Finite Group Databasebeta

← #21457839

Subgroups — #21457839

Order 7808.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840450C211yesmaximal, characteristic, complemented
2#16840397C211yesmaximal, characteristic
3#16840084C211yesmaximal, characteristic, complemented
4#16840074C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16840007C211yesmaximal, characteristic, complemented
7#16839990C211yesmaximal, characteristic, complemented
8#16839959C211yesmaximal, characteristic, complemented
9#16839914C211yesmaximal, characteristic, complemented
10#16839914C211yesmaximal, characteristic, complemented
11#16839864C211yesmaximal, 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×#11758190C2211yescharacteristic
20C2×#11758200C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic, complemented
22C2×#11758189C2211yescharacteristic, complemented
23C2×C8×D61C2211yescharacteristic, complemented
24#14519772—21no—
25#14519768—21no—
26#14519762—21no—
27#14519757C2211yescharacteristic, complemented
28#14519757C2211yescharacteristic, complemented
29#14519748—21no—
30#14519748C2211yescharacteristic
31#14519748C2211yescharacteristic
32#14519745—21no—
33#14519745—21no—
34C4×Dic122C2211yescharacteristic, complemented
35C4×D244C2211yescharacteristic
36C4×D244C2211yescharacteristic
37#14519735—21no—
38#14519735C2211yescharacteristic, complemented
39C4⋊C4×D61C2211yescharacteristic, complemented
40#14519711C2211yescharacteristic, complemented
41#14519710C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43C4⋊#92418C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
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×D244D411yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×C4×D61C2311yescharacteristic
80C2×Dic122C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758200—41no—
91#11758200—41no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198D411yescharacteristic
97#11758198D411yescharacteristic
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61D411yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758190—22no—
110#11758189—41no—
111C8×D61—41no—
112C23×C61—21no—
113C23×C61—21no—
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61C2×D411yescharacteristic
122C22×D61C2×D411yescharacteristic
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—42no—
128D4×C61—81no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—42no—
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143D244—22no—
144D244—21no—
145D244#4112yes—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—42no—
151C4×D61—42no—
152Dic122—21no—
153Dic122—21no—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—22no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—84no—
174C2×D61—84no—
175C2×D61AGL(1,ℤ/8)12yes—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61C2×#4111yescharacteristic
181C4×C61H(5,𝔽2)11yescharacteristic
182Dic61—21no—
183Dic61—21no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187#3310—611nomaximal, Sylow
188C2×C61—81no—
189C2×C61—81no—
190C2×C61#54611yescharacteristic
191C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C61#57711yescharacteristic
193D61—22no—
194D61—41no—
195D61—42no—
196#552—611no—
197D42—611no—
198#490D6111yescharacteristic, complemented
199#482—611no—
200#480—611no—
201#478—611no—
202#468—611no—
203#465—611no—
204#460—611no—
205#450—611no—
206#450—611no—
207#440—611no—
208#435—611no—
209#418—611no—
210C2×#102—611no—
211C61#331011yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C22×D4—611no—
214C22×D4—1221no—
215C2×SD16—611no—
216C2×SD16—611no—
217C2×SD16—611no—
218C2×M16—611no—
219C22×C8—611no—
220#127C2×D6111yescharacteristic
221#126—1221no—
222#125—1221no—
223#125C2×D6111yescharacteristic, complemented
224#123—1221no—
225C22⋊Q8—611no—
226C22⋊Q8—611no—
227#121—611no—
228#121—611no—
229#121—1221no—
230#120—1221no—
231#120—1221no—
232C4×Q8—611no—
233C4×D4—611no—
234C4×D4—611no—
235#117—611no—
236#117—1221no—
237C2×C4⋊C4—611no—
238#107—611no—
239#107—611no—
240#106—611no—
241C4⋊C8—611no—
242#103—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102C2×D6111yescharacteristic, complemented
249#102C2×D6111yescharacteristic, complemented
250#102C2×D6111yescharacteristic, complemented
251#102C2×D6111yescharacteristic, complemented
252C22⋊C8—611no—
253C22⋊C8—611no—
254#97C2×D6111yescharacteristic, complemented
255C24—1221no—
256C24—1221no—
257C2×Q8—611no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—611no—
261C2×D4—611no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1222no—
265C2×D4—1222no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—2441no—
269C2×D4—2441no—
270C2×D4—2444no—
271C2×D4C22×D6111yescharacteristic
272C2×D4C22×D6111yescharacteristic
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277SD16—1222no—
278SD16—2441no—
279SD16—2441no—
280M16—2441no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8—2441no—
284C2×C8C22×D6111yescharacteristic
285C2×C8C22×D6111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—611no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4C22×D6111yescharacteristic
296C4⋊C4C22×D6111yescharacteristic
297C22⋊C4—611no—
298C22⋊C4—611no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C42—1221no—
306C42—1221no—
307C42C22×D6111yescharacteristic
308C23—21no—
309C23—21no—
310C23—611no—
311C23—611no—
312C23—1221no—
313C23—4881no—
314C23—4881no—
315C23—2442no—
316C23—2442no—
317C23—2442no—
318C23—2442no—
319Q8—1221no—
320Q8—1221no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—612no—
328D4—1222no—
329D4—1221no—
330D4—2442no—
331D4—2442no—
332D4—2442no—
333D4—2442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—611no—
337C2×C4—611no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4D4×D6111yescharacteristic
348C2×C4D4×D6111yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—21no—
351C8—21no—
352C8—1221no—
353C8—1221no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—612no—
361C22—1221no—
362C22—1221no—
363C22—1221no—
364C22—1221no—
365C22—1221no—
366C22—1222no—
367C22—4884no—
368C22—4884no—
369C22—2441no—
370C22—2441no—
371C22C2×D4×D6111yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—1221no—
377C4—1221no—
378C4—2441no—
379C4—2441no—
380C4—2441no—
381C4#41×D6111yescharacteristic
382C4#1451982311yescharacteristic
383C2—81no—
384C2—81no—
385C2—1222no—
386C2—2441no—
387C2—2442no—
388C2#1684040511yescharacteristic
389C2AGL(1,ℤ/8)×D6111yescharacteristic
390C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#490C2
socleC22×C61C22×D4
hypercenter#490D61
hypocenterC61#3310
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. #16840450C2semidirect
3. #16840084C2semidirect
4. #16840074C2semidirect
5. #16840059C2semidirect
6. #16840007C2semidirect
7. #16839990C2semidirect
8. #16839959C2semidirect
9. #16839914C2semidirect
10. #16839914C2semidirect
11. #16839864C2semidirect
12. #16839835C2semidirect
13. #16839765C2semidirect
14. #102×D61C2semidirect
15. C61×#490C2semidirect
20. C2×#11758200C22semidirect
21. C2×#11758200C22semidirect
22. C2×#11758189C22semidirect
23. C2×C8×D61C22semidirect
27. #14519757C22semidirect
28. #14519757C22semidirect
34. C4×Dic122C22semidirect
38. #14519735C22semidirect
39. C4⋊C4×D61C22semidirect
40. #14519711C22semidirect
41. #14519710C22semidirect
42. #14519708C22semidirect
43. C4⋊#92418C22semidirect
44. #14519702C22semidirect
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
198. #490D61semidirect
211. C61#3310semidirect
223. #125C2×D61semidirect
248. #102C2×D61semidirect
249. #102C2×D61semidirect
250. #102C2×D61semidirect
251. #102C2×D61semidirect
254. #97C2×D61semidirect