Finite Group Databasebeta

← #485×D61 #21455707

Subgroups — #485×D61 #21455707

Order 7808.

416 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D61C211yesmaximal, characteristic
2#117×D61C211yesmaximal, characteristic
3#16840106C211yesmaximal, characteristic, complemented
4#16840105C211yesmaximal, characteristic, complemented
5#16840104C211yesmaximal, characteristic, complemented
6#16840103C211yesmaximal, characteristic, complemented
7#16840102C211yesmaximal, characteristic, complemented
8#16840101C211yesmaximal, characteristic, complemented
9#16840100C211yesmaximal, characteristic, complemented
10#107×D61C211yesmaximal, characteristic, complemented
11#106×D61C211yesmaximal, characteristic, complemented
12#103×D61C211yesmaximal, characteristic, complemented
13#103×D61C211yesmaximal, characteristic, complemented
14C22⋊C8×D61C211yesmaximal, characteristic
15C61×#485C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C2×C8×D61C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519757C2211yescharacteristic
21#14519756C2211yescharacteristic
22#14519755—21no—
23#14519754—21no—
24#14519753C2211yescharacteristic
25#14519736C2211yescharacteristic
26#14519735C2211yescharacteristic
27#14519735C2211yescharacteristic
28#14519734—21no—
29#14519733—21no—
30C4⋊C4×D61—21no—
31C4⋊C4×D61C2211yescharacteristic
32C4⋊C4×D61C2211yescharacteristic
33C4⋊C4×D61C2211yescharacteristic
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#14519702C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519701C2211yescharacteristic, complemented
46#14519701C2211yescharacteristic, complemented
47#14519700C2211yescharacteristic, complemented
48#14519700C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61D411yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×Dic61D411yescharacteristic
63Q8×D61—22no—
64Q8×D61—22no—
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61D411yescharacteristic
72C2×C4×D61D411yescharacteristic
73C2×C4×D61C2311yescharacteristic
74C2×C4×D61C2311yescharacteristic
75C2×Dic122—21no—
76C2×Dic122C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C42×C61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61C2311yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C8×D61—22no—
107C8×D61—22no—
108C23×C61C2×D411yescharacteristic
109C22×D61—22no—
110C22×D61—22no—
111C22×D61—22no—
112C22×D61C2×D411yescharacteristic
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C2×Dic61—22no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C4×D61—22no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—22no—
135C4×D61—42no—
136C4×D61—42no—
137C4×D61—42no—
138C4×D61—42no—
139C4×D61#4112yes—
140C4×D61#4112yes—
141Dic122—21no—
142Dic122—21no—
143Dic122—42no—
144C8×C61—21no—
145C8×C61—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C22×D411yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—44no—
156C2×D61#12312yes—
157C2×D61#13512yes—
158C2×D61#13712yes—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61C2×#4111yescharacteristic
165C4×C61C2×#4111yescharacteristic
166Dic61—21no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171Dic61#12312yes—
172C2×#485—611nomaximal, Sylow
173C2×C61—41no—
174C2×C61C2×#12311yescharacteristic
175C2×C61C2×#13511yescharacteristic
176C2×C61C2×#13711yescharacteristic
177D61—41no—
178D61#48514yesdirect product factor
179C2×C22⋊Q8—611no—
180C2×#117—611no—
181#485—611no—
182#485—611no—
183#485—611no—
184#485—611no—
185#485—611no—
186#485—611no—
187#485—611no—
188#485D6111yescharacteristic, direct product factor
189C2×#107—611no—
190C2×#106—611no—
191C2×#103—611no—
192C2×#103—611no—
193C2×C22⋊C8—611no—
194C61C2×#48511yescharacteristic, complemented, Sylow
195C22×Q8—611no—
196C23×C4—611no—
197C22×C8—611no—
198C22×C8—611no—
199C22⋊Q8—611no—
200C22⋊Q8—611no—
201C22⋊Q8—611no—
202C22⋊Q8—1221no—
203C22⋊Q8—1221no—
204C22⋊Q8C2×D6111yescharacteristic
205#117—611no—
206#117—611no—
207#117—611no—
208#117—1221no—
209#117—1221no—
210#117C2×D6111yescharacteristic
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—1221no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C42—1221no—
218#107—611no—
219#107—611no—
220#107—611no—
221#107C2×D6111yescharacteristic, complemented
222#106—611no—
223#106—611no—
224#106—611no—
225#106C2×D6111yescharacteristic, complemented
226#103—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103C2×D6111yescharacteristic, complemented
233#103C2×D6111yescharacteristic, complemented
234C22⋊C8—611no—
235C22⋊C8—611no—
236C22⋊C8—611no—
237C22⋊C8C2×D6111yescharacteristic
238C24—611no—
239C2×Q8—611no—
240C2×Q8—1221no—
241C2×Q8—1222no—
242C2×Q8—1222no—
243C2×Q8C22×D6111yescharacteristic
244C22×C4—611no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—611no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4C22×D6111yescharacteristic
256C2×C8—611no—
257C2×C8—611no—
258C2×C8—1222no—
259C2×C8—1222no—
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—611no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4C22×D6111yescharacteristic
273C4⋊C4C22×D6111yescharacteristic
274C4⋊C4C22×D6111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C42—21no—
284C42—1221no—
285C42—1221no—
286C42—1221no—
287C23—611no—
288C23—611no—
289C23—1222no—
290C23—1222no—
291C23—1222no—
292C23D4×D6111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—1221no—
296Q8—1221no—
297Q8—2442no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—611no—
305C2×C4—612no—
306C2×C4—612no—
307C2×C4—611no—
308C2×C4—1222no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4—2442no—
321C2×C4D4×D6111yescharacteristic
322C2×C4C23×D6111yescharacteristic
323C8—21no—
324C8—21no—
325C8—1221no—
326C8—1221no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—612no—
331C22—612no—
332C22—612no—
333C22—1221no—
334C22—1221no—
335C22—1221no—
336C22—2444no—
337C22C2×D4×D6111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—612no—
344C4—1221no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4#41×D6111yescharacteristic
350C4#41×D6111yescharacteristic
351C2—41no—
352C2—614no—
353C2—2441no—
354C2#123×D6111yescharacteristic
355C2#135×D6111yescharacteristic
356C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61C2×#485
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #16840106C2semidirect
4. #16840105C2semidirect
5. #16840104C2semidirect
6. #16840103C2semidirect
7. #16840102C2semidirect
8. #16840101C2semidirect
9. #16840100C2semidirect
10. #107×D61C2semidirect
11. #106×D61C2semidirect
12. #103×D61C2semidirect
13. #103×D61C2semidirect
15. C61×#485C2semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519710C22semidirect
40. #14519709C22semidirect
41. #14519708C22semidirect
42. #14519708C22semidirect
43. #14519702C22semidirect
44. #14519702C22semidirect
45. #14519701C22semidirect
46. #14519701C22semidirect
47. #14519700C22semidirect
48. #14519700C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #103×C61C22semidirect
57. #103×C61C22semidirect
178. D61#485direct (N × H)
188. #485D61direct (N × H)
194. C61C2×#485semidirect
221. #107C2×D61semidirect
225. #106C2×D61semidirect
232. #103C2×D61semidirect
233. #103C2×D61semidirect