Finite Group Databasebeta

← #22572352

Subgroups — #22572352

Order 8576.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16864092C211yesmaximal, characteristic, complemented
2D4×D268C211yesmaximal, characteristic, complemented
3#16863761C211yesmaximal, characteristic, complemented
4#16863721C211yesmaximal, characteristic, complemented
5#16863715C211yesmaximal, characteristic, complemented
6#16863697C211yesmaximal, characteristic, complemented
7#16863649C211yesmaximal, characteristic, complemented
8#16863632C211yesmaximal, characteristic, complemented
9#16863592C211yesmaximal, characteristic, complemented
10#16863532C211yesmaximal, characteristic, complemented
11#16863532C211yesmaximal, characteristic, complemented
12#16863509C211yesmaximal, characteristic, complemented
13#16863402C211yesmaximal, characteristic, complemented
14C2×#14523965C211yesmaximal, characteristic, complemented
15#435×C67C211yesmaximal, characteristic, complemented
16C22×D268C2211yescharacteristic
17C22×D268C2211yescharacteristic
18C2×D4×D67—21no—
19C2×D536C2211yescharacteristic
20C2×D536C2211yescharacteristic, complemented
21C2×D536C2211yescharacteristic, complemented
22#14524040C2211yescharacteristic
23#14524038—21no—
24#14524035C2211yescharacteristic, complemented
25#14524025—21no—
26#14524018—21no—
27#14524017C2211yescharacteristic
28#14524017C2211yescharacteristic
29#14524017C2211yescharacteristic, complemented
30#14524017C2211yescharacteristic, complemented
31#14524015—21no—
32#14524013—21no—
33#14524013—21no—
34C4×D268C2211yescharacteristic
35C4×D268C2211yescharacteristic, complemented
36(C22⋊D67)⋊C4—21no—
37#14524002C2211yescharacteristic, complemented
38C2×C4⋊Dic67C2211yescharacteristic, complemented
39#14523977C2211yescharacteristic, complemented
40#14523975C2211yescharacteristic, complemented
41#14523975C2211yescharacteristic, complemented
42#14523965C2211yescharacteristic
43#14523965C2211yescharacteristic
44#14523965C2211yescharacteristic
45#14523965C2211yescharacteristic, complemented
46#14523965C2211yescharacteristic, complemented
47#14523965C2211yescharacteristic, complemented
48#14523965C2211yescharacteristic, complemented
49#14523965C2211yescharacteristic, complemented
50#14523965C2211yescharacteristic, complemented
51#14523965C2211yescharacteristic, complemented
52C2×M16×C67C2211yescharacteristic, complemented
53C22×C8×C67C2211yescharacteristic, complemented
54C4×D4×C67C2211yescharacteristic
55C4⋊C8×C67C2211yescharacteristic, complemented
56C22⋊C8×C67C2211yescharacteristic, complemented
57C22⋊C8×C67C2211yescharacteristic, complemented
58#97×C67C2211yescharacteristic, complemented
59C23×D67—21no—
60C23×D67—21no—
61C2×D268—22no—
62C2×D268—22no—
63C2×D268—21no—
64C2×D268—21no—
65C2×D268—21no—
66C2×D268—21no—
67C2×D268—41no—
68C2×D268—41no—
69C2×D268C2311yescharacteristic
70C2×D268C2311yescharacteristic
71C2×D268C2311yescharacteristic
72C2×D268C2311yescharacteristic
73C2×C22⋊D67—21no—
74C2×C22⋊D67—21no—
75C2×C22⋊D67—21no—
76C2×C22⋊D67—21no—
77D4×D67—44no—
78C22×Dic67—21no—
79C2×C4×D67—21no—
80C2×C4×D67—21no—
81D536—22no—
82D536—41no—
83D536—41no—
84C4⋊Dic67—21no—
85C4⋊Dic67C2311yescharacteristic
86C4⋊Dic67C2311yescharacteristic
87C4⋊Dic67C2311yescharacteristic
88C4⋊Dic67C2311yescharacteristic
89Dic67⋊C4—21no—
90Dic67⋊C4—21no—
91C22⋊Dic67—21no—
92(C2×D67)⋊C4—21no—
93(C2×D67)⋊C4—21no—
94(C2×D67)⋊C4—21no—
95(C2×D67)⋊C4—21no—
96(C2×D67)⋊C4—21no—
97(C2×D67)⋊C4—21no—
98C4×Dic67—21no—
99C2×D4×C67D411yescharacteristic
100C22×C4×C67C2311yescharacteristic
101C22×C4×C67C2311yescharacteristic
102M16×C67—41no—
103C2×C8×C67—41no—
104C2×C8×C67C2311yescharacteristic
105C2×C8×C67C2311yescharacteristic
106C2×C8×C67C2311yescharacteristic
107C2×C8×C67C2311yescharacteristic
108C4⋊C4×C67D411yescharacteristic
109C22⋊C4×C67D411yescharacteristic
110C22⋊C4×C67D411yescharacteristic
111C42×C67C2311yescharacteristic
112C23×C67C2×D411yescharacteristic
113C23×C67C2×D411yescharacteristic
114C22×D67—21no—
115C22×D67—21no—
116C22×D67—21no—
117C22×D67—21no—
118C22×D67—42no—
119C22×D67—42no—
120C22×D67—42no—
121C22×D67—42no—
122C22×D67—81no—
123C22×D67—81no—
124D4×C67—22no—
125C2×C4×C67—21no—
126C2×C4×C67—21no—
127C2×C4×C67—21no—
128C2×C4×C67—21no—
129C2×C4×C67C2×D411yescharacteristic
130C2×C4×C67C2×D411yescharacteristic
131C2×C4×C67C2×D411yescharacteristic
132C2×C4×C67C2×D411yescharacteristic
133C2×C4×C67C2411yescharacteristic
134C22⋊D67—42no—
135C22⋊D67—42no—
136C22⋊D67—42no—
137C22⋊D67—81no—
138C2×Dic67—21no—
139C2×Dic67—21no—
140C2×Dic67—21no—
141C2×Dic67—21no—
142C2×Dic67—81no—
143D268—21no—
144D268—21no—
145D268—21no—
146D268—21no—
147D268—21no—
148D268—21no—
149D268—21no—
150D268—42no—
151D268—42no—
152D268—42no—
153D268—81no—
154D268#4112yes—
155C4×D67—42no—
156C4×D67—81no—
157C8×C67—21no—
158C8×C67—21no—
159C8×C67—21no—
160C8×C67—21no—
161C22×C67—21no—
162C22×C67—21no—
163C22×C67—21no—
164C22×C67—21no—
165C22×C67—21no—
166C22×C67AGL(1,ℤ/8)12yes—
167C22×C67C22×D411yescharacteristic
168C2×D67—22no—
169C2×D67—41no—
170C2×D67—41no—
171C2×D67—41no—
172C2×D67—41no—
173C2×D67—41no—
174C2×D67—41no—
175C2×D67—41no—
176C2×D67—41no—
177C2×D67—41no—
178C2×D67—41no—
179C2×D67—41no—
180C2×D67—84no—
181C2×D67—84no—
182C4×C67—21no—
183C4×C67—21no—
184C4×C67—21no—
185C4×C67—21no—
186C4×C67C2×#4111yescharacteristic
187C4×C67H(5,𝔽2)11yescharacteristic
188Dic67—41no—
189Dic67—41no—
190Dic67—41no—
191Dic67—41no—
192C2×C67—22no—
193C2×C67—41no—
194C2×C67#54611yescharacteristic
195C2×C67C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C67#57611yescharacteristic
197D67—42no—
198D67—81no—
199D67—81no—
200D67—81no—
201#3318—671nomaximal, Sylow
202C67#331811yescharacteristic, complemented, Sylow
203#553—671no—
204D42—671no—
205#490—671no—
206#482—671no—
207#481—671no—
208#478—671no—
209#469—671no—
210#466—671no—
211#459—671no—
212#447—671no—
213#447—671no—
214#442—671no—
215#435D6711yescharacteristic, complemented
216#418—671no—
217C2×#102—671no—
218C22×D4—671no—
219C22×D4—671no—
220C22×D4—1341no—
221C2×D8—671no—
222C2×D8—671no—
223C2×D8—671no—
224C2×M16C2×D6711yescharacteristic, complemented
225C22×C8C2×D6711yescharacteristic, complemented
226#127—671no—
227#126—1341no—
228#125—671no—
229#123—1341no—
230#121—671no—
231#121—671no—
232#121—671no—
233#121—671no—
234#121—1341no—
235#121—1341no—
236#120—1341no—
237#120—1341no—
238C4×D4—671no—
239C4×D4—671no—
240C4×D4—1341no—
241C4×D4C2×D6711yescharacteristic
242#117—671no—
243C2×C4⋊C4—671no—
244#107—671no—
245#106—671no—
246#106—671no—
247C4⋊C8C2×D6711yescharacteristic, complemented
248#102—671no—
249#102—671no—
250#102—671no—
251#102—671no—
252#102—671no—
253#102—671no—
254#102—671no—
255#102—671no—
256#102—671no—
257#102—671no—
258C22⋊C8C2×D6711yescharacteristic, complemented
259C22⋊C8C2×D6711yescharacteristic, complemented
260#97C2×D6711yescharacteristic, complemented
261C24—1341no—
262C24—1341no—
263C2×D4—2681no—
264C2×D4—2681no—
265C2×D4—2684no—
266C2×D4—671no—
267C2×D4—671no—
268C2×D4—671no—
269C2×D4—671no—
270C2×D4—1342no—
271C2×D4—1342no—
272C2×D4—1341no—
273C2×D4—1341no—
274C2×D4—1341no—
275C2×D4—1341no—
276C2×D4—1341no—
277C2×D4—1341no—
278C2×D4—1341no—
279C2×D4—1341no—
280C2×D4D26811yescharacteristic
281C22×C4—1341no—
282C22×C4—1341no—
283C22×C4—1341no—
284C22×C4C22×D6711yescharacteristic
285C22×C4C22×D6711yescharacteristic
286D8—2681no—
287D8—2681no—
288D8—1342no—
289M16—41no—
290C2×C8—41no—
291C2×C8C22×D6711yescharacteristic
292C2×C8C22×D6711yescharacteristic
293C2×C8C22×D6711yescharacteristic
294C2×C8C22×D6711yescharacteristic
295C4⋊C4—671no—
296C4⋊C4—671no—
297C4⋊C4—671no—
298C4⋊C4—671no—
299C4⋊C4—1341no—
300C4⋊C4—1341no—
301C4⋊C4—1341no—
302C4⋊C4D26811yescharacteristic
303C22⋊C4—1341no—
304C22⋊C4—1341no—
305C22⋊C4—1341no—
306C22⋊C4—1341no—
307C22⋊C4—1341no—
308C22⋊C4—1341no—
309C22⋊C4—1341no—
310C22⋊C4D26811yescharacteristic
311C22⋊C4D26811yescharacteristic
312C42—1341no—
313C42C22×D6711yescharacteristic
314C23—2682no—
315C23—2682no—
316C23—2682no—
317C23—2682no—
318C23—5361no—
319C23—5361no—
320C23—1341no—
321C23—1341no—
322C23—1341no—
323C23—1341no—
324C23C2×D26811yescharacteristic
325C23C2×D26811yescharacteristic
326D4—22no—
327D4—2682no—
328D4—2682no—
329D4—2682no—
330D4—2682no—
331D4—2682no—
332D4—2682no—
333D4—5361no—
334D4—5361no—
335D4—672no—
336D4—1341no—
337D4—1341no—
338D4—1341no—
339D4—1341no—
340D4—1341no—
341D4—1341no—
342D4—1341no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—2682no—
348C2×C4—5361no—
349C2×C4—5361no—
350C2×C4—1341no—
351C2×C4—1341no—
352C2×C4—1341no—
353C2×C4—1341no—
354C2×C4C2×D26811yescharacteristic
355C2×C4C2×D26811yescharacteristic
356C2×C4C2×D26811yescharacteristic
357C2×C4C2×D26811yescharacteristic
358C2×C4C23×D6711yescharacteristic
359C8—21no—
360C8—21no—
361C8—21no—
362C8—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—2681no—
369C22—2681no—
370C22—2681no—
371C22—2681no—
372C22—2681no—
373C22—2681no—
374C22—2681no—
375C22—2681no—
376C22—2681no—
377C22—2681no—
378C22—2681no—
379C22—5364no—
380C22—5364no—
381C22—1342no—
382C22#1452407112yes—
383C22C22×D26811yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—2681no—
389C4—2681no—
390C4—2681no—
391C4—2681no—
392C4#41×D6711yescharacteristic
393C4#1452408811yescharacteristic
394C2—22no—
395C2—41no—
396C2—2682no—
397C2—5361no—
398C2—5361no—
399C2—5361no—
400C2#1686404111yescharacteristic
401C2C2×#1452407111yescharacteristic
402C2#1686420111yescharacteristic
subgroupG/H
centerC22C22×D268
commutatorC2×C4×C67C24
FrattiniC2×C4C23×D67
Fitting#435×C67C2
socleC22×C67C22×D4
hypercenter#435D67
hypocenterC67#3318
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16864092C2semidirect
2. D4×D268C2semidirect
3. #16863761C2semidirect
4. #16863721C2semidirect
5. #16863715C2semidirect
6. #16863697C2semidirect
7. #16863649C2semidirect
8. #16863632C2semidirect
9. #16863592C2semidirect
10. #16863532C2semidirect
11. #16863532C2semidirect
12. #16863509C2semidirect
13. #16863402C2semidirect
14. C2×#14523965C2semidirect
15. #435×C67C2semidirect
20. C2×D536C22semidirect
21. C2×D536C22semidirect
24. #14524035C22semidirect
29. #14524017C22semidirect
30. #14524017C22semidirect
35. C4×D268C22semidirect
37. #14524002C22semidirect
38. C2×C4⋊Dic67C22semidirect
39. #14523977C22semidirect
40. #14523975C22semidirect
41. #14523975C22semidirect
45. #14523965C22semidirect
46. #14523965C22semidirect
47. #14523965C22semidirect
48. #14523965C22semidirect
49. #14523965C22semidirect
50. #14523965C22semidirect
51. #14523965C22semidirect
52. C2×M16×C67C22semidirect
53. C22×C8×C67C22semidirect
55. C4⋊C8×C67C22semidirect
56. C22⋊C8×C67C22semidirect
57. C22⋊C8×C67C22semidirect
58. #97×C67C22semidirect
202. C67#3318semidirect
215. #435D67semidirect
224. C2×M16C2×D67semidirect
225. C22×C8C2×D67semidirect
247. C4⋊C8C2×D67semidirect
258. C22⋊C8C2×D67semidirect
259. C22⋊C8C2×D67semidirect
260. #97C2×D67semidirect