Finite Group Databasebeta

← #22572172

Subgroups — #22572172

Order 8576.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16864050C211yesmaximal, characteristic, complemented
2#16864042C211yesmaximal, characteristic, complemented
3#16863756C211yesmaximal, characteristic, complemented
4#16863727C211yesmaximal, characteristic, complemented
5#16863715C211yesmaximal, characteristic, complemented
6#16863687C211yesmaximal, characteristic, complemented
7#16863649C211yesmaximal, characteristic, complemented
8#16863625C211yesmaximal, characteristic, complemented
9#16863612C211yesmaximal, characteristic, complemented
10#16863543C211yesmaximal, characteristic, complemented
11#16863532C211yesmaximal, characteristic, complemented
12#16863509C211yesmaximal, characteristic, complemented
13#16863398C211yesmaximal, characteristic, complemented
14C2×#14523965C211yesmaximal, characteristic, complemented
15#435×C67C211yesmaximal, characteristic, complemented
16C2×#11761628C2211yescharacteristic
17C2×#11761627—21no—
18C22×D268C2211yescharacteristic
19C2×#11761617C2211yescharacteristic, complemented
20C2×D536C2211yescharacteristic
21C2×D536C2211yescharacteristic
22#14524043C2211yescharacteristic, complemented
23#14524031C2211yescharacteristic
24#14524028—21no—
25#14524027—21no—
26#14524027—21no—
27#14524023—21no—
28#14524022C2211yescharacteristic
29#14524017C2211yescharacteristic
30#14524017C2211yescharacteristic
31#14524017C2211yescharacteristic, complemented
32#14524016—21no—
33#14524011—21no—
34C4×D268C2211yescharacteristic
35C4×D268C2211yescharacteristic, complemented
36C2×C4⋊Dic67C2211yescharacteristic
37C2×C4⋊Dic67C2211yescharacteristic, complemented
38C22⋊C4×D67—21no—
39#14523975C2211yescharacteristic, complemented
40#14523975C2211yescharacteristic, complemented
41#14523975C2211yescharacteristic, complemented
42#14523968C2211yescharacteristic, complemented
43#14523968C2211yescharacteristic, complemented
44#14523968C2211yescharacteristic, complemented
45#14523965C2211yescharacteristic
46#14523965C2211yescharacteristic
47#14523965C2211yescharacteristic
48#14523965C2211yescharacteristic
49#14523965C2211yescharacteristic
50#14523965C2211yescharacteristic
51#14523965C2211yescharacteristic, complemented
52C2×M16×C67C2211yescharacteristic, complemented
53C22×C8×C67C2211yescharacteristic
54C4×D4×C67C2211yescharacteristic
55C4⋊C8×C67C2211yescharacteristic, complemented
56C22⋊C8×C67C2211yescharacteristic
57C22⋊C8×C67C2211yescharacteristic, complemented
58#97×C67C2211yescharacteristic, complemented
59C23×D67—21no—
60#11761628—22no—
61#11761628—41no—
62#11761627—44no—
63C2×Dic134—21no—
64C2×Dic134C2311yescharacteristic
65C2×D268—22no—
66C2×D268—21no—
67C2×D268—41no—
68C2×D268C2311yescharacteristic
69C2×D268C2311yescharacteristic
70C2×D268C2311yescharacteristic
71C2×C22⋊D67—21no—
72C2×C22⋊D67—21no—
73C2×C22⋊D67—21no—
74C2×C22⋊D67—21no—
75C22×Dic67—21no—
76C22×Dic67—21no—
77C2×C4×D67—21no—
78C2×C4×D67—21no—
79C2×C4×D67—21no—
80#11761617—41no—
81D536—22no—
82D536—41no—
83C4⋊Dic67—21no—
84C4⋊Dic67—21no—
85C4⋊Dic67—21no—
86C4⋊Dic67C2311yescharacteristic
87C4⋊Dic67C2311yescharacteristic
88C4⋊Dic67C2311yescharacteristic
89C4⋊Dic67C2311yescharacteristic
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—
98(C2×D67)⋊C4—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—42no—
118C22×D67—42no—
119C22×D67—81no—
120D4×C67—22no—
121C2×C4×C67—21no—
122C2×C4×C67—21no—
123C2×C4×C67—21no—
124C2×C4×C67—21no—
125C2×C4×C67C2×D411yescharacteristic
126C2×C4×C67C2×D411yescharacteristic
127C2×C4×C67C2×D411yescharacteristic
128C2×C4×C67C2×D411yescharacteristic
129C2×C4×C67C2411yescharacteristic
130C22⋊D67—42no—
131C22⋊D67—42no—
132C22⋊D67—42no—
133C22⋊D67—81no—
134C2×Dic67—21no—
135C2×Dic67—21no—
136C2×Dic67—21no—
137C2×Dic67—21no—
138C2×Dic67—21no—
139C2×Dic67—42no—
140C2×Dic67—42no—
141D268—21no—
142D268—21no—
143D268—21no—
144D268—21no—
145D268—21no—
146D268—42no—
147D268#4112yescomplemented
148C4×D67—42no—
149C4×D67—42no—
150C4×D67—81no—
151Dic134—21no—
152Dic134—21no—
153Dic134—42no—
154C8×C67—21no—
155C8×C67—21no—
156C8×C67—21no—
157C8×C67—21no—
158C22×C67—21no—
159C22×C67—21no—
160C22×C67—21no—
161C22×C67—21no—
162C22×C67—21no—
163C22×C67AGL(1,ℤ/8)12yes—
164C22×C67C22×D411yescharacteristic
165C2×D67—22no—
166C2×D67—41no—
167C2×D67—41no—
168C2×D67—41no—
169C2×D67—41no—
170C2×D67—41no—
171C2×D67—41no—
172C2×D67—41no—
173C2×D67—41no—
174C2×D67—84no—
175C4×C67—21no—
176C4×C67—21no—
177C4×C67—21no—
178C4×C67—21no—
179C4×C67C2×#4111yescharacteristic
180C4×C67H(5,𝔽2)11yescharacteristic
181Dic67—41no—
182Dic67—41no—
183Dic67—41no—
184Dic67—41no—
185Dic67—41no—
186C2×C67—22no—
187C2×C67—41no—
188C2×C67#54611yescharacteristic
189C2×C67C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C67#57711yescharacteristic
191D67—42no—
192D67—81no—
193D67—81no—
194#3306—671nomaximal, Sylow
195C67#330611yescharacteristic, complemented, Sylow
196#547—671no—
197#546—671no—
198#489—671no—
199#483—671no—
200#481—671no—
201#476—671no—
202#469—671no—
203#465—671no—
204#463—671no—
205#449—671no—
206#447—671no—
207#442—671no—
208#435D6711yescharacteristic, complemented
209#417—671no—
210C2×#102—671no—
211C2×#41—671no—
212C2×#41—1341no—
213C22×D4—671no—
214C2×SD16—671no—
215C2×D8—671no—
216C2×D8—671no—
217C2×M16C2×D6711yescharacteristic, complemented
218C22×C8C2×D6711yescharacteristic
219C4⋊Q8—671no—
220#124—671no—
221#123—1341no—
222#123—1341no—
223#123—1341no—
224C22⋊Q8—671no—
225C22⋊Q8—1341no—
226#121—671no—
227#121—671no—
228#121—671no—
229#121—1341no—
230#120—1341no—
231C4×D4—671no—
232C4×D4—671no—
233C4×D4C2×D6711yescharacteristic
234C2×C4⋊C4—671no—
235C2×C4⋊C4—671no—
236C2×C22⋊C4—1341no—
237#106—671no—
238#106—671no—
239#106—671no—
240C4⋊C8C2×D6711yescharacteristic, complemented
241#103—671no—
242#103—671no—
243#103—671no—
244#102—671no—
245#102—671no—
246#102—671no—
247#102—671no—
248#102—671no—
249#102—671no—
250#102—671no—
251C22⋊C8C2×D6711yescharacteristic
252C22⋊C8C2×D6711yescharacteristic, complemented
253#97C2×D6711yescharacteristic, complemented
254C24—1341no—
255#41—2681no—
256#41—2684no—
257#41—1342no—
258C2×Q8—671no—
259C2×Q8—1341no—
260C2×D4—2681no—
261C2×D4—671no—
262C2×D4—671no—
263C2×D4—671no—
264C2×D4—1342no—
265C2×D4—1341no—
266C2×D4—1341no—
267C2×D4—1341no—
268C2×D4—1341no—
269C2×D4—1341no—
270C2×D4D26811yescharacteristic
271C22×C4—1341no—
272C22×C4—1341no—
273C22×C4—1341no—
274C22×C4—1341no—
275C22×C4—1341no—
276C22×C4C22×D6711yescharacteristic
277C22×C4C22×D6711yescharacteristic
278SD16—2681no—
279D8—2681no—
280D8—1342no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D6711yescharacteristic
284C2×C8C22×D6711yescharacteristic
285C2×C8C22×D6711yescharacteristic
286C2×C8C22×D6711yescharacteristic
287C4⋊C4—671no—
288C4⋊C4—671no—
289C4⋊C4—671no—
290C4⋊C4—671no—
291C4⋊C4—1341no—
292C4⋊C4—1341no—
293C4⋊C4—1341no—
294C4⋊C4—1341no—
295C4⋊C4D26811yescharacteristic
296C22⋊C4—1341no—
297C22⋊C4—1341no—
298C22⋊C4—1341no—
299C22⋊C4—1341no—
300C22⋊C4—1341no—
301C22⋊C4—1341no—
302C22⋊C4—1341no—
303C22⋊C4—1341no—
304C22⋊C4D26811yescharacteristic
305C22⋊C4D26811yescharacteristic
306C42C22×D6711yescharacteristic
307C23—2682no—
308C23—2682no—
309C23—5361no—
310C23—1341no—
311C23—1341no—
312C23—1341no—
313C23C2×D26811yescharacteristic
314C23C2×D26811yescharacteristic
315Q8—2682no—
316Q8—1341no—
317Q8—1341no—
318D4—22no—
319D4—2682no—
320D4—2682no—
321D4—2682no—
322D4—2682no—
323D4—5361no—
324D4—672no—
325D4—1341no—
326D4—1341no—
327D4—1341no—
328D4—1341no—
329D4—1341no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—2682no—
335C2×C4—2682no—
336C2×C4—2682no—
337C2×C4—2682no—
338C2×C4—5361no—
339C2×C4—1341no—
340C2×C4—1341no—
341C2×C4—1341no—
342C2×C4—1341no—
343C2×C4—1341no—
344C2×C4C2×D26811yescharacteristic
345C2×C4C2×D26811yescharacteristic
346C2×C4C2×D26811yescharacteristic
347C2×C4C2×D26811yescharacteristic
348C2×C4C23×D6711yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—2681no—
359C22—2681no—
360C22—2681no—
361C22—2681no—
362C22—2681no—
363C22—2681no—
364C22—2681no—
365C22—2681no—
366C22—5364no—
367C22—1342no—
368C22#1452407112yes—
369C22C22×D26811yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—2681no—
375C4—2681no—
376C4—2681no—
377C4—2681no—
378C4—2681no—
379C4#41×D6711yescharacteristic
380C4#1452408811yescharacteristic
381C2—22no—
382C2—41no—
383C2—2682no—
384C2—5361no—
385C2—5361no—
386C2#1686404111yescharacteristic
387C2C2×#1452407111yescharacteristic
388C2#1686420811yescharacteristic
subgroupG/H
centerC22C22×D268
commutatorC2×C4×C67C24
FrattiniC2×C4C23×D67
Fitting#435×C67C2
socleC22×C67C22×D4
hypercenter#435D67
hypocenterC67#3306
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. #16864050C2semidirect
2. #16864042C2semidirect
3. #16863756C2semidirect
4. #16863727C2semidirect
5. #16863715C2semidirect
6. #16863687C2semidirect
7. #16863649C2semidirect
8. #16863625C2semidirect
9. #16863612C2semidirect
10. #16863543C2semidirect
11. #16863532C2semidirect
12. #16863509C2semidirect
13. #16863398C2semidirect
14. C2×#14523965C2semidirect
15. #435×C67C2semidirect
19. C2×#11761617C22semidirect
22. #14524043C22semidirect
31. #14524017C22semidirect
35. C4×D268C22semidirect
37. C2×C4⋊Dic67C22semidirect
39. #14523975C22semidirect
40. #14523975C22semidirect
41. #14523975C22semidirect
42. #14523968C22semidirect
43. #14523968C22semidirect
44. #14523968C22semidirect
51. #14523965C22semidirect
52. C2×M16×C67C22semidirect
55. C4⋊C8×C67C22semidirect
57. C22⋊C8×C67C22semidirect
58. #97×C67C22semidirect
147. D268#41semidirect
195. C67#3306semidirect
208. #435D67semidirect
217. C2×M16C2×D67semidirect
240. C4⋊C8C2×D67semidirect
252. C22⋊C8C2×D67semidirect
253. #97C2×D67semidirect