Finite Group Databasebeta

← #21455870

Subgroups — #21455870

Order 7808.

454 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840299C211yesmaximal, characteristic, complemented
2C4×D4×D61C211yesmaximal, characteristic, complemented
3#16840096C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic, complemented
5#16840061C211yesmaximal, characteristic, complemented
6#16840060C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839911C211yesmaximal, characteristic, complemented
10#16839897C211yesmaximal, characteristic
11C4×#11758201C211yesmaximal, characteristic, complemented
12C4×D488C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839813C211yesmaximal, characteristic, complemented
15C4×SD16×C61C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C22×C4×D61—21no—
18C2×#11758201C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21#14519772—21no—
22#14519768C2211yescharacteristic, complemented
23#14519766C2211yescharacteristic, complemented
24#14519762—21no—
25#14519753C2211yescharacteristic
26#14519752C2211yescharacteristic
27C4×D244—21no—
28C4×D244C2211yescharacteristic
29C4×D244C2211yescharacteristic, complemented
30D4×Dic61C2211yescharacteristic
31#14519739C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519734—21no—
35C4⋊C4×D61C2211yescharacteristic
36C22⋊C4×D61—21no—
37C42×D61C2211yescharacteristic
38#14519711C2211yescharacteristic, complemented
39#14519710C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic, complemented
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic, complemented
54C4×D4×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65D4×D61—22no—
66D4×D61—22no—
67C2×D244—21no—
68C2×D244C2311yescharacteristic
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—44no—
75C2×C4×D61D411yescharacteristic
76C2×C4×D61D411yescharacteristic
77C2×C4×D61C2311yescharacteristic
78SD16×C61—22no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C42×C61—21no—
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88#11758201—22no—
89#11758199—22no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103C4×Dic61D411yescharacteristic
104C4×Dic61D411yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108D488—22no—
109C23×C61—21no—
110C22×D61—24no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—42no—
114C22×D61—42no—
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61—21no—
118D4×C61—21no—
119D4×C61#4112yes—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—24no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—42no—
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134D244—21no—
135D244—21no—
136D244—21no—
137D244—42no—
138D244#4112yes—
139C4×D61—22no—
140C4×D61—22no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—42no—
144C4×D61—42no—
145C4×D61—42no—
146C4×D61—42no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—22no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—22no—
158C2×D61—48no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61#13512yes—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61AGL(1,ℤ/8)12yes—
170C4×C61C2×#4111yescharacteristic
171C4×C61C2×#4111yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176Dic61—41no—
177#3105—611nomaximal, Sylow
178C2×C61—42no—
179C2×C61#52511yescharacteristic
180C2×C61C2×#13511yescharacteristic
181C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
182D61—22no—
183D61—42no—
184D61—81no—
185#529—611no—
186C2×C4×D4—611no—
187#484—611no—
188#481—611no—
189#478—611no—
190#478—611no—
191#463—611no—
192#463—611no—
193#450—611no—
194#447—611no—
195C4×SD16—611no—
196C4×SD16D6111yescharacteristic, complemented
197C4×D8—611no—
198C4×D8—611no—
199#431—611no—
200C61#310511yescharacteristic, complemented, Sylow
201C22×D4—611no—
202C23×C4—1221no—
203C2×SD16—611no—
204C2×SD16C2×D6111yescharacteristic
205C2×D8—611no—
206C2×D8—611no—
207#126—1221no—
208#125—611no—
209#124—611no—
210#123—1221no—
211C22⋊Q8—611no—
212#121—611no—
213C4×Q8C2×D6111yescharacteristic, complemented
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—611no—
217C4×D4—611no—
218C4×D4—1221no—
219C4×D4—1221no—
220C4×D4—1221no—
221C4×D4C2×D6111yescharacteristic
222#117—1221no—
223C2×C4⋊C4—611no—
224C2×C22⋊C4—1221no—
225C2×C42—611no—
226#107—611no—
227#107—611no—
228#106—611no—
229#106C2×D6111yescharacteristic, complemented
230C4⋊C8—611no—
231C4⋊C8—611no—
232#103—611no—
233#103C2×D6111yescharacteristic, complemented
234#102—611no—
235#102—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102C2×D6111yescharacteristic
240C22⋊C8—611no—
241C22⋊C8—611no—
242C4×C8—611no—
243C4×C8C2×D6111yescharacteristic, complemented
244C24—1221no—
245C2×Q8C22×D6111yescharacteristic
246C2×D4—611no—
247C2×D4—611no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1222no—
251C2×D4—1222no—
252C2×D4C22×D6111yescharacteristic
253C22×C4—21no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—2444no—
263SD16—22no—
264SD16—1222no—
265D8—1222no—
266D8—1222no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4C22×D6111yescharacteristic
279C4⋊C4C22×D6111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—21no—
290C42—611no—
291C42—611no—
292C42—611no—
293C42C22×D6111yescharacteristic
294C23—21no—
295C23—611no—
296C23—1224no—
297C23—1221no—
298C23—1221no—
299C23—2442no—
300C23—2442no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—612no—
305D4—1224no—
306D4—1221no—
307D4—1221no—
308D4—1221no—
309D4—2442no—
310D4#1175822212yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—1222no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1222no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4D4×D6111yescharacteristic
330C2×C4D4×D6111yescharacteristic
331C2×C4C23×D6111yescharacteristic
332C8—21no—
333C8—21no—
334C8—1221no—
335C8—1221no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—612no—
340C22—1221no—
341C22—1221no—
342C22—1222no—
343C22—2448no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—1221no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4—2441no—
359C4#1451980412yes—
360C4#41×D6111yescharacteristic
361C4C2×#1175822211yescharacteristic
362C2—42no—
363C2—1222no—
364C2—4881no—
365C2—2442no—
366C2#1684027111yescharacteristic
367C2#135×D6111yescharacteristic
368C2C2×#1451980411yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×SD16×C61C2
socleC22×C61C22×D4
hypercenterC4×SD16D61
hypocenterC61#3105
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #16840299C2semidirect
2. C4×D4×D61C2semidirect
3. #16840096C2semidirect
4. #16840082C2semidirect
5. #16840061C2semidirect
6. #16840060C2semidirect
7. #16839980C2semidirect
8. #16839979C2semidirect
9. #16839911C2semidirect
11. C4×#11758201C2semidirect
12. C4×D488C2semidirect
13. C4×#11758199C2semidirect
14. #16839813C2semidirect
15. C4×SD16×C61C2semidirect
22. #14519768C22semidirect
23. #14519766C22semidirect
29. C4×D244C22semidirect
38. #14519711C22semidirect
39. #14519710C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519701C22semidirect
45. #14519699C22semidirect
48. #14519697C22semidirect
51. C4×#92418C22semidirect
53. C4×Q8×C61C22semidirect
55. #106×C61C22semidirect
56. #103×C61C22semidirect
58. C4×C8×C61C22semidirect
196. C4×SD16D61semidirect
200. C61#3105semidirect
213. C4×Q8C2×D61semidirect
229. #106C2×D61semidirect
233. #103C2×D61semidirect
243. C4×C8C2×D61semidirect