Finite Group Databasebeta

← #46822386

Subgroups — #46822386

Order 34432.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575477C211yesmaximal, characteristic, complemented
2C2×SD16×D269C211yesmaximal, characteristic, complemented
3#31771263C211yesmaximal, characteristic, complemented
4D4×D1076C211yesmaximal, characteristic, complemented
5#31770995C211yesmaximal, characteristic, complemented
6#31770854C211yesmaximal, characteristic, complemented
7#31770840C211yesmaximal, characteristic, complemented
8#31770806C211yesmaximal, characteristic, complemented
9#31770754C211yesmaximal, characteristic, complemented
10#31770751C211yesmaximal, characteristic, complemented
11#31770745C211yesmaximal, characteristic, complemented
12#31770737C211yesmaximal, characteristic, complemented
13#31770705C211yesmaximal, characteristic, complemented
14#31770675C211yesmaximal, characteristic, complemented
15#463×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic, complemented
17C2×Q8×D269C2211yescharacteristic, complemented
18C22×D1076—21no—
19C2×D4×D269C2211yescharacteristic
20C2×D4×D269C2211yescharacteristic
21#22575477—24no—
22C2×#16864391C2211yescharacteristic, complemented
23C2×#16864391C2211yescharacteristic, complemented
24C2×#16864390C2211yescharacteristic
25C2×#16864389C2211yescharacteristic, complemented
26C2×#16864389C2211yescharacteristic, complemented
27SD16×D269—24no—
28C2×#16864387C2211yescharacteristic, complemented
29C2×#16864387C2211yescharacteristic, complemented
30C2×#16864385C2211yescharacteristic, complemented
31C2×C8×D269C2211yescharacteristic, complemented
32#22575450C2211yescharacteristic
33#22575439—21no—
34#22575430—21no—
35#22575429C2211yescharacteristic, complemented
36#22575428C2211yescharacteristic
37#22575428C2211yescharacteristic
38#22575427—21no—
39#22575426—21no—
40#22575424C2211yescharacteristic, complemented
41#22575423—21no—
42#22575423—21no—
43C4×Dic538C2211yescharacteristic, complemented
44C4×D1076C2211yescharacteristic
45#22575413—21no—
46#22575386C2211yescharacteristic, complemented
47#22575376C2211yescharacteristic, complemented
48#22575375C2211yescharacteristic, complemented
49#22575375C2211yescharacteristic, complemented
50#22575374C2211yescharacteristic
51#22575365C2211yescharacteristic, complemented
52#22575365C2211yescharacteristic, complemented
53#22575364C2211yescharacteristic, complemented
54C2×SD16×C269C2211yescharacteristic
55C2×D8×C269C2211yescharacteristic
56#124×C269C2211yescharacteristic, complemented
57C4×D4×C269C2211yescharacteristic
58C4⋊C8×C269C2211yescharacteristic, complemented
59#103×C269C2211yescharacteristic, complemented
60#102×C269C2211yescharacteristic, complemented
61C23×D269—21no—
62C23×D269—21no—
63#16864401—22no—
64#16864401—41no—
65C2×Dic538—21no—
66C2×Dic538C2311yescharacteristic
67Q8×D269—22no—
68Q8×D269—41no—
69C2×D1076—21no—
70C2×D1076—21no—
71C2×D1076—21no—
72C2×D1076—21no—
73C2×D1076—44no—
74C2×D1076D411yescharacteristic
75C2×D1076C2311yescharacteristic
76C2×D1076C2311yescharacteristic
77C2×C22⋊D269—21no—
78C2×C22⋊D269—21no—
79C2×C22⋊D269—21no—
80C2×C22⋊D269—21no—
81D4×D269—22no—
82D4×D269—22no—
83D4×D269—41no—
84D4×D269—41no—
85C22×Dic269—21no—
86C2×C4×D269—21no—
87C2×C4×D269C2311yescharacteristic
88C2×C4×D269C2311yescharacteristic
89#16864391—22no—
90#16864391—22no—
91#16864390D414yescomplemented
92#16864389—22no—
93#16864389—41no—
94#16864387—22no—
95#16864387—41no—
96#16864385—22no—
97C2×#14524130C2311yescharacteristic
98C2×#14524130C2311yescharacteristic
99C8×D269—22no—
100C4⋊Dic269D411yescharacteristic
101C4⋊Dic269C2311yescharacteristic
102#16864381—21no—
103#16864381—21no—
104C22⋊Dic269—21no—
105#16864379—21no—
106#16864379—21no—
107#16864379—21no—
108#16864379D411yescharacteristic
109#16864379D411yescharacteristic
110C4×Dic269—21no—
111C2×Q8×C269C2311yescharacteristic
112C2×D4×C269C2311yescharacteristic
113C2×D4×C269C2311yescharacteristic
114C22×C4×C269—21no—
115SD16×C269—22no—
116D8×C269—22no—
117C2×C8×C269C2311yescharacteristic
118C2×C8×C269C2311yescharacteristic
119C4⋊C4×C269C2311yescharacteristic
120C22⋊C4×C269—21no—
121C22⋊C4×C269—21no—
122C22⋊C4×C269—21no—
123C42×C269C2311yescharacteristic
124C22×D269—21no—
125C22×D269—21no—
126C22×D269—42no—
127C22×D269—42no—
128C22×D269—42no—
129C22×D269—42no—
130C22×D269—81no—
131C22×D269—81no—
132C22×D269C2×D411yescharacteristic
133C22×D269C2×D411yescharacteristic
134Dic538—21no—
135Dic538—42no—
136Dic538C2×D412yescomplemented
137D1076—22no—
138D1076—21no—
139D1076—21no—
140D1076—21no—
141D1076—21no—
142D1076—42no—
143D1076—42no—
144D1076—42no—
145D1076—81no—
146C22⋊D269—42no—
147C22⋊D269—42no—
148C22⋊D269—42no—
149C22⋊D269—42no—
150C2×Dic269—21no—
151C2×Dic269—21no—
152C2×Dic269—42no—
153C2×Dic269C2×D411yescharacteristic
154C2×Dic269C2×D411yescharacteristic
155C4×D269—21no—
156C4×D269—21no—
157C4×D269—21no—
158C4×D269—21no—
159C4×D269—42no—
160#14524130—21no—
161#14524130C2×D412yescomplemented
162C23×C269—21no—
163C23×C269—21no—
164Q8×C269—21no—
165Q8×C269—21no—
166D4×C269—21no—
167D4×C269—21no—
168D4×C269—21no—
169D4×C269C2×D412yes—
170C2×C4×C269—21no—
171C2×C4×C269—21no—
172C2×C4×C269—42no—
173C2×C4×C269C2×D411yescharacteristic
174C2×C4×C269C2×D411yescharacteristic
175C2×C4×C269C2411yescharacteristic
176C8×C269—21no—
177C8×C269—21no—
178C22×C269—22no—
179C22×C269—41no—
180C22×C269—41no—
181C22×C269—41no—
182C22×C269—41no—
183C22×C269—41no—
184C22×C269C22×D411yescharacteristic
185C2×D269—21no—
186C2×D269—21no—
187C2×D269—21no—
188C2×D269—21no—
189C2×D269—21no—
190C2×D269—41no—
191C2×D269—41no—
192C2×D269—41no—
193C2×D269—41no—
194C2×D269—41no—
195C2×D269—41no—
196C2×D269—84no—
197C2×D269—84no—
198C2×D269AGL(1,ℤ/8)12yescomplemented
199C4×C269—21no—
200C4×C269—21no—
201C4×C269—41no—
202C4×C269—41no—
203C4×C269C22×D411yescharacteristic
204C4×C269H(5,𝔽2)11yescharacteristic
205Dic269—21no—
206Dic269—21no—
207Dic269—22no—
208Dic269—41no—
209C2×C269—42no—
210C2×C269—81no—
211C2×C269D4211yescharacteristic
212C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C269#57711yescharacteristic
214D269—22no—
215D269—41no—
216D269—81no—
217D269—81no—
218C269#326511yescharacteristic, complemented, Sylow
219#3265—2691nomaximal, Sylow
220C2×AGL(1,ℤ/8)—2691no—
221C22×SD16—2691no—
222#548—2691no—
223D42—2691no—
224#496—2691no—
225#468—2691no—
226#466—2691no—
227#463D26911yescharacteristic, complemented
228#460—2691no—
229#450—2691no—
230#449—2691no—
231#448—2691no—
232#447—2691no—
233#440—2691no—
234#435—2691no—
235C2×#41—2691no—
236C22×Q8—2691no—
237C22×D4—2691no—
238C22×D4—2691no—
239C22×D4—5381no—
240AGL(1,ℤ/8)—5384no—
241C2×SD16—2691no—
242C2×SD16—2691no—
243C2×SD16—2691no—
244C2×SD16—2691no—
245C2×SD16—2691no—
246C2×SD16—5384no—
247C2×SD16C2×D26911yescharacteristic
248C2×D8—2691no—
249C2×D8—2691no—
250C2×D8C2×D26911yescharacteristic
251C2×M16—2691no—
252C22×C8—2691no—
253#127—2691no—
254#124—5381no—
255#124C2×D26911yescharacteristic, complemented
256C22⋊Q8—2691no—
257C22⋊Q8—5381no—
258#121—2691no—
259#121—2691no—
260#121—2691no—
261#121—5381no—
262#121—5381no—
263#120—5381no—
264#120—5381no—
265C4×Q8—2691no—
266C4×D4—2691no—
267C4×D4—5381no—
268C4×D4C2×D26911yescharacteristic
269#107—2691no—
270C4⋊C8C2×D26911yescharacteristic, complemented
271#103—2691no—
272#103C2×D26911yescharacteristic, complemented
273#102—2691no—
274#102—2691no—
275#102—2691no—
276#102C2×D26911yescharacteristic, complemented
277C22⋊C8—2691no—
278C22⋊C8—2691no—
279#97—2691no—
280C24—5381no—
281C24—5381no—
282#41—5382no—
283#41—10761no—
284C2×Q8—2691no—
285C2×Q8—5381no—
286C2×Q8—5382no—
287C2×Q8—10761no—
288C2×Q8C22×D26911yescharacteristic
289C2×D4—2691no—
290C2×D4—2691no—
291C2×D4—2691no—
292C2×D4—5381no—
293C2×D4—5381no—
294C2×D4—5381no—
295C2×D4—5381no—
296C2×D4—5382no—
297C2×D4—5382no—
298C2×D4—5381no—
299C2×D4—5381no—
300C2×D4—5381no—
301C2×D4—5381no—
302C2×D4—10764no—
303C2×D4—10761no—
304C2×D4—10761no—
305C2×D4C22×D26911yescharacteristic
306C2×D4C22×D26911yescharacteristic
307C22×C4—21no—
308C22×C4—2691no—
309C22×C4—2691no—
310C22×C4—5381no—
311C22×C4—5381no—
312SD16—22no—
313SD16—2694no—
314SD16—5382no—
315SD16—5382no—
316SD16—5382no—
317SD16—10761no—
318D8—22no—
319D8—5382no—
320D8—10761no—
321M16—5382no—
322C2×C8—2691no—
323C2×C8—2691no—
324C2×C8—5382no—
325C2×C8C22×D26911yescharacteristic
326C2×C8C22×D26911yescharacteristic
327C4⋊C4—2691no—
328C4⋊C4—2691no—
329C4⋊C4—5381no—
330C4⋊C4—5381no—
331C4⋊C4C22×D26911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—2691no—
336C22⋊C4—2691no—
337C22⋊C4—5381no—
338C22⋊C4—5381no—
339C22⋊C4—5381no—
340C22⋊C4—5381no—
341C42—5381no—
342C42C22×D26911yescharacteristic
343C23—21no—
344C23—21no—
345C23—2691no—
346C23—2691no—
347C23—5381no—
348C23—5381no—
349C23—10762no—
350C23—10762no—
351C23—10762no—
352C23—10762no—
353C23—21521no—
354C23—21521no—
355Q8—21no—
356Q8—21no—
357Q8—2692no—
358Q8—5381no—
359Q8—10762no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—5382no—
364D4—5381no—
365D4—5381no—
366D4—5381no—
367D4—5381no—
368D4—10762no—
369D4—10762no—
370D4—10762no—
371D4—10762no—
372D4—10762no—
373D4—10762no—
374D4—10762no—
375D4—21521no—
376D4D4×D26912yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—2691no—
381C2×C4—2691no—
382C2×C4—5381no—
383C2×C4—5381no—
384C2×C4—5381no—
385C2×C4—5381no—
386C2×C4—5381no—
387C2×C4—5381no—
388C2×C4—10762no—
389C2×C4—10762no—
390C2×C4D4×D26911yescharacteristic
391C2×C4D4×D26911yescharacteristic
392C2×C4C23×D26911yescharacteristic
393C8—21no—
394C8—21no—
395C8—2692no—
396C8—5381no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—2692no—
404C22—5381no—
405C22—5381no—
406C22—5381no—
407C22—5381no—
408C22—5381no—
409C22—10761no—
410C22—10761no—
411C22—10761no—
412C22—10761no—
413C22—10761no—
414C22—10761no—
415C22—21524no—
416C22—21524no—
417C22C2×D4×D26911yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—5381no—
423C4—5381no—
424C4—5382no—
425C4—10761no—
426C4C2×D4×D26911yescharacteristic
427C4#2257549911yescharacteristic
428C2—42no—
429C2—81no—
430C2—5382no—
431C2—10761no—
432C2—21521no—
433C2—21521no—
434C2#3177123911yescharacteristic
435C2AGL(1,ℤ/8)×D26911yescharacteristic
436C2#3177141211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#463×C269C2
socleC22×C269C22×D4
hypercenter#463D269
hypocenterC269#3265
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#22575477C2semidirect
2. C2×SD16×D269C2semidirect
3. #31771263C2semidirect
4. D4×D1076C2semidirect
5. #31770995C2semidirect
6. #31770854C2semidirect
7. #31770840C2semidirect
8. #31770806C2semidirect
9. #31770754C2semidirect
10. #31770751C2semidirect
11. #31770745C2semidirect
12. #31770737C2semidirect
13. #31770705C2semidirect
14. #31770675C2semidirect
15. #463×C269C2semidirect
16. C2×#16864401C22semidirect
17. C2×Q8×D269C22semidirect
22. C2×#16864391C22semidirect
23. C2×#16864391C22semidirect
25. C2×#16864389C22semidirect
26. C2×#16864389C22semidirect
28. C2×#16864387C22semidirect
29. C2×#16864387C22semidirect
30. C2×#16864385C22semidirect
31. C2×C8×D269C22semidirect
35. #22575429C22semidirect
40. #22575424C22semidirect
43. C4×Dic538C22semidirect
46. #22575386C22semidirect
47. #22575376C22semidirect
48. #22575375C22semidirect
49. #22575375C22semidirect
51. #22575365C22semidirect
52. #22575365C22semidirect
53. #22575364C22semidirect
56. #124×C269C22semidirect
58. C4⋊C8×C269C22semidirect
59. #103×C269C22semidirect
60. #102×C269C22semidirect
91. #16864390D4semidirect
136. Dic538C2×D4semidirect
161. #14524130C2×D4semidirect
198. C2×D269AGL(1,ℤ/8)semidirect
218. C269#3265semidirect
227. #463D269semidirect
255. #124C2×D269semidirect
270. C4⋊C8C2×D269semidirect
272. #103C2×D269semidirect
276. #102C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754772
C2×SD16×D2692
#317712632
D4×D10762
#317709952
#317708542
#317708402
#317708062
#317707542
#317707512
#317707452
#317707372
#317707052
#317706752
#463×C2692
#3265269