Finite Group Databasebeta

← #21456683

Subgroups — #21456683

Order 7808.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840331C211yesmaximal, characteristic, complemented
2#16840328C211yesmaximal, characteristic, complemented
3#16840089C211yesmaximal, characteristic, complemented
4#16840088C211yesmaximal, characteristic, complemented
5#16840086C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16839999C211yesmaximal, characteristic, complemented
9#16839997C211yesmaximal, characteristic, complemented
10#16839898C211yesmaximal, characteristic, complemented
11#16839897C211yesmaximal, characteristic, complemented
12#16839897C211yesmaximal, characteristic, complemented
13#16839895C211yesmaximal, characteristic, complemented
14#16839727C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×D244C2211yescharacteristic, complemented
18C2×D4×D61C2211yescharacteristic, complemented
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758189C2211yescharacteristic, complemented
24C2×C8×D61C2211yescharacteristic, complemented
25#14519774—21no—
26#14519773—21no—
27#14519765—21no—
28#14519763—21no—
29#14519752C2211yescharacteristic
30#14519752C2211yescharacteristic
31#14519752C2211yescharacteristic, complemented
32#14519752C2211yescharacteristic, complemented
33#14519752C2211yescharacteristic, complemented
34#14519751C2211yescharacteristic
35#14519748C2211yescharacteristic, complemented
36#14519747—21no—
37#14519747—21no—
38#14519747—21no—
39#14519745—21no—
40#14519735C2211yescharacteristic, complemented
41#14519710C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519697C2211yescharacteristic, complemented
46#14519697C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic, complemented
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61D411yescharacteristic
68C2×C22⋊D61D411yescharacteristic
69D4×D61—41no—
70D4×D61—41no—
71#11758222—41no—
72#11758222—41no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244D411yescharacteristic
82C2×D244C2311yescharacteristic
83C2×D244C2311yescharacteristic
84C2×D244C2311yescharacteristic
85C2×C4×D61C2311yescharacteristic
86C2×C4×D61C2311yescharacteristic
87C2×Dic122D411yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C2×C8×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C4⋊C4×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C42×C61—21no—
96C22⋊Dic61—21no—
97#11758199—41no—
98#11758199—41no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61C2311yescharacteristic
107C4×Dic61—21no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110D488—41no—
111D488—41no—
112#11758189—41no—
113C8×D61—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—81no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—81no—
125C22×D61C2×D411yescharacteristic
126C22×D61C2×D411yescharacteristic
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—81no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—41no—
138C22⋊D61—41no—
139C22⋊D61—42no—
140C22⋊D61—81no—
141C22⋊D61—81no—
142C2×Dic61—21no—
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147D244—21no—
148D244—21no—
149D244—21no—
150D244—21no—
151D244—41no—
152D244—42no—
153D244—81no—
154D244—81no—
155D244—81no—
156D244—81no—
157D244—81no—
158C4×D61—21no—
159C4×D61—21no—
160C4×D61—21no—
161C4×D61—21no—
162Dic122—41no—
163C8×C61—21no—
164C8×C61—21no—
165#92418—21no—
166#92418—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61C22×D411yescharacteristic
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—84no—
190C2×D61—84no—
191C4×C61—21no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61—41no—
195C4×C61H(5,𝔽2)11yescharacteristic
196C4×C61H(5,𝔽2)11yescharacteristic
197Dic61—21no—
198Dic61—21no—
199Dic61—41no—
200#3199—611nomaximal, Sylow
201C2×C61—41no—
202C2×C61—81no—
203C2×C61#53411yescharacteristic
204C2×C61#57611yescharacteristic
205C2×C61#57611yescharacteristic
206D61—41no—
207D61—41no—
208D61—81no—
209D61—81no—
210D61—81no—
211#535—611no—
212#535—611no—
213#482—611no—
214#482—611no—
215#482—611no—
216#482D6111yescharacteristic, complemented
217#469—611no—
218#469—611no—
219#466—611no—
220#466—611no—
221#447—611no—
222#447—611no—
223#447—611no—
224#447—611no—
225#408—611no—
226C61#319911yescharacteristic, complemented, Sylow
227C2×#41—611no—
228C22×D4—611no—
229C22×D4—611no—
230C2×D8—611no—
231C2×D8—611no—
232C2×D8—611no—
233C2×D8—611no—
234C2×M16—611no—
235C22×C8—611no—
236#127—1221no—
237#127—1221no—
238#124—1221no—
239#124—1221no—
240#121—611no—
241#121—611no—
242#121—611no—
243#121—611no—
244#121—611no—
245#121—611no—
246#121—611no—
247#121C2×D6111yescharacteristic
248#120—1221no—
249#120—1221no—
250#120—1221no—
251#120—1221no—
252#117—611no—
253#117C2×D6111yescharacteristic, complemented
254#107—611no—
255#107C2×D6111yescharacteristic, complemented
256#106—611no—
257#106C2×D6111yescharacteristic, complemented
258#102—611no—
259#102—611no—
260#102—611no—
261#102—611no—
262#102—611no—
263#102—611no—
264#102C2×D6111yescharacteristic, complemented
265#102C2×D6111yescharacteristic, complemented
266C22⋊C8—611no—
267C22⋊C8—611no—
268C22⋊C8—611no—
269C22⋊C8C2×D6111yescharacteristic, complemented
270C24—1221no—
271C24—1221no—
272#41—2441no—
273#41—2441no—
274C2×Q8—611no—
275C2×D4—21no—
276C2×D4—611no—
277C2×D4—611no—
278C2×D4—611no—
279C2×D4—611no—
280C2×D4—611no—
281C2×D4—611no—
282C2×D4—1221no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—2441no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4C22×D6111yescharacteristic
296C22×C4—611no—
297C22×C4—611no—
298C22×C4C22×D6111yescharacteristic
299D8—2441no—
300D8—2441no—
301D8—2441no—
302D8—2441no—
303M16—2441no—
304C2×C8—611no—
305C2×C8—611no—
306C2×C8—2441no—
307C2×C8C22×D6111yescharacteristic
308C2×C8C22×D6111yescharacteristic
309C4⋊C4—611no—
310C4⋊C4C22×D6111yescharacteristic
311C4⋊C4C22×D6111yescharacteristic
312C4⋊C4C22×D6111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C22⋊C4—1221no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C42—21no—
324C42—1221no—
325C23—21no—
326C23—611no—
327C23—611no—
328C23—1221no—
329C23—1221no—
330C23—1221no—
331C23—4881no—
332C23—4881no—
333C23—4881no—
334C23—4881no—
335C23—2442no—
336C23—2442no—
337C23D4×D6111yescharacteristic
338Q8—2441no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—1221no—
343D4—1221no—
344D4—1221no—
345D4—1221no—
346D4—1221no—
347D4—1221no—
348D4—4881no—
349D4—4881no—
350D4—4881no—
351D4—4881no—
352D4—4881no—
353D4—4881no—
354D4—4881no—
355D4—2441no—
356D4—2442no—
357D4—2441no—
358D4—2441no—
359D4—2442no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—611no—
366C2×C4—611no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4D4×D6111yescharacteristic
373C2×C4C23×D6111yescharacteristic
374C8—21no—
375C8—21no—
376C8—1221no—
377C8—1221no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—1221no—
385C22—1221no—
386C22—1221no—
387C22—1221no—
388C22—1221no—
389C22—1221no—
390C22—4884no—
391C22—4884no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22—2441no—
396C22—2441no—
397C22—2441no—
398C22—2441no—
399C22—2441no—
400C22—2441no—
401C22C2×D4×D6111yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—1221no—
407C4—1221no—
408C4—2441no—
409C4#1451982311yescharacteristic
410C4#1451982311yescharacteristic
411C2—41no—
412C2—81no—
413C2—4881no—
414C2—4881no—
415C2—4881no—
416C2—2441no—
417C2—2441no—
418C2#1684032311yescharacteristic
419C2#1684056411yescharacteristic
420C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3199
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #16840331C2semidirect
2. #16840328C2semidirect
3. #16840089C2semidirect
4. #16840088C2semidirect
5. #16840086C2semidirect
6. #16840016C2semidirect
7. #16840014C2semidirect
8. #16839999C2semidirect
9. #16839997C2semidirect
10. #16839898C2semidirect
11. #16839897C2semidirect
12. #16839897C2semidirect
13. #16839895C2semidirect
14. #16839727C2semidirect
15. C61×#482C2semidirect
17. C22×D244C22semidirect
18. C2×D4×D61C22semidirect
23. C2×#11758189C22semidirect
24. C2×C8×D61C22semidirect
31. #14519752C22semidirect
32. #14519752C22semidirect
33. #14519752C22semidirect
35. #14519748C22semidirect
40. #14519735C22semidirect
41. #14519710C22semidirect
42. #14519708C22semidirect
43. #14519699C22semidirect
44. #14519699C22semidirect
45. #14519697C22semidirect
46. #14519697C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
49. C22⋊#92418C22semidirect
50. #14519689C22semidirect
51. #14519689C22semidirect
53. #117×C61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #102×C61C22semidirect
57. #102×C61C22semidirect
58. C22⋊C8×C61C22semidirect
216. #482D61semidirect
226. C61#3199semidirect
253. #117C2×D61semidirect
255. #107C2×D61semidirect
257. #106C2×D61semidirect
264. #102C2×D61semidirect
265. #102C2×D61semidirect
269. C22⋊C8C2×D61semidirect