Finite Group Databasebeta

← #21455614

Subgroups — #21455614

Order 7808.

440 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840318C211yesmaximal, characteristic, complemented
2C4×D4×D61C211yesmaximal, characteristic
3#16840063C211yesmaximal, characteristic, complemented
4#16840062C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16840051C211yesmaximal, characteristic, complemented
7#16840050C211yesmaximal, characteristic, complemented
8#16840041C211yesmaximal, characteristic, complemented
9#16840040C211yesmaximal, characteristic, complemented
10#16839803C211yesmaximal, characteristic, complemented
11#16839801C211yesmaximal, characteristic, complemented
12#16839784C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic
14#16839765C211yesmaximal, characteristic
15C61×#478C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C22×C4×D61—21no—
18C2×#11758189C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20#14519776C2211yescharacteristic, complemented
21#14519776C2211yescharacteristic, complemented
22#14519769C2211yescharacteristic, complemented
23#14519755—21no—
24#14519755—21no—
25#14519742—21no—
26#14519742—21no—
27C4×D244C2211yescharacteristic
28D4×Dic61C2211yescharacteristic
29#14519739C2211yescharacteristic
30C4×C22⋊D61—21no—
31#14519737—21no—
32#14519735C2211yescharacteristic
33#14519735C2211yescharacteristic
34C4⋊C4×D61C2211yescharacteristic
35C22⋊C4×D61—21no—
36C42×D61C2211yescharacteristic
37#14519711C2211yescharacteristic, complemented
38#14519710C2211yescharacteristic, complemented
39#14519710C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43C4⋊#92418C2211yescharacteristic, complemented
44#14519706C2211yescharacteristic, complemented
45#14519706C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519698C2211yescharacteristic
50#14519697C2211yescharacteristic
51#14519697C2211yescharacteristic
52#125×C61C2211yescharacteristic, complemented
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C22×Dic61—21no—
64D4×D61—22no—
65D4×D61Q814yescomplemented
66C2×D244C2311yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—44no—
71C2×C4×D61D411yescharacteristic
72C2×C4×D61D411yescharacteristic
73C2×C4×D61C2311yescharacteristic
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90C4⋊Dic61C2311yescharacteristic
91C4⋊Dic61C2311yescharacteristic
92C4⋊Dic61C2311yescharacteristic
93#11758196—21no—
94#11758196—21no—
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61D411yescharacteristic
101C4×Dic61D411yescharacteristic
102C4×Dic61C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105#11758189—22no—
106#11758189—22no—
107C23×C61—21no—
108C22×D61—21no—
109C22×D61—24no—
110C22×D61—42no—
111C22×D61—42no—
112C22×D61C2×D411yescharacteristic
113D4×C61—21no—
114D4×C61C2×Q812yes—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—42no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C22⋊D61—24no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—42no—
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—21no—
131D244C2×Q812yes—
132C4×D61—22no—
133C4×D61—41no—
134C4×D61—42no—
135C4×D61—42no—
136C4×D61—42no—
137C4×D61C2×Q812yes—
138C4×D61#4112yes—
139Dic122—42no—
140Dic122—42no—
141C8×C61—21no—
142C8×C61—21no—
143#92418—21no—
144#92418—21no—
145C22×C61—22no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61C22×D411yescharacteristic
149C2×D61—21no—
150C2×D61—21no—
151C2×D61—22no—
152C2×D61—48no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61C22⋊Q812yes—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61C22×Q811yescharacteristic
162C4×C61C2×#4111yescharacteristic
163Dic61—21no—
164Dic61—41no—
165Dic61—41no—
166Dic61—41no—
167Dic61C22⋊Q812yes—
168Dic61AGL(1,ℤ/8)12yes—
169#3077—611nomaximal, Sylow
170C2×C61—42no—
171C2×C61C2×C22⋊Q811yescharacteristic
172C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C61#57511yescharacteristic
174D61—22no—
175D61—42no—
176#533—611no—
177C2×C4×D4—611no—
178#478—611no—
179#478—611no—
180#478—611no—
181#478D6111yescharacteristic, complemented
182#476—611no—
183#476—611no—
184#474—611no—
185#474—611no—
186#428—611no—
187#428—611no—
188#423—611no—
189#418—611no—
190#418—611no—
191C61#307711yescharacteristic, complemented, Sylow
192C22×D4—611no—
193C23×C4—1221no—
194C2×M16—611no—
195C2×M16—611no—
196C4⋊Q8—611no—
197C4⋊Q8—611no—
198#125—611no—
199#125C2×D6111yescharacteristic, complemented
200C22⋊Q8—1221no—
201C22⋊Q8—1221no—
202C4×Q8—1221no—
203C4×Q8—1221no—
204C4×D4—611no—
205C4×D4—611no—
206C4×D4—611no—
207C4×D4—1221no—
208C4×D4—1221no—
209C4×D4C2×D6111yescharacteristic
210#117—611no—
211#117—611no—
212C2×C4⋊C4—611no—
213C2×C22⋊C4—1221no—
214C2×C42—611no—
215#107—611no—
216#107—611no—
217#107—611no—
218#107C2×D6111yescharacteristic, complemented
219#106—611no—
220#106—611no—
221#106—611no—
222#106C2×D6111yescharacteristic, complemented
223C4⋊C8—611no—
224C4⋊C8—611no—
225C4⋊C8—611no—
226C4⋊C8C2×D6111yescharacteristic, complemented
227#102—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102C2×D6111yescharacteristic
234#102C2×D6111yescharacteristic
235C24—1221no—
236C2×Q8—1221no—
237C2×Q8—1221no—
238C2×D4—614no—
239C2×D4—611no—
240C2×D4—1222no—
241C2×D4—1221no—
242C2×D4C22×D6111yescharacteristic
243C22×C4—21no—
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—2444no—
252M16—1222no—
253M16—1222no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8C22×D6111yescharacteristic
257C2×C8C22×D6111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—611no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4C22×D6111yescharacteristic
269C4⋊C4C22×D6111yescharacteristic
270C4⋊C4C22×D6111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C42—611no—
278C42—611no—
279C42—611no—
280C42—1221no—
281C42—1221no—
282C42C22×D6111yescharacteristic
283C23—21no—
284C23—611no—
285C23—1224no—
286C23—1221no—
287C23—2442no—
288C23—2442no—
289Q8—2442no—
290Q8—2442no—
291D4—21no—
292D4—612no—
293D4—1224no—
294D4—1221no—
295D4Q8×D6112yes—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—612no—
303C2×C4—612no—
304C2×C4—611no—
305C2×C4—1222no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—2441no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4—2442no—
314C2×C4D4×D6111yescharacteristic
315C2×C4D4×D6111yescharacteristic
316C2×C4C23×D6111yescharacteristic
317C8—21no—
318C8—21no—
319C8—1221no—
320C8—1221no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—612no—
325C22—1221no—
326C22—1221no—
327C22—1222no—
328C22—2448no—
329C22—2441no—
330C22—2441no—
331C22C2×D4×D6111yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—612no—
338C4—612no—
339C4—1221no—
340C4—2441no—
341C4—2441no—
342C4—2441no—
343C4C2×Q8×D6111yescharacteristic
344C4#41×D6111yescharacteristic
345C2—42no—
346C2—1222no—
347C2—2442no—
348C2C22⋊Q8×D6111yescharacteristic
349C2AGL(1,ℤ/8)×D6111yescharacteristic
350C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3077
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16840318C2semidirect
3. #16840063C2semidirect
4. #16840062C2semidirect
5. #16840059C2semidirect
6. #16840051C2semidirect
7. #16840050C2semidirect
8. #16840041C2semidirect
9. #16840040C2semidirect
10. #16839803C2semidirect
11. #16839801C2semidirect
12. #16839784C2semidirect
15. C61×#478C2semidirect
20. #14519776C22semidirect
21. #14519776C22semidirect
22. #14519769C22semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519710C22semidirect
40. #14519709C22semidirect
41. #14519708C22semidirect
42. #14519708C22semidirect
43. C4⋊#92418C22semidirect
44. #14519706C22semidirect
45. #14519706C22semidirect
52. #125×C61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. C4⋊C8×C61C22semidirect
65. D4×D61Q8semidirect
181. #478D61semidirect
191. C61#3077semidirect
199. #125C2×D61semidirect
218. #107C2×D61semidirect
222. #106C2×D61semidirect
226. C4⋊C8C2×D61semidirect