Finite Group Databasebeta

← #21457412

Subgroups — #21457412

Order 7808.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519802C211yesmaximal, characteristic, complemented
2C2×#14519801C211yesmaximal, characteristic, complemented
3#16840411C211yesmaximal, characteristic, complemented
4#16840396C211yesmaximal, characteristic, complemented
5#16840133C211yesmaximal, characteristic, complemented
6#16840011C211yesmaximal, characteristic, complemented
7#16840006C211yesmaximal, characteristic, complemented
8#16839966C211yesmaximal, characteristic, complemented
9#16839955C211yesmaximal, characteristic, complemented
10#16839915C211yesmaximal, characteristic, complemented
11#16839911C211yesmaximal, characteristic, complemented
12#16839908C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839837C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic, complemented
17C22×D244C2211yescharacteristic
18C2×D4×D61—21no—
19C2×D4×D61C2211yescharacteristic
20#14519802—24no—
21#14519801—24no—
22C2×#11758190C2211yescharacteristic
23C2×#11758190C2211yescharacteristic, complemented
24C2×#11758200C2211yescharacteristic, complemented
25C2×#11758201C2211yescharacteristic
26C2×#11758201C2211yescharacteristic, complemented
27C2×#11758199C2211yescharacteristic
28C2×#11758199C2211yescharacteristic, complemented
29C2×#11758194C2211yescharacteristic, complemented
30C2×#11758189C2211yescharacteristic, complemented
31#14519775C2211yescharacteristic, complemented
32#14519773C2211yescharacteristic
33#14519760—21no—
34#14519758—21no—
35#14519756C2211yescharacteristic, complemented
36#14519753C2211yescharacteristic, complemented
37#14519752C2211yescharacteristic
38#14519750—21no—
39#14519749—21no—
40#14519747—21no—
41#14519745—21no—
42D4×Dic61C2211yescharacteristic, complemented
43#14519739C2211yescharacteristic
44C4×C22⋊D61C2211yescharacteristic
45C2×#11758196—21no—
46#14519710C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519700C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53C8×Dic61C2211yescharacteristic, complemented
54C2×#41×C61C2211yescharacteristic, complemented
55C2×SD16×C61C2211yescharacteristic, complemented
56C2×D8×C61C2211yescharacteristic, complemented
57#121×C61C2211yescharacteristic
58#103×C61C2211yescharacteristic, complemented
59#102×C61C2211yescharacteristic, complemented
60C22⋊C8×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63#41×C61—22no—
64#41×C61—41no—
65C2×Q8×C61C2311yescharacteristic
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61C2311yescharacteristic
69C2×D4×C61C2311yescharacteristic
70C22×C4×C61—21no—
71C22×C4×C61C2311yescharacteristic
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C2×C22⋊D61—21no—
76C2×C22⋊D61D411yescharacteristic
77C22×Dic61—21no—
78C22×Dic61—21no—
79#11758224—22no—
80#11758224—41no—
81D4×D61—22no—
82D4×D61—41no—
83D4×D61—44no—
84C2×D244—22no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—41no—
88C2×D244C2311yescharacteristic
89C2×D244C2311yescharacteristic
90C2×C4×D61—21no—
91C2×C4×D61C2311yescharacteristic
92C2×Dic122C2311yescharacteristic
93SD16×C61—41no—
94D8×C61—22no—
95C2×C8×C61C2311yescharacteristic
96C2×C8×C61C2311yescharacteristic
97C4⋊C4×C61C2311yescharacteristic
98C22⋊C4×C61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61D411yescharacteristic
102#11758201—22no—
103#11758201—22no—
104#11758200—22no—
105#11758199—22no—
106#11758199D414yescomplemented
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198D411yescharacteristic
111C4⋊Dic61C2311yescharacteristic
112#11758196—21no—
113#11758196—21no—
114#11758196—21no—
115#11758196—21no—
116#11758196D411yescharacteristic
117C4×Dic61C2311yescharacteristic
118#11758194—22no—
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121#11758190—22no—
122#11758190—41no—
123#11758189—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61C2×D411yescharacteristic
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—42no—
133C22×D61—81no—
134C22×D61—81no—
135C22×D61C2×D411yescharacteristic
136Q8×C61—21no—
137Q8×C61—21no—
138D4×C61—21no—
139D4×C61—21no—
140D4×C61—21no—
141D4×C61—42no—
142D4×C61—42no—
143D4×C61C2×D412yescomplemented
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—42no—
149C2×C4×C61C2×D411yescharacteristic
150C2×C4×C61C2411yescharacteristic
151C22⋊D61—22no—
152C22⋊D61—42no—
153C22⋊D61—42no—
154C22⋊D61—42no—
155C22⋊D61—81no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61C2×D411yescharacteristic
161C2×Dic61C2×D411yescharacteristic
162C2×Dic61C2×D411yescharacteristic
163D244—21no—
164D244—21no—
165D244—21no—
166D244—42no—
167D244—42no—
168D244C2×D412yes—
169C4×D61—21no—
170C4×D61—21no—
171C4×D61—42no—
172Dic122—21no—
173Dic122—21no—
174C8×C61—21no—
175C8×C61—21no—
176#92418—21no—
177#92418C2×D412yescomplemented
178C22×C61—22no—
179C22×C61—21no—
180C22×C61—21no—
181C22×C61—21no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61C22×D411yescharacteristic
188C2×D61—21no—
189C2×D61—22no—
190C2×D61—21no—
191C2×D61—21no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—84no—
198C2×D61—84no—
199C4×C61—21no—
200C4×C61—41no—
201C4×C61—41no—
202C4×C61C22×D411yescharacteristic
203C4×C61H(5,𝔽2)11yescharacteristic
204Dic61—21no—
205Dic61—21no—
206Dic61—41no—
207Dic61—41no—
208Dic61AGL(1,ℤ/8)12yescomplemented
209#3272—611nomaximal, Sylow
210C2×C61—41no—
211C2×C61—42no—
212C2×C61—81no—
213C2×C61D4211yescharacteristic
214C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C61#57711yescharacteristic
216D61—41no—
217D61—42no—
218D61—81no—
219C2×AGL(1,ℤ/8)—611no—
220C2×AGL(1,ℤ/8)—611no—
221#547—611no—
222D42—611no—
223#492—611no—
224#468—611no—
225#468—611no—
226#461—611no—
227#459—611no—
228#450—611no—
229#450—611no—
230#449—611no—
231#449D6111yescharacteristic, complemented
232C4×D8—611no—
233#436—611no—
234C61#327211yescharacteristic, complemented, Sylow
235C2×#41—611no—
236C2×#41C2×D6111yescharacteristic, complemented
237C22×D4—611no—
238C22×D4—611no—
239C22×D4—1221no—
240AGL(1,ℤ/8)—1224no—
241AGL(1,ℤ/8)—1224no—
242C2×SD16—611no—
243C2×SD16—611no—
244C2×SD16—611no—
245C2×SD16—611no—
246C2×SD16—611no—
247C2×SD16C2×D6111yescharacteristic, complemented
248C2×D8—611no—
249C2×D8—611no—
250C2×D8C2×D6111yescharacteristic, complemented
251C2×M16—611no—
252C2×M16—611no—
253C4⋊Q8—611no—
254#127—611no—
255#123—1221no—
256#123—1221no—
257C22⋊Q8—611no—
258C22⋊Q8—611no—
259#121—611no—
260#121—1221no—
261#121—1221no—
262#121C2×D6111yescharacteristic
263#120—1221no—
264#120—1221no—
265C4×D4—611no—
266C4×D4—611no—
267C4×D4—611no—
268C2×C4⋊C4—1221no—
269#107—611no—
270C4⋊C8—611no—
271#103—611no—
272#103C2×D6111yescharacteristic, complemented
273#102—611no—
274#102—611no—
275#102—611no—
276#102C2×D6111yescharacteristic, complemented
277C22⋊C8—611no—
278C22⋊C8C2×D6111yescharacteristic, complemented
279C4×C8—611no—
280C24—1221no—
281C24—1221no—
282#41—22no—
283#41—41no—
284#41—1222no—
285#41—2441no—
286C2×Q8—611no—
287C2×Q8C22×D6111yescharacteristic
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—611no—
291C2×D4—611no—
292C2×D4—611no—
293C2×D4—1222no—
294C2×D4—1221no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—1222no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2444no—
304C2×D4C22×D6111yescharacteristic
305C2×D4C22×D6111yescharacteristic
306C22×C4—21no—
307C22×C4—611no—
308C22×C4—1221no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4C22×D6111yescharacteristic
312SD16—41no—
313SD16—1222no—
314SD16—1222no—
315SD16—1222no—
316SD16—1222no—
317SD16—2441no—
318D8—22no—
319D8—614no—
320D8—1222no—
321M16—1222no—
322M16—1222no—
323C2×C8—611no—
324C2×C8—611no—
325C2×C8C22×D6111yescharacteristic
326C2×C8C22×D6111yescharacteristic
327C4⋊C4—611no—
328C4⋊C4—611no—
329C4⋊C4—1221no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—1221no—
333C4⋊C4C22×D6111yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—611no—
336C22⋊C4—611no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C22⋊C4—1221no—
342C42—611no—
343C23—21no—
344C23—21no—
345C23—611no—
346C23—1221no—
347C23—1221no—
348C23—4881no—
349C23—4881no—
350C23—2442no—
351C23—2442no—
352C23—2442no—
353C23—2442no—
354C23D4×D6111yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—1221no—
358Q8—1221no—
359D4—21no—
360D4—21no—
361D4—21no—
362D4—42no—
363D4—42no—
364D4—612no—
365D4—1222no—
366D4—1221no—
367D4—1221no—
368D4—1221no—
369D4—4881no—
370D4—2442no—
371D4—2442no—
372D4—2442no—
373D4—2442no—
374D4—2442no—
375D4D4×D6112yescomplemented
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—611no—
382C2×C4—611no—
383C2×C4—611no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4—2442no—
391C2×C4D4×D6111yescharacteristic
392C2×C4C23×D6111yescharacteristic
393C8—21no—
394C8—21no—
395C8—612no—
396C8—1221no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—1221no—
407C22—1221no—
408C22—1221no—
409C22—1222no—
410C22—4884no—
411C22—4884no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22—2441no—
417C22C2×D4×D6111yescharacteristic
418C4—21no—
419C4—41no—
420C4—41no—
421C4—612no—
422C4—1221no—
423C4—1221no—
424C4—2441no—
425C4—2441no—
426C4C2×D4×D6111yescharacteristic
427C4#1451982211yescharacteristic
428C2—41no—
429C2—42no—
430C2—81no—
431C2—4881no—
432C2—2441no—
433C2—2442no—
434C2#1684039411yescharacteristic
435C2AGL(1,ℤ/8)×D6111yescharacteristic
436C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3272
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#14519802C2semidirect
2. C2×#14519801C2semidirect
3. #16840411C2semidirect
4. #16840396C2semidirect
5. #16840133C2semidirect
6. #16840011C2semidirect
7. #16840006C2semidirect
8. #16839966C2semidirect
9. #16839955C2semidirect
10. #16839915C2semidirect
11. #16839911C2semidirect
12. #16839908C2semidirect
13. #16839842C2semidirect
14. #16839837C2semidirect
15. C61×#449C2semidirect
16. C2×#11758224C22semidirect
23. C2×#11758190C22semidirect
24. C2×#11758200C22semidirect
26. C2×#11758201C22semidirect
28. C2×#11758199C22semidirect
29. C2×#11758194C22semidirect
30. C2×#11758189C22semidirect
31. #14519775C22semidirect
35. #14519756C22semidirect
36. #14519753C22semidirect
42. D4×Dic61C22semidirect
46. #14519710C22semidirect
47. #14519706C22semidirect
48. #14519700C22semidirect
50. #14519699C22semidirect
51. #14519698C22semidirect
52. #14519689C22semidirect
53. C8×Dic61C22semidirect
54. C2×#41×C61C22semidirect
55. C2×SD16×C61C22semidirect
56. C2×D8×C61C22semidirect
58. #103×C61C22semidirect
59. #102×C61C22semidirect
60. C22⋊C8×C61C22semidirect
106. #11758199D4semidirect
143. D4×C61C2×D4semidirect
177. #92418C2×D4semidirect
208. Dic61AGL(1,ℤ/8)semidirect
231. #449D61semidirect
234. C61#3272semidirect
236. C2×#41C2×D61semidirect
247. C2×SD16C2×D61semidirect
250. C2×D8C2×D61semidirect
272. #103C2×D61semidirect
276. #102C2×D61semidirect
278. C22⋊C8C2×D61semidirect
375. D4D4×D61semidirect