Finite Group Databasebeta

← #21456058

Subgroups — #21456058

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#16840365C211yesmaximal, characteristic, complemented
2#16840236C211yesmaximal, characteristic, complemented
3#16840086C211yesmaximal, characteristic, complemented
4#16840065C211yesmaximal, characteristic, complemented
5#16840061C211yesmaximal, characteristic, complemented
6#16839956C211yesmaximal, characteristic, complemented
7#16839956C211yesmaximal, characteristic, complemented
8#16839898C211yesmaximal, characteristic, complemented
9#16839895C211yesmaximal, characteristic, complemented
10#16839873C211yesmaximal, characteristic, complemented
11#16839871C211yesmaximal, characteristic, complemented
12#16839844C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#482C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×D488C2211yescharacteristic
18C2×D488C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21#14519773C2211yescharacteristic, complemented
22#14519768C2211yescharacteristic, complemented
23#14519761—21no—
24#14519759—21no—
25#14519751C2211yescharacteristic
26#14519749—21no—
27#14519748—21no—
28C4×D244—21no—
29C4×D244—21no—
30D4×Dic61C2211yescharacteristic, complemented
31#14519739C2211yescharacteristic
32#14519739C2211yescharacteristic
33#14519739C2211yescharacteristic
34#14519739C2211yescharacteristic
35#14519739C2211yescharacteristic, complemented
36#14519736C2211yescharacteristic
37C22⋊C4×D61—21no—
38C22⋊C4×D61—21no—
39#14519710C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52#121×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C2×D244—21no—
68C2×D244—22no—
69C2×D244—22no—
70C2×D244C2311yescharacteristic
71C2×D244C2311yescharacteristic
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C42×C61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61D411yescharacteristic
88C22⋊Dic61D411yescharacteristic
89#11758199—22no—
90#11758199—22no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61D411yescharacteristic
99C4⋊Dic61D411yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102C4×Dic61C2311yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106D488—22no—
107D488—22no—
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—24no—
113C22×D61—21no—
114C22×D61—81no—
115C22×D61—81no—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—81no—
127C22⋊D61—81no—
128C22⋊D61—81no—
129C2×Dic61—21no—
130C2×Dic61—81no—
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135D244—24no—
136D244—21no—
137D244—21no—
138D244—21no—
139D244—21no—
140D244#4112yes—
141D244#4112yes—
142C4×D61—81no—
143C4×D61—81no—
144C4×D61—81no—
145C4×D61—81no—
146C4×D61—81no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C2×D61—22no—
159C2×D61—22no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C2×#4111yescharacteristic
173C4×C61C2×#4111yescharacteristic
174Dic61—21no—
175Dic61—21no—
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179#3122—611nomaximal, Sylow
180C2×C61—41no—
181C2×C61—81no—
182C2×C61#52511yescharacteristic
183C2×C61#57611yescharacteristic
184C2×C61#57611yescharacteristic
185D61—42no—
186D61—42no—
187D61—81no—
188#540—611no—
189#518—611no—
190#482—611no—
191#482D6111yescharacteristic, complemented
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×D8—611no—
202#433—611no—
203C61#312211yescharacteristic, complemented, Sylow
204C22×D4—611no—
205C2×D8—611no—
206C2×D8—611no—
207C2×D8—611no—
208C2×D8—611no—
209#127—611no—
210#125—611no—
211#123—1221no—
212#123—1221no—
213#121—611no—
214#121—1221no—
215#121—1221no—
216#121C2×D6111yescharacteristic
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—611no—
223C4×D4—1221no—
224C4×D4—1221no—
225#117—611no—
226#117C2×D6111yescharacteristic
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229#107—611no—
230#107C2×D6111yescharacteristic, complemented
231#106—611no—
232#106C2×D6111yescharacteristic, complemented
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, complemented
242#102C2×D6111yescharacteristic, complemented
243C22⋊C8—611no—
244C22⋊C8C2×D6111yescharacteristic
245#97—611no—
246C4×C8—611no—
247C24—1221no—
248C2×D4—21no—
249C2×D4—611no—
250C2×D4—611no—
251C2×D4—611no—
252C2×D4—1222no—
253C2×D4—1222no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4C22×D6111yescharacteristic
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4C22×D6111yescharacteristic
266D8—1222no—
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—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22×D6111yescharacteristic
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—21no—
294C42—611no—
295C42—611no—
296C23—21no—
297C23—1224no—
298C23—1221no—
299C23—1221no—
300C23—1221no—
301C23—4881no—
302C23—4881no—
303C23D4×D6111yescharacteristic
304D4—21no—
305D4—21no—
306D4—81no—
307D4—612no—
308D4—612no—
309D4—1224no—
310D4—1221no—
311D4—1221no—
312D4—1221no—
313D4—1221no—
314D4—4881no—
315D4—4881no—
316D4—4881no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4D4×D6111yescharacteristic
334C2×C4C23×D6111yescharacteristic
335C8—21no—
336C8—21no—
337C8—1221no—
338C8—1221no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—1222no—
346C22—1222no—
347C22—4884no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—1221no—
361C4—1221no—
362C4—1221no—
363C4—1221no—
364C4—2441no—
365C4#41×D6111yescharacteristic
366C4#41×D6111yescharacteristic
367C2—41no—
368C2—81no—
369C2—4881no—
370C2—2442no—
371C2—2442no—
372C2#1684027011yescharacteristic
373C2#1684056411yescharacteristic
374C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#482C2
socleC22×C61C22×D4
hypercenter#482D61
hypocenterC61#3122
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. #16840365C2semidirect
2. #16840236C2semidirect
3. #16840086C2semidirect
4. #16840065C2semidirect
5. #16840061C2semidirect
6. #16839956C2semidirect
7. #16839956C2semidirect
8. #16839898C2semidirect
9. #16839895C2semidirect
10. #16839873C2semidirect
11. #16839871C2semidirect
12. #16839844C2semidirect
13. #16839842C2semidirect
14. #16839820C2semidirect
15. C61×#482C2semidirect
21. #14519773C22semidirect
22. #14519768C22semidirect
30. D4×Dic61C22semidirect
35. #14519739C22semidirect
39. #14519710C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #102×C61C22semidirect
57. #102×C61C22semidirect
191. #482D61semidirect
203. C61#3122semidirect
230. #107C2×D61semidirect
232. #106C2×D61semidirect
241. #102C2×D61semidirect
242. #102C2×D61semidirect