Finite Group Databasebeta

← #22572029

Subgroups — #22572029

Order 8576.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16864101C211yesmaximal, characteristic, complemented
2D4×C22⋊D67C211yesmaximal, characteristic
3#16863741C211yesmaximal, characteristic, complemented
4#16863714C211yesmaximal, characteristic, complemented
5#16863713C211yesmaximal, characteristic, complemented
6#16863684C211yesmaximal, characteristic, complemented
7#16863625C211yesmaximal, characteristic, complemented
8#16863624C211yesmaximal, characteristic, complemented
9#16863595C211yesmaximal, characteristic, complemented
10#16863548C211yesmaximal, characteristic, complemented
11#16863547C211yesmaximal, characteristic, complemented
12#16863487C211yesmaximal, characteristic, complemented
13C8×C22⋊D67C211yesmaximal, characteristic, complemented
14#102×D67C211yesmaximal, characteristic, complemented
15C2×#102×C67C211yesmaximal, characteristic, complemented
16C22×C22⋊D67—21no—
17C2×D4×D67C2211yescharacteristic
18C2×#11761617C2211yescharacteristic, complemented
19C2×#11761616C2211yescharacteristic
20C2×#11761616C2211yescharacteristic, complemented
21C2×C8×D67C2211yescharacteristic, complemented
22#14524042C2211yescharacteristic, complemented
23#14524039C2211yescharacteristic
24#14524033—21no—
25#14524023C2211yescharacteristic, complemented
26#14524022—21no—
27#14524022C2211yescharacteristic, complemented
28#14524021—21no—
29#14524017C2211yescharacteristic
30#14524015—21no—
31#14524014C2211yescharacteristic
32#14524012—21no—
33#14524011—21no—
34#14524008C2211yescharacteristic, complemented
35D4×Dic67C2211yescharacteristic
36C4×C22⋊D67—21no—
37C4×C22⋊D67C2211yescharacteristic
38C4⋊C4×D67C2211yescharacteristic, complemented
39#14523975C2211yescharacteristic, complemented
40#14523974C2211yescharacteristic, complemented
41#14523974C2211yescharacteristic, complemented
42Dic67⋊C8C2211yescharacteristic, complemented
43#14523968C2211yescharacteristic, complemented
44#14523965C2211yescharacteristic, complemented
45#14523964C2211yescharacteristic
46#14523964C2211yescharacteristic, complemented
47#14523963C2211yescharacteristic, complemented
48#14523963C2211yescharacteristic, complemented
49C22⋊(C67⋊C8)C2211yescharacteristic, complemented
50(C2×D67)⋊C8C2211yescharacteristic, complemented
51C8×Dic67C2211yescharacteristic, complemented
52C22×D4×C67C2211yescharacteristic
53C22×C8×C67C2211yescharacteristic, complemented
54C2×C4⋊C4×C67C2211yescharacteristic, complemented
55#102×C67C2211yescharacteristic
56#102×C67C2211yescharacteristic
57#102×C67C2211yescharacteristic, complemented
58#102×C67C2211yescharacteristic, complemented
59C23×D67—21no—
60C2×Dic134—21no—
61C2×Dic134C2311yescharacteristic
62C2×D268C2311yescharacteristic
63C2×C22⋊D67—21no—
64C2×C22⋊D67—21no—
65C2×C22⋊D67—21no—
66C2×C22⋊D67—21no—
67C2×C22⋊D67—21no—
68C2×C22⋊D67—44no—
69C2×C22⋊D67D411yescharacteristic
70D4×D67—22no—
71D4×D67—41no—
72C22×Dic67—21no—
73C2×C4×D67—21no—
74C2×C4×D67C2311yescharacteristic
75#11761617—41no—
76#11761616—22no—
77#11761616—41no—
78C2×C67⋊C8C2311yescharacteristic
79C2×C67⋊C8C2311yescharacteristic
80C8×D67—41no—
81C4⋊Dic67—21no—
82C4⋊Dic67C2311yescharacteristic
83C4⋊Dic67C2311yescharacteristic
84Dic67⋊C4—21no—
85Dic67⋊C4—21no—
86Dic67⋊C4—21no—
87Dic67⋊C4—21no—
88Dic67⋊C4D411yescharacteristic
89C22⋊Dic67—21no—
90C22⋊Dic67—21no—
91C22⋊Dic67—21no—
92C22⋊Dic67D411yescharacteristic
93(C2×D67)⋊C4—21no—
94(C2×D67)⋊C4—21no—
95(C2×D67)⋊C4D411yescharacteristic
96C4×Dic67—21no—
97C4×Dic67C2311yescharacteristic
98C24×C67—21no—
99C2×D4×C67—22no—
100C2×D4×C67—21no—
101C2×D4×C67—41no—
102C2×D4×C67C2311yescharacteristic
103C2×D4×C67C2311yescharacteristic
104C22×C4×C67—21no—
105C22×C4×C67C2311yescharacteristic
106C2×C8×C67—41no—
107C2×C8×C67C2311yescharacteristic
108C2×C8×C67C2311yescharacteristic
109C4⋊C4×C67—21no—
110C4⋊C4×C67C2311yescharacteristic
111C4⋊C4×C67C2311yescharacteristic
112C23×C67—21no—
113C23×C67—21no—
114C23×C67—42no—
115C23×C67—42no—
116C23×C67—81no—
117C23×C67C2×D411yescharacteristic
118C22×D67—21no—
119C22×D67—42no—
120C22×D67—42no—
121C22×D67—81no—
122C22×D67C2×D411yescharacteristic
123D4×C67—21no—
124D4×C67—21no—
125D4×C67—21no—
126D4×C67—42no—
127D4×C67#4112yes—
128C2×C4×C67—21no—
129C2×C4×C67—21no—
130C2×C4×C67—21no—
131C2×C4×C67—21no—
132C2×C4×C67—81no—
133C2×C4×C67C2×D411yescharacteristic
134C2×C4×C67C2411yescharacteristic
135C22⋊D67—42no—
136C22⋊D67—42no—
137C22⋊D67—42no—
138C22⋊D67—42no—
139C22⋊D67—81no—
140C22⋊D67SD1614yescomplemented
141C2×Dic67—21no—
142C2×Dic67—21no—
143C2×Dic67—21no—
144C2×Dic67—42no—
145C2×Dic67C2×D411yescharacteristic
146C2×Dic67C2×D411yescharacteristic
147C2×Dic67C2×D411yescharacteristic
148D268—21no—
149D268—21no—
150C4×D67—21no—
151C4×D67—21no—
152C4×D67—81no—
153Dic134—21no—
154Dic134—21no—
155Dic134—81no—
156C8×C67—21no—
157C8×C67—21no—
158C67⋊C8—21no—
159C67⋊C8—21no—
160C22×C67—21no—
161C22×C67—21no—
162C22×C67—22no—
163C22×C67—41no—
164C22×C67—41no—
165C22×C67—41no—
166C22×C67—41no—
167C22×C67—41no—
168C22×C67—84no—
169C22×C67C2×SD1612yes—
170C22×C67C22×D411yescharacteristic
171C2×D67—21no—
172C2×D67—21no—
173C2×D67—41no—
174C2×D67—41no—
175C2×D67—41no—
176C2×D67—84no—
177C2×D67C2×SD1612yes—
178C4×C67—21no—
179C4×C67—41no—
180C4×C67—41no—
181C4×C67C2×#4111yescharacteristic
182C4×C67H(5,𝔽2)11yescharacteristic
183Dic67—21no—
184Dic67—21no—
185Dic67—41no—
186Dic67—41no—
187Dic67—41no—
188Dic67C2×SD1612yes—
189C2×C67—22no—
190C2×C67—42no—
191C2×C67—81no—
192C2×C67#54611yescharacteristic
193C2×C67C22×SD1611yescharacteristic
194C2×C67#57611yescharacteristic
195D67—22no—
196D67—81no—
197#3295—671nomaximal, Sylow
198C67#329511yescharacteristic, complemented, Sylow
199#554—671no—
200D42—671no—
201#486—671no—
202#481—671no—
203#481—671no—
204#476—671no—
205#465—671no—
206#465—671no—
207#460—671no—
208#450—671no—
209#450—671no—
210C4×SD16—671no—
211C8×D4—671no—
212C2×#102—671no—
213C2×#102D6711yescharacteristic, complemented
214C22×D4—671no—
215C22×D4—1341no—
216C22×D4C2×D6711yescharacteristic
217C2×SD16—671no—
218C2×SD16—671no—
219C2×SD16—671no—
220C22×C8—671no—
221C22×C8C2×D6711yescharacteristic, complemented
222C4⋊Q8—671no—
223#127—671no—
224#125—1341no—
225C22⋊Q8—671no—
226C22⋊Q8—671no—
227C22⋊Q8—1341no—
228C22⋊Q8—1341no—
229#121—671no—
230#121—671no—
231#121—1341no—
232#120—1341no—
233#120—1341no—
234C4×Q8—671no—
235C4×D4—671no—
236C4×D4—671no—
237C4×D4—1341no—
238C2×C4⋊C4—671no—
239C2×C4⋊C4C2×D6711yescharacteristic, complemented
240#106—671no—
241#106—671no—
242#106—671no—
243C4⋊C8—671no—
244#103—671no—
245#102—671no—
246#102—671no—
247#102—671no—
248#102—671no—
249#102—671no—
250#102C2×D6711yescharacteristic
251#102C2×D6711yescharacteristic
252#102C2×D6711yescharacteristic, complemented
253#102C2×D6711yescharacteristic, complemented
254C22⋊C8—671no—
255C22⋊C8—671no—
256C4×C8—671no—
257C24—21no—
258C24—1341no—
259C2×Q8—671no—
260C2×Q8—1341no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—2684no—
265C2×D4—2681no—
266C2×D4—671no—
267C2×D4—671no—
268C2×D4—1341no—
269C2×D4—1341no—
270C2×D4—1341no—
271C2×D4—1341no—
272C2×D4—1341no—
273C2×D4—1342no—
274C2×D4C22×D6711yescharacteristic
275C2×D4C22×D6711yescharacteristic
276C22×C4—21no—
277C22×C4—671no—
278C22×C4—1341no—
279C22×C4—1341no—
280C22×C4C22×D6711yescharacteristic
281SD16—2681no—
282SD16—2681no—
283SD16—1342no—
284C2×C8—41no—
285C2×C8—2681no—
286C2×C8—671no—
287C2×C8—671no—
288C2×C8C22×D6711yescharacteristic
289C2×C8C22×D6711yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—671no—
292C4⋊C4—671no—
293C4⋊C4—671no—
294C4⋊C4—1341no—
295C4⋊C4—1341no—
296C4⋊C4—1341no—
297C4⋊C4—1341no—
298C4⋊C4—1341no—
299C4⋊C4C22×D6711yescharacteristic
300C4⋊C4C22×D6711yescharacteristic
301C22⋊C4—671no—
302C22⋊C4—671no—
303C22⋊C4—1341no—
304C22⋊C4—1341no—
305C22⋊C4—1341no—
306C22⋊C4—1341no—
307C22⋊C4—1341no—
308C42—671no—
309C42—1341no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—2682no—
316C23—2682no—
317C23—5361no—
318C23—671no—
319C23—1341no—
320C23D4×D6711yescharacteristic
321Q8—5361no—
322Q8—1341no—
323Q8—1341no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—2682no—
329D4—2682no—
330D4—2682no—
331D4—2682no—
332D4—5361no—
333D4—674no—
334D4—1341no—
335D4—1341no—
336D4#1176162812yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—2682no—
343C2×C4—5361no—
344C2×C4—671no—
345C2×C4—671no—
346C2×C4—671no—
347C2×C4—1341no—
348C2×C4—1341no—
349C2×C4—1341no—
350C2×C4—1341no—
351C2×C4—1341no—
352C2×C4D4×D6711yescharacteristic
353C2×C4C23×D6711yescharacteristic
354C8—21no—
355C8—21no—
356C8—1341no—
357C8—1341no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—2681no—
368C22—2681no—
369C22—2681no—
370C22—5364no—
371C22—672no—
372C22—1341no—
373C22—1341no—
374C22SD16×D6712yes—
375C22C2×D4×D6711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2681no—
380C4—2681no—
381C4—2681no—
382C4—672no—
383C4—1341no—
384C4—1341no—
385C4C2×#1176162811yescharacteristic
386C4#1452408811yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—5361no—
391C2—1342no—
392C2#1686403611yescharacteristic
393C2C2×SD16×D6711yescharacteristic
394C2#1686419711yescharacteristic
subgroupG/H
centerC22C2×D4×D67
commutatorC2×C4×C67C24
FrattiniC2×C4C23×D67
FittingC2×#102×C67C2
socleC22×C67C22×D4
hypercenterC2×#102D67
hypocenterC67#3295
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #16864101C2semidirect
3. #16863741C2semidirect
4. #16863714C2semidirect
5. #16863713C2semidirect
6. #16863684C2semidirect
7. #16863625C2semidirect
8. #16863624C2semidirect
9. #16863595C2semidirect
10. #16863548C2semidirect
11. #16863547C2semidirect
12. #16863487C2semidirect
13. C8×C22⋊D67C2semidirect
14. #102×D67C2semidirect
15. C2×#102×C67C2semidirect
18. C2×#11761617C22semidirect
20. C2×#11761616C22semidirect
21. C2×C8×D67C22semidirect
22. #14524042C22semidirect
25. #14524023C22semidirect
27. #14524022C22semidirect
34. #14524008C22semidirect
38. C4⋊C4×D67C22semidirect
39. #14523975C22semidirect
40. #14523974C22semidirect
41. #14523974C22semidirect
42. Dic67⋊C8C22semidirect
43. #14523968C22semidirect
44. #14523965C22semidirect
46. #14523964C22semidirect
47. #14523963C22semidirect
48. #14523963C22semidirect
49. C22⋊(C67⋊C8)C22semidirect
50. (C2×D67)⋊C8C22semidirect
51. C8×Dic67C22semidirect
53. C22×C8×C67C22semidirect
54. C2×C4⋊C4×C67C22semidirect
57. #102×C67C22semidirect
58. #102×C67C22semidirect
140. C22⋊D67SD16semidirect
198. C67#3295semidirect
213. C2×#102D67semidirect
221. C22×C8C2×D67semidirect
239. C2×C4⋊C4C2×D67semidirect
252. #102C2×D67semidirect
253. #102C2×D67semidirect