Finite Group Databasebeta

← #21457300

Subgroups — #21457300

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×#14519802C211yesmaximal, characteristic, complemented
2C22×#11758199C211yesmaximal, characteristic, complemented
3D4×D244C211yesmaximal, characteristic, complemented
4#16840152C211yesmaximal, characteristic, complemented
5#16840013C211yesmaximal, characteristic, complemented
6#16839993C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839957C211yesmaximal, characteristic, complemented
9#16839912C211yesmaximal, characteristic, complemented
10#16839907C211yesmaximal, characteristic, complemented
11#16839896C211yesmaximal, characteristic, complemented
12#16839895C211yesmaximal, characteristic, complemented
13#16839872C211yesmaximal, characteristic, complemented
14#16839834C211yesmaximal, characteristic, complemented
15C61×#546C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic, complemented
18C2×D4×D61—21no—
19#14519802—24no—
20C2×#11758201C2211yescharacteristic, complemented
21C2×#11758201C2211yescharacteristic, complemented
22C2×#11758201C2211yescharacteristic, complemented
23C2×#11758199—24no—
24C2×#11758199C2211yescharacteristic
25C2×#11758199C2211yescharacteristic
26C2×#11758199C2211yescharacteristic, complemented
27C2×#11758199C2211yescharacteristic, complemented
28C2×#11758199C2211yescharacteristic, complemented
29C2×#11758199C2211yescharacteristic, complemented
30C2×#11758194C2211yescharacteristic, complemented
31C22×#92418C2211yescharacteristic, complemented
32#14519774C2211yescharacteristic, complemented
33#14519752—21no—
34#14519751C2211yescharacteristic
35#14519751C2211yescharacteristic, complemented
36#14519747—21no—
37#14519747—21no—
38C4×D244C2211yescharacteristic, complemented
39#14519708C2211yescharacteristic, complemented
40C4⋊#92418C2211yescharacteristic, complemented
41#14519701C2211yescharacteristic, complemented
42#14519698C2211yescharacteristic, complemented
43#14519698C2211yescharacteristic, complemented
44#14519697C2211yescharacteristic, complemented
45#14519697C2211yescharacteristic, complemented
46#14519697C2211yescharacteristic, complemented
47C22⋊#92418C2211yescharacteristic, complemented
48C22⋊#92418C2211yescharacteristic, complemented
49#14519688C2211yescharacteristic, complemented
50C2×#41×C61C2211yescharacteristic, complemented
51C22×D4×C61C2211yescharacteristic, complemented
52#124×C61C2211yescharacteristic, complemented
53#123×C61—21no—
54C22⋊Q8×C61C2211yescharacteristic, complemented
55#121×C61—21no—
56#121×C61C2211yescharacteristic, complemented
57#120×C61—21no—
58C4×D4×C61C2211yescharacteristic
59C4×D4×C61C2211yescharacteristic, complemented
60C2×C22⋊C4×C61—21no—
61C24×C61—21no—
62C23×D61—21no—
63C23×D61—21no—
64#41×C61—22no—
65#41×C61—41no—
66C2×Q8×C61C2311yescharacteristic
67C2×D4×C61—22no—
68C2×D4×C61—21no—
69C2×D4×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—41no—
72C2×D4×C61D411yescharacteristic
73C2×D4×C61C2311yescharacteristic
74C2×D4×C61C2311yescharacteristic
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C2311yescharacteristic
78C22×C4×C61C2311yescharacteristic
79C2×C22⋊D61—21no—
80C2×C22⋊D61—21no—
81D4×D61—44no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244C2311yescharacteristic
91C2×D244C2311yescharacteristic
92C2×D244C2311yescharacteristic
93C2×C4×D61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61D411yescharacteristic
96C4⋊C4×C61C2311yescharacteristic
97C22⋊C4×C61—21no—
98C22⋊C4×C61—21no—
99C22⋊C4×C61—21no—
100C22⋊C4×C61—21no—
101C22⋊C4×C61—21no—
102C22⋊C4×C61D411yescharacteristic
103C22⋊C4×C61D411yescharacteristic
104C42×C61C2311yescharacteristic
105#11758201—22no—
106#11758201—22no—
107#11758201—41no—
108#11758199—22no—
109#11758199—22no—
110#11758199—22no—
111#11758199—22no—
112#11758199—41no—
113#11758199D414yescomplemented
114#11758198—21no—
115#11758198—21no—
116#11758198—21no—
117C4⋊Dic61C2311yescharacteristic
118#11758194—22no—
119C2×#92418—22no—
120C2×#92418C2311yescharacteristic
121C2×#92418C2311yescharacteristic
122C2×#92418C2311yescharacteristic
123C2×#92418C2311yescharacteristic
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61—81no—
129C23×C61C2×D411yescharacteristic
130C23×C61C2×D411yescharacteristic
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—42no—
135C22×D61—42no—
136C22×D61—42no—
137C22×D61—42no—
138C22×D61—81no—
139C22×D61—81no—
140Q8×C61—21no—
141Q8×C61—21no—
142D4×C61—22no—
143D4×C61—21no—
144D4×C61—21no—
145D4×C61—21no—
146D4×C61—42no—
147D4×C61—42no—
148D4×C61—81no—
149D4×C61C2×D412yescomplemented
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—42no—
157C2×C4×C61—81no—
158C2×C4×C61C2×D411yescharacteristic
159C2×C4×C61C2×D411yescharacteristic
160C2×C4×C61C2×D411yescharacteristic
161C2×C4×C61C2×D411yescharacteristic
162C2×C4×C61C2411yescharacteristic
163C22⋊D61—42no—
164C22⋊D61—42no—
165C2×Dic61—21no—
166D244—21no—
167D244—21no—
168D244—21no—
169D244—21no—
170D244—21no—
171D244—42no—
172D244—42no—
173D244—42no—
174D244—81no—
175D244C2×D412yes—
176C4×D61—42no—
177#92418—21no—
178#92418—21no—
179#92418—21no—
180#92418C2×D412yescomplemented
181C22×C61—21no—
182C22×C61—21no—
183C22×C61—21no—
184C22×C61—22no—
185C22×C61—21no—
186C22×C61—21no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61—41no—
190C22×C61—41no—
191C22×C61—41no—
192C22×C61—84no—
193C22×C61AGL(1,ℤ/8)12yescomplemented
194C22×C61C22×D411yescharacteristic
195C2×D61—22no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—84no—
205C2×D61—84no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61C22×D411yescharacteristic
213C4×C61H(5,𝔽2)11yescharacteristic
214Dic61—41no—
215#3264—611nomaximal, Sylow
216C2×C61—22no—
217C2×C61—41no—
218C2×C61—42no—
219C2×C61—81no—
220C2×C61D4211yescharacteristic
221C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
222C2×C61#57611yescharacteristic
223D61—42no—
224D61—81no—
225D61—81no—
226C2×AGL(1,ℤ/8)—611no—
227C22×D8—611no—
228#546D6111yescharacteristic, complemented
229D42—611no—
230#496—611no—
231#469—611no—
232#465—611no—
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×#41C2×D6111yescharacteristic, complemented
243C22×D4—611no—
244C22×D4—611no—
245C22×D4—1221no—
246C22×D4C2×D6111yescharacteristic, complemented
247AGL(1,ℤ/8)—1224no—
248C2×SD16—611no—
249C2×SD16—611no—
250C2×SD16—611no—
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×C8—611no—
260#127—611no—
261#124C2×D6111yescharacteristic, complemented
262#123—21no—
263C22⋊Q8C2×D6111yescharacteristic, complemented
264#121—21no—
265#121—611no—
266#121—611no—
267#121—1221no—
268#121C2×D6111yescharacteristic, complemented
269#120—21no—
270#120—1221no—
271#120—1221no—
272C4×D4—611no—
273C4×D4C2×D6111yescharacteristic
274C4×D4C2×D6111yescharacteristic, complemented
275C2×C22⋊C4—21no—
276#106—611no—
277C4⋊C8—611no—
278#103—611no—
279#102—611no—
280#102—611no—
281#102—611no—
282#102—611no—
283#102—611no—
284C22⋊C8—611no—
285C22⋊C8—611no—
286#97—611no—
287C24—21no—
288C24—1221no—
289C24—1221no—
290#41—22no—
291#41—41no—
292C2×Q8C22×D6111yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—611no—
299C2×D4—611no—
300C2×D4—611no—
301C2×D4—1222no—
302C2×D4—1222no—
303C2×D4—1221no—
304C2×D4—1221no—
305C2×D4—1221no—
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—1221no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2444no—
312C2×D4C22⋊D6111yescharacteristic
313C2×D4C22×D6111yescharacteristic
314C2×D4C22×D6111yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—1221no—
318C22×C4C22×D6111yescharacteristic
319C22×C4C22×D6111yescharacteristic
320SD16—1222no—
321SD16—1222no—
322SD16—2441no—
323D8—614no—
324D8—1222no—
325D8—1222no—
326D8—1222no—
327D8—1222no—
328D8—2441no—
329M16—1222no—
330C2×C8—611no—
331C2×C8—611no—
332C2×C8—611no—
333C2×C8—611no—
334C2×C8—1222no—
335C4⋊C4—21no—
336C4⋊C4—611no—
337C4⋊C4C22⋊D6111yescharacteristic
338C4⋊C4C22×D6111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—1221no—
345C22⋊C4—1221no—
346C22⋊C4—1221no—
347C22⋊C4C22⋊D6111yescharacteristic
348C22⋊C4C22⋊D6111yescharacteristic
349C42C22×D6111yescharacteristic
350C23—21no—
351C23—21no—
352C23—42no—
353C23—42no—
354C23—81no—
355C23—1221no—
356C23—1221no—
357C23—1221no—
358C23—4881no—
359C23—4881no—
360C23—2442no—
361C23—2442no—
362C23—2442no—
363C23—2442no—
364C23C2×C22⋊D6111yescharacteristic
365C23C2×C22⋊D6111yescharacteristic
366Q8—21no—
367Q8—21no—
368D4—22no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—42no—
373D4—42no—
374D4—81no—
375D4—612no—
376D4—1221no—
377D4—1221no—
378D4—1221no—
379D4—1221no—
380D4—1221no—
381D4—4881no—
382D4—2442no—
383D4—2442no—
384D4—2442no—
385D4—2442no—
386D4—2442no—
387D4D4×D6112yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—81no—
396C2×C4—1221no—
397C2×C4—2442no—
398C2×C4C2×C22⋊D6111yescharacteristic
399C2×C4C2×C22⋊D6111yescharacteristic
400C2×C4C2×C22⋊D6111yescharacteristic
401C2×C4C2×C22⋊D6111yescharacteristic
402C2×C4C23×D6111yescharacteristic
403C8—612no—
404C8—1221no—
405C8—1221no—
406C8—1221no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—22no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—84no—
419C22—1222no—
420C22—4884no—
421C22—4884no—
422C22—2441no—
423C22—2441no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22#1451980212yescomplemented
431C22C22×C22⋊D6111yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—41no—
437C4—41no—
438C4—2441no—
439C4C2×D4×D6111yescharacteristic
440C4#1451982211yescharacteristic
441C2—22no—
442C2—41no—
443C2—42no—
444C2—81no—
445C2—4881no—
446C2—4881no—
447C2—2442no—
448C2D4×C22⋊D6111yescharacteristic
449C2C2×#1451980211yescharacteristic
450C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#546C2
socleC22×C61C22×D4
hypercenter#546D61
hypocenterC61#3264
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14519802C2semidirect
2. C22×#11758199C2semidirect
3. D4×D244C2semidirect
4. #16840152C2semidirect
5. #16840013C2semidirect
6. #16839993C2semidirect
7. #16839974C2semidirect
8. #16839957C2semidirect
9. #16839912C2semidirect
10. #16839907C2semidirect
11. #16839896C2semidirect
12. #16839895C2semidirect
13. #16839872C2semidirect
14. #16839834C2semidirect
15. C61×#546C2semidirect
17. C22×D244C22semidirect
20. C2×#11758201C22semidirect
21. C2×#11758201C22semidirect
22. C2×#11758201C22semidirect
26. C2×#11758199C22semidirect
27. C2×#11758199C22semidirect
28. C2×#11758199C22semidirect
29. C2×#11758199C22semidirect
30. C2×#11758194C22semidirect
31. C22×#92418C22semidirect
32. #14519774C22semidirect
35. #14519751C22semidirect
38. C4×D244C22semidirect
39. #14519708C22semidirect
40. C4⋊#92418C22semidirect
41. #14519701C22semidirect
42. #14519698C22semidirect
43. #14519698C22semidirect
44. #14519697C22semidirect
45. #14519697C22semidirect
46. #14519697C22semidirect
47. C22⋊#92418C22semidirect
48. C22⋊#92418C22semidirect
49. #14519688C22semidirect
50. C2×#41×C61C22semidirect
51. C22×D4×C61C22semidirect
52. #124×C61C22semidirect
54. C22⋊Q8×C61C22semidirect
56. #121×C61C22semidirect
59. C4×D4×C61C22semidirect
113. #11758199D4semidirect
149. D4×C61C2×D4semidirect
180. #92418C2×D4semidirect
193. C22×C61AGL(1,ℤ/8)semidirect
228. #546D61semidirect
241. C61#3264semidirect
242. C2×#41C2×D61semidirect
246. C22×D4C2×D61semidirect
261. #124C2×D61semidirect
263. C22⋊Q8C2×D61semidirect
268. #121C2×D61semidirect
274. C4×D4C2×D61semidirect
387. D4D4×D61semidirect
430. C22#14519802semidirect