Finite Group Databasebeta

← #21455758

Subgroups — #21455758

Order 7808.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D61C211yesmaximal, characteristic
2#117×D61C211yesmaximal, characteristic, complemented
3#16840087C211yesmaximal, characteristic, complemented
4#16840086C211yesmaximal, characteristic, complemented
5#16840083C211yesmaximal, characteristic, complemented
6#16840082C211yesmaximal, characteristic, complemented
7#16840079C211yesmaximal, characteristic, complemented
8#16840077C211yesmaximal, characteristic, complemented
9#16840074C211yesmaximal, characteristic, complemented
10#16839803C211yesmaximal, characteristic, complemented
11#16839801C211yesmaximal, characteristic, complemented
12#16839765C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#16839724C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C2×D4×D61—21no—
17C2×D4×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21#14519752C2211yescharacteristic
22#14519751C2211yescharacteristic
23#14519750—21no—
24#14519749—21no—
25#14519748C2211yescharacteristic
26#14519736C2211yescharacteristic, complemented
27#14519735C2211yescharacteristic
28#14519735C2211yescharacteristic
29#14519734—21no—
30#14519733—21no—
31C4⋊C4×D61C2211yescharacteristic
32C4⋊C4×D61C2211yescharacteristic, complemented
33C4⋊C4×D61C2211yescharacteristic, complemented
34C22⋊C4×D61—21no—
35C22⋊C4×D61—21no—
36C42×D61—21no—
37#14519711C2211yescharacteristic, complemented
38#14519710C2211yescharacteristic, complemented
39#14519710C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic, complemented
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61D411yescharacteristic
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61D411yescharacteristic
68D4×D61—22no—
69D4×D61—22no—
70D4×D61—44no—
71C2×D244—21no—
72C2×D244C2311yescharacteristic
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61D411yescharacteristic
79C2×C4×D61D411yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×C4×D61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊C4×C61—21no—
89C42×C61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107#11758189—22no—
108#11758189—22no—
109C23×C61—21no—
110C23×C61C2×D411yescharacteristic
111C22×D61—22no—
112C22×D61—22no—
113C22×D61—21no—
114C22×D61—41no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61C2×D411yescharacteristic
119C22×D61C2×D411yescharacteristic
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—42no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—42no—
131C22⋊D61—42no—
132C22⋊D61—42no—
133C2×Dic61—22no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139D244—21no—
140D244—21no—
141D244—42no—
142C4×D61—22no—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—22no—
146C4×D61—42no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61#4112yes—
150C4×D61#4112yes—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—44no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—84no—
171C2×D61#12312yes—
172C2×D61AGL(1,ℤ/8)12yes—
173C4×C61—21no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61C2×#4111yescharacteristic
178C4×C61C2×#4111yescharacteristic
179Dic61—21no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183Dic61#12312yes—
184#3094—611nomaximal, Sylow
185C2×C61—41no—
186C2×C61—81no—
187C2×C61C2×#12311yescharacteristic
188C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C61#57511yescharacteristic
190D61—22no—
191D61—22no—
192D61—81no—
193C2×#121—611no—
194C2×#117—611no—
195#482—611no—
196#482—611no—
197#482—611no—
198#482D6111yescharacteristic, complemented
199#481—611no—
200#481—611no—
201#480—611no—
202#480—611no—
203#428—611no—
204#428—611no—
205#418—611no—
206#418—611no—
207#407—611no—
208C61#309411yescharacteristic, complemented, Sylow
209C22×D4—611no—
210C22×D4—1221no—
211C23×C4—611no—
212C2×M16—611no—
213C2×M16—611no—
214#121—611no—
215#121—611no—
216#121—611no—
217#121—1221no—
218#121—1221no—
219#121C2×D6111yescharacteristic
220#117—611no—
221#117—611no—
222#117—611no—
223#117—1221no—
224#117—1221no—
225#117C2×D6111yescharacteristic, complemented
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C42—1221no—
232#107—611no—
233#107—611no—
234#107—611no—
235#107C2×D6111yescharacteristic, complemented
236#106—611no—
237#106—611no—
238#106—611no—
239#106C2×D6111yescharacteristic, complemented
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102C2×D6111yescharacteristic, complemented
247#102C2×D6111yescharacteristic, complemented
248C22⋊C8—611no—
249C22⋊C8—611no—
250C22⋊C8—611no—
251C22⋊C8C2×D6111yescharacteristic, complemented
252C24—611no—
253C24—1221no—
254C2×D4—21no—
255C2×D4—611no—
256C2×D4—1221no—
257C2×D4—1222no—
258C2×D4—1222no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—2444no—
263C2×D4C22×D6111yescharacteristic
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1222no—
270C22×C4—1222no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4C22×D6111yescharacteristic
275M16—1222no—
276M16—1222no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4C22×D6111yescharacteristic
288C4⋊C4C22×D6111yescharacteristic
289C4⋊C4C22×D6111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C42—21no—
299C42—1221no—
300C42—1221no—
301C42—1221no—
302C23—21no—
303C23—611no—
304C23—611no—
305C23—1222no—
306C23—1222no—
307C23—1221no—
308C23—2441no—
309C23—2442no—
310C23—2442no—
311C23—2442no—
312C23D4×D6111yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—1221no—
317D4—1221no—
318D4—2442no—
319D4—2442no—
320D4—2442no—
321D4—2442no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—611no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—611no—
331C2×C4—1222no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4D4×D6111yescharacteristic
343C2×C4C23×D6111yescharacteristic
344C8—21no—
345C8—21no—
346C8—1221no—
347C8—1221no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—612no—
355C22—612no—
356C22—1221no—
357C22—1221no—
358C22—1221no—
359C22—1221no—
360C22—4884no—
361C22—2444no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22C2×D4×D6111yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—612no—
371C4—1221no—
372C4—2441no—
373C4—2441no—
374C4—2441no—
375C4#41×D6111yescharacteristic
376C4#41×D6111yescharacteristic
377C2—41no—
378C2—81no—
379C2—1222no—
380C2—1222no—
381C2—4881no—
382C2#123×D6111yescharacteristic
383C2AGL(1,ℤ/8)×D6111yescharacteristic
384C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3094
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #117×D61C2semidirect
3. #16840087C2semidirect
4. #16840086C2semidirect
5. #16840083C2semidirect
6. #16840082C2semidirect
7. #16840079C2semidirect
8. #16840077C2semidirect
9. #16840074C2semidirect
10. #16839803C2semidirect
11. #16839801C2semidirect
12. #16839765C2semidirect
13. #16839765C2semidirect
14. #16839724C2semidirect
15. C61×#482C2semidirect
26. #14519736C22semidirect
32. C4⋊C4×D61C22semidirect
33. C4⋊C4×D61C22semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519710C22semidirect
40. #14519709C22semidirect
41. #14519708C22semidirect
42. #14519708C22semidirect
43. #14519699C22semidirect
44. #14519699C22semidirect
45. #14519698C22semidirect
46. #14519698C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
49. C22⋊#92418C22semidirect
50. #14519689C22semidirect
51. #14519689C22semidirect
53. #117×C61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #102×C61C22semidirect
57. #102×C61C22semidirect
58. C22⋊C8×C61C22semidirect
198. #482D61semidirect
208. C61#3094semidirect
225. #117C2×D61semidirect
235. #107C2×D61semidirect
239. #106C2×D61semidirect
246. #102C2×D61semidirect
247. #102C2×D61semidirect
251. C22⋊C8C2×D61semidirect