Finite Group Databasebeta

← #22572018

Subgroups — #22572018

Order 8576.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16864047C211yesmaximal, characteristic, complemented
2D4×C22⋊D67C211yesmaximal, characteristic, complemented
3#16863741C211yesmaximal, characteristic, complemented
4#16863709C211yesmaximal, characteristic, complemented
5#16863708C211yesmaximal, characteristic, complemented
6#16863674C211yesmaximal, characteristic, complemented
7#16863632C211yesmaximal, characteristic, complemented
8#16863631C211yesmaximal, characteristic, complemented
9#16863590C211yesmaximal, characteristic, complemented
10#16863531C211yesmaximal, characteristic, complemented
11#16863530C211yesmaximal, characteristic, complemented
12#16863476C211yesmaximal, characteristic, complemented
13C8×C22⋊D67C211yesmaximal, characteristic, complemented
14#102×D67C211yesmaximal, characteristic, complemented
15C2×#102×C67C211yesmaximal, characteristic, complemented
16C2×#11761628—21no—
17C22×C22⋊D67—21no—
18C2×D4×D67C2211yescharacteristic
19C2×D536C2211yescharacteristic, complemented
20C2×#11761613C2211yescharacteristic
21C2×#11761613C2211yescharacteristic, complemented
22C2×C8×D67C2211yescharacteristic, complemented
23#14524042C2211yescharacteristic, complemented
24#14524039C2211yescharacteristic
25#14524028—21no—
26#14524026—21no—
27#14524021—21no—
28#14524018C2211yescharacteristic, complemented
29#14524017C2211yescharacteristic
30#14524017C2211yescharacteristic, complemented
31#14524015—21no—
32#14524014C2211yescharacteristic
33#14524012—21no—
34#14524011—21no—
35D4×Dic67C2211yescharacteristic
36#14524005C2211yescharacteristic, complemented
37C4×C22⋊D67C2211yescharacteristic
38C4⋊C4×D67C2211yescharacteristic, complemented
39#14523977C2211yescharacteristic, complemented
40#14523976C2211yescharacteristic, complemented
41#14523976C2211yescharacteristic, complemented
42Dic67⋊C8C2211yescharacteristic, complemented
43#14523965C2211yescharacteristic, 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—
60#11761628—44no—
61C2×Dic134—21no—
62C2×D268—21no—
63C2×D268C2311yescharacteristic
64C2×D268C2311yescharacteristic
65C2×C22⋊D67—21no—
66C2×C22⋊D67—21no—
67C2×C22⋊D67—21no—
68C2×C22⋊D67—21no—
69C2×C22⋊D67—21no—
70C2×C22⋊D67—21no—
71C2×C22⋊D67—44no—
72C2×C22⋊D67D411yescharacteristic
73D4×D67—22no—
74D4×D67—41no—
75C22×Dic67—21no—
76C2×C4×D67—21no—
77C2×C4×D67—21no—
78C2×C4×D67C2311yescharacteristic
79D536—41no—
80#11761613—22no—
81#11761613—41no—
82C2×C67⋊C8C2311yescharacteristic
83C2×C67⋊C8C2311yescharacteristic
84C8×D67—41no—
85C4⋊Dic67C2311yescharacteristic
86C4⋊Dic67C2311yescharacteristic
87Dic67⋊C4—21no—
88Dic67⋊C4—21no—
89Dic67⋊C4D411yescharacteristic
90C22⋊Dic67—21no—
91C22⋊Dic67—21no—
92C22⋊Dic67D411yescharacteristic
93(C2×D67)⋊C4—21no—
94(C2×D67)⋊C4—21no—
95(C2×D67)⋊C4—21no—
96(C2×D67)⋊C4—21no—
97(C2×D67)⋊C4D411yescharacteristic
98C4×Dic67C2311yescharacteristic
99C24×C67—21no—
100C2×D4×C67—22no—
101C2×D4×C67—21no—
102C2×D4×C67—41no—
103C2×D4×C67C2311yescharacteristic
104C2×D4×C67C2311yescharacteristic
105C22×C4×C67—21no—
106C22×C4×C67C2311yescharacteristic
107C2×C8×C67—41no—
108C2×C8×C67C2311yescharacteristic
109C2×C8×C67C2311yescharacteristic
110C4⋊C4×C67—21no—
111C4⋊C4×C67C2311yescharacteristic
112C4⋊C4×C67C2311yescharacteristic
113C23×C67—21no—
114C23×C67—21no—
115C23×C67—42no—
116C23×C67—42no—
117C23×C67—81no—
118C23×C67C2×D411yescharacteristic
119C22×D67—21no—
120C22×D67—21no—
121C22×D67—42no—
122C22×D67—42no—
123C22×D67—81no—
124C22×D67C2×D411yescharacteristic
125D4×C67—21no—
126D4×C67—21no—
127D4×C67—21no—
128D4×C67—42no—
129D4×C67#4112yescomplemented
130C2×C4×C67—21no—
131C2×C4×C67—21no—
132C2×C4×C67—21no—
133C2×C4×C67—21no—
134C2×C4×C67—42no—
135C2×C4×C67C2×D411yescharacteristic
136C2×C4×C67C2411yescharacteristic
137C22⋊D67—42no—
138C22⋊D67—42no—
139C22⋊D67—42no—
140C22⋊D67—42no—
141C22⋊D67—42no—
142C22⋊D67—81no—
143C22⋊D67D814yescomplemented
144C2×Dic67—21no—
145C2×Dic67—21no—
146C2×Dic67—42no—
147C2×Dic67C2×D411yescharacteristic
148C2×Dic67C2×D411yescharacteristic
149C2×Dic67C2×D411yescharacteristic
150D268—21no—
151D268—21no—
152D268—21no—
153D268—21no—
154D268—42no—
155C4×D67—21no—
156C4×D67—21no—
157C4×D67—42no—
158C4×D67—42no—
159Dic134—42no—
160C8×C67—21no—
161C8×C67—21no—
162C67⋊C8—21no—
163C67⋊C8—21no—
164C22×C67—21no—
165C22×C67—21no—
166C22×C67—22no—
167C22×C67—41no—
168C22×C67—41no—
169C22×C67—41no—
170C22×C67—41no—
171C22×C67—41no—
172C22×C67—84no—
173C22×C67C2×D812yes—
174C22×C67C22×D411yescharacteristic
175C2×D67—21no—
176C2×D67—21no—
177C2×D67—41no—
178C2×D67—41no—
179C2×D67—41no—
180C2×D67—41no—
181C2×D67—41no—
182C2×D67—41no—
183C2×D67—84no—
184C2×D67C2×D812yes—
185C4×C67—21no—
186C4×C67—41no—
187C4×C67—41no—
188C4×C67C2×#4111yescharacteristic
189C4×C67H(5,𝔽2)11yescharacteristic
190Dic67—21no—
191Dic67—21no—
192Dic67—41no—
193Dic67—41no—
194Dic67C2×D812yes—
195C2×C67—22no—
196C2×C67—42no—
197C2×C67—81no—
198C2×C67#54611yescharacteristic
199C2×C67C22×D811yescharacteristic
200C2×C67#57711yescharacteristic
201D67—22no—
202D67—81no—
203D67—81no—
204#3294—671nomaximal, Sylow
205C67#329411yescharacteristic, complemented, Sylow
206#547—671no—
207D42—671no—
208#486—671no—
209#480—671no—
210#480—671no—
211#474—671no—
212#466—671no—
213#466—671no—
214#459—671no—
215#447—671no—
216#447—671no—
217C4×D8—671no—
218C8×D4—671no—
219C2×#102—671no—
220C2×#102D6711yescharacteristic, complemented
221C2×#41—1341no—
222C22×D4—671no—
223C22×D4—1341no—
224C22×D4C2×D6711yescharacteristic
225C2×D8—671no—
226C2×D8—671no—
227C2×D8—671no—
228C22×C8—671no—
229C22×C8C2×D6711yescharacteristic, complemented
230C4⋊Q8—671no—
231#127—671no—
232#123—1341no—
233#123—1341no—
234C22⋊Q8—1341no—
235#121—671no—
236#121—671no—
237#121—671no—
238#121—671no—
239#121—1341no—
240#120—1341no—
241#120—1341no—
242C4×D4—671no—
243C4×D4—671no—
244C4×D4—671no—
245C2×C4⋊C4—671no—
246C2×C4⋊C4C2×D6711yescharacteristic, complemented
247#107—671no—
248#107—671no—
249#107—671no—
250C4⋊C8—671no—
251#102—671no—
252#102—671no—
253#102—671no—
254#102—671no—
255#102—671no—
256#102—671no—
257#102C2×D6711yescharacteristic
258#102C2×D6711yescharacteristic
259#102C2×D6711yescharacteristic, complemented
260#102C2×D6711yescharacteristic, complemented
261C22⋊C8—671no—
262C22⋊C8—671no—
263C4×C8—671no—
264C24—21no—
265C24—1341no—
266#41—2684no—
267C2×Q8—1341no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—2684no—
272C2×D4—2681no—
273C2×D4—671no—
274C2×D4—671no—
275C2×D4—671no—
276C2×D4—1341no—
277C2×D4—1341no—
278C2×D4—1341no—
279C2×D4—1341no—
280C2×D4—1341no—
281C2×D4—1341no—
282C2×D4—1341no—
283C2×D4—1342no—
284C2×D4C22×D6711yescharacteristic
285C2×D4C22×D6711yescharacteristic
286C22×C4—21no—
287C22×C4—671no—
288C22×C4—1341no—
289C22×C4—1341no—
290C22×C4—1341no—
291C22×C4C22×D6711yescharacteristic
292D8—2681no—
293D8—2681no—
294D8—1342no—
295C2×C8—41no—
296C2×C8—2681no—
297C2×C8—671no—
298C2×C8—671no—
299C2×C8C22×D6711yescharacteristic
300C2×C8C22×D6711yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—671no—
303C4⋊C4—671no—
304C4⋊C4—671no—
305C4⋊C4—1341no—
306C4⋊C4—1341no—
307C4⋊C4C22×D6711yescharacteristic
308C4⋊C4C22×D6711yescharacteristic
309C22⋊C4—671no—
310C22⋊C4—671no—
311C22⋊C4—1341no—
312C22⋊C4—1341no—
313C22⋊C4—1341no—
314C22⋊C4—1341no—
315C22⋊C4—1341no—
316C22⋊C4—1341no—
317C42—671no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—2682no—
324C23—2682no—
325C23—5361no—
326C23—671no—
327C23—1341no—
328C23—1341no—
329C23D4×D6711yescharacteristic
330Q8—2682no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—2682no—
336D4—2682no—
337D4—2682no—
338D4—2682no—
339D4—2682no—
340D4—2682no—
341D4—5361no—
342D4—674no—
343D4—1341no—
344D4—1341no—
345D4—1341no—
346D4—1341no—
347D4#1176162812yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—2682no—
354C2×C4—2682no—
355C2×C4—2682no—
356C2×C4—671no—
357C2×C4—671no—
358C2×C4—671no—
359C2×C4—1341no—
360C2×C4—1341no—
361C2×C4—1341no—
362C2×C4—1341no—
363C2×C4D4×D6711yescharacteristic
364C2×C4C23×D6711yescharacteristic
365C8—21no—
366C8—21no—
367C8—1341no—
368C8—1341no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—2681no—
379C22—2681no—
380C22—2681no—
381C22—2681no—
382C22—2681no—
383C22—2681no—
384C22—5364no—
385C22—672no—
386C22—1341no—
387C22—1341no—
388C22D8×D6712yes—
389C22C2×D4×D6711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—2681no—
394C4—2681no—
395C4—672no—
396C4—1341no—
397C4—1341no—
398C4C2×#1176162811yescharacteristic
399C4#1452408811yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—5361no—
404C2—5361no—
405C2—1342no—
406C2#1686403611yescharacteristic
407C2C2×D8×D6711yescharacteristic
408C2#1686420211yescharacteristic
subgroupG/H
centerC22C2×D4×D67
commutatorC2×C4×C67C24
FrattiniC2×C4C23×D67
FittingC2×#102×C67C2
socleC22×C67C22×D4
hypercenterC2×#102D67
hypocenterC67#3294
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. #16864047C2semidirect
2. D4×C22⋊D67C2semidirect
3. #16863741C2semidirect
4. #16863709C2semidirect
5. #16863708C2semidirect
6. #16863674C2semidirect
7. #16863632C2semidirect
8. #16863631C2semidirect
9. #16863590C2semidirect
10. #16863531C2semidirect
11. #16863530C2semidirect
12. #16863476C2semidirect
13. C8×C22⋊D67C2semidirect
14. #102×D67C2semidirect
15. C2×#102×C67C2semidirect
19. C2×D536C22semidirect
21. C2×#11761613C22semidirect
22. C2×C8×D67C22semidirect
23. #14524042C22semidirect
28. #14524018C22semidirect
30. #14524017C22semidirect
36. #14524005C22semidirect
38. C4⋊C4×D67C22semidirect
39. #14523977C22semidirect
40. #14523976C22semidirect
41. #14523976C22semidirect
42. Dic67⋊C8C22semidirect
43. #14523965C22semidirect
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
129. D4×C67#41semidirect
143. C22⋊D67D8semidirect
205. C67#3294semidirect
220. C2×#102D67semidirect
229. C22×C8C2×D67semidirect
246. C2×C4⋊C4C2×D67semidirect
259. #102C2×D67semidirect
260. #102C2×D67semidirect
347. D4#11761628semidirect