Finite Group Databasebeta

← #21456059

Subgroups — #21456059

Order 7808.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840363C211yesmaximal, characteristic, complemented
2#16840234C211yesmaximal, characteristic, complemented
3#16840089C211yesmaximal, characteristic, complemented
4#16840084C211yesmaximal, characteristic, complemented
5#16840065C211yesmaximal, characteristic, complemented
6#16840060C211yesmaximal, characteristic, complemented
7#16839956C211yesmaximal, characteristic, complemented
8#16839955C211yesmaximal, characteristic, complemented
9#16839897C211yesmaximal, characteristic, complemented
10#16839894C211yesmaximal, characteristic, complemented
11#16839872C211yesmaximal, characteristic, complemented
12#16839872C211yesmaximal, characteristic, complemented
13C4×D488C211yesmaximal, characteristic, complemented
14#16839821C211yesmaximal, characteristic, complemented
15C4×D8×C61C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×D488C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20#14519773C2211yescharacteristic, complemented
21#14519768C2211yescharacteristic, complemented
22#14519760—21no—
23#14519759—21no—
24#14519752C2211yescharacteristic
25#14519751—21no—
26#14519750—21no—
27#14519748C2211yescharacteristic
28C4×D244C2211yescharacteristic
29C4×D244C2211yescharacteristic, complemented
30D4×Dic61C2211yescharacteristic
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519735C2211yescharacteristic
35#14519734C2211yescharacteristic
36C2×#11758198—21no—
37C22⋊C4×D61—21no—
38#14519711C2211yescharacteristic, complemented
39#14519708C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic, complemented
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519688C2211yescharacteristic, complemented
52C2×D8×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic, complemented
55#107×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic, complemented
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69D4×D61—22no—
70D4×D61—22no—
71C2×D244—21no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78D8×C61—22no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C42×C61C2311yescharacteristic
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88#11758199—22no—
89#11758199—22no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198D411yescharacteristic
96#11758198D411yescharacteristic
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196D411yescharacteristic
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107D488—22no—
108C23×C61—21no—
109C23×C61—21no—
110C22×D61—21no—
111C22×D61—24no—
112C22×D61—21no—
113C22×D61—81no—
114C22×D61—81no—
115C22×D61C2×D411yescharacteristic
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61#4112yes—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—81no—
123C2×C4×C61—81no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—24no—
128C22⋊D61—81no—
129C22⋊D61—81no—
130C22⋊D61—81no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—81no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137D244—21no—
138D244—21no—
139D244—21no—
140D244—81no—
141D244#4112yes—
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—81no—
145C4×D61—81no—
146C4×D61—81no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—22no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C2×D61—21no—
159C2×D61—22no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C2×#4111yescharacteristic
173C4×C61C2×#4111yescharacteristic
174Dic61—21no—
175Dic61—21no—
176Dic61—21no—
177Dic61—41no—
178Dic61—41no—
179#3122—611nomaximal, Sylow
180C2×C61—42no—
181C2×C61—81no—
182C2×C61#52511yescharacteristic
183C2×C61#57611yescharacteristic
184C2×C61#57611yescharacteristic
185D61—41no—
186D61—42no—
187D61—81no—
188#540—611no—
189#518—611no—
190#482—611no—
191#482—611no—
192#478—611no—
193#478—611no—
194#459—611no—
195#459—611no—
196#447—611no—
197#447—611no—
198#442—611no—
199#442—611no—
200C4×D8—611no—
201C4×D8D6111yescharacteristic, complemented
202#433—611no—
203C61#312211yescharacteristic, complemented, Sylow
204C22×D4—611no—
205C2×D8—611no—
206C2×D8—611no—
207C2×D8—611no—
208C2×D8C2×D6111yescharacteristic
209#127—611no—
210#125—611no—
211#123—1221no—
212#123—1221no—
213#121—611no—
214#121—611no—
215#121—1221no—
216#121—1221no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—611no—
221C4×D4—1221no—
222C4×D4—1221no—
223C4×D4C2×D6111yescharacteristic
224C4×D4C2×D6111yescharacteristic, complemented
225#117—611no—
226#117—611no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229#107—611no—
230#107C2×D6111yescharacteristic, complemented
231#106—611no—
232#106—611no—
233C4⋊C8—611no—
234C4⋊C8—611no—
235#102—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241#102C2×D6111yescharacteristic
242#102C2×D6111yescharacteristic, complemented
243C22⋊C8—611no—
244C22⋊C8—611no—
245#97—611no—
246C4×C8C2×D6111yescharacteristic, complemented
247C24—1221no—
248C2×D4—611no—
249C2×D4—611no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4—1221no—
254C2×D4—1222no—
255C2×D4—1222no—
256C2×D4—1221no—
257C2×D4C22×D6111yescharacteristic
258C2×D4C22×D6111yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—611no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266D8—22no—
267D8—1222no—
268D8—1222no—
269D8—1222no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8C22×D6111yescharacteristic
273C2×C8C22×D6111yescharacteristic
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—611no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4C22×D6111yescharacteristic
281C4⋊C4C22×D6111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—611no—
285C22⋊C4—611no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—611no—
294C42—1221no—
295C42C22×D6111yescharacteristic
296C23—21no—
297C23—21no—
298C23—611no—
299C23—1224no—
300C23—1221no—
301C23—1221no—
302C23—4881no—
303C23—4881no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—612no—
308D4—1224no—
309D4—1221no—
310D4—1221no—
311D4—1221no—
312D4—4881no—
313D4—4881no—
314D4—4881no—
315D4—4881no—
316D4#1175822212yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4D4×D6111yescharacteristic
333C2×C4D4×D6111yescharacteristic
334C2×C4C23×D6111yescharacteristic
335C8—21no—
336C8—21no—
337C8—1221no—
338C8—1221no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—1221no—
346C22—1222no—
347C22—1221no—
348C22—1221no—
349C22—4884no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—1221no—
361C4—1221no—
362C4—1221no—
363C4—2441no—
364C4—2441no—
365C4#41×D6111yescharacteristic
366C4C2×#1175822211yescharacteristic
367C2—42no—
368C2—81no—
369C2—4881no—
370C2—2441no—
371C2—2442no—
372C2#1684027111yescharacteristic
373C2#1684056311yescharacteristic
374C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×D8×C61C2
socleC22×C61C22×D4
hypercenterC4×D8D61
hypocenterC61#3122
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #16840363C2semidirect
2. #16840234C2semidirect
3. #16840089C2semidirect
4. #16840084C2semidirect
5. #16840065C2semidirect
6. #16840060C2semidirect
7. #16839956C2semidirect
8. #16839955C2semidirect
9. #16839897C2semidirect
10. #16839894C2semidirect
11. #16839872C2semidirect
12. #16839872C2semidirect
13. C4×D488C2semidirect
14. #16839821C2semidirect
15. C4×D8×C61C2semidirect
20. #14519773C22semidirect
21. #14519768C22semidirect
29. C4×D244C22semidirect
38. #14519711C22semidirect
39. #14519708C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
44. #14519699C22semidirect
46. #14519698C22semidirect
48. #14519697C22semidirect
51. #14519688C22semidirect
54. C4×D4×C61C22semidirect
55. #107×C61C22semidirect
57. #102×C61C22semidirect
58. C4×C8×C61C22semidirect
201. C4×D8D61semidirect
203. C61#3122semidirect
224. C4×D4C2×D61semidirect
230. #107C2×D61semidirect
242. #102C2×D61semidirect
246. C4×C8C2×D61semidirect