Finite Group Databasebeta

← #21457296

Subgroups — #21457296

Order 7808.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519804C211yesmaximal, characteristic, complemented
2C22×D488C211yesmaximal, characteristic, complemented
3#16840403C211yesmaximal, characteristic, complemented
4#16840396C211yesmaximal, characteristic, complemented
5#16840148C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839956C211yesmaximal, characteristic, complemented
9#16839912C211yesmaximal, characteristic, complemented
10#16839910C211yesmaximal, characteristic, complemented
11#16839897C211yesmaximal, characteristic, complemented
12#16839895C211yesmaximal, characteristic, complemented
13#16839873C211yesmaximal, characteristic, complemented
14#16839833C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic, complemented
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic, complemented
19C2×D4×D61—21no—
20C2×D4×D61C2211yescharacteristic, complemented
21#14519804—24no—
22C2×#11758201C2211yescharacteristic, complemented
23C2×#11758201C2211yescharacteristic, complemented
24C2×D488—24no—
25C2×D488C2211yescharacteristic
26C2×D488C2211yescharacteristic
27C2×D488C2211yescharacteristic, complemented
28C2×D488C2211yescharacteristic, complemented
29C2×#11758199C2211yescharacteristic, complemented
30C2×#11758199C2211yescharacteristic, complemented
31C2×#11758189C2211yescharacteristic, complemented
32#14519773C2211yescharacteristic, complemented
33#14519766C2211yescharacteristic, complemented
34#14519762—21no—
35#14519752—21no—
36#14519752C2211yescharacteristic, complemented
37#14519752C2211yescharacteristic, complemented
38#14519750—21no—
39#14519747—21no—
40#14519747—21no—
41#14519745—21no—
42#14519739C2211yescharacteristic, complemented
43#14519739C2211yescharacteristic, complemented
44C4×C22⋊D61C2211yescharacteristic
45C22⋊C4×D61—21no—
46#14519706C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic, complemented
50#14519697C2211yescharacteristic, complemented
51C22⋊#92418C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519687C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C22×C8×C61C2211yescharacteristic, complemented
56C22⋊Q8×C61C2211yescharacteristic, complemented
57#121×C61C2211yescharacteristic
58#106×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C23×D61—21no—
64C2×Q8×C61C2311yescharacteristic
65C2×D4×C61—21no—
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61D411yescharacteristic
72#11758226—22no—
73#11758226—41no—
74D4×D61—22no—
75D4×D61—41no—
76D4×D61—44no—
77C2×D244—22no—
78C2×D244—22no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244C2311yescharacteristic
87C2×D244C2311yescharacteristic
88C2×D244C2311yescharacteristic
89C2×D244C2311yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—21no—
93C2×C4×D61C2311yescharacteristic
94SD16×C61—22no—
95C2×C8×C61—22no—
96C2×C8×C61C2311yescharacteristic
97C2×C8×C61C2311yescharacteristic
98C4⋊C4×C61—21no—
99C4⋊C4×C61C2311yescharacteristic
100C4⋊C4×C61C2311yescharacteristic
101C22⋊C4×C61—21no—
102C22⋊C4×C61—21no—
103C22⋊Dic61D411yescharacteristic
104#11758201—22no—
105#11758201—41no—
106#11758199—22no—
107#11758199—41no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198—21no—
113#11758198—21no—
114#11758198D411yescharacteristic
115#11758196D411yescharacteristic
116C4×Dic61C2311yescharacteristic
117C2×#92418C2311yescharacteristic
118C2×#92418C2311yescharacteristic
119D488—22no—
120D488—22no—
121D488—22no—
122D488D414yescomplemented
123#11758189—22no—
124C23×C61—21no—
125C23×C61C2×D411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—42no—
134C22×D61—42no—
135C22×D61—42no—
136C22×D61—81no—
137C22×D61—81no—
138C22×D61—81no—
139C22×D61C2×D411yescharacteristic
140Q8×C61—21no—
141Q8×C61—21no—
142D4×C61—21no—
143D4×C61—21no—
144D4×C61—42no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61C2×D411yescharacteristic
151C2×C4×C61C2411yescharacteristic
152C22⋊D61—22no—
153C22⋊D61—42no—
154C22⋊D61—42no—
155C22⋊D61—81no—
156C2×Dic61C2×D411yescharacteristic
157C2×Dic61C2×D411yescharacteristic
158C2×Dic61C2×D411yescharacteristic
159D244—21no—
160D244—21no—
161D244—21no—
162D244—21no—
163D244—21no—
164D244—21no—
165D244—42no—
166D244—42no—
167D244—42no—
168D244—42no—
169D244—81no—
170D244C2×D412yes—
171D244C2×D412yescomplemented
172C4×D61—21no—
173C4×D61—21no—
174C4×D61—42no—
175C4×D61—42no—
176C4×D61—81no—
177C8×C61—21no—
178C8×C61C2×D412yescomplemented
179#92418—21no—
180#92418—21no—
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61AGL(1,ℤ/8)12yescomplemented
187C22×C61C22×D411yescharacteristic
188C2×D61—21no—
189C2×D61—22no—
190C2×D61—22no—
191C2×D61—21no—
192C2×D61—21no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—84no—
204C2×D61—84no—
205C2×D61—84no—
206C4×C61—21no—
207C4×C61—41no—
208C4×C61—41no—
209C4×C61—41no—
210C4×C61C22×D411yescharacteristic
211C4×C61H(5,𝔽2)11yescharacteristic
212Dic61—21no—
213Dic61—21no—
214Dic61—21no—
215#3264—611nomaximal, Sylow
216C2×C61—22no—
217C2×C61—81no—
218C2×C61D4211yescharacteristic
219C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C61#57611yescharacteristic
221D61—41no—
222D61—42no—
223D61—42no—
224D61—81no—
225D61—81no—
226C2×AGL(1,ℤ/8)—611no—
227C22×D8—611no—
228#546—611no—
229D42—611no—
230#496—611no—
231#469—611no—
232#465D6111yescharacteristic, complemented
233#463—611no—
234#459—611no—
235#450—611no—
236#449—611no—
237#447—611no—
238#447—611no—
239#442—611no—
240#435—611no—
241C61#326411yescharacteristic, complemented, Sylow
242C2×#41—611no—
243C22×D4—611no—
244C22×D4—611no—
245C22×D4—611no—
246C22×D4—1221no—
247AGL(1,ℤ/8)—1224no—
248C2×SD16—611no—
249C2×SD16—611no—
250C2×SD16C2×D6111yescharacteristic, complemented
251C2×D8—611no—
252C2×D8—611no—
253C2×D8—611no—
254C2×D8—611no—
255C2×D8—611no—
256C2×D8—611no—
257C2×D8—1224no—
258C2×M16—611no—
259C22×C8C2×D6111yescharacteristic, complemented
260#127—611no—
261#124—611no—
262#123—1221no—
263C22⋊Q8C2×D6111yescharacteristic, complemented
264#121—611no—
265#121—611no—
266#121—1221no—
267#121—1221no—
268#121C2×D6111yescharacteristic
269#120—1221no—
270#120—1221no—
271#120—1221no—
272C4×D4—611no—
273C4×D4—611no—
274C4×D4—611no—
275C2×C22⋊C4—1221no—
276#106C2×D6111yescharacteristic, complemented
277C4⋊C8—611no—
278#103C2×D6111yescharacteristic, complemented
279#102—611no—
280#102—611no—
281#102—611no—
282#102—611no—
283#102C2×D6111yescharacteristic, complemented
284C22⋊C8—611no—
285C22⋊C8—611no—
286#97—611no—
287C24—1221no—
288C24—1221no—
289C24—1221no—
290#41—1222no—
291#41—2441no—
292C2×Q8C22×D6111yescharacteristic
293C2×D4—21no—
294C2×D4—611no—
295C2×D4—611no—
296C2×D4—611no—
297C2×D4—611no—
298C2×D4—611no—
299C2×D4—1222no—
300C2×D4—1222no—
301C2×D4—1221no—
302C2×D4—1221no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1222no—
308C2×D4—1221no—
309C2×D4—1221no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C2×D4—2444no—
314C2×D4C22×D6111yescharacteristic
315C22×C4—611no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1221no—
319C22×C4C22×D6111yescharacteristic
320SD16—22no—
321SD16—1222no—
322SD16—2441no—
323D8—614no—
324D8—1222no—
325D8—1222no—
326D8—1222no—
327D8—1222no—
328D8—2441no—
329M16—1222no—
330C2×C8—22no—
331C2×C8—611no—
332C2×C8—611no—
333C2×C8C22×D6111yescharacteristic
334C2×C8C22×D6111yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—611no—
337C4⋊C4C22×D6111yescharacteristic
338C4⋊C4C22×D6111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—611no—
342C22⋊C4—611no—
343C22⋊C4—1221no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—1221no—
347C22⋊C4—1221no—
348C22⋊C4—1221no—
349C42—611no—
350C23—21no—
351C23—611no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—4881no—
357C23—4881no—
358C23—4881no—
359C23—2442no—
360C23—2442no—
361C23—2442no—
362C23—2442no—
363C23—2442no—
364C23—2442no—
365C23D4×D6111yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—21no—
369D4—21no—
370D4—42no—
371D4—612no—
372D4—612no—
373D4—1222no—
374D4—1221no—
375D4—1221no—
376D4—1221no—
377D4—1221no—
378D4—1221no—
379D4—1221no—
380D4—4881no—
381D4—4881no—
382D4—2442no—
383D4—2442no—
384D4—2442no—
385D4—2442no—
386D4—2442no—
387D4—2442no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—611no—
394C2×C4—611no—
395C2×C4—611no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—4881no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4D4×D6111yescharacteristic
402C2×C4C23×D6111yescharacteristic
403C8—21no—
404C8—1221no—
405C8—1221no—
406C8D4×D6112yescomplemented
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—1221no—
413C22—1221no—
414C22—1221no—
415C22—1222no—
416C22—1222no—
417C22—4884no—
418C22—4884no—
419C22—4884no—
420C22—2441no—
421C22—2441no—
422C22—2441no—
423C22—2441no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22#1451980412yescomplemented
431C22C2×D4×D6111yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—1221no—
437C4—1221no—
438C4—1221no—
439C4C2×D4×D6111yescharacteristic
440C4#1451982311yescharacteristic
441C2—22no—
442C2—81no—
443C2—4881no—
444C2—4881no—
445C2—2441no—
446C2—2442no—
447C2—2442no—
448C2#1684039611yescharacteristic
449C2C2×#1451980411yescharacteristic
450C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61#3264
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#14519804C2semidirect
2. C22×D488C2semidirect
3. #16840403C2semidirect
4. #16840396C2semidirect
5. #16840148C2semidirect
6. #16840016C2semidirect
7. #16839980C2semidirect
8. #16839956C2semidirect
9. #16839912C2semidirect
10. #16839910C2semidirect
11. #16839897C2semidirect
12. #16839895C2semidirect
13. #16839873C2semidirect
14. #16839833C2semidirect
15. C61×#465C2semidirect
16. C2×#11758226C22semidirect
18. C22×D244C22semidirect
20. C2×D4×D61C22semidirect
22. C2×#11758201C22semidirect
23. C2×#11758201C22semidirect
27. C2×D488C22semidirect
28. C2×D488C22semidirect
29. C2×#11758199C22semidirect
30. C2×#11758199C22semidirect
31. C2×#11758189C22semidirect
32. #14519773C22semidirect
33. #14519766C22semidirect
36. #14519752C22semidirect
37. #14519752C22semidirect
42. #14519739C22semidirect
43. #14519739C22semidirect
46. #14519706C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
49. #14519697C22semidirect
50. #14519697C22semidirect
51. C22⋊#92418C22semidirect
52. #14519689C22semidirect
53. #14519687C22semidirect
54. C2×SD16×C61C22semidirect
55. C22×C8×C61C22semidirect
56. C22⋊Q8×C61C22semidirect
58. #106×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
122. D488D4semidirect
171. D244C2×D4semidirect
178. C8×C61C2×D4semidirect
186. C22×C61AGL(1,ℤ/8)semidirect
232. #465D61semidirect
241. C61#3264semidirect
250. C2×SD16C2×D61semidirect
259. C22×C8C2×D61semidirect
263. C22⋊Q8C2×D61semidirect
276. #106C2×D61semidirect
278. #103C2×D61semidirect
283. #102C2×D61semidirect
406. C8D4×D61semidirect
430. C22#14519804semidirect