Finite Group Databasebeta

← #21456631

Subgroups — #21456631

Order 7808.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840269C211yesmaximal, characteristic, complemented
2#121×D61C211yesmaximal, characteristic, complemented
3#16840091C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840083C211yesmaximal, characteristic, complemented
6#16840074C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16840012C211yesmaximal, characteristic, complemented
9#16840011C211yesmaximal, characteristic, complemented
10#16840005C211yesmaximal, characteristic, complemented
11#16839911C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic, complemented
13#16839894C211yesmaximal, characteristic, complemented
14#16839724C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C2×D4×D61—21no—
17C2×D4×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C2×#11758201C2211yescharacteristic, complemented
20C2×#11758199C2211yescharacteristic, complemented
21C2×#11758189C2211yescharacteristic, complemented
22C2×#11758189C2211yescharacteristic, complemented
23#14519758—21no—
24#14519753C2211yescharacteristic
25#14519753C2211yescharacteristic, complemented
26#14519752C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519750—21no—
29#14519749—21no—
30#14519748C2211yescharacteristic
31#14519748C2211yescharacteristic
32#14519748C2211yescharacteristic, complemented
33#14519745—21no—
34C4×C22⋊D61—21no—
35C4×C22⋊D61—21no—
36#14519736C2211yescharacteristic, complemented
37C4⋊C4×D61C2211yescharacteristic
38C22⋊C4×D61—21no—
39#14519711C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic, complemented
48#14519698C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic, complemented
53C2×SD16×C61C2211yescharacteristic, complemented
54C2×D8×C61C2211yescharacteristic, complemented
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61D411yescharacteristic
61#41×C61—41no—
62#41×C61—41no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C22×C4×C61—21no—
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C22×Dic61D411yescharacteristic
76D4×D61—41no—
77D4×D61—41no—
78D4×D61—44no—
79C2×D244—21no—
80C2×D244C2311yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61D411yescharacteristic
85C2×C4×D61D411yescharacteristic
86C2×C4×D61C2311yescharacteristic
87C2×C4×D61C2311yescharacteristic
88SD16×C61—41no—
89D8×C61—41no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98#11758201—41no—
99#11758199—41no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196—21no—
109#11758196—21no—
110C4×Dic61—21no—
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113#11758189—41no—
114#11758189—41no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61C2×D411yescharacteristic
118C22×D61—22no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61C2×D411yescharacteristic
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61—21no—
129D4×C61—21no—
130D4×C61—21no—
131D4×C61—21no—
132D4×C61—21no—
133D4×C61—42no—
134D4×C61—42no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—42no—
140C2×C4×C61C2×D411yescharacteristic
141C2×C4×C61C2411yescharacteristic
142C22⋊D61—42no—
143C22⋊D61—42no—
144C22⋊D61—42no—
145C22⋊D61—42no—
146C22⋊D61—42no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—41no—
151C2×Dic61C2×D411yescharacteristic
152C2×Dic61C2×D411yescharacteristic
153D244—21no—
154D244—21no—
155D244—42no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—41no—
161C4×D61—41no—
162C4×D61—42no—
163C8×C61—21no—
164C8×C61—21no—
165#92418—21no—
166#92418—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61C22×D411yescharacteristic
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—44no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—84no—
187C2×D61AGL(1,ℤ/8)12yes—
188C4×C61—21no—
189C4×C61—41no—
190C4×C61—41no—
191C4×C61H(5,𝔽2)11yescharacteristic
192C4×C61H(5,𝔽2)11yescharacteristic
193Dic61—21no—
194Dic61—21no—
195Dic61—41no—
196Dic61—41no—
197Dic61—41no—
198#3194—611nomaximal, Sylow
199C2×C61—41no—
200C2×C61—81no—
201C2×C61—81no—
202C2×C61#53411yescharacteristic
203C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
204C2×C61#57511yescharacteristic
205D61—22no—
206D61—41no—
207D61—81no—
208#525—611no—
209C2×#121—611no—
210#483—611no—
211#482—611no—
212#482—611no—
213#480—611no—
214#469—611no—
215#469—611no—
216#468—611no—
217#468—611no—
218#450—611no—
219#449—611no—
220#449D6111yescharacteristic, complemented
221#447—611no—
222#407—611no—
223C61#319411yescharacteristic, complemented, Sylow
224C2×#41C2×D6111yescharacteristic, complemented
225C22×D4—611no—
226C22×D4—1221no—
227C23×C4—611no—
228C2×SD16—611no—
229C2×SD16C2×D6111yescharacteristic, complemented
230C2×D8—611no—
231C2×D8C2×D6111yescharacteristic, complemented
232C2×M16—611no—
233C2×M16—611no—
234#123—1221no—
235C22⋊Q8—611no—
236C22⋊Q8—611no—
237#121—611no—
238#121—611no—
239#121—611no—
240#121—611no—
241#121—611no—
242#121—1221no—
243#121—1221no—
244#121C2×D6111yescharacteristic
245#120—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248#117—611no—
249C2×C4⋊C4—611no—
250C2×C22⋊C4—1221no—
251#107—611no—
252#107—611no—
253#106—611no—
254#106—611no—
255#103—611no—
256#103C2×D6111yescharacteristic, complemented
257#102—611no—
258#102—611no—
259#102—611no—
260#102—611no—
261#102—611no—
262#102C2×D6111yescharacteristic, complemented
263C22⋊C8—611no—
264C22⋊C8—611no—
265C22⋊C8—611no—
266C22⋊C8C2×D6111yescharacteristic, complemented
267C24—611no—
268C24—1221no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D6111yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—611no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2444no—
284C2×D4C22×D6111yescharacteristic
285C2×D4C22×D6111yescharacteristic
286C22×C4—21no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—1221no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4C22×D6111yescharacteristic
296SD16—41no—
297SD16—2441no—
298D8—41no—
299D8—2441no—
300M16—2441no—
301M16—2441no—
302C2×C8—611no—
303C2×C8—611no—
304C2×C8C22×D6111yescharacteristic
305C2×C8C22×D6111yescharacteristic
306C4⋊C4—611no—
307C4⋊C4—611no—
308C4⋊C4—611no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4C22×D6111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C42—1221no—
323C23—21no—
324C23—21no—
325C23—611no—
326C23—611no—
327C23—1222no—
328C23—1221no—
329C23—2441no—
330C23—2441no—
331C23—2442no—
332C23—2442no—
333C23—2442no—
334C23D4×D6111yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—1221no—
344D4—1221no—
345D4—2442no—
346D4—2442no—
347D4—2442no—
348D4—2442no—
349D4—2442no—
350D4—2442no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2442no—
368C2×C4—2441no—
369C2×C4D4×D6111yescharacteristic
370C2×C4C23×D6111yescharacteristic
371C8—21no—
372C8—21no—
373C8—1221no—
374C8—1221no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—612no—
385C22—1221no—
386C22—1221no—
387C22—1221no—
388C22—1221no—
389C22—1221no—
390C22—4884no—
391C22—2444no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22C2×D4×D6111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—1221no—
400C4—1221no—
401C4—2441no—
402C4—2441no—
403C4—2441no—
404C4#1451982211yescharacteristic
405C4#1451982211yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—1222no—
410C2—4881no—
411C2—2441no—
412C2#1684032211yescharacteristic
413C2AGL(1,ℤ/8)×D6111yescharacteristic
414C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3194
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16840269C2semidirect
2. #121×D61C2semidirect
3. #16840091C2semidirect
4. #16840087C2semidirect
5. #16840083C2semidirect
6. #16840074C2semidirect
7. #16840014C2semidirect
8. #16840012C2semidirect
9. #16840011C2semidirect
10. #16840005C2semidirect
11. #16839911C2semidirect
12. #16839907C2semidirect
13. #16839894C2semidirect
14. #16839724C2semidirect
15. C61×#449C2semidirect
19. C2×#11758201C22semidirect
20. C2×#11758199C22semidirect
21. C2×#11758189C22semidirect
22. C2×#11758189C22semidirect
25. #14519753C22semidirect
32. #14519748C22semidirect
36. #14519736C22semidirect
39. #14519711C22semidirect
40. #14519710C22semidirect
41. #14519709C22semidirect
42. #14519708C22semidirect
43. #14519701C22semidirect
44. #14519699C22semidirect
45. #14519699C22semidirect
46. #14519698C22semidirect
47. #14519698C22semidirect
48. #14519698C22semidirect
49. C22⋊#92418C22semidirect
52. C2×#41×C61C22semidirect
53. C2×SD16×C61C22semidirect
54. C2×D8×C61C22semidirect
56. #103×C61C22semidirect
57. #102×C61C22semidirect
58. C22⋊C8×C61C22semidirect
220. #449D61semidirect
223. C61#3194semidirect
224. C2×#41C2×D61semidirect
229. C2×SD16C2×D61semidirect
231. C2×D8C2×D61semidirect
256. #103C2×D61semidirect
262. #102C2×D61semidirect
266. C22⋊C8C2×D61semidirect