Finite Group Databasebeta

← #46822555

Subgroups — #46822555

Order 34432.

620 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#16864387C211yesmaximal, characteristic, complemented
2C2×D8×D269C211yesmaximal, characteristic, complemented
3#31771239C211yesmaximal, characteristic, complemented
4D4×C22⋊D269C211yesmaximal, characteristic, complemented
5#31770980C211yesmaximal, characteristic, complemented
6#31770840C211yesmaximal, characteristic, complemented
7#31770839C211yesmaximal, characteristic, complemented
8#31770799C211yesmaximal, characteristic, complemented
9#31770798C211yesmaximal, characteristic, complemented
10#31770741C211yesmaximal, characteristic, complemented
11#31770740C211yesmaximal, characteristic, complemented
12#31770737C211yesmaximal, characteristic, complemented
13#31770685C211yesmaximal, characteristic, complemented
14#31770668C211yesmaximal, characteristic, complemented
15#447×C269C211yesmaximal, characteristic, complemented
16C22×D1076C2211yescharacteristic, complemented
17C22×C22⋊D269—21no—
18C2×D4×D269—21no—
19C2×D4×D269C2211yescharacteristic, complemented
20C2×D4×D269C2211yescharacteristic, complemented
21C2×D2152C2211yescharacteristic, complemented
22C2×D2152C2211yescharacteristic, complemented
23C2×#16864387—24no—
24C2×#16864387C2211yescharacteristic
25C2×#16864387C2211yescharacteristic, complemented
26C2×#16864387C2211yescharacteristic, complemented
27C2×#16864387C2211yescharacteristic, complemented
28C2×#16864387C2211yescharacteristic, complemented
29D8×D269—24no—
30C22×#14524130C2211yescharacteristic, complemented
31C2×C8×D269C2211yescharacteristic, complemented
32#22575449C2211yescharacteristic, complemented
33#22575449C2211yescharacteristic, complemented
34#22575428C2211yescharacteristic, complemented
35#22575427C2211yescharacteristic, complemented
36#22575426—21no—
37#22575425—21no—
38#22575424C2211yescharacteristic, complemented
39#22575423—21no—
40#22575422—21no—
41#22575421—21no—
42#22575421—21no—
43D4×Dic269C2211yescharacteristic, complemented
44#22575415C2211yescharacteristic, complemented
45C4×C22⋊D269C2211yescharacteristic
46#22575386C2211yescharacteristic, complemented
47#22575382C2211yescharacteristic, complemented
48#22575375C2211yescharacteristic, complemented
49#22575375C2211yescharacteristic, complemented
50#22575374C2211yescharacteristic, complemented
51#22575373C2211yescharacteristic, complemented
52#22575365C2211yescharacteristic, complemented
53C8×Dic269C2211yescharacteristic, complemented
54C22×D4×C269C2211yescharacteristic, complemented
55C2×D8×C269C2211yescharacteristic, complemented
56C2×D8×C269C2211yescharacteristic, complemented
57#121×C269C2211yescharacteristic, complemented
58#102×C269C2211yescharacteristic, complemented
59#102×C269C2211yescharacteristic, complemented
60C22⋊C8×C269C2211yescharacteristic, complemented
61C23×D269—21no—
62C23×D269—21no—
63C23×D269—21no—
64C2×D1076—22no—
65C2×D1076—21no—
66C2×D1076—21no—
67C2×D1076—41no—
68C2×D1076C2311yescharacteristic
69C2×D1076C2311yescharacteristic
70C2×D1076C2311yescharacteristic
71C2×C22⋊D269—21no—
72C2×C22⋊D269—21no—
73C2×C22⋊D269—21no—
74C2×C22⋊D269—21no—
75C2×C22⋊D269—21no—
76C2×C22⋊D269—21no—
77C2×C22⋊D269—21no—
78C2×C22⋊D269—21no—
79C2×C22⋊D269—44no—
80C2×C22⋊D269D411yescharacteristic
81D4×D269—22no—
82D4×D269—22no—
83D4×D269—41no—
84D4×D269—41no—
85D4×D269—44no—
86C22×Dic269—21no—
87C2×C4×D269—21no—
88C2×C4×D269C2311yescharacteristic
89D2152—22no—
90D2152—41no—
91#16864387—22no—
92#16864387—22no—
93#16864387—22no—
94#16864387—22no—
95#16864387D414yescomplemented
96C2×#14524130—22no—
97C2×#14524130C2311yescharacteristic
98C2×#14524130C2311yescharacteristic
99C8×D269—22no—
100C4⋊Dic269C2311yescharacteristic
101#16864381D411yescharacteristic
102C22⋊Dic269—21no—
103C22⋊Dic269—21no—
104C22⋊Dic269D411yescharacteristic
105#16864379—21no—
106#16864379—21no—
107#16864379—21no—
108#16864379D411yescharacteristic
109C4×Dic269C2311yescharacteristic
110C24×C269—21no—
111C2×D4×C269—22no—
112C2×D4×C269—21no—
113C2×D4×C269—21no—
114C2×D4×C269—41no—
115C2×D4×C269C2311yescharacteristic
116C2×D4×C269C2311yescharacteristic
117C2×D4×C269C2311yescharacteristic
118C22×C4×C269C2311yescharacteristic
119D8×C269—22no—
120D8×C269—41no—
121C2×C8×C269C2311yescharacteristic
122C2×C8×C269C2311yescharacteristic
123C4⋊C4×C269C2311yescharacteristic
124C22⋊C4×C269—21no—
125C22×D269—21no—
126C22×D269—21no—
127C22×D269—21no—
128C22×D269—42no—
129C22×D269—42no—
130C22×D269—42no—
131C22×D269—42no—
132C22×D269—42no—
133C22×D269—42no—
134C22×D269—81no—
135C22×D269—81no—
136C22×D269—81no—
137C22×D269C2×D411yescharacteristic
138D1076—21no—
139D1076—21no—
140D1076—21no—
141D1076—21no—
142D1076—21no—
143D1076—42no—
144D1076—42no—
145D1076C2×D412yescomplemented
146C22⋊D269—42no—
147C22⋊D269—42no—
148C22⋊D269—42no—
149C22⋊D269—42no—
150C22⋊D269—42no—
151C22⋊D269—42no—
152C22⋊D269—81no—
153C22⋊D269—81no—
154C22⋊D269D814yescomplemented
155C2×Dic269—21no—
156C2×Dic269—42no—
157C2×Dic269C2×D411yescharacteristic
158C2×Dic269C2×D411yescharacteristic
159C2×Dic269C2×D411yescharacteristic
160C4×D269—21no—
161C4×D269—21no—
162C4×D269—42no—
163#14524130—21no—
164#14524130C2×D412yescomplemented
165C23×C269—21no—
166C23×C269—21no—
167C23×C269—21no—
168C23×C269—42no—
169C23×C269—42no—
170C23×C269—81no—
171C23×C269C2×D411yescharacteristic
172D4×C269—21no—
173D4×C269—21no—
174D4×C269—21no—
175D4×C269—21no—
176D4×C269—21no—
177D4×C269—42no—
178D4×C269—42no—
179D4×C269C2×D412yescomplemented
180C2×C4×C269—21no—
181C2×C4×C269—21no—
182C2×C4×C269—21no—
183C2×C4×C269C2×D411yescharacteristic
184C2×C4×C269C2411yescharacteristic
185C8×C269—21no—
186C8×C269—21no—
187C22×C269—21no—
188C22×C269—21no—
189C22×C269—22no—
190C22×C269—41no—
191C22×C269—41no—
192C22×C269—41no—
193C22×C269—41no—
194C22×C269—41no—
195C22×C269—41no—
196C22×C269—41no—
197C22×C269—41no—
198C22×C269—84no—
199C22×C269C2×D812yescomplemented
200C22×C269C22×D411yescharacteristic
201C2×D269—21no—
202C2×D269—21no—
203C2×D269—22no—
204C2×D269—41no—
205C2×D269—41no—
206C2×D269—41no—
207C2×D269—41no—
208C2×D269—41no—
209C2×D269—41no—
210C2×D269—41no—
211C2×D269—41no—
212C2×D269—84no—
213C2×D269—84no—
214C2×D269—84no—
215C2×D269C2×D812yescomplemented
216C4×C269—21no—
217C4×C269—41no—
218C4×C269C22×D411yescharacteristic
219C4×C269H(5,𝔽2)11yescharacteristic
220Dic269—21no—
221Dic269—21no—
222Dic269—41no—
223Dic269C2×D812yescomplemented
224C2×C269—22no—
225C2×C269—42no—
226C2×C269—81no—
227C2×C269—81no—
228C2×C269D4211yescharacteristic
229C2×C269C22×D811yescharacteristic
230C2×C269#57611yescharacteristic
231D269—22no—
232D269—42no—
233D269—81no—
234D269—81no—
235C269D4×D811yescharacteristic, complemented, Sylow
236D4×D8—2691nomaximal, Sylow
237C22×D8—2691no—
238C22×D8—2691no—
239D42—2691no—
240D42—2691no—
241#493—2691no—
242#466—2691no—
243#466—2691no—
244#459—2691no—
245#459—2691no—
246#447—2691no—
247#447—2691no—
248#447—2691no—
249#447D26911yescharacteristic, complemented
250C4×D8—2691no—
251C8×D4—2691no—
252C22×D4—2691no—
253C22×D4—2691no—
254C22×D4—2691no—
255C22×D4—5381no—
256C22×D4—5381no—
257C22×D4C2×D26911yescharacteristic, complemented
258C2×D8—2691no—
259C2×D8—2691no—
260C2×D8—2691no—
261C2×D8—2691no—
262C2×D8—2691no—
263C2×D8—2691no—
264C2×D8—2691no—
265C2×D8—5384no—
266C2×D8—5384no—
267C2×D8C2×D26911yescharacteristic, complemented
268C2×D8C2×D26911yescharacteristic, complemented
269C22×C8—2691no—
270C22×C8—2691no—
271#127—2691no—
272#127—2691no—
273#121—2691no—
274#121—2691no—
275#121—2691no—
276#121—5381no—
277#121—5381no—
278#121C2×D26911yescharacteristic, complemented
279#120—5381no—
280#120—5381no—
281#120—5381no—
282#120—5381no—
283C4×D4—2691no—
284C4×D4—2691no—
285C4×D4—2691no—
286#107—2691no—
287C4⋊C8—2691no—
288#102—2691no—
289#102—2691no—
290#102—2691no—
291#102—2691no—
292#102C2×D26911yescharacteristic, complemented
293#102C2×D26911yescharacteristic, complemented
294C22⋊C8—2691no—
295C22⋊C8C2×D26911yescharacteristic, complemented
296C4×C8—2691no—
297C24—21no—
298C24—5381no—
299C24—5381no—
300C24—5381no—
301C2×D4—22no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4—2691no—
306C2×D4—2691no—
307C2×D4—2691no—
308C2×D4—2691no—
309C2×D4—5382no—
310C2×D4—5381no—
311C2×D4—5381no—
312C2×D4—5381no—
313C2×D4—5381no—
314C2×D4—5381no—
315C2×D4—5381no—
316C2×D4—5381no—
317C2×D4—5382no—
318C2×D4—5382no—
319C2×D4—5381no—
320C2×D4—5381no—
321C2×D4—5381no—
322C2×D4—10761no—
323C2×D4—10761no—
324C2×D4—10761no—
325C2×D4—10764no—
326C2×D4—10764no—
327C2×D4C22×D26911yescharacteristic
328C2×D4C22×D26911yescharacteristic
329C2×D4C22×D26911yescharacteristic
330C22×C4—2691no—
331C22×C4—5381no—
332C22×C4—5381no—
333C22×C4C22×D26911yescharacteristic
334D8—22no—
335D8—41no—
336D8—2694no—
337D8—5382no—
338D8—5382no—
339D8—5382no—
340D8—5382no—
341D8—5382no—
342D8—10761no—
343C2×C8—2691no—
344C2×C8—2691no—
345C2×C8—5382no—
346C2×C8—5382no—
347C2×C8C22×D26911yescharacteristic
348C2×C8C22×D26911yescharacteristic
349C4⋊C4—2691no—
350C4⋊C4—2691no—
351C4⋊C4C22×D26911yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—2691no—
354C22⋊C4—2691no—
355C22⋊C4—5381no—
356C22⋊C4—5381no—
357C22⋊C4—5381no—
358C22⋊C4—5381no—
359C22⋊C4—5381no—
360C42—2691no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—42no—
365C23—42no—
366C23—81no—
367C23—2691no—
368C23—5381no—
369C23—5381no—
370C23—5381no—
371C23—10762no—
372C23—10762no—
373C23—10762no—
374C23—10762no—
375C23—10762no—
376C23—10762no—
377C23—21521no—
378C23—21521no—
379C23—21521no—
380C23D4×D26911yescharacteristic
381D4—21no—
382D4—21no—
383D4—21no—
384D4—21no—
385D4—21no—
386D4—42no—
387D4—42no—
388D4—2694no—
389D4—2692no—
390D4—5381no—
391D4—5381no—
392D4—5381no—
393D4—5381no—
394D4—5381no—
395D4—10762no—
396D4—10762no—
397D4—10762no—
398D4—10762no—
399D4—10762no—
400D4—10762no—
401D4—10762no—
402D4—10762no—
403D4—21521no—
404D4—21521no—
405D4D4×D26912yescomplemented
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—2691no—
410C2×C4—2691no—
411C2×C4—2691no—
412C2×C4—5381no—
413C2×C4—5381no—
414C2×C4—5381no—
415C2×C4—10762no—
416C2×C4—10762no—
417C2×C4D4×D26911yescharacteristic
418C2×C4C23×D26911yescharacteristic
419C8—21no—
420C8—21no—
421C8—2692no—
422C8—5381no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—84no—
435C22—2692no—
436C22—5381no—
437C22—5381no—
438C22—5382no—
439C22—10761no—
440C22—10761no—
441C22—10761no—
442C22—10761no—
443C22—10761no—
444C22—10761no—
445C22—10761no—
446C22—10761no—
447C22—21524no—
448C22—21524no—
449C22—21524no—
450C22D8×D26912yescomplemented
451C22C2×D4×D26911yescharacteristic
452C4—21no—
453C4—41no—
454C4—2692no—
455C4—5381no—
456C4—5381no—
457C4—10761no—
458C4C2×D4×D26911yescharacteristic
459C4#2257549811yescharacteristic
460C2—22no—
461C2—42no—
462C2—81no—
463C2—81no—
464C2—5382no—
465C2—10762no—
466C2—21521no—
467C2—21521no—
468C2#3177123711yescharacteristic
469C2C2×D8×D26911yescharacteristic
470C2#3177140911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#447×C269C2
socleC22×C269C22×D4
hypercenter#447D269
hypocenterC269D4×D8
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×#16864387C2semidirect
2. C2×D8×D269C2semidirect
3. #31771239C2semidirect
4. D4×C22⋊D269C2semidirect
5. #31770980C2semidirect
6. #31770840C2semidirect
7. #31770839C2semidirect
8. #31770799C2semidirect
9. #31770798C2semidirect
10. #31770741C2semidirect
11. #31770740C2semidirect
12. #31770737C2semidirect
13. #31770685C2semidirect
14. #31770668C2semidirect
15. #447×C269C2semidirect
16. C22×D1076C22semidirect
19. C2×D4×D269C22semidirect
20. C2×D4×D269C22semidirect
21. C2×D2152C22semidirect
22. C2×D2152C22semidirect
25. C2×#16864387C22semidirect
26. C2×#16864387C22semidirect
27. C2×#16864387C22semidirect
28. C2×#16864387C22semidirect
30. C22×#14524130C22semidirect
31. C2×C8×D269C22semidirect
32. #22575449C22semidirect
33. #22575449C22semidirect
34. #22575428C22semidirect
35. #22575427C22semidirect
38. #22575424C22semidirect
43. D4×Dic269C22semidirect
44. #22575415C22semidirect
46. #22575386C22semidirect
47. #22575382C22semidirect
48. #22575375C22semidirect
49. #22575375C22semidirect
50. #22575374C22semidirect
51. #22575373C22semidirect
52. #22575365C22semidirect
53. C8×Dic269C22semidirect
54. C22×D4×C269C22semidirect
55. C2×D8×C269C22semidirect
56. C2×D8×C269C22semidirect
57. #121×C269C22semidirect
58. #102×C269C22semidirect
59. #102×C269C22semidirect
60. C22⋊C8×C269C22semidirect
95. #16864387D4semidirect
145. D1076C2×D4semidirect
154. C22⋊D269D8semidirect
164. #14524130C2×D4semidirect
179. D4×C269C2×D4semidirect
199. C22×C269C2×D8semidirect
215. C2×D269C2×D8semidirect
223. Dic269C2×D8semidirect
235. C269D4×D8semidirect
249. #447D269semidirect
257. C22×D4C2×D269semidirect
267. C2×D8C2×D269semidirect
268. C2×D8C2×D269semidirect
278. #121C2×D269semidirect
292. #102C2×D269semidirect
293. #102C2×D269semidirect
295. C22⋊C8C2×D269semidirect
405. D4D4×D269semidirect
450. C22D8×D269semidirect

Maximal subgroups

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

subgroupindex
C22×#168643872
C2×D8×D2692
#317712392
D4×C22⋊D2692
#317709802
#317708402
#317708392
#317707992
#317707982
#317707412
#317707402
#317707372
#317706852
#317706682
#447×C2692
D4×D8269