Finite Group Databasebeta

← #21455865

Subgroups — #21455865

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#16840291C211yesmaximal, characteristic, complemented
2C4×D4×D61C211yesmaximal, characteristic, complemented
3#16840096C211yesmaximal, characteristic, complemented
4#16840079C211yesmaximal, characteristic, complemented
5#16840063C211yesmaximal, characteristic, complemented
6#16840062C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839911C211yesmaximal, characteristic, complemented
9#16839894C211yesmaximal, characteristic
10SD16×Dic61C211yesmaximal, characteristic, complemented
11#16839847C211yesmaximal, characteristic, complemented
12D8×Dic61C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839814C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C22×C4×D61—21no—
18C2×#11758201C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20#14519770—21no—
21#14519769C2211yescharacteristic, complemented
22#14519759—21no—
23#14519753C2211yescharacteristic
24#14519748C2211yescharacteristic
25Q8×Dic61C2211yescharacteristic, complemented
26C4×D244C2211yescharacteristic
27D4×Dic61C2211yescharacteristic
28D4×Dic61C2211yescharacteristic, complemented
29#14519739C2211yescharacteristic
30C4×C22⋊D61—21no—
31#14519737—21no—
32#14519737—21no—
33#14519733—21no—
34C4⋊C4×D61C2211yescharacteristic
35C22⋊C4×D61—21no—
36C42×D61C2211yescharacteristic
37#14519711C2211yescharacteristic, complemented
38#14519710C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41C4⋊#92418C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50C8×Dic61C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic, complemented
55C4×D4×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68D4×D61—22no—
69D4×D61—22no—
70C2×D244C2311yescharacteristic
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—
79D8×C61—22no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758201—22no—
91#11758199—22no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103C4×Dic61—21no—
104C4×Dic61D411yescharacteristic
105C4×Dic61D411yescharacteristic
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C23×C61—21no—
110C23×C61—21no—
111C22×D61—24no—
112C22×D61—21no—
113C22×D61—42no—
114C22×D61—42no—
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61#4112yes—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—42no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—24no—
129C22⋊D61—42no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—21no—
139D244#4112yes—
140C4×D61—22no—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—22no—
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×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—22no—
161C2×D61—48no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61#13512yes—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61C2×#4111yescharacteristic
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61AGL(1,ℤ/8)12yes—
177#3105—611nomaximal, Sylow
178C2×C61—42no—
179C2×C61—81no—
180C2×C61#52511yescharacteristic
181C2×C61C2×#13511yescharacteristic
182C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
183D61—22no—
184D61—42no—
185#529—611no—
186C2×C4×D4—611no—
187#484—611no—
188#481—611no—
189#478—611no—
190#478—611no—
191#463—611no—
192#463D6111yescharacteristic, complemented
193#450—611no—
194#447—611no—
195C4×SD16—611no—
196C4×SD16—611no—
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×D8C2×D6111yescharacteristic
207#126—1221no—
208#125—611no—
209#124C2×D6111yescharacteristic, complemented
210#123—1221no—
211C22⋊Q8—611no—
212#121—611no—
213C4×Q8—611no—
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#106—611no—
230C4⋊C8—611no—
231C4⋊C8C2×D6111yescharacteristic, complemented
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, complemented
240C22⋊C8—611no—
241C22⋊C8—611no—
242C4×C8—611no—
243C4×C8—611no—
244C24—1221no—
245C2×Q8C22×D6111yescharacteristic
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4—1222no—
249C2×D4—1222no—
250C2×D4—1221no—
251C2×D4C22×D6111yescharacteristic
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—22no—
266D8—1222no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C4⋊C4—611no—
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4C22×D6111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C42—611no—
290C42—611no—
291C42—611no—
292C42—1221no—
293C42C22×D6111yescharacteristic
294C23—21no—
295C23—21no—
296C23—611no—
297C23—1224no—
298C23—1221no—
299C23—2442no—
300C23—2442no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—612no—
307D4—1224no—
308D4—1221no—
309D4—2442no—
310D4#1175822412yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—611no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
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—41no—
340C22—41no—
341C22—41no—
342C22—612no—
343C22—1221no—
344C22—1221no—
345C22—1222no—
346C22—2448no—
347C22—2441no—
348C22—2441no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—612no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4#41×D6111yescharacteristic
361C4C2×#1175822411yescharacteristic
362C2—42no—
363C2—81no—
364C2—1222no—
365C2—2442no—
366C2#1684027211yescharacteristic
367C2#135×D6111yescharacteristic
368C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3105
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16840291C2semidirect
2. C4×D4×D61C2semidirect
3. #16840096C2semidirect
4. #16840079C2semidirect
5. #16840063C2semidirect
6. #16840062C2semidirect
7. #16839974C2semidirect
8. #16839911C2semidirect
10. SD16×Dic61C2semidirect
11. #16839847C2semidirect
12. D8×Dic61C2semidirect
13. #16839842C2semidirect
14. #16839814C2semidirect
15. C61×#463C2semidirect
21. #14519769C22semidirect
25. Q8×Dic61C22semidirect
28. D4×Dic61C22semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. C4⋊#92418C22semidirect
42. #14519701C22semidirect
47. #14519698C22semidirect
50. C8×Dic61C22semidirect
51. C8×Dic61C22semidirect
54. #124×C61C22semidirect
56. C4⋊C8×C61C22semidirect
57. #103×C61C22semidirect
58. #102×C61C22semidirect
192. #463D61semidirect
200. C61#3105semidirect
209. #124C2×D61semidirect
231. C4⋊C8C2×D61semidirect
233. #103C2×D61semidirect
239. #102C2×D61semidirect