Finite Group Databasebeta

← #21458037

Subgroups — #21458037

Order 7808.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840452C211yesmaximal, characteristic, complemented
2#16840408C211yesmaximal, characteristic
3#16840117C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840081C211yesmaximal, characteristic, complemented
6#16840063C211yesmaximal, characteristic, complemented
7#16840020C211yesmaximal, characteristic, complemented
8#16840008C211yesmaximal, characteristic, complemented
9#16839985C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839915C211yesmaximal, characteristic, complemented
12C4×#11758190C211yesmaximal, characteristic, complemented
13#16839768C211yesmaximal, characteristic, complemented
14#16839764C211yesmaximal, characteristic, complemented
15C61×#436C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×Dic244C2211yescharacteristic, complemented
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21#14519770—21no—
22#14519769C2211yescharacteristic, complemented
23#14519767—21no—
24#14519765C2211yescharacteristic
25#14519762—21no—
26#14519758—21no—
27#14519756C2211yescharacteristic
28#14519756C2211yescharacteristic
29#14519756C2211yescharacteristic, complemented
30#14519751C2211yescharacteristic
31#14519750—21no—
32#14519745—21no—
33C4×Dic122C2211yescharacteristic, complemented
34C4×D244C2211yescharacteristic
35#14519736C2211yescharacteristic
36#14519733—21no—
37C2×C4⋊Dic61C2211yescharacteristic, complemented
38C22⋊C4×D61—21no—
39#14519711C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519702C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52C2×M16×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic, complemented
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic, complemented
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic, complemented
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61D411yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C22×Dic61—21no—
66#11758222—22no—
67#11758222—41no—
68C2×D244—22no—
69C2×D244—21no—
70C2×D244—41no—
71C2×D244C2311yescharacteristic
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×Dic122C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77M16×C61—41no—
78M16×C61—41no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61D411yescharacteristic
84C22⋊C4×C61D411yescharacteristic
85C22⋊C4×C61D411yescharacteristic
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108Dic244—41no—
109#11758190—22no—
110#11758190—41no—
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—81no—
118D4×C61—41no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—42no—
129C22⋊D61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—42no—
137D244—21no—
138D244—21no—
139D244—21no—
140D244—42no—
141D244#4112yes—
142C4×D61—42no—
143C4×D61—81no—
144Dic122—21no—
145Dic122—21no—
146Dic122—21no—
147Dic122—21no—
148C8×C61—21no—
149C8×C61—21no—
150C8×C61—21no—
151C8×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61C22×D411yescharacteristic
159C2×D61—22no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—84no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61C2×#4111yescharacteristic
171C4×C61H(5,𝔽2)11yescharacteristic
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178#3323—611nomaximal, Sylow
179C2×C61—41no—
180C2×C61—41no—
181C2×C61#54611yescharacteristic
182C2×C61#57511yescharacteristic
183C2×C61#57711yescharacteristic
184D61—42no—
185D61—81no—
186#552—611no—
187#546—611no—
188#488—611no—
189#485—611no—
190#481—611no—
191#478—611no—
192#470—611no—
193#468—611no—
194#464—611no—
195#452—611no—
196#450—611no—
197C4×SD16—611no—
198#436D6111yescharacteristic, complemented
199#418—611no—
200#417—611no—
201C61#332311yescharacteristic, complemented, Sylow
202C2×#41—611no—
203C22×D4—611no—
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×M16C2×D6111yescharacteristic
208C2×M16C2×D6111yescharacteristic, complemented
209#126—1221no—
210#125—611no—
211#125—1221no—
212#124—611no—
213#123—1221no—
214#123—1221no—
215C22⋊Q8—611no—
216C22⋊Q8—611no—
217C22⋊Q8—611no—
218#121—611no—
219#121—1221no—
220#120—1221no—
221C4×Q8—611no—
222C4×D4—611no—
223C4×D4C2×D6111yescharacteristic
224#117—611no—
225#117—1221no—
226C2×C4⋊C4—611no—
227C2×C22⋊C4—1221no—
228#107—611no—
229#106—611no—
230#106—611no—
231C4⋊C8C2×D6111yescharacteristic, complemented
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242C22⋊C8C2×D6111yescharacteristic
243C22⋊C8C2×D6111yescharacteristic, complemented
244C4×C8C2×D6111yescharacteristic, complemented
245C24—1221no—
246#41—1222no—
247#41—2441no—
248C2×Q8—611no—
249C2×Q8—611no—
250C2×D4—611no—
251C2×D4—611no—
252C2×D4—1222no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—2441no—
257C2×D4D24411yescharacteristic
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4C22×D6111yescharacteristic
262C22×C4C22×D6111yescharacteristic
263Q16—2441no—
264SD16—1222no—
265SD16—2441no—
266M16—41no—
267M16—41no—
268C2×C8C22×D6111yescharacteristic
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4D24411yescharacteristic
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4D24411yescharacteristic
293C22⋊C4D24411yescharacteristic
294C42—1221no—
295C42—1221no—
296C42C22×D6111yescharacteristic
297C23—1221no—
298C23—1221no—
299C23—4881no—
300C23—2442no—
301C23—2442no—
302C23C2×D24411yescharacteristic
303C23C2×D24411yescharacteristic
304Q8—1221no—
305Q8—1221no—
306Q8—1221no—
307Q8—1221no—
308D4—41no—
309D4—612no—
310D4—1221no—
311D4—1221no—
312D4—1221no—
313D4—4881no—
314D4—2442no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—4881no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4C2×D24411yescharacteristic
330C2×C4C2×D24411yescharacteristic
331C2×C4C2×D24411yescharacteristic
332C2×C4C2×D24411yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—1222no—
345C22—4884no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22C22×D24411yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4—2441no—
361C4—2441no—
362C4#41×D6111yescharacteristic
363C4#1451982211yescharacteristic
364C2—41no—
365C2—41no—
366C2—4881no—
367C2—2442no—
368C2#1684040711yescharacteristic
369C2#1684056211yescharacteristic
370C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#436C2
socleC22×C61C22×D4
hypercenter#436D61
hypocenterC61#3323
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #16840452C2semidirect
3. #16840117C2semidirect
4. #16840104C2semidirect
5. #16840081C2semidirect
6. #16840063C2semidirect
7. #16840020C2semidirect
8. #16840008C2semidirect
9. #16839985C2semidirect
10. #16839926C2semidirect
11. #16839915C2semidirect
12. C4×#11758190C2semidirect
13. #16839768C2semidirect
14. #16839764C2semidirect
15. C61×#436C2semidirect
18. C2×Dic244C22semidirect
22. #14519769C22semidirect
29. #14519756C22semidirect
33. C4×Dic122C22semidirect
37. C2×C4⋊Dic61C22semidirect
39. #14519711C22semidirect
40. #14519709C22semidirect
41. #14519709C22semidirect
42. #14519702C22semidirect
43. #14519702C22semidirect
44. #14519702C22semidirect
45. #14519702C22semidirect
53. C2×M16×C61C22semidirect
55. C4⋊C8×C61C22semidirect
57. C22⋊C8×C61C22semidirect
58. C4×C8×C61C22semidirect
198. #436D61semidirect
201. C61#3323semidirect
208. C2×M16C2×D61semidirect
231. C4⋊C8C2×D61semidirect
243. C22⋊C8C2×D61semidirect
244. C4×C8C2×D61semidirect