Finite Group Databasebeta

← #46822376

Subgroups — #46822376

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×#22575479C211yesmaximal, characteristic, complemented
2C22×#16864390C211yesmaximal, characteristic, complemented
3#31771264C211yesmaximal, characteristic, complemented
4#31770992C211yesmaximal, characteristic, complemented
5#31770849C211yesmaximal, characteristic, complemented
6#31770839C211yesmaximal, characteristic, complemented
7#31770820C211yesmaximal, characteristic, complemented
8#31770802C211yesmaximal, characteristic, complemented
9#31770756C211yesmaximal, characteristic, complemented
10#31770748C211yesmaximal, characteristic, complemented
11#31770743C211yesmaximal, characteristic, complemented
12#31770739C211yesmaximal, characteristic, complemented
13#31770705C211yesmaximal, characteristic, complemented
14#31770677C211yesmaximal, characteristic, complemented
15D42×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic, complemented
17C22×Dic538C2211yescharacteristic, complemented
18#22575479—24no—
19C2×#16864390—24no—
20C2×#16864390C2211yescharacteristic
21C2×#16864390C2211yescharacteristic
22C2×#16864390C2211yescharacteristic, complemented
23C2×#16864390C2211yescharacteristic, complemented
24C2×#16864390C2211yescharacteristic, complemented
25C2×#16864390C2211yescharacteristic, complemented
26C2×#16864387C2211yescharacteristic
27C2×#16864387C2211yescharacteristic, complemented
28C2×#16864387C2211yescharacteristic, complemented
29C2×#16864386C2211yescharacteristic, complemented
30C22×#14524130C2211yescharacteristic, complemented
31#22575441C2211yescharacteristic, complemented
32#22575439—21no—
33#22575432C2211yescharacteristic, complemented
34#22575431—21no—
35#22575427C2211yescharacteristic, complemented
36#22575425—21no—
37C4×Dic538C2211yescharacteristic, complemented
38#22575413—21no—
39#22575386C2211yescharacteristic, complemented
40C4⋊#14524130C2211yescharacteristic, complemented
41#22575376C2211yescharacteristic, complemented
42#22575376C2211yescharacteristic, complemented
43#22575374C2211yescharacteristic
44#22575374C2211yescharacteristic, complemented
45#22575374C2211yescharacteristic, complemented
46#22575373C2211yescharacteristic, complemented
47C22⋊#14524130C2211yescharacteristic, complemented
48C22⋊#14524130C2211yescharacteristic, complemented
49#22575364C2211yescharacteristic, complemented
50C22×D4×C269—21no—
51C22×D4×C269C2211yescharacteristic
52C22×D4×C269C2211yescharacteristic
53#127×C269C2211yescharacteristic
54#121×C269—21no—
55#121×C269C2211yescharacteristic
56#121×C269C2211yescharacteristic
57#120×C269—21no—
58#120×C269—21no—
59C4×D4×C269C2211yescharacteristic
60C4×D4×C269C2211yescharacteristic
61#16864402—22no—
62#16864402—41no—
63C2×Dic538—22no—
64C2×Dic538—21no—
65C2×Dic538—41no—
66C2×Dic538C2311yescharacteristic
67C2×Dic538C2311yescharacteristic
68C2×D1076C2311yescharacteristic
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71C22×Dic269—21no—
72C2×C4×D269—21no—
73#16864390—22no—
74#16864390—22no—
75#16864390—22no—
76#16864390—22no—
77#16864390—41no—
78#16864390D414yescomplemented
79#16864387—22no—
80#16864387—22no—
81#16864387—41no—
82#16864386—22no—
83C2×#14524130—22no—
84C2×#14524130C2311yescharacteristic
85C2×#14524130C2311yescharacteristic
86C2×#14524130C2311yescharacteristic
87C2×#14524130C2311yescharacteristic
88C4⋊Dic269C2311yescharacteristic
89#16864381—21no—
90#16864381—21no—
91C22⋊Dic269—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95C4×Dic269—21no—
96C24×C269—21no—
97C24×C269—21no—
98C2×D4×C269—22no—
99C2×D4×C269—22no—
100C2×D4×C269—21no—
101C2×D4×C269—21no—
102C2×D4×C269—21no—
103C2×D4×C269—21no—
104C2×D4×C269—21no—
105C2×D4×C269—21no—
106C2×D4×C269—41no—
107C2×D4×C269—41no—
108C2×D4×C269—44no—
109C2×D4×C269D411yescharacteristic
110C2×D4×C269C2311yescharacteristic
111C2×D4×C269C2311yescharacteristic
112C2×D4×C269C2311yescharacteristic
113C22×C4×C269—21no—
114C22×C4×C269C2311yescharacteristic
115C22×C4×C269C2311yescharacteristic
116C4⋊C4×C269D411yescharacteristic
117C4⋊C4×C269C2311yescharacteristic
118C22⋊C4×C269—21no—
119C22⋊C4×C269—21no—
120C22⋊C4×C269—21no—
121C22⋊C4×C269D411yescharacteristic
122C22⋊C4×C269D411yescharacteristic
123C42×C269C2311yescharacteristic
124C22×D269—21no—
125Dic538—21no—
126Dic538—21no—
127Dic538—21no—
128Dic538—42no—
129Dic538C2×D412yescomplemented
130D1076—21no—
131D1076—21no—
132C22⋊D269—42no—
133C22⋊D269—42no—
134C2×Dic269—21no—
135C2×Dic269—21no—
136C2×Dic269—21no—
137C2×Dic269—42no—
138C4×D269—42no—
139#14524130—21no—
140#14524130—21no—
141#14524130—21no—
142#14524130C2×D412yescomplemented
143C23×C269—21no—
144C23×C269—21no—
145C23×C269—21no—
146C23×C269—42no—
147C23×C269—42no—
148C23×C269—42no—
149C23×C269—42no—
150C23×C269—81no—
151C23×C269—81no—
152C23×C269C2×D411yescharacteristic
153C23×C269C2×D411yescharacteristic
154D4×C269—22no—
155D4×C269—21no—
156D4×C269—21no—
157D4×C269—21no—
158D4×C269—21no—
159D4×C269—21no—
160D4×C269—42no—
161D4×C269—42no—
162D4×C269—42no—
163D4×C269—42no—
164D4×C269—42no—
165D4×C269—81no—
166D4×C269C2×D412yes—
167C2×C4×C269—21no—
168C2×C4×C269—21no—
169C2×C4×C269—21no—
170C2×C4×C269—21no—
171C2×C4×C269—21no—
172C2×C4×C269—42no—
173C2×C4×C269C2×D411yescharacteristic
174C2×C4×C269C2×D411yescharacteristic
175C2×C4×C269C2×D411yescharacteristic
176C2×C4×C269C2×D411yescharacteristic
177C2×C4×C269C2411yescharacteristic
178C22×C269—21no—
179C22×C269—21no—
180C22×C269—21no—
181C22×C269—22no—
182C22×C269—21no—
183C22×C269—21no—
184C22×C269—41no—
185C22×C269—41no—
186C22×C269—41no—
187C22×C269—41no—
188C22×C269—41no—
189C22×C269—41no—
190C22×C269—41no—
191C22×C269—41no—
192C22×C269—84no—
193C22×C269—84no—
194C22×C269AGL(1,ℤ/8)12yescomplemented
195C22×C269C22×D411yescharacteristic
196C2×D269—41no—
197C2×D269—41no—
198C2×D269—41no—
199C4×C269—21no—
200C4×C269—21no—
201C4×C269—21no—
202C4×C269—21no—
203C4×C269—41no—
204C4×C269C22×D411yescharacteristic
205C4×C269H(5,𝔽2)11yescharacteristic
206Dic269—22no—
207Dic269—41no—
208Dic269—41no—
209C2×C269—22no—
210C2×C269—41no—
211C2×C269—42no—
212C2×C269—81no—
213C2×C269—81no—
214C2×C269D4211yescharacteristic
215C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
216C2×C269#57711yescharacteristic
217D269—81no—
218C269#326511yescharacteristic, complemented, Sylow
219#3265—2691nomaximal, Sylow
220C2×AGL(1,ℤ/8)—2691no—
221C22×SD16—2691no—
222#548—2691no—
223D42D26911yescharacteristic, complemented
224#496—2691no—
225#468—2691no—
226#466—2691no—
227#463—2691no—
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—21no—
238C22×D4C2×D26911yescharacteristic
239C22×D4C2×D26911yescharacteristic
240AGL(1,ℤ/8)—5384no—
241C2×SD16—2691no—
242C2×SD16—2691no—
243C2×SD16—2691no—
244C2×SD16—2691no—
245C2×SD16—2691no—
246C2×SD16—2691no—
247C2×SD16—5384no—
248C2×D8—2691no—
249C2×D8—2691no—
250C2×D8—2691no—
251C2×M16—2691no—
252C22×C8—2691no—
253#127C2×D26911yescharacteristic
254#124—2691no—
255#124—5381no—
256C22⋊Q8—2691no—
257C22⋊Q8—5381no—
258#121—21no—
259#121—2691no—
260#121—5381no—
261#121C2×D26911yescharacteristic
262#121C2×D26911yescharacteristic
263#120—21no—
264#120—21no—
265C4×Q8—2691no—
266C4×D4—5381no—
267C4×D4C2×D26911yescharacteristic
268C4×D4C2×D26911yescharacteristic
269#107—2691no—
270C4⋊C8—2691no—
271#103—2691no—
272#103—2691no—
273#102—2691no—
274#102—2691no—
275#102—2691no—
276#102—2691no—
277C22⋊C8—2691no—
278C22⋊C8—2691no—
279#97—2691no—
280C24—21no—
281C24—21no—
282#41—5382no—
283#41—10761no—
284C2×Q8—2691no—
285C2×Q8—2691no—
286C2×Q8—5382no—
287C2×Q8—5381no—
288C2×Q8—10761no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—2691no—
301C2×D4—5381no—
302C2×D4—5381no—
303C2×D4C22⋊D26911yescharacteristic
304C2×D4C22×D26911yescharacteristic
305C2×D4C22×D26911yescharacteristic
306C2×D4C22×D26911yescharacteristic
307C22×C4—21no—
308C22×C4—5381no—
309C22×C4—5381no—
310C22×C4C22×D26911yescharacteristic
311C22×C4C22×D26911yescharacteristic
312SD16—2694no—
313SD16—5382no—
314SD16—5382no—
315SD16—5382no—
316SD16—5382no—
317SD16—10761no—
318D8—5382no—
319D8—5382no—
320D8—10761no—
321M16—5382no—
322C2×C8—2691no—
323C2×C8—2691no—
324C2×C8—2691no—
325C2×C8—2691no—
326C2×C8—5382no—
327C4⋊C4—2691no—
328C4⋊C4—5381no—
329C4⋊C4—5381no—
330C4⋊C4C22⋊D26911yescharacteristic
331C4⋊C4C22×D26911yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—5381no—
336C22⋊C4—5381no—
337C22⋊C4—5381no—
338C22⋊C4—5381no—
339C22⋊C4C22⋊D26911yescharacteristic
340C22⋊C4C22⋊D26911yescharacteristic
341C42—5381no—
342C42C22×D26911yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—5381no—
353C23C2×C22⋊D26911yescharacteristic
354C23C2×C22⋊D26911yescharacteristic
355Q8—2692no—
356Q8—5381no—
357Q8—5381no—
358Q8—5381no—
359Q8—10762no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—5381no—
373D4—5381no—
374D4—10762no—
375D4—10762no—
376D4D4×D26912yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—5381no—
384C2×C4—5381no—
385C2×C4—5381no—
386C2×C4—10762no—
387C2×C4—10762no—
388C2×C4C2×C22⋊D26911yescharacteristic
389C2×C4C2×C22⋊D26911yescharacteristic
390C2×C4C2×C22⋊D26911yescharacteristic
391C2×C4C2×C22⋊D26911yescharacteristic
392C2×C4C23×D26911yescharacteristic
393C8—2692no—
394C8—5381no—
395C8—5381no—
396C8—5381no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—10761no—
414C22—10761no—
415C22—10761no—
416C22#2257547912yescomplemented
417C22C22×C22⋊D26911yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—5382no—
424C4—10761no—
425C4—10761no—
426C4C2×D4×D26911yescharacteristic
427C4#2257549811yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—21521no—
434C2D4×C22⋊D26911yescharacteristic
435C2C2×#2257547911yescharacteristic
436C2#3177141611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingD42×C269C2
socleC22×C269C22×D4
hypercenterD42D269
hypocenterC269#3265
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#22575479C2semidirect
2. C22×#16864390C2semidirect
3. #31771264C2semidirect
4. #31770992C2semidirect
5. #31770849C2semidirect
6. #31770839C2semidirect
7. #31770820C2semidirect
8. #31770802C2semidirect
9. #31770756C2semidirect
10. #31770748C2semidirect
11. #31770743C2semidirect
12. #31770739C2semidirect
13. #31770705C2semidirect
14. #31770677C2semidirect
15. D42×C269C2semidirect
16. C2×#16864402C22semidirect
17. C22×Dic538C22semidirect
22. C2×#16864390C22semidirect
23. C2×#16864390C22semidirect
24. C2×#16864390C22semidirect
25. C2×#16864390C22semidirect
27. C2×#16864387C22semidirect
28. C2×#16864387C22semidirect
29. C2×#16864386C22semidirect
30. C22×#14524130C22semidirect
31. #22575441C22semidirect
33. #22575432C22semidirect
35. #22575427C22semidirect
37. C4×Dic538C22semidirect
39. #22575386C22semidirect
40. C4⋊#14524130C22semidirect
41. #22575376C22semidirect
42. #22575376C22semidirect
44. #22575374C22semidirect
45. #22575374C22semidirect
46. #22575373C22semidirect
47. C22⋊#14524130C22semidirect
48. C22⋊#14524130C22semidirect
49. #22575364C22semidirect
78. #16864390D4semidirect
129. Dic538C2×D4semidirect
142. #14524130C2×D4semidirect
194. C22×C269AGL(1,ℤ/8)semidirect
218. C269#3265semidirect
223. D42D269semidirect
416. C22#22575479semidirect

Maximal subgroups

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

subgroupindex
C2×#225754792
C22×#168643902
#317712642
#317709922
#317708492
#317708392
#317708202
#317708022
#317707562
#317707482
#317707432
#317707392
#317707052
#317706772
D42×C2692
#3265269