Finite Group Databasebeta

← #21458048

Subgroups — #21458048

Order 7808.

448 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#16840480C211yesmaximal, characteristic, complemented
2#16840396C211yesmaximal, characteristic
3#16840107C211yesmaximal, characteristic, complemented
4#16840088C211yesmaximal, characteristic, complemented
5#16840041C211yesmaximal, characteristic, complemented
6#16840009C211yesmaximal, characteristic, complemented
7#16840006C211yesmaximal, characteristic, complemented
8#16839961C211yesmaximal, characteristic, complemented
9#16839915C211yesmaximal, characteristic, complemented
10#16839914C211yesmaximal, characteristic, complemented
11#16839849C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839766C211yesmaximal, characteristic, complemented
14#16839765C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×D4×D61—21no—
18C2×D4×D61C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic, complemented
22C2×#11758194C2211yescharacteristic, complemented
23C2×#11758189C2211yescharacteristic, complemented
24#14519776C2211yescharacteristic, complemented
25#14519773C2211yescharacteristic
26#14519771—21no—
27#14519770—21no—
28#14519763—21no—
29#14519757C2211yescharacteristic, complemented
30#14519756C2211yescharacteristic, complemented
31#14519752C2211yescharacteristic
32#14519750—21no—
33#14519747—21no—
34#14519745—21no—
35C4×Dic122—21no—
36#14519742C2211yescharacteristic, complemented
37#14519739C2211yescharacteristic
38C4×C22⋊D61C2211yescharacteristic
39#14519735C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519700C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic, complemented
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic, complemented
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61D411yescharacteristic
68D4×D61—22no—
69D4×D61—41no—
70D4×D61—44no—
71C2×D244—22no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—41no—
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×Dic122—21no—
80C2×Dic122C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C42×C61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61D411yescharacteristic
91#11758200—41no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198D411yescharacteristic
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61C2311yescharacteristic
106#11758194—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758190—22no—
110#11758190—41no—
111#11758189—41no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
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
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—42no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—22no—
134C22⋊D61—42no—
135C22⋊D61—42no—
136C22⋊D61—81no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142D244—21no—
143D244—21no—
144D244—21no—
145D244—42no—
146D244—42no—
147D244#4112yes—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—42no—
151Dic122—21no—
152Dic122—21no—
153Dic122—42no—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—22no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—84no—
175C2×D61—84no—
176C4×C61—21no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61C2×#4111yescharacteristic
181C4×C61H(5,𝔽2)11yescharacteristic
182Dic61—21no—
183Dic61—21no—
184Dic61—41no—
185Dic61—41no—
186Dic61AGL(1,ℤ/8)12yes—
187#3324—611nomaximal, Sylow
188C2×C61—41no—
189C2×C61—81no—
190C2×C61#54611yescharacteristic
191C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C61#57711yescharacteristic
193D61—41no—
194D61—42no—
195D61—81no—
196#556—611no—
197D42—611no—
198#486—611no—
199#482—611no—
200#482D6111yescharacteristic, complemented
201#474—611no—
202#468—611no—
203#468—611no—
204#460—611no—
205#450—611no—
206#450—611no—
207C4×SD16—611no—
208#436—611no—
209#418—611no—
210#418—611no—
211C61#332411yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C22×D4—611no—
214C22×D4—1221no—
215C2×SD16—611no—
216C2×SD16—611no—
217C2×SD16—611no—
218C2×M16—611no—
219C2×M16—611no—
220C4⋊Q8—611no—
221#127—611no—
222#126—1221no—
223#126—1221no—
224#124—1221no—
225C22⋊Q8—611no—
226C22⋊Q8—611no—
227#121—611no—
228#121—1221no—
229#121C2×D6111yescharacteristic
230#120—1221no—
231#120—1221no—
232C4×Q8—611no—
233C4×Q8—1221no—
234C4×D4—611no—
235C4×D4—611no—
236#117—611no—
237#117C2×D6111yescharacteristic, complemented
238#107—611no—
239#107C2×D6111yescharacteristic, complemented
240#106C2×D6111yescharacteristic, complemented
241C4⋊C8—611no—
242#103—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102C2×D6111yescharacteristic, complemented
251#102C2×D6111yescharacteristic, complemented
252C22⋊C8—611no—
253C22⋊C8C2×D6111yescharacteristic, complemented
254C4×C8—611no—
255C24—1221no—
256C24—1221no—
257C2×Q8—611no—
258C2×Q8—1221no—
259C2×D4—21no—
260C2×D4—611no—
261C2×D4—611no—
262C2×D4—611no—
263C2×D4—1222no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1222no—
269C2×D4—1221no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4—2444no—
273C2×D4C22×D6111yescharacteristic
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4C22×D6111yescharacteristic
277SD16—1222no—
278SD16—2441no—
279SD16—2441no—
280M16—2441no—
281M16—2441no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8C22×D6111yescharacteristic
285C2×C8C22×D6111yescharacteristic
286C4⋊C4—611no—
287C4⋊C4—611no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4C22×D6111yescharacteristic
293C4⋊C4C22×D6111yescharacteristic
294C4⋊C4C22×D6111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—611no—
298C22⋊C4—611no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C42—21no—
305C42—611no—
306C42—1221no—
307C42—1221no—
308C23—21no—
309C23—611no—
310C23—1221no—
311C23—1221no—
312C23—4881no—
313C23—4881no—
314C23—2442no—
315C23—2442no—
316C23—2442no—
317C23—2442no—
318C23D4×D6111yescharacteristic
319Q8—1221no—
320Q8—1221no—
321Q8—2442no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—612no—
326D4—1222no—
327D4—1221no—
328D4—1221no—
329D4—1221no—
330D4—4881no—
331D4—2442no—
332D4—2442no—
333D4—2442no—
334D4—2442no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—2442no—
348C2×C4D4×D6111yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—21no—
351C8—21no—
352C8—1221no—
353C8—1221no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—1221no—
361C22—1221no—
362C22—1221no—
363C22—1222no—
364C22—4884no—
365C22—4884no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22C2×D4×D6111yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—612no—
377C4—1221no—
378C4—1221no—
379C4—2441no—
380C4—2441no—
381C4#41×D6111yescharacteristic
382C4#1451982311yescharacteristic
383C2—41no—
384C2—81no—
385C2—4881no—
386C2—2441no—
387C2—2442no—
388C2#1684040411yescharacteristic
389C2AGL(1,ℤ/8)×D6111yescharacteristic
390C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3324
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16840480C2semidirect
3. #16840107C2semidirect
4. #16840088C2semidirect
5. #16840041C2semidirect
6. #16840009C2semidirect
7. #16840006C2semidirect
8. #16839961C2semidirect
9. #16839915C2semidirect
10. #16839914C2semidirect
11. #16839849C2semidirect
12. #16839837C2semidirect
13. #16839766C2semidirect
14. #16839765C2semidirect
15. C61×#482C2semidirect
20. C2×#11758190C22semidirect
21. C2×#11758200C22semidirect
22. C2×#11758194C22semidirect
23. C2×#11758189C22semidirect
24. #14519776C22semidirect
29. #14519757C22semidirect
30. #14519756C22semidirect
36. #14519742C22semidirect
39. #14519735C22semidirect
40. #14519710C22semidirect
41. #14519706C22semidirect
42. #14519700C22semidirect
44. #14519699C22semidirect
45. #14519698C22semidirect
48. #14519697C22semidirect
49. #14519697C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
53. #117×C61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #102×C61C22semidirect
57. #102×C61C22semidirect
58. C22⋊C8×C61C22semidirect
200. #482D61semidirect
211. C61#3324semidirect
237. #117C2×D61semidirect
239. #107C2×D61semidirect
240. #106C2×D61semidirect
250. #102C2×D61semidirect
251. #102C2×D61semidirect
253. C22⋊C8C2×D61semidirect