Finite Group Databasebeta

← #21457959

Subgroups — #21457959

Order 7808.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840465C211yesmaximal, characteristic, complemented
2#16840397C211yesmaximal, characteristic, complemented
3#16840085C211yesmaximal, characteristic, complemented
4#16840079C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16840014C211yesmaximal, characteristic, complemented
7#16839997C211yesmaximal, characteristic, complemented
8#16839954C211yesmaximal, characteristic, complemented
9#16839897C211yesmaximal, characteristic, complemented
10#16839897C211yesmaximal, characteristic, complemented
11#16839875C211yesmaximal, characteristic, complemented
12#16839835C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#490C211yesmaximal, characteristic, complemented
16C2×D4×D61—21no—
17C2×D4×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×#11758199C2211yescharacteristic, complemented
21C2×#11758199C2211yescharacteristic, complemented
22C2×#11758189C2211yescharacteristic, complemented
23C2×C8×D61C2211yescharacteristic, complemented
24#14519772—21no—
25#14519762—21no—
26#14519752—21no—
27#14519752C2211yescharacteristic, complemented
28#14519752C2211yescharacteristic, complemented
29#14519748—21no—
30#14519748C2211yescharacteristic
31#14519748C2211yescharacteristic
32#14519745—21no—
33#14519745—21no—
34C4×D244C2211yescharacteristic
35C4×D244C2211yescharacteristic
36C4×D244C2211yescharacteristic, complemented
37#14519739—21no—
38#14519735C2211yescharacteristic, complemented
39C4⋊C4×D61C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43C4⋊#92418C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52#127×C61C2211yescharacteristic
53#125×C61C2211yescharacteristic, complemented
54#102×C61C2211yescharacteristic, complemented
55#102×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69D4×D61—22no—
70D4×D61—22no—
71D4×D61—41no—
72D4×D61—41no—
73D4×D61—44no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244D411yescharacteristic
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61C2311yescharacteristic
83C2×C4×D61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93#11758199—41no—
94#11758199—41no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198D411yescharacteristic
101#11758198D411yescharacteristic
102C4⋊Dic61D411yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109D488—22no—
110#11758189—41no—
111C8×D61—41no—
112C23×C61—21no—
113C23×C61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61C2×D411yescharacteristic
123C22×D61C2×D411yescharacteristic
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—42no—
129D4×C61—81no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143D244—22no—
144D244—21no—
145D244—21no—
146D244—21no—
147D244—42no—
148D244—81no—
149D244#4112yes—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—42no—
155C4×D61—81no—
156C4×D61—81no—
157C8×C61—21no—
158C8×C61—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C22×D411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—22no—
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—84no—
180C2×D61—84no—
181C2×D61AGL(1,ℤ/8)12yes—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—41no—
185C4×C61—41no—
186C4×C61C2×#4111yescharacteristic
187C4×C61H(5,𝔽2)11yescharacteristic
188Dic61—21no—
189Dic61—21no—
190Dic61—41no—
191Dic61—41no—
192#3318—611nomaximal, Sylow
193C2×C61—81no—
194C2×C61—81no—
195C2×C61#54611yescharacteristic
196C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C61#57611yescharacteristic
198D61—22no—
199D61—41no—
200D61—42no—
201D61—81no—
202#553—611no—
203D42—611no—
204#490D6111yescharacteristic, complemented
205#482—611no—
206#481—611no—
207#478—611no—
208#469—611no—
209#466—611no—
210#459—611no—
211#447—611no—
212#447—611no—
213#442—611no—
214#435—611no—
215#418—611no—
216C2×#102—611no—
217C61#331811yescharacteristic, complemented, Sylow
218C22×D4—611no—
219C22×D4—611no—
220C22×D4—1221no—
221C2×D8—611no—
222C2×D8—611no—
223C2×D8—611no—
224C2×M16—611no—
225C22×C8—611no—
226#127C2×D6111yescharacteristic
227#126—1221no—
228#125C2×D6111yescharacteristic, complemented
229#123—1221no—
230#121—611no—
231#121—611no—
232#121—611no—
233#121—611no—
234#121—1221no—
235#121—1221no—
236#120—1221no—
237#120—1221no—
238C4×D4—611no—
239C4×D4—611no—
240C4×D4—611no—
241C4×D4—1221no—
242#117—611no—
243C2×C4⋊C4—611no—
244#107—611no—
245#106—611no—
246#106—611no—
247C4⋊C8—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252#102—611no—
253#102—611no—
254#102C2×D6111yescharacteristic, complemented
255#102C2×D6111yescharacteristic, complemented
256#102C2×D6111yescharacteristic, complemented
257#102C2×D6111yescharacteristic, complemented
258C22⋊C8—611no—
259C22⋊C8—611no—
260#97C2×D6111yescharacteristic, complemented
261C24—1221no—
262C24—1221no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—611no—
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1222no—
273C2×D4—1222no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2444no—
279C2×D4C22×D6111yescharacteristic
280C2×D4C22×D6111yescharacteristic
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286D8—1222no—
287D8—2441no—
288D8—2441no—
289M16—2441no—
290C2×C8—611no—
291C2×C8—611no—
292C2×C8—2441no—
293C2×C8C22×D6111yescharacteristic
294C2×C8C22×D6111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—611no—
298C4⋊C4—611no—
299C4⋊C4—611no—
300C4⋊C4—1221no—
301C4⋊C4C22×D6111yescharacteristic
302C4⋊C4C22×D6111yescharacteristic
303C22⋊C4—611no—
304C22⋊C4—611no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C42—1221no—
313C42C22×D6111yescharacteristic
314C23—21no—
315C23—21no—
316C23—611no—
317C23—611no—
318C23—1221no—
319C23—1221no—
320C23—4881no—
321C23—4881no—
322C23—2442no—
323C23—2442no—
324C23—2442no—
325C23—2442no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—81no—
332D4—612no—
333D4—1222no—
334D4—1221no—
335D4—1221no—
336D4—1221no—
337D4—4881no—
338D4—2442no—
339D4—2442no—
340D4—2442no—
341D4—2442no—
342D4—2442no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—4881no—
354C2×C4—4881no—
355C2×C4—2442no—
356C2×C4D4×D6111yescharacteristic
357C2×C4D4×D6111yescharacteristic
358C2×C4C23×D6111yescharacteristic
359C8—21no—
360C8—21no—
361C8—1221no—
362C8—1221no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—612no—
370C22—1221no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—1222no—
376C22—4884no—
377C22—4884no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22C2×D4×D6111yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—1221no—
389C4—1221no—
390C4—2441no—
391C4—2441no—
392C4#41×D6111yescharacteristic
393C4#1451982311yescharacteristic
394C2—81no—
395C2—81no—
396C2—1222no—
397C2—4881no—
398C2—2441no—
399C2—2442no—
400C2#1684040511yescharacteristic
401C2AGL(1,ℤ/8)×D6111yescharacteristic
402C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#490C2
socleC22×C61C22×D4
hypercenter#490D61
hypocenterC61#3318
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #16840465C2semidirect
2. #16840397C2semidirect
3. #16840085C2semidirect
4. #16840079C2semidirect
5. #16840059C2semidirect
6. #16840014C2semidirect
7. #16839997C2semidirect
8. #16839954C2semidirect
9. #16839897C2semidirect
10. #16839897C2semidirect
11. #16839875C2semidirect
12. #16839835C2semidirect
13. #16839765C2semidirect
14. #102×D61C2semidirect
15. C61×#490C2semidirect
20. C2×#11758199C22semidirect
21. C2×#11758199C22semidirect
22. C2×#11758189C22semidirect
23. C2×C8×D61C22semidirect
27. #14519752C22semidirect
28. #14519752C22semidirect
36. C4×D244C22semidirect
38. #14519735C22semidirect
39. C4⋊C4×D61C22semidirect
40. #14519710C22semidirect
41. #14519709C22semidirect
42. #14519708C22semidirect
43. C4⋊#92418C22semidirect
45. #14519699C22semidirect
46. #14519698C22semidirect
47. #14519698C22semidirect
50. #14519689C22semidirect
51. #14519689C22semidirect
53. #125×C61C22semidirect
54. #102×C61C22semidirect
55. #102×C61C22semidirect
56. #102×C61C22semidirect
57. #102×C61C22semidirect
58. #97×C61C22semidirect
204. #490D61semidirect
217. C61#3318semidirect
228. #125C2×D61semidirect
254. #102C2×D61semidirect
255. #102C2×D61semidirect
256. #102C2×D61semidirect
257. #102C2×D61semidirect
260. #97C2×D61semidirect