Finite Group Databasebeta

← #21455751

Subgroups — #21455751

Order 7808.

414 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840275C211yesmaximal, characteristic
2#117×D61C211yesmaximal, characteristic, complemented
3#16840102C211yesmaximal, characteristic, complemented
4#16840101C211yesmaximal, characteristic, complemented
5#16840100C211yesmaximal, characteristic, complemented
6#16840089C211yesmaximal, characteristic, complemented
7#16840088C211yesmaximal, characteristic, complemented
8#16840087C211yesmaximal, characteristic, complemented
9#16840086C211yesmaximal, characteristic, complemented
10#16839803C211yesmaximal, characteristic, complemented
11#16839801C211yesmaximal, characteristic, complemented
12#16839762C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#16839724C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C2×#11758189C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20#14519762—21no—
21#14519753C2211yescharacteristic
22#14519752C2211yescharacteristic
23#14519751C2211yescharacteristic
24#14519747—21no—
25#14519739—21no—
26#14519737—21no—
27#14519736C2211yescharacteristic
28#14519735C2211yescharacteristic
29#14519735C2211yescharacteristic
30#14519735C2211yescharacteristic
31#14519734—21no—
32#14519733—21no—
33C4⋊C4×D61C2211yescharacteristic
34C4⋊C4×D61C2211yescharacteristic
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#14519701C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, 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
62C2×C22⋊D61—21no—
63C22×Dic61D411yescharacteristic
64#11758226—22no—
65#11758226—22no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244C2311yescharacteristic
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61D411yescharacteristic
75C2×C4×D61D411yescharacteristic
76C2×C4×D61C2311yescharacteristic
77C2×C4×D61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C42×C61—21no—
87C22⋊Dic61—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758189—22no—
107#11758189—22no—
108C23×C61C2×D411yescharacteristic
109C22×D61—22no—
110C22×D61—21no—
111C22×D61—41no—
112C22×D61—41no—
113C22×D61C2×D411yescharacteristic
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—42no—
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132D244—21no—
133D244—21no—
134D244—42no—
135D244—42no—
136C4×D61—22no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—22no—
140C4×D61—42no—
141C4×D61—42no—
142C4×D61—42no—
143C4×D61#4112yes—
144C4×D61#4112yes—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61C22×D411yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—44no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61#12312yes—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61C2×#4111yescharacteristic
169C4×C61C2×#4111yescharacteristic
170Dic61—21no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174Dic61#12312yes—
175#3093—611nomaximal, Sylow
176C2×C61—41no—
177C2×C61C2×#12311yescharacteristic
178C2×C61#57511yescharacteristic
179C2×C61#57511yescharacteristic
180D61—22no—
181D61—41no—
182D61—81no—
183#525—611no—
184C2×#117—611no—
185#485—611no—
186#485—611no—
187#485—611no—
188#485D6111yescharacteristic, complemented
189#482—611no—
190#482—611no—
191#482—611no—
192#482—611no—
193#428—611no—
194#428—611no—
195#417—611no—
196#417—611no—
197#407—611no—
198C61#309311yescharacteristic, complemented, Sylow
199C2×#41—611no—
200C23×C4—611no—
201C2×M16—611no—
202C2×M16—611no—
203#123—1221no—
204C22⋊Q8—611no—
205C22⋊Q8C2×D6111yescharacteristic
206#121—611no—
207#121—611no—
208#120—1221no—
209C4×D4—1221no—
210C4×D4—1221no—
211#117—611no—
212#117—611no—
213#117—611no—
214#117—611no—
215#117—1221no—
216#117—1221no—
217#117C2×D6111yescharacteristic
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C22⋊C4—1221no—
221C2×C42—1221no—
222#107—611no—
223#107—611no—
224#107—611no—
225#107C2×D6111yescharacteristic, complemented
226#106—611no—
227#106—611no—
228#106—611no—
229#106C2×D6111yescharacteristic, complemented
230#103—611no—
231#103—611no—
232#103C2×D6111yescharacteristic, complemented
233#103C2×D6111yescharacteristic, complemented
234#102—611no—
235#102—611no—
236#102—611no—
237#102—611no—
238C22⋊C8—611no—
239C22⋊C8—611no—
240C22⋊C8—611no—
241C22⋊C8C2×D6111yescharacteristic
242C24—611no—
243#41—1222no—
244#41—1222no—
245C2×Q8C22×D6111yescharacteristic
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—1222no—
256C22×C4—1222no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4C22×D6111yescharacteristic
261M16—1222no—
262M16—1222no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8C22×D6111yescharacteristic
266C2×C8C22×D6111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4C22×D6111yescharacteristic
275C4⋊C4C22×D6111yescharacteristic
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C42—21no—
287C42—1221no—
288C42—1221no—
289C42—1221no—
290C42—1221no—
291C23—611no—
292C23—611no—
293C23—1222no—
294C23—1221no—
295C23—2441no—
296C23—2441no—
297C23D4×D6111yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—1221no—
301D4—1221no—
302D4—2442no—
303D4—2442no—
304D4—2442no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—611no—
312C2×C4—612no—
313C2×C4—612no—
314C2×C4—611no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4D4×D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—21no—
329C8—21no—
330C8—1221no—
331C8—1221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—612no—
336C22—1221no—
337C22—1221no—
338C22—1221no—
339C22—1221no—
340C22—1221no—
341C22—2444no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22C2×D4×D6111yescharacteristic
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—612no—
352C4—1221no—
353C4—2441no—
354C4—2441no—
355C4—2441no—
356C4#41×D6111yescharacteristic
357C4#41×D6111yescharacteristic
358C2—41no—
359C2—1222no—
360C2—4881no—
361C2—2441no—
362C2#123×D6111yescharacteristic
363C2#1684055911yescharacteristic
364C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3093
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
2. #117×D61C2semidirect
3. #16840102C2semidirect
4. #16840101C2semidirect
5. #16840100C2semidirect
6. #16840089C2semidirect
7. #16840088C2semidirect
8. #16840087C2semidirect
9. #16840086C2semidirect
10. #16839803C2semidirect
11. #16839801C2semidirect
12. #16839762C2semidirect
13. #16839762C2semidirect
14. #16839724C2semidirect
15. C61×#485C2semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519710C22semidirect
40. #14519709C22semidirect
41. #14519708C22semidirect
42. #14519708C22semidirect
43. #14519701C22semidirect
44. #14519701C22semidirect
45. #14519699C22semidirect
46. #14519699C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #103×C61C22semidirect
57. #103×C61C22semidirect
188. #485D61semidirect
198. C61#3093semidirect
225. #107C2×D61semidirect
229. #106C2×D61semidirect
232. #103C2×D61semidirect
233. #103C2×D61semidirect