Finite Group Databasebeta

← #21457427

Subgroups — #21457427

Order 7808.

520 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519805C211yesmaximal, characteristic, complemented
2C2×#14519804C211yesmaximal, characteristic, complemented
3#16840409C211yesmaximal, characteristic, complemented
4#16840403C211yesmaximal, characteristic, complemented
5#16840143C211yesmaximal, characteristic, complemented
6#16840009C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839976C211yesmaximal, characteristic, complemented
9#16839927C211yesmaximal, characteristic, complemented
10#16839922C211yesmaximal, characteristic, complemented
11#16839897C211yesmaximal, characteristic, complemented
12#16839895C211yesmaximal, characteristic, complemented
13#16839844C211yesmaximal, characteristic, complemented
14#16839838C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C22×D244C2211yescharacteristic, complemented
19C2×D4×D61C2211yescharacteristic, complemented
20#14519805—24no—
21#14519804—24no—
22C2×#11758202C2211yescharacteristic, complemented
23C2×#11758190C2211yescharacteristic, complemented
24C2×#11758190C2211yescharacteristic, complemented
25C2×#11758201C2211yescharacteristic, complemented
26C2×D488C2211yescharacteristic
27C2×D488C2211yescharacteristic
28C2×#11758199C2211yescharacteristic
29C2×#11758199C2211yescharacteristic
30C2×#11758189C2211yescharacteristic, complemented
31#14519766C2211yescharacteristic, complemented
32#14519764C2211yescharacteristic, complemented
33#14519762—21no—
34#14519759—21no—
35#14519757C2211yescharacteristic, complemented
36#14519752—21no—
37#14519752C2211yescharacteristic
38#14519748—21no—
39#14519747—21no—
40#14519745—21no—
41#14519739C2211yescharacteristic, complemented
42#14519739C2211yescharacteristic, complemented
43C4×C22⋊D61C2211yescharacteristic
44C22⋊C4×D61—21no—
45C22⋊C4×D61—21no—
46#14519706C2211yescharacteristic, complemented
47#14519700C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic, complemented
50#14519697C2211yescharacteristic, complemented
51C22⋊#92418C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53C8×Dic61C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×M16×C61C2211yescharacteristic, complemented
56C22⋊Q8×C61C2211yescharacteristic, complemented
57#121×C61C2211yescharacteristic
58#107×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61—21no—
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61D411yescharacteristic
70#11758226—22no—
71#11758226—41no—
72D4×D61—22no—
73D4×D61—41no—
74#11758222—22no—
75#11758222—41no—
76C2×D244—22no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—41no—
81C2×D244C2311yescharacteristic
82C2×D244C2311yescharacteristic
83C2×D244C2311yescharacteristic
84C2×C4×D61—21no—
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61C2311yescharacteristic
89C2×Dic122C2311yescharacteristic
90SD16×C61—22no—
91M16×C61—22no—
92C2×C8×C61C2311yescharacteristic
93C2×C8×C61C2311yescharacteristic
94C4⋊C4×C61—21no—
95C4⋊C4×C61C2311yescharacteristic
96C4⋊C4×C61C2311yescharacteristic
97C22⋊C4×C61—21no—
98C22⋊C4×C61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61—21no—
101C22⋊Dic61D411yescharacteristic
102#11758202—41no—
103#11758201—22no—
104#11758199—22no—
105#11758199—41no—
106#11758198—21no—
107#11758198—21no—
108#11758198—21no—
109#11758198—21no—
110#11758198—21no—
111#11758198—21no—
112#11758198D411yescharacteristic
113C4⋊Dic61—21no—
114#11758196D411yescharacteristic
115C4×Dic61C2311yescharacteristic
116C2×#92418C2311yescharacteristic
117C2×#92418C2311yescharacteristic
118D488—22no—
119D488D414yescomplemented
120#11758190—22no—
121#11758190—22no—
122#11758189—22no—
123C23×C61—21no—
124C23×C61C2×D411yescharacteristic
125C22×D61—21no—
126C22×D61—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
135Q8×C61—21no—
136Q8×C61—21no—
137D4×C61—21no—
138D4×C61—21no—
139D4×C61—81no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61C2×D411yescharacteristic
146C2×C4×C61C2411yescharacteristic
147C22⋊D61—41no—
148C22⋊D61—42no—
149C22⋊D61—42no—
150C2×Dic61—21no—
151C2×Dic61C2×D411yescharacteristic
152C2×Dic61C2×D411yescharacteristic
153C2×Dic61C2×D411yescharacteristic
154D244—21no—
155D244—21no—
156D244—21no—
157D244—21no—
158D244—42no—
159D244—42no—
160D244—81no—
161D244C2×D412yes—
162D244C2×D412yes—
163C4×D61—21no—
164C4×D61—21no—
165C4×D61—42no—
166C4×D61—42no—
167C4×D61—81no—
168C4×D61—81no—
169Dic122—21no—
170Dic122—21no—
171C8×C61—21no—
172C8×C61C2×D412yes—
173#92418—21no—
174#92418—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61C22×D411yescharacteristic
182C2×D61—21no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—21no—
186C2×D61—21no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—84no—
195C2×D61—84no—
196C4×C61—21no—
197C4×C61—41no—
198C4×C61—41no—
199C4×C61—41no—
200C4×C61C22×D411yescharacteristic
201C4×C61H(5,𝔽2)11yescharacteristic
202Dic61—21no—
203Dic61—21no—
204Dic61—21no—
205Dic61—41no—
206#3273—611nomaximal, Sylow
207C2×C61—41no—
208C2×C61—81no—
209C2×C61D4211yescharacteristic
210C2×C61#57511yescharacteristic
211C2×C61#57611yescharacteristic
212D61—41no—
213D61—42no—
214D61—42no—
215D61—81no—
216C2×AGL(1,ℤ/8)—611no—
217C2×AGL(1,ℤ/8)—611no—
218#546—611no—
219#546—611no—
220#495—611no—
221#468—611no—
222#468D6111yescharacteristic, complemented
223#463—611no—
224#463—611no—
225#452—611no—
226#452—611no—
227#447—611no—
228#447—611no—
229C4×D8—611no—
230#436—611no—
231C61#327311yescharacteristic, complemented, Sylow
232C2×#41—611no—
233C2×#41—611no—
234C22×D4—611no—
235C22×D4—611no—
236AGL(1,ℤ/8)—1224no—
237AGL(1,ℤ/8)—1224no—
238C2×Q16—611no—
239C2×SD16—611no—
240C2×SD16—611no—
241C2×SD16—611no—
242C2×SD16C2×D6111yescharacteristic, complemented
243C2×D8—611no—
244C2×D8—611no—
245C2×D8—611no—
246C2×D8—611no—
247C2×M16—611no—
248C2×M16C2×D6111yescharacteristic, complemented
249#124—611no—
250#124—611no—
251#123—1221no—
252#123—1221no—
253C22⋊Q8—611no—
254C22⋊Q8C2×D6111yescharacteristic, complemented
255#121—611no—
256#121—1221no—
257#121—1221no—
258#121C2×D6111yescharacteristic
259#120—1221no—
260#120—1221no—
261C4×D4—611no—
262C4×D4—611no—
263C4×D4—611no—
264C2×C22⋊C4—1221no—
265C2×C22⋊C4—1221no—
266#107C2×D6111yescharacteristic, complemented
267C4⋊C8—611no—
268#103—611no—
269#103C2×D6111yescharacteristic, complemented
270#102—611no—
271#102—611no—
272#102—611no—
273#102C2×D6111yescharacteristic, complemented
274C22⋊C8—611no—
275C22⋊C8—611no—
276C4×C8—611no—
277C24—1221no—
278C24—1221no—
279#41—1222no—
280#41—1222no—
281#41—2441no—
282#41—2441no—
283C2×Q8—611no—
284C2×Q8C22×D6111yescharacteristic
285C2×D4—21no—
286C2×D4—611no—
287C2×D4—611no—
288C2×D4—611no—
289C2×D4—611no—
290C2×D4—1222no—
291C2×D4—1221no—
292C2×D4—1221no—
293C2×D4—1221no—
294C2×D4—1222no—
295C2×D4—1221no—
296C2×D4—1221no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4C22×D6111yescharacteristic
300C22×C4—611no—
301C22×C4—1221no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4C22×D6111yescharacteristic
306Q16—2441no—
307SD16—22no—
308SD16—1222no—
309SD16—1222no—
310SD16—1222no—
311D8—614no—
312D8—1222no—
313D8—1222no—
314D8—2441no—
315M16—22no—
316M16—1222no—
317C2×C8—611no—
318C2×C8—611no—
319C2×C8C22×D6111yescharacteristic
320C2×C8C22×D6111yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—611no—
323C4⋊C4—1221no—
324C4⋊C4C22×D6111yescharacteristic
325C4⋊C4C22×D6111yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—611no—
329C22⋊C4—611no—
330C22⋊C4—1221no—
331C22⋊C4—1221no—
332C22⋊C4—1221no—
333C22⋊C4—1221no—
334C22⋊C4—1221no—
335C22⋊C4—1221no—
336C22⋊C4—1221no—
337C22⋊C4—1221no—
338C42—611no—
339C23—21no—
340C23—611no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—4881no—
345C23—4881no—
346C23—2442no—
347C23—2442no—
348C23—2442no—
349C23—2442no—
350C23D4×D6111yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—1221no—
354Q8—1221no—
355D4—21no—
356D4—21no—
357D4—81no—
358D4—612no—
359D4—612no—
360D4—1221no—
361D4—1221no—
362D4—1221no—
363D4—1221no—
364D4—4881no—
365D4—2442no—
366D4—2442no—
367D4—2441no—
368D4—2442no—
369D4—2442no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—611no—
376C2×C4—611no—
377C2×C4—611no—
378C2×C4—1221no—
379C2×C4—1221no—
380C2×C4—1221no—
381C2×C4—4881no—
382C2×C4—4881no—
383C2×C4—2442no—
384C2×C4—2442no—
385C2×C4D4×D6111yescharacteristic
386C2×C4C23×D6111yescharacteristic
387C8—21no—
388C8—1221no—
389C8—1221no—
390C8D4×D6112yes—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—1221no—
398C22—1221no—
399C22—1221no—
400C22—1222no—
401C22—1222no—
402C22—4884no—
403C22—4884no—
404C22—2441no—
405C22—2441no—
406C22—2441no—
407C22—2441no—
408C22—2441no—
409C22—2441no—
410C22—2441no—
411C22C2×D4×D6111yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—1221no—
417C4—1221no—
418C4—1221no—
419C4—2441no—
420C4C2×D4×D6111yescharacteristic
421C4#1451982311yescharacteristic
422C2—41no—
423C2—81no—
424C2—4881no—
425C2—2441no—
426C2—2442no—
427C2—2442no—
428C2#1684039611yescharacteristic
429C2#1684056111yescharacteristic
430C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3273
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. C2×#14519804C2semidirect
3. #16840409C2semidirect
4. #16840403C2semidirect
5. #16840143C2semidirect
6. #16840009C2semidirect
7. #16839980C2semidirect
8. #16839976C2semidirect
9. #16839927C2semidirect
10. #16839922C2semidirect
11. #16839897C2semidirect
12. #16839895C2semidirect
13. #16839844C2semidirect
14. #16839838C2semidirect
15. C61×#468C2semidirect
18. C22×D244C22semidirect
19. C2×D4×D61C22semidirect
22. C2×#11758202C22semidirect
23. C2×#11758190C22semidirect
24. C2×#11758190C22semidirect
25. C2×#11758201C22semidirect
30. C2×#11758189C22semidirect
31. #14519766C22semidirect
32. #14519764C22semidirect
35. #14519757C22semidirect
41. #14519739C22semidirect
42. #14519739C22semidirect
46. #14519706C22semidirect
47. #14519700C22semidirect
48. #14519697C22semidirect
49. #14519697C22semidirect
50. #14519697C22semidirect
51. C22⋊#92418C22semidirect
52. #14519689C22semidirect
53. C8×Dic61C22semidirect
54. C2×SD16×C61C22semidirect
55. C2×M16×C61C22semidirect
56. C22⋊Q8×C61C22semidirect
58. #107×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
119. D488D4semidirect
222. #468D61semidirect
231. C61#3273semidirect
242. C2×SD16C2×D61semidirect
248. C2×M16C2×D61semidirect
254. C22⋊Q8C2×D61semidirect
266. #107C2×D61semidirect
269. #103C2×D61semidirect
273. #102C2×D61semidirect