—
424C2—21521no—
425C2—21521no—
426C2D4×D107611yescharacteristic
427C2#3177140511yescharacteristic
428C2#3177141011yescharacteristic
subgroupG/H
centerC22C22×D1076
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#435×C269C2
socleC22×C269C22×D4
hypercenter#435D269
hypocenterC269#3268
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#22575481C2semidirect
2. C2×#22575475C2semidirect
3. #31771276C2semidirect
4. #31771251C2semidirect
5. #31770994C2semidirect
6. #31770851C2semidirect
7. #31770841C2semidirect
8. #31770828C2semidirect
9. #31770801C2semidirect
10. #31770769C2semidirect
11. #31770752C2semidirect
12. #31770752C2semidirect
13. #31770741C2semidirect
14. #31770707C2semidirect
15. #435×C269C2semidirect
18. C2×#16864402C22semidirect
22. C2×Dic1076C22semidirect
25. C2×#16864391C22semidirect
26. C2×#16864391C22semidirect
31. #22575450C22semidirect
38. #22575427C22semidirect
43. C4×Dic538C22semidirect
47. #22575387C22semidirect
48. #22575378C22semidirect
49. #22575378C22semidirect
52. #22575375C22semidirect
53. #22575375C22semidirect
55. C22×C8×C269C22semidirect
57. C4⋊C8×C269C22semidirect
59. C22⋊C8×C269C22semidirect
60. #97×C269C22semidirect
93. #16864391D4semidirect
214. C269#3268semidirect
230. #435D269semidirect
247. C22×C8C2×D269semidirect
266. C4⋊C8C2×D269semidirect
274. C22⋊C8C2×D269semidirect
275. #97C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754812
C2×#225754752
#317712762
#317712512
#317709942
#317708512
#317708412
#317708282
#317708012
#317707692
#317707522
#317707412
#317707072
#435×C2692
#3268269