Finite Group Databasebeta

← #21457313

Subgroups — #21457313

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×#14519801C211yesmaximal, characteristic, complemented
2C2×SD16×D61C211yesmaximal, characteristic, complemented
3#16840420C211yesmaximal, characteristic, complemented
4#16840397C211yesmaximal, characteristic, complemented
5#16840005C211yesmaximal, characteristic, complemented
6#16839995C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839959C211yesmaximal, characteristic, complemented
9#16839911C211yesmaximal, characteristic, complemented
10#16839904C211yesmaximal, characteristic, complemented
11#16839899C211yesmaximal, characteristic, complemented
12#16839894C211yesmaximal, characteristic, complemented
13#16839864C211yesmaximal, characteristic, complemented
14#16839835C211yesmaximal, characteristic, complemented
15C61×#496C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic, complemented
17C2×Q8×D61C2211yescharacteristic, complemented
18C2×D4×D61—21no—
19C2×D4×D61C2211yescharacteristic
20C2×D4×D61C2211yescharacteristic
21#14519801—24no—
22C2×#11758190C2211yescharacteristic
23C2×#11758200C2211yescharacteristic, complemented
24C2×#11758200C2211yescharacteristic, complemented
25C2×#11758201C2211yescharacteristic
26SD16×D61—24no—
27C2×#11758199C2211yescharacteristic
28C2×#11758189C2211yescharacteristic, complemented
29C2×C8×D61C2211yescharacteristic, complemented
30#14519763—21no—
31#14519754—21no—
32#14519753C2211yescharacteristic, complemented
33#14519750—21no—
34#14519748—21no—
35#14519748C2211yescharacteristic
36#14519748C2211yescharacteristic
37#14519748C2211yescharacteristic, complemented
38#14519745—21no—
39#14519745—21no—
40C4×Dic122C2211yescharacteristic, complemented
41C4×D244C2211yescharacteristic
42C4×D244C2211yescharacteristic
43#14519737—21no—
44#14519711C2211yescharacteristic, complemented
45C4⋊#92418C2211yescharacteristic, complemented
46#14519702C2211yescharacteristic, complemented
47#14519701C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic
49#14519698C2211yescharacteristic, complemented
50#14519698C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519689C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×SD16×C61C2211yescharacteristic, complemented
56C2×D8×C61C2211yescharacteristic, complemented
57C2×D8×C61C2211yescharacteristic, complemented
58#127×C61C2211yescharacteristic
59#124×C61C2211yescharacteristic, complemented
60#97×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C2×D4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C2×C22⋊D61—21no—
75C22×Dic61—21no—
76Q8×D61—22no—
77Q8×D61—41no—
78#11758224—22no—
79#11758224—41no—
80D4×D61—22no—
81D4×D61—22no—
82D4×D61—41no—
83D4×D61—41no—
84D4×D61—44no—
85C2×D244D411yescharacteristic
86C2×D244C2311yescharacteristic
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×C4×D61C2311yescharacteristic
90C2×C4×D61C2311yescharacteristic
91C2×Dic122—21no—
92C2×Dic122C2311yescharacteristic
93SD16×C61—22no—
94SD16×C61—41no—
95D8×C61—22no—
96D8×C61—41no—
97C2×C8×C61C2311yescharacteristic
98C2×C8×C61C2311yescharacteristic
99C22⋊C4×C61—21no—
100C22⋊C4×C61—21no—
101C42×C61C2311yescharacteristic
102C22⋊Dic61—21no—
103C22⋊Dic61—21no—
104C22⋊Dic61—21no—
105#11758201—22no—
106#11758200—22no—
107#11758200—22no—
108#11758199—22no—
109#11758198—21no—
110#11758198—21no—
111#11758198D411yescharacteristic
112#11758198D411yescharacteristic
113C4⋊Dic61D411yescharacteristic
114C4⋊Dic61C2311yescharacteristic
115C4⋊Dic61C2311yescharacteristic
116#11758196—21no—
117#11758196—21no—
118C4×Dic61—21no—
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121#11758190D414yescomplemented
122#11758189—22no—
123C8×D61—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C22×D61—21no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—81no—
133C22×D61—81no—
134C22×D61C2×D411yescharacteristic
135C22×D61C2×D411yescharacteristic
136Q8×C61—21no—
137Q8×C61—21no—
138D4×C61—21no—
139D4×C61—21no—
140D4×C61—21no—
141D4×C61—21no—
142D4×C61—21no—
143D4×C61—21no—
144D4×C61—42no—
145D4×C61—81no—
146C2×C4×C61—21no—
147C2×C4×C61C2×D411yescharacteristic
148C2×C4×C61C2×D411yescharacteristic
149C2×C4×C61C2411yescharacteristic
150C22⋊D61—42no—
151C22⋊D61—42no—
152C22⋊D61—42no—
153C22⋊D61—42no—
154C22⋊D61—42no—
155C22⋊D61—42no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—42no—
160C2×Dic61C2×D411yescharacteristic
161C2×Dic61C2×D411yescharacteristic
162D244—22no—
163D244—21no—
164D244C2×D412yes—
165C4×D61—21no—
166C4×D61—21no—
167C4×D61—21no—
168C4×D61—21no—
169C4×D61—42no—
170C4×D61—42no—
171Dic122—21no—
172Dic122—42no—
173Dic122C2×D412yescomplemented
174C8×C61—21no—
175C8×C61C2×D412yescomplemented
176#92418—21no—
177#92418—21no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61C22×D411yescharacteristic
188C2×D61—21no—
189C2×D61—21no—
190C2×D61—21no—
191C2×D61—22no—
192C2×D61—21no—
193C2×D61—21no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—84no—
197C2×D61—84no—
198C2×D61AGL(1,ℤ/8)12yescomplemented
199C4×C61—21no—
200C4×C61—21no—
201C4×C61—41no—
202C4×C61C22×D411yescharacteristic
203C4×C61H(5,𝔽2)11yescharacteristic
204Dic61—22no—
205Dic61—21no—
206Dic61—21no—
207Dic61—41no—
208Dic61—41no—
209#3265—611nomaximal, Sylow
210C2×C61—81no—
211C2×C61—81no—
212C2×C61—81no—
213C2×C61D4211yescharacteristic
214C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C61#57711yescharacteristic
216D61—22no—
217D61—41no—
218D61—42no—
219C2×AGL(1,ℤ/8)—611no—
220C22×SD16—611no—
221#548—611no—
222D42—611no—
223#496D6111yescharacteristic, complemented
224#468—611no—
225#466—611no—
226#463—611no—
227#460—611no—
228#450—611no—
229#449—611no—
230#448—611no—
231#447—611no—
232#440—611no—
233#435—611no—
234C61#326511yescharacteristic, complemented, Sylow
235C2×#41—611no—
236C22×Q8—611no—
237C22×D4—611no—
238C22×D4—611no—
239C22×D4—1221no—
240AGL(1,ℤ/8)—1224no—
241C2×SD16—611no—
242C2×SD16—611no—
243C2×SD16—611no—
244C2×SD16—611no—
245C2×SD16—1224no—
246C2×SD16C2×D6111yescharacteristic, complemented
247C2×SD16C2×D6111yescharacteristic, complemented
248C2×D8—611no—
249C2×D8C2×D6111yescharacteristic, complemented
250C2×D8C2×D6111yescharacteristic, complemented
251C2×M16—611no—
252C22×C8—611no—
253#127C2×D6111yescharacteristic
254#124—1221no—
255#124C2×D6111yescharacteristic, complemented
256C22⋊Q8—611no—
257C22⋊Q8—1221no—
258#121—611no—
259#121—611no—
260#121—611no—
261#121—1221no—
262#121—1221no—
263#120—1221no—
264#120—1221no—
265C4×Q8—611no—
266C4×D4—611no—
267C4×D4—611no—
268C4×D4—1221no—
269#107—611no—
270C4⋊C8—611no—
271#103—611no—
272#103—611no—
273#102—611no—
274#102—611no—
275#102—611no—
276#102—611no—
277C22⋊C8—611no—
278C22⋊C8—611no—
279#97C2×D6111yescharacteristic, complemented
280C24—1221no—
281C24—1221no—
282#41—1222no—
283#41—2441no—
284C2×Q8—611no—
285C2×Q8—1221no—
286C2×Q8—1222no—
287C2×Q8—2441no—
288C2×Q8C22×D6111yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—611no—
292C2×D4—611no—
293C2×D4—1221no—
294C2×D4—1221no—
295C2×D4—1222no—
296C2×D4—1222no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1221no—
300C2×D4—1221no—
301C2×D4—2441no—
302C2×D4—2441no—
303C2×D4—2444no—
304C2×D4C22×D6111yescharacteristic
305C2×D4C22×D6111yescharacteristic
306C2×D4C22×D6111yescharacteristic
307C22×C4—611no—
308C22×C4—611no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4—1221no—
312SD16—22no—
313SD16—41no—
314SD16—614no—
315SD16—1222no—
316SD16—1222no—
317SD16—1222no—
318D8—22no—
319D8—41no—
320D8—1222no—
321M16—1222no—
322C2×C8—611no—
323C2×C8—611no—
324C2×C8—1222no—
325C2×C8C22×D6111yescharacteristic
326C2×C8C22×D6111yescharacteristic
327C4⋊C4—611no—
328C4⋊C4—611no—
329C4⋊C4—611no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—611no—
335C22⋊C4—611no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C42—1221no—
342C42C22×D6111yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—611no—
347C23—611no—
348C23—1221no—
349C23—4881no—
350C23—4881no—
351C23—2442no—
352C23—2442no—
353C23—2442no—
354C23—2442no—
355Q8—21no—
356Q8—21no—
357Q8—612no—
358Q8—1221no—
359Q8—2442no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—81no—
368D4—612no—
369D4—1222no—
370D4—1221no—
371D4—2442no—
372D4—2442no—
373D4—2442no—
374D4—2442no—
375D4—2442no—
376D4—2442no—
377C2×C4—21no—
378C2×C4—611no—
379C2×C4—611no—
380C2×C4—1221no—
381C2×C4—1221no—
382C2×C4—1221no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—2442no—
388C2×C4—2442no—
389C2×C4—2442no—
390C2×C4D4×D6111yescharacteristic
391C2×C4D4×D6111yescharacteristic
392C2×C4C23×D6111yescharacteristic
393C8—21no—
394C8—1221no—
395C8—1221no—
396C8D4×D6112yescomplemented
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—612no—
407C22—1221no—
408C22—1221no—
409C22—1221no—
410C22—1221no—
411C22—1221no—
412C22—1222no—
413C22—4884no—
414C22—4884no—
415C22—2441no—
416C22—2441no—
417C22C2×D4×D6111yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—1221no—
422C4—1221no—
423C4—1222no—
424C4—2441no—
425C4—2441no—
426C4C2×D4×D6111yescharacteristic
427C4#1451982211yescharacteristic
428C2—81no—
429C2—81no—
430C2—81no—
431C2—1222no—
432C2—2441no—
433C2—2442no—
434C2#1684039711yescharacteristic
435C2AGL(1,ℤ/8)×D6111yescharacteristic
436C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3265
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#14519801C2semidirect
2. C2×SD16×D61C2semidirect
3. #16840420C2semidirect
4. #16840397C2semidirect
5. #16840005C2semidirect
6. #16839995C2semidirect
7. #16839974C2semidirect
8. #16839959C2semidirect
9. #16839911C2semidirect
10. #16839904C2semidirect
11. #16839899C2semidirect
12. #16839894C2semidirect
13. #16839864C2semidirect
14. #16839835C2semidirect
15. C61×#496C2semidirect
16. C2×#11758224C22semidirect
17. C2×Q8×D61C22semidirect
23. C2×#11758200C22semidirect
24. C2×#11758200C22semidirect
28. C2×#11758189C22semidirect
29. C2×C8×D61C22semidirect
32. #14519753C22semidirect
37. #14519748C22semidirect
40. C4×Dic122C22semidirect
44. #14519711C22semidirect
45. C4⋊#92418C22semidirect
46. #14519702C22semidirect
47. #14519701C22semidirect
49. #14519698C22semidirect
50. #14519698C22semidirect
51. #14519698C22semidirect
52. #14519689C22semidirect
53. #14519689C22semidirect
54. C2×SD16×C61C22semidirect
55. C2×SD16×C61C22semidirect
56. C2×D8×C61C22semidirect
57. C2×D8×C61C22semidirect
59. #124×C61C22semidirect
60. #97×C61C22semidirect
121. #11758190D4semidirect
173. Dic122C2×D4semidirect
175. C8×C61C2×D4semidirect
198. C2×D61AGL(1,ℤ/8)semidirect
223. #496D61semidirect
234. C61#3265semidirect
246. C2×SD16C2×D61semidirect
247. C2×SD16C2×D61semidirect
249. C2×D8C2×D61semidirect
250. C2×D8C2×D61semidirect
255. #124C2×D61semidirect
279. #97C2×D61semidirect
396. C8D4×D61semidirect