Finite Group Databasebeta

← #21457317

Subgroups — #21457317

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×SD16×D61C211yesmaximal, characteristic, complemented
3#16840419C211yesmaximal, characteristic, complemented
4#16840396C211yesmaximal, characteristic, complemented
5#16840150C211yesmaximal, characteristic, complemented
6#16840006C211yesmaximal, characteristic, complemented
7#16839997C211yesmaximal, characteristic, complemented
8#16839976C211yesmaximal, characteristic, complemented
9#16839960C211yesmaximal, characteristic, complemented
10#16839915C211yesmaximal, characteristic, complemented
11#16839902C211yesmaximal, characteristic, complemented
12#16839894C211yesmaximal, characteristic, complemented
13#16839865C211yesmaximal, characteristic, complemented
14#16839836C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic, complemented
17C22×D244C2211yescharacteristic
18C2×D4×D61—21no—
19C2×D4×D61C2211yescharacteristic
20#14519802—24no—
21C2×#11758190C2211yescharacteristic
22C2×#11758190C2211yescharacteristic, complemented
23C2×#11758200C2211yescharacteristic, complemented
24C2×#11758201C2211yescharacteristic
25C2×#11758201C2211yescharacteristic, complemented
26SD16×D61—24no—
27C2×#11758199C2211yescharacteristic
28C2×#11758199C2211yescharacteristic, complemented
29C2×#11758194C2211yescharacteristic, complemented
30C2×C8×D61C2211yescharacteristic, complemented
31#14519773C2211yescharacteristic
32#14519764—21no—
33#14519764C2211yescharacteristic, complemented
34#14519756—21no—
35#14519756C2211yescharacteristic, complemented
36#14519752C2211yescharacteristic
37#14519750—21no—
38#14519748—21no—
39#14519748C2211yescharacteristic, complemented
40#14519747—21no—
41#14519745—21no—
42Q8×Dic61C2211yescharacteristic, complemented
43#14519739C2211yescharacteristic
44C4×C22⋊D61—21no—
45C4×C22⋊D61C2211yescharacteristic
46#14519710C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519700C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic, complemented
51#14519698C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519687C2211yescharacteristic, 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
77Q8×D61—22no—
78Q8×D61—41no—
79D4×D61—22no—
80D4×D61—41no—
81D4×D61—44no—
82C2×D244—22no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—41no—
86C2×D244C2311yescharacteristic
87C2×D244C2311yescharacteristic
88C2×C4×D61—21no—
89C2×C4×D61—21no—
90C2×C4×D61C2311yescharacteristic
91C2×Dic122—21no—
92C2×Dic122C2311yescharacteristic
93SD16×C61—22no—
94D8×C61—41no—
95C2×C8×C61C2311yescharacteristic
96C2×C8×C61C2311yescharacteristic
97C4⋊C4×C61C2311yescharacteristic
98C22⋊C4×C61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61—21no—
102C22⋊Dic61—21no—
103C22⋊Dic61D411yescharacteristic
104#11758201—22no—
105#11758201D414yescomplemented
106#11758200—22no—
107#11758199—22no—
108#11758199—22no—
109#11758198—21no—
110#11758198—21no—
111#11758198D411yescharacteristic
112C4⋊Dic61—21no—
113C4⋊Dic61C2311yescharacteristic
114#11758196—21no—
115#11758196D411yescharacteristic
116C4×Dic61—21no—
117C4×Dic61C2311yescharacteristic
118#11758194—22no—
119C2×#92418C2311yescharacteristic
120C2×#92418C2311yescharacteristic
121#11758190—22no—
122#11758190—41no—
123C8×D61—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×C61C2×D412yescomplemented
138D4×C61—21no—
139D4×C61—21no—
140D4×C61—21no—
141D4×C61—21no—
142D4×C61—42no—
143D4×C61—42no—
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×Dic61C2×D411yescharacteristic
159C2×Dic61C2×D411yescharacteristic
160C2×Dic61C2×D411yescharacteristic
161D244—21no—
162D244—21no—
163D244—21no—
164D244—42no—
165D244—42no—
166D244C2×D412yes—
167C4×D61—21no—
168C4×D61—21no—
169C4×D61—42no—
170C4×D61—42no—
171Dic122—21no—
172Dic122—21no—
173Dic122—42no—
174C8×C61—21no—
175C8×C61—21no—
176#92418—21no—
177#92418C2×D412yescomplemented
178C22×C61—21no—
179C22×C61—21no—
180C22×C61—21no—
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—22no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—84no—
197C2×D61—84no—
198C2×D61AGL(1,ℤ/8)12yescomplemented
199C4×C61—22no—
200C4×C61—21no—
201C4×C61—41no—
202C4×C61C22×D411yescharacteristic
203C4×C61H(5,𝔽2)11yescharacteristic
204Dic61—21no—
205Dic61—21no—
206Dic61—21no—
207Dic61—41no—
208Dic61—41no—
209#3265—611nomaximal, Sylow
210C2×C61—41no—
211C2×C61—81no—
212C2×C61—81no—
213C2×C61D4211yescharacteristic
214C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C61#57711yescharacteristic
216D61—22no—
217D61—42no—
218D61—81no—
219C2×AGL(1,ℤ/8)—611no—
220C22×SD16—611no—
221#548—611no—
222D42—611no—
223#496—611no—
224#468—611no—
225#466—611no—
226#463—611no—
227#460—611no—
228#450—611no—
229#449D6111yescharacteristic, complemented
230#448—611no—
231#447—611no—
232#440—611no—
233#435—611no—
234C61#326511yescharacteristic, complemented, Sylow
235C2×#41C2×D6111yescharacteristic, complemented
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—611no—
246C2×SD16—1224no—
247C2×SD16C2×D6111yescharacteristic, complemented
248C2×D8—611no—
249C2×D8—611no—
250C2×D8C2×D6111yescharacteristic, complemented
251C2×M16—611no—
252C22×C8—611no—
253#127—611no—
254#124—611no—
255#124—1221no—
256C22⋊Q8—611no—
257C22⋊Q8—1221no—
258#121—611no—
259#121—611no—
260#121—1221no—
261#121—1221no—
262#121C2×D6111yescharacteristic
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#103C2×D6111yescharacteristic, complemented
273#102—611no—
274#102—611no—
275#102—611no—
276#102C2×D6111yescharacteristic, complemented
277C22⋊C8—611no—
278C22⋊C8C2×D6111yescharacteristic, complemented
279#97—611no—
280C24—1221no—
281C24—1221no—
282#41—22no—
283#41—41no—
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—611no—
294C2×D4—1222no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—1221no—
298C2×D4—1221no—
299C2×D4—1222no—
300C2×D4—1221no—
301C2×D4—1221no—
302C2×D4—2441no—
303C2×D4—2441no—
304C2×D4—2444no—
305C2×D4C22×D6111yescharacteristic
306C2×D4C22×D6111yescharacteristic
307C22×C4—21no—
308C22×C4—611no—
309C22×C4—1221no—
310C22×C4—1221no—
311C22×C4C22×D6111yescharacteristic
312SD16—22no—
313SD16—614no—
314SD16—1222no—
315SD16—1222no—
316SD16—1222no—
317SD16—2441no—
318D8—41no—
319D8—1222no—
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—1221no—
330C4⋊C4—1221no—
331C4⋊C4C22×D6111yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—611no—
334C22⋊C4—611no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C22⋊C4—1221no—
339C22⋊C4—1221no—
340C22⋊C4—1221no—
341C42—611no—
342C42—1221no—
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—1221no—
357Q8—1221no—
358Q8—2442no—
359Q8D4×D6112yescomplemented
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—612no—
367D4—1222no—
368D4—1221no—
369D4—1221no—
370D4—1221no—
371D4—4881no—
372D4—2442no—
373D4—2442no—
374D4—2442no—
375D4—2442no—
376D4—2442no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—611no—
383C2×C4—611no—
384C2×C4—611no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
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—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—612no—
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—22no—
420C4—41no—
421C4—1221no—
422C4—1221no—
423C4—1221no—
424C4—2441no—
425C4—2441no—
426C4C2×D4×D6111yescharacteristic
427C4#1451982211yescharacteristic
428C2—41no—
429C2—81no—
430C2—81no—
431C2—1222no—
432C2—4881no—
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#3265
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×SD16×D61C2semidirect
3. #16840419C2semidirect
4. #16840396C2semidirect
5. #16840150C2semidirect
6. #16840006C2semidirect
7. #16839997C2semidirect
8. #16839976C2semidirect
9. #16839960C2semidirect
10. #16839915C2semidirect
11. #16839902C2semidirect
12. #16839894C2semidirect
13. #16839865C2semidirect
14. #16839836C2semidirect
15. C61×#449C2semidirect
16. C2×Q8×D61C22semidirect
22. C2×#11758190C22semidirect
23. C2×#11758200C22semidirect
25. C2×#11758201C22semidirect
28. C2×#11758199C22semidirect
29. C2×#11758194C22semidirect
30. C2×C8×D61C22semidirect
33. #14519764C22semidirect
35. #14519756C22semidirect
39. #14519748C22semidirect
42. Q8×Dic61C22semidirect
46. #14519710C22semidirect
47. #14519706C22semidirect
48. #14519700C22semidirect
50. #14519699C22semidirect
51. #14519698C22semidirect
52. #14519689C22semidirect
53. #14519687C22semidirect
54. C2×#41×C61C22semidirect
55. C2×SD16×C61C22semidirect
56. C2×D8×C61C22semidirect
58. #103×C61C22semidirect
59. #102×C61C22semidirect
60. C22⋊C8×C61C22semidirect
105. #11758201D4semidirect
137. Q8×C61C2×D4semidirect
177. #92418C2×D4semidirect
198. C2×D61AGL(1,ℤ/8)semidirect
229. #449D61semidirect
234. C61#3265semidirect
235. C2×#41C2×D61semidirect
247. C2×SD16C2×D61semidirect
250. C2×D8C2×D61semidirect
272. #103C2×D61semidirect
276. #102C2×D61semidirect
278. C22⋊C8C2×D61semidirect
359. Q8D4×D61semidirect