Finite Group Databasebeta

← #22570395

Subgroups — #22570395

Order 8576.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16864017C211yesmaximal, characteristic, complemented
2#16863870C211yesmaximal, characteristic, complemented
3#16863738C211yesmaximal, characteristic, complemented
4#16863721C211yesmaximal, characteristic, complemented
5#16863687C211yesmaximal, characteristic, complemented
6#16863677C211yesmaximal, characteristic, complemented
7#16863612C211yesmaximal, characteristic, complemented
8#16863612C211yesmaximal, characteristic, complemented
9#16863549C211yesmaximal, characteristic, complemented
10#16863532C211yesmaximal, characteristic
11#16863509C211yesmaximal, characteristic, complemented
12#16863498C211yesmaximal, characteristic, complemented
13C4×#11761617C211yesmaximal, characteristic, complemented
14C4×D536C211yesmaximal, characteristic, complemented
15#433×C67C211yesmaximal, characteristic, complemented
16C22×D268C2211yescharacteristic
17C2×#11761617C2211yescharacteristic
18C2×#11761617C2211yescharacteristic
19C2×D536C2211yescharacteristic
20C2×D536C2211yescharacteristic
21#14524043C2211yescharacteristic, complemented
22#14524038—21no—
23#14524031C2211yescharacteristic, complemented
24#14524029—21no—
25#14524025—21no—
26#14524022C2211yescharacteristic
27#14524021—21no—
28#14524017C2211yescharacteristic
29C4×Dic134C2211yescharacteristic, complemented
30C4×D268C2211yescharacteristic
31C4×D268C2211yescharacteristic
32C4×D268C2211yescharacteristic
33C4×D268C2211yescharacteristic
34C4×D268C2211yescharacteristic, complemented
35#14524005—21no—
36#14524005—21no—
37#14524002C2211yescharacteristic
38C22⋊C4×D67—21no—
39C22⋊C4×D67—21no—
40#14523977C2211yescharacteristic, complemented
41#14523977C2211yescharacteristic, complemented
42#14523975C2211yescharacteristic, complemented
43#14523975C2211yescharacteristic, complemented
44#14523968C2211yescharacteristic, complemented
45#14523968C2211yescharacteristic, complemented
46#14523965C2211yescharacteristic
47#14523965C2211yescharacteristic
48#14523965C2211yescharacteristic
49#14523965C2211yescharacteristic
50#14523965C2211yescharacteristic, complemented
51#14523965C2211yescharacteristic, complemented
52#117×C67C2211yescharacteristic
53C4⋊C8×C67C2211yescharacteristic, complemented
54C4⋊C8×C67C2211yescharacteristic, complemented
55C22⋊C8×C67C2211yescharacteristic
56C22⋊C8×C67C2211yescharacteristic
57#97×C67C2211yescharacteristic, complemented
58C4×C8×C67C2211yescharacteristic, complemented
59C23×D67—21no—
60C2×Dic134—21no—
61C2×Dic134C2311yescharacteristic
62C2×D268—21no—
63C2×D268—22no—
64C2×D268—22no—
65C2×D268C2311yescharacteristic
66C2×D268C2311yescharacteristic
67C2×D268C2311yescharacteristic
68C2×C22⋊D67—21no—
69C2×C4×D67—21no—
70C2×C4×D67—21no—
71C2×C4×D67—21no—
72C2×C4×D67—21no—
73C2×C4×D67—21no—
74#11761617—22no—
75#11761617—22no—
76D536—22no—
77D536—22no—
78C4⋊Dic67—21no—
79C4⋊Dic67C2311yescharacteristic
80C4⋊Dic67C2311yescharacteristic
81C4⋊Dic67C2311yescharacteristic
82C4⋊Dic67C2311yescharacteristic
83Dic67⋊C4—21no—
84Dic67⋊C4—21no—
85C22⋊Dic67—21no—
86C22⋊Dic67—21no—
87(C2×D67)⋊C4—21no—
88(C2×D67)⋊C4—21no—
89(C2×D67)⋊C4—21no—
90(C2×D67)⋊C4—21no—
91(C2×D67)⋊C4—21no—
92(C2×D67)⋊C4—21no—
93(C2×D67)⋊C4—21no—
94(C2×D67)⋊C4—21no—
95C4×Dic67—21no—
96C4×Dic67—21no—
97C22×C4×C67C2311yescharacteristic
98C2×C8×C67C2311yescharacteristic
99C2×C8×C67C2311yescharacteristic
100C2×C8×C67C2311yescharacteristic
101C2×C8×C67C2311yescharacteristic
102C4⋊C4×C67D411yescharacteristic
103C4⋊C4×C67D411yescharacteristic
104C22⋊C4×C67D411yescharacteristic
105C22⋊C4×C67D411yescharacteristic
106C42×C67C2311yescharacteristic
107C42×C67C2311yescharacteristic
108C23×C67C2×D411yescharacteristic
109C22×D67—21no—
110C22×D67—21no—
111C22×D67—24no—
112C22×D67—21no—
113C22×D67—81no—
114C22×D67—81no—
115C2×C4×C67—21no—
116C2×C4×C67—21no—
117C2×C4×C67C2×D411yescharacteristic
118C2×C4×C67C2×D411yescharacteristic
119C2×C4×C67C2×D411yescharacteristic
120C2×C4×C67C2×D411yescharacteristic
121C2×C4×C67C2×D411yescharacteristic
122C2×C4×C67C2411yescharacteristic
123C22⋊D67—81no—
124C2×Dic67—21no—
125C2×Dic67—21no—
126C2×Dic67—21no—
127C2×Dic67—21no—
128C2×Dic67—21no—
129D268—24no—
130D268—21no—
131D268—21no—
132D268—21no—
133D268—21no—
134D268#4112yes—
135D268#4112yes—
136C4×D67—81no—
137C4×D67—81no—
138C4×D67—81no—
139C4×D67—81no—
140C4×D67—81no—
141Dic134—21no—
142Dic134—21no—
143Dic134—81no—
144C8×C67—21no—
145C8×C67—21no—
146C8×C67—21no—
147C8×C67—21no—
148C22×C67—21no—
149C22×C67—21no—
150C22×C67—21no—
151C22×C67C22×D411yescharacteristic
152C2×D67—22no—
153C2×D67—22no—
154C2×D67—41no—
155C2×D67—41no—
156C2×D67—41no—
157C2×D67—41no—
158C2×D67—41no—
159C2×D67—41no—
160C2×D67—41no—
161C2×D67—84no—
162C4×C67—21no—
163C4×C67—21no—
164C4×C67—21no—
165C4×C67—21no—
166C4×C67—21no—
167C4×C67C2×#4111yescharacteristic
168C4×C67C2×#4111yescharacteristic
169Dic67—41no—
170Dic67—41no—
171Dic67—41no—
172Dic67—41no—
173Dic67—41no—
174C2×C67—41no—
175C2×C67#52511yescharacteristic
176C2×C67#57611yescharacteristic
177C2×C67#57711yescharacteristic
178D67—42no—
179D67—42no—
180D67—81no—
181#3118—671nomaximal, Sylow
182C67#311811yescharacteristic, complemented, Sylow
183#542—671no—
184#518—671no—
185#485—671no—
186#482—671no—
187#476—671no—
188#474—671no—
189#463—671no—
190#463—671no—
191#450—671no—
192#447—671no—
193#442—671no—
194#440—671no—
195C4×SD16—671no—
196C4×D8—671no—
197#433D6711yescharacteristic, complemented
198C22×D4—671no—
199C2×SD16—671no—
200C2×SD16—671no—
201C2×D8—671no—
202C2×D8—671no—
203C4⋊Q8—671no—
204#126—1341no—
205#124—671no—
206#124—1341no—
207#123—1341no—
208C22⋊Q8—671no—
209C22⋊Q8—1341no—
210#121—671no—
211C4×Q8—671no—
212C4×D4—671no—
213C4×D4—671no—
214C4×D4—671no—
215C4×D4—671no—
216C4×D4—671no—
217C4×D4—1341no—
218C4×D4—1341no—
219#117—671no—
220#117C2×D6711yescharacteristic
221C2×C22⋊C4—1341no—
222C2×C22⋊C4—1341no—
223#107—671no—
224#107—671no—
225#106—671no—
226#106—671no—
227C4⋊C8C2×D6711yescharacteristic, complemented
228C4⋊C8C2×D6711yescharacteristic, complemented
229#103—671no—
230#103—671no—
231#102—671no—
232#102—671no—
233#102—671no—
234#102—671no—
235#102—671no—
236#102—671no—
237C22⋊C8C2×D6711yescharacteristic
238C22⋊C8C2×D6711yescharacteristic
239#97C2×D6711yescharacteristic, complemented
240C4×C8C2×D6711yescharacteristic, complemented
241C24—1341no—
242C2×Q8—671no—
243C2×Q8—1341no—
244C2×D4—671no—
245C2×D4—671no—
246C2×D4—671no—
247C2×D4—1342no—
248C2×D4—1342no—
249C2×D4—1341no—
250C2×D4—1341no—
251C22×C4—1341no—
252C22×C4—1341no—
253C22×C4—1341no—
254C22×C4—1341no—
255C22×C4—1341no—
256C22×C4C22×D6711yescharacteristic
257SD16—1342no—
258SD16—1342no—
259D8—1342no—
260D8—1342no—
261C2×C8C22×D6711yescharacteristic
262C2×C8C22×D6711yescharacteristic
263C2×C8C22×D6711yescharacteristic
264C2×C8C22×D6711yescharacteristic
265C4⋊C4—671no—
266C4⋊C4—671no—
267C4⋊C4—671no—
268C4⋊C4—671no—
269C4⋊C4—1341no—
270C4⋊C4—1341no—
271C4⋊C4—1341no—
272C4⋊C4D26811yescharacteristic
273C4⋊C4D26811yescharacteristic
274C22⋊C4—1341no—
275C22⋊C4—1341no—
276C22⋊C4—1341no—
277C22⋊C4—1341no—
278C22⋊C4—1341no—
279C22⋊C4—1341no—
280C22⋊C4—1341no—
281C22⋊C4—1341no—
282C22⋊C4—1341no—
283C22⋊C4—1341no—
284C22⋊C4D26811yescharacteristic
285C22⋊C4D26811yescharacteristic
286C42—1341no—
287C42—1341no—
288C42C22×D6711yescharacteristic
289C42C22×D6711yescharacteristic
290C23—5361no—
291C23—5361no—
292C23—1344no—
293C23—1341no—
294C23—1341no—
295C23—1341no—
296C23C2×D26811yescharacteristic
297Q8—5361no—
298Q8—1341no—
299Q8—1341no—
300D4—5361no—
301D4—672no—
302D4—672no—
303D4—1344no—
304D4—1341no—
305D4—1341no—
306D4—1341no—
307D4—1341no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—5361no—
311C2×C4—5361no—
312C2×C4—5361no—
313C2×C4—5361no—
314C2×C4—5361no—
315C2×C4—1341no—
316C2×C4—1341no—
317C2×C4—1341no—
318C2×C4—1341no—
319C2×C4—1341no—
320C2×C4C2×D26811yescharacteristic
321C2×C4C2×D26811yescharacteristic
322C2×C4C2×D26811yescharacteristic
323C2×C4C2×D26811yescharacteristic
324C2×C4C2×D26811yescharacteristic
325C2×C4C23×D6711yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—2681no—
334C22—2681no—
335C22—2681no—
336C22—2681no—
337C22—2681no—
338C22—2681no—
339C22—2681no—
340C22—5364no—
341C22—1342no—
342C22—1342no—
343C22C22×D26811yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—2681no—
350C4—2681no—
351C4—2681no—
352C4—2681no—
353C4—2681no—
354C4#41×D6711yescharacteristic
355C4#41×D6711yescharacteristic
356C2—41no—
357C2—2682no—
358C2—2682no—
359C2—5361no—
360C2#1686390811yescharacteristic
361C2#1686420111yescharacteristic
362C2#1686420811yescharacteristic
subgroupG/H
centerC22C22×D268
commutatorC2×C4×C67C24
FrattiniC2×C4C23×D67
Fitting#433×C67C2
socleC22×C67C22×D4
hypercenter#433D67
hypocenterC67#3118
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16864017C2semidirect
2. #16863870C2semidirect
3. #16863738C2semidirect
4. #16863721C2semidirect
5. #16863687C2semidirect
6. #16863677C2semidirect
7. #16863612C2semidirect
8. #16863612C2semidirect
9. #16863549C2semidirect
11. #16863509C2semidirect
12. #16863498C2semidirect
13. C4×#11761617C2semidirect
14. C4×D536C2semidirect
15. #433×C67C2semidirect
21. #14524043C22semidirect
23. #14524031C22semidirect
29. C4×Dic134C22semidirect
34. C4×D268C22semidirect
40. #14523977C22semidirect
41. #14523977C22semidirect
42. #14523975C22semidirect
43. #14523975C22semidirect
44. #14523968C22semidirect
45. #14523968C22semidirect
50. #14523965C22semidirect
51. #14523965C22semidirect
53. C4⋊C8×C67C22semidirect
54. C4⋊C8×C67C22semidirect
57. #97×C67C22semidirect
58. C4×C8×C67C22semidirect
182. C67#3118semidirect
197. #433D67semidirect
227. C4⋊C8C2×D67semidirect
228. C4⋊C8C2×D67semidirect
239. #97C2×D67semidirect
240. C4×C8C2×D67semidirect