Finite Group Databasebeta

← #21455908

Subgroups — #21455908

Order 7808.

488 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840309C211yesmaximal, characteristic, complemented
2C4×D4×D61C211yesmaximal, characteristic, complemented
3#16840082C211yesmaximal, characteristic, complemented
4#16840079C211yesmaximal, characteristic, complemented
5#16840051C211yesmaximal, characteristic, complemented
6#16840050C211yesmaximal, characteristic, complemented
7#16839956C211yesmaximal, characteristic, complemented
8#16839955C211yesmaximal, characteristic, complemented
9#16839897C211yesmaximal, characteristic, complemented
10#16839894C211yesmaximal, characteristic, complemented
11#16839875C211yesmaximal, characteristic, complemented
12#16839872C211yesmaximal, characteristic, complemented
13#16839872C211yesmaximal, characteristic, complemented
14#16839817C211yesmaximal, characteristic, complemented
15C61×#442C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×D4×D61C2211yescharacteristic
18C22×C4×D61—21no—
19C2×D488C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22#14519776C2211yescharacteristic, complemented
23#14519773C2211yescharacteristic, complemented
24#14519763—21no—
25#14519752C2211yescharacteristic
26#14519750—21no—
27#14519748C2211yescharacteristic
28C4×D244C2211yescharacteristic
29C4×D244C2211yescharacteristic, complemented
30D4×Dic61C2211yescharacteristic
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33C4×C22⋊D61—21no—
34#14519737—21no—
35C4⋊C4×D61C2211yescharacteristic
36C22⋊C4×D61—21no—
37C42×D61C2211yescharacteristic
38#14519709C2211yescharacteristic, complemented
39#14519708C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic, complemented
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519688C2211yescharacteristic, complemented
52C2×D8×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic, complemented
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69D4×D61—22no—
70D4×D61—22no—
71#11758222—44no—
72C2×D244—21no—
73C2×D244C2311yescharacteristic
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—44no—
80C2×C4×D61D411yescharacteristic
81C2×C4×D61D411yescharacteristic
82C2×C4×D61C2311yescharacteristic
83C2×Dic122—21no—
84D8×C61—22no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C42×C61C2311yescharacteristic
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94#11758199—22no—
95#11758199—22no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61D411yescharacteristic
105C4×Dic61D411yescharacteristic
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109D488—22no—
110C23×C61—21no—
111C23×C61—21no—
112C22×D61—24no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61C2×D411yescharacteristic
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61#4112yescomplemented
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61—24no—
130C22⋊D61—42no—
131C22⋊D61—42no—
132C22⋊D61—42no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—42no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139D244—21no—
140D244—21no—
141D244—21no—
142D244—42no—
143D244#4112yescomplemented
144C4×D61—22no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—22no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—42no—
151C4×D61—42no—
152Dic122—42no—
153C8×C61—21no—
154C8×C61—21no—
155#92418—21no—
156#92418—21no—
157C22×C61—22no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61C22×D411yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—22no—
167C2×D61—48no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61AGL(1,ℤ/8)12yes—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61C2×#4111yescharacteristic
179C4×C61C2×#4111yescharacteristic
180Dic61—21no—
181Dic61—21no—
182Dic61—41no—
183Dic61—41no—
184Dic61AGL(1,ℤ/8)12yes—
185#3109—611nomaximal, Sylow
186C2×C61—42no—
187C2×C61—81no—
188C2×C61#52511yescharacteristic
189C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
191D61—22no—
192D61—42no—
193D61—81no—
194#532—611no—
195C2×C4×D4—611no—
196#481—611no—
197#481—611no—
198#476—611no—
199#476—611no—
200#459—611no—
201#459—611no—
202#447—611no—
203#447—611no—
204#442—611no—
205#442—611no—
206#442—611no—
207#442D6111yescharacteristic, complemented
208#432—611no—
209C61#310911yescharacteristic, complemented, Sylow
210C2×#41—1221no—
211C22×D4—611no—
212C23×C4—1221no—
213C2×D8—611no—
214C2×D8—611no—
215C2×D8—611no—
216C2×D8C2×D6111yescharacteristic
217C4⋊Q8—611no—
218#127—611no—
219#124—1221no—
220#121—611no—
221#121—611no—
222#121—1221no—
223C4×D4—611no—
224C4×D4—611no—
225C4×D4—611no—
226C4×D4—611no—
227C4×D4—1221no—
228C4×D4—1221no—
229C4×D4—1221no—
230C4×D4C2×D6111yescharacteristic
231C4×D4C2×D6111yescharacteristic, complemented
232C2×C4⋊C4—611no—
233C2×C22⋊C4—1221no—
234C2×C42—611no—
235#106—611no—
236#106—611no—
237#106—611no—
238#106C2×D6111yescharacteristic, complemented
239C4⋊C8—611no—
240C4⋊C8—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102C2×D6111yescharacteristic
248#102C2×D6111yescharacteristic, complemented
249C22⋊C8—611no—
250C22⋊C8—611no—
251#97—611no—
252#97C2×D6111yescharacteristic, complemented
253C24—1221no—
254#41—2444no—
255C2×Q8—1221no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1222no—
263C2×D4—1222no—
264C2×D4—1221no—
265C2×D4C22×D6111yescharacteristic
266C2×D4C22×D6111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—2444no—
278D8—22no—
279D8—1222no—
280D8—1222no—
281D8—1222no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8C22×D6111yescharacteristic
285C2×C8C22×D6111yescharacteristic
286C4⋊C4—611no—
287C4⋊C4—611no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4C22×D6111yescharacteristic
291C4⋊C4C22×D6111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C42—611no—
301C42—611no—
302C42—611no—
303C42C22×D6111yescharacteristic
304C23—21no—
305C23—21no—
306C23—611no—
307C23—1224no—
308C23—1221no—
309C23—1221no—
310C23—2442no—
311C23—2442no—
312Q8—2442no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—612no—
317D4—1224no—
318D4—1221no—
319D4—1221no—
320D4—1221no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324D4—2442no—
325D4#1175822212yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4D4×D6111yescharacteristic
345C2×C4D4×D6111yescharacteristic
346C2×C4C23×D6111yescharacteristic
347C8—21no—
348C8—21no—
349C8—1221no—
350C8—1221no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—612no—
358C22—1221no—
359C22—1221no—
360C22—1222no—
361C22—2448no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22C2×D4×D6111yescharacteristic
368C4—21no—
369C4—21no—
370C4—41no—
371C4—41no—
372C4—612no—
373C4—1221no—
374C4—1221no—
375C4—2441no—
376C4—2441no—
377C4#41×D6111yescharacteristic
378C4C2×#1175822211yescharacteristic
379C2—42no—
380C2—81no—
381C2—1222no—
382C2—4881no—
383C2—2442no—
384C2#1684027111yescharacteristic
385C2AGL(1,ℤ/8)×D6111yescharacteristic
386C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#3109
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16840309C2semidirect
2. C4×D4×D61C2semidirect
3. #16840082C2semidirect
4. #16840079C2semidirect
5. #16840051C2semidirect
6. #16840050C2semidirect
7. #16839956C2semidirect
8. #16839955C2semidirect
9. #16839897C2semidirect
10. #16839894C2semidirect
11. #16839875C2semidirect
12. #16839872C2semidirect
13. #16839872C2semidirect
14. #16839817C2semidirect
15. C61×#442C2semidirect
22. #14519776C22semidirect
23. #14519773C22semidirect
29. C4×D244C22semidirect
38. #14519709C22semidirect
39. #14519708C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
44. #14519699C22semidirect
46. #14519698C22semidirect
48. #14519697C22semidirect
51. #14519688C22semidirect
54. C4×D4×C61C22semidirect
55. #106×C61C22semidirect
57. #102×C61C22semidirect
58. #97×C61C22semidirect
121. D4×C61#41semidirect
143. D244#41semidirect
207. #442D61semidirect
209. C61#3109semidirect
231. C4×D4C2×D61semidirect
238. #106C2×D61semidirect
248. #102C2×D61semidirect
252. #97C2×D61semidirect
325. D4#11758222semidirect