Finite Group Databasebeta

← #21456634

Subgroups — #21456634

Order 7808.

466 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840275C211yesmaximal, characteristic, complemented
2#121×D61C211yesmaximal, characteristic, complemented
3#16840091C211yesmaximal, characteristic, complemented
4#16840089C211yesmaximal, characteristic, complemented
5#16840085C211yesmaximal, characteristic, complemented
6#16840077C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16840013C211yesmaximal, characteristic, complemented
9#16840010C211yesmaximal, characteristic, complemented
10#16839911C211yesmaximal, characteristic, complemented
11#16839910C211yesmaximal, characteristic, complemented
12#16839906C211yesmaximal, characteristic, complemented
13#16839897C211yesmaximal, characteristic, complemented
14#16839725C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic, complemented
17C2×D4×D61—21no—
18C2×D4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C2×#11758201C2211yescharacteristic, complemented
21C2×D488C2211yescharacteristic, complemented
22C2×#11758199C2211yescharacteristic, complemented
23C2×#11758194C2211yescharacteristic, complemented
24#14519762—21no—
25#14519753C2211yescharacteristic
26#14519752C2211yescharacteristic
27#14519752C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519751C2211yescharacteristic, complemented
30#14519750—21no—
31#14519749—21no—
32#14519748C2211yescharacteristic
33#14519747—21no—
34#14519739—21no—
35#14519737—21no—
36#14519735C2211yescharacteristic, complemented
37C4⋊C4×D61C2211yescharacteristic
38C22⋊C4×D61—21no—
39#14519710C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic, complemented
46#14519697C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic, complemented
53C2×M16×C61C2211yescharacteristic, complemented
54C22⋊Q8×C61C2211yescharacteristic, complemented
55#121×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61D411yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61D411yescharacteristic
70#11758226—41no—
71#11758226—41no—
72D4×D61—41no—
73D4×D61—41no—
74D4×D61—44no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61D411yescharacteristic
85C2×C4×D61D411yescharacteristic
86C2×C4×D61C2311yescharacteristic
87C2×C4×D61C2311yescharacteristic
88SD16×C61—41no—
89M16×C61—41no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—21no—
93C4⋊C4×C61C2311yescharacteristic
94C4⋊C4×C61C2311yescharacteristic
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊Dic61—21no—
98#11758201—41no—
99#11758199—41no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61C2311yescharacteristic
107C4⋊Dic61C2311yescharacteristic
108#11758196—21no—
109#11758196—21no—
110C4×Dic61—21no—
111#11758194—41no—
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114D488—41no—
115C23×C61—21no—
116C23×C61C2×D411yescharacteristic
117C22×D61—22no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61C2×D411yescharacteristic
126C22×D61C2×D411yescharacteristic
127Q8×C61—21no—
128Q8×C61—21no—
129D4×C61—21no—
130D4×C61—21no—
131D4×C61—42no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2411yescharacteristic
139C22⋊D61—42no—
140C22⋊D61—42no—
141C22⋊D61—42no—
142C22⋊D61—42no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—41no—
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148D244—21no—
149D244—21no—
150D244—21no—
151D244—21no—
152D244—42no—
153D244—42no—
154D244—42no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—41no—
160C4×D61—41no—
161C4×D61—42no—
162C4×D61—42no—
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—44no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—84no—
187C2×D61AGL(1,ℤ/8)12yes—
188C4×C61—21no—
189C4×C61—41no—
190C4×C61—41no—
191C4×C61—41no—
192C4×C61H(5,𝔽2)11yescharacteristic
193C4×C61H(5,𝔽2)11yescharacteristic
194Dic61—21no—
195Dic61—21no—
196Dic61—41no—
197Dic61—41no—
198#3194—611nomaximal, Sylow
199C2×C61—41no—
200C2×C61—81no—
201C2×C61#53411yescharacteristic
202C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
203C2×C61#57511yescharacteristic
204D61—22no—
205D61—41no—
206D61—81no—
207D61—81no—
208#525—611no—
209C2×#121—611no—
210#483—611no—
211#482—611no—
212#482—611no—
213#480—611no—
214#469—611no—
215#469—611no—
216#468—611no—
217#468D6111yescharacteristic, complemented
218#450—611no—
219#449—611no—
220#449—611no—
221#447—611no—
222#407—611no—
223C61#319411yescharacteristic, complemented, Sylow
224C2×#41—611no—
225C22×D4—611no—
226C22×D4—1221no—
227C23×C4—611no—
228C2×SD16—611no—
229C2×SD16C2×D6111yescharacteristic, complemented
230C2×D8—611no—
231C2×D8—611no—
232C2×M16—611no—
233C2×M16C2×D6111yescharacteristic, complemented
234#123—1221no—
235C22⋊Q8—611no—
236C22⋊Q8C2×D6111yescharacteristic, complemented
237#121—611no—
238#121—611no—
239#121—611no—
240#121—611no—
241#121—611no—
242#121—1221no—
243#121—1221no—
244#121C2×D6111yescharacteristic
245#120—1221no—
246C4×D4—1221no—
247C4×D4—1221no—
248#117—611no—
249C2×C4⋊C4—611no—
250C2×C22⋊C4—1221no—
251#107—611no—
252#107C2×D6111yescharacteristic, complemented
253#106—611no—
254#106—611no—
255#103—611no—
256#103C2×D6111yescharacteristic, complemented
257#102—611no—
258#102—611no—
259#102—611no—
260#102—611no—
261#102—611no—
262#102C2×D6111yescharacteristic, complemented
263C22⋊C8—611no—
264C22⋊C8—611no—
265C22⋊C8—611no—
266C22⋊C8—611no—
267C24—611no—
268C24—1221no—
269#41—2441no—
270#41—2441no—
271C2×Q8C22×D6111yescharacteristic
272C2×D4—21no—
273C2×D4—611no—
274C2×D4—611no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—1221no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—2441no—
283C2×D4—2441no—
284C2×D4—2444no—
285C2×D4C22×D6111yescharacteristic
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—1221no—
292C22×C4—1221no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4C22×D6111yescharacteristic
296SD16—41no—
297SD16—2441no—
298D8—2441no—
299D8—2441no—
300M16—41no—
301M16—2441no—
302C2×C8—611no—
303C2×C8—611no—
304C2×C8C22×D6111yescharacteristic
305C2×C8C22×D6111yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—611no—
308C4⋊C4—611no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
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—
322C42—1221no—
323C23—21no—
324C23—611no—
325C23—611no—
326C23—1222no—
327C23—1221no—
328C23—1221no—
329C23—2441no—
330C23—2441no—
331C23—2442no—
332C23—2442no—
333C23—2442no—
334C23D4×D6111yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—1221no—
341D4—1221no—
342D4—1221no—
343D4—1221no—
344D4—2442no—
345D4—2442no—
346D4—2442no—
347D4—2442no—
348D4—2442no—
349D4—2442no—
350D4—2442no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—611no—
357C2×C4—611no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2442no—
367C2×C4—2442no—
368C2×C4—2441no—
369C2×C4D4×D6111yescharacteristic
370C2×C4C23×D6111yescharacteristic
371C8—21no—
372C8—21no—
373C8—1221no—
374C8—1221no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—612no—
382C22—1221no—
383C22—1221no—
384C22—1221no—
385C22—1221no—
386C22—1221no—
387C22—4884no—
388C22—2444no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22—2441no—
393C22—2441no—
394C22—2441no—
395C22C2×D4×D6111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—1221no—
401C4—1221no—
402C4—2441no—
403C4—2441no—
404C4#1451982211yescharacteristic
405C4#1451982311yescharacteristic
406C2—41no—
407C2—81no—
408C2—1222no—
409C2—4881no—
410C2—4881no—
411C2—2441no—
412C2#1684032011yescharacteristic
413C2AGL(1,ℤ/8)×D6111yescharacteristic
414C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3194
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. #16840275C2semidirect
2. #121×D61C2semidirect
3. #16840091C2semidirect
4. #16840089C2semidirect
5. #16840085C2semidirect
6. #16840077C2semidirect
7. #16840015C2semidirect
8. #16840013C2semidirect
9. #16840010C2semidirect
10. #16839911C2semidirect
11. #16839910C2semidirect
12. #16839906C2semidirect
13. #16839897C2semidirect
14. #16839725C2semidirect
15. C61×#468C2semidirect
16. C2×#11758226C22semidirect
20. C2×#11758201C22semidirect
21. C2×D488C22semidirect
22. C2×#11758199C22semidirect
23. C2×#11758194C22semidirect
29. #14519751C22semidirect
36. #14519735C22semidirect
39. #14519710C22semidirect
40. #14519709C22semidirect
41. #14519708C22semidirect
42. #14519701C22semidirect
43. #14519699C22semidirect
44. #14519699C22semidirect
45. #14519698C22semidirect
46. #14519697C22semidirect
47. #14519697C22semidirect
50. #14519689C22semidirect
51. #14519689C22semidirect
52. C2×SD16×C61C22semidirect
53. C2×M16×C61C22semidirect
54. C22⋊Q8×C61C22semidirect
56. #107×C61C22semidirect
57. #103×C61C22semidirect
58. #102×C61C22semidirect
217. #468D61semidirect
223. C61#3194semidirect
229. C2×SD16C2×D61semidirect
233. C2×M16C2×D61semidirect
236. C22⋊Q8C2×D61semidirect
252. #107C2×D61semidirect
256. #103C2×D61semidirect
262. #102C2×D61semidirect